%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP028-4 : TPTP v9.2.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n015.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 04:23:36 PM UTC 2026
% Result : Unsatisfiable 0.23s 1.60s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 5
% Syntax : Number of clauses : 11 ( 7 unt; 0 nHn; 7 RR)
% Number of literals : 23 ( 0 equ; 14 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; 0 con; 1-2 aty)
% Number of variables : 34 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity2,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity2) ).
cnf(associativity1,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity1) ).
cnf(prove_there_is_a_right_identity,negated_conjecture,
~ product(not_identity(X1),X1,not_identity(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_a_right_identity) ).
cnf(left_soln,hypothesis,
product(left_solution(X1,X2),X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_soln) ).
cnf(right_soln,hypothesis,
product(X1,right_solution(X1,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_soln) ).
cnf(i_0_5,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
associativity2,
[final] ).
cnf(i_0_6,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity1,
[final] ).
cnf(i_0_7,negated_conjecture,
~ product(not_identity(X1),X1,not_identity(X1)),
prove_there_is_a_right_identity,
[final] ).
cnf(i_0_8,hypothesis,
product(left_solution(X1,X2),X1,X2),
left_soln,
[final] ).
cnf(i_0_9,hypothesis,
product(X1,right_solution(X1,X2),X2),
right_soln,
[final] ).
cnf(i_0_10,plain,
$false,
inference(scs_inference,[],[i_0_7,i_0_8,i_0_9,i_0_6]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP028-4 : TPTP v9.2.1. Released v2.6.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.13/0.32 % Computer : n015.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Mon May 4 18:17:46 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 0.23/1.60 % Version : CSE_E---1.7
% 0.23/1.60 % Problem : theBenchmark.p
% 0.23/1.60 % SZS status Unsatisfiable for theBenchmark.p
% 0.23/1.60 % SZS output start CNFRefutation
% See solution above
% 0.23/1.62 % Total time : 1.270s
%------------------------------------------------------------------------------