%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP039-3 : 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 : n023.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 1.74s 1.88s
% Output : CNFRefutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 20
% Syntax : Number of clauses : 101 ( 35 unt; 13 nHn; 83 RR)
% Number of literals : 214 ( 22 equ; 108 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 171 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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/GRP003-0.ax',associativity2) ).
cnf(a_times_c_is_d,negated_conjecture,
product(a,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c_is_d) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
cnf(product_left_cancellation,axiom,
( X4 = X1
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
cnf(total_function1,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',total_function1) ).
cnf(product_right_cancellation,axiom,
( X4 = X2
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(closure_of_product_and_inverse,axiom,
( subgroup_member(X3)
| ~ subgroup_member(X1)
| ~ subgroup_member(X2)
| ~ product(X1,inverse(X2),X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-2.ax',closure_of_product_and_inverse) ).
cnf(inverse_is_self_cancelling,axiom,
inverse(inverse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_is_self_cancelling) ).
cnf(property_of_O2,axiom,
( product(X1,element_in_O2(X1,X2),X2)
| subgroup_member(X2)
| subgroup_member(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_O2) ).
cnf(prove_d_is_in_subgroup,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_d_is_in_subgroup) ).
cnf(b_times_a_inverse_is_c,negated_conjecture,
product(b,inverse(a),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
cnf(b_is_in_subgroup,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_in_subgroup) ).
cnf(an_element_in_O2,axiom,
( subgroup_member(element_in_O2(X1,X2))
| subgroup_member(X2)
| subgroup_member(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',an_element_in_O2) ).
cnf(subgroup_member_inverse_are_in_subgroup,axiom,
( subgroup_member(inverse(X1))
| ~ subgroup_member(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subgroup_member_inverse_are_in_subgroup) ).
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/GRP003-0.ax',associativity1) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_identity) ).
cnf(total_function2,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',total_function2) ).
cnf(right_identity,axiom,
product(X1,identity,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_identity) ).
cnf(right_inverse,axiom,
product(X1,inverse(X1),identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
cnf(identity_is_in_subgroup,axiom,
subgroup_member(identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_is_in_subgroup) ).
cnf(c_0_20,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity2 ).
cnf(c_0_21,negated_conjecture,
product(a,c,d),
a_times_c_is_d ).
cnf(c_0_22,negated_conjecture,
( product(X1,c,X2)
| ~ product(X3,d,X2)
| ~ product(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,axiom,
product(inverse(X1),X1,identity),
left_inverse ).
cnf(c_0_24,axiom,
( X4 = X1
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
product_left_cancellation ).
cnf(c_0_25,negated_conjecture,
( product(X1,c,identity)
| ~ product(inverse(d),a,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1 ).
cnf(c_0_27,axiom,
( X4 = X2
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
product_right_cancellation ).
cnf(c_0_28,plain,
( X1 = inverse(X2)
| ~ product(X1,X2,identity) ),
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_29,negated_conjecture,
product(multiply(inverse(d),a),c,identity),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,axiom,
( subgroup_member(X3)
| ~ subgroup_member(X1)
| ~ subgroup_member(X2)
| ~ product(X1,inverse(X2),X3) ),
closure_of_product_and_inverse ).
cnf(c_0_31,axiom,
inverse(inverse(X1)) = X1,
inverse_is_self_cancelling ).
cnf(c_0_32,negated_conjecture,
( X1 = c
| ~ product(a,X1,d) ),
inference(spm,[status(thm)],[c_0_27,c_0_21]) ).
cnf(c_0_33,axiom,
( product(X1,element_in_O2(X1,X2),X2)
| subgroup_member(X2)
| subgroup_member(X1) ),
property_of_O2 ).
cnf(c_0_34,negated_conjecture,
~ subgroup_member(d),
prove_d_is_in_subgroup ).
cnf(c_0_35,negated_conjecture,
product(b,inverse(a),c),
b_times_a_inverse_is_c ).
cnf(c_0_36,negated_conjecture,
subgroup_member(b),
b_is_in_subgroup ).
cnf(c_0_37,negated_conjecture,
multiply(inverse(d),a) = inverse(c),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_38,plain,
( subgroup_member(X1)
| ~ subgroup_member(inverse(X2))
| ~ subgroup_member(X3)
| ~ product(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_39,axiom,
( subgroup_member(element_in_O2(X1,X2))
| subgroup_member(X2)
| subgroup_member(X1) ),
an_element_in_O2 ).
cnf(c_0_40,negated_conjecture,
( element_in_O2(a,d) = c
| subgroup_member(a) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_41,negated_conjecture,
( subgroup_member(c)
| ~ subgroup_member(a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_35]),c_0_36])]) ).
cnf(c_0_42,plain,
( X1 = element_in_O2(X2,X3)
| subgroup_member(X2)
| subgroup_member(X3)
| ~ product(X2,X1,X3) ),
inference(spm,[status(thm)],[c_0_27,c_0_33]) ).
cnf(c_0_43,negated_conjecture,
product(inverse(d),a,inverse(c)),
inference(spm,[status(thm)],[c_0_26,c_0_37]) ).
cnf(c_0_44,negated_conjecture,
( ~ subgroup_member(inverse(c))
| ~ subgroup_member(a) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_21]),c_0_34]) ).
cnf(c_0_45,axiom,
( subgroup_member(inverse(X1))
| ~ subgroup_member(X1) ),
subgroup_member_inverse_are_in_subgroup ).
cnf(c_0_46,negated_conjecture,
subgroup_member(c),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_34]),c_0_41]) ).
cnf(c_0_47,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
associativity1 ).
cnf(c_0_48,negated_conjecture,
( element_in_O2(inverse(d),inverse(c)) = a
| subgroup_member(inverse(c))
| subgroup_member(inverse(d)) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,negated_conjecture,
~ subgroup_member(a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46])]) ).
cnf(c_0_50,negated_conjecture,
( product(X1,X2,d)
| ~ product(X3,c,X2)
| ~ product(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_47,c_0_21]) ).
cnf(c_0_51,axiom,
product(identity,X1,X1),
left_identity ).
cnf(c_0_52,plain,
( subgroup_member(X1)
| ~ subgroup_member(inverse(X1)) ),
inference(spm,[status(thm)],[c_0_45,c_0_31]) ).
cnf(c_0_53,negated_conjecture,
( subgroup_member(inverse(d))
| subgroup_member(inverse(c)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_48]),c_0_49]) ).
cnf(c_0_54,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
total_function2 ).
cnf(c_0_55,plain,
( subgroup_member(X1)
| subgroup_member(X2)
| product(X3,element_in_O2(X1,X2),X4)
| ~ product(X5,X2,X4)
| ~ product(X5,X1,X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_33]) ).
cnf(c_0_56,negated_conjecture,
( product(X1,c,d)
| ~ product(X1,identity,a) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_57,negated_conjecture,
subgroup_member(inverse(c)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_34]) ).
cnf(c_0_58,plain,
( product(X1,X2,X3)
| ~ product(X1,X4,identity)
| ~ product(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_51]) ).
cnf(c_0_59,axiom,
product(X1,identity,X1),
right_identity ).
cnf(c_0_60,plain,
( X1 = X2
| ~ product(identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_51]) ).
cnf(c_0_61,negated_conjecture,
( subgroup_member(X1)
| product(X2,element_in_O2(X1,a),inverse(c))
| ~ product(inverse(d),X1,X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_43]),c_0_49]) ).
cnf(c_0_62,negated_conjecture,
( ~ subgroup_member(X1)
| ~ product(X1,identity,a) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_56]),c_0_57])]),c_0_34]) ).
cnf(c_0_63,plain,
( product(inverse(X1),X2,X3)
| ~ product(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_58,c_0_23]) ).
cnf(c_0_64,plain,
( product(X1,X2,identity)
| ~ product(X1,X3,inverse(X4))
| ~ product(X3,X4,X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_23]) ).
cnf(c_0_65,axiom,
product(X1,inverse(X1),identity),
right_inverse ).
cnf(c_0_66,plain,
( X1 = X2
| ~ product(X2,identity,X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_59]) ).
cnf(c_0_67,negated_conjecture,
( element_in_O2(X1,a) = inverse(c)
| subgroup_member(X1)
| ~ product(inverse(d),X1,identity) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_68,negated_conjecture,
( ~ subgroup_member(inverse(X1))
| ~ product(X1,a,identity) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_69,plain,
( product(inverse(X1),X2,identity)
| ~ product(identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_64,c_0_59]) ).
cnf(c_0_70,plain,
( product(X1,inverse(X2),X3)
| ~ product(X4,identity,X3)
| ~ product(X4,X2,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_65]) ).
cnf(c_0_71,plain,
multiply(X1,identity) = X1,
inference(spm,[status(thm)],[c_0_66,c_0_26]) ).
cnf(c_0_72,negated_conjecture,
element_in_O2(d,a) = inverse(c),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_65]),c_0_31]),c_0_31]),c_0_34]) ).
cnf(c_0_73,negated_conjecture,
( ~ subgroup_member(X1)
| ~ product(identity,X1,a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_31]) ).
cnf(c_0_74,plain,
( product(X1,inverse(X2),X3)
| ~ product(X3,X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_26]),c_0_71]) ).
cnf(c_0_75,plain,
( product(X1,X2,identity)
| ~ product(X3,inverse(X4),X2)
| ~ product(X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_47,c_0_65]) ).
cnf(c_0_76,negated_conjecture,
product(d,inverse(c),a),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_72]),c_0_49]),c_0_34]) ).
cnf(c_0_77,negated_conjecture,
( ~ subgroup_member(inverse(X1))
| ~ product(a,X1,identity) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_78,plain,
( product(X1,inverse(X2),identity)
| ~ product(X1,identity,X2) ),
inference(spm,[status(thm)],[c_0_75,c_0_51]) ).
cnf(c_0_79,plain,
( product(X1,X2,X3)
| ~ product(X4,multiply(X5,X2),X3)
| ~ product(X4,X5,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_26]) ).
cnf(c_0_80,negated_conjecture,
( product(X1,X2,a)
| ~ product(X3,inverse(c),X2)
| ~ product(X1,X3,d) ),
inference(spm,[status(thm)],[c_0_47,c_0_76]) ).
cnf(c_0_81,negated_conjecture,
( ~ subgroup_member(X1)
| ~ product(a,identity,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_31]) ).
cnf(c_0_82,plain,
( product(X1,X2,multiply(X3,multiply(X4,X2)))
| ~ product(X3,X4,X1) ),
inference(spm,[status(thm)],[c_0_79,c_0_26]) ).
cnf(c_0_83,plain,
( subgroup_member(multiply(X1,inverse(X2)))
| ~ subgroup_member(X2)
| ~ subgroup_member(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_26]) ).
cnf(c_0_84,negated_conjecture,
( product(X1,inverse(a),X2)
| ~ product(X3,c,X2)
| ~ product(X3,b,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_35]) ).
cnf(c_0_85,negated_conjecture,
( product(X1,a,a)
| ~ product(X1,d,d) ),
inference(spm,[status(thm)],[c_0_80,c_0_76]) ).
cnf(c_0_86,negated_conjecture,
( ~ subgroup_member(multiply(X1,X2))
| ~ product(X1,X2,a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_71]) ).
cnf(c_0_87,plain,
( subgroup_member(multiply(X1,X2))
| ~ subgroup_member(inverse(X2))
| ~ subgroup_member(X1) ),
inference(spm,[status(thm)],[c_0_83,c_0_31]) ).
cnf(c_0_88,negated_conjecture,
( product(X1,inverse(a),d)
| ~ product(a,b,X1) ),
inference(spm,[status(thm)],[c_0_84,c_0_21]) ).
cnf(c_0_89,negated_conjecture,
( product(inverse(X1),a,a)
| ~ product(X1,d,d) ),
inference(spm,[status(thm)],[c_0_85,c_0_63]) ).
cnf(c_0_90,negated_conjecture,
( ~ subgroup_member(inverse(X1))
| ~ subgroup_member(X2)
| ~ product(X2,X1,a) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_91,negated_conjecture,
( element_in_O2(X1,d) = inverse(a)
| subgroup_member(X1)
| ~ product(a,b,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_88]),c_0_34]) ).
cnf(c_0_92,negated_conjecture,
( ~ subgroup_member(inverse(a))
| ~ subgroup_member(inverse(X1))
| ~ product(X1,d,d) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_89]),c_0_49]) ).
cnf(c_0_93,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_60,c_0_65]) ).
cnf(c_0_94,axiom,
subgroup_member(identity),
identity_is_in_subgroup ).
cnf(c_0_95,negated_conjecture,
( ~ subgroup_member(X1)
| ~ subgroup_member(X2)
| ~ product(a,X1,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_74]),c_0_31]) ).
cnf(c_0_96,negated_conjecture,
( element_in_O2(multiply(a,b),d) = inverse(a)
| subgroup_member(multiply(a,b)) ),
inference(spm,[status(thm)],[c_0_91,c_0_26]) ).
cnf(c_0_97,negated_conjecture,
~ subgroup_member(inverse(a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_51]),c_0_93]),c_0_94])]) ).
cnf(c_0_98,negated_conjecture,
( ~ subgroup_member(multiply(a,X1))
| ~ subgroup_member(X1) ),
inference(spm,[status(thm)],[c_0_95,c_0_26]) ).
cnf(c_0_99,negated_conjecture,
subgroup_member(multiply(a,b)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_96]),c_0_97]),c_0_34]) ).
cnf(c_0_100,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_36])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP039-3 : 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
% 0.15/0.33 % Computer : n023.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 18:19:23 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.74/1.88 % Version : CSE_E---1.7
% 1.74/1.88 % Problem : theBenchmark.p
% 1.74/1.88 % SZS status Unsatisfiable for theBenchmark.p
% 1.74/1.88 % SZS output start CNFRefutation
% See solution above
% 1.74/1.88 % Total time : 1.372s
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