%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP153-1 : 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 : n001.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 04:24:35 PM UTC 2026
% Result : Unsatisfiable 0.40s 1.60s
% Output : CNFRefutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 34
% Syntax : Number of clauses : 152 ( 136 unt; 0 nHn; 24 RR)
% Number of literals : 170 ( 169 equ; 37 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 : 285 ( 18 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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_glb1) ).
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/GRP004-2.ax',associativity_of_glb) ).
cnf(prove_ax_lub3b,negated_conjecture,
greatest_lower_bound(b,least_upper_bound(a,b)) != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ax_lub3b) ).
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(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(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(idempotence_of_lub,axiom,
least_upper_bound(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',idempotence_of_lub) ).
cnf(idempotence_of_gld,axiom,
greatest_lower_bound(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',idempotence_of_gld) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(i_0_16,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_lub2,
[final] ).
cnf(i_0_17,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_glb2,
[final] ).
cnf(i_0_18,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_lub1,
[final] ).
cnf(i_0_19,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_glb1,
[final] ).
cnf(i_0_20,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity,
[final] ).
cnf(i_0_21,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_22,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_23,negated_conjecture,
greatest_lower_bound(b,least_upper_bound(a,b)) != b,
prove_ax_lub3b,
[final] ).
cnf(i_0_24,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
lub_absorbtion,
[final] ).
cnf(i_0_25,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
glb_absorbtion,
[final] ).
cnf(i_0_26,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
symmetry_of_lub,
[final] ).
cnf(i_0_27,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
symmetry_of_glb,
[final] ).
cnf(i_0_28,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse,
[final] ).
cnf(i_0_29,axiom,
least_upper_bound(X1,X1) = X1,
idempotence_of_lub,
[final] ).
cnf(i_0_30,axiom,
greatest_lower_bound(X1,X1) = X1,
idempotence_of_gld,
[final] ).
cnf(i_0_31,axiom,
multiply(identity,X1) = X1,
left_identity,
[final] ).
cnf(i_0_32,axiom,
X1 = X1 ).
cnf(i_0_33,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_34,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_35,axiom,
( X1 != X2
| multiply(X1,X3) = multiply(X2,X3) ) ).
cnf(i_0_36,axiom,
( X1 != X2
| multiply(X3,X1) = multiply(X3,X2) ) ).
cnf(i_0_37,axiom,
( X1 != X2
| least_upper_bound(X1,X3) = least_upper_bound(X2,X3) ) ).
cnf(i_0_38,axiom,
( X1 != X2
| least_upper_bound(X3,X1) = least_upper_bound(X3,X2) ) ).
cnf(i_0_39,axiom,
( X1 != X2
| greatest_lower_bound(X1,X3) = greatest_lower_bound(X2,X3) ) ).
cnf(i_0_40,axiom,
( X1 != X2
| greatest_lower_bound(X3,X1) = greatest_lower_bound(X3,X2) ) ).
cnf(i_0_32_001,axiom,
X1 = X1 ).
cnf(i_0_33_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_34_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_35_004,axiom,
( X1 != X2
| multiply(X1,X3) = multiply(X2,X3) ) ).
cnf(i_0_36_005,axiom,
( X1 != X2
| multiply(X3,X1) = multiply(X3,X2) ) ).
cnf(i_0_37_006,axiom,
( X1 != X2
| least_upper_bound(X1,X3) = least_upper_bound(X2,X3) ) ).
cnf(i_0_38_007,axiom,
( X1 != X2
| least_upper_bound(X3,X1) = least_upper_bound(X3,X2) ) ).
cnf(i_0_39_008,axiom,
( X1 != X2
| greatest_lower_bound(X1,X3) = greatest_lower_bound(X2,X3) ) ).
cnf(i_0_40_009,axiom,
( X1 != X2
| greatest_lower_bound(X3,X1) = greatest_lower_bound(X3,X2) ) ).
cnf(i_0_41,plain,
X1 = least_upper_bound(X1,X1),
inference(scs_inference,[],[i_0_29,i_0_33]) ).
cnf(i_0_42,plain,
greatest_lower_bound(b,least_upper_bound(a,b)) != least_upper_bound(b,b),
inference(scs_inference,[],[i_0_23,i_0_29,i_0_33,i_0_34]) ).
cnf(i_0_43,plain,
least_upper_bound(X1,X1) = X1,
inference(rename_variables,[],[i_0_29]) ).
cnf(i_0_44,plain,
X1 = greatest_lower_bound(X1,X1),
inference(scs_inference,[],[i_0_30,i_0_33]) ).
cnf(i_0_45,plain,
greatest_lower_bound(b,least_upper_bound(a,b)) != greatest_lower_bound(b,b),
inference(scs_inference,[],[i_0_23,i_0_30,i_0_33,i_0_34]) ).
cnf(i_0_46,plain,
greatest_lower_bound(X1,X1) = X1,
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_47,plain,
least_upper_bound(a,b) != b,
inference(scs_inference,[],[i_0_23,i_0_30,i_0_33,i_0_34,i_0_40]) ).
cnf(i_0_48,plain,
X1 = multiply(identity,X1),
inference(scs_inference,[],[i_0_31,i_0_33]) ).
cnf(i_0_49,plain,
greatest_lower_bound(b,least_upper_bound(a,b)) != multiply(identity,b),
inference(scs_inference,[],[i_0_23,i_0_31,i_0_33,i_0_34]) ).
cnf(i_0_50,plain,
multiply(identity,X1) = X1,
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_51,plain,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
inference(scs_inference,[],[i_0_16,i_0_33]) ).
cnf(i_0_52,plain,
least_upper_bound(X1,X2) = least_upper_bound(multiply(identity,X1),multiply(identity,X2)),
inference(scs_inference,[],[i_0_48,i_0_16,i_0_18,i_0_33,i_0_34]) ).
cnf(i_0_53,plain,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
inference(rename_variables,[],[i_0_18]) ).
cnf(i_0_54,plain,
X1 = multiply(identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_55,plain,
least_upper_bound(multiply(identity,X1),multiply(identity,X2)) = least_upper_bound(X1,X2),
inference(scs_inference,[],[i_0_52,i_0_33]) ).
cnf(i_0_56,plain,
multiply(X1,X2) = multiply(least_upper_bound(X1,X1),X2),
inference(scs_inference,[],[i_0_41,i_0_51,i_0_52,i_0_33,i_0_34]) ).
cnf(i_0_57,plain,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_58,plain,
X1 = least_upper_bound(X1,X1),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_59,plain,
multiply(least_upper_bound(X1,X1),X2) = multiply(X1,X2),
inference(scs_inference,[],[i_0_56,i_0_33]) ).
cnf(i_0_60,plain,
greatest_lower_bound(b,least_upper_bound(a,b)) != least_upper_bound(multiply(identity,b),multiply(identity,b)),
inference(scs_inference,[],[i_0_55,i_0_56,i_0_42,i_0_33,i_0_34]) ).
cnf(i_0_61,plain,
least_upper_bound(multiply(identity,X1),multiply(identity,X2)) = least_upper_bound(X1,X2),
inference(rename_variables,[],[i_0_55]) ).
cnf(i_0_62,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2),
inference(scs_inference,[],[i_0_17,i_0_33]) ).
cnf(i_0_63,plain,
greatest_lower_bound(b,least_upper_bound(a,b)) != multiply(least_upper_bound(identity,identity),b),
inference(scs_inference,[],[i_0_59,i_0_49,i_0_17,i_0_33,i_0_34]) ).
cnf(i_0_64,plain,
multiply(least_upper_bound(X1,X1),X2) = multiply(X1,X2),
inference(rename_variables,[],[i_0_59]) ).
cnf(i_0_65,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,greatest_lower_bound(X2,X3)),
inference(scs_inference,[],[i_0_19,i_0_33]) ).
cnf(i_0_66,plain,
multiply(X1,X2) = multiply(greatest_lower_bound(X1,X1),X2),
inference(scs_inference,[],[i_0_44,i_0_62,i_0_19,i_0_33,i_0_34]) ).
cnf(i_0_67,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_68,plain,
X1 = greatest_lower_bound(X1,X1),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_69,plain,
multiply(greatest_lower_bound(X1,X1),X2) = multiply(X1,X2),
inference(scs_inference,[],[i_0_66,i_0_33]) ).
cnf(i_0_70,plain,
multiply(X1,X2) = multiply(X1,greatest_lower_bound(X2,X2)),
inference(scs_inference,[],[i_0_65,i_0_44,i_0_66,i_0_33,i_0_34]) ).
cnf(i_0_71,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,greatest_lower_bound(X2,X3)),
inference(rename_variables,[],[i_0_65]) ).
cnf(i_0_72,plain,
X1 = greatest_lower_bound(X1,X1),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_73,plain,
multiply(X1,greatest_lower_bound(X2,X2)) = multiply(X1,X2),
inference(scs_inference,[],[i_0_70,i_0_33]) ).
cnf(i_0_74,plain,
multiply(greatest_lower_bound(X1,X1),X2) = multiply(X1,greatest_lower_bound(X2,X2)),
inference(scs_inference,[],[i_0_69,i_0_70,i_0_33,i_0_34]) ).
cnf(i_0_75,plain,
multiply(X1,X2) = multiply(X1,greatest_lower_bound(X2,X2)),
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_76,plain,
multiply(X1,greatest_lower_bound(X2,X2)) = multiply(greatest_lower_bound(X1,X1),X2),
inference(scs_inference,[],[i_0_74,i_0_33]) ).
cnf(i_0_77,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_73,i_0_74,i_0_63,i_0_33,i_0_34]) ).
cnf(i_0_78,plain,
multiply(X1,greatest_lower_bound(X2,X2)) = multiply(X1,X2),
inference(rename_variables,[],[i_0_73]) ).
cnf(i_0_79,plain,
multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3),
inference(scs_inference,[],[i_0_20,i_0_33]) ).
cnf(i_0_80,plain,
multiply(least_upper_bound(X1,X1),greatest_lower_bound(X2,X2)) = multiply(greatest_lower_bound(X1,X1),X2),
inference(scs_inference,[],[i_0_76,i_0_59,i_0_20,i_0_33,i_0_34]) ).
cnf(i_0_81,plain,
multiply(X1,greatest_lower_bound(X2,X2)) = multiply(greatest_lower_bound(X1,X1),X2),
inference(rename_variables,[],[i_0_76]) ).
cnf(i_0_82,plain,
multiply(least_upper_bound(X1,X1),X2) = multiply(X1,X2),
inference(rename_variables,[],[i_0_59]) ).
cnf(i_0_83,plain,
multiply(greatest_lower_bound(X1,X1),X2) = multiply(least_upper_bound(X1,X1),greatest_lower_bound(X2,X2)),
inference(scs_inference,[],[i_0_80,i_0_33]) ).
cnf(i_0_84,plain,
multiply(greatest_lower_bound(X1,X1),multiply(X2,X3)) = multiply(multiply(X1,X2),X3),
inference(scs_inference,[],[i_0_79,i_0_69,i_0_80,i_0_33,i_0_34]) ).
cnf(i_0_85,plain,
multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3),
inference(rename_variables,[],[i_0_79]) ).
cnf(i_0_86,plain,
multiply(greatest_lower_bound(X1,X1),X2) = multiply(X1,X2),
inference(rename_variables,[],[i_0_69]) ).
cnf(i_0_87,plain,
multiply(multiply(X1,X2),X3) = multiply(greatest_lower_bound(X1,X1),multiply(X2,X3)),
inference(scs_inference,[],[i_0_84,i_0_33]) ).
cnf(i_0_88,plain,
greatest_lower_bound(b,least_upper_bound(a,b)) != multiply(greatest_lower_bound(identity,identity),b),
inference(scs_inference,[],[i_0_83,i_0_84,i_0_77,i_0_33,i_0_34]) ).
cnf(i_0_89,plain,
multiply(greatest_lower_bound(X1,X1),X2) = multiply(least_upper_bound(X1,X1),greatest_lower_bound(X2,X2)),
inference(rename_variables,[],[i_0_83]) ).
cnf(i_0_90,plain,
least_upper_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(X1,least_upper_bound(X2,X3)),
inference(scs_inference,[],[i_0_21,i_0_33]) ).
cnf(i_0_91,plain,
multiply(multiply(X1,X2),greatest_lower_bound(X3,X3)) = multiply(greatest_lower_bound(X1,X1),multiply(X2,X3)),
inference(scs_inference,[],[i_0_87,i_0_73,i_0_21,i_0_33,i_0_34]) ).
cnf(i_0_92,plain,
multiply(multiply(X1,X2),X3) = multiply(greatest_lower_bound(X1,X1),multiply(X2,X3)),
inference(rename_variables,[],[i_0_87]) ).
cnf(i_0_93,plain,
multiply(X1,greatest_lower_bound(X2,X2)) = multiply(X1,X2),
inference(rename_variables,[],[i_0_73]) ).
cnf(i_0_94,plain,
multiply(greatest_lower_bound(X1,X1),multiply(X2,X3)) = multiply(multiply(X1,X2),greatest_lower_bound(X3,X3)),
inference(scs_inference,[],[i_0_91,i_0_33]) ).
cnf(i_0_95,plain,
least_upper_bound(X1,X2) = least_upper_bound(X1,least_upper_bound(X2,least_upper_bound(X1,X2))),
inference(scs_inference,[],[i_0_90,i_0_41,i_0_91,i_0_33,i_0_34]) ).
cnf(i_0_96,plain,
least_upper_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(X1,least_upper_bound(X2,X3)),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_97,plain,
X1 = least_upper_bound(X1,X1),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_98,plain,
least_upper_bound(X1,least_upper_bound(X2,least_upper_bound(X1,X2))) = least_upper_bound(X1,X2),
inference(scs_inference,[],[i_0_95,i_0_33]) ).
cnf(i_0_99,plain,
greatest_lower_bound(b,least_upper_bound(a,b)) != multiply(identity,greatest_lower_bound(b,b)),
inference(scs_inference,[],[i_0_76,i_0_95,i_0_88,i_0_33,i_0_34]) ).
cnf(i_0_100,plain,
multiply(X1,greatest_lower_bound(X2,X2)) = multiply(greatest_lower_bound(X1,X1),X2),
inference(rename_variables,[],[i_0_76]) ).
cnf(i_0_101,plain,
greatest_lower_bound(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)),
inference(scs_inference,[],[i_0_22,i_0_33]) ).
cnf(i_0_102,plain,
greatest_lower_bound(b,least_upper_bound(a,b)) != greatest_lower_bound(multiply(identity,b),multiply(identity,b)),
inference(scs_inference,[],[i_0_62,i_0_22,i_0_88,i_0_33,i_0_34]) ).
cnf(i_0_103,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_104,plain,
X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)),
inference(scs_inference,[],[i_0_24,i_0_33]) ).
cnf(i_0_105,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X1,X2))),
inference(scs_inference,[],[i_0_101,i_0_44,i_0_24,i_0_33,i_0_34]) ).
cnf(i_0_106,plain,
greatest_lower_bound(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)),
inference(rename_variables,[],[i_0_101]) ).
cnf(i_0_107,plain,
X1 = greatest_lower_bound(X1,X1),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_108,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X1,X2))) = greatest_lower_bound(X1,X2),
inference(scs_inference,[],[i_0_105,i_0_33]) ).
cnf(i_0_109,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_69,i_0_105,i_0_99,i_0_33,i_0_34]) ).
cnf(i_0_110,plain,
multiply(greatest_lower_bound(X1,X1),X2) = multiply(X1,X2),
inference(rename_variables,[],[i_0_69]) ).
cnf(i_0_111,plain,
X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)),
inference(scs_inference,[],[i_0_25,i_0_33]) ).
cnf(i_0_112,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_59,i_0_109,i_0_25,i_0_33,i_0_34]) ).
cnf(i_0_113,plain,
multiply(least_upper_bound(X1,X1),X2) = multiply(X1,X2),
inference(rename_variables,[],[i_0_59]) ).
cnf(i_0_114,plain,
identity = multiply(inverse(X1),X1),
inference(scs_inference,[],[i_0_28,i_0_33]) ).
cnf(i_0_115,plain,
greatest_lower_bound(b,least_upper_bound(a,b)) != multiply(identity,least_upper_bound(b,b)),
inference(scs_inference,[],[i_0_60,i_0_28,i_0_18,i_0_33,i_0_34]) ).
cnf(i_0_116,plain,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
inference(rename_variables,[],[i_0_18]) ).
cnf(i_0_117,plain,
least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)),
inference(scs_inference,[],[i_0_18,i_0_33]) ).
cnf(i_0_118,plain,
least_upper_bound(identity,greatest_lower_bound(identity,X1)) = multiply(inverse(X2),X2),
inference(scs_inference,[],[i_0_114,i_0_24,i_0_18,i_0_33,i_0_34]) ).
cnf(i_0_119,plain,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_120,plain,
multiply(inverse(X1),X1) = least_upper_bound(identity,greatest_lower_bound(identity,X2)),
inference(scs_inference,[],[i_0_118,i_0_33]) ).
cnf(i_0_121,plain,
greatest_lower_bound(identity,least_upper_bound(identity,X1)) = multiply(inverse(X2),X2),
inference(scs_inference,[],[i_0_114,i_0_118,i_0_25,i_0_33,i_0_34]) ).
cnf(i_0_122,plain,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
inference(rename_variables,[],[i_0_25]) ).
cnf(i_0_123,plain,
multiply(inverse(X1),X1) = greatest_lower_bound(identity,least_upper_bound(identity,X2)),
inference(scs_inference,[],[i_0_121,i_0_33]) ).
cnf(i_0_124,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(scs_inference,[],[i_0_114,i_0_121,i_0_28,i_0_33,i_0_34]) ).
cnf(i_0_125,plain,
least_upper_bound(identity,identity) = multiply(inverse(X1),X1),
inference(scs_inference,[],[i_0_114,i_0_29,i_0_34]) ).
cnf(i_0_126,plain,
least_upper_bound(X1,X1) = X1,
inference(rename_variables,[],[i_0_29]) ).
cnf(i_0_127,plain,
multiply(inverse(X1),X1) = least_upper_bound(identity,identity),
inference(scs_inference,[],[i_0_114,i_0_29,i_0_34,i_0_33]) ).
cnf(i_0_128,plain,
greatest_lower_bound(identity,identity) = multiply(inverse(X1),X1),
inference(scs_inference,[],[i_0_114,i_0_30,i_0_34]) ).
cnf(i_0_129,plain,
greatest_lower_bound(X1,X1) = X1,
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_130,plain,
multiply(inverse(X1),X1) = greatest_lower_bound(identity,identity),
inference(scs_inference,[],[i_0_114,i_0_30,i_0_34,i_0_33]) ).
cnf(i_0_131,plain,
multiply(identity,identity) = multiply(inverse(X1),X1),
inference(scs_inference,[],[i_0_114,i_0_31,i_0_34]) ).
cnf(i_0_132,plain,
multiply(identity,X1) = X1,
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_133,plain,
multiply(inverse(X1),X1) = multiply(identity,identity),
inference(scs_inference,[],[i_0_114,i_0_31,i_0_34,i_0_33]) ).
cnf(i_0_134,plain,
greatest_lower_bound(b,least_upper_bound(a,b)) != least_upper_bound(b,greatest_lower_bound(b,X1)),
inference(scs_inference,[],[i_0_23,i_0_24,i_0_34]) ).
cnf(i_0_135,plain,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_136,plain,
greatest_lower_bound(b,least_upper_bound(a,b)) != least_upper_bound(greatest_lower_bound(b,X1),b),
inference(scs_inference,[],[i_0_134,i_0_26,i_0_34]) ).
cnf(i_0_137,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_138,plain,
greatest_lower_bound(b,least_upper_bound(a,b)) != least_upper_bound(multiply(identity,greatest_lower_bound(b,X1)),multiply(identity,b)),
inference(scs_inference,[],[i_0_55,i_0_136,i_0_34]) ).
cnf(i_0_139,plain,
least_upper_bound(multiply(identity,X1),multiply(identity,X2)) = least_upper_bound(X1,X2),
inference(rename_variables,[],[i_0_55]) ).
cnf(i_0_140,plain,
greatest_lower_bound(b,least_upper_bound(a,b)) != greatest_lower_bound(b,least_upper_bound(b,X1)),
inference(scs_inference,[],[i_0_23,i_0_25,i_0_34]) ).
cnf(i_0_141,plain,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
inference(rename_variables,[],[i_0_25]) ).
cnf(i_0_142,plain,
$false,
inference(scs_inference,[],[i_0_23,i_0_26,i_0_25,i_0_34,i_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP153-1 : 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
% 0.13/0.32 % Computer : n001.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Mon May 4 18:26:48 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 0.40/1.60 % Version : CSE_E---1.7
% 0.40/1.60 % Problem : theBenchmark.p
% 0.40/1.60 % SZS status Unsatisfiable for theBenchmark.p
% 0.40/1.60 % SZS output start CNFRefutation
% See solution above
% 0.52/1.75 % Total time : 1.270s
%------------------------------------------------------------------------------