## TSTP Solution File: LAT270-2 by SPASS---3.9

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LAT270-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n027.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  : 600s
% DateTime : Sun Jul 17 06:49:57 EDT 2022

% Result   : Unsatisfiable 0.17s 0.39s
% Output   : Refutation 0.17s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    7 (   5 unt;   0 nHn;   7 RR)
%            Number of literals    :   12 (   0 equ;   6 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   9 con; 0-4 aty)
%            Number of variables   :    0 (   0 sgn)

%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c_in(u,v_A,t_a)
| ~ c_in(v,v_A,t_a)
| ~ c_lessequals(w,c_Tarski_Ointerval(v_r,u,v,t_a),tc_set(t_a))
| c_lessequals(w,v_A,tc_set(t_a)) ),
file('LAT270-2.p',unknown),
[] ).

cnf(2,axiom,
c_in(v_a,v_A,t_a),
file('LAT270-2.p',unknown),
[] ).

cnf(3,axiom,
c_in(v_b,v_A,t_a),
file('LAT270-2.p',unknown),
[] ).

cnf(4,axiom,
c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)),
file('LAT270-2.p',unknown),
[] ).

cnf(5,axiom,
~ c_lessequals(v_S,v_A,tc_set(t_a)),
file('LAT270-2.p',unknown),
[] ).

cnf(11,plain,
( ~ c_in(v_a,v_A,t_a)
| ~ c_in(v_b,v_A,t_a)
| c_lessequals(v_S,v_A,tc_set(t_a)) ),
inference(res,[status(thm),theory(equality)],[4,1]),
[iquote('0:Res:4.0,1.2')] ).

cnf(12,plain,
\$false,
inference(mrr,[status(thm)],[11,2,3,5]),
[iquote('0:MRR:11.0,11.1,11.2,2.0,3.0,5.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : LAT270-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.11  % Command  : run_spass %d %s
% 0.11/0.32  % Computer : n027.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 600
% 0.11/0.32  % DateTime : Tue Jun 28 22:50:34 EDT 2022
% 0.11/0.32  % CPUTime  :
% 0.17/0.39
% 0.17/0.39  SPASS V 3.9
% 0.17/0.39  SPASS beiseite: Proof found.
% 0.17/0.39  % SZS status Theorem
% 0.17/0.39  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.39  SPASS derived 6 clauses, backtracked 0 clauses, performed 0 splits and kept 11 clauses.
% 0.17/0.39  SPASS allocated 63092 KBytes.
% 0.17/0.39  SPASS spent	0:00:00.06 on the problem.
% 0.17/0.39  		0:00:00.04 for the input.
% 0.17/0.39  		0:00:00.00 for the FLOTTER CNF translation.
% 0.17/0.39  		0:00:00.00 for inferences.
% 0.17/0.39  		0:00:00.00 for the backtracking.
% 0.17/0.39  		0:00:00.00 for the reduction.
% 0.17/0.39
% 0.17/0.39
% 0.17/0.39  Here is a proof with depth 1, length 7 :
% 0.17/0.39  % SZS output start Refutation
% See solution above
% 0.17/0.39  Formulae used in the proof : cls_Tarski_O_91_124_Aa1_A_58_AA_59_Ab1_A_58_AA_59_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_A_124_93_A_61_61_62_AS1_A_60_61_AA_A_61_61_ATrue_0 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_6
% 0.17/0.39
%------------------------------------------------------------------------------
```