## TSTP Solution File: SYN721+1 by Goeland---1.0.0

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : Goeland---1.0.0
% Problem  : SYN721+1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : goeland -dmt -presko -proof %s

% Computer : n004.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 29 22:24:25 EDT 2022

% Result   : Theorem 0.19s 0.37s
% Output   : Proof 0.19s
% Verified :
% SZS Type : -

%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SYN721+1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13  % Command    : goeland -dmt -presko -proof %s
% 0.13/0.34  % Computer : n004.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon Sep  5 06:41:49 EDT 2022
% 0.13/0.34  % CPUTime    :
% 0.13/0.35  [DMT] DMT loaded with preskolemization
% 0.13/0.35  [EQ] equality loaded.
% 0.13/0.35  [0.000036s][1][MAIN] Problem : theBenchmark.p
% 0.13/0.35  Start search
% 0.13/0.35  nb_step : 1 - limit : 5
% 0.13/0.35  Launch Gotab with destructive = true
% 0.13/0.37  % SZS output start Proof for theBenchmark.p
% 0.19/0.37  [0] ALPHA_NOT_IMPLY : ~(((r(a, b) & ! [X6_6] :  ((? [Y7_7] :  (r(X6_6, Y7_7)) => q(X6_6, X6_6)))) & ! [U8_8, V9_9] :  ((q(U8_8, V9_9) => ! [Z10_10] :  (r(Z10_10, V9_9))))) => ? [W11_11] :  ((r(b, W11_11) & q(W11_11, a))))
% 0.19/0.37  	-> [1] ((r(a, b) & ! [X6_6] :  ((? [Y7_7] :  (r(X6_6, Y7_7)) => q(X6_6, X6_6)))) & ! [U8_8, V9_9] :  ((q(U8_8, V9_9) => ! [Z10_10] :  (r(Z10_10, V9_9))))), ~? [W11_11] :  ((r(b, W11_11) & q(W11_11, a)))
% 0.19/0.37
% 0.19/0.37  [1] ALPHA_AND : ((r(a, b) & ! [X6_6] :  ((? [Y7_7] :  (r(X6_6, Y7_7)) => q(X6_6, X6_6)))) & ! [U8_8, V9_9] :  ((q(U8_8, V9_9) => ! [Z10_10] :  (r(Z10_10, V9_9)))))
% 0.19/0.37  	-> [2] (r(a, b) & ! [X6_6] :  ((? [Y7_7] :  (r(X6_6, Y7_7)) => q(X6_6, X6_6)))), ! [U8_8, V9_9] :  ((q(U8_8, V9_9) => ! [Z10_10] :  (r(Z10_10, V9_9))))
% 0.19/0.37
% 0.19/0.37  [2] ALPHA_AND : (r(a, b) & ! [X6_6] :  ((? [Y7_7] :  (r(X6_6, Y7_7)) => q(X6_6, X6_6))))
% 0.19/0.37  	-> [3] r(a, b), ! [X6_6] :  ((? [Y7_7] :  (r(X6_6, Y7_7)) => q(X6_6, X6_6)))
% 0.19/0.37
% 0.19/0.37  [3] GAMMA_NOT_EXISTS : ~? [W11_11] :  ((r(b, W11_11) & q(W11_11, a)))
% 0.19/0.37  	-> [4] ~(r(b, a) & q(a, a))
% 0.19/0.37
% 0.19/0.37  [4] BETA_NOT_AND : ~(r(b, a) & q(a, a))
% 0.19/0.37  	-> [5] ~r(b, a)
% 0.19/0.37  	-> [6] ~q(a, a)
% 0.19/0.37
% 0.19/0.37  [6] GAMMA_FORALL : ! [U8_8, V9_9] :  ((q(U8_8, V9_9) => ! [Z10_10] :  (r(Z10_10, V9_9))))
% 0.19/0.37  	-> [8] (q(U8_1_1, V9_1_1) => ! [Z10_10] :  (r(Z10_10, V9_1_1)))
% 0.19/0.37
% 0.19/0.37  [8] BETA_IMPLY : (q(U8_1_1, V9_1_1) => ! [Z10_10] :  (r(Z10_10, V9_1_1)))
% 0.19/0.37  	-> [11] ~q(U8_1_1, V9_1_1)
% 0.19/0.37  	-> [12] ! [Z10_10] :  (r(Z10_10, V9_1_1))
% 0.19/0.37
% 0.19/0.37  [12] GAMMA_FORALL : ! [X6_6] :  ((? [Y7_7] :  (r(X6_6, Y7_7)) => q(X6_6, X6_6)))
% 0.19/0.37  	-> [14] (? [Y7_7] :  (r(a, Y7_7)) => q(a, a))
% 0.19/0.37
% 0.19/0.37  [14] BETA_IMPLY : (? [Y7_7] :  (r(a, Y7_7)) => q(a, a))
% 0.19/0.37  	-> [19] ~? [Y7_7] :  (r(a, Y7_7))
% 0.19/0.37  	-> [20] q(a, a)
% 0.19/0.37
% 0.19/0.37  [20] CLOSURE : q(a, a)
% 0.19/0.37
% 0.19/0.37  [19] GAMMA_FORALL : ! [Z10_10] :  (r(Z10_10, V9_1_1))
% 0.19/0.37  	-> [26] r(Z10_0_3, V9_1_1)
% 0.19/0.37
% 0.19/0.37  [26] GAMMA_NOT_EXISTS : ~? [Y7_7] :  (r(a, Y7_7))
% 0.19/0.37  	-> [29] ~r(a, Y7_2_4)
% 0.19/0.37
% 0.19/0.37  [29] CLOSURE : ~r(a, Y7_2_4)
% 0.19/0.37
% 0.19/0.37  [11] GAMMA_FORALL : ! [X6_6] :  ((? [Y7_7] :  (r(X6_6, Y7_7)) => q(X6_6, X6_6)))
% 0.19/0.37  	-> [16] (? [Y7_7] :  (r(a, Y7_7)) => q(a, a))
% 0.19/0.37
% 0.19/0.37  [16] BETA_IMPLY : (? [Y7_7] :  (r(a, Y7_7)) => q(a, a))
% 0.19/0.37  	-> [23] ~? [Y7_7] :  (r(a, Y7_7))
% 0.19/0.37  	-> [24] q(a, a)
% 0.19/0.37
% 0.19/0.37  [23] GAMMA_NOT_EXISTS : ~? [Y7_7] :  (r(a, Y7_7))
% 0.19/0.37  	-> [27] ~r(a, Y7_1_3)
% 0.19/0.37
% 0.19/0.37  [27] CLOSURE : ~r(a, Y7_1_3)
% 0.19/0.37
% 0.19/0.37  [24] CLOSURE : q(a, a)
% 0.19/0.37
% 0.19/0.37  [5] GAMMA_FORALL : ! [U8_8, V9_9] :  ((q(U8_8, V9_9) => ! [Z10_10] :  (r(Z10_10, V9_9))))
% 0.19/0.37  	-> [7] (q(a, a) => ! [Z10_10] :  (r(Z10_10, a)))
% 0.19/0.37
% 0.19/0.37  [7] BETA_IMPLY : (q(a, a) => ! [Z10_10] :  (r(Z10_10, a)))
% 0.19/0.37  	-> [9] ~q(a, a)
% 0.19/0.37  	-> [10] ! [Z10_10] :  (r(Z10_10, a))
% 0.19/0.37
% 0.19/0.37  [9] GAMMA_FORALL : ! [X6_6] :  ((? [Y7_7] :  (r(X6_6, Y7_7)) => q(X6_6, X6_6)))
% 0.19/0.37  	-> [13] (? [Y7_7] :  (r(a, Y7_7)) => q(a, a))
% 0.19/0.37
% 0.19/0.37  [13] BETA_IMPLY : (? [Y7_7] :  (r(a, Y7_7)) => q(a, a))
% 0.19/0.37  	-> [17] ~? [Y7_7] :  (r(a, Y7_7))
% 0.19/0.37  	-> [18] q(a, a)
% 0.19/0.37
% 0.19/0.37  [17] GAMMA_NOT_EXISTS : ~? [Y7_7] :  (r(a, Y7_7))
% 0.19/0.37  	-> [25] ~r(a, Y7_0_3)
% 0.19/0.37
% 0.19/0.37  [25] CLOSURE : ~r(a, Y7_0_3)
% 0.19/0.37
% 0.19/0.37  [18] CLOSURE : q(a, a)
% 0.19/0.37
% 0.19/0.37  [15] BETA_IMPLY : (? [Y7_7] :  (r(X6_2_2, Y7_7)) => q(X6_2_2, X6_2_2))
% 0.19/0.37  	-> [31] ~? [Y7_7] :  (r(X6_2_2, Y7_7))
% 0.19/0.37  	-> [32] q(X6_2_2, X6_2_2)
% 0.19/0.37
% 0.19/0.37  [31] GAMMA_FORALL : ! [Z10_10] :  (r(Z10_10, a))
% 0.19/0.37  	-> [33] r(Z10_3_3, a)
% 0.19/0.37
% 0.19/0.37  [33] CLOSURE : r(Z10_3_3, a)
% 0.19/0.37
% 0.19/0.37  [32] GAMMA_FORALL : ! [Z10_10] :  (r(Z10_10, a))
% 0.19/0.37  	-> [34] r(Z10_4_3, a)
% 0.19/0.37
% 0.19/0.37  [34] CLOSURE : r(Z10_4_3, a)
% 0.19/0.37
% 0.19/0.37  % SZS output end Proof for theBenchmark.p
% 0.19/0.37  [0.025563s][1][Res] 54 goroutines created
% 0.19/0.37  ==== Result ====
% 0.19/0.37  [0.025598s][1][Res] VALID
% 0.19/0.37  % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------
```