%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP047-2 : 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 : n028.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 3.80s 3.08s
% Output : CNFRefutation 3.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of clauses : 38 ( 17 unt; 0 nHn; 31 RR)
% Number of literals : 71 ( 0 equ; 38 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; 4 con; 0-2 aty)
% Number of variables : 81 ( 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/sandbox2/benchmark/Axioms/GRP005-0.ax',associativity1) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',left_identity) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',left_inverse) ).
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(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(total_function1,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',total_function1) ).
cnf(a_equals_b,hypothesis,
equalish(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_equals_b) ).
cnf(prove_multiply_substitution2,negated_conjecture,
~ equalish(multiply(c,a),multiply(c,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_multiply_substitution2) ).
cnf(c_0_8,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
associativity1 ).
cnf(c_0_9,axiom,
product(identity,X1,X1),
left_identity ).
cnf(c_0_10,plain,
( product(X1,X2,X3)
| ~ product(X1,X4,identity)
| ~ product(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,axiom,
product(inverse(X1),X1,identity),
left_inverse ).
cnf(c_0_12,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
total_function2 ).
cnf(c_0_13,plain,
( product(inverse(X1),X2,X3)
| ~ product(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,axiom,
( product(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ product(X3,X4,X1) ),
product_substitution3 ).
cnf(c_0_15,plain,
( equalish(X1,X2)
| ~ product(inverse(X3),X4,X1)
| ~ product(X3,X2,X4) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1 ).
cnf(c_0_17,plain,
( product(identity,X1,X2)
| ~ equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_9]) ).
cnf(c_0_18,plain,
( equalish(X1,X2)
| ~ product(identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_9]) ).
cnf(c_0_19,hypothesis,
equalish(a,b),
a_equals_b ).
cnf(c_0_20,plain,
( equalish(X1,X2)
| ~ product(X3,X2,X4)
| ~ product(X3,X1,X4) ),
inference(spm,[status(thm)],[c_0_15,c_0_13]) ).
cnf(c_0_21,negated_conjecture,
~ equalish(multiply(c,a),multiply(c,b)),
prove_multiply_substitution2 ).
cnf(c_0_22,plain,
( equalish(X1,multiply(X2,X3))
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_16]) ).
cnf(c_0_23,plain,
( product(identity,X1,X2)
| ~ product(identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,hypothesis,
product(identity,a,b),
inference(spm,[status(thm)],[c_0_17,c_0_19]) ).
cnf(c_0_25,plain,
( equalish(X1,X2)
| ~ product(inverse(X2),X1,identity) ),
inference(spm,[status(thm)],[c_0_20,c_0_11]) ).
cnf(c_0_26,negated_conjecture,
~ product(identity,multiply(c,b),multiply(c,a)),
inference(spm,[status(thm)],[c_0_21,c_0_18]) ).
cnf(c_0_27,plain,
( product(identity,X1,multiply(X2,X3))
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_22]) ).
cnf(c_0_28,plain,
( product(X1,X2,multiply(X3,X4))
| ~ product(X5,X4,X2)
| ~ product(X1,X5,X3) ),
inference(spm,[status(thm)],[c_0_8,c_0_16]) ).
cnf(c_0_29,hypothesis,
product(identity,b,a),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,plain,
( product(X1,X2,X3)
| ~ equalish(multiply(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_16]) ).
cnf(c_0_31,plain,
( equalish(X1,X2)
| ~ product(X2,identity,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_13]) ).
cnf(c_0_32,negated_conjecture,
~ product(c,a,multiply(c,b)),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,hypothesis,
( product(X1,a,multiply(X2,b))
| ~ product(X1,identity,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
( product(X1,X2,X3)
| ~ product(X3,identity,multiply(X1,X2)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,negated_conjecture,
~ product(c,identity,c),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,plain,
product(X1,identity,X1),
inference(spm,[status(thm)],[c_0_34,c_0_16]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP047-2 : 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
% 0.14/0.33 % Computer : n028.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 18:19:46 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 3.80/3.08 % Version : CSE_E---1.7
% 3.80/3.08 % Problem : theBenchmark.p
% 3.80/3.08 % SZS status Unsatisfiable for theBenchmark.p
% 3.80/3.08 % SZS output start CNFRefutation
% See solution above
% 3.80/3.09 % Total time : 2.373s
%------------------------------------------------------------------------------