%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP044-2 : TPTP v9.2.1. Released v1.0.0.
% 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 04:23:40 PM UTC 2026
% Result : Unsatisfiable 0.27s 1.62s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 10
% Syntax : Number of clauses : 31 ( 20 unt; 0 nHn; 19 RR)
% Number of literals : 58 ( 0 equ; 29 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 69 ( 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/GRP005-0.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/GRP005-0.ax',associativity2) ).
cnf(total_function2,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',total_function2) ).
cnf(product_substitution3,axiom,
( product(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ product(X3,X4,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',product_substitution3) ).
cnf(total_function1,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',total_function1) ).
cnf(prove_product_with_b,negated_conjecture,
~ product(b,c,result),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_product_with_b) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',left_inverse) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',left_identity) ).
cnf(product_with_a,hypothesis,
product(a,c,result),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_with_a) ).
cnf(a_equals_b,hypothesis,
equalish(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_equals_b) ).
cnf(i_0_10,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
associativity1,
[final] ).
cnf(i_0_11,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity2,
[final] ).
cnf(i_0_12,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
total_function2,
[final] ).
cnf(i_0_13,axiom,
( product(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ product(X3,X4,X1) ),
product_substitution3,
[final] ).
cnf(i_0_14,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1,
[final] ).
cnf(i_0_15,negated_conjecture,
~ product(b,c,result),
prove_product_with_b,
[final] ).
cnf(i_0_16,axiom,
product(inverse(X1),X1,identity),
left_inverse,
[final] ).
cnf(i_0_17,axiom,
product(identity,X1,X1),
left_identity,
[final] ).
cnf(i_0_18,hypothesis,
product(a,c,result),
product_with_a,
[final] ).
cnf(i_0_19,hypothesis,
equalish(a,b),
a_equals_b,
[final] ).
cnf(i_0_20,plain,
product(identity,a,b),
inference(scs_inference,[],[i_0_17,i_0_19,i_0_13]) ).
cnf(i_0_21,plain,
product(identity,X1,X1),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_22,plain,
( ~ product(X1,X2,X3)
| product(X1,X2,X4)
| ~ equalish(X3,X4) ),
inference(rename_variables,[],[i_0_13]) ).
cnf(i_0_23,plain,
equalish(X1,X1),
inference(scs_inference,[],[i_0_17,i_0_21,i_0_19,i_0_13,i_0_12]) ).
cnf(i_0_24,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X3)
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_12]) ).
cnf(i_0_25,plain,
product(identity,multiply(inverse(X1),X1),identity),
inference(scs_inference,[],[i_0_17,i_0_21,i_0_14,i_0_16,i_0_19,i_0_13,i_0_12,i_0_10]) ).
cnf(i_0_26,plain,
product(inverse(X1),X1,identity),
inference(rename_variables,[],[i_0_16]) ).
cnf(i_0_27,plain,
product(identity,X1,X1),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_28,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_14]) ).
cnf(i_0_29,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X4,X6,X1)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_10]) ).
cnf(i_0_30,plain,
$false,
inference(scs_inference,[],[i_0_15,i_0_17,i_0_21,i_0_27,i_0_14,i_0_16,i_0_18,i_0_19,i_0_13,i_0_12,i_0_10,i_0_11]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP044-2 : TPTP v9.2.1. Released v1.0.0.
% 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
% 0.14/0.33 % Computer : n015.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 18:27:02 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 0.27/1.62 % Version : CSE_E---1.7
% 0.27/1.62 % Problem : theBenchmark.p
% 0.27/1.62 % SZS status Unsatisfiable for theBenchmark.p
% 0.27/1.62 % SZS output start CNFRefutation
% See solution above
% 0.27/1.65 % Total time : 1.271s
%------------------------------------------------------------------------------