%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP189-2 : 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 : n003.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 04:24:46 PM UTC 2026
% Result : Unsatisfiable 0.34s 1.61s
% Output : CNFRefutation 0.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 39
% Syntax : Number of clauses : 141 ( 123 unt; 0 nHn; 24 RR)
% Number of literals : 161 ( 160 equ; 35 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 270 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
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_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(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_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(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
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(p38b_3,hypothesis,
inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p38b_3) ).
cnf(prove_p38b,negated_conjecture,
greatest_lower_bound(b,least_upper_bound(a,b)) != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p38b) ).
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(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(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(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(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(idempotence_of_lub,axiom,
least_upper_bound(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',idempotence_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(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(p38b_2,hypothesis,
inverse(inverse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p38b_2) ).
cnf(p38b_1,hypothesis,
inverse(identity) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p38b_1) ).
cnf(i_0_19,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_lub2,
[final] ).
cnf(i_0_20,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_glb2,
[final] ).
cnf(i_0_21,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_lub1,
[final] ).
cnf(i_0_22,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_glb1,
[final] ).
cnf(i_0_23,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity,
[final] ).
cnf(i_0_24,axiom,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3),
associativity_of_lub,
[final] ).
cnf(i_0_25,axiom,
greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3),
associativity_of_glb,
[final] ).
cnf(i_0_26,hypothesis,
inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
p38b_3,
[final] ).
cnf(i_0_27,negated_conjecture,
greatest_lower_bound(b,least_upper_bound(a,b)) != b,
prove_p38b,
[final] ).
cnf(i_0_28,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
lub_absorbtion,
[final] ).
cnf(i_0_29,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
glb_absorbtion,
[final] ).
cnf(i_0_30,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
symmetry_of_lub,
[final] ).
cnf(i_0_31,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
symmetry_of_glb,
[final] ).
cnf(i_0_32,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse,
[final] ).
cnf(i_0_33,axiom,
least_upper_bound(X1,X1) = X1,
idempotence_of_lub,
[final] ).
cnf(i_0_34,axiom,
greatest_lower_bound(X1,X1) = X1,
idempotence_of_gld,
[final] ).
cnf(i_0_35,axiom,
multiply(identity,X1) = X1,
left_identity,
[final] ).
cnf(i_0_36,hypothesis,
inverse(inverse(X1)) = X1,
p38b_2,
[final] ).
cnf(i_0_37,hypothesis,
inverse(identity) = identity,
p38b_1,
[final] ).
cnf(i_0_38,axiom,
X1 = X1 ).
cnf(i_0_39,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_40,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_41,axiom,
( X1 != X2
| multiply(X1,X3) = multiply(X2,X3) ) ).
cnf(i_0_42,axiom,
( X1 != X2
| multiply(X3,X1) = multiply(X3,X2) ) ).
cnf(i_0_43,axiom,
( X1 != X2
| least_upper_bound(X1,X3) = least_upper_bound(X2,X3) ) ).
cnf(i_0_44,axiom,
( X1 != X2
| least_upper_bound(X3,X1) = least_upper_bound(X3,X2) ) ).
cnf(i_0_45,axiom,
( X1 != X2
| greatest_lower_bound(X1,X3) = greatest_lower_bound(X2,X3) ) ).
cnf(i_0_46,axiom,
( X1 != X2
| greatest_lower_bound(X3,X1) = greatest_lower_bound(X3,X2) ) ).
cnf(i_0_47,axiom,
( X1 != X2
| inverse(X1) = inverse(X2) ) ).
cnf(i_0_38_001,axiom,
X1 = X1 ).
cnf(i_0_39_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_40_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_41_004,axiom,
( X1 != X2
| multiply(X1,X3) = multiply(X2,X3) ) ).
cnf(i_0_42_005,axiom,
( X1 != X2
| multiply(X3,X1) = multiply(X3,X2) ) ).
cnf(i_0_43_006,axiom,
( X1 != X2
| least_upper_bound(X1,X3) = least_upper_bound(X2,X3) ) ).
cnf(i_0_44_007,axiom,
( X1 != X2
| least_upper_bound(X3,X1) = least_upper_bound(X3,X2) ) ).
cnf(i_0_45_008,axiom,
( X1 != X2
| greatest_lower_bound(X1,X3) = greatest_lower_bound(X2,X3) ) ).
cnf(i_0_46_009,axiom,
( X1 != X2
| greatest_lower_bound(X3,X1) = greatest_lower_bound(X3,X2) ) ).
cnf(i_0_47_010,axiom,
( X1 != X2
| inverse(X1) = inverse(X2) ) ).
cnf(i_0_48,plain,
X1 = least_upper_bound(X1,X1),
inference(scs_inference,[],[i_0_33,i_0_39]) ).
cnf(i_0_49,plain,
greatest_lower_bound(b,least_upper_bound(a,b)) != least_upper_bound(b,b),
inference(scs_inference,[],[i_0_27,i_0_33,i_0_39,i_0_40]) ).
cnf(i_0_50,plain,
least_upper_bound(X1,X1) = X1,
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_51,plain,
X1 = greatest_lower_bound(X1,X1),
inference(scs_inference,[],[i_0_34,i_0_39]) ).
cnf(i_0_52,plain,
greatest_lower_bound(b,least_upper_bound(a,b)) != greatest_lower_bound(b,b),
inference(scs_inference,[],[i_0_27,i_0_34,i_0_39,i_0_40]) ).
cnf(i_0_53,plain,
greatest_lower_bound(X1,X1) = X1,
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_54,plain,
least_upper_bound(a,b) != b,
inference(scs_inference,[],[i_0_27,i_0_34,i_0_39,i_0_40,i_0_46]) ).
cnf(i_0_55,plain,
X1 = multiply(identity,X1),
inference(scs_inference,[],[i_0_35,i_0_39]) ).
cnf(i_0_56,plain,
greatest_lower_bound(b,least_upper_bound(a,b)) != multiply(identity,b),
inference(scs_inference,[],[i_0_27,i_0_35,i_0_39,i_0_40]) ).
cnf(i_0_57,plain,
multiply(identity,X1) = X1,
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_58,plain,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
inference(scs_inference,[],[i_0_19,i_0_39]) ).
cnf(i_0_59,plain,
least_upper_bound(X1,X2) = least_upper_bound(multiply(identity,X1),multiply(identity,X2)),
inference(scs_inference,[],[i_0_55,i_0_19,i_0_21,i_0_39,i_0_40]) ).
cnf(i_0_60,plain,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
inference(rename_variables,[],[i_0_21]) ).
cnf(i_0_61,plain,
X1 = multiply(identity,X1),
inference(rename_variables,[],[i_0_55]) ).
cnf(i_0_62,plain,
least_upper_bound(multiply(identity,X1),multiply(identity,X2)) = least_upper_bound(X1,X2),
inference(scs_inference,[],[i_0_59,i_0_39]) ).
cnf(i_0_63,plain,
multiply(X1,X2) = multiply(least_upper_bound(X1,X1),X2),
inference(scs_inference,[],[i_0_48,i_0_58,i_0_59,i_0_39,i_0_40]) ).
cnf(i_0_64,plain,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
inference(rename_variables,[],[i_0_58]) ).
cnf(i_0_65,plain,
X1 = least_upper_bound(X1,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_66,plain,
multiply(least_upper_bound(X1,X1),X2) = multiply(X1,X2),
inference(scs_inference,[],[i_0_63,i_0_39]) ).
cnf(i_0_67,plain,
greatest_lower_bound(b,least_upper_bound(a,b)) != least_upper_bound(multiply(identity,b),multiply(identity,b)),
inference(scs_inference,[],[i_0_62,i_0_63,i_0_49,i_0_39,i_0_40]) ).
cnf(i_0_68,plain,
least_upper_bound(multiply(identity,X1),multiply(identity,X2)) = least_upper_bound(X1,X2),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_69,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2),
inference(scs_inference,[],[i_0_20,i_0_39]) ).
cnf(i_0_70,plain,
greatest_lower_bound(b,least_upper_bound(a,b)) != multiply(least_upper_bound(identity,identity),b),
inference(scs_inference,[],[i_0_66,i_0_56,i_0_20,i_0_39,i_0_40]) ).
cnf(i_0_71,plain,
multiply(least_upper_bound(X1,X1),X2) = multiply(X1,X2),
inference(rename_variables,[],[i_0_66]) ).
cnf(i_0_72,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,greatest_lower_bound(X2,X3)),
inference(scs_inference,[],[i_0_22,i_0_39]) ).
cnf(i_0_73,plain,
multiply(X1,X2) = multiply(greatest_lower_bound(X1,X1),X2),
inference(scs_inference,[],[i_0_51,i_0_69,i_0_22,i_0_39,i_0_40]) ).
cnf(i_0_74,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2),
inference(rename_variables,[],[i_0_69]) ).
cnf(i_0_75,plain,
X1 = greatest_lower_bound(X1,X1),
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_76,plain,
multiply(greatest_lower_bound(X1,X1),X2) = multiply(X1,X2),
inference(scs_inference,[],[i_0_73,i_0_39]) ).
cnf(i_0_77,plain,
multiply(X1,X2) = multiply(X1,greatest_lower_bound(X2,X2)),
inference(scs_inference,[],[i_0_72,i_0_51,i_0_73,i_0_39,i_0_40]) ).
cnf(i_0_78,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,greatest_lower_bound(X2,X3)),
inference(rename_variables,[],[i_0_72]) ).
cnf(i_0_79,plain,
X1 = greatest_lower_bound(X1,X1),
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_80,plain,
multiply(X1,greatest_lower_bound(X2,X2)) = multiply(X1,X2),
inference(scs_inference,[],[i_0_77,i_0_39]) ).
cnf(i_0_81,plain,
multiply(greatest_lower_bound(X1,X1),X2) = multiply(X1,greatest_lower_bound(X2,X2)),
inference(scs_inference,[],[i_0_76,i_0_77,i_0_39,i_0_40]) ).
cnf(i_0_82,plain,
multiply(X1,X2) = multiply(X1,greatest_lower_bound(X2,X2)),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_83,plain,
multiply(X1,greatest_lower_bound(X2,X2)) = multiply(greatest_lower_bound(X1,X1),X2),
inference(scs_inference,[],[i_0_81,i_0_39]) ).
cnf(i_0_84,plain,
greatest_lower_bound(b,least_upper_bound(a,b)) != multiply(least_upper_bound(identity,identity),greatest_lower_bound(b,b)),
inference(scs_inference,[],[i_0_80,i_0_81,i_0_70,i_0_39,i_0_40]) ).
cnf(i_0_85,plain,
multiply(X1,greatest_lower_bound(X2,X2)) = multiply(X1,X2),
inference(rename_variables,[],[i_0_80]) ).
cnf(i_0_86,plain,
multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3),
inference(scs_inference,[],[i_0_23,i_0_39]) ).
cnf(i_0_87,plain,
multiply(least_upper_bound(X1,X1),greatest_lower_bound(X2,X2)) = multiply(greatest_lower_bound(X1,X1),X2),
inference(scs_inference,[],[i_0_83,i_0_66,i_0_23,i_0_39,i_0_40]) ).
cnf(i_0_88,plain,
multiply(X1,greatest_lower_bound(X2,X2)) = multiply(greatest_lower_bound(X1,X1),X2),
inference(rename_variables,[],[i_0_83]) ).
cnf(i_0_89,plain,
multiply(least_upper_bound(X1,X1),X2) = multiply(X1,X2),
inference(rename_variables,[],[i_0_66]) ).
cnf(i_0_90,plain,
multiply(greatest_lower_bound(X1,X1),X2) = multiply(least_upper_bound(X1,X1),greatest_lower_bound(X2,X2)),
inference(scs_inference,[],[i_0_87,i_0_39]) ).
cnf(i_0_91,plain,
multiply(greatest_lower_bound(X1,X1),multiply(X2,X3)) = multiply(multiply(X1,X2),X3),
inference(scs_inference,[],[i_0_86,i_0_76,i_0_87,i_0_39,i_0_40]) ).
cnf(i_0_92,plain,
multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3),
inference(rename_variables,[],[i_0_86]) ).
cnf(i_0_93,plain,
multiply(greatest_lower_bound(X1,X1),X2) = multiply(X1,X2),
inference(rename_variables,[],[i_0_76]) ).
cnf(i_0_94,plain,
multiply(multiply(X1,X2),X3) = multiply(greatest_lower_bound(X1,X1),multiply(X2,X3)),
inference(scs_inference,[],[i_0_91,i_0_39]) ).
cnf(i_0_95,plain,
greatest_lower_bound(b,least_upper_bound(a,b)) != multiply(greatest_lower_bound(identity,identity),b),
inference(scs_inference,[],[i_0_90,i_0_91,i_0_84,i_0_39,i_0_40]) ).
cnf(i_0_96,plain,
multiply(greatest_lower_bound(X1,X1),X2) = multiply(least_upper_bound(X1,X1),greatest_lower_bound(X2,X2)),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_97,plain,
least_upper_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(X1,least_upper_bound(X2,X3)),
inference(scs_inference,[],[i_0_24,i_0_39]) ).
cnf(i_0_98,plain,
multiply(multiply(X1,X2),greatest_lower_bound(X3,X3)) = multiply(greatest_lower_bound(X1,X1),multiply(X2,X3)),
inference(scs_inference,[],[i_0_94,i_0_80,i_0_24,i_0_39,i_0_40]) ).
cnf(i_0_99,plain,
multiply(multiply(X1,X2),X3) = multiply(greatest_lower_bound(X1,X1),multiply(X2,X3)),
inference(rename_variables,[],[i_0_94]) ).
cnf(i_0_100,plain,
multiply(X1,greatest_lower_bound(X2,X2)) = multiply(X1,X2),
inference(rename_variables,[],[i_0_80]) ).
cnf(i_0_101,plain,
multiply(greatest_lower_bound(X1,X1),multiply(X2,X3)) = multiply(multiply(X1,X2),greatest_lower_bound(X3,X3)),
inference(scs_inference,[],[i_0_98,i_0_39]) ).
cnf(i_0_102,plain,
least_upper_bound(X1,X2) = least_upper_bound(X1,least_upper_bound(X2,least_upper_bound(X1,X2))),
inference(scs_inference,[],[i_0_97,i_0_48,i_0_98,i_0_39,i_0_40]) ).
cnf(i_0_103,plain,
least_upper_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(X1,least_upper_bound(X2,X3)),
inference(rename_variables,[],[i_0_97]) ).
cnf(i_0_104,plain,
X1 = least_upper_bound(X1,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_105,plain,
least_upper_bound(X1,least_upper_bound(X2,least_upper_bound(X1,X2))) = least_upper_bound(X1,X2),
inference(scs_inference,[],[i_0_102,i_0_39]) ).
cnf(i_0_106,plain,
greatest_lower_bound(b,least_upper_bound(a,b)) != multiply(identity,greatest_lower_bound(b,b)),
inference(scs_inference,[],[i_0_83,i_0_102,i_0_95,i_0_39,i_0_40]) ).
cnf(i_0_107,plain,
multiply(X1,greatest_lower_bound(X2,X2)) = multiply(greatest_lower_bound(X1,X1),X2),
inference(rename_variables,[],[i_0_83]) ).
cnf(i_0_108,plain,
greatest_lower_bound(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)),
inference(scs_inference,[],[i_0_25,i_0_39]) ).
cnf(i_0_109,plain,
greatest_lower_bound(b,least_upper_bound(a,b)) != greatest_lower_bound(multiply(identity,b),multiply(identity,b)),
inference(scs_inference,[],[i_0_69,i_0_25,i_0_95,i_0_39,i_0_40]) ).
cnf(i_0_110,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2),
inference(rename_variables,[],[i_0_69]) ).
cnf(i_0_111,plain,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
inference(scs_inference,[],[i_0_26,i_0_39]) ).
cnf(i_0_112,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X1,X2))),
inference(scs_inference,[],[i_0_108,i_0_51,i_0_26,i_0_39,i_0_40]) ).
cnf(i_0_113,plain,
greatest_lower_bound(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)),
inference(rename_variables,[],[i_0_108]) ).
cnf(i_0_114,plain,
X1 = greatest_lower_bound(X1,X1),
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_115,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X1,X2))) = greatest_lower_bound(X1,X2),
inference(scs_inference,[],[i_0_112,i_0_39]) ).
cnf(i_0_116,plain,
multiply(least_upper_bound(inverse(X1),inverse(X1)),inverse(X2)) = inverse(multiply(X2,X1)),
inference(scs_inference,[],[i_0_111,i_0_66,i_0_112,i_0_39,i_0_40]) ).
cnf(i_0_117,plain,
multiply(least_upper_bound(X1,X1),X2) = multiply(X1,X2),
inference(rename_variables,[],[i_0_66]) ).
cnf(i_0_118,plain,
inverse(multiply(X1,X2)) = multiply(least_upper_bound(inverse(X2),inverse(X2)),inverse(X1)),
inference(scs_inference,[],[i_0_116,i_0_39]) ).
cnf(i_0_119,plain,
multiply(greatest_lower_bound(inverse(X1),inverse(X1)),inverse(X2)) = inverse(multiply(X2,X1)),
inference(scs_inference,[],[i_0_111,i_0_76,i_0_116,i_0_39,i_0_40]) ).
cnf(i_0_120,plain,
multiply(greatest_lower_bound(X1,X1),X2) = multiply(X1,X2),
inference(rename_variables,[],[i_0_76]) ).
cnf(i_0_121,plain,
inverse(multiply(X1,X2)) = multiply(greatest_lower_bound(inverse(X2),inverse(X2)),inverse(X1)),
inference(scs_inference,[],[i_0_119,i_0_39]) ).
cnf(i_0_122,plain,
greatest_lower_bound(b,least_upper_bound(a,b)) != multiply(greatest_lower_bound(identity,identity),greatest_lower_bound(b,b)),
inference(scs_inference,[],[i_0_76,i_0_119,i_0_106,i_0_39,i_0_40]) ).
cnf(i_0_123,plain,
multiply(greatest_lower_bound(X1,X1),X2) = multiply(X1,X2),
inference(rename_variables,[],[i_0_76]) ).
cnf(i_0_124,plain,
X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)),
inference(scs_inference,[],[i_0_28,i_0_39]) ).
cnf(i_0_125,plain,
greatest_lower_bound(b,least_upper_bound(a,b)) != multiply(least_upper_bound(greatest_lower_bound(identity,identity),greatest_lower_bound(identity,identity)),greatest_lower_bound(b,b)),
inference(scs_inference,[],[i_0_66,i_0_122,i_0_28,i_0_39,i_0_40]) ).
cnf(i_0_126,plain,
multiply(least_upper_bound(X1,X1),X2) = multiply(X1,X2),
inference(rename_variables,[],[i_0_66]) ).
cnf(i_0_127,plain,
X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)),
inference(scs_inference,[],[i_0_29,i_0_39]) ).
cnf(i_0_128,plain,
greatest_lower_bound(b,least_upper_bound(a,b)) != greatest_lower_bound(b,least_upper_bound(b,X1)),
inference(scs_inference,[],[i_0_27,i_0_29,i_0_39,i_0_40]) ).
cnf(i_0_129,plain,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
inference(rename_variables,[],[i_0_29]) ).
cnf(i_0_130,plain,
$false,
inference(scs_inference,[],[i_0_27,i_0_30,i_0_29,i_0_39,i_0_40,i_0_46]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP189-2 : 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
% 0.15/0.33 % Computer : n003.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 18:27:56 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.34/1.61 % Version : CSE_E---1.7
% 0.34/1.61 % Problem : theBenchmark.p
% 0.34/1.61 % SZS status Unsatisfiable for theBenchmark.p
% 0.34/1.61 % SZS output start CNFRefutation
% See solution above
% 0.44/1.74 % Total time : 1.271s
%------------------------------------------------------------------------------