%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP167-2 : TPTP v9.2.1. Bugfixed v1.2.1.
% 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 : n007.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 04:24:38 PM UTC 2026
% Result : Unsatisfiable 20.83s 13.19s
% Output : CNFRefutation 20.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 22
% Syntax : Number of clauses : 166 ( 166 unt; 0 nHn; 8 RR)
% Number of literals : 166 ( 165 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 306 ( 32 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(lat4_2,axiom,
inverse(inverse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_2) ).
cnf(monotony_glb2,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',symmetry_of_glb) ).
cnf(associativity_of_glb,axiom,
greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',associativity_of_glb) ).
cnf(idempotence_of_gld,axiom,
greatest_lower_bound(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',idempotence_of_gld) ).
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_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(monotony_glb1,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_glb1) ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',lub_absorbtion) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',symmetry_of_lub) ).
cnf(lat4_3,axiom,
inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_3) ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',glb_absorbtion) ).
cnf(lat4_1,axiom,
inverse(identity) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_1) ).
cnf(lat4_6,axiom,
least_upper_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_6) ).
cnf(monotony_lub1,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_lub1) ).
cnf(monotony_lub2,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_lub2) ).
cnf(lat4_7,axiom,
greatest_lower_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_7) ).
cnf(associativity_of_lub,axiom,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',associativity_of_lub) ).
cnf(prove_lat4,negated_conjecture,
a != multiply(positive_part(a),negative_part(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lat4) ).
cnf(lat4_4,axiom,
positive_part(X1) = least_upper_bound(X1,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_4) ).
cnf(lat4_5,axiom,
negative_part(X1) = greatest_lower_bound(X1,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_5) ).
cnf(c_0_22,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_23,axiom,
inverse(inverse(X1)) = X1,
lat4_2 ).
cnf(c_0_24,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_glb2 ).
cnf(c_0_25,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
symmetry_of_glb ).
cnf(c_0_27,axiom,
greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3),
associativity_of_glb ).
cnf(c_0_28,axiom,
greatest_lower_bound(X1,X1) = X1,
idempotence_of_gld ).
cnf(c_0_29,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_30,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_31,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_glb1 ).
cnf(c_0_32,plain,
multiply(greatest_lower_bound(X1,X2),inverse(X2)) = greatest_lower_bound(identity,multiply(X1,inverse(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_33,plain,
greatest_lower_bound(X1,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,X2),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_25]),c_0_30]) ).
cnf(c_0_35,plain,
multiply(X1,greatest_lower_bound(X2,inverse(X1))) = greatest_lower_bound(identity,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_25]),c_0_26]) ).
cnf(c_0_36,plain,
greatest_lower_bound(identity,multiply(X1,inverse(greatest_lower_bound(X1,X2)))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_25]) ).
cnf(c_0_37,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_22]),c_0_30]) ).
cnf(c_0_38,plain,
multiply(X1,greatest_lower_bound(identity,multiply(inverse(X1),X2))) = greatest_lower_bound(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_23]) ).
cnf(c_0_39,plain,
greatest_lower_bound(identity,multiply(X1,inverse(greatest_lower_bound(X2,X1)))) = identity,
inference(spm,[status(thm)],[c_0_36,c_0_26]) ).
cnf(c_0_40,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_22]),c_0_23]) ).
cnf(c_0_41,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
lub_absorbtion ).
cnf(c_0_42,plain,
greatest_lower_bound(X1,inverse(greatest_lower_bound(X2,inverse(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_26]) ).
cnf(c_0_43,plain,
least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_41,c_0_26]) ).
cnf(c_0_44,plain,
greatest_lower_bound(inverse(X1),inverse(greatest_lower_bound(X2,X1))) = inverse(X1),
inference(spm,[status(thm)],[c_0_42,c_0_23]) ).
cnf(c_0_45,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
symmetry_of_lub ).
cnf(c_0_46,plain,
greatest_lower_bound(X1,inverse(greatest_lower_bound(inverse(X1),X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_36]),c_0_40]),c_0_26]) ).
cnf(c_0_47,plain,
multiply(inverse(X1),greatest_lower_bound(X2,multiply(X1,X3))) = greatest_lower_bound(multiply(inverse(X1),X2),X3),
inference(spm,[status(thm)],[c_0_31,c_0_37]) ).
cnf(c_0_48,axiom,
inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
lat4_3 ).
cnf(c_0_49,plain,
least_upper_bound(inverse(X1),inverse(greatest_lower_bound(X2,X1))) = inverse(greatest_lower_bound(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).
cnf(c_0_50,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
glb_absorbtion ).
cnf(c_0_51,plain,
greatest_lower_bound(inverse(X1),inverse(greatest_lower_bound(X1,X2))) = inverse(X1),
inference(spm,[status(thm)],[c_0_46,c_0_23]) ).
cnf(c_0_52,plain,
greatest_lower_bound(inverse(X1),multiply(inverse(X1),X2)) = multiply(inverse(X1),greatest_lower_bound(X2,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_25]),c_0_26]) ).
cnf(c_0_53,plain,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(spm,[status(thm)],[c_0_48,c_0_23]) ).
cnf(c_0_54,plain,
least_upper_bound(inverse(X1),inverse(least_upper_bound(X1,X2))) = inverse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_45]) ).
cnf(c_0_55,plain,
multiply(X1,multiply(greatest_lower_bound(X2,inverse(X1)),X3)) = multiply(greatest_lower_bound(identity,multiply(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_29,c_0_35]) ).
cnf(c_0_56,plain,
greatest_lower_bound(X1,multiply(inverse(greatest_lower_bound(X2,identity)),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_23]),c_0_53]),c_0_23]) ).
cnf(c_0_57,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_50,c_0_45]) ).
cnf(c_0_58,plain,
least_upper_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) = X1,
inference(spm,[status(thm)],[c_0_54,c_0_23]) ).
cnf(c_0_59,plain,
multiply(greatest_lower_bound(identity,multiply(X1,X2)),X1) = multiply(X1,greatest_lower_bound(identity,multiply(X2,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_32]),c_0_23]),c_0_23]) ).
cnf(c_0_60,plain,
greatest_lower_bound(X1,multiply(inverse(greatest_lower_bound(identity,X2)),X1)) = X1,
inference(spm,[status(thm)],[c_0_56,c_0_26]) ).
cnf(c_0_61,plain,
greatest_lower_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) = inverse(least_upper_bound(inverse(X1),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_26]) ).
cnf(c_0_62,axiom,
inverse(identity) = identity,
lat4_1 ).
cnf(c_0_63,plain,
multiply(greatest_lower_bound(identity,X1),X1) = multiply(X1,greatest_lower_bound(identity,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_40]),c_0_30]) ).
cnf(c_0_64,plain,
greatest_lower_bound(X1,multiply(least_upper_bound(identity,X2),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]),c_0_23]) ).
cnf(c_0_65,plain,
multiply(inverse(X1),multiply(inverse(X2),X3)) = multiply(inverse(multiply(X2,X1)),X3),
inference(spm,[status(thm)],[c_0_29,c_0_48]) ).
cnf(c_0_66,plain,
multiply(inverse(greatest_lower_bound(identity,X1)),multiply(X1,greatest_lower_bound(identity,X1))) = X1,
inference(spm,[status(thm)],[c_0_37,c_0_63]) ).
cnf(c_0_67,plain,
least_upper_bound(X1,multiply(least_upper_bound(identity,X2),X1)) = multiply(least_upper_bound(identity,X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_64]),c_0_45]) ).
cnf(c_0_68,plain,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_48,c_0_23]) ).
cnf(c_0_69,plain,
multiply(inverse(greatest_lower_bound(identity,X1)),greatest_lower_bound(identity,inverse(X1))) = inverse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_35]),c_0_40]) ).
cnf(c_0_70,plain,
multiply(inverse(X1),greatest_lower_bound(X2,X1)) = greatest_lower_bound(identity,multiply(inverse(X1),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_22]),c_0_26]) ).
cnf(c_0_71,plain,
least_upper_bound(X1,least_upper_bound(X1,X2)) = least_upper_bound(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_50]),c_0_45]) ).
cnf(c_0_72,plain,
least_upper_bound(X1,multiply(X1,inverse(least_upper_bound(identity,X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_67]),c_0_68]) ).
cnf(c_0_73,plain,
least_upper_bound(X1,inverse(greatest_lower_bound(inverse(X1),X2))) = inverse(greatest_lower_bound(inverse(X1),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_46]),c_0_45]) ).
cnf(c_0_74,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_34]),c_0_23]) ).
cnf(c_0_75,plain,
multiply(inverse(greatest_lower_bound(X1,identity)),greatest_lower_bound(identity,inverse(X1))) = inverse(X1),
inference(spm,[status(thm)],[c_0_69,c_0_26]) ).
cnf(c_0_76,plain,
multiply(greatest_lower_bound(X1,inverse(X2)),X2) = greatest_lower_bound(identity,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_22]),c_0_26]) ).
cnf(c_0_77,plain,
greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X1,X2)),X1)) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_33]),c_0_22]) ).
cnf(c_0_78,axiom,
least_upper_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X1,X3)),
lat4_6 ).
cnf(c_0_79,plain,
least_upper_bound(X1,least_upper_bound(X2,X1)) = least_upper_bound(X2,X1),
inference(spm,[status(thm)],[c_0_71,c_0_45]) ).
cnf(c_0_80,plain,
least_upper_bound(X1,multiply(X1,greatest_lower_bound(identity,X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_62]),c_0_23]) ).
cnf(c_0_81,plain,
multiply(greatest_lower_bound(X1,inverse(multiply(X2,X3))),X2) = greatest_lower_bound(multiply(X1,X2),inverse(X3)),
inference(spm,[status(thm)],[c_0_24,c_0_74]) ).
cnf(c_0_82,plain,
multiply(X1,inverse(greatest_lower_bound(X1,identity))) = inverse(greatest_lower_bound(identity,inverse(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_23]) ).
cnf(c_0_83,plain,
multiply(greatest_lower_bound(X1,greatest_lower_bound(X2,inverse(X3))),X3) = greatest_lower_bound(identity,multiply(greatest_lower_bound(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_76,c_0_27]) ).
cnf(c_0_84,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X2,greatest_lower_bound(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_26]),c_0_27]) ).
cnf(c_0_85,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_48]),c_0_23]) ).
cnf(c_0_86,plain,
multiply(greatest_lower_bound(X1,identity),X1) = multiply(X1,greatest_lower_bound(X1,identity)),
inference(spm,[status(thm)],[c_0_63,c_0_26]) ).
cnf(c_0_87,plain,
greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X1))) = identity,
inference(spm,[status(thm)],[c_0_77,c_0_40]) ).
cnf(c_0_88,plain,
greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X2,X3)) = least_upper_bound(X2,greatest_lower_bound(least_upper_bound(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_89,plain,
greatest_lower_bound(X1,multiply(X1,X2)) = multiply(X1,greatest_lower_bound(X2,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_40]),c_0_26]) ).
cnf(c_0_90,plain,
greatest_lower_bound(X1,multiply(X1,greatest_lower_bound(identity,X2))) = multiply(X1,greatest_lower_bound(identity,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_80]),c_0_26]) ).
cnf(c_0_91,plain,
greatest_lower_bound(X1,greatest_lower_bound(identity,multiply(X2,X1))) = greatest_lower_bound(identity,multiply(greatest_lower_bound(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_81,c_0_82]),c_0_23]),c_0_83]),c_0_23]),c_0_84]),c_0_26]) ).
cnf(c_0_92,plain,
multiply(X1,inverse(multiply(X1,greatest_lower_bound(X1,identity)))) = inverse(greatest_lower_bound(X1,identity)),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_93,plain,
greatest_lower_bound(identity,inverse(greatest_lower_bound(X1,identity))) = identity,
inference(spm,[status(thm)],[c_0_87,c_0_26]) ).
cnf(c_0_94,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_lub1 ).
cnf(c_0_95,plain,
least_upper_bound(X1,greatest_lower_bound(least_upper_bound(X2,X1),X3)) = least_upper_bound(X1,greatest_lower_bound(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_45]),c_0_88]) ).
cnf(c_0_96,plain,
multiply(greatest_lower_bound(identity,X1),greatest_lower_bound(X1,identity)) = greatest_lower_bound(identity,multiply(X1,greatest_lower_bound(identity,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_63]),c_0_27]),c_0_90]) ).
cnf(c_0_97,plain,
greatest_lower_bound(identity,inverse(multiply(X1,greatest_lower_bound(X1,identity)))) = greatest_lower_bound(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93]),c_0_85]),c_0_26]) ).
cnf(c_0_98,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X1))),X1) = multiply(X1,inverse(greatest_lower_bound(identity,inverse(X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_63]),c_0_53]) ).
cnf(c_0_99,plain,
multiply(X1,least_upper_bound(X2,inverse(X1))) = least_upper_bound(identity,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_25]),c_0_45]) ).
cnf(c_0_100,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_lub2 ).
cnf(c_0_101,plain,
greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X2,X3)) = least_upper_bound(X2,greatest_lower_bound(X1,X3)),
inference(rw,[status(thm)],[c_0_88,c_0_95]) ).
cnf(c_0_102,plain,
multiply(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,X1)) = greatest_lower_bound(identity,multiply(X1,greatest_lower_bound(identity,X1))),
inference(spm,[status(thm)],[c_0_96,c_0_26]) ).
cnf(c_0_103,plain,
greatest_lower_bound(identity,multiply(X1,inverse(greatest_lower_bound(identity,inverse(X1))))) = greatest_lower_bound(identity,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_53]),c_0_26]),c_0_98]),c_0_23]) ).
cnf(c_0_104,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X1))),greatest_lower_bound(identity,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_69]),c_0_23]) ).
cnf(c_0_105,plain,
multiply(X1,multiply(least_upper_bound(X2,inverse(X1)),X3)) = multiply(least_upper_bound(identity,multiply(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_29,c_0_99]) ).
cnf(c_0_106,plain,
multiply(least_upper_bound(X1,X2),inverse(X2)) = least_upper_bound(identity,multiply(X1,inverse(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_25]),c_0_45]) ).
cnf(c_0_107,plain,
multiply(inverse(X1),least_upper_bound(X2,X1)) = least_upper_bound(identity,multiply(inverse(X1),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_22]),c_0_45]) ).
cnf(c_0_108,plain,
least_upper_bound(X1,greatest_lower_bound(X2,multiply(X1,greatest_lower_bound(identity,X3)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_80]),c_0_26]),c_0_57]) ).
cnf(c_0_109,plain,
greatest_lower_bound(identity,multiply(X1,greatest_lower_bound(identity,X1))) = greatest_lower_bound(identity,multiply(X1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_102]),c_0_29]),c_0_104]) ).
cnf(c_0_110,plain,
multiply(least_upper_bound(identity,multiply(X1,X2)),X1) = multiply(X1,least_upper_bound(identity,multiply(X2,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_23]),c_0_23]) ).
cnf(c_0_111,plain,
least_upper_bound(identity,multiply(inverse(least_upper_bound(X1,X2)),X1)) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_71]),c_0_22]) ).
cnf(c_0_112,plain,
least_upper_bound(X1,inverse(greatest_lower_bound(X2,inverse(X1)))) = inverse(greatest_lower_bound(X2,inverse(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_42]),c_0_45]) ).
cnf(c_0_113,plain,
multiply(X1,least_upper_bound(inverse(X1),X2)) = least_upper_bound(identity,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_94,c_0_25]) ).
cnf(c_0_114,plain,
least_upper_bound(X1,greatest_lower_bound(identity,multiply(X1,X1))) = X1,
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_115,plain,
multiply(X1,greatest_lower_bound(X2,inverse(multiply(X3,X1)))) = greatest_lower_bound(multiply(X1,X2),inverse(X3)),
inference(spm,[status(thm)],[c_0_31,c_0_85]) ).
cnf(c_0_116,plain,
multiply(least_upper_bound(identity,X1),X1) = multiply(X1,least_upper_bound(identity,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_40]),c_0_30]) ).
cnf(c_0_117,plain,
least_upper_bound(identity,inverse(least_upper_bound(identity,X1))) = identity,
inference(spm,[status(thm)],[c_0_111,c_0_40]) ).
cnf(c_0_118,plain,
least_upper_bound(X1,multiply(X1,greatest_lower_bound(X2,identity))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_112]),c_0_62]),c_0_23]) ).
cnf(c_0_119,plain,
multiply(X1,inverse(multiply(X1,greatest_lower_bound(identity,X1)))) = inverse(greatest_lower_bound(identity,X1)),
inference(spm,[status(thm)],[c_0_85,c_0_63]) ).
cnf(c_0_120,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(identity,X1))) = inverse(greatest_lower_bound(identity,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_87]),c_0_45]) ).
cnf(c_0_121,plain,
least_upper_bound(identity,greatest_lower_bound(X1,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_113,c_0_114]),c_0_25]),c_0_48]),c_0_115]),c_0_40]) ).
cnf(c_0_122,axiom,
greatest_lower_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X1,X3)),
lat4_7 ).
cnf(c_0_123,plain,
multiply(X1,inverse(multiply(X1,least_upper_bound(identity,X1)))) = inverse(least_upper_bound(identity,X1)),
inference(spm,[status(thm)],[c_0_85,c_0_116]) ).
cnf(c_0_124,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1))) = inverse(least_upper_bound(identity,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_117]),c_0_26]) ).
cnf(c_0_125,plain,
multiply(X1,greatest_lower_bound(inverse(X1),X2)) = greatest_lower_bound(identity,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_31,c_0_25]) ).
cnf(c_0_126,plain,
greatest_lower_bound(X1,multiply(X1,greatest_lower_bound(X2,identity))) = multiply(X1,greatest_lower_bound(X2,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_118]),c_0_26]) ).
cnf(c_0_127,plain,
multiply(inverse(greatest_lower_bound(identity,X1)),X1) = multiply(X1,inverse(greatest_lower_bound(identity,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_119]),c_0_120]),c_0_74]),c_0_120]) ).
cnf(c_0_128,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,X1)) = greatest_lower_bound(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_41]),c_0_27]) ).
cnf(c_0_129,plain,
greatest_lower_bound(inverse(X1),multiply(X2,inverse(X1))) = multiply(greatest_lower_bound(identity,X2),inverse(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_37]),c_0_29]),c_0_47]),c_0_40]) ).
cnf(c_0_130,plain,
least_upper_bound(identity,greatest_lower_bound(X1,greatest_lower_bound(inverse(X1),X2))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_121]),c_0_50]),c_0_27]) ).
cnf(c_0_131,plain,
least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X3,X1)) = greatest_lower_bound(X1,least_upper_bound(X2,X3)),
inference(spm,[status(thm)],[c_0_122,c_0_26]) ).
cnf(c_0_132,plain,
least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_43,c_0_27]) ).
cnf(c_0_133,axiom,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3),
associativity_of_lub ).
cnf(c_0_134,plain,
multiply(inverse(X1),least_upper_bound(X2,multiply(X1,X3))) = least_upper_bound(multiply(inverse(X1),X2),X3),
inference(spm,[status(thm)],[c_0_94,c_0_37]) ).
cnf(c_0_135,plain,
multiply(inverse(least_upper_bound(identity,X1)),X1) = multiply(X1,inverse(least_upper_bound(identity,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_123]),c_0_124]),c_0_74]),c_0_124]) ).
cnf(c_0_136,plain,
multiply(X1,multiply(greatest_lower_bound(inverse(X1),X2),X3)) = multiply(greatest_lower_bound(identity,multiply(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_29,c_0_125]) ).
cnf(c_0_137,plain,
multiply(greatest_lower_bound(X1,identity),inverse(greatest_lower_bound(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_126,c_0_127]),c_0_128]),c_0_128]),c_0_129]),c_0_128]),c_0_25]),c_0_128]) ).
cnf(c_0_138,plain,
least_upper_bound(identity,greatest_lower_bound(X1,inverse(least_upper_bound(X1,X2)))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_61]),c_0_23]) ).
cnf(c_0_139,plain,
greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X2,X1))) = inverse(least_upper_bound(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_57]),c_0_26]) ).
cnf(c_0_140,plain,
greatest_lower_bound(least_upper_bound(X1,X2),greatest_lower_bound(least_upper_bound(X1,X3),X4)) = greatest_lower_bound(least_upper_bound(X1,greatest_lower_bound(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_27,c_0_78]) ).
cnf(c_0_141,plain,
least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X3,X2)) = greatest_lower_bound(X2,least_upper_bound(X1,X3)),
inference(spm,[status(thm)],[c_0_131,c_0_26]) ).
cnf(c_0_142,plain,
least_upper_bound(X1,least_upper_bound(X2,greatest_lower_bound(X3,X1))) = least_upper_bound(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_50]),c_0_133]) ).
cnf(c_0_143,negated_conjecture,
a != multiply(positive_part(a),negative_part(a)),
prove_lat4 ).
cnf(c_0_144,axiom,
positive_part(X1) = least_upper_bound(X1,identity),
lat4_4 ).
cnf(c_0_145,axiom,
negative_part(X1) = greatest_lower_bound(X1,identity),
lat4_5 ).
cnf(c_0_146,plain,
least_upper_bound(inverse(X1),multiply(inverse(X1),X2)) = multiply(inverse(X1),least_upper_bound(X2,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_25]),c_0_45]) ).
cnf(c_0_147,plain,
multiply(inverse(least_upper_bound(X1,identity)),X1) = multiply(X1,inverse(least_upper_bound(X1,identity))),
inference(spm,[status(thm)],[c_0_135,c_0_45]) ).
cnf(c_0_148,plain,
least_upper_bound(inverse(X1),multiply(X2,inverse(X1))) = multiply(least_upper_bound(identity,X2),inverse(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_37]),c_0_29]),c_0_134]),c_0_40]) ).
cnf(c_0_149,plain,
least_upper_bound(X1,multiply(X2,X1)) = multiply(least_upper_bound(X2,identity),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_30]),c_0_45]) ).
cnf(c_0_150,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(X2),X3),
inference(spm,[status(thm)],[c_0_29,c_0_74]) ).
cnf(c_0_151,plain,
multiply(greatest_lower_bound(identity,X1),inverse(greatest_lower_bound(identity,inverse(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_40]),c_0_40]) ).
cnf(c_0_152,plain,
least_upper_bound(identity,inverse(least_upper_bound(X1,inverse(X1)))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_45]) ).
cnf(c_0_153,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X3)) = greatest_lower_bound(least_upper_bound(X3,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_140]),c_0_141]),c_0_133]),c_0_142]),c_0_79]) ).
cnf(c_0_154,negated_conjecture,
a != multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_143,c_0_144]),c_0_145]) ).
cnf(c_0_155,plain,
multiply(least_upper_bound(identity,X1),inverse(least_upper_bound(X1,identity))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_148]),c_0_22]) ).
cnf(c_0_156,plain,
multiply(X1,inverse(least_upper_bound(X1,multiply(X2,X1)))) = inverse(least_upper_bound(X2,identity)),
inference(spm,[status(thm)],[c_0_85,c_0_149]) ).
cnf(c_0_157,plain,
multiply(inverse(X1),multiply(greatest_lower_bound(identity,X1),X2)) = multiply(greatest_lower_bound(identity,inverse(X1)),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_151]),c_0_23]) ).
cnf(c_0_158,plain,
greatest_lower_bound(identity,least_upper_bound(X1,inverse(X1))) = identity,
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_139,c_0_152]),c_0_23]),c_0_62]),c_0_62]),c_0_153]),c_0_45]) ).
cnf(c_0_159,negated_conjecture,
multiply(least_upper_bound(identity,a),greatest_lower_bound(identity,a)) != a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_154,c_0_26]),c_0_45]) ).
cnf(c_0_160,plain,
multiply(least_upper_bound(identity,X1),greatest_lower_bound(identity,X1)) = multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_151]),c_0_104]) ).
cnf(c_0_161,plain,
multiply(least_upper_bound(identity,X1),inverse(least_upper_bound(identity,inverse(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_155]),c_0_40]),c_0_40]),c_0_45]) ).
cnf(c_0_162,plain,
inverse(least_upper_bound(identity,inverse(X1))) = greatest_lower_bound(identity,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_157]),c_0_100]),c_0_122]),c_0_158]),c_0_30]),c_0_29]),c_0_25]),c_0_40]),c_0_45]) ).
cnf(c_0_163,negated_conjecture,
multiply(greatest_lower_bound(identity,a),least_upper_bound(identity,a)) != a,
inference(rw,[status(thm)],[c_0_159,c_0_160]) ).
cnf(c_0_164,plain,
multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_161,c_0_162]),c_0_160]) ).
cnf(c_0_165,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_163,c_0_164])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP167-2 : TPTP v9.2.1. Bugfixed v1.2.1.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n007.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 18:25:38 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 20.83/13.19 % Version : CSE_E---1.7
% 20.83/13.19 % Problem : theBenchmark.p
% 20.83/13.19 % SZS status Unsatisfiable for theBenchmark.p
% 20.83/13.19 % SZS output start CNFRefutation
% See solution above
% 20.90/13.28 % Total time : 9.384s
%------------------------------------------------------------------------------