%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP039-6 : 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 : n013.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 04:23:39 PM UTC 2026
% Result : Unsatisfiable 2.16s 1.96s
% Output : CNFRefutation 2.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of clauses : 68 ( 27 unt; 5 nHn; 55 RR)
% Number of literals : 140 ( 0 equ; 66 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 111 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(well_defined,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_defined) ).
cnf(b_times_a_inverse_is_c,negated_conjecture,
product(b,inverse(a),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
cnf(product_substitution3,axiom,
( product(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ product(X3,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_substitution3) ).
cnf(product_right_cancellation,axiom,
( equalish(X4,X2)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
cnf(closure_of_product,axiom,
( subgroup_member(X3)
| ~ subgroup_member(X1)
| ~ subgroup_member(X2)
| ~ product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_product) ).
cnf(b_is_in_subgroup,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_in_subgroup) ).
cnf(a_times_c_is_d,negated_conjecture,
product(a,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c_is_d) ).
cnf(prove_d_is_in_subgroup,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_d_is_in_subgroup) ).
cnf(right_inverse,axiom,
product(X1,inverse(X1),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
cnf(property_of_O2,axiom,
( product(X1,element_in_O2(X1,X2),X2)
| subgroup_member(X2)
| subgroup_member(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_O2) ).
cnf(closure_of_inverse,axiom,
( subgroup_member(inverse(X1))
| ~ subgroup_member(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_inverse) ).
cnf(associativity2,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity2) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
cnf(subgroup_member_substitution,axiom,
( subgroup_member(X2)
| ~ equalish(X1,X2)
| ~ subgroup_member(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subgroup_member_substitution) ).
cnf(associativity1,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity1) ).
cnf(right_identity,axiom,
product(X1,identity,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
cnf(an_element_in_O2,axiom,
( subgroup_member(element_in_O2(X1,X2))
| subgroup_member(X2)
| subgroup_member(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',an_element_in_O2) ).
cnf(c_0_18,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
well_defined ).
cnf(c_0_19,negated_conjecture,
product(b,inverse(a),c),
b_times_a_inverse_is_c ).
cnf(c_0_20,axiom,
( product(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ product(X3,X4,X1) ),
product_substitution3 ).
cnf(c_0_21,axiom,
( equalish(X4,X2)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
product_right_cancellation ).
cnf(c_0_22,axiom,
product(inverse(X1),X1,identity),
left_inverse ).
cnf(c_0_23,axiom,
( subgroup_member(X3)
| ~ subgroup_member(X1)
| ~ subgroup_member(X2)
| ~ product(X1,X2,X3) ),
closure_of_product ).
cnf(c_0_24,negated_conjecture,
subgroup_member(b),
b_is_in_subgroup ).
cnf(c_0_25,negated_conjecture,
product(a,c,d),
a_times_c_is_d ).
cnf(c_0_26,negated_conjecture,
~ subgroup_member(d),
prove_d_is_in_subgroup ).
cnf(c_0_27,negated_conjecture,
( equalish(X1,c)
| ~ product(b,inverse(a),X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_28,negated_conjecture,
( product(b,inverse(a),X1)
| ~ equalish(c,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_29,plain,
( equalish(X1,X2)
| ~ product(inverse(X1),X2,identity) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_30,axiom,
product(X1,inverse(X1),identity),
right_inverse ).
cnf(c_0_31,axiom,
( product(X1,element_in_O2(X1,X2),X2)
| subgroup_member(X2)
| subgroup_member(X1) ),
property_of_O2 ).
cnf(c_0_32,negated_conjecture,
( subgroup_member(c)
| ~ subgroup_member(inverse(a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_19]),c_0_24])]) ).
cnf(c_0_33,axiom,
( subgroup_member(inverse(X1))
| ~ subgroup_member(X1) ),
closure_of_inverse ).
cnf(c_0_34,negated_conjecture,
( ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_25]),c_0_26]) ).
cnf(c_0_35,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity2 ).
cnf(c_0_36,axiom,
product(identity,X1,X1),
left_identity ).
cnf(c_0_37,negated_conjecture,
( equalish(X1,c)
| ~ equalish(c,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_38,plain,
equalish(X1,inverse(inverse(X1))),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_39,plain,
( subgroup_member(X1)
| subgroup_member(X2)
| equalish(element_in_O2(X1,X2),X3)
| ~ product(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_31]) ).
cnf(c_0_40,negated_conjecture,
~ subgroup_member(a),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_41,plain,
( product(X1,X2,X3)
| ~ product(X4,inverse(X2),X1)
| ~ product(X4,identity,X3) ),
inference(spm,[status(thm)],[c_0_35,c_0_22]) ).
cnf(c_0_42,axiom,
( subgroup_member(X2)
| ~ equalish(X1,X2)
| ~ subgroup_member(X1) ),
subgroup_member_substitution ).
cnf(c_0_43,plain,
( equalish(inverse(X1),X2)
| ~ product(X1,X2,identity) ),
inference(spm,[status(thm)],[c_0_21,c_0_30]) ).
cnf(c_0_44,plain,
( equalish(X1,X2)
| ~ product(identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_36]) ).
cnf(c_0_45,plain,
( product(identity,X1,X2)
| ~ equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_36]) ).
cnf(c_0_46,negated_conjecture,
equalish(inverse(inverse(c)),c),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_47,negated_conjecture,
equalish(element_in_O2(a,d),c),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_25]),c_0_40]),c_0_26]) ).
cnf(c_0_48,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
associativity1 ).
cnf(c_0_49,negated_conjecture,
( product(X1,a,X2)
| ~ product(b,identity,X2)
| ~ equalish(c,X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_28]) ).
cnf(c_0_50,axiom,
product(X1,identity,X1),
right_identity ).
cnf(c_0_51,plain,
( subgroup_member(X1)
| ~ product(X2,X1,identity)
| ~ subgroup_member(inverse(X2)) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_52,plain,
( subgroup_member(X1)
| ~ product(identity,X1,X2)
| ~ subgroup_member(X2) ),
inference(spm,[status(thm)],[c_0_42,c_0_44]) ).
cnf(c_0_53,negated_conjecture,
product(identity,inverse(inverse(c)),c),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_54,negated_conjecture,
( subgroup_member(c)
| ~ subgroup_member(element_in_O2(a,d)) ),
inference(spm,[status(thm)],[c_0_42,c_0_47]) ).
cnf(c_0_55,axiom,
( subgroup_member(element_in_O2(X1,X2))
| subgroup_member(X2)
| subgroup_member(X1) ),
an_element_in_O2 ).
cnf(c_0_56,plain,
( product(X1,X2,X3)
| ~ product(X1,X4,identity)
| ~ product(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_36]) ).
cnf(c_0_57,negated_conjecture,
( product(X1,a,b)
| ~ equalish(c,X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_58,plain,
( subgroup_member(X1)
| ~ subgroup_member(inverse(inverse(X1))) ),
inference(spm,[status(thm)],[c_0_51,c_0_22]) ).
cnf(c_0_59,negated_conjecture,
( subgroup_member(inverse(inverse(c)))
| ~ subgroup_member(c) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_60,negated_conjecture,
subgroup_member(c),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_26]),c_0_40]) ).
cnf(c_0_61,plain,
( product(X1,X2,X3)
| ~ product(inverse(X1),X3,X2) ),
inference(spm,[status(thm)],[c_0_56,c_0_30]) ).
cnf(c_0_62,negated_conjecture,
product(inverse(inverse(c)),a,b),
inference(spm,[status(thm)],[c_0_57,c_0_38]) ).
cnf(c_0_63,plain,
( subgroup_member(X1)
| ~ subgroup_member(inverse(X1)) ),
inference(spm,[status(thm)],[c_0_58,c_0_33]) ).
cnf(c_0_64,negated_conjecture,
subgroup_member(inverse(inverse(c))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60])]) ).
cnf(c_0_65,negated_conjecture,
product(inverse(c),b,a),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_66,negated_conjecture,
subgroup_member(inverse(c)),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_67,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_65]),c_0_24]),c_0_66])]),c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP039-6 : 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
% 0.16/0.33 % Computer : n013.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 18:18:11 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 2.16/1.96 % Version : CSE_E---1.7
% 2.16/1.96 % Problem : theBenchmark.p
% 2.16/1.96 % SZS status Unsatisfiable for theBenchmark.p
% 2.16/1.96 % SZS output start CNFRefutation
% See solution above
% 2.16/1.96 % Total time : 1.373s
%------------------------------------------------------------------------------