%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP184-1 : 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 : 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 04:24:44 PM UTC 2026
% Result : Unsatisfiable 25.90s 15.93s
% Output : CNFRefutation 26.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 16
% Syntax : Number of clauses : 129 ( 129 unt; 0 nHn; 7 RR)
% Number of literals : 129 ( 128 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 234 ( 19 sgn)
% Comments :
%------------------------------------------------------------------------------
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(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(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(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(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(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(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(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(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(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(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(idempotence_of_gld,axiom,
greatest_lower_bound(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',idempotence_of_gld) ).
cnf(prove_p21,negated_conjecture,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p21) ).
cnf(idempotence_of_lub,axiom,
least_upper_bound(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',idempotence_of_lub) ).
cnf(c_0_16,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_17,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_18,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_19,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_20,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_17]) ).
cnf(c_0_21,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_19,c_0_19]) ).
cnf(c_0_22,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_22]) ).
cnf(c_0_24,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_lub1 ).
cnf(c_0_25,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
symmetry_of_lub ).
cnf(c_0_26,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_lub2 ).
cnf(c_0_27,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_17,c_0_23]) ).
cnf(c_0_28,plain,
least_upper_bound(X1,multiply(X1,X2)) = multiply(X1,least_upper_bound(X2,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_22]),c_0_25]) ).
cnf(c_0_29,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_glb1 ).
cnf(c_0_30,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
symmetry_of_glb ).
cnf(c_0_31,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
glb_absorbtion ).
cnf(c_0_32,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_26,c_0_18]),c_0_25]) ).
cnf(c_0_33,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
inference(spm,[status(thm)],[c_0_16,c_0_27]) ).
cnf(c_0_34,plain,
multiply(inverse(X1),least_upper_bound(X1,identity)) = least_upper_bound(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_17]),c_0_25]) ).
cnf(c_0_35,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
lub_absorbtion ).
cnf(c_0_36,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_29,c_0_22]),c_0_30]) ).
cnf(c_0_37,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_38,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_31,c_0_25]) ).
cnf(c_0_39,plain,
multiply(least_upper_bound(X1,identity),X1) = multiply(X1,least_upper_bound(X1,identity)),
inference(spm,[status(thm)],[c_0_28,c_0_32]) ).
cnf(c_0_40,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_glb2 ).
cnf(c_0_41,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_33]),c_0_22]) ).
cnf(c_0_42,plain,
multiply(inverse(X1),least_upper_bound(identity,X1)) = least_upper_bound(identity,inverse(X1)),
inference(spm,[status(thm)],[c_0_34,c_0_25]) ).
cnf(c_0_43,plain,
least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_35,c_0_30]) ).
cnf(c_0_44,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_45,plain,
multiply(inverse(X1),greatest_lower_bound(X1,identity)) = greatest_lower_bound(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_17]),c_0_30]) ).
cnf(c_0_46,axiom,
greatest_lower_bound(X1,X1) = X1,
idempotence_of_gld ).
cnf(c_0_47,plain,
greatest_lower_bound(X1,greatest_lower_bound(least_upper_bound(X2,X1),X3)) = greatest_lower_bound(X1,X3),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_48,plain,
multiply(least_upper_bound(identity,X1),X1) = multiply(X1,least_upper_bound(identity,X1)),
inference(spm,[status(thm)],[c_0_39,c_0_25]) ).
cnf(c_0_49,plain,
greatest_lower_bound(X1,multiply(X2,X1)) = multiply(greatest_lower_bound(X2,identity),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_18]),c_0_30]) ).
cnf(c_0_50,plain,
multiply(least_upper_bound(identity,X1),inverse(least_upper_bound(identity,inverse(X1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_23]) ).
cnf(c_0_51,plain,
least_upper_bound(X1,least_upper_bound(X2,X1)) = least_upper_bound(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_31]),c_0_44]) ).
cnf(c_0_52,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_41]),c_0_23]) ).
cnf(c_0_53,plain,
multiply(inverse(X1),greatest_lower_bound(identity,X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(spm,[status(thm)],[c_0_45,c_0_30]) ).
cnf(c_0_54,plain,
greatest_lower_bound(X1,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,X2),
inference(spm,[status(thm)],[c_0_37,c_0_46]) ).
cnf(c_0_55,plain,
greatest_lower_bound(X1,multiply(least_upper_bound(X2,X1),greatest_lower_bound(X3,identity))) = greatest_lower_bound(X1,multiply(least_upper_bound(X2,X1),X3)),
inference(spm,[status(thm)],[c_0_47,c_0_36]) ).
cnf(c_0_56,plain,
multiply(least_upper_bound(identity,X1),greatest_lower_bound(X1,identity)) = multiply(greatest_lower_bound(X1,identity),least_upper_bound(identity,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_48]),c_0_49]) ).
cnf(c_0_57,plain,
multiply(inverse(X1),least_upper_bound(multiply(X1,X2),X3)) = least_upper_bound(X2,multiply(inverse(X1),X3)),
inference(spm,[status(thm)],[c_0_24,c_0_19]) ).
cnf(c_0_58,plain,
least_upper_bound(X1,inverse(least_upper_bound(identity,inverse(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_50]),c_0_44]),c_0_51]),c_0_50]),c_0_25]) ).
cnf(c_0_59,plain,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_41]) ).
cnf(c_0_60,plain,
multiply(least_upper_bound(X1,inverse(multiply(X2,X3))),X2) = least_upper_bound(multiply(X1,X2),inverse(X3)),
inference(spm,[status(thm)],[c_0_26,c_0_52]) ).
cnf(c_0_61,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_19,c_0_23]) ).
cnf(c_0_62,plain,
greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X1))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_17]) ).
cnf(c_0_63,plain,
greatest_lower_bound(X1,multiply(greatest_lower_bound(X1,identity),least_upper_bound(identity,X1))) = 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_55,c_0_56]),c_0_48]),c_0_36]),c_0_30]),c_0_31]),c_0_22]) ).
cnf(c_0_64,plain,
least_upper_bound(X1,inverse(least_upper_bound(X2,inverse(X1)))) = 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_19]),c_0_59]),c_0_60]),c_0_18]) ).
cnf(c_0_65,plain,
multiply(greatest_lower_bound(inverse(multiply(X1,X2)),X3),X1) = greatest_lower_bound(inverse(X2),multiply(X3,X1)),
inference(spm,[status(thm)],[c_0_40,c_0_52]) ).
cnf(c_0_66,plain,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_61,c_0_41]) ).
cnf(c_0_67,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_62]),c_0_25]) ).
cnf(c_0_68,plain,
greatest_lower_bound(identity,multiply(inverse(X1),X2)) = multiply(inverse(X1),greatest_lower_bound(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_17]),c_0_30]) ).
cnf(c_0_69,plain,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(spm,[status(thm)],[c_0_52,c_0_61]) ).
cnf(c_0_70,plain,
greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,X1))) = X1,
inference(spm,[status(thm)],[c_0_63,c_0_30]) ).
cnf(c_0_71,plain,
least_upper_bound(X1,least_upper_bound(greatest_lower_bound(X1,X2),X3)) = least_upper_bound(X1,X3),
inference(spm,[status(thm)],[c_0_44,c_0_35]) ).
cnf(c_0_72,plain,
least_upper_bound(inverse(X1),inverse(least_upper_bound(X2,X1))) = inverse(X1),
inference(spm,[status(thm)],[c_0_64,c_0_23]) ).
cnf(c_0_73,plain,
multiply(greatest_lower_bound(multiply(X1,inverse(X2)),X3),X2) = greatest_lower_bound(X1,multiply(X3,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_23]) ).
cnf(c_0_74,plain,
least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X1,X2)),X2)) = multiply(inverse(greatest_lower_bound(X1,X2)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69]),c_0_69]) ).
cnf(c_0_75,plain,
greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X1),least_upper_bound(X1,identity))) = X1,
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_28]),c_0_18]),c_0_18]),c_0_18]),c_0_18]) ).
cnf(c_0_76,plain,
multiply(inverse(X1),multiply(greatest_lower_bound(identity,X1),X2)) = multiply(greatest_lower_bound(identity,inverse(X1)),X2),
inference(spm,[status(thm)],[c_0_16,c_0_53]) ).
cnf(c_0_77,plain,
least_upper_bound(X1,multiply(greatest_lower_bound(X1,X2),least_upper_bound(X3,identity))) = least_upper_bound(X1,multiply(greatest_lower_bound(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_71,c_0_28]) ).
cnf(c_0_78,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_40,c_0_17]),c_0_30]) ).
cnf(c_0_79,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_80,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_38,c_0_72]),c_0_30]) ).
cnf(c_0_81,plain,
multiply(X1,inverse(greatest_lower_bound(X2,multiply(X3,X1)))) = inverse(greatest_lower_bound(multiply(X2,inverse(X1)),X3)),
inference(spm,[status(thm)],[c_0_41,c_0_73]) ).
cnf(c_0_82,plain,
multiply(greatest_lower_bound(identity,inverse(X1)),least_upper_bound(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(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]),c_0_77]),c_0_78]),c_0_18]),c_0_35]),c_0_76]) ).
cnf(c_0_83,plain,
multiply(inverse(inverse(identity)),X1) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_79]) ).
cnf(c_0_84,plain,
greatest_lower_bound(inverse(X1),inverse(greatest_lower_bound(X1,X2))) = inverse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_35]),c_0_30]) ).
cnf(c_0_85,plain,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X2,least_upper_bound(X3,X1)),
inference(spm,[status(thm)],[c_0_44,c_0_25]) ).
cnf(c_0_86,plain,
multiply(X1,multiply(inverse(greatest_lower_bound(X1,X2)),X2)) = inverse(greatest_lower_bound(inverse(X1),inverse(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_68]),c_0_69]),c_0_18]) ).
cnf(c_0_87,plain,
inverse(greatest_lower_bound(identity,inverse(X1))) = least_upper_bound(X1,identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_82]),c_0_22]) ).
cnf(c_0_88,plain,
multiply(least_upper_bound(X1,identity),inverse(X1)) = least_upper_bound(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_27]),c_0_25]) ).
cnf(c_0_89,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_17,c_0_83]) ).
cnf(c_0_90,plain,
greatest_lower_bound(X1,inverse(greatest_lower_bound(inverse(X1),X2))) = X1,
inference(spm,[status(thm)],[c_0_84,c_0_23]) ).
cnf(c_0_91,plain,
least_upper_bound(X1,least_upper_bound(greatest_lower_bound(X2,X1),X3)) = least_upper_bound(X1,X3),
inference(spm,[status(thm)],[c_0_44,c_0_43]) ).
cnf(c_0_92,plain,
multiply(greatest_lower_bound(X1,identity),inverse(X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_27]),c_0_30]) ).
cnf(c_0_93,plain,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X3,least_upper_bound(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_51]),c_0_44]),c_0_51]) ).
cnf(c_0_94,plain,
least_upper_bound(identity,inverse(X1)) = inverse(greatest_lower_bound(identity,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_88]),c_0_18]),c_0_89]),c_0_23]) ).
cnf(c_0_95,plain,
multiply(X1,least_upper_bound(X2,inverse(multiply(X3,X1)))) = least_upper_bound(multiply(X1,X2),inverse(X3)),
inference(spm,[status(thm)],[c_0_24,c_0_41]) ).
cnf(c_0_96,plain,
greatest_lower_bound(X1,inverse(greatest_lower_bound(X2,inverse(X1)))) = X1,
inference(spm,[status(thm)],[c_0_90,c_0_30]) ).
cnf(c_0_97,plain,
least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_43,c_0_37]) ).
cnf(c_0_98,plain,
least_upper_bound(X1,multiply(greatest_lower_bound(X2,X1),least_upper_bound(X3,identity))) = least_upper_bound(X1,multiply(greatest_lower_bound(X2,X1),X3)),
inference(spm,[status(thm)],[c_0_91,c_0_28]) ).
cnf(c_0_99,plain,
multiply(greatest_lower_bound(identity,X1),inverse(X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(spm,[status(thm)],[c_0_92,c_0_30]) ).
cnf(c_0_100,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_38,c_0_35]),c_0_37]) ).
cnf(c_0_101,plain,
greatest_lower_bound(identity,inverse(greatest_lower_bound(X1,identity))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_36]),c_0_18]) ).
cnf(c_0_102,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_40,c_0_52]) ).
cnf(c_0_103,negated_conjecture,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
prove_p21 ).
cnf(c_0_104,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_24,c_0_27]),c_0_25]) ).
cnf(c_0_105,plain,
least_upper_bound(identity,least_upper_bound(X1,inverse(X2))) = least_upper_bound(X1,inverse(greatest_lower_bound(identity,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_85]) ).
cnf(c_0_106,plain,
inverse(greatest_lower_bound(inverse(X1),X2)) = least_upper_bound(X1,inverse(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_94]),c_0_81]),c_0_18]),c_0_22]) ).
cnf(c_0_107,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_96]),c_0_25]) ).
cnf(c_0_108,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_97,c_0_31]),c_0_44]) ).
cnf(c_0_109,plain,
least_upper_bound(inverse(X1),greatest_lower_bound(identity,X1)) = inverse(greatest_lower_bound(identity,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_82]),c_0_25]),c_0_78]),c_0_18]),c_0_94]) ).
cnf(c_0_110,axiom,
least_upper_bound(X1,X1) = X1,
idempotence_of_lub ).
cnf(c_0_111,plain,
multiply(greatest_lower_bound(identity,X1),inverse(greatest_lower_bound(X1,identity))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_101]) ).
cnf(c_0_112,plain,
greatest_lower_bound(identity,multiply(X1,inverse(X2))) = multiply(greatest_lower_bound(X1,X2),inverse(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_27]),c_0_30]) ).
cnf(c_0_113,plain,
multiply(greatest_lower_bound(X1,multiply(X2,inverse(X3))),X3) = greatest_lower_bound(multiply(X1,X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_66]),c_0_23]) ).
cnf(c_0_114,negated_conjecture,
multiply(inverse(greatest_lower_bound(identity,a)),least_upper_bound(a,identity)) != multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(identity,a))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_30]),c_0_30]) ).
cnf(c_0_115,plain,
least_upper_bound(X1,least_upper_bound(inverse(greatest_lower_bound(identity,X2)),multiply(X2,X1))) = multiply(least_upper_bound(X2,identity),least_upper_bound(X1,inverse(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_104]),c_0_44]),c_0_85]),c_0_105]),c_0_25]) ).
cnf(c_0_116,plain,
multiply(inverse(X1),least_upper_bound(identity,X1)) = inverse(greatest_lower_bound(identity,X1)),
inference(rw,[status(thm)],[c_0_42,c_0_94]) ).
cnf(c_0_117,plain,
inverse(greatest_lower_bound(X1,inverse(X2))) = least_upper_bound(X2,inverse(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_100]),c_0_106]),c_0_107]) ).
cnf(c_0_118,plain,
least_upper_bound(X1,inverse(greatest_lower_bound(identity,X1))) = least_upper_bound(X1,inverse(X1)),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_119,plain,
least_upper_bound(X1,least_upper_bound(X1,X2)) = least_upper_bound(X1,X2),
inference(spm,[status(thm)],[c_0_44,c_0_110]) ).
cnf(c_0_120,plain,
greatest_lower_bound(least_upper_bound(X1,inverse(X2)),least_upper_bound(identity,multiply(X2,X1))) = multiply(greatest_lower_bound(X2,identity),least_upper_bound(X1,inverse(X2))),
inference(spm,[status(thm)],[c_0_49,c_0_104]) ).
cnf(c_0_121,plain,
multiply(greatest_lower_bound(X1,X2),inverse(greatest_lower_bound(X2,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_111,c_0_112]),c_0_30]),c_0_16]),c_0_59]),c_0_113]),c_0_18]) ).
cnf(c_0_122,negated_conjecture,
multiply(inverse(greatest_lower_bound(identity,a)),least_upper_bound(identity,a)) != multiply(least_upper_bound(identity,a),inverse(greatest_lower_bound(identity,a))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_25]),c_0_25]) ).
cnf(c_0_123,plain,
multiply(inverse(greatest_lower_bound(identity,X1)),least_upper_bound(identity,X1)) = least_upper_bound(X1,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(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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_117]),c_0_89]),c_0_44]),c_0_94]),c_0_54]),c_0_118]),c_0_44]),c_0_119]),c_0_105]),c_0_118]),c_0_25]),c_0_94]),c_0_23]),c_0_44]),c_0_110]) ).
cnf(c_0_124,plain,
multiply(X1,multiply(inverse(greatest_lower_bound(X1,X2)),X2)) = least_upper_bound(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_106]),c_0_23]) ).
cnf(c_0_125,plain,
greatest_lower_bound(least_upper_bound(identity,X1),inverse(greatest_lower_bound(identity,X1))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_94]),c_0_22]),c_0_121]),c_0_30]) ).
cnf(c_0_126,negated_conjecture,
multiply(least_upper_bound(identity,a),inverse(greatest_lower_bound(identity,a))) != least_upper_bound(a,inverse(a)),
inference(rw,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_127,plain,
multiply(least_upper_bound(identity,X1),inverse(greatest_lower_bound(identity,X1))) = least_upper_bound(X1,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_124,c_0_125]),c_0_89]),c_0_18]),c_0_44]),c_0_118]),c_0_105]),c_0_118]) ).
cnf(c_0_128,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_126,c_0_127])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP184-1 : TPTP v9.2.1. Bugfixed v1.2.1.
% 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
% 0.16/0.33 % Computer : n023.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 18:28:23 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 25.90/15.93 % Version : CSE_E---1.7
% 25.90/15.93 % Problem : theBenchmark.p
% 25.90/15.93 % SZS status Unsatisfiable for theBenchmark.p
% 25.90/15.93 % SZS output start CNFRefutation
% See solution above
% 26.02/16.04 % Total time : 11.392s
%------------------------------------------------------------------------------