%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO012-3 : 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 : n014.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 04:18:59 PM UTC 2026
% Result : Unsatisfiable 2.48s 2.03s
% Output : CNFRefutation 2.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 29
% Syntax : Number of clauses : 175 ( 25 unt; 95 nHn; 158 RR)
% Number of literals : 473 ( 57 equ; 138 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-4 aty)
% Number of variables : 222 ( 32 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t10_1,axiom,
( colinear(X3,X2,X1)
| ~ colinear(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_1) ).
cnf(abd_colinear,hypothesis,
colinear(a,b,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abd_colinear) ).
cnf(colinearity4,axiom,
( between(X1,X2,X3)
| between(X2,X3,X1)
| between(X3,X1,X2)
| ~ colinear(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-1.ax',colinearity4) ).
cnf(t1,axiom,
( between(X3,X2,X1)
| ~ between(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1) ).
cnf(abc_colinear,hypothesis,
colinear(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abc_colinear) ).
cnf(prove_colinearity,negated_conjecture,
( ~ colinear(a,c,d)
| ~ colinear(b,c,d) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_colinearity) ).
cnf(c2_3,axiom,
( colinear(X2,X1,X3)
| ~ between(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c2_3) ).
cnf(b7,axiom,
( between(X1,X2,X4)
| X2 = X3
| ~ between(X1,X2,X3)
| ~ between(X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b7) ).
cnf(a_not_b,hypothesis,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_b) ).
cnf(b6,axiom,
( between(X1,X3,X4)
| X2 = X3
| ~ between(X1,X2,X3)
| ~ between(X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b6) ).
cnf(c2_2,axiom,
( colinear(X1,X3,X2)
| ~ between(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c2_2) ).
cnf(b12,axiom,
( X1 = X2
| between(X1,X3,X4)
| between(X1,X4,X3)
| ~ between(X1,X2,X3)
| ~ between(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b12) ).
cnf(colinearity1,axiom,
( colinear(X1,X2,X3)
| ~ between(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-1.ax',colinearity1) ).
cnf(b13,axiom,
( X1 = X2
| between(X2,X3,X4)
| between(X2,X4,X3)
| ~ between(X1,X2,X3)
| ~ between(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b13) ).
cnf(b9,axiom,
( between(X1,X2,X4)
| ~ between(X1,X2,X3)
| ~ between(X1,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b9) ).
cnf(segment_construction1,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',segment_construction1) ).
cnf(b5,axiom,
( between(X2,X3,X4)
| ~ between(X1,X2,X3)
| ~ between(X1,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b5) ).
cnf(e1,axiom,
X1 = extension(X2,X1,X3,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e1) ).
cnf(i3,axiom,
( X2 = insertion(X1,X3,X1,X2)
| ~ between(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i3) ).
cnf(insertion,axiom,
insertion(X1,X2,X3,X4) = extension(extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),X1,X3,X4),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-3.ax',insertion) ).
cnf(colinearity3,axiom,
( colinear(X2,X3,X1)
| ~ between(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-1.ax',colinearity3) ).
cnf(e3_1,axiom,
X1 != extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e3_1) ).
cnf(t10_4,axiom,
( colinear(X3,X1,X2)
| ~ colinear(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_4) ).
cnf(colinearity2,axiom,
( colinear(X3,X1,X2)
| ~ between(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-1.ax',colinearity2) ).
cnf(c2_1,axiom,
( colinear(X3,X2,X1)
| ~ between(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c2_1) ).
cnf(b3,axiom,
( X2 = X3
| ~ between(X1,X2,X3)
| ~ between(X1,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b3) ).
cnf(b8,axiom,
( between(X1,X4,X3)
| ~ between(X1,X2,X3)
| ~ between(X2,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b8) ).
cnf(d10_1,axiom,
( X1 = X2
| X3 = extension(X1,X2,X2,X3)
| ~ between(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_1) ).
cnf(c3_2,axiom,
colinear(X1,X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c3_2) ).
cnf(c_0_29,axiom,
( colinear(X3,X2,X1)
| ~ colinear(X1,X2,X3) ),
t10_1 ).
cnf(c_0_30,hypothesis,
colinear(a,b,d),
abd_colinear ).
cnf(c_0_31,axiom,
( between(X1,X2,X3)
| between(X2,X3,X1)
| between(X3,X1,X2)
| ~ colinear(X1,X2,X3) ),
colinearity4 ).
cnf(c_0_32,hypothesis,
colinear(d,b,a),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,axiom,
( between(X3,X2,X1)
| ~ between(X1,X2,X3) ),
t1 ).
cnf(c_0_34,hypothesis,
( between(d,b,a)
| between(b,a,d)
| between(a,d,b) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,hypothesis,
colinear(a,b,c),
abc_colinear ).
cnf(c_0_36,negated_conjecture,
( ~ colinear(a,c,d)
| ~ colinear(b,c,d) ),
prove_colinearity ).
cnf(c_0_37,axiom,
( colinear(X2,X1,X3)
| ~ between(X1,X2,X3) ),
c2_3 ).
cnf(c_0_38,axiom,
( between(X1,X2,X4)
| X2 = X3
| ~ between(X1,X2,X3)
| ~ between(X2,X3,X4) ),
b7 ).
cnf(c_0_39,hypothesis,
( between(a,d,b)
| between(b,a,d)
| between(a,b,d) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,hypothesis,
a != b,
a_not_b ).
cnf(c_0_41,hypothesis,
colinear(c,b,a),
inference(spm,[status(thm)],[c_0_29,c_0_35]) ).
cnf(c_0_42,axiom,
( between(X1,X3,X4)
| X2 = X3
| ~ between(X1,X2,X3)
| ~ between(X2,X3,X4) ),
b6 ).
cnf(c_0_43,negated_conjecture,
( ~ colinear(a,c,d)
| ~ between(c,b,d) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_44,hypothesis,
( between(a,b,d)
| between(a,d,b)
| between(X1,b,d)
| ~ between(X1,b,a) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
cnf(c_0_45,hypothesis,
( between(c,b,a)
| between(b,a,c)
| between(a,c,b) ),
inference(spm,[status(thm)],[c_0_31,c_0_41]) ).
cnf(c_0_46,hypothesis,
( between(a,b,d)
| between(a,d,b)
| between(X1,a,d)
| ~ between(X1,b,a) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_39]),c_0_40]) ).
cnf(c_0_47,axiom,
( colinear(X1,X3,X2)
| ~ between(X1,X2,X3) ),
c2_2 ).
cnf(c_0_48,axiom,
( X1 = X2
| between(X1,X3,X4)
| between(X1,X4,X3)
| ~ between(X1,X2,X3)
| ~ between(X1,X2,X4) ),
b12 ).
cnf(c_0_49,negated_conjecture,
( ~ between(c,b,d)
| ~ between(c,a,d) ),
inference(spm,[status(thm)],[c_0_43,c_0_37]) ).
cnf(c_0_50,hypothesis,
( between(a,c,b)
| between(b,a,c)
| between(c,b,d)
| between(a,d,b)
| between(a,b,d) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_51,hypothesis,
( between(a,c,b)
| between(b,a,c)
| between(c,a,d)
| between(a,d,b)
| between(a,b,d) ),
inference(spm,[status(thm)],[c_0_46,c_0_45]) ).
cnf(c_0_52,axiom,
( colinear(X1,X2,X3)
| ~ between(X1,X2,X3) ),
colinearity1 ).
cnf(c_0_53,negated_conjecture,
( ~ colinear(a,c,d)
| ~ between(b,d,c) ),
inference(spm,[status(thm)],[c_0_36,c_0_47]) ).
cnf(c_0_54,hypothesis,
( between(a,b,d)
| between(a,d,b)
| between(b,X1,d)
| between(b,d,X1)
| ~ between(b,a,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_39]),c_0_40]) ).
cnf(c_0_55,negated_conjecture,
( between(a,b,d)
| between(a,d,b)
| between(b,a,c)
| between(a,c,b) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).
cnf(c_0_56,negated_conjecture,
( ~ colinear(a,c,d)
| ~ between(b,c,d) ),
inference(spm,[status(thm)],[c_0_36,c_0_52]) ).
cnf(c_0_57,axiom,
( X1 = X2
| between(X2,X3,X4)
| between(X2,X4,X3)
| ~ between(X1,X2,X3)
| ~ between(X1,X2,X4) ),
b13 ).
cnf(c_0_58,negated_conjecture,
( ~ between(b,d,c)
| ~ between(a,d,c) ),
inference(spm,[status(thm)],[c_0_53,c_0_47]) ).
cnf(c_0_59,hypothesis,
( between(a,c,b)
| between(b,d,c)
| between(b,c,d)
| between(a,d,b)
| between(a,b,d) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_60,negated_conjecture,
( ~ between(b,c,d)
| ~ between(a,d,c) ),
inference(spm,[status(thm)],[c_0_56,c_0_47]) ).
cnf(c_0_61,axiom,
( between(X1,X2,X4)
| ~ between(X1,X2,X3)
| ~ between(X1,X3,X4) ),
b9 ).
cnf(c_0_62,hypothesis,
( between(a,b,d)
| between(a,d,b)
| between(a,X1,d)
| between(a,d,X1)
| ~ between(b,a,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_39]),c_0_40]) ).
cnf(c_0_63,hypothesis,
( between(a,c,b)
| between(b,a,c)
| between(a,b,c) ),
inference(spm,[status(thm)],[c_0_33,c_0_45]) ).
cnf(c_0_64,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
segment_construction1 ).
cnf(c_0_65,negated_conjecture,
( between(a,b,d)
| between(a,d,b)
| ~ between(a,d,c) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]),c_0_61]) ).
cnf(c_0_66,hypothesis,
( between(a,c,b)
| between(a,d,c)
| between(a,c,d)
| between(a,d,b)
| between(a,b,d) ),
inference(spm,[status(thm)],[c_0_62,c_0_55]) ).
cnf(c_0_67,hypothesis,
( between(a,b,c)
| between(a,c,b)
| between(X1,a,c)
| ~ between(X1,b,a) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_63]),c_0_40]) ).
cnf(c_0_68,plain,
between(extension(X1,X2,X3,X4),X2,X1),
inference(spm,[status(thm)],[c_0_33,c_0_64]) ).
cnf(c_0_69,negated_conjecture,
( ~ between(b,d,c)
| ~ between(a,c,d) ),
inference(spm,[status(thm)],[c_0_53,c_0_52]) ).
cnf(c_0_70,hypothesis,
( between(a,c,d)
| between(a,c,b)
| between(a,d,b)
| between(a,b,d) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_71,axiom,
( between(X2,X3,X4)
| ~ between(X1,X2,X3)
| ~ between(X1,X3,X4) ),
b5 ).
cnf(c_0_72,hypothesis,
( between(extension(a,b,X1,X2),a,c)
| between(a,c,b)
| between(a,b,c) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_73,negated_conjecture,
( ~ between(b,c,d)
| ~ between(a,c,d) ),
inference(spm,[status(thm)],[c_0_56,c_0_52]) ).
cnf(c_0_74,negated_conjecture,
( between(a,b,d)
| between(a,d,b)
| between(b,c,d)
| between(a,c,b) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_59]),c_0_70]) ).
cnf(c_0_75,hypothesis,
( between(a,b,c)
| between(a,c,b)
| between(X1,a,c)
| ~ between(extension(a,b,X2,X3),X1,a) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_76,axiom,
X1 = extension(X2,X1,X3,X3),
e1 ).
cnf(c_0_77,negated_conjecture,
( between(a,c,b)
| between(a,d,b)
| between(a,b,d) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_70]) ).
cnf(c_0_78,axiom,
( X2 = insertion(X1,X3,X1,X2)
| ~ between(X1,X2,X3) ),
i3 ).
cnf(c_0_79,axiom,
insertion(X1,X2,X3,X4) = extension(extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),X1,X3,X4),
insertion ).
cnf(c_0_80,axiom,
( colinear(X2,X3,X1)
| ~ between(X1,X2,X3) ),
colinearity3 ).
cnf(c_0_81,hypothesis,
( between(a,c,b)
| between(a,b,c)
| between(X1,a,c)
| ~ between(b,X1,a) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_82,negated_conjecture,
( between(a,b,d)
| between(a,c,b)
| between(b,d,a) ),
inference(spm,[status(thm)],[c_0_33,c_0_77]) ).
cnf(c_0_83,hypothesis,
( between(a,b,c)
| between(a,c,b)
| between(b,X1,c)
| ~ between(b,X1,a) ),
inference(spm,[status(thm)],[c_0_61,c_0_63]) ).
cnf(c_0_84,plain,
( X2 = extension(extension(X3,X1,lower_dimension_point_1,lower_dimension_point_2),X1,X1,X2)
| ~ between(X1,X2,X3) ),
inference(rw,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_85,hypothesis,
( between(extension(a,b,X1,X2),b,d)
| between(a,d,b)
| between(a,b,d) ),
inference(spm,[status(thm)],[c_0_44,c_0_68]) ).
cnf(c_0_86,plain,
( between(X1,X2,extension(X3,X2,X4,X5))
| ~ between(X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_71,c_0_64]) ).
cnf(c_0_87,hypothesis,
( between(extension(a,b,X1,X2),a,d)
| between(a,d,b)
| between(a,b,d) ),
inference(spm,[status(thm)],[c_0_46,c_0_68]) ).
cnf(c_0_88,negated_conjecture,
( ~ between(b,d,c)
| ~ between(d,a,c) ),
inference(spm,[status(thm)],[c_0_53,c_0_80]) ).
cnf(c_0_89,hypothesis,
( between(a,b,d)
| between(d,a,c)
| between(a,b,c)
| between(a,c,b) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_90,hypothesis,
( between(a,b,d)
| between(b,d,c)
| between(a,c,b)
| between(a,b,c) ),
inference(spm,[status(thm)],[c_0_83,c_0_82]) ).
cnf(c_0_91,plain,
( between(extension(X1,X2,lower_dimension_point_1,lower_dimension_point_2),X2,X3)
| ~ between(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_84]) ).
cnf(c_0_92,axiom,
X1 != extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),
e3_1 ).
cnf(c_0_93,hypothesis,
( between(d,b,extension(a,b,X1,X2))
| between(a,b,d) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_85]),c_0_86]) ).
cnf(c_0_94,hypothesis,
( between(a,b,d)
| between(a,d,b)
| between(X1,a,d)
| ~ between(extension(a,b,X2,X3),X1,a) ),
inference(spm,[status(thm)],[c_0_71,c_0_87]) ).
cnf(c_0_95,negated_conjecture,
( between(a,c,b)
| between(a,b,c)
| between(a,b,d) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_90]) ).
cnf(c_0_96,axiom,
( colinear(X3,X1,X2)
| ~ colinear(X1,X2,X3) ),
t10_4 ).
cnf(c_0_97,plain,
( between(X1,X2,X3)
| between(X1,X3,X2)
| ~ between(extension(X4,X1,lower_dimension_point_1,lower_dimension_point_2),X1,X2)
| ~ between(X1,X3,X4) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_91]),c_0_92]) ).
cnf(c_0_98,hypothesis,
( between(extension(a,b,X1,X2),b,d)
| between(a,b,d) ),
inference(spm,[status(thm)],[c_0_33,c_0_93]) ).
cnf(c_0_99,hypothesis,
( between(a,d,b)
| between(a,b,d)
| between(X1,a,d)
| ~ between(b,X1,a) ),
inference(spm,[status(thm)],[c_0_94,c_0_76]) ).
cnf(c_0_100,negated_conjecture,
( between(a,b,d)
| between(a,b,c)
| between(b,c,a) ),
inference(spm,[status(thm)],[c_0_33,c_0_95]) ).
cnf(c_0_101,hypothesis,
( between(a,b,d)
| between(a,d,b)
| between(b,X1,d)
| ~ between(b,X1,a) ),
inference(spm,[status(thm)],[c_0_61,c_0_39]) ).
cnf(c_0_102,hypothesis,
colinear(d,a,b),
inference(spm,[status(thm)],[c_0_96,c_0_30]) ).
cnf(c_0_103,axiom,
( colinear(X3,X1,X2)
| ~ between(X1,X2,X3) ),
colinearity2 ).
cnf(c_0_104,hypothesis,
( between(a,b,d)
| between(b,X1,d)
| between(b,d,X1)
| ~ between(b,X1,a) ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_105,negated_conjecture,
( ~ between(b,c,d)
| ~ between(c,a,d) ),
inference(spm,[status(thm)],[c_0_56,c_0_37]) ).
cnf(c_0_106,hypothesis,
( between(a,b,c)
| between(c,a,d)
| between(a,b,d)
| between(a,d,b) ),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_107,hypothesis,
( between(a,b,c)
| between(b,c,d)
| between(a,d,b)
| between(a,b,d) ),
inference(spm,[status(thm)],[c_0_101,c_0_100]) ).
cnf(c_0_108,hypothesis,
( between(d,a,b)
| between(a,b,d)
| between(b,d,a) ),
inference(spm,[status(thm)],[c_0_31,c_0_102]) ).
cnf(c_0_109,negated_conjecture,
( ~ colinear(a,c,d)
| ~ between(c,d,b) ),
inference(spm,[status(thm)],[c_0_36,c_0_103]) ).
cnf(c_0_110,axiom,
( colinear(X3,X2,X1)
| ~ between(X1,X2,X3) ),
c2_1 ).
cnf(c_0_111,negated_conjecture,
( between(a,b,c)
| between(a,b,d)
| between(X1,c,a)
| ~ between(b,X1,c) ),
inference(spm,[status(thm)],[c_0_71,c_0_100]) ).
cnf(c_0_112,hypothesis,
( between(a,b,c)
| between(b,d,c)
| between(b,c,d)
| between(a,b,d) ),
inference(spm,[status(thm)],[c_0_104,c_0_100]) ).
cnf(c_0_113,negated_conjecture,
( between(a,d,b)
| between(a,b,d)
| between(a,b,c) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107]) ).
cnf(c_0_114,hypothesis,
( between(b,d,a)
| between(a,b,d)
| between(b,a,d) ),
inference(spm,[status(thm)],[c_0_33,c_0_108]) ).
cnf(c_0_115,negated_conjecture,
( ~ between(c,d,b)
| ~ between(d,c,a) ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_116,hypothesis,
( between(b,c,d)
| between(d,c,a)
| between(a,b,d)
| between(a,b,c) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_117,hypothesis,
( between(a,b,d)
| between(b,c,d)
| between(a,b,c)
| between(c,d,b) ),
inference(spm,[status(thm)],[c_0_33,c_0_112]) ).
cnf(c_0_118,negated_conjecture,
( ~ between(c,d,b)
| ~ between(c,d,a) ),
inference(spm,[status(thm)],[c_0_109,c_0_103]) ).
cnf(c_0_119,negated_conjecture,
( ~ between(b,c,d)
| ~ between(c,d,a) ),
inference(spm,[status(thm)],[c_0_56,c_0_103]) ).
cnf(c_0_120,hypothesis,
colinear(c,a,b),
inference(spm,[status(thm)],[c_0_96,c_0_35]) ).
cnf(c_0_121,axiom,
( X2 = X3
| ~ between(X1,X2,X3)
| ~ between(X1,X3,X2) ),
b3 ).
cnf(c_0_122,negated_conjecture,
( between(a,b,c)
| between(a,b,d)
| between(b,d,a) ),
inference(spm,[status(thm)],[c_0_33,c_0_113]) ).
cnf(c_0_123,hypothesis,
( between(b,a,d)
| between(a,b,d)
| between(X1,d,a)
| ~ between(b,X1,d) ),
inference(spm,[status(thm)],[c_0_71,c_0_114]) ).
cnf(c_0_124,negated_conjecture,
( between(a,b,c)
| between(a,b,d)
| between(b,c,d) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_117]) ).
cnf(c_0_125,negated_conjecture,
( between(a,b,c)
| between(a,b,d)
| ~ between(c,d,a) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_117]),c_0_119]) ).
cnf(c_0_126,hypothesis,
( between(c,a,b)
| between(a,b,c)
| between(b,c,a) ),
inference(spm,[status(thm)],[c_0_31,c_0_120]) ).
cnf(c_0_127,negated_conjecture,
( d = a
| between(a,b,d)
| between(a,b,c)
| ~ between(b,a,d) ),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_128,hypothesis,
( between(a,b,c)
| between(a,b,d)
| between(b,a,d) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_125]) ).
cnf(c_0_129,hypothesis,
( between(a,b,c)
| between(a,c,b)
| between(X1,b,c)
| ~ between(X1,b,a) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_63]),c_0_40]) ).
cnf(c_0_130,axiom,
( between(X1,X4,X3)
| ~ between(X1,X2,X3)
| ~ between(X2,X4,X3) ),
b8 ).
cnf(c_0_131,hypothesis,
( between(b,c,a)
| between(a,b,c)
| between(b,a,c) ),
inference(spm,[status(thm)],[c_0_33,c_0_126]) ).
cnf(c_0_132,negated_conjecture,
( d = a
| between(a,b,c)
| between(a,b,d) ),
inference(spm,[status(thm)],[c_0_127,c_0_128]) ).
cnf(c_0_133,hypothesis,
( between(extension(a,b,X1,X2),b,c)
| between(a,c,b)
| between(a,b,c) ),
inference(spm,[status(thm)],[c_0_129,c_0_68]) ).
cnf(c_0_134,axiom,
( X1 = X2
| X3 = extension(X1,X2,X2,X3)
| ~ between(X1,X2,X3) ),
d10_1 ).
cnf(c_0_135,hypothesis,
( between(b,a,c)
| between(a,b,c)
| between(X1,c,a)
| ~ between(X1,b,a) ),
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_136,negated_conjecture,
( d = a
| between(a,b,c)
| between(d,b,a) ),
inference(spm,[status(thm)],[c_0_33,c_0_132]) ).
cnf(c_0_137,hypothesis,
( between(c,b,extension(a,b,X1,X2))
| between(a,b,c) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_133]),c_0_86]) ).
cnf(c_0_138,negated_conjecture,
( extension(a,b,b,d) = d
| d = a
| between(a,b,c) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_132]),c_0_40]) ).
cnf(c_0_139,negated_conjecture,
( ~ between(c,b,d)
| ~ between(d,c,a) ),
inference(spm,[status(thm)],[c_0_43,c_0_110]) ).
cnf(c_0_140,hypothesis,
( d = a
| between(d,c,a)
| between(a,b,c)
| between(b,a,c) ),
inference(spm,[status(thm)],[c_0_135,c_0_136]) ).
cnf(c_0_141,hypothesis,
( d = a
| between(a,b,c)
| between(c,b,d) ),
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_142,negated_conjecture,
( d = a
| between(b,a,c)
| between(a,b,c) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_141]) ).
cnf(c_0_143,negated_conjecture,
( d = a
| between(a,b,c)
| between(X1,a,d)
| ~ between(X1,a,b) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_132]),c_0_40]) ).
cnf(c_0_144,negated_conjecture,
( d = a
| between(a,b,c)
| between(c,a,b) ),
inference(spm,[status(thm)],[c_0_33,c_0_142]) ).
cnf(c_0_145,negated_conjecture,
( d = a
| between(a,b,c)
| ~ between(c,a,d) ),
inference(spm,[status(thm)],[c_0_49,c_0_141]) ).
cnf(c_0_146,negated_conjecture,
( d = a
| between(a,b,c) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_145]) ).
cnf(c_0_147,negated_conjecture,
( ~ colinear(a,c,d)
| ~ between(d,b,c) ),
inference(spm,[status(thm)],[c_0_36,c_0_80]) ).
cnf(c_0_148,negated_conjecture,
( extension(a,b,b,c) = c
| d = a ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_146]),c_0_40]) ).
cnf(c_0_149,negated_conjecture,
( ~ between(d,b,c)
| ~ between(c,a,d) ),
inference(spm,[status(thm)],[c_0_147,c_0_37]) ).
cnf(c_0_150,hypothesis,
( d = a
| between(a,b,d)
| between(d,b,c) ),
inference(spm,[status(thm)],[c_0_93,c_0_148]) ).
cnf(c_0_151,negated_conjecture,
( d = a
| between(c,b,a) ),
inference(spm,[status(thm)],[c_0_33,c_0_146]) ).
cnf(c_0_152,negated_conjecture,
( d = a
| between(a,b,d)
| ~ between(c,a,d) ),
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_153,negated_conjecture,
( ~ between(d,b,c)
| ~ between(a,d,c) ),
inference(spm,[status(thm)],[c_0_147,c_0_47]) ).
cnf(c_0_154,negated_conjecture,
( d = a
| between(a,X1,c)
| ~ between(a,X1,b) ),
inference(spm,[status(thm)],[c_0_61,c_0_146]) ).
cnf(c_0_155,hypothesis,
( d = a
| between(a,d,b)
| between(a,b,d) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_151]),c_0_152]) ).
cnf(c_0_156,negated_conjecture,
( d = a
| between(a,b,d)
| ~ between(a,d,c) ),
inference(spm,[status(thm)],[c_0_153,c_0_150]) ).
cnf(c_0_157,negated_conjecture,
( d = a
| between(b,X1,c)
| between(b,c,X1)
| ~ between(a,b,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_146]),c_0_40]) ).
cnf(c_0_158,negated_conjecture,
( d = a
| between(a,b,d) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_156]) ).
cnf(c_0_159,negated_conjecture,
( d = a
| between(b,c,d)
| between(b,d,c) ),
inference(spm,[status(thm)],[c_0_157,c_0_158]) ).
cnf(c_0_160,negated_conjecture,
( d = a
| between(b,c,d)
| between(c,d,b) ),
inference(spm,[status(thm)],[c_0_33,c_0_159]) ).
cnf(c_0_161,negated_conjecture,
( d = a
| between(c,X1,a)
| ~ between(c,X1,b) ),
inference(spm,[status(thm)],[c_0_61,c_0_151]) ).
cnf(c_0_162,negated_conjecture,
( d = a
| ~ between(c,d,a) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_160]),c_0_119]) ).
cnf(c_0_163,negated_conjecture,
( ~ colinear(a,c,d)
| ~ between(d,c,b) ),
inference(spm,[status(thm)],[c_0_36,c_0_110]) ).
cnf(c_0_164,negated_conjecture,
( d = a
| between(b,c,d) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_160]),c_0_162]) ).
cnf(c_0_165,negated_conjecture,
( d = a
| between(d,b,a) ),
inference(spm,[status(thm)],[c_0_33,c_0_158]) ).
cnf(c_0_166,negated_conjecture,
( ~ between(d,c,b)
| ~ between(d,c,a) ),
inference(spm,[status(thm)],[c_0_163,c_0_110]) ).
cnf(c_0_167,negated_conjecture,
( d = a
| between(d,c,b) ),
inference(spm,[status(thm)],[c_0_33,c_0_164]) ).
cnf(c_0_168,negated_conjecture,
( d = a
| between(d,X1,a)
| ~ between(d,X1,b) ),
inference(spm,[status(thm)],[c_0_61,c_0_165]) ).
cnf(c_0_169,negated_conjecture,
( d = a
| ~ between(d,c,a) ),
inference(spm,[status(thm)],[c_0_166,c_0_167]) ).
cnf(c_0_170,hypothesis,
colinear(a,c,b),
inference(spm,[status(thm)],[c_0_96,c_0_41]) ).
cnf(c_0_171,negated_conjecture,
d = a,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_167]),c_0_169]) ).
cnf(c_0_172,axiom,
colinear(X1,X2,X1),
c3_2 ).
cnf(c_0_173,hypothesis,
colinear(b,c,a),
inference(spm,[status(thm)],[c_0_29,c_0_170]) ).
cnf(c_0_174,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_36,c_0_171]),c_0_172]),c_0_171]),c_0_173])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO012-3 : 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
% 0.16/0.33 % Computer : n014.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 17:36:51 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 2.48/2.03 % Version : CSE_E---1.7
% 2.48/2.03 % Problem : theBenchmark.p
% 2.48/2.03 % SZS status Unsatisfiable for theBenchmark.p
% 2.48/2.03 % SZS output start CNFRefutation
% See solution above
% 2.48/2.04 % Total time : 1.372s
%------------------------------------------------------------------------------