%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP045-2 : 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 : n010.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 1.45s 1.78s
% Output : CNFRefutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of clauses : 34 ( 16 unt; 0 nHn; 30 RR)
% Number of literals : 62 ( 0 equ; 30 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(product_substitution3,axiom,
( product(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ product(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',product_substitution3) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',left_identity) ).
cnf(total_function2,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',total_function2) ).
cnf(a_equals_b,hypothesis,
equalish(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_equals_b) ).
cnf(associativity2,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',associativity2) ).
cnf(product_with_a,hypothesis,
product(c,a,result),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_with_a) ).
cnf(total_function1,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',total_function1) ).
cnf(prove_product_with_b,negated_conjecture,
~ product(c,b,result),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_product_with_b) ).
cnf(c_0_8,axiom,
( product(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ product(X3,X4,X1) ),
product_substitution3 ).
cnf(c_0_9,axiom,
product(identity,X1,X1),
left_identity ).
cnf(c_0_10,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
total_function2 ).
cnf(c_0_11,plain,
( product(identity,X1,X2)
| ~ equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,plain,
( equalish(X1,X2)
| ~ product(identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_9]) ).
cnf(c_0_13,hypothesis,
equalish(a,b),
a_equals_b ).
cnf(c_0_14,plain,
( product(identity,X1,X2)
| ~ product(identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,hypothesis,
product(identity,a,b),
inference(spm,[status(thm)],[c_0_11,c_0_13]) ).
cnf(c_0_16,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity2 ).
cnf(c_0_17,hypothesis,
product(identity,b,a),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,hypothesis,
( product(X1,b,X2)
| ~ product(X3,a,X2)
| ~ product(X3,identity,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,hypothesis,
product(c,a,result),
product_with_a ).
cnf(c_0_20,hypothesis,
( product(X1,b,result)
| ~ product(c,identity,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1 ).
cnf(c_0_22,hypothesis,
product(multiply(c,identity),b,result),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,plain,
( product(X1,X2,X3)
| ~ product(X4,identity,X1)
| ~ product(X4,X2,X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_9]) ).
cnf(c_0_24,hypothesis,
( equalish(X1,result)
| ~ product(multiply(c,identity),b,X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_22]) ).
cnf(c_0_25,plain,
( product(multiply(X1,identity),X2,X3)
| ~ product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_26,hypothesis,
( equalish(X1,result)
| ~ product(c,b,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,hypothesis,
( product(identity,X1,result)
| ~ product(c,b,X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_26]) ).
cnf(c_0_28,plain,
( product(X1,X2,X3)
| ~ equalish(multiply(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_8,c_0_21]) ).
cnf(c_0_29,hypothesis,
product(identity,multiply(c,b),result),
inference(spm,[status(thm)],[c_0_27,c_0_21]) ).
cnf(c_0_30,plain,
( product(X1,X2,X3)
| ~ product(identity,X3,multiply(X1,X2)) ),
inference(spm,[status(thm)],[c_0_28,c_0_12]) ).
cnf(c_0_31,hypothesis,
product(identity,result,multiply(c,b)),
inference(spm,[status(thm)],[c_0_14,c_0_29]) ).
cnf(c_0_32,negated_conjecture,
~ product(c,b,result),
prove_product_with_b ).
cnf(c_0_33,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP045-2 : 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
% 0.16/0.33 % Computer : n010.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 18:18:21 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.45/1.78 % Version : CSE_E---1.7
% 1.45/1.78 % Problem : theBenchmark.p
% 1.45/1.78 % SZS status Unsatisfiable for theBenchmark.p
% 1.45/1.78 % SZS output start CNFRefutation
% See solution above
% 1.45/1.78 % Total time : 1.372s
%------------------------------------------------------------------------------