%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP028-2 : TPTP v9.2.1. Released v1.1.0.
% 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 : n017.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 0.26s 1.62s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 19
% Syntax : Number of clauses : 27 ( 11 unt; 0 nHn; 19 RR)
% Number of literals : 61 ( 20 equ; 36 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 0 con; 1-2 aty)
% Number of variables : 82 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity1,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP002-0.ax',associativity1) ).
cnf(associativity2,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP002-0.ax',associativity2) ).
cnf(total_function2,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP002-0.ax',total_function2) ).
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(total_function1,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP002-0.ax',total_function1) ).
cnf(i_0_7,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
associativity1,
[final] ).
cnf(i_0_8,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity2,
[final] ).
cnf(i_0_9,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
total_function2,
[final] ).
cnf(i_0_10,negated_conjecture,
~ product(not_identity(X1),X1,not_identity(X1)),
prove_there_is_a_right_identity,
[final] ).
cnf(i_0_11,hypothesis,
product(left_solution(X1,X2),X1,X2),
left_soln,
[final] ).
cnf(i_0_12,hypothesis,
product(X1,right_solution(X1,X2),X2),
right_soln,
[final] ).
cnf(i_0_13,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1,
[final] ).
cnf(i_0_14,axiom,
X1 = X1 ).
cnf(i_0_15,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_16,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_17,axiom,
( X1 != X2
| ~ product(X1,X3,X4)
| product(X2,X3,X4) ) ).
cnf(i_0_18,axiom,
( X1 != X2
| ~ product(X3,X1,X4)
| product(X3,X2,X4) ) ).
cnf(i_0_19,axiom,
( X1 != X2
| ~ product(X3,X4,X1)
| product(X3,X4,X2) ) ).
cnf(i_0_14_001,axiom,
X1 = X1 ).
cnf(i_0_15_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_16_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_17_004,axiom,
( X1 != X2
| ~ product(X1,X3,X4)
| product(X2,X3,X4) ) ).
cnf(i_0_18_005,axiom,
( X1 != X2
| ~ product(X3,X1,X4)
| product(X3,X2,X4) ) ).
cnf(i_0_19_006,axiom,
( X1 != X2
| ~ product(X3,X4,X1)
| product(X3,X4,X2) ) ).
cnf(i_0_20,plain,
$false,
inference(scs_inference,[],[i_0_10,i_0_11,i_0_12,i_0_8]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP028-2 : TPTP v9.2.1. Released v1.1.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n017.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 18:16:13 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.26/1.62 % Version : CSE_E---1.7
% 0.26/1.62 % Problem : theBenchmark.p
% 0.26/1.62 % SZS status Unsatisfiable for theBenchmark.p
% 0.26/1.62 % SZS output start CNFRefutation
% See solution above
% 0.26/1.63 % Total time : 1.271s
%------------------------------------------------------------------------------