%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP114-1 : TPTP v9.2.1. Released v1.2.0.
% 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 : n022.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 04:23:52 PM UTC 2026
% Result : Unsatisfiable 55.05s 35.19s
% Output : CNFRefutation 55.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 20
% Syntax : Number of clauses : 136 ( 136 unt; 0 nHn; 8 RR)
% Number of literals : 136 ( 135 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 237 ( 25 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(inverse_involution,axiom,
inverse(inverse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_involution) ).
cnf(multiply_intersection1,axiom,
multiply(X1,intersection(X2,X3)) = intersection(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_intersection1) ).
cnf(intersection_commutative,axiom,
intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_commutative) ).
cnf(intersection_union_absorbtion,axiom,
intersection(union(X1,X2),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_union_absorbtion) ).
cnf(union_intersection_absorbtion,axiom,
union(intersection(X1,X2),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_intersection_absorbtion) ).
cnf(union_commutative,axiom,
union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_commutative) ).
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(multiply_intersection2,axiom,
multiply(intersection(X1,X2),X3) = intersection(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_intersection2) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(inverse_product_lemma,axiom,
inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_product_lemma) ).
cnf(inverse_of_identity,axiom,
inverse(identity) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_of_identity) ).
cnf(multiply_union1,axiom,
multiply(X1,union(X2,X3)) = union(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_union1) ).
cnf(union_associative,axiom,
union(X1,union(X2,X3)) = union(union(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_associative) ).
cnf(union_idempotent,axiom,
union(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_idempotent) ).
cnf(multiply_union2,axiom,
multiply(union(X1,X2),X3) = union(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_union2) ).
cnf(intersection_associative,axiom,
intersection(X1,intersection(X2,X3)) = intersection(intersection(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_associative) ).
cnf(prove_product,negated_conjecture,
multiply(positive_part(a),negative_part(a)) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_product) ).
cnf(positive_part,axiom,
positive_part(X1) = union(X1,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',positive_part) ).
cnf(negative_part,axiom,
negative_part(X1) = intersection(X1,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',negative_part) ).
cnf(c_0_20,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_21,axiom,
inverse(inverse(X1)) = X1,
inverse_involution ).
cnf(c_0_22,axiom,
multiply(X1,intersection(X2,X3)) = intersection(multiply(X1,X2),multiply(X1,X3)),
multiply_intersection1 ).
cnf(c_0_23,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,axiom,
intersection(X1,X2) = intersection(X2,X1),
intersection_commutative ).
cnf(c_0_25,axiom,
intersection(union(X1,X2),X2) = X2,
intersection_union_absorbtion ).
cnf(c_0_26,axiom,
union(intersection(X1,X2),X2) = X2,
union_intersection_absorbtion ).
cnf(c_0_27,axiom,
union(X1,X2) = union(X2,X1),
union_commutative ).
cnf(c_0_28,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_29,plain,
multiply(X1,intersection(X2,inverse(X1))) = intersection(identity,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_30,axiom,
multiply(intersection(X1,X2),X3) = intersection(multiply(X1,X3),multiply(X2,X3)),
multiply_intersection2 ).
cnf(c_0_31,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_32,plain,
intersection(X1,union(X2,X1)) = X1,
inference(rw,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_33,plain,
union(X1,intersection(X2,X1)) = X1,
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,plain,
multiply(X1,multiply(intersection(X2,inverse(X1)),X3)) = multiply(intersection(identity,multiply(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,plain,
multiply(intersection(X1,X2),inverse(X2)) = intersection(identity,multiply(X1,inverse(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_23]),c_0_24]) ).
cnf(c_0_36,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_20]),c_0_31]) ).
cnf(c_0_37,plain,
intersection(X1,intersection(X2,X1)) = intersection(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_24]) ).
cnf(c_0_38,plain,
multiply(intersection(identity,multiply(X1,X2)),X1) = multiply(X1,intersection(identity,multiply(X2,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_21]),c_0_21]) ).
cnf(c_0_39,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_20]),c_0_21]) ).
cnf(c_0_40,axiom,
inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
inverse_product_lemma ).
cnf(c_0_41,plain,
intersection(X1,intersection(X1,X2)) = intersection(X1,X2),
inference(spm,[status(thm)],[c_0_37,c_0_24]) ).
cnf(c_0_42,plain,
multiply(intersection(identity,X1),X1) = multiply(X1,intersection(identity,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_31]) ).
cnf(c_0_43,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_40]),c_0_21]) ).
cnf(c_0_44,plain,
multiply(inverse(X1),intersection(X2,X1)) = intersection(identity,multiply(inverse(X1),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_20]),c_0_24]) ).
cnf(c_0_45,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_23]),c_0_31]) ).
cnf(c_0_46,plain,
multiply(inverse(X1),intersection(X2,multiply(X1,X3))) = intersection(multiply(inverse(X1),X2),X3),
inference(spm,[status(thm)],[c_0_22,c_0_36]) ).
cnf(c_0_47,plain,
intersection(identity,multiply(X1,inverse(intersection(X1,X2)))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_41]),c_0_23]) ).
cnf(c_0_48,plain,
multiply(intersection(X1,identity),X1) = multiply(X1,intersection(X1,identity)),
inference(spm,[status(thm)],[c_0_42,c_0_24]) ).
cnf(c_0_49,plain,
multiply(X1,inverse(multiply(X1,intersection(identity,X1)))) = inverse(intersection(identity,X1)),
inference(spm,[status(thm)],[c_0_43,c_0_42]) ).
cnf(c_0_50,plain,
intersection(identity,multiply(inverse(intersection(X1,X2)),X2)) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_37]),c_0_20]) ).
cnf(c_0_51,plain,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(spm,[status(thm)],[c_0_40,c_0_21]) ).
cnf(c_0_52,plain,
multiply(X1,intersection(X2,multiply(inverse(X1),X3))) = intersection(multiply(X1,X2),X3),
inference(spm,[status(thm)],[c_0_22,c_0_45]) ).
cnf(c_0_53,axiom,
inverse(identity) = identity,
inverse_of_identity ).
cnf(c_0_54,plain,
intersection(identity,multiply(X1,inverse(intersection(X2,X1)))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_37]),c_0_23]) ).
cnf(c_0_55,plain,
intersection(inverse(X1),inverse(intersection(X1,X2))) = inverse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_39]),c_0_39]) ).
cnf(c_0_56,plain,
intersection(inverse(X1),multiply(inverse(X1),X2)) = multiply(inverse(X1),intersection(X2,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_23]),c_0_24]) ).
cnf(c_0_57,axiom,
multiply(X1,union(X2,X3)) = union(multiply(X1,X2),multiply(X1,X3)),
multiply_union1 ).
cnf(c_0_58,axiom,
union(X1,union(X2,X3)) = union(union(X1,X2),X3),
union_associative ).
cnf(c_0_59,axiom,
union(X1,X1) = X1,
union_idempotent ).
cnf(c_0_60,plain,
multiply(inverse(intersection(X1,identity)),multiply(X1,intersection(X1,identity))) = X1,
inference(spm,[status(thm)],[c_0_36,c_0_48]) ).
cnf(c_0_61,plain,
multiply(inverse(intersection(X1,X2)),intersection(X2,X1)) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_28]),c_0_39]),c_0_51]),c_0_44]),c_0_28]),c_0_52]),c_0_39]),c_0_53]) ).
cnf(c_0_62,plain,
multiply(inverse(X1),multiply(inverse(X2),X3)) = multiply(inverse(multiply(X2,X1)),X3),
inference(spm,[status(thm)],[c_0_28,c_0_40]) ).
cnf(c_0_63,plain,
multiply(inverse(intersection(identity,X1)),multiply(X1,intersection(identity,X1))) = X1,
inference(spm,[status(thm)],[c_0_36,c_0_42]) ).
cnf(c_0_64,plain,
intersection(inverse(X1),inverse(intersection(X2,X1))) = inverse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_54]),c_0_39]),c_0_39]) ).
cnf(c_0_65,plain,
intersection(X1,multiply(inverse(intersection(X2,identity)),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_21]),c_0_51]),c_0_21]) ).
cnf(c_0_66,plain,
multiply(inverse(X1),union(X2,X1)) = union(identity,multiply(inverse(X1),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_20]),c_0_27]) ).
cnf(c_0_67,plain,
union(X1,union(X1,X2)) = union(X1,X2),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_68,plain,
multiply(X1,union(X2,inverse(X1))) = union(identity,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_23]),c_0_27]) ).
cnf(c_0_69,axiom,
multiply(union(X1,X2),X3) = union(multiply(X1,X3),multiply(X2,X3)),
multiply_union2 ).
cnf(c_0_70,plain,
multiply(intersection(identity,X1),inverse(intersection(X1,identity))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_60]),c_0_28]),c_0_23]),c_0_39]),c_0_61]) ).
cnf(c_0_71,plain,
multiply(inverse(intersection(identity,X1)),intersection(identity,inverse(X1))) = inverse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_29]),c_0_39]) ).
cnf(c_0_72,plain,
intersection(X1,inverse(intersection(X2,inverse(X1)))) = X1,
inference(spm,[status(thm)],[c_0_64,c_0_21]) ).
cnf(c_0_73,plain,
intersection(X1,multiply(inverse(intersection(identity,X2)),X1)) = X1,
inference(spm,[status(thm)],[c_0_65,c_0_24]) ).
cnf(c_0_74,plain,
union(identity,multiply(inverse(union(X1,X2)),X1)) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_20]) ).
cnf(c_0_75,axiom,
intersection(X1,intersection(X2,X3)) = intersection(intersection(X1,X2),X3),
intersection_associative ).
cnf(c_0_76,plain,
multiply(X1,multiply(union(X2,inverse(X1)),X3)) = multiply(union(identity,multiply(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_28,c_0_68]) ).
cnf(c_0_77,plain,
multiply(union(X1,X2),inverse(X2)) = union(identity,multiply(X1,inverse(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_23]),c_0_27]) ).
cnf(c_0_78,plain,
multiply(intersection(identity,X1),inverse(intersection(identity,inverse(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_70]),c_0_39]),c_0_39]),c_0_24]) ).
cnf(c_0_79,plain,
multiply(inverse(intersection(identity,inverse(X1))),intersection(identity,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_71]),c_0_21]) ).
cnf(c_0_80,plain,
intersection(X1,inverse(intersection(inverse(X1),X2))) = X1,
inference(spm,[status(thm)],[c_0_72,c_0_24]) ).
cnf(c_0_81,plain,
intersection(X1,multiply(intersection(identity,X2),X1)) = multiply(intersection(identity,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_73]),c_0_21]),c_0_21]),c_0_24]) ).
cnf(c_0_82,plain,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_40,c_0_21]) ).
cnf(c_0_83,plain,
union(identity,inverse(union(identity,X1))) = identity,
inference(spm,[status(thm)],[c_0_74,c_0_39]) ).
cnf(c_0_84,plain,
intersection(X1,intersection(union(X2,X1),X3)) = intersection(X1,X3),
inference(spm,[status(thm)],[c_0_75,c_0_32]) ).
cnf(c_0_85,plain,
intersection(X1,multiply(X1,X2)) = multiply(X1,intersection(X2,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_39]),c_0_24]) ).
cnf(c_0_86,plain,
multiply(union(identity,multiply(X1,X2)),X1) = multiply(X1,union(identity,multiply(X2,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_21]),c_0_21]) ).
cnf(c_0_87,plain,
multiply(intersection(X1,identity),inverse(intersection(identity,inverse(X1)))) = X1,
inference(spm,[status(thm)],[c_0_78,c_0_24]) ).
cnf(c_0_88,plain,
multiply(inverse(intersection(identity,inverse(X1))),intersection(X1,identity)) = X1,
inference(spm,[status(thm)],[c_0_79,c_0_24]) ).
cnf(c_0_89,plain,
intersection(X1,multiply(X1,inverse(intersection(identity,X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]) ).
cnf(c_0_90,plain,
intersection(identity,inverse(union(identity,X1))) = inverse(union(identity,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_83]),c_0_24]) ).
cnf(c_0_91,plain,
intersection(X1,multiply(union(X2,X1),intersection(X3,identity))) = intersection(X1,multiply(union(X2,X1),X3)),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_92,plain,
multiply(union(identity,X1),intersection(X1,identity)) = multiply(intersection(X1,identity),union(identity,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_88]) ).
cnf(c_0_93,plain,
multiply(union(identity,X1),X1) = multiply(X1,union(identity,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_39]),c_0_31]) ).
cnf(c_0_94,plain,
intersection(X1,multiply(X1,union(identity,X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_21]) ).
cnf(c_0_95,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_45]),c_0_21]) ).
cnf(c_0_96,plain,
union(identity,inverse(union(X1,identity))) = identity,
inference(spm,[status(thm)],[c_0_83,c_0_27]) ).
cnf(c_0_97,plain,
intersection(X1,multiply(intersection(X1,identity),union(identity,X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93]),c_0_94]) ).
cnf(c_0_98,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(X2),X3),
inference(spm,[status(thm)],[c_0_28,c_0_95]) ).
cnf(c_0_99,plain,
union(X1,intersection(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_33,c_0_24]) ).
cnf(c_0_100,plain,
intersection(identity,inverse(union(X1,identity))) = inverse(union(X1,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_96]),c_0_24]) ).
cnf(c_0_101,plain,
multiply(inverse(X1),intersection(X1,X2)) = intersection(identity,multiply(inverse(X1),X2)),
inference(spm,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_102,plain,
intersection(X1,multiply(intersection(X1,identity),union(X1,identity))) = X1,
inference(spm,[status(thm)],[c_0_97,c_0_27]) ).
cnf(c_0_103,plain,
multiply(inverse(X1),multiply(intersection(X1,identity),X2)) = multiply(intersection(identity,inverse(X1)),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_87]),c_0_21]) ).
cnf(c_0_104,plain,
union(X1,union(intersection(X1,X2),X3)) = union(X1,X3),
inference(spm,[status(thm)],[c_0_58,c_0_99]) ).
cnf(c_0_105,plain,
union(X1,multiply(X1,X2)) = multiply(X1,union(X2,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_39]),c_0_27]) ).
cnf(c_0_106,plain,
intersection(X1,multiply(X1,union(X2,identity))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_100]),c_0_21]) ).
cnf(c_0_107,plain,
multiply(X1,inverse(multiply(X1,union(identity,X1)))) = inverse(union(identity,X1)),
inference(spm,[status(thm)],[c_0_43,c_0_93]) ).
cnf(c_0_108,plain,
intersection(X1,union(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_32,c_0_27]) ).
cnf(c_0_109,plain,
multiply(inverse(X1),union(X2,multiply(X1,X3))) = union(multiply(inverse(X1),X2),X3),
inference(spm,[status(thm)],[c_0_57,c_0_36]) ).
cnf(c_0_110,plain,
union(identity,multiply(inverse(intersection(X1,X2)),X2)) = multiply(inverse(intersection(X1,X2)),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_50]),c_0_27]) ).
cnf(c_0_111,plain,
intersection(identity,multiply(intersection(identity,inverse(X1)),union(X1,identity))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_20]),c_0_103]) ).
cnf(c_0_112,plain,
union(X1,multiply(intersection(X1,X2),union(X3,identity))) = union(X1,multiply(intersection(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_113,plain,
multiply(intersection(X1,inverse(X2)),X2) = intersection(identity,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_20]),c_0_24]) ).
cnf(c_0_114,negated_conjecture,
multiply(positive_part(a),negative_part(a)) != a,
prove_product ).
cnf(c_0_115,axiom,
positive_part(X1) = union(X1,identity),
positive_part ).
cnf(c_0_116,axiom,
negative_part(X1) = intersection(X1,identity),
negative_part ).
cnf(c_0_117,plain,
multiply(X1,union(inverse(X1),X2)) = union(identity,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_57,c_0_23]) ).
cnf(c_0_118,plain,
union(X1,multiply(X1,union(X2,identity))) = multiply(X1,union(X2,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_106]),c_0_27]) ).
cnf(c_0_119,plain,
multiply(inverse(union(identity,X1)),X1) = multiply(X1,inverse(union(identity,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_107]),c_0_90]),c_0_95]),c_0_90]) ).
cnf(c_0_120,plain,
union(X1,union(X2,X1)) = union(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_108]),c_0_58]) ).
cnf(c_0_121,plain,
union(inverse(X1),multiply(X2,inverse(X1))) = multiply(union(identity,X2),inverse(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_36]),c_0_28]),c_0_109]),c_0_39]) ).
cnf(c_0_122,plain,
multiply(inverse(union(identity,X1)),multiply(X1,union(identity,X1))) = X1,
inference(spm,[status(thm)],[c_0_36,c_0_93]) ).
cnf(c_0_123,plain,
multiply(intersection(identity,inverse(X1)),union(X1,identity)) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_53]),c_0_31]),c_0_112]),c_0_113]),c_0_31]),c_0_99]),c_0_53]),c_0_31]) ).
cnf(c_0_124,negated_conjecture,
multiply(union(a,identity),intersection(a,identity)) != a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_115]),c_0_116]) ).
cnf(c_0_125,plain,
multiply(X1,multiply(union(inverse(X1),X2),X3)) = multiply(union(identity,multiply(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_28,c_0_117]) ).
cnf(c_0_126,plain,
multiply(union(X1,identity),inverse(union(identity,X1))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_120]),c_0_120]),c_0_121]),c_0_120]),c_0_23]),c_0_120]) ).
cnf(c_0_127,plain,
multiply(inverse(union(identity,X1)),union(identity,inverse(X1))) = inverse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_122]),c_0_68]),c_0_39]) ).
cnf(c_0_128,plain,
inverse(union(X1,identity)) = intersection(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_123]),c_0_53]),c_0_31]) ).
cnf(c_0_129,negated_conjecture,
multiply(union(identity,a),intersection(identity,a)) != a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_124,c_0_24]),c_0_27]) ).
cnf(c_0_130,plain,
multiply(union(identity,X1),intersection(identity,X1)) = multiply(intersection(identity,X1),union(identity,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_78]),c_0_79]) ).
cnf(c_0_131,plain,
multiply(union(identity,X1),inverse(union(identity,inverse(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_39]),c_0_39]) ).
cnf(c_0_132,plain,
inverse(union(identity,X1)) = intersection(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_120]),c_0_99]),c_0_39]) ).
cnf(c_0_133,negated_conjecture,
multiply(intersection(identity,a),union(identity,a)) != a,
inference(rw,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_134,plain,
multiply(intersection(identity,X1),union(identity,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_131,c_0_132]),c_0_21]),c_0_130]) ).
cnf(c_0_135,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_133,c_0_134])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP114-1 : TPTP v9.2.1. Released v1.2.0.
% 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 : n022.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 18:22:21 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 55.05/35.19 % Version : CSE_E---1.7
% 55.05/35.19 % Problem : theBenchmark.p
% 55.05/35.19 % SZS status Unsatisfiable for theBenchmark.p
% 55.05/35.19 % SZS output start CNFRefutation
% See solution above
% 55.33/35.40 % Total time : 27.430s
%------------------------------------------------------------------------------