%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP181-1 : 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 : n026.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 04:24:42 PM UTC 2026
% Result : Unsatisfiable 31.32s 18.94s
% Output : CNFRefutation 31.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 16
% Syntax : Number of clauses : 119 ( 119 unt; 0 nHn; 15 RR)
% Number of literals : 119 ( 118 equ; 2 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; 4 con; 0-2 aty)
% Number of variables : 217 ( 10 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_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(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(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(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(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(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_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(p12_2,hypothesis,
least_upper_bound(a,c) = least_upper_bound(b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12_2) ).
cnf(p12_1,hypothesis,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12_1) ).
cnf(prove_p12,negated_conjecture,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p12) ).
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,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_17,c_0_23]) ).
cnf(c_0_25,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_glb1 ).
cnf(c_0_26,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
symmetry_of_glb ).
cnf(c_0_27,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
inference(spm,[status(thm)],[c_0_16,c_0_24]) ).
cnf(c_0_28,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_lub2 ).
cnf(c_0_29,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
symmetry_of_lub ).
cnf(c_0_30,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_25,c_0_22]),c_0_26]) ).
cnf(c_0_31,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_19,c_0_23]) ).
cnf(c_0_32,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_27]),c_0_22]) ).
cnf(c_0_33,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_28,c_0_18]),c_0_29]) ).
cnf(c_0_34,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_30,c_0_17]),c_0_26]) ).
cnf(c_0_35,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
glb_absorbtion ).
cnf(c_0_36,plain,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,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_33,c_0_24]),c_0_29]) ).
cnf(c_0_38,plain,
multiply(inverse(X1),greatest_lower_bound(identity,X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(spm,[status(thm)],[c_0_34,c_0_26]) ).
cnf(c_0_39,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_35,c_0_29]) ).
cnf(c_0_40,plain,
multiply(X1,inverse(least_upper_bound(X1,identity))) = inverse(least_upper_bound(identity,inverse(X1))),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(X1,identity))) = inverse(least_upper_bound(X1,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_22]) ).
cnf(c_0_42,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_32]),c_0_23]) ).
cnf(c_0_43,plain,
multiply(inverse(X1),greatest_lower_bound(multiply(X1,X2),X3)) = greatest_lower_bound(X2,multiply(inverse(X1),X3)),
inference(spm,[status(thm)],[c_0_25,c_0_19]) ).
cnf(c_0_44,plain,
greatest_lower_bound(X1,inverse(least_upper_bound(identity,inverse(X1)))) = inverse(least_upper_bound(identity,inverse(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_40]),c_0_26]),c_0_41]),c_0_40]) ).
cnf(c_0_45,plain,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_32]) ).
cnf(c_0_46,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_28,c_0_42]) ).
cnf(c_0_47,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
lub_absorbtion ).
cnf(c_0_48,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_glb2 ).
cnf(c_0_49,plain,
greatest_lower_bound(X1,inverse(least_upper_bound(X2,inverse(X1)))) = inverse(least_upper_bound(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_43,c_0_44]),c_0_45]),c_0_46]),c_0_18]),c_0_45]),c_0_46]),c_0_18]) ).
cnf(c_0_50,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_51,plain,
least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_47,c_0_26]) ).
cnf(c_0_52,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_48,c_0_18]),c_0_26]) ).
cnf(c_0_53,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_54,plain,
greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X2,X1))) = inverse(least_upper_bound(X2,X1)),
inference(spm,[status(thm)],[c_0_49,c_0_23]) ).
cnf(c_0_55,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_56,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_lub1 ).
cnf(c_0_57,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_50,c_0_51]) ).
cnf(c_0_58,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_52,c_0_24]),c_0_26]) ).
cnf(c_0_59,plain,
greatest_lower_bound(multiply(X1,X2),greatest_lower_bound(multiply(X3,X2),X4)) = greatest_lower_bound(multiply(greatest_lower_bound(X1,X3),X2),X4),
inference(spm,[status(thm)],[c_0_53,c_0_48]) ).
cnf(c_0_60,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_48,c_0_42]) ).
cnf(c_0_61,plain,
multiply(X1,greatest_lower_bound(inverse(X1),X2)) = greatest_lower_bound(identity,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_62,plain,
greatest_lower_bound(inverse(X1),inverse(greatest_lower_bound(X1,X2))) = inverse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_47]),c_0_26]) ).
cnf(c_0_63,plain,
multiply(inverse(inverse(identity)),X1) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_55]) ).
cnf(c_0_64,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_56,c_0_22]),c_0_29]) ).
cnf(c_0_65,plain,
greatest_lower_bound(X1,greatest_lower_bound(least_upper_bound(X1,X2),X3)) = greatest_lower_bound(X1,X3),
inference(spm,[status(thm)],[c_0_53,c_0_35]) ).
cnf(c_0_66,plain,
greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(greatest_lower_bound(X3,X1),X2)) = least_upper_bound(greatest_lower_bound(X3,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_57]),c_0_26]) ).
cnf(c_0_67,plain,
multiply(X1,inverse(greatest_lower_bound(X1,identity))) = inverse(greatest_lower_bound(identity,inverse(X1))),
inference(spm,[status(thm)],[c_0_36,c_0_58]) ).
cnf(c_0_68,plain,
greatest_lower_bound(multiply(greatest_lower_bound(X1,X2),inverse(X1)),X3) = greatest_lower_bound(identity,greatest_lower_bound(multiply(X2,inverse(X1)),X3)),
inference(spm,[status(thm)],[c_0_59,c_0_24]) ).
cnf(c_0_69,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,X1)) = greatest_lower_bound(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_51]),c_0_26]) ).
cnf(c_0_70,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_60,c_0_36]),c_0_23]) ).
cnf(c_0_71,plain,
greatest_lower_bound(identity,multiply(X1,inverse(greatest_lower_bound(X1,X2)))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_24]) ).
cnf(c_0_72,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_17,c_0_63]) ).
cnf(c_0_73,plain,
multiply(least_upper_bound(X1,identity),X1) = multiply(X1,least_upper_bound(X1,identity)),
inference(spm,[status(thm)],[c_0_64,c_0_33]) ).
cnf(c_0_74,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_56,c_0_19]) ).
cnf(c_0_75,plain,
greatest_lower_bound(X1,multiply(least_upper_bound(X1,X2),greatest_lower_bound(X3,identity))) = greatest_lower_bound(X1,multiply(least_upper_bound(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_65,c_0_30]) ).
cnf(c_0_76,plain,
multiply(least_upper_bound(identity,inverse(X1)),greatest_lower_bound(X1,identity)) = least_upper_bound(greatest_lower_bound(X1,identity),greatest_lower_bound(identity,inverse(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_29]) ).
cnf(c_0_77,plain,
greatest_lower_bound(X1,least_upper_bound(greatest_lower_bound(X2,X1),greatest_lower_bound(X1,X3))) = least_upper_bound(greatest_lower_bound(X2,X1),greatest_lower_bound(X1,X3)),
inference(spm,[status(thm)],[c_0_66,c_0_47]) ).
cnf(c_0_78,plain,
multiply(least_upper_bound(X1,inverse(X2)),X2) = least_upper_bound(identity,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_17]),c_0_29]) ).
cnf(c_0_79,plain,
multiply(least_upper_bound(inverse(multiply(X1,X2)),X3),X1) = least_upper_bound(inverse(X2),multiply(X3,X1)),
inference(spm,[status(thm)],[c_0_28,c_0_42]) ).
cnf(c_0_80,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69]),c_0_16]),c_0_45]),c_0_70]),c_0_18]),c_0_36]),c_0_71]),c_0_72]) ).
cnf(c_0_81,plain,
multiply(least_upper_bound(identity,X1),X1) = multiply(X1,least_upper_bound(identity,X1)),
inference(spm,[status(thm)],[c_0_73,c_0_29]) ).
cnf(c_0_82,plain,
least_upper_bound(X1,least_upper_bound(X2,X1)) = least_upper_bound(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_39]),c_0_29]) ).
cnf(c_0_83,plain,
multiply(X1,least_upper_bound(X2,greatest_lower_bound(identity,inverse(X1)))) = least_upper_bound(greatest_lower_bound(identity,X1),multiply(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_38]),c_0_23]),c_0_23]),c_0_29]) ).
cnf(c_0_84,plain,
least_upper_bound(greatest_lower_bound(X1,identity),greatest_lower_bound(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_75,c_0_76]),c_0_77]),c_0_78]),c_0_18]),c_0_35]) ).
cnf(c_0_85,plain,
least_upper_bound(greatest_lower_bound(X1,X2),multiply(X3,greatest_lower_bound(X2,X1))) = multiply(least_upper_bound(identity,X3),greatest_lower_bound(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_72]),c_0_23]) ).
cnf(c_0_86,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_30,c_0_81]),c_0_52]) ).
cnf(c_0_87,plain,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(spm,[status(thm)],[c_0_42,c_0_31]) ).
cnf(c_0_88,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_64,c_0_17]),c_0_29]) ).
cnf(c_0_89,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_56,c_0_24]),c_0_29]) ).
cnf(c_0_90,plain,
least_upper_bound(X1,least_upper_bound(X2,least_upper_bound(X1,X3))) = least_upper_bound(X2,least_upper_bound(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_82]),c_0_50]),c_0_50]) ).
cnf(c_0_91,plain,
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(spm,[status(thm)],[c_0_83,c_0_84]),c_0_22]),c_0_85]),c_0_86]) ).
cnf(c_0_92,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_56,c_0_32]) ).
cnf(c_0_93,plain,
multiply(inverse(least_upper_bound(X1,identity)),X1) = inverse(least_upper_bound(identity,inverse(X1))),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_94,plain,
multiply(X1,least_upper_bound(X2,least_upper_bound(X3,inverse(X1)))) = least_upper_bound(identity,multiply(X1,least_upper_bound(X2,X3))),
inference(spm,[status(thm)],[c_0_89,c_0_50]) ).
cnf(c_0_95,plain,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X2,least_upper_bound(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_35]),c_0_50]),c_0_50]),c_0_90]) ).
cnf(c_0_96,plain,
inverse(least_upper_bound(identity,X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_91]),c_0_34]) ).
cnf(c_0_97,plain,
least_upper_bound(X1,least_upper_bound(identity,multiply(X1,X2))) = least_upper_bound(identity,multiply(X1,least_upper_bound(X2,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_92,c_0_93]),c_0_23]),c_0_94]),c_0_23]),c_0_95]),c_0_29]) ).
cnf(c_0_98,plain,
greatest_lower_bound(X1,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_47]),c_0_26]) ).
cnf(c_0_99,plain,
least_upper_bound(multiply(X1,X2),least_upper_bound(multiply(X1,X3),X4)) = least_upper_bound(multiply(X1,least_upper_bound(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_50,c_0_56]) ).
cnf(c_0_100,plain,
multiply(greatest_lower_bound(inverse(X1),X2),X1) = greatest_lower_bound(identity,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_48,c_0_17]) ).
cnf(c_0_101,plain,
greatest_lower_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) = inverse(least_upper_bound(inverse(X1),X2)),
inference(spm,[status(thm)],[c_0_49,c_0_29]) ).
cnf(c_0_102,plain,
inverse(least_upper_bound(X1,identity)) = greatest_lower_bound(identity,inverse(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_96,c_0_97]),c_0_18]),c_0_82]),c_0_18]),c_0_96]),c_0_98]) ).
cnf(c_0_103,plain,
least_upper_bound(multiply(inverse(X1),least_upper_bound(X1,X2)),X3) = least_upper_bound(identity,least_upper_bound(multiply(inverse(X1),X2),X3)),
inference(spm,[status(thm)],[c_0_99,c_0_17]) ).
cnf(c_0_104,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_51,c_0_35]),c_0_29]) ).
cnf(c_0_105,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X1,X2)),X1)) = multiply(inverse(least_upper_bound(X1,X2)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_23]),c_0_23]) ).
cnf(c_0_106,hypothesis,
least_upper_bound(a,c) = least_upper_bound(b,c),
p12_2 ).
cnf(c_0_107,plain,
multiply(inverse(least_upper_bound(X1,X2)),X1) = greatest_lower_bound(identity,multiply(inverse(X2),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_102,c_0_103]),c_0_29]),c_0_104]),c_0_96]),c_0_87]),c_0_87]),c_0_105]) ).
cnf(c_0_108,hypothesis,
least_upper_bound(c,a) = least_upper_bound(c,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_106,c_0_29]),c_0_29]) ).
cnf(c_0_109,hypothesis,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
p12_1 ).
cnf(c_0_110,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_25,c_0_19]) ).
cnf(c_0_111,hypothesis,
greatest_lower_bound(identity,multiply(inverse(a),c)) = greatest_lower_bound(identity,multiply(inverse(b),c)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_107]) ).
cnf(c_0_112,hypothesis,
greatest_lower_bound(c,a) = greatest_lower_bound(c,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_26]),c_0_26]) ).
cnf(c_0_113,hypothesis,
multiply(a,greatest_lower_bound(identity,multiply(inverse(b),c))) = greatest_lower_bound(c,b),
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_23]),c_0_23]),c_0_22]),c_0_26]),c_0_112]) ).
cnf(c_0_114,hypothesis,
greatest_lower_bound(identity,multiply(inverse(b),c)) = multiply(inverse(a),greatest_lower_bound(c,b)),
inference(spm,[status(thm)],[c_0_19,c_0_113]) ).
cnf(c_0_115,hypothesis,
multiply(b,multiply(inverse(a),greatest_lower_bound(c,b))) = greatest_lower_bound(c,b),
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_114]),c_0_23]),c_0_23]),c_0_22]),c_0_26]) ).
cnf(c_0_116,hypothesis,
inverse(a) = inverse(b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_115]),c_0_16]),c_0_24]),c_0_22]) ).
cnf(c_0_117,negated_conjecture,
a != b,
prove_p12 ).
cnf(c_0_118,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_116]),c_0_23]),c_0_117]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP181-1 : 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 : n026.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 18:27:23 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 31.32/18.94 % Version : CSE_E---1.7
% 31.32/18.94 % Problem : theBenchmark.p
% 31.32/18.94 % SZS status Unsatisfiable for theBenchmark.p
% 31.32/18.94 % SZS output start CNFRefutation
% See solution above
% 31.44/19.08 % Total time : 13.395s
%------------------------------------------------------------------------------