%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GEO009-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:26:50 PM UTC 2026
% Result : Unsatisfiable 195.62s 34.42s
% Output : CNFRefutation 195.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 14
% Syntax : Number of clauses : 115 ( 42 unt; 4 nHn; 67 RR)
% Number of literals : 229 ( 14 equ; 121 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-5 aty)
% Number of variables : 344 ( 124 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(identity_for_betweeness,axiom,
( ~ between(X1,X2,X1)
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',identity_for_betweeness) ).
cnf(outer_pasch1,axiom,
( ~ between(X4,X3,X5)
| ~ between(X1,X2,X3)
| between(X1,outer_pasch(X2,X1,X4,X5,X3),X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',outer_pasch1) ).
cnf(identity_for_equidistance,axiom,
( ~ equidistant(X1,X2,X3,X3)
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',identity_for_equidistance) ).
cnf(outer_pasch2,axiom,
( ~ between(X4,X3,X5)
| ~ between(X1,X2,X3)
| between(X5,X2,outer_pasch(X2,X1,X4,X5,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',outer_pasch2) ).
cnf(segment_construction2,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',segment_construction2) ).
cnf(segment_construction1,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',segment_construction1) ).
cnf(transitivity_for_betweeness,axiom,
( ~ between(X2,X4,X3)
| ~ between(X1,X2,X3)
| between(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',transitivity_for_betweeness) ).
cnf(d_between_a_and_e,hypothesis,
between(a,d,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_between_a_and_e) ).
cnf(c_between_a_and_e,hypothesis,
between(a,c,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_between_a_and_e) ).
cnf(c_between_a_and_d,hypothesis,
~ between(a,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_between_a_and_d) ).
cnf(prove_d_between_a_and_c,negated_conjecture,
~ between(a,d,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_d_between_a_and_c) ).
cnf(transitivity_for_equidistance,axiom,
( ~ equidistant(X1,X2,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| equidistant(X3,X4,X5,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',transitivity_for_equidistance) ).
cnf(connectivity_for_betweeness,axiom,
( ~ between(X1,X2,X4)
| ~ between(X1,X2,X3)
| between(X1,X4,X3)
| between(X1,X3,X4)
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',connectivity_for_betweeness) ).
cnf(reflexivity_for_equidistance,axiom,
equidistant(X1,X2,X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',reflexivity_for_equidistance) ).
cnf(c_0_14,plain,
( ~ between(X1,X2,X1)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[identity_for_betweeness]) ).
cnf(c_0_15,plain,
( ~ between(X4,X3,X5)
| ~ between(X1,X2,X3)
| between(X1,outer_pasch(X2,X1,X4,X5,X3),X4) ),
inference(fof_simplification,[status(thm)],[outer_pasch1]) ).
cnf(c_0_16,plain,
( ~ equidistant(X1,X2,X3,X3)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[identity_for_equidistance]) ).
cnf(c_0_17,plain,
( ~ between(X4,X3,X5)
| ~ between(X1,X2,X3)
| between(X5,X2,outer_pasch(X2,X1,X4,X5,X3)) ),
inference(fof_simplification,[status(thm)],[outer_pasch2]) ).
cnf(c_0_18,plain,
( ~ between(X1,X2,X1)
| X1 = X2 ),
c_0_14 ).
cnf(c_0_19,plain,
( ~ between(X4,X3,X5)
| ~ between(X1,X2,X3)
| between(X1,outer_pasch(X2,X1,X4,X5,X3),X4) ),
c_0_15 ).
cnf(c_0_20,plain,
( ~ equidistant(X1,X2,X3,X3)
| X1 = X2 ),
c_0_16 ).
cnf(c_0_21,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
segment_construction2 ).
cnf(c_0_22,plain,
( ~ between(X4,X3,X5)
| ~ between(X1,X2,X3)
| between(X5,X2,outer_pasch(X2,X1,X4,X5,X3)) ),
c_0_17 ).
cnf(c_0_23,plain,
( ~ between(X2,X1,X4)
| ~ between(X2,X4,X3)
| outer_pasch(X1,X2,X2,X3,X4) = X2 ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
segment_construction1 ).
cnf(c_0_25,plain,
extension(X1,X2,X3,X3) = X2,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
( ~ between(X3,X2,X4)
| ~ between(X3,X4,X1)
| between(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
between(X1,X2,X2),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,plain,
( ~ between(X2,X4,X3)
| ~ between(X1,X2,X3)
| between(X1,X2,X4) ),
inference(fof_simplification,[status(thm)],[transitivity_for_betweeness]) ).
cnf(c_0_29,plain,
( ~ between(X3,X2,X1)
| between(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,plain,
( ~ between(X1,X5,X2)
| between(extension(X1,X2,X3,X4),X5,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_24]) ).
cnf(c_0_31,plain,
( ~ between(X2,X4,X3)
| ~ between(X1,X2,X3)
| between(X1,X2,X4) ),
c_0_28 ).
cnf(c_0_32,plain,
( ~ between(X1,X2,X3)
| between(X1,X2,extension(X1,X3,X4,X5)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,hypothesis,
between(a,d,e),
d_between_a_and_e ).
cnf(c_0_34,plain,
( ~ between(X2,X6,X3)
| ~ between(X1,extension(X2,X3,X4,X5),X2)
| between(X1,extension(X2,X3,X4,X5),X6) ),
inference(spm,[status(thm)],[c_0_31,c_0_30]) ).
cnf(c_0_35,hypothesis,
between(a,c,e),
c_between_a_and_e ).
cnf(c_0_36,plain,
( ~ between(X1,X6,X2)
| ~ between(X1,X5,X6)
| between(extension(X1,X2,X3,X4),X5,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_32]) ).
cnf(c_0_37,hypothesis,
between(e,d,a),
inference(spm,[status(thm)],[c_0_29,c_0_33]) ).
cnf(c_0_38,plain,
( ~ between(X4,X3,X2)
| ~ between(X1,X2,X4)
| between(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_25]) ).
cnf(c_0_39,plain,
between(extension(X1,X2,X3,X4),X2,X1),
inference(spm,[status(thm)],[c_0_29,c_0_24]) ).
cnf(c_0_40,hypothesis,
between(e,c,a),
inference(spm,[status(thm)],[c_0_29,c_0_35]) ).
cnf(c_0_41,hypothesis,
( ~ between(e,a,X1)
| between(extension(e,X1,X2,X3),d,e) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,plain,
( ~ between(X1,X5,X2)
| between(extension(X1,X2,X3,X4),X2,X5) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,plain,
( ~ between(X1,X2,extension(X2,X3,X4,X5))
| between(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_31,c_0_24]) ).
cnf(c_0_44,hypothesis,
( ~ between(e,a,X1)
| between(extension(e,X1,X2,X3),c,e) ),
inference(spm,[status(thm)],[c_0_36,c_0_40]) ).
cnf(c_0_45,hypothesis,
( ~ between(e,a,X1)
| between(X1,d,e) ),
inference(spm,[status(thm)],[c_0_41,c_0_25]) ).
cnf(c_0_46,plain,
( ~ between(X3,X1,X2)
| between(X1,X2,extension(X3,X2,X4,X5)) ),
inference(spm,[status(thm)],[c_0_29,c_0_42]) ).
cnf(c_0_47,plain,
between(extension(extension(X1,X2,X3,X4),X1,X5,X6),X1,X2),
inference(spm,[status(thm)],[c_0_43,c_0_39]) ).
cnf(c_0_48,hypothesis,
( ~ between(e,a,X1)
| between(X1,c,e) ),
inference(spm,[status(thm)],[c_0_44,c_0_25]) ).
cnf(c_0_49,plain,
( ~ between(X1,X6,X3)
| ~ between(extension(X1,X3,X4,X5),X2,X6)
| between(X1,X2,extension(X1,X3,X4,X5)) ),
inference(spm,[status(thm)],[c_0_26,c_0_30]) ).
cnf(c_0_50,hypothesis,
( ~ between(X1,e,a)
| between(extension(X1,a,X2,X3),d,e) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,plain,
between(X1,X2,extension(extension(X2,X1,X3,X4),X2,X5,X6)),
inference(spm,[status(thm)],[c_0_29,c_0_47]) ).
cnf(c_0_52,hypothesis,
( ~ between(X1,e,a)
| between(extension(X1,a,X2,X3),c,e) ),
inference(spm,[status(thm)],[c_0_48,c_0_46]) ).
cnf(c_0_53,hypothesis,
( ~ between(e,a,X1)
| between(e,d,extension(e,X1,X2,X3)) ),
inference(spm,[status(thm)],[c_0_29,c_0_41]) ).
cnf(c_0_54,hypothesis,
( ~ between(X1,e,a)
| between(X1,d,extension(X1,a,X2,X3)) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_55,hypothesis,
between(extension(extension(a,e,X1,X2),a,X3,X4),c,e),
inference(spm,[status(thm)],[c_0_48,c_0_51]) ).
cnf(c_0_56,hypothesis,
( ~ between(e,a,X1)
| between(e,c,extension(e,X1,X2,X3)) ),
inference(spm,[status(thm)],[c_0_29,c_0_44]) ).
cnf(c_0_57,hypothesis,
( ~ between(X1,e,a)
| between(X1,c,extension(X1,a,X2,X3)) ),
inference(spm,[status(thm)],[c_0_49,c_0_52]) ).
cnf(c_0_58,hypothesis,
between(extension(extension(a,e,X1,X2),a,X3,X4),d,e),
inference(spm,[status(thm)],[c_0_45,c_0_51]) ).
cnf(c_0_59,hypothesis,
( ~ between(e,a,X1)
| between(e,d,X1) ),
inference(spm,[status(thm)],[c_0_53,c_0_25]) ).
cnf(c_0_60,hypothesis,
( ~ between(X1,e,a)
| ~ between(extension(X1,a,X3,X4),X2,d)
| between(X1,d,X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_54]) ).
cnf(c_0_61,hypothesis,
( ~ between(e,X5,c)
| between(extension(extension(a,e,X1,X2),a,X3,X4),c,X5) ),
inference(spm,[status(thm)],[c_0_38,c_0_55]) ).
cnf(c_0_62,hypothesis,
~ between(a,c,d),
inference(fof_simplification,[status(thm)],[c_between_a_and_d]) ).
cnf(c_0_63,hypothesis,
( ~ between(e,a,X1)
| between(e,c,X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_25]) ).
cnf(c_0_64,hypothesis,
( ~ between(X1,e,a)
| ~ between(extension(X1,a,X3,X4),X2,c)
| between(X1,c,X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_57]) ).
cnf(c_0_65,hypothesis,
( ~ between(e,X5,d)
| between(extension(extension(a,e,X1,X2),a,X3,X4),d,X5) ),
inference(spm,[status(thm)],[c_0_38,c_0_58]) ).
cnf(c_0_66,negated_conjecture,
~ between(a,d,c),
inference(fof_simplification,[status(thm)],[prove_d_between_a_and_c]) ).
cnf(c_0_67,hypothesis,
( ~ between(X1,a,e)
| between(X1,a,d) ),
inference(spm,[status(thm)],[c_0_31,c_0_33]) ).
cnf(c_0_68,hypothesis,
( ~ between(X2,X1,d)
| ~ between(e,a,X2)
| between(e,d,X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_59]) ).
cnf(c_0_69,hypothesis,
( ~ between(X1,e,a)
| between(extension(X1,a,X2,X3),c,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_57]) ).
cnf(c_0_70,plain,
( ~ between(X1,X2,X4)
| ~ between(extension(X1,X4,X5,X6),X3,X2)
| between(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_38,c_0_32]) ).
cnf(c_0_71,hypothesis,
( ~ between(e,d,c)
| between(extension(a,e,X1,X2),d,c) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_39])]) ).
cnf(c_0_72,hypothesis,
~ between(a,c,d),
c_0_62 ).
cnf(c_0_73,hypothesis,
( ~ between(X2,X1,c)
| ~ between(e,a,X2)
| between(e,c,X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_63]) ).
cnf(c_0_74,hypothesis,
( ~ between(X1,e,a)
| between(extension(X1,a,X2,X3),d,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_54]) ).
cnf(c_0_75,hypothesis,
( ~ between(e,c,d)
| between(extension(a,e,X1,X2),c,d) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_39])]) ).
cnf(c_0_76,negated_conjecture,
~ between(a,d,c),
c_0_66 ).
cnf(c_0_77,hypothesis,
( ~ between(e,a,X1)
| between(extension(e,X1,X2,X3),a,d) ),
inference(spm,[status(thm)],[c_0_67,c_0_30]) ).
cnf(c_0_78,hypothesis,
( ~ between(X2,e,a)
| ~ between(extension(X2,a,X3,X4),X1,d)
| between(e,d,X1) ),
inference(spm,[status(thm)],[c_0_68,c_0_46]) ).
cnf(c_0_79,hypothesis,
( ~ between(X1,X4,c)
| ~ between(X1,e,a)
| between(extension(X1,a,X2,X3),c,X4) ),
inference(spm,[status(thm)],[c_0_38,c_0_69]) ).
cnf(c_0_80,hypothesis,
~ between(e,d,c),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_35])]),c_0_72]) ).
cnf(c_0_81,hypothesis,
( ~ between(X2,e,a)
| ~ between(extension(X2,a,X3,X4),X1,c)
| between(e,c,X1) ),
inference(spm,[status(thm)],[c_0_73,c_0_46]) ).
cnf(c_0_82,hypothesis,
( ~ between(X1,X4,d)
| ~ between(X1,e,a)
| between(extension(X1,a,X2,X3),d,X4) ),
inference(spm,[status(thm)],[c_0_38,c_0_74]) ).
cnf(c_0_83,hypothesis,
~ between(e,c,d),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_75]),c_0_33])]),c_0_76]) ).
cnf(c_0_84,plain,
( ~ equidistant(X1,X2,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| equidistant(X3,X4,X5,X6) ),
inference(fof_simplification,[status(thm)],[transitivity_for_equidistance]) ).
cnf(c_0_85,plain,
( ~ between(X1,X2,X4)
| ~ between(X1,X2,X3)
| between(X1,X4,X3)
| between(X1,X3,X4)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[connectivity_for_betweeness]) ).
cnf(c_0_86,hypothesis,
( ~ between(X1,a,e)
| between(X1,a,c) ),
inference(spm,[status(thm)],[c_0_31,c_0_35]) ).
cnf(c_0_87,hypothesis,
( ~ between(e,a,X2)
| ~ between(extension(e,X2,X3,X4),X1,a)
| between(d,X1,extension(e,X2,X3,X4)) ),
inference(spm,[status(thm)],[c_0_26,c_0_77]) ).
cnf(c_0_88,hypothesis,
( ~ between(X1,d,c)
| ~ between(X1,e,a) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80]) ).
cnf(c_0_89,hypothesis,
( ~ between(X1,c,d)
| ~ between(X1,e,a) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83]) ).
cnf(c_0_90,plain,
( ~ equidistant(X1,X2,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| equidistant(X3,X4,X5,X6) ),
c_0_84 ).
cnf(c_0_91,axiom,
equidistant(X1,X2,X2,X1),
reflexivity_for_equidistance ).
cnf(c_0_92,plain,
( ~ between(X1,X2,X4)
| ~ between(X1,X2,X3)
| between(X1,X4,X3)
| between(X1,X3,X4)
| X1 = X2 ),
c_0_85 ).
cnf(c_0_93,hypothesis,
between(extension(e,a,X1,X2),a,c),
inference(spm,[status(thm)],[c_0_86,c_0_39]) ).
cnf(c_0_94,hypothesis,
( ~ between(e,a,X1)
| between(d,X1,extension(e,X1,X2,X3)) ),
inference(spm,[status(thm)],[c_0_87,c_0_42]) ).
cnf(c_0_95,hypothesis,
~ between(extension(extension(e,a,X1,X2),e,X3,X4),d,c),
inference(spm,[status(thm)],[c_0_88,c_0_47]) ).
cnf(c_0_96,plain,
( ~ between(X1,X5,X2)
| ~ between(X1,X6,X5)
| between(extension(X1,X2,X3,X4),X5,X6) ),
inference(spm,[status(thm)],[c_0_38,c_0_30]) ).
cnf(c_0_97,hypothesis,
between(extension(e,a,X1,X2),d,e),
inference(spm,[status(thm)],[c_0_45,c_0_24]) ).
cnf(c_0_98,hypothesis,
~ between(extension(extension(e,a,X1,X2),e,X3,X4),c,d),
inference(spm,[status(thm)],[c_0_89,c_0_47]) ).
cnf(c_0_99,hypothesis,
between(extension(e,a,X1,X2),c,e),
inference(spm,[status(thm)],[c_0_48,c_0_24]) ).
cnf(c_0_100,plain,
( ~ equidistant(X4,X3,X1,X2)
| equidistant(X1,X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_101,hypothesis,
( ~ between(extension(e,a,X1,X2),a,X3)
| between(extension(e,a,X1,X2),X3,c)
| between(extension(e,a,X1,X2),c,X3)
| extension(e,a,X1,X2) = a ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_102,hypothesis,
( ~ between(d,X4,X1)
| ~ between(e,a,X1)
| between(extension(e,X1,X2,X3),X4,d) ),
inference(spm,[status(thm)],[c_0_26,c_0_94]) ).
cnf(c_0_103,hypothesis,
~ between(extension(e,a,X1,X2),c,d),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97])]) ).
cnf(c_0_104,hypothesis,
~ between(extension(e,a,X1,X2),d,c),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_96]),c_0_99])]) ).
cnf(c_0_105,hypothesis,
( ~ between(a,e,X1)
| between(extension(a,X1,X2,X3),c,a) ),
inference(spm,[status(thm)],[c_0_36,c_0_35]) ).
cnf(c_0_106,plain,
equidistant(X1,X2,extension(X3,X4,X1,X2),X4),
inference(spm,[status(thm)],[c_0_100,c_0_21]) ).
cnf(c_0_107,hypothesis,
extension(e,a,X1,X2) = a,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_27]),c_0_27])]),c_0_103]),c_0_104]) ).
cnf(c_0_108,hypothesis,
( ~ between(a,e,X1)
| between(X1,c,a) ),
inference(spm,[status(thm)],[c_0_105,c_0_25]) ).
cnf(c_0_109,hypothesis,
equidistant(X1,X2,a,a),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_110,hypothesis,
between(extension(a,e,X1,X2),c,a),
inference(spm,[status(thm)],[c_0_108,c_0_24]) ).
cnf(c_0_111,hypothesis,
X1 = X2,
inference(spm,[status(thm)],[c_0_20,c_0_109]) ).
cnf(c_0_112,hypothesis,
between(a,c,extension(a,e,X1,X2)),
inference(spm,[status(thm)],[c_0_29,c_0_110]) ).
cnf(c_0_113,hypothesis,
~ between(a,c,X1),
inference(spm,[status(thm)],[c_0_72,c_0_111]) ).
cnf(c_0_114,hypothesis,
$false,
inference(sr,[status(thm)],[c_0_112,c_0_113]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO009-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.54 % Computer : n016.cluster.edu
% 0.11/0.54 % Model : x86_64 x86_64
% 0.11/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.54 % Memory : 8046.5625MB
% 0.11/0.54 % OS : Linux 6.8.0-71-generic
% 0.11/0.54 % CPULimit : 300
% 0.11/0.54 % WCLimit : 300
% 0.11/0.54 % DateTime : Sun Sep 20 08:19:36 UTC 2026
% 0.11/0.54 % CPUTime :
% 0.11/0.54 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.58 Running first-order theorem proving
% 0.15/0.58 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 195.62/34.42 % Version: 3.5.1
% 195.62/34.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 195.62/34.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 195.62/34.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 195.62/34.42 % Starting new_bool_3 with 300s (1) cores
% 195.62/34.42 % Starting new_bool_1 with 300s (1) cores
% 195.62/34.42 % Starting sh5l with 300s (1) cores
% 195.62/34.42 % new_bool_3 with pid 4090347 completed with status 9
% 195.62/34.42 % new_bool_1 with pid 4090348 completed with status 9
% 195.62/34.42 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 4090346 completed with status 0
% 195.62/34.42 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 195.62/34.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 195.62/34.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 195.62/34.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 195.62/34.42 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 195.62/34.42 % No SInE strategy applied
% 195.62/34.42 % Search class: FGUSS-FFMF33-SFFFFFNN
% 195.62/34.42 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 195.62/34.42 % Starting SubtermCWHack with 136s (1) cores
% 195.62/34.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 195.62/34.42 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S4c with 136s (1) cores
% 195.62/34.42 % Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 195.62/34.42 % Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 195.62/34.42 % SubtermCWHack with pid 4090350 completed with status 0
% 195.62/34.42 % Result found by SubtermCWHack
% 195.62/34.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 195.62/34.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 195.62/34.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 195.62/34.42 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 195.62/34.42 % No SInE strategy applied
% 195.62/34.42 % Search class: FGUSS-FFMF33-SFFFFFNN
% 195.62/34.42 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 195.62/34.42 % Starting SubtermCWHack with 136s (1) cores
% 195.62/34.42 % Preprocessing time : 0.001 s
% 195.62/34.42
% 195.62/34.42 % Proof found!
% 195.62/34.42 % SZS status Unsatisfiable
% 195.62/34.42 % SZS output start CNFRefutation
% See solution above
% 195.62/34.42 % Parsed axioms : 24
% 195.62/34.42 % Removed by relevancy pruning/SinE : 0
% 195.62/34.42 % Initial clauses : 24
% 195.62/34.42 % Removed in clause preprocessing : 0
% 195.62/34.42 % Initial clauses in saturation : 24
% 195.62/34.42 % Processed clauses : 48095
% 195.62/34.42 % ...of these trivial : 307
% 195.62/34.42 % ...subsumed : 41110
% 195.62/34.42 % ...remaining for further processing : 6678
% 195.62/34.42 % Other redundant clauses eliminated : 0
% 195.62/34.42 % Clauses deleted for lack of memory : 0
% 195.62/34.42 % Backward-subsumed : 3075
% 195.62/34.42 % Backward-rewritten : 453
% 195.62/34.42 % Generated clauses : 911188
% 195.62/34.42 % ...of the previous two non-redundant : 830824
% 195.62/34.42 % ...aggressively subsumed : 0
% 195.62/34.42 % Contextual simplify-reflections : 16
% 195.62/34.42 % Paramodulations : 911180
% 195.62/34.42 % Factorizations : 2
% 195.62/34.42 % NegExts : 0
% 195.62/34.42 % Equation resolutions : 0
% 195.62/34.42 % Disequality decompositions : 0
% 195.62/34.42 % Total rewrite steps : 491199
% 195.62/34.42 % ...of those cached : 484389
% 195.62/34.42 % Propositional unsat checks : 0
% 195.62/34.42 % Propositional check models : 0
% 195.62/34.42 % Propositional check unsatisfiable : 0
% 195.62/34.42 % Propositional clauses : 0
% 195.62/34.42 % Propositional clauses after purity: 0
% 195.62/34.42 % Propositional unsat core size : 0
% 195.62/34.42 % Propositional preprocessing time : 0.000
% 195.62/34.42 % Propositional encoding time : 0.000
% 195.62/34.42 % Propositional solver time : 0.000
% 195.62/34.42 % Success case prop preproc time : 0.000
% 195.62/34.42 % Success case prop encoding time : 0.000
% 195.62/34.42 % Success case prop solver time : 0.000
% 195.62/34.42 % Current number of processed clauses : 3144
% 195.62/34.42 % Positive orientable unit clauses : 231
% 195.62/34.42 % Positive unorientable unit clauses: 1
% 195.62/34.42 % Negative unit clauses : 163
% 195.62/34.42 % Non-unit-clauses : 2749
% 195.62/34.42 % Current number of unprocessed clauses: 779770
% 195.62/34.42 % ...number of literals in the above : 4363876
% 195.62/34.42 % Current number of archived formulas : 0
% 195.62/34.42 % Current number of archived clauses : 3534
% 195.62/34.42 % Clause-clause subsumption calls (NU) : 14033339
% 195.62/34.42 % Rec. Clause-clause subsumption calls : 3885591
% 195.62/34.42 % Non-unit clause-clause subsumptions : 21239
% 195.62/34.42 % Unit Clause-clause subsumption calls : 499176
% 195.62/34.42 % Rewrite failures with RHS unbound : 3716
% 195.62/34.42 % BW rewrite match attempts : 65519
% 195.62/34.42 % BW rewrite match successes : 3684
% 195.62/34.42 % Condensation attempts : 0
% 195.62/34.42 % Condensation successes : 0
% 195.62/34.42 % Termbank termtop insertions : 21014425
% 195.62/34.42 % Search garbage collected termcells : 82
% 195.62/34.42
% 195.62/34.42 % -------------------------------------------------
% 195.62/34.42 % User time : 32.264 s
% 195.62/34.42 % System time : 0.806 s
% 195.62/34.42 % Total time : 33.070 s
% 195.62/34.42 % Maximum resident set size: 3656 pages
% 195.62/34.42
% 195.62/34.42 % -------------------------------------------------
% 195.62/34.42 % User time : 162.249 s
% 195.62/34.42 % System time : 5.126 s
% 195.62/34.42 % Total time : 167.374 s
% 195.62/34.42 % Maximum resident set size: 4864 pages
% 195.62/34.42 % E exiting
%------------------------------------------------------------------------------