%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GEO012-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 12:26:52 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.60s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 26
% Syntax : Number of clauses : 177 ( 24 unt; 74 nHn; 173 RR)
% Number of literals : 462 ( 27 equ; 190 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 246 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t10_1,axiom,
( ~ colinear(X1,X2,X3)
| colinear(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_1) ).
cnf(colinearity4,axiom,
( ~ colinear(X1,X2,X3)
| between(X3,X1,X2)
| between(X2,X3,X1)
| between(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-1.ax',colinearity4) ).
cnf(abd_colinear,hypothesis,
colinear(a,b,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abd_colinear) ).
cnf(abc_colinear,hypothesis,
colinear(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abc_colinear) ).
cnf(prove_colinearity,negated_conjecture,
( ~ colinear(b,c,d)
| ~ colinear(a,c,d) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_colinearity) ).
cnf(colinearity3,axiom,
( ~ between(X1,X2,X3)
| colinear(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-1.ax',colinearity3) ).
cnf(t8,axiom,
( ~ between(X1,X5,X3)
| ~ between(X2,X4,X5)
| ~ between(X1,X2,X3)
| between(X1,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8) ).
cnf(t1,axiom,
( ~ between(X1,X2,X3)
| between(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1) ).
cnf(b6,axiom,
( ~ between(X2,X3,X4)
| ~ between(X1,X2,X3)
| X2 = X3
| between(X1,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b6) ).
cnf(a_not_b,hypothesis,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_b) ).
cnf(t2,axiom,
between(X1,X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2) ).
cnf(b2,axiom,
( ~ between(X2,X1,X3)
| ~ between(X1,X2,X3)
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b2) ).
cnf(colinearity2,axiom,
( ~ between(X1,X2,X3)
| colinear(X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-1.ax',colinearity2) ).
cnf(b9,axiom,
( ~ between(X1,X3,X4)
| ~ between(X1,X2,X3)
| between(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b9) ).
cnf(b5,axiom,
( ~ between(X1,X3,X4)
| ~ between(X1,X2,X3)
| between(X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b5) ).
cnf(t10_4,axiom,
( ~ colinear(X1,X2,X3)
| colinear(X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_4) ).
cnf(c2_3,axiom,
( ~ between(X1,X2,X3)
| colinear(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c2_3) ).
cnf(c2_1,axiom,
( ~ between(X1,X2,X3)
| colinear(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c2_1) ).
cnf(t7,axiom,
( ~ between(X4,X2,X3)
| ~ between(X1,X2,X3)
| between(X4,X1,X2)
| between(X1,X4,X2)
| X2 = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7) ).
cnf(c2_2,axiom,
( ~ between(X1,X2,X3)
| colinear(X1,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c2_2) ).
cnf(t9,axiom,
( ~ between(X1,X4,X3)
| ~ between(X1,X2,X3)
| between(X1,X4,X2)
| between(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9) ).
cnf(colinearity1,axiom,
( ~ between(X1,X2,X3)
| colinear(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-1.ax',colinearity1) ).
cnf(b8,axiom,
( ~ between(X2,X4,X3)
| ~ between(X1,X2,X3)
| between(X1,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b8) ).
cnf(b7,axiom,
( ~ between(X2,X3,X4)
| ~ between(X1,X2,X3)
| X2 = X3
| between(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b7) ).
cnf(b3,axiom,
( ~ between(X1,X3,X2)
| ~ between(X1,X2,X3)
| X2 = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b3) ).
cnf(t3,axiom,
between(X1,X2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3) ).
cnf(c_0_26,plain,
( ~ colinear(X1,X2,X3)
| colinear(X3,X2,X1) ),
inference(fof_simplification,[status(thm)],[t10_1]) ).
cnf(c_0_27,plain,
( ~ colinear(X1,X2,X3)
| between(X3,X1,X2)
| between(X2,X3,X1)
| between(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[colinearity4]) ).
cnf(c_0_28,plain,
( ~ colinear(X1,X2,X3)
| colinear(X3,X2,X1) ),
c_0_26 ).
cnf(c_0_29,hypothesis,
colinear(a,b,d),
abd_colinear ).
cnf(c_0_30,hypothesis,
colinear(a,b,c),
abc_colinear ).
cnf(c_0_31,negated_conjecture,
( ~ colinear(b,c,d)
| ~ colinear(a,c,d) ),
inference(fof_simplification,[status(thm)],[prove_colinearity]) ).
cnf(c_0_32,plain,
( ~ between(X1,X2,X3)
| colinear(X2,X3,X1) ),
inference(fof_simplification,[status(thm)],[colinearity3]) ).
cnf(c_0_33,plain,
( ~ between(X1,X5,X3)
| ~ between(X2,X4,X5)
| ~ between(X1,X2,X3)
| between(X1,X4,X3) ),
inference(fof_simplification,[status(thm)],[t8]) ).
cnf(c_0_34,plain,
( ~ colinear(X1,X2,X3)
| between(X3,X1,X2)
| between(X2,X3,X1)
| between(X1,X2,X3) ),
c_0_27 ).
cnf(c_0_35,hypothesis,
colinear(d,b,a),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,plain,
( ~ between(X1,X2,X3)
| between(X3,X2,X1) ),
inference(fof_simplification,[status(thm)],[t1]) ).
cnf(c_0_37,hypothesis,
colinear(c,b,a),
inference(spm,[status(thm)],[c_0_28,c_0_30]) ).
cnf(c_0_38,negated_conjecture,
( ~ colinear(b,c,d)
| ~ colinear(a,c,d) ),
c_0_31 ).
cnf(c_0_39,plain,
( ~ between(X1,X2,X3)
| colinear(X2,X3,X1) ),
c_0_32 ).
cnf(c_0_40,plain,
( ~ between(X1,X5,X3)
| ~ between(X2,X4,X5)
| ~ between(X1,X2,X3)
| between(X1,X4,X3) ),
c_0_33 ).
cnf(c_0_41,hypothesis,
( between(d,b,a)
| between(b,a,d)
| between(a,d,b) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_42,plain,
( ~ between(X2,X3,X4)
| ~ between(X1,X2,X3)
| X2 = X3
| between(X1,X3,X4) ),
inference(fof_simplification,[status(thm)],[b6]) ).
cnf(c_0_43,plain,
( ~ between(X1,X2,X3)
| between(X3,X2,X1) ),
c_0_36 ).
cnf(c_0_44,hypothesis,
( between(c,b,a)
| between(b,a,c)
| between(a,c,b) ),
inference(spm,[status(thm)],[c_0_34,c_0_37]) ).
cnf(c_0_45,hypothesis,
a != b,
inference(fof_simplification,[status(thm)],[a_not_b]) ).
cnf(c_0_46,negated_conjecture,
( ~ between(d,b,c)
| ~ colinear(a,c,d) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_47,hypothesis,
( ~ between(X1,d,X2)
| ~ between(X1,a,X2)
| between(X1,b,X2)
| between(a,d,b)
| between(b,a,d) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_48,axiom,
between(X1,X1,X2),
t2 ).
cnf(c_0_49,plain,
( ~ between(X2,X3,X4)
| ~ between(X1,X2,X3)
| X2 = X3
| between(X1,X3,X4) ),
c_0_42 ).
cnf(c_0_50,hypothesis,
( between(a,b,c)
| between(a,c,b)
| between(b,a,c) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_51,hypothesis,
a != b,
c_0_45 ).
cnf(c_0_52,negated_conjecture,
( ~ between(d,a,c)
| ~ between(d,b,c) ),
inference(spm,[status(thm)],[c_0_46,c_0_39]) ).
cnf(c_0_53,hypothesis,
( ~ between(d,a,X1)
| between(d,b,X1)
| between(b,a,d)
| between(a,d,b) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_54,plain,
( ~ between(X2,X1,X3)
| ~ between(X1,X2,X3)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[b2]) ).
cnf(c_0_55,hypothesis,
( ~ between(X1,b,a)
| between(X1,a,c)
| between(a,c,b)
| between(a,b,c) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).
cnf(c_0_56,negated_conjecture,
( ~ between(d,a,c)
| between(a,d,b)
| between(b,a,d) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_57,plain,
( ~ between(X1,X2,X3)
| colinear(X3,X1,X2) ),
inference(fof_simplification,[status(thm)],[colinearity2]) ).
cnf(c_0_58,plain,
( ~ between(X1,X3,X4)
| ~ between(X1,X2,X3)
| between(X1,X2,X4) ),
inference(fof_simplification,[status(thm)],[b9]) ).
cnf(c_0_59,plain,
( ~ between(X1,X3,X4)
| ~ between(X1,X2,X3)
| between(X2,X3,X4) ),
inference(fof_simplification,[status(thm)],[b5]) ).
cnf(c_0_60,plain,
( ~ between(X2,X1,X3)
| ~ between(X1,X2,X3)
| X1 = X2 ),
c_0_54 ).
cnf(c_0_61,hypothesis,
( between(a,b,c)
| between(a,c,b)
| between(a,d,b)
| between(b,a,d) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_41]),c_0_56]) ).
cnf(c_0_62,plain,
( ~ colinear(X1,X2,X3)
| colinear(X3,X1,X2) ),
inference(fof_simplification,[status(thm)],[t10_4]) ).
cnf(c_0_63,plain,
( ~ between(X1,X2,X3)
| colinear(X3,X1,X2) ),
c_0_57 ).
cnf(c_0_64,plain,
( ~ between(X1,X2,X3)
| colinear(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c2_3]) ).
cnf(c_0_65,plain,
( ~ between(X1,X3,X4)
| ~ between(X1,X2,X3)
| between(X1,X2,X4) ),
c_0_58 ).
cnf(c_0_66,plain,
( ~ between(X1,X3,X4)
| ~ between(X1,X2,X3)
| between(X2,X3,X4) ),
c_0_59 ).
cnf(c_0_67,hypothesis,
( ~ between(a,b,d)
| between(a,d,b)
| between(a,c,b)
| between(a,b,c) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_51]) ).
cnf(c_0_68,plain,
( ~ colinear(X1,X2,X3)
| colinear(X3,X1,X2) ),
c_0_62 ).
cnf(c_0_69,negated_conjecture,
( ~ between(c,d,b)
| ~ colinear(a,c,d) ),
inference(spm,[status(thm)],[c_0_38,c_0_63]) ).
cnf(c_0_70,plain,
( ~ between(X1,X2,X3)
| colinear(X2,X1,X3) ),
c_0_64 ).
cnf(c_0_71,hypothesis,
( ~ between(b,X1,a)
| between(b,X1,c)
| between(a,c,b)
| between(a,b,c) ),
inference(spm,[status(thm)],[c_0_65,c_0_50]) ).
cnf(c_0_72,hypothesis,
( ~ between(b,X1,a)
| between(X1,a,c)
| between(a,c,b)
| between(a,b,c) ),
inference(spm,[status(thm)],[c_0_66,c_0_50]) ).
cnf(c_0_73,hypothesis,
( ~ between(a,b,d)
| between(b,d,a)
| between(a,b,c)
| between(a,c,b) ),
inference(spm,[status(thm)],[c_0_43,c_0_67]) ).
cnf(c_0_74,hypothesis,
colinear(d,a,b),
inference(spm,[status(thm)],[c_0_68,c_0_29]) ).
cnf(c_0_75,negated_conjecture,
( ~ between(c,a,d)
| ~ between(c,d,b) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_76,hypothesis,
( ~ between(b,X1,a)
| between(c,X1,b)
| between(a,b,c)
| between(a,c,b) ),
inference(spm,[status(thm)],[c_0_43,c_0_71]) ).
cnf(c_0_77,hypothesis,
( ~ between(a,b,d)
| between(a,b,c)
| between(a,c,b)
| between(d,a,c) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_78,hypothesis,
( between(d,a,b)
| between(a,b,d)
| between(b,d,a) ),
inference(spm,[status(thm)],[c_0_34,c_0_74]) ).
cnf(c_0_79,negated_conjecture,
( ~ between(b,d,a)
| ~ between(c,a,d)
| between(a,c,b)
| between(a,b,c) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_80,hypothesis,
( ~ between(a,b,d)
| between(c,a,d)
| between(a,c,b)
| between(a,b,c) ),
inference(spm,[status(thm)],[c_0_43,c_0_77]) ).
cnf(c_0_81,hypothesis,
( between(b,a,d)
| between(b,d,a)
| between(a,b,d) ),
inference(spm,[status(thm)],[c_0_43,c_0_78]) ).
cnf(c_0_82,negated_conjecture,
( ~ between(a,b,d)
| between(a,b,c)
| between(a,c,b) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_73]) ).
cnf(c_0_83,hypothesis,
( between(a,b,c)
| between(a,c,b)
| between(d,a,c)
| between(b,a,d) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_81]),c_0_82]) ).
cnf(c_0_84,hypothesis,
( between(c,a,d)
| between(b,a,d)
| between(a,c,b)
| between(a,b,c) ),
inference(spm,[status(thm)],[c_0_43,c_0_83]) ).
cnf(c_0_85,plain,
( ~ between(X1,X2,X3)
| colinear(X3,X2,X1) ),
inference(fof_simplification,[status(thm)],[c2_1]) ).
cnf(c_0_86,negated_conjecture,
( ~ between(b,d,a)
| between(a,b,c)
| between(a,c,b)
| between(b,a,d) ),
inference(spm,[status(thm)],[c_0_79,c_0_84]) ).
cnf(c_0_87,plain,
( ~ between(X1,X2,X3)
| colinear(X3,X2,X1) ),
c_0_85 ).
cnf(c_0_88,hypothesis,
( between(b,a,d)
| between(a,c,b)
| between(a,b,c) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_81]),c_0_82]) ).
cnf(c_0_89,plain,
( ~ between(X4,X2,X3)
| ~ between(X1,X2,X3)
| between(X4,X1,X2)
| between(X1,X4,X2)
| X2 = X3 ),
inference(fof_simplification,[status(thm)],[t7]) ).
cnf(c_0_90,negated_conjecture,
( ~ between(d,c,b)
| ~ colinear(a,c,d) ),
inference(spm,[status(thm)],[c_0_38,c_0_87]) ).
cnf(c_0_91,hypothesis,
( between(d,a,b)
| between(a,b,c)
| between(a,c,b) ),
inference(spm,[status(thm)],[c_0_43,c_0_88]) ).
cnf(c_0_92,hypothesis,
( between(c,a,b)
| between(a,c,b)
| between(a,b,c) ),
inference(spm,[status(thm)],[c_0_43,c_0_50]) ).
cnf(c_0_93,plain,
( ~ between(X4,X2,X3)
| ~ between(X1,X2,X3)
| between(X4,X1,X2)
| between(X1,X4,X2)
| X2 = X3 ),
c_0_89 ).
cnf(c_0_94,negated_conjecture,
( ~ between(d,c,a)
| ~ between(d,c,b) ),
inference(spm,[status(thm)],[c_0_90,c_0_87]) ).
cnf(c_0_95,hypothesis,
( ~ between(d,X1,a)
| between(d,X1,b)
| between(a,c,b)
| between(a,b,c) ),
inference(spm,[status(thm)],[c_0_65,c_0_91]) ).
cnf(c_0_96,negated_conjecture,
( ~ between(c,d,a)
| ~ between(c,d,b) ),
inference(spm,[status(thm)],[c_0_69,c_0_63]) ).
cnf(c_0_97,hypothesis,
( ~ between(c,X1,a)
| between(c,X1,b)
| between(a,b,c)
| between(a,c,b) ),
inference(spm,[status(thm)],[c_0_65,c_0_92]) ).
cnf(c_0_98,hypothesis,
( between(a,b,d)
| between(a,d,b)
| between(b,a,d) ),
inference(spm,[status(thm)],[c_0_43,c_0_41]) ).
cnf(c_0_99,plain,
( ~ between(X1,X2,X3)
| colinear(X1,X3,X2) ),
inference(fof_simplification,[status(thm)],[c2_2]) ).
cnf(c_0_100,plain,
( ~ between(X1,X4,X3)
| ~ between(X1,X2,X3)
| between(X1,X4,X2)
| between(X1,X2,X4) ),
inference(fof_simplification,[status(thm)],[t9]) ).
cnf(c_0_101,hypothesis,
( ~ between(X1,a,b)
| between(X1,c,a)
| between(c,X1,a)
| between(a,b,c)
| between(a,c,b) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_92]),c_0_51]) ).
cnf(c_0_102,negated_conjecture,
( ~ between(d,c,a)
| between(a,b,c)
| between(a,c,b) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_103,negated_conjecture,
( ~ between(c,d,a)
| between(a,c,b)
| between(a,b,c) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_104,plain,
( ~ between(X1,X2,X3)
| colinear(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[colinearity1]) ).
cnf(c_0_105,hypothesis,
( ~ between(b,X1,a)
| between(b,X1,d)
| between(a,d,b)
| between(a,b,d) ),
inference(spm,[status(thm)],[c_0_65,c_0_98]) ).
cnf(c_0_106,plain,
( ~ between(X1,X2,X3)
| colinear(X1,X3,X2) ),
c_0_99 ).
cnf(c_0_107,plain,
( ~ between(X1,X4,X3)
| ~ between(X1,X2,X3)
| between(X1,X4,X2)
| between(X1,X2,X4) ),
c_0_100 ).
cnf(c_0_108,hypothesis,
( between(a,c,b)
| between(a,b,c) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_91]),c_0_102]),c_0_103]) ).
cnf(c_0_109,plain,
( ~ between(X1,X2,X3)
| colinear(X1,X2,X3) ),
c_0_104 ).
cnf(c_0_110,negated_conjecture,
( ~ between(c,a,d)
| ~ between(d,c,b) ),
inference(spm,[status(thm)],[c_0_90,c_0_70]) ).
cnf(c_0_111,hypothesis,
( ~ between(b,X1,a)
| between(d,X1,b)
| between(a,b,d)
| between(a,d,b) ),
inference(spm,[status(thm)],[c_0_43,c_0_105]) ).
cnf(c_0_112,hypothesis,
( ~ between(b,X1,a)
| between(X1,a,d)
| between(a,d,b)
| between(a,b,d) ),
inference(spm,[status(thm)],[c_0_66,c_0_98]) ).
cnf(c_0_113,negated_conjecture,
( ~ between(b,d,c)
| ~ colinear(a,c,d) ),
inference(spm,[status(thm)],[c_0_38,c_0_106]) ).
cnf(c_0_114,hypothesis,
( ~ between(b,X1,a)
| between(b,X1,d)
| between(b,d,X1)
| between(a,b,d) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_81]),c_0_65]) ).
cnf(c_0_115,hypothesis,
( between(b,c,a)
| between(a,b,c) ),
inference(spm,[status(thm)],[c_0_43,c_0_108]) ).
cnf(c_0_116,negated_conjecture,
( ~ between(b,c,d)
| ~ colinear(a,c,d) ),
inference(spm,[status(thm)],[c_0_38,c_0_109]) ).
cnf(c_0_117,negated_conjecture,
( ~ between(b,c,a)
| between(a,d,b)
| between(a,b,d) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_112]) ).
cnf(c_0_118,negated_conjecture,
( ~ between(a,d,c)
| ~ between(b,d,c) ),
inference(spm,[status(thm)],[c_0_113,c_0_106]) ).
cnf(c_0_119,hypothesis,
( between(a,b,d)
| between(b,d,c)
| between(b,c,d)
| between(a,b,c) ),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_120,negated_conjecture,
( ~ between(a,d,c)
| ~ between(b,c,d) ),
inference(spm,[status(thm)],[c_0_116,c_0_106]) ).
cnf(c_0_121,hypothesis,
( ~ between(a,X1,b)
| between(a,X1,c)
| between(a,c,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_65]) ).
cnf(c_0_122,negated_conjecture,
( between(a,b,d)
| between(a,d,b)
| between(a,b,c) ),
inference(spm,[status(thm)],[c_0_117,c_0_115]) ).
cnf(c_0_123,negated_conjecture,
( ~ between(a,c,d)
| ~ between(b,d,c) ),
inference(spm,[status(thm)],[c_0_113,c_0_109]) ).
cnf(c_0_124,negated_conjecture,
( ~ between(a,c,d)
| ~ between(b,c,d) ),
inference(spm,[status(thm)],[c_0_116,c_0_109]) ).
cnf(c_0_125,plain,
( ~ between(X2,X4,X3)
| ~ between(X1,X2,X3)
| between(X1,X4,X3) ),
inference(fof_simplification,[status(thm)],[b8]) ).
cnf(c_0_126,negated_conjecture,
( ~ between(a,d,c)
| between(a,b,c) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_65]),c_0_120]) ).
cnf(c_0_127,negated_conjecture,
( between(a,c,d)
| between(a,d,c)
| between(a,b,c)
| between(a,b,d) ),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_128,negated_conjecture,
( ~ between(a,c,d)
| between(a,b,d) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_119]),c_0_124]),c_0_65]) ).
cnf(c_0_129,plain,
( ~ between(X2,X4,X3)
| ~ between(X1,X2,X3)
| between(X1,X4,X3) ),
c_0_125 ).
cnf(c_0_130,negated_conjecture,
( between(a,b,c)
| between(a,b,d) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_128]) ).
cnf(c_0_131,negated_conjecture,
( ~ between(c,b,d)
| ~ colinear(a,c,d) ),
inference(spm,[status(thm)],[c_0_38,c_0_70]) ).
cnf(c_0_132,hypothesis,
( ~ between(X1,b,a)
| between(X1,c,a)
| between(a,b,c) ),
inference(spm,[status(thm)],[c_0_129,c_0_115]) ).
cnf(c_0_133,negated_conjecture,
( between(d,b,a)
| between(a,b,c) ),
inference(spm,[status(thm)],[c_0_43,c_0_130]) ).
cnf(c_0_134,negated_conjecture,
( ~ between(d,c,a)
| ~ between(c,b,d) ),
inference(spm,[status(thm)],[c_0_131,c_0_87]) ).
cnf(c_0_135,hypothesis,
( between(a,b,c)
| between(d,c,a) ),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_136,negated_conjecture,
( ~ between(a,X1,b)
| between(X1,b,d)
| between(a,b,c) ),
inference(spm,[status(thm)],[c_0_66,c_0_130]) ).
cnf(c_0_137,negated_conjecture,
( ~ between(c,b,d)
| between(a,b,c) ),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_138,hypothesis,
between(a,b,c),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_108]),c_0_137]) ).
cnf(c_0_139,plain,
( ~ between(X2,X3,X4)
| ~ between(X1,X2,X3)
| X2 = X3
| between(X1,X2,X4) ),
inference(fof_simplification,[status(thm)],[b7]) ).
cnf(c_0_140,hypothesis,
( ~ between(X1,a,c)
| between(X1,b,c) ),
inference(spm,[status(thm)],[c_0_129,c_0_138]) ).
cnf(c_0_141,plain,
( ~ between(X2,X3,X4)
| ~ between(X1,X2,X3)
| X2 = X3
| between(X1,X2,X4) ),
c_0_139 ).
cnf(c_0_142,negated_conjecture,
~ between(d,a,c),
inference(spm,[status(thm)],[c_0_52,c_0_140]) ).
cnf(c_0_143,hypothesis,
( ~ between(X1,a,b)
| between(X1,a,c) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_138]),c_0_51]) ).
cnf(c_0_144,hypothesis,
( between(d,a,b)
| between(a,d,b)
| between(a,b,d) ),
inference(spm,[status(thm)],[c_0_43,c_0_98]) ).
cnf(c_0_145,hypothesis,
~ between(d,a,b),
inference(spm,[status(thm)],[c_0_142,c_0_143]) ).
cnf(c_0_146,hypothesis,
( ~ between(a,X1,b)
| between(a,X1,c) ),
inference(spm,[status(thm)],[c_0_65,c_0_138]) ).
cnf(c_0_147,hypothesis,
( ~ between(a,X1,b)
| between(X1,b,c) ),
inference(spm,[status(thm)],[c_0_66,c_0_138]) ).
cnf(c_0_148,hypothesis,
( between(a,b,d)
| between(a,d,b) ),
inference(sr,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_149,negated_conjecture,
( ~ between(c,d,a)
| ~ between(c,b,d) ),
inference(spm,[status(thm)],[c_0_131,c_0_63]) ).
cnf(c_0_150,hypothesis,
( ~ between(a,X1,b)
| between(c,X1,a) ),
inference(spm,[status(thm)],[c_0_43,c_0_146]) ).
cnf(c_0_151,hypothesis,
( between(d,b,c)
| between(a,b,d) ),
inference(spm,[status(thm)],[c_0_147,c_0_148]) ).
cnf(c_0_152,negated_conjecture,
( ~ between(a,d,b)
| ~ between(c,b,d) ),
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_153,hypothesis,
( between(c,b,d)
| between(a,b,d) ),
inference(spm,[status(thm)],[c_0_43,c_0_151]) ).
cnf(c_0_154,plain,
( ~ between(X1,X3,X2)
| ~ between(X1,X2,X3)
| X2 = X3 ),
inference(fof_simplification,[status(thm)],[b3]) ).
cnf(c_0_155,negated_conjecture,
between(a,b,d),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_148]) ).
cnf(c_0_156,plain,
( ~ between(X1,X3,X2)
| ~ between(X1,X2,X3)
| X2 = X3 ),
c_0_154 ).
cnf(c_0_157,negated_conjecture,
~ between(b,a,d),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_155]),c_0_51]) ).
cnf(c_0_158,negated_conjecture,
( ~ between(a,d,b)
| d = b ),
inference(spm,[status(thm)],[c_0_156,c_0_155]) ).
cnf(c_0_159,negated_conjecture,
( ~ between(a,X1,b)
| between(a,X1,d) ),
inference(spm,[status(thm)],[c_0_65,c_0_155]) ).
cnf(c_0_160,hypothesis,
( ~ between(d,a,X2)
| ~ between(X1,d,b)
| between(X1,b,X2)
| d = b ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_53]),c_0_157]),c_0_158]) ).
cnf(c_0_161,negated_conjecture,
( ~ between(a,X1,b)
| between(d,X1,a) ),
inference(spm,[status(thm)],[c_0_43,c_0_159]) ).
cnf(c_0_162,negated_conjecture,
( ~ between(a,X1,b)
| between(X1,b,d) ),
inference(spm,[status(thm)],[c_0_66,c_0_155]) ).
cnf(c_0_163,negated_conjecture,
between(d,b,a),
inference(spm,[status(thm)],[c_0_43,c_0_155]) ).
cnf(c_0_164,hypothesis,
( ~ between(X1,b,a)
| between(X1,c,b)
| between(c,X1,b)
| between(a,c,b)
| between(b,a,c) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_44]),c_0_51]) ).
cnf(c_0_165,hypothesis,
( ~ between(d,a,X1)
| between(d,b,X1)
| d = b ),
inference(spm,[status(thm)],[c_0_160,c_0_48]) ).
cnf(c_0_166,axiom,
between(X1,X2,X2),
t3 ).
cnf(c_0_167,hypothesis,
~ between(b,a,c),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_138]),c_0_51]) ).
cnf(c_0_168,negated_conjecture,
~ between(a,c,b),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_161]),c_0_162]) ).
cnf(c_0_169,negated_conjecture,
( ~ between(d,X1,b)
| between(d,X1,a) ),
inference(spm,[status(thm)],[c_0_65,c_0_163]) ).
cnf(c_0_170,hypothesis,
( between(c,d,b)
| between(d,c,b)
| d = b ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_165]),c_0_166])]),c_0_167]),c_0_168]) ).
cnf(c_0_171,negated_conjecture,
( between(d,c,a)
| between(c,d,b)
| d = b ),
inference(spm,[status(thm)],[c_0_169,c_0_170]) ).
cnf(c_0_172,negated_conjecture,
( ~ between(X1,d,b)
| between(X1,d,a)
| d = b ),
inference(spm,[status(thm)],[c_0_141,c_0_163]) ).
cnf(c_0_173,negated_conjecture,
( between(c,d,b)
| d = b ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_170]),c_0_171]) ).
cnf(c_0_174,negated_conjecture,
( between(c,d,a)
| d = b ),
inference(spm,[status(thm)],[c_0_172,c_0_173]) ).
cnf(c_0_175,negated_conjecture,
d = b,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_173]),c_0_174]) ).
cnf(c_0_176,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_152,c_0_175]),c_0_166]),c_0_175]),c_0_166])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO012-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 08:21:42 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.17/0.60 % Version: 3.5.1
% 0.17/0.60 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.60 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.60 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.60 % Starting new_bool_1 with 300s (1) cores
% 0.17/0.60 % Starting sh5l with 300s (1) cores
% 0.17/0.60 % new_bool_1 with pid 402885 completed with status 0
% 0.17/0.60 % Result found by new_bool_1
% 0.17/0.60 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.60 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.60 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.60 % Starting new_bool_1 with 300s (1) cores
% 0.17/0.60 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.17/0.60 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.60 % Search class: FGHSM-FFMF00-SFFFFFNN
% 0.17/0.60 % partial match(2): FGHSM-FFMF21-SFFFFFNN
% 0.17/0.60 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.60 % Starting SubtermCWHack with 31s (1) cores
% 0.17/0.60 % SubtermCWHack with pid 402889 completed with status 0
% 0.17/0.60 % Result found by SubtermCWHack
% 0.17/0.60 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.60 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.60 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.60 % Starting new_bool_1 with 300s (1) cores
% 0.17/0.60 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.17/0.60 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.60 % Search class: FGHSM-FFMF00-SFFFFFNN
% 0.17/0.60 % partial match(2): FGHSM-FFMF21-SFFFFFNN
% 0.17/0.60 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.60 % Starting SubtermCWHack with 31s (1) cores
% 0.17/0.60 % Preprocessing time : 0.002 s
% 0.17/0.60
% 0.17/0.60 % Proof found!
% 0.17/0.60 % SZS status Unsatisfiable
% 0.17/0.60 % SZS output start CNFRefutation
% See solution above
% 0.17/0.60 % Parsed axioms : 105
% 0.17/0.60 % Removed by relevancy pruning/SinE : 39
% 0.17/0.60 % Initial clauses : 66
% 0.17/0.60 % Removed in clause preprocessing : 1
% 0.17/0.60 % Initial clauses in saturation : 65
% 0.17/0.60 % Processed clauses : 1150
% 0.17/0.60 % ...of these trivial : 4
% 0.17/0.60 % ...subsumed : 575
% 0.17/0.60 % ...remaining for further processing : 571
% 0.17/0.60 % Other redundant clauses eliminated : 2
% 0.17/0.60 % Clauses deleted for lack of memory : 0
% 0.17/0.60 % Backward-subsumed : 260
% 0.17/0.60 % Backward-rewritten : 177
% 0.17/0.60 % Generated clauses : 3889
% 0.17/0.60 % ...of the previous two non-redundant : 2808
% 0.17/0.60 % ...aggressively subsumed : 0
% 0.17/0.60 % Contextual simplify-reflections : 33
% 0.17/0.60 % Paramodulations : 3882
% 0.17/0.60 % Factorizations : 0
% 0.17/0.60 % NegExts : 0
% 0.17/0.60 % Equation resolutions : 2
% 0.17/0.60 % Disequality decompositions : 0
% 0.17/0.60 % Total rewrite steps : 1598
% 0.17/0.60 % ...of those cached : 1519
% 0.17/0.60 % Propositional unsat checks : 0
% 0.17/0.60 % Propositional check models : 0
% 0.17/0.60 % Propositional check unsatisfiable : 0
% 0.17/0.60 % Propositional clauses : 0
% 0.17/0.60 % Propositional clauses after purity: 0
% 0.17/0.60 % Propositional unsat core size : 0
% 0.17/0.60 % Propositional preprocessing time : 0.000
% 0.17/0.60 % Propositional encoding time : 0.000
% 0.17/0.60 % Propositional solver time : 0.000
% 0.17/0.60 % Success case prop preproc time : 0.000
% 0.17/0.60 % Success case prop encoding time : 0.000
% 0.17/0.60 % Success case prop solver time : 0.000
% 0.17/0.60 % Current number of processed clauses : 127
% 0.17/0.60 % Positive orientable unit clauses : 17
% 0.17/0.60 % Positive unorientable unit clauses: 0
% 0.17/0.60 % Negative unit clauses : 6
% 0.17/0.60 % Non-unit-clauses : 104
% 0.17/0.60 % Current number of unprocessed clauses: 1392
% 0.17/0.60 % ...number of literals in the above : 7031
% 0.17/0.60 % Current number of archived formulas : 0
% 0.17/0.60 % Current number of archived clauses : 442
% 0.17/0.60 % Clause-clause subsumption calls (NU) : 42994
% 0.17/0.60 % Rec. Clause-clause subsumption calls : 18509
% 0.17/0.60 % Non-unit clause-clause subsumptions : 751
% 0.17/0.60 % Unit Clause-clause subsumption calls : 552
% 0.17/0.60 % Rewrite failures with RHS unbound : 0
% 0.17/0.60 % BW rewrite match attempts : 28
% 0.17/0.60 % BW rewrite match successes : 5
% 0.17/0.60 % Condensation attempts : 0
% 0.17/0.60 % Condensation successes : 0
% 0.17/0.60 % Termbank termtop insertions : 68922
% 0.17/0.60 % Search garbage collected termcells : 320
% 0.17/0.60
% 0.17/0.60 % -------------------------------------------------
% 0.17/0.60 % User time : 0.140 s
% 0.17/0.60 % System time : 0.005 s
% 0.17/0.60 % Total time : 0.145 s
% 0.17/0.60 % Maximum resident set size: 3712 pages
% 0.17/0.60
% 0.17/0.60 % -------------------------------------------------
% 0.17/0.60 % User time : 0.142 s
% 0.17/0.60 % System time : 0.009 s
% 0.17/0.60 % Total time : 0.151 s
% 0.17/0.60 % Maximum resident set size: 4608 pages
% 0.17/0.60 % E exiting
%------------------------------------------------------------------------------