TSTP Solution File: GRP041-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP041-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 : Sat Jul 16 11:44:58 EDT 2022
% Result : Unsatisfiable 0.19s 0.40s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of clauses : 6 ( 4 unt; 0 nHn; 6 RR)
% Number of literals : 9 ( 0 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equalish(a,a),
file('GRP041-2.p',unknown),
[] ).
cnf(2,axiom,
product(identity,u,u),
file('GRP041-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equalish(x,w) ),
file('GRP041-2.p',unknown),
[] ).
cnf(9,plain,
( ~ product(u,v,a)
| ~ product(u,v,a) ),
inference(res,[status(thm),theory(equality)],[5,1]),
[iquote('0:Res:5.2,1.0')] ).
cnf(10,plain,
~ product(u,v,a),
inference(obv,[status(thm),theory(equality)],[9]),
[iquote('0:Obv:9.0')] ).
cnf(11,plain,
$false,
inference(unc,[status(thm)],[10,2]),
[iquote('0:UnC:10.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP041-2 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.12 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 12:25:21 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.40
% 0.19/0.40 SPASS V 3.9
% 0.19/0.40 SPASS beiseite: Proof found.
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.40 SPASS derived 1 clauses, backtracked 0 clauses, performed 0 splits and kept 9 clauses.
% 0.19/0.40 SPASS allocated 63084 KBytes.
% 0.19/0.40 SPASS spent 0:00:00.05 on the problem.
% 0.19/0.40 0:00:00.03 for the input.
% 0.19/0.40 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.40 0:00:00.00 for inferences.
% 0.19/0.40 0:00:00.00 for the backtracking.
% 0.19/0.40 0:00:00.00 for the reduction.
% 0.19/0.40
% 0.19/0.40
% 0.19/0.40 Here is a proof with depth 1, length 6 :
% 0.19/0.40 % SZS output start Refutation
% See solution above
% 0.19/0.40 Formulae used in the proof : prove_reflexivity left_identity total_function2
% 0.19/0.40
%------------------------------------------------------------------------------