TSTP Solution File: GRP114-1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP114-1 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n011.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 : Thu Aug 31 00:16:06 EDT 2023
% Result : Unsatisfiable 0.77s 0.89s
% Output : CNFRefutation 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 26
% Syntax : Number of formulae : 111 ( 103 unt; 8 typ; 0 def)
% Number of atoms : 103 ( 102 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 9 ( 6 >; 3 *; 0 +; 0 <<)
% 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 : 175 ( 11 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
identity: $i ).
tff(decl_23,type,
multiply: ( $i * $i ) > $i ).
tff(decl_24,type,
inverse: $i > $i ).
tff(decl_25,type,
intersection: ( $i * $i ) > $i ).
tff(decl_26,type,
union: ( $i * $i ) > $i ).
tff(decl_27,type,
positive_part: $i > $i ).
tff(decl_28,type,
negative_part: $i > $i ).
tff(decl_29,type,
a: $i ).
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
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(inverse_product_lemma,axiom,
inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_product_lemma) ).
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(union_commutative,axiom,
union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_commutative) ).
cnf(union_intersection_absorbtion,axiom,
union(intersection(X1,X2),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_intersection_absorbtion) ).
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(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(intersection_union_absorbtion,axiom,
intersection(union(X1,X2),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_union_absorbtion) ).
cnf(union_associative,axiom,
union(X1,union(X2,X3)) = union(union(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_associative) ).
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_18,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_19,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_20,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_21,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_22,axiom,
inverse(inverse(X1)) = X1,
inverse_involution ).
cnf(c_0_23,axiom,
multiply(X1,intersection(X2,X3)) = intersection(multiply(X1,X2),multiply(X1,X3)),
multiply_intersection1 ).
cnf(c_0_24,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_19]),c_0_22]) ).
cnf(c_0_25,axiom,
intersection(X1,X2) = intersection(X2,X1),
intersection_commutative ).
cnf(c_0_26,axiom,
inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
inverse_product_lemma ).
cnf(c_0_27,plain,
intersection(X1,multiply(X1,X2)) = multiply(X1,intersection(X2,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_28,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_19,c_0_22]) ).
cnf(c_0_29,axiom,
multiply(union(X1,X2),X3) = union(multiply(X1,X3),multiply(X2,X3)),
multiply_union2 ).
cnf(c_0_30,axiom,
union(X1,X2) = union(X2,X1),
union_commutative ).
cnf(c_0_31,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_26]),c_0_22]) ).
cnf(c_0_32,plain,
multiply(inverse(X1),intersection(X1,identity)) = intersection(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_19]),c_0_25]) ).
cnf(c_0_33,axiom,
union(intersection(X1,X2),X2) = X2,
union_intersection_absorbtion ).
cnf(c_0_34,plain,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(spm,[status(thm)],[c_0_26,c_0_22]) ).
cnf(c_0_35,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_28]),c_0_20]) ).
cnf(c_0_36,axiom,
multiply(X1,union(X2,X3)) = union(multiply(X1,X2),multiply(X1,X3)),
multiply_union1 ).
cnf(c_0_37,plain,
union(X1,multiply(X2,X1)) = multiply(union(X2,identity),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_20]),c_0_30]) ).
cnf(c_0_38,plain,
multiply(intersection(X1,identity),inverse(intersection(identity,inverse(X1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_22]) ).
cnf(c_0_39,plain,
union(X1,intersection(X2,X1)) = X1,
inference(rw,[status(thm)],[c_0_33,c_0_30]) ).
cnf(c_0_40,axiom,
multiply(intersection(X1,X2),X3) = intersection(multiply(X1,X3),multiply(X2,X3)),
multiply_intersection2 ).
cnf(c_0_41,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_22]) ).
cnf(c_0_42,plain,
multiply(inverse(X1),union(multiply(X1,X2),X3)) = union(X2,multiply(inverse(X1),X3)),
inference(spm,[status(thm)],[c_0_36,c_0_21]) ).
cnf(c_0_43,plain,
union(X1,inverse(intersection(identity,inverse(X1)))) = inverse(intersection(identity,inverse(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_30]),c_0_39]),c_0_20]),c_0_30]) ).
cnf(c_0_44,plain,
multiply(intersection(X1,inverse(multiply(X2,X3))),X2) = intersection(multiply(X1,X2),inverse(X3)),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,plain,
union(X1,inverse(intersection(X2,inverse(X1)))) = inverse(intersection(X2,inverse(X1))),
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_42,c_0_43]),c_0_26]),c_0_44]),c_0_20]),c_0_26]),c_0_44]),c_0_20]) ).
cnf(c_0_46,axiom,
intersection(union(X1,X2),X2) = X2,
intersection_union_absorbtion ).
cnf(c_0_47,plain,
union(inverse(X1),inverse(intersection(X2,X1))) = inverse(intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_45,c_0_22]) ).
cnf(c_0_48,plain,
intersection(X1,union(X2,X1)) = X1,
inference(rw,[status(thm)],[c_0_46,c_0_25]) ).
cnf(c_0_49,plain,
union(inverse(X1),inverse(union(X2,X1))) = inverse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_30]) ).
cnf(c_0_50,plain,
union(X1,multiply(X1,X2)) = multiply(X1,union(X2,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_24]),c_0_30]) ).
cnf(c_0_51,plain,
multiply(union(X1,identity),inverse(X1)) = union(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_28]),c_0_30]) ).
cnf(c_0_52,plain,
multiply(inverse(X1),intersection(identity,X1)) = intersection(identity,inverse(X1)),
inference(spm,[status(thm)],[c_0_32,c_0_25]) ).
cnf(c_0_53,plain,
intersection(X1,union(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_48,c_0_30]) ).
cnf(c_0_54,plain,
union(X1,inverse(union(X2,inverse(X1)))) = X1,
inference(spm,[status(thm)],[c_0_49,c_0_22]) ).
cnf(c_0_55,plain,
intersection(X1,multiply(X2,X1)) = multiply(intersection(X2,identity),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_20]),c_0_25]) ).
cnf(c_0_56,plain,
multiply(inverse(X1),union(X1,identity)) = union(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_19]),c_0_30]) ).
cnf(c_0_57,plain,
intersection(inverse(X1),inverse(multiply(X2,X1))) = multiply(inverse(X1),intersection(identity,inverse(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_26]),c_0_25]) ).
cnf(c_0_58,plain,
multiply(union(identity,X1),inverse(X1)) = union(identity,inverse(X1)),
inference(spm,[status(thm)],[c_0_51,c_0_30]) ).
cnf(c_0_59,plain,
intersection(identity,inverse(union(identity,X1))) = inverse(union(identity,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_24]) ).
cnf(c_0_60,plain,
intersection(X1,inverse(union(X2,inverse(X1)))) = inverse(union(X2,inverse(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_54]),c_0_25]) ).
cnf(c_0_61,plain,
intersection(inverse(X1),inverse(multiply(X1,X2))) = multiply(intersection(identity,inverse(X2)),inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_26]),c_0_25]) ).
cnf(c_0_62,plain,
multiply(inverse(X1),union(identity,X1)) = union(identity,inverse(X1)),
inference(spm,[status(thm)],[c_0_56,c_0_30]) ).
cnf(c_0_63,plain,
inverse(union(identity,inverse(X1))) = multiply(X1,inverse(union(identity,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_22]),c_0_22]),c_0_59]),c_0_60]) ).
cnf(c_0_64,plain,
inverse(union(identity,inverse(X1))) = multiply(inverse(union(identity,X1)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_22]),c_0_59]),c_0_22]),c_0_60]) ).
cnf(c_0_65,plain,
intersection(X1,intersection(X2,X1)) = intersection(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_39]),c_0_25]) ).
cnf(c_0_66,plain,
multiply(inverse(union(identity,X1)),X1) = multiply(X1,inverse(union(identity,X1))),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_67,plain,
multiply(X1,union(X2,inverse(X1))) = union(identity,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_28]),c_0_30]) ).
cnf(c_0_68,axiom,
union(X1,union(X2,X3)) = union(union(X1,X2),X3),
union_associative ).
cnf(c_0_69,plain,
intersection(identity,inverse(intersection(X1,identity))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_65]),c_0_19]) ).
cnf(c_0_70,plain,
multiply(X1,union(X2,inverse(multiply(X3,X1)))) = union(multiply(X1,X2),inverse(X3)),
inference(spm,[status(thm)],[c_0_36,c_0_31]) ).
cnf(c_0_71,plain,
multiply(inverse(union(X1,identity)),X1) = multiply(X1,inverse(union(X1,identity))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_50]),c_0_20]),c_0_20]),c_0_20]),c_0_20]) ).
cnf(c_0_72,plain,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_26,c_0_22]) ).
cnf(c_0_73,plain,
multiply(X1,union(X2,union(X3,inverse(X1)))) = union(identity,multiply(X1,union(X2,X3))),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_74,plain,
multiply(intersection(X1,identity),inverse(X1)) = intersection(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_28]),c_0_25]) ).
cnf(c_0_75,plain,
union(inverse(X1),inverse(multiply(X2,X1))) = multiply(inverse(X1),union(identity,inverse(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_26]),c_0_30]) ).
cnf(c_0_76,plain,
union(identity,inverse(intersection(X1,identity))) = inverse(intersection(X1,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_69]),c_0_30]) ).
cnf(c_0_77,plain,
multiply(intersection(X1,inverse(X2)),X2) = intersection(identity,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_19]),c_0_25]) ).
cnf(c_0_78,axiom,
intersection(X1,intersection(X2,X3)) = intersection(intersection(X1,X2),X3),
intersection_associative ).
cnf(c_0_79,plain,
multiply(union(X1,identity),X1) = multiply(X1,union(X1,identity)),
inference(spm,[status(thm)],[c_0_50,c_0_37]) ).
cnf(c_0_80,plain,
union(X1,union(identity,multiply(X1,X2))) = union(identity,multiply(X1,union(X2,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_70,c_0_71]),c_0_72]),c_0_51]),c_0_73]),c_0_22]),c_0_30]),c_0_68]) ).
cnf(c_0_81,plain,
multiply(intersection(identity,X1),inverse(X1)) = intersection(identity,inverse(X1)),
inference(spm,[status(thm)],[c_0_74,c_0_25]) ).
cnf(c_0_82,plain,
union(X1,intersection(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_39,c_0_25]) ).
cnf(c_0_83,plain,
inverse(intersection(identity,inverse(X1))) = multiply(X1,inverse(intersection(X1,identity))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_74]),c_0_22]),c_0_22]),c_0_76]),c_0_45]) ).
cnf(c_0_84,plain,
multiply(intersection(X1,intersection(X2,inverse(X3))),X3) = intersection(identity,multiply(intersection(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_85,negated_conjecture,
multiply(positive_part(a),negative_part(a)) != a,
prove_product ).
cnf(c_0_86,axiom,
positive_part(X1) = union(X1,identity),
positive_part ).
cnf(c_0_87,axiom,
negative_part(X1) = intersection(X1,identity),
negative_part ).
cnf(c_0_88,plain,
multiply(union(identity,X1),X1) = multiply(X1,union(identity,X1)),
inference(spm,[status(thm)],[c_0_79,c_0_30]) ).
cnf(c_0_89,plain,
union(identity,multiply(intersection(identity,X1),union(identity,inverse(X1)))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]),c_0_30]),c_0_82]),c_0_30]) ).
cnf(c_0_90,plain,
intersection(X1,intersection(identity,multiply(X2,X1))) = intersection(identity,multiply(intersection(X2,identity),X1)),
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_44,c_0_83]),c_0_22]),c_0_84]),c_0_22]),c_0_25]),c_0_78]) ).
cnf(c_0_91,negated_conjecture,
multiply(union(a,identity),intersection(a,identity)) != a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_86]),c_0_87]) ).
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_27,c_0_88]),c_0_55]) ).
cnf(c_0_93,plain,
multiply(X1,intersection(X2,inverse(X1))) = intersection(identity,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_28]),c_0_25]) ).
cnf(c_0_94,plain,
union(identity,multiply(intersection(identity,inverse(X1)),union(identity,X1))) = identity,
inference(spm,[status(thm)],[c_0_89,c_0_22]) ).
cnf(c_0_95,plain,
intersection(identity,multiply(intersection(identity,inverse(X1)),union(identity,X1))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_62]),c_0_53]),c_0_25]),c_0_53]),c_0_25]) ).
cnf(c_0_96,negated_conjecture,
multiply(union(identity,a),intersection(identity,a)) != a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_25]),c_0_30]) ).
cnf(c_0_97,plain,
multiply(union(identity,X1),intersection(identity,X1)) = multiply(intersection(identity,X1),union(identity,X1)),
inference(spm,[status(thm)],[c_0_92,c_0_25]) ).
cnf(c_0_98,plain,
multiply(X1,multiply(intersection(X2,inverse(X1)),X3)) = multiply(intersection(identity,multiply(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_18,c_0_93]) ).
cnf(c_0_99,plain,
multiply(intersection(identity,inverse(X1)),union(identity,X1)) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_94]),c_0_25]),c_0_95]) ).
cnf(c_0_100,negated_conjecture,
multiply(intersection(identity,a),union(identity,a)) != a,
inference(rw,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_101,plain,
multiply(intersection(identity,X1),union(identity,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_24]),c_0_24]) ).
cnf(c_0_102,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_101])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP114-1 : TPTP v8.1.2. Released v1.2.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.35 % Computer : n011.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Tue Aug 29 00:04:26 EDT 2023
% 0.12/0.35 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.77/0.89 % Version : CSE_E---1.5
% 0.77/0.89 % Problem : theBenchmark.p
% 0.77/0.89 % Proof found
% 0.77/0.89 % SZS status Theorem for theBenchmark.p
% 0.77/0.89 % SZS output start Proof
% See solution above
% 0.77/0.90 % Total time : 0.320000 s
% 0.77/0.90 % SZS output end Proof
% 0.77/0.90 % Total time : 0.323000 s
%------------------------------------------------------------------------------