%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP031-2 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n003.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 : Tue May 5 04:23:37 PM UTC 2026
% Result : Unsatisfiable 1.25s 1.72s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of clauses : 17 ( 8 unt; 0 nHn; 12 RR)
% Number of literals : 37 ( 0 equ; 22 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 48 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity2,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity2) ).
cnf(right_inverse,hypothesis,
product(X1,inverse(X1),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
cnf(associativity1,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity1) ).
cnf(right_identity,hypothesis,
product(X1,identity,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
cnf(prove_a_has_a_left_inverse,negated_conjecture,
~ product(X1,a,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_has_a_left_inverse) ).
cnf(c_0_5,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity2 ).
cnf(c_0_6,hypothesis,
product(X1,inverse(X1),identity),
right_inverse ).
cnf(c_0_7,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
associativity1 ).
cnf(c_0_8,hypothesis,
( product(X1,inverse(X2),X3)
| ~ product(X4,identity,X3)
| ~ product(X4,X2,X1) ),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_9,hypothesis,
product(X1,identity,X1),
right_identity ).
cnf(c_0_10,hypothesis,
( product(X1,X2,identity)
| ~ product(X3,inverse(X4),X2)
| ~ product(X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_11,hypothesis,
( product(X1,inverse(X2),X3)
| ~ product(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,hypothesis,
( product(X1,X2,identity)
| ~ product(X1,X3,X4)
| ~ product(X2,X4,X3) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_13,hypothesis,
( product(X1,X2,identity)
| ~ product(X2,X1,identity) ),
inference(spm,[status(thm)],[c_0_12,c_0_9]) ).
cnf(c_0_14,negated_conjecture,
~ product(X1,a,identity),
prove_a_has_a_left_inverse ).
cnf(c_0_15,hypothesis,
product(inverse(X1),X1,identity),
inference(spm,[status(thm)],[c_0_13,c_0_6]) ).
cnf(c_0_16,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_14,c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP031-2 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.32 % Computer : n003.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Mon May 4 18:17:56 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.25/1.72 % Version : CSE_E---1.7
% 1.25/1.72 % Problem : theBenchmark.p
% 1.25/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.25/1.72 % SZS output start CNFRefutation
% See solution above
% 1.25/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------