%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP184-2 : TPTP v9.2.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n029.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 34.89s 21.14s
% Output : CNFRefutation 34.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 17
% Syntax : Number of clauses : 144 ( 144 unt; 0 nHn; 7 RR)
% Number of literals : 144 ( 143 equ; 4 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 : 273 ( 20 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(p21_3,hypothesis,
inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21_3) ).
cnf(p21_1,hypothesis,
inverse(identity) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21_1) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(p21_2,hypothesis,
inverse(inverse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21_2) ).
cnf(monotony_glb1,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GRP004-2.ax',symmetry_of_glb) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',glb_absorbtion) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',symmetry_of_lub) ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(monotony_lub1,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_lub2) ).
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/sandbox/benchmark/Axioms/GRP004-2.ax',associativity_of_glb) ).
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/sandbox/benchmark/Axioms/GRP004-2.ax',associativity_of_lub) ).
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/sandbox/benchmark/theBenchmark.p',prove_p21) ).
cnf(c_0_17,hypothesis,
inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
p21_3 ).
cnf(c_0_18,hypothesis,
inverse(identity) = identity,
p21_1 ).
cnf(c_0_19,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_20,hypothesis,
multiply(inverse(X1),identity) = inverse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_21,hypothesis,
inverse(inverse(X1)) = X1,
p21_2 ).
cnf(c_0_22,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_glb1 ).
cnf(c_0_23,hypothesis,
multiply(X1,identity) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
symmetry_of_glb ).
cnf(c_0_25,hypothesis,
greatest_lower_bound(X1,multiply(X1,X2)) = multiply(X1,greatest_lower_bound(X2,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_26,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_27,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
glb_absorbtion ).
cnf(c_0_28,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
symmetry_of_lub ).
cnf(c_0_29,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
lub_absorbtion ).
cnf(c_0_30,hypothesis,
multiply(inverse(X1),greatest_lower_bound(X1,identity)) = greatest_lower_bound(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_24]) ).
cnf(c_0_31,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_29,c_0_24]) ).
cnf(c_0_33,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_glb2 ).
cnf(c_0_34,hypothesis,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(spm,[status(thm)],[c_0_17,c_0_21]) ).
cnf(c_0_35,hypothesis,
multiply(inverse(X1),greatest_lower_bound(identity,X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(spm,[status(thm)],[c_0_30,c_0_24]) ).
cnf(c_0_36,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_31,c_0_32]),c_0_24]) ).
cnf(c_0_37,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_38,hypothesis,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_26,c_0_21]) ).
cnf(c_0_39,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_lub1 ).
cnf(c_0_40,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_lub2 ).
cnf(c_0_41,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_33,c_0_19]),c_0_24]) ).
cnf(c_0_42,hypothesis,
multiply(inverse(greatest_lower_bound(X1,identity)),X1) = inverse(greatest_lower_bound(identity,inverse(X1))),
inference(spm,[status(thm)],[c_0_34,c_0_30]) ).
cnf(c_0_43,hypothesis,
greatest_lower_bound(identity,inverse(greatest_lower_bound(X1,identity))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_26]) ).
cnf(c_0_44,hypothesis,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_19]) ).
cnf(c_0_45,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_46,hypothesis,
least_upper_bound(X1,multiply(X1,X2)) = multiply(X1,least_upper_bound(X2,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_23]),c_0_28]) ).
cnf(c_0_47,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_40,c_0_19]),c_0_28]) ).
cnf(c_0_48,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_26]),c_0_19]) ).
cnf(c_0_49,hypothesis,
greatest_lower_bound(X1,inverse(greatest_lower_bound(identity,inverse(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_24]),c_0_43]),c_0_19]) ).
cnf(c_0_50,hypothesis,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_44]),c_0_21]) ).
cnf(c_0_51,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_45,c_0_27]) ).
cnf(c_0_52,hypothesis,
multiply(least_upper_bound(X1,identity),X1) = multiply(X1,least_upper_bound(X1,identity)),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_53,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_39,c_0_48]) ).
cnf(c_0_54,hypothesis,
least_upper_bound(X1,inverse(greatest_lower_bound(identity,inverse(X1)))) = inverse(greatest_lower_bound(identity,inverse(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_49]),c_0_28]) ).
cnf(c_0_55,hypothesis,
multiply(greatest_lower_bound(X1,inverse(multiply(X2,X3))),X2) = greatest_lower_bound(multiply(X1,X2),inverse(X3)),
inference(spm,[status(thm)],[c_0_33,c_0_50]) ).
cnf(c_0_56,hypothesis,
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_51,c_0_25]) ).
cnf(c_0_57,hypothesis,
multiply(least_upper_bound(X1,identity),greatest_lower_bound(X1,identity)) = multiply(greatest_lower_bound(X1,identity),least_upper_bound(X1,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_52]),c_0_41]) ).
cnf(c_0_58,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_59,plain,
multiply(least_upper_bound(inverse(X1),X2),X1) = least_upper_bound(identity,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_40,c_0_26]) ).
cnf(c_0_60,hypothesis,
least_upper_bound(X1,inverse(greatest_lower_bound(X2,inverse(X1)))) = inverse(greatest_lower_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_53,c_0_54]),c_0_17]),c_0_55]),c_0_19]),c_0_17]),c_0_55]),c_0_19]) ).
cnf(c_0_61,hypothesis,
greatest_lower_bound(X1,multiply(greatest_lower_bound(X1,identity),least_upper_bound(X1,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_56,c_0_57]),c_0_52]),c_0_25]),c_0_24]),c_0_31]),c_0_23]) ).
cnf(c_0_62,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_58,c_0_29]) ).
cnf(c_0_63,hypothesis,
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_59,c_0_60]),c_0_21]),c_0_21]) ).
cnf(c_0_64,hypothesis,
greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X1),least_upper_bound(X1,identity))) = X1,
inference(spm,[status(thm)],[c_0_61,c_0_24]) ).
cnf(c_0_65,hypothesis,
multiply(inverse(X1),multiply(greatest_lower_bound(identity,X1),X2)) = multiply(greatest_lower_bound(identity,inverse(X1)),X2),
inference(spm,[status(thm)],[c_0_37,c_0_35]) ).
cnf(c_0_66,hypothesis,
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_62,c_0_46]) ).
cnf(c_0_67,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_33,c_0_26]),c_0_24]) ).
cnf(c_0_68,hypothesis,
multiply(greatest_lower_bound(X1,identity),X1) = multiply(X1,greatest_lower_bound(X1,identity)),
inference(spm,[status(thm)],[c_0_25,c_0_41]) ).
cnf(c_0_69,hypothesis,
multiply(X1,least_upper_bound(X2,multiply(inverse(X1),X3))) = least_upper_bound(multiply(X1,X2),X3),
inference(spm,[status(thm)],[c_0_39,c_0_44]) ).
cnf(c_0_70,hypothesis,
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_63,c_0_64]),c_0_65]),c_0_66]),c_0_67]),c_0_19]),c_0_29]),c_0_65]) ).
cnf(c_0_71,hypothesis,
multiply(greatest_lower_bound(X1,identity),inverse(X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_38]),c_0_24]) ).
cnf(c_0_72,hypothesis,
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_22,c_0_38]),c_0_24]) ).
cnf(c_0_73,hypothesis,
multiply(greatest_lower_bound(identity,X1),X1) = multiply(X1,greatest_lower_bound(identity,X1)),
inference(spm,[status(thm)],[c_0_68,c_0_24]) ).
cnf(c_0_74,hypothesis,
multiply(inverse(least_upper_bound(multiply(X1,X2),X3)),X1) = inverse(least_upper_bound(X2,multiply(inverse(X1),X3))),
inference(spm,[status(thm)],[c_0_50,c_0_69]) ).
cnf(c_0_75,hypothesis,
inverse(least_upper_bound(X1,identity)) = greatest_lower_bound(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_70]),c_0_18]),c_0_19]) ).
cnf(c_0_76,hypothesis,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_17,c_0_21]) ).
cnf(c_0_77,hypothesis,
multiply(greatest_lower_bound(identity,X1),inverse(X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(spm,[status(thm)],[c_0_71,c_0_24]) ).
cnf(c_0_78,hypothesis,
multiply(X1,greatest_lower_bound(X2,greatest_lower_bound(X3,inverse(X1)))) = greatest_lower_bound(identity,multiply(X1,greatest_lower_bound(X2,X3))),
inference(spm,[status(thm)],[c_0_72,c_0_45]) ).
cnf(c_0_79,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_31,c_0_29]),c_0_24]) ).
cnf(c_0_80,hypothesis,
multiply(greatest_lower_bound(X1,multiply(X2,X3)),inverse(X3)) = greatest_lower_bound(multiply(X1,inverse(X3)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_17]),c_0_21]),c_0_21]) ).
cnf(c_0_81,hypothesis,
greatest_lower_bound(identity,multiply(X1,greatest_lower_bound(X1,identity))) = multiply(greatest_lower_bound(identity,X1),greatest_lower_bound(X1,identity)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_73]),c_0_45]),c_0_25]),c_0_45]),c_0_36]) ).
cnf(c_0_82,hypothesis,
inverse(greatest_lower_bound(identity,multiply(inverse(X1),X2))) = multiply(inverse(greatest_lower_bound(X2,X1)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_72]),c_0_21]) ).
cnf(c_0_83,hypothesis,
multiply(X1,greatest_lower_bound(X2,multiply(inverse(X1),X3))) = greatest_lower_bound(multiply(X1,X2),X3),
inference(spm,[status(thm)],[c_0_22,c_0_44]) ).
cnf(c_0_84,plain,
greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X1,least_upper_bound(X2,X3))) = least_upper_bound(X1,X2),
inference(spm,[status(thm)],[c_0_27,c_0_58]) ).
cnf(c_0_85,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_32,c_0_31]),c_0_28]) ).
cnf(c_0_86,hypothesis,
multiply(least_upper_bound(X1,inverse(multiply(X2,X3))),X2) = least_upper_bound(multiply(X1,X2),inverse(X3)),
inference(spm,[status(thm)],[c_0_40,c_0_50]) ).
cnf(c_0_87,hypothesis,
multiply(least_upper_bound(identity,X1),X1) = multiply(X1,least_upper_bound(identity,X1)),
inference(spm,[status(thm)],[c_0_52,c_0_28]) ).
cnf(c_0_88,hypothesis,
inverse(least_upper_bound(X1,inverse(X2))) = greatest_lower_bound(X2,inverse(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_55]),c_0_19]),c_0_23]) ).
cnf(c_0_89,hypothesis,
multiply(X1,inverse(greatest_lower_bound(identity,X1))) = inverse(greatest_lower_bound(identity,inverse(X1))),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_90,hypothesis,
greatest_lower_bound(identity,multiply(X1,greatest_lower_bound(X2,identity))) = greatest_lower_bound(X1,greatest_lower_bound(identity,multiply(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_72]),c_0_45]),c_0_24]),c_0_78]) ).
cnf(c_0_91,hypothesis,
greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X1))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_79]),c_0_26]) ).
cnf(c_0_92,hypothesis,
greatest_lower_bound(X1,inverse(greatest_lower_bound(X1,identity))) = 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(spm,[status(thm)],[c_0_80,c_0_81]),c_0_37]),c_0_38]),c_0_23]),c_0_19]),c_0_24]) ).
cnf(c_0_93,hypothesis,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_17]),c_0_21]) ).
cnf(c_0_94,hypothesis,
multiply(inverse(greatest_lower_bound(X1,X2)),greatest_lower_bound(X2,X1)) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_82]),c_0_37]),c_0_83]),c_0_23]) ).
cnf(c_0_95,plain,
greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X2,X1)) = least_upper_bound(X1,X2),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_96,hypothesis,
multiply(least_upper_bound(X1,multiply(X2,X3)),inverse(X3)) = least_upper_bound(multiply(X1,inverse(X3)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_17]),c_0_21]),c_0_21]) ).
cnf(c_0_97,hypothesis,
least_upper_bound(identity,multiply(X1,least_upper_bound(X1,identity))) = multiply(least_upper_bound(identity,X1),least_upper_bound(X1,identity)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_87]),c_0_58]),c_0_46]),c_0_58]),c_0_85]) ).
cnf(c_0_98,hypothesis,
inverse(greatest_lower_bound(X1,inverse(X2))) = least_upper_bound(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_21,c_0_88]) ).
cnf(c_0_99,hypothesis,
multiply(greatest_lower_bound(identity,X1),inverse(greatest_lower_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_89,c_0_90]),c_0_19]),c_0_19]),c_0_36]),c_0_19]),c_0_91]),c_0_18]) ).
cnf(c_0_100,hypothesis,
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_33,c_0_38]),c_0_24]) ).
cnf(c_0_101,hypothesis,
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_55,c_0_76]),c_0_21]) ).
cnf(c_0_102,hypothesis,
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_76,c_0_80]) ).
cnf(c_0_103,plain,
greatest_lower_bound(identity,multiply(inverse(X1),X2)) = multiply(inverse(X1),greatest_lower_bound(X1,X2)),
inference(spm,[status(thm)],[c_0_22,c_0_26]) ).
cnf(c_0_104,plain,
least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X1,greatest_lower_bound(X2,X3))) = greatest_lower_bound(X1,X2),
inference(spm,[status(thm)],[c_0_29,c_0_45]) ).
cnf(c_0_105,hypothesis,
greatest_lower_bound(X1,inverse(greatest_lower_bound(identity,X1))) = greatest_lower_bound(identity,X1),
inference(spm,[status(thm)],[c_0_92,c_0_24]) ).
cnf(c_0_106,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_45,c_0_31]) ).
cnf(c_0_107,hypothesis,
greatest_lower_bound(inverse(X1),multiply(X2,inverse(multiply(X1,X3)))) = multiply(greatest_lower_bound(X2,X3),inverse(multiply(X1,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_93]),c_0_24]) ).
cnf(c_0_108,hypothesis,
multiply(inverse(least_upper_bound(X1,X2)),least_upper_bound(X2,X1)) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_95]) ).
cnf(c_0_109,plain,
least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_32,c_0_45]) ).
cnf(c_0_110,hypothesis,
least_upper_bound(X1,inverse(least_upper_bound(X1,identity))) = least_upper_bound(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_96,c_0_97]),c_0_37]),c_0_38]),c_0_23]),c_0_19]),c_0_28]) ).
cnf(c_0_111,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_58,c_0_32]) ).
cnf(c_0_112,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_58,c_0_85]),c_0_58]),c_0_58]) ).
cnf(c_0_113,hypothesis,
least_upper_bound(identity,inverse(X1)) = inverse(greatest_lower_bound(X1,identity)),
inference(spm,[status(thm)],[c_0_98,c_0_18]) ).
cnf(c_0_114,hypothesis,
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_39,c_0_38]),c_0_28]) ).
cnf(c_0_115,hypothesis,
least_upper_bound(inverse(X1),multiply(inverse(multiply(X2,X1)),X3)) = multiply(inverse(multiply(X2,X1)),least_upper_bound(X3,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_50]),c_0_28]) ).
cnf(c_0_116,hypothesis,
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_99,c_0_100]),c_0_24]),c_0_37]),c_0_17]),c_0_101]),c_0_19]) ).
cnf(c_0_117,hypothesis,
multiply(X1,multiply(inverse(greatest_lower_bound(X2,X1)),X2)) = inverse(greatest_lower_bound(inverse(X1),inverse(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_34]),c_0_19]) ).
cnf(c_0_118,plain,
least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X2,X1)) = greatest_lower_bound(X1,X2),
inference(spm,[status(thm)],[c_0_104,c_0_36]) ).
cnf(c_0_119,hypothesis,
greatest_lower_bound(inverse(X1),least_upper_bound(X1,identity)) = greatest_lower_bound(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_98]),c_0_18]) ).
cnf(c_0_120,plain,
least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(least_upper_bound(X3,X1),X2)) = greatest_lower_bound(least_upper_bound(X3,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_106]),c_0_28]) ).
cnf(c_0_121,hypothesis,
greatest_lower_bound(least_upper_bound(X1,X2),X3) = greatest_lower_bound(X3,least_upper_bound(X2,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_107,c_0_108]),c_0_21]),c_0_18]),c_0_23]),c_0_18]),c_0_23]) ).
cnf(c_0_122,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_109,c_0_27]),c_0_58]) ).
cnf(c_0_123,hypothesis,
least_upper_bound(X1,greatest_lower_bound(identity,inverse(X1))) = least_upper_bound(identity,X1),
inference(rw,[status(thm)],[c_0_110,c_0_75]) ).
cnf(c_0_124,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_111,c_0_27]),c_0_58]),c_0_58]),c_0_112]) ).
cnf(c_0_125,hypothesis,
least_upper_bound(identity,least_upper_bound(inverse(X1),X2)) = least_upper_bound(inverse(greatest_lower_bound(X1,identity)),X2),
inference(spm,[status(thm)],[c_0_58,c_0_113]) ).
cnf(c_0_126,hypothesis,
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_41,c_0_114]) ).
cnf(c_0_127,plain,
least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X1,X3))) = X1,
inference(spm,[status(thm)],[c_0_109,c_0_24]) ).
cnf(c_0_128,hypothesis,
least_upper_bound(greatest_lower_bound(X1,X2),X3) = least_upper_bound(X3,greatest_lower_bound(X2,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_115,c_0_116]),c_0_21]),c_0_18]),c_0_19]),c_0_18]),c_0_19]) ).
cnf(c_0_129,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_130,hypothesis,
multiply(X1,multiply(inverse(greatest_lower_bound(X2,X1)),X2)) = least_upper_bound(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_117,c_0_98]),c_0_21]) ).
cnf(c_0_131,hypothesis,
greatest_lower_bound(inverse(X1),least_upper_bound(identity,X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_120]),c_0_121]) ).
cnf(c_0_132,hypothesis,
least_upper_bound(X1,inverse(greatest_lower_bound(X1,identity))) = least_upper_bound(X1,inverse(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_124]),c_0_125]),c_0_28]),c_0_28]) ).
cnf(c_0_133,hypothesis,
greatest_lower_bound(least_upper_bound(identity,X1),inverse(greatest_lower_bound(X1,identity))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_113]),c_0_23]),c_0_38]),c_0_24]) ).
cnf(c_0_134,plain,
least_upper_bound(X1,least_upper_bound(X2,greatest_lower_bound(X1,X3))) = least_upper_bound(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_51]),c_0_58]) ).
cnf(c_0_135,hypothesis,
least_upper_bound(inverse(X1),greatest_lower_bound(X1,identity)) = inverse(greatest_lower_bound(identity,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_105]),c_0_128]) ).
cnf(c_0_136,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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_129,c_0_24]),c_0_24]),c_0_28]),c_0_28]) ).
cnf(c_0_137,hypothesis,
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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_17]),c_0_72]),c_0_23]),c_0_124]),c_0_125]),c_0_28]),c_0_132]) ).
cnf(c_0_138,hypothesis,
greatest_lower_bound(least_upper_bound(identity,X1),inverse(greatest_lower_bound(identity,X1))) = identity,
inference(spm,[status(thm)],[c_0_133,c_0_24]) ).
cnf(c_0_139,hypothesis,
least_upper_bound(X1,inverse(greatest_lower_bound(identity,X1))) = least_upper_bound(X1,inverse(X1)),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_140,hypothesis,
least_upper_bound(identity,least_upper_bound(X1,inverse(X2))) = least_upper_bound(X1,inverse(greatest_lower_bound(X2,identity))),
inference(spm,[status(thm)],[c_0_124,c_0_113]) ).
cnf(c_0_141,negated_conjecture,
multiply(inverse(greatest_lower_bound(identity,a)),least_upper_bound(identity,a)) != least_upper_bound(a,inverse(a)),
inference(rw,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_142,hypothesis,
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(spm,[status(thm)],[c_0_130,c_0_138]),c_0_18]),c_0_19]),c_0_58]),c_0_139]),c_0_140]),c_0_132]) ).
cnf(c_0_143,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_141,c_0_142])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP184-2 : TPTP v9.2.1. Bugfixed v1.2.1.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n029.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 18:29:29 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 34.89/21.14 % Version : CSE_E---1.7
% 34.89/21.14 % Problem : theBenchmark.p
% 34.89/21.14 % SZS status Unsatisfiable for theBenchmark.p
% 34.89/21.14 % SZS output start CNFRefutation
% See solution above
% 34.96/21.29 % Total time : 15.395s
%------------------------------------------------------------------------------