%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP048-2 : 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 : n016.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 04:23:41 PM UTC 2026
% Result : Unsatisfiable 1.40s 1.96s
% Output : CNFRefutation 1.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of clauses : 45 ( 22 unt; 0 nHn; 34 RR)
% Number of literals : 83 ( 0 equ; 42 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 89 ( 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(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GRP005-0.ax',total_function2) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',left_inverse) ).
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(a_equals_b,hypothesis,
equalish(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_equals_b) ).
cnf(total_function1,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',total_function1) ).
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(prove_inverse_substitution,negated_conjecture,
~ equalish(inverse(a),inverse(b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_substitution) ).
cnf(c_0_9,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
associativity1 ).
cnf(c_0_10,axiom,
product(identity,X1,X1),
left_identity ).
cnf(c_0_11,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
total_function2 ).
cnf(c_0_12,axiom,
product(inverse(X1),X1,identity),
left_inverse ).
cnf(c_0_13,plain,
( product(X1,X2,X3)
| ~ product(X1,X4,identity)
| ~ product(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
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,identity)
| ~ product(inverse(X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
( product(inverse(X1),X2,X3)
| ~ product(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_17,plain,
( product(identity,X1,X2)
| ~ equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_10]) ).
cnf(c_0_18,hypothesis,
equalish(a,b),
a_equals_b ).
cnf(c_0_19,plain,
( equalish(X1,identity)
| ~ product(X2,X1,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,hypothesis,
product(identity,a,b),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1 ).
cnf(c_0_22,plain,
( equalish(X1,identity)
| ~ product(X2,inverse(X2),X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_23,hypothesis,
( product(X1,X2,b)
| ~ product(X3,a,X2)
| ~ product(X1,X3,identity) ),
inference(spm,[status(thm)],[c_0_9,c_0_20]) ).
cnf(c_0_24,plain,
( product(X1,X2,X3)
| ~ equalish(multiply(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_21]) ).
cnf(c_0_25,plain,
equalish(multiply(X1,inverse(X1)),identity),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_26,hypothesis,
( product(X1,identity,b)
| ~ product(X1,inverse(a),identity) ),
inference(spm,[status(thm)],[c_0_23,c_0_12]) ).
cnf(c_0_27,plain,
product(X1,inverse(X1),identity),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,hypothesis,
product(inverse(inverse(a)),identity,b),
inference(spm,[status(thm)],[c_0_26,c_0_12]) ).
cnf(c_0_29,plain,
( product(X1,X2,X3)
| ~ product(inverse(X1),X3,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_27]) ).
cnf(c_0_30,hypothesis,
( equalish(X1,b)
| ~ product(inverse(inverse(a)),identity,X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_28]) ).
cnf(c_0_31,plain,
product(X1,identity,X1),
inference(spm,[status(thm)],[c_0_29,c_0_12]) ).
cnf(c_0_32,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity2 ).
cnf(c_0_33,plain,
equalish(multiply(inverse(X1),X1),identity),
inference(spm,[status(thm)],[c_0_15,c_0_21]) ).
cnf(c_0_34,hypothesis,
( equalish(X1,b)
| ~ product(inverse(a),X1,identity) ),
inference(spm,[status(thm)],[c_0_30,c_0_16]) ).
cnf(c_0_35,negated_conjecture,
~ equalish(inverse(a),inverse(b)),
prove_inverse_substitution ).
cnf(c_0_36,plain,
( equalish(X1,X2)
| ~ product(X2,identity,X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_31]) ).
cnf(c_0_37,plain,
( product(X1,X2,X3)
| ~ product(X4,multiply(X5,X2),X3)
| ~ product(X4,X5,X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_21]) ).
cnf(c_0_38,plain,
product(identity,multiply(inverse(X1),X1),identity),
inference(spm,[status(thm)],[c_0_17,c_0_33]) ).
cnf(c_0_39,hypothesis,
equalish(inverse(inverse(a)),b),
inference(spm,[status(thm)],[c_0_34,c_0_27]) ).
cnf(c_0_40,negated_conjecture,
~ product(inverse(b),identity,inverse(a)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,plain,
( product(X1,X2,identity)
| ~ product(identity,inverse(X2),X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,hypothesis,
product(identity,inverse(inverse(a)),b),
inference(spm,[status(thm)],[c_0_17,c_0_39]) ).
cnf(c_0_43,negated_conjecture,
~ product(b,inverse(a),identity),
inference(spm,[status(thm)],[c_0_40,c_0_16]) ).
cnf(c_0_44,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.21 % Problem : GRP048-2 : TPTP v9.2.1. Released v1.0.0.
% 0.02/0.21 % 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
% 0.12/0.44 % Computer : n016.cluster.edu
% 0.12/0.44 % Model : x86_64 x86_64
% 0.12/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.44 % Memory : 8042.1875MB
% 0.12/0.44 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.44 % CPULimit : 300
% 0.12/0.44 % WCLimit : 300
% 0.12/0.44 % DateTime : Mon May 4 18:20:06 EDT 2026
% 0.15/0.45 % CPUTime :
% 0.15/0.46 % start to proof: theBenchmark
% 1.40/1.96 % Version : CSE_E---1.7
% 1.40/1.96 % Problem : theBenchmark.p
% 1.40/1.96 % SZS status Unsatisfiable for theBenchmark.p
% 1.40/1.96 % SZS output start CNFRefutation
% See solution above
% 1.40/1.96 % Total time : 1.394s
%------------------------------------------------------------------------------