TSTP Solution File: GEO012-3 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GEO012-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n013.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 : Wed Aug 30 22:45:30 EDT 2023
% Result : Unsatisfiable 1.64s 1.69s
% Output : CNFRefutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 47
% Syntax : Number of formulae : 227 ( 22 unt; 17 typ; 0 def)
% Number of atoms : 591 ( 86 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 570 ( 189 ~; 381 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 41 ( 10 >; 31 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-6 aty)
% Number of variables : 276 ( 54 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
equidistant: ( $i * $i * $i * $i ) > $o ).
tff(decl_23,type,
extension: ( $i * $i * $i * $i ) > $i ).
tff(decl_24,type,
between: ( $i * $i * $i ) > $o ).
tff(decl_25,type,
inner_pasch: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_26,type,
lower_dimension_point_1: $i ).
tff(decl_27,type,
lower_dimension_point_2: $i ).
tff(decl_28,type,
lower_dimension_point_3: $i ).
tff(decl_29,type,
euclid1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_30,type,
euclid2: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_31,type,
continuous: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_32,type,
colinear: ( $i * $i * $i ) > $o ).
tff(decl_33,type,
reflection: ( $i * $i ) > $i ).
tff(decl_34,type,
insertion: ( $i * $i * $i * $i ) > $i ).
tff(decl_35,type,
a: $i ).
tff(decl_36,type,
b: $i ).
tff(decl_37,type,
c: $i ).
tff(decl_38,type,
d: $i ).
cnf(t10_1,axiom,
( colinear(X3,X2,X1)
| ~ colinear(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_1) ).
cnf(abd_colinear,hypothesis,
colinear(a,b,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abd_colinear) ).
cnf(abc_colinear,hypothesis,
colinear(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abc_colinear) ).
cnf(colinearity4,axiom,
( between(X1,X2,X3)
| between(X2,X3,X1)
| between(X3,X1,X2)
| ~ colinear(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-1.ax',colinearity4) ).
cnf(t1,axiom,
( between(X3,X2,X1)
| ~ between(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1) ).
cnf(b6,axiom,
( between(X1,X3,X4)
| X2 = X3
| ~ between(X1,X2,X3)
| ~ between(X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b6) ).
cnf(a_not_b,hypothesis,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_b) ).
cnf(segment_construction1,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction1) ).
cnf(prove_colinearity,negated_conjecture,
( ~ colinear(a,c,d)
| ~ colinear(b,c,d) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_colinearity) ).
cnf(colinearity3,axiom,
( colinear(X2,X3,X1)
| ~ between(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-1.ax',colinearity3) ).
cnf(b7,axiom,
( between(X1,X2,X4)
| X2 = X3
| ~ between(X1,X2,X3)
| ~ between(X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b7) ).
cnf(c2_3,axiom,
( colinear(X2,X1,X3)
| ~ between(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c2_3) ).
cnf(t10_4,axiom,
( colinear(X3,X1,X2)
| ~ colinear(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_4) ).
cnf(c2_2,axiom,
( colinear(X1,X3,X2)
| ~ between(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c2_2) ).
cnf(d10_1,axiom,
( X1 = X2
| X3 = extension(X1,X2,X2,X3)
| ~ between(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_1) ).
cnf(c2_1,axiom,
( colinear(X3,X2,X1)
| ~ between(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c2_1) ).
cnf(b2,axiom,
( X1 = X2
| ~ between(X1,X2,X3)
| ~ between(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b2) ).
cnf(colinearity2,axiom,
( colinear(X3,X1,X2)
| ~ between(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-1.ax',colinearity2) ).
cnf(b9,axiom,
( between(X1,X2,X4)
| ~ between(X1,X2,X3)
| ~ between(X1,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b9) ).
cnf(t7,axiom,
( X2 = X3
| between(X1,X4,X2)
| between(X4,X1,X2)
| ~ between(X1,X2,X3)
| ~ between(X4,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7) ).
cnf(b5,axiom,
( between(X2,X3,X4)
| ~ between(X1,X2,X3)
| ~ between(X1,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b5) ).
cnf(b8,axiom,
( between(X1,X4,X3)
| ~ between(X1,X2,X3)
| ~ between(X2,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b8) ).
cnf(colinearity1,axiom,
( colinear(X1,X2,X3)
| ~ between(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-1.ax',colinearity1) ).
cnf(d9,axiom,
( X1 = X2
| X3 = X4
| ~ between(X1,X2,X3)
| ~ between(X1,X2,X4)
| ~ equidistant(X2,X3,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9) ).
cnf(segment_construction2,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction2) ).
cnf(b3,axiom,
( X2 = X3
| ~ between(X1,X2,X3)
| ~ between(X1,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b3) ).
cnf(b14,axiom,
( between(X2,X4,X3)
| between(X4,X2,X3)
| ~ between(X1,X2,X3)
| ~ between(X1,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b14) ).
cnf(t9,axiom,
( between(X1,X2,X4)
| between(X1,X4,X2)
| ~ between(X1,X2,X3)
| ~ between(X1,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9) ).
cnf(c3_2,axiom,
colinear(X1,X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c3_2) ).
cnf(t2,axiom,
between(X1,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2) ).
cnf(c_0_30,axiom,
( colinear(X3,X2,X1)
| ~ colinear(X1,X2,X3) ),
t10_1 ).
cnf(c_0_31,hypothesis,
colinear(a,b,d),
abd_colinear ).
cnf(c_0_32,hypothesis,
colinear(a,b,c),
abc_colinear ).
cnf(c_0_33,axiom,
( between(X1,X2,X3)
| between(X2,X3,X1)
| between(X3,X1,X2)
| ~ colinear(X1,X2,X3) ),
colinearity4 ).
cnf(c_0_34,hypothesis,
colinear(d,b,a),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,hypothesis,
colinear(c,b,a),
inference(spm,[status(thm)],[c_0_30,c_0_32]) ).
cnf(c_0_36,axiom,
( between(X3,X2,X1)
| ~ between(X1,X2,X3) ),
t1 ).
cnf(c_0_37,hypothesis,
( between(d,b,a)
| between(b,a,d)
| between(a,d,b) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,hypothesis,
( between(c,b,a)
| between(b,a,c)
| between(a,c,b) ),
inference(spm,[status(thm)],[c_0_33,c_0_35]) ).
cnf(c_0_39,axiom,
( between(X1,X3,X4)
| X2 = X3
| ~ between(X1,X2,X3)
| ~ between(X2,X3,X4) ),
b6 ).
cnf(c_0_40,hypothesis,
( between(a,d,b)
| between(b,a,d)
| between(a,b,d) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,hypothesis,
a != b,
a_not_b ).
cnf(c_0_42,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
segment_construction1 ).
cnf(c_0_43,hypothesis,
( between(a,c,b)
| between(b,a,c)
| between(a,b,c) ),
inference(spm,[status(thm)],[c_0_36,c_0_38]) ).
cnf(c_0_44,negated_conjecture,
( ~ colinear(a,c,d)
| ~ colinear(b,c,d) ),
prove_colinearity ).
cnf(c_0_45,axiom,
( colinear(X2,X3,X1)
| ~ between(X1,X2,X3) ),
colinearity3 ).
cnf(c_0_46,axiom,
( between(X1,X2,X4)
| X2 = X3
| ~ between(X1,X2,X3)
| ~ between(X2,X3,X4) ),
b7 ).
cnf(c_0_47,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_39,c_0_40]),c_0_41]) ).
cnf(c_0_48,plain,
between(extension(X1,X2,X3,X4),X2,X1),
inference(spm,[status(thm)],[c_0_36,c_0_42]) ).
cnf(c_0_49,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_39,c_0_43]),c_0_41]) ).
cnf(c_0_50,negated_conjecture,
( ~ colinear(a,c,d)
| ~ between(d,b,c) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_51,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_46,c_0_43]),c_0_41]) ).
cnf(c_0_52,axiom,
( colinear(X2,X1,X3)
| ~ between(X1,X2,X3) ),
c2_3 ).
cnf(c_0_53,hypothesis,
( between(extension(a,b,X1,X2),a,d)
| between(a,d,b)
| between(a,b,d) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_54,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_46,c_0_40]),c_0_41]) ).
cnf(c_0_55,axiom,
( colinear(X3,X1,X2)
| ~ colinear(X1,X2,X3) ),
t10_4 ).
cnf(c_0_56,axiom,
( colinear(X1,X3,X2)
| ~ between(X1,X2,X3) ),
c2_2 ).
cnf(c_0_57,hypothesis,
( between(extension(a,b,X1,X2),a,c)
| between(a,c,b)
| between(a,b,c) ),
inference(spm,[status(thm)],[c_0_49,c_0_48]) ).
cnf(c_0_58,negated_conjecture,
( ~ between(d,b,c)
| ~ between(d,a,c) ),
inference(spm,[status(thm)],[c_0_50,c_0_45]) ).
cnf(c_0_59,hypothesis,
( between(a,d,b)
| between(b,a,d)
| between(d,b,c)
| between(a,c,b)
| between(a,b,c) ),
inference(spm,[status(thm)],[c_0_51,c_0_37]) ).
cnf(c_0_60,hypothesis,
( between(a,d,b)
| between(b,a,d)
| between(d,a,c)
| between(a,c,b)
| between(a,b,c) ),
inference(spm,[status(thm)],[c_0_49,c_0_37]) ).
cnf(c_0_61,negated_conjecture,
( ~ colinear(a,c,d)
| ~ between(c,b,d) ),
inference(spm,[status(thm)],[c_0_44,c_0_52]) ).
cnf(c_0_62,hypothesis,
( between(d,a,extension(a,b,X1,X2))
| between(a,b,d)
| between(a,d,b) ),
inference(spm,[status(thm)],[c_0_36,c_0_53]) ).
cnf(c_0_63,axiom,
( X1 = X2
| X3 = extension(X1,X2,X2,X3)
| ~ between(X1,X2,X3) ),
d10_1 ).
cnf(c_0_64,hypothesis,
( between(extension(a,b,X1,X2),b,d)
| between(a,d,b)
| between(a,b,d) ),
inference(spm,[status(thm)],[c_0_54,c_0_48]) ).
cnf(c_0_65,axiom,
( colinear(X3,X2,X1)
| ~ between(X1,X2,X3) ),
c2_1 ).
cnf(c_0_66,hypothesis,
colinear(d,a,b),
inference(spm,[status(thm)],[c_0_55,c_0_31]) ).
cnf(c_0_67,negated_conjecture,
( ~ colinear(a,c,d)
| ~ between(b,d,c) ),
inference(spm,[status(thm)],[c_0_44,c_0_56]) ).
cnf(c_0_68,hypothesis,
( between(c,a,extension(a,b,X1,X2))
| between(a,b,c)
| between(a,c,b) ),
inference(spm,[status(thm)],[c_0_36,c_0_57]) ).
cnf(c_0_69,axiom,
( X1 = X2
| ~ between(X1,X2,X3)
| ~ between(X2,X1,X3) ),
b2 ).
cnf(c_0_70,negated_conjecture,
( between(a,b,c)
| between(a,c,b)
| between(b,a,d)
| between(a,d,b) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]) ).
cnf(c_0_71,axiom,
( colinear(X3,X1,X2)
| ~ between(X1,X2,X3) ),
colinearity2 ).
cnf(c_0_72,hypothesis,
colinear(c,a,b),
inference(spm,[status(thm)],[c_0_55,c_0_32]) ).
cnf(c_0_73,negated_conjecture,
( ~ between(c,b,d)
| ~ between(d,a,c) ),
inference(spm,[status(thm)],[c_0_61,c_0_45]) ).
cnf(c_0_74,hypothesis,
( between(a,d,b)
| between(a,b,d)
| between(d,a,X1)
| ~ between(a,b,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_41]) ).
cnf(c_0_75,hypothesis,
( between(a,b,d)
| between(a,d,b)
| between(X1,b,d)
| ~ between(a,b,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_63]),c_0_41]) ).
cnf(c_0_76,negated_conjecture,
( ~ colinear(a,c,d)
| ~ between(d,c,b) ),
inference(spm,[status(thm)],[c_0_44,c_0_65]) ).
cnf(c_0_77,axiom,
( between(X1,X2,X4)
| ~ between(X1,X2,X3)
| ~ between(X1,X3,X4) ),
b9 ).
cnf(c_0_78,hypothesis,
( between(d,a,b)
| between(a,b,d)
| between(b,d,a) ),
inference(spm,[status(thm)],[c_0_33,c_0_66]) ).
cnf(c_0_79,negated_conjecture,
( ~ between(b,d,c)
| ~ between(c,a,d) ),
inference(spm,[status(thm)],[c_0_67,c_0_52]) ).
cnf(c_0_80,hypothesis,
( between(a,c,b)
| between(a,b,c)
| between(c,a,X1)
| ~ between(a,b,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_63]),c_0_41]) ).
cnf(c_0_81,negated_conjecture,
( between(a,d,b)
| between(a,c,b)
| between(a,b,c)
| ~ between(a,b,d) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_41]) ).
cnf(c_0_82,negated_conjecture,
( ~ colinear(a,c,d)
| ~ between(c,d,b) ),
inference(spm,[status(thm)],[c_0_44,c_0_71]) ).
cnf(c_0_83,hypothesis,
( between(c,a,b)
| between(a,b,c)
| between(b,c,a) ),
inference(spm,[status(thm)],[c_0_33,c_0_72]) ).
cnf(c_0_84,axiom,
( X2 = X3
| between(X1,X4,X2)
| between(X4,X1,X2)
| ~ between(X1,X2,X3)
| ~ between(X4,X2,X3) ),
t7 ).
cnf(c_0_85,negated_conjecture,
( between(a,b,d)
| between(a,d,b)
| ~ between(a,b,c) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75]) ).
cnf(c_0_86,negated_conjecture,
( ~ between(d,c,b)
| ~ between(d,c,a) ),
inference(spm,[status(thm)],[c_0_76,c_0_65]) ).
cnf(c_0_87,hypothesis,
( between(b,d,a)
| between(a,b,d)
| between(d,X1,b)
| ~ between(d,X1,a) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_88,negated_conjecture,
( between(a,b,c)
| between(a,c,b)
| ~ between(b,d,c)
| ~ between(a,b,d) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_89,hypothesis,
( between(a,b,c)
| between(a,c,b)
| between(b,X1,c)
| ~ between(b,X1,a) ),
inference(spm,[status(thm)],[c_0_77,c_0_43]) ).
cnf(c_0_90,negated_conjecture,
( between(a,b,c)
| between(a,c,b)
| between(b,d,a)
| ~ between(a,b,d) ),
inference(spm,[status(thm)],[c_0_36,c_0_81]) ).
cnf(c_0_91,negated_conjecture,
( ~ between(c,d,b)
| ~ between(c,d,a) ),
inference(spm,[status(thm)],[c_0_82,c_0_71]) ).
cnf(c_0_92,hypothesis,
( between(b,c,a)
| between(a,b,c)
| between(c,X1,b)
| ~ between(c,X1,a) ),
inference(spm,[status(thm)],[c_0_77,c_0_83]) ).
cnf(c_0_93,hypothesis,
( between(b,d,a)
| between(a,b,d)
| between(X1,d,a)
| between(d,X1,a)
| ~ between(X1,a,b) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_78]),c_0_41]) ).
cnf(c_0_94,negated_conjecture,
( between(a,b,d)
| between(b,d,a)
| ~ between(a,b,c) ),
inference(spm,[status(thm)],[c_0_36,c_0_85]) ).
cnf(c_0_95,negated_conjecture,
( between(a,b,d)
| between(b,d,a)
| ~ between(d,c,a) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_96,hypothesis,
( 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_97,hypothesis,
( between(a,b,d)
| between(a,d,b)
| between(b,X1,d)
| ~ between(b,X1,a) ),
inference(spm,[status(thm)],[c_0_77,c_0_40]) ).
cnf(c_0_98,axiom,
( between(X2,X3,X4)
| ~ between(X1,X2,X3)
| ~ between(X1,X3,X4) ),
b5 ).
cnf(c_0_99,negated_conjecture,
( between(a,b,c)
| between(b,c,a)
| ~ between(c,d,a) ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_100,hypothesis,
( between(b,c,a)
| between(c,d,a)
| between(a,b,d)
| between(b,d,a) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_83]),c_0_94]),c_0_95]) ).
cnf(c_0_101,hypothesis,
( between(a,b,c)
| between(b,c,a)
| ~ between(a,b,d) ),
inference(spm,[status(thm)],[c_0_36,c_0_96]) ).
cnf(c_0_102,negated_conjecture,
( ~ between(d,c,b)
| ~ between(c,a,d) ),
inference(spm,[status(thm)],[c_0_76,c_0_52]) ).
cnf(c_0_103,hypothesis,
( between(a,d,b)
| between(a,b,d)
| between(d,X1,b)
| ~ between(b,X1,a) ),
inference(spm,[status(thm)],[c_0_36,c_0_97]) ).
cnf(c_0_104,hypothesis,
( between(a,b,d)
| between(a,d,b)
| between(X1,a,d)
| ~ between(b,X1,a) ),
inference(spm,[status(thm)],[c_0_98,c_0_40]) ).
cnf(c_0_105,negated_conjecture,
( between(b,d,a)
| between(b,c,a)
| between(a,b,c) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_101]) ).
cnf(c_0_106,negated_conjecture,
( between(a,b,d)
| between(a,d,b)
| ~ between(b,c,a) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_104]) ).
cnf(c_0_107,negated_conjecture,
( between(a,b,c)
| between(b,c,a)
| between(a,d,b) ),
inference(spm,[status(thm)],[c_0_36,c_0_105]) ).
cnf(c_0_108,negated_conjecture,
( between(a,d,b)
| between(a,b,d) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_85]) ).
cnf(c_0_109,axiom,
( between(X1,X4,X3)
| ~ between(X1,X2,X3)
| ~ between(X2,X4,X3) ),
b8 ).
cnf(c_0_110,negated_conjecture,
( between(a,b,d)
| between(b,d,a) ),
inference(spm,[status(thm)],[c_0_36,c_0_108]) ).
cnf(c_0_111,negated_conjecture,
( between(a,b,d)
| between(X1,d,a)
| ~ between(X1,b,a) ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_112,hypothesis,
( between(d,b,extension(a,b,X1,X2))
| between(a,b,d)
| between(a,d,b) ),
inference(spm,[status(thm)],[c_0_36,c_0_64]) ).
cnf(c_0_113,negated_conjecture,
( between(extension(a,b,X1,X2),d,a)
| between(a,b,d) ),
inference(spm,[status(thm)],[c_0_111,c_0_48]) ).
cnf(c_0_114,negated_conjecture,
( between(a,d,b)
| between(a,b,c)
| between(a,c,b) ),
inference(spm,[status(thm)],[c_0_36,c_0_107]) ).
cnf(c_0_115,negated_conjecture,
( ~ between(d,b,c)
| ~ between(a,d,c) ),
inference(spm,[status(thm)],[c_0_50,c_0_56]) ).
cnf(c_0_116,hypothesis,
( between(a,b,d)
| between(d,b,X1)
| ~ between(a,b,X1) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_63]),c_0_41]),c_0_98]) ).
cnf(c_0_117,negated_conjecture,
( between(a,d,extension(a,b,X1,X2))
| between(a,b,d) ),
inference(spm,[status(thm)],[c_0_36,c_0_113]) ).
cnf(c_0_118,hypothesis,
( between(a,b,c)
| between(a,c,b)
| between(X1,a,c)
| ~ between(b,X1,a) ),
inference(spm,[status(thm)],[c_0_98,c_0_43]) ).
cnf(c_0_119,negated_conjecture,
( between(a,c,b)
| between(a,b,c)
| between(b,d,a) ),
inference(spm,[status(thm)],[c_0_36,c_0_114]) ).
cnf(c_0_120,negated_conjecture,
( between(a,b,d)
| ~ between(a,d,c)
| ~ between(a,b,c) ),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_121,negated_conjecture,
( between(a,b,d)
| between(a,d,X1)
| ~ between(a,b,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_63]),c_0_41]) ).
cnf(c_0_122,negated_conjecture,
( ~ between(b,d,c)
| ~ between(d,a,c) ),
inference(spm,[status(thm)],[c_0_67,c_0_45]) ).
cnf(c_0_123,hypothesis,
( between(d,a,c)
| between(a,c,b)
| between(a,b,c) ),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_124,negated_conjecture,
( between(a,b,d)
| ~ between(a,b,c) ),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_125,negated_conjecture,
( between(a,b,c)
| between(a,c,b)
| ~ between(b,d,c) ),
inference(spm,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_126,hypothesis,
( between(a,c,b)
| between(b,a,c)
| between(X1,c,b)
| between(c,X1,b)
| ~ between(X1,b,a) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_38]),c_0_41]) ).
cnf(c_0_127,negated_conjecture,
( between(d,b,a)
| ~ between(a,b,c) ),
inference(spm,[status(thm)],[c_0_36,c_0_124]) ).
cnf(c_0_128,hypothesis,
( between(a,c,b)
| between(a,b,c) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_89]),c_0_119]) ).
cnf(c_0_129,axiom,
( colinear(X1,X2,X3)
| ~ between(X1,X2,X3) ),
colinearity1 ).
cnf(c_0_130,hypothesis,
( between(c,d,b)
| between(d,c,b)
| between(b,a,c)
| between(a,c,b) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_128]) ).
cnf(c_0_131,negated_conjecture,
( ~ colinear(a,c,d)
| ~ between(b,c,d) ),
inference(spm,[status(thm)],[c_0_44,c_0_129]) ).
cnf(c_0_132,hypothesis,
( between(a,c,b)
| between(b,a,c)
| between(c,d,b)
| between(b,c,d) ),
inference(spm,[status(thm)],[c_0_36,c_0_130]) ).
cnf(c_0_133,negated_conjecture,
( ~ between(b,c,d)
| ~ between(c,d,a) ),
inference(spm,[status(thm)],[c_0_131,c_0_71]) ).
cnf(c_0_134,hypothesis,
( between(a,c,b)
| between(b,a,c)
| between(c,X1,a)
| ~ between(c,X1,b) ),
inference(spm,[status(thm)],[c_0_77,c_0_38]) ).
cnf(c_0_135,negated_conjecture,
( between(b,a,c)
| between(a,c,b)
| ~ between(c,d,a) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_132]),c_0_133]) ).
cnf(c_0_136,hypothesis,
( between(b,c,d)
| between(b,a,c)
| between(a,c,b) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_132]),c_0_135]) ).
cnf(c_0_137,negated_conjecture,
( ~ between(c,d,b)
| ~ between(d,c,a) ),
inference(spm,[status(thm)],[c_0_82,c_0_65]) ).
cnf(c_0_138,hypothesis,
( c = b
| between(a,c,b)
| between(b,a,c)
| between(X1,c,a)
| ~ between(X1,c,b) ),
inference(spm,[status(thm)],[c_0_46,c_0_38]) ).
cnf(c_0_139,hypothesis,
( between(a,c,b)
| between(b,a,c)
| between(d,c,b) ),
inference(spm,[status(thm)],[c_0_36,c_0_136]) ).
cnf(c_0_140,negated_conjecture,
( between(a,c,b)
| between(b,a,c)
| ~ between(d,c,a) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_130]),c_0_137]) ).
cnf(c_0_141,hypothesis,
( c = b
| between(b,a,c)
| between(a,c,b) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_140]) ).
cnf(c_0_142,hypothesis,
( c = b
| between(a,c,b) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_141]),c_0_41]),c_0_128]) ).
cnf(c_0_143,hypothesis,
( c = b
| between(b,c,a) ),
inference(spm,[status(thm)],[c_0_36,c_0_142]) ).
cnf(c_0_144,hypothesis,
( c = b
| between(X1,b,a)
| ~ between(X1,b,c) ),
inference(spm,[status(thm)],[c_0_46,c_0_143]) ).
cnf(c_0_145,axiom,
( X1 = X2
| X3 = X4
| ~ between(X1,X2,X3)
| ~ between(X1,X2,X4)
| ~ equidistant(X2,X3,X2,X4) ),
d9 ).
cnf(c_0_146,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
segment_construction2 ).
cnf(c_0_147,hypothesis,
( c = b
| between(extension(c,b,X1,X2),b,a) ),
inference(spm,[status(thm)],[c_0_144,c_0_48]) ).
cnf(c_0_148,plain,
( extension(X1,X2,X2,X3) = X3
| X4 = X2
| ~ between(X4,X2,extension(X1,X2,X2,X3))
| ~ between(X4,X2,X3) ),
inference(spm,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_149,hypothesis,
( c = b
| between(a,b,extension(c,b,X1,X2)) ),
inference(spm,[status(thm)],[c_0_36,c_0_147]) ).
cnf(c_0_150,hypothesis,
( c = b
| between(X1,c,a)
| ~ between(X1,b,a) ),
inference(spm,[status(thm)],[c_0_109,c_0_143]) ).
cnf(c_0_151,axiom,
( X2 = X3
| ~ between(X1,X2,X3)
| ~ between(X1,X3,X2) ),
b3 ).
cnf(c_0_152,hypothesis,
( extension(c,b,b,X1) = X1
| c = b
| ~ between(a,b,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_41]) ).
cnf(c_0_153,hypothesis,
( between(a,b,d)
| between(X1,b,d)
| ~ between(a,b,X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_116]) ).
cnf(c_0_154,hypothesis,
( c = b
| between(a,c,X1)
| ~ between(X1,b,a) ),
inference(spm,[status(thm)],[c_0_36,c_0_150]) ).
cnf(c_0_155,hypothesis,
( between(a,b,c)
| between(X1,c,b)
| ~ between(X1,a,b) ),
inference(spm,[status(thm)],[c_0_109,c_0_128]) ).
cnf(c_0_156,plain,
( X1 = X2
| ~ between(extension(X1,X2,X3,X4),X1,X2) ),
inference(spm,[status(thm)],[c_0_151,c_0_48]) ).
cnf(c_0_157,hypothesis,
( c = b
| between(X1,b,c)
| ~ between(a,b,X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_152]) ).
cnf(c_0_158,hypothesis,
( between(extension(a,b,X1,X2),b,d)
| between(a,b,d) ),
inference(spm,[status(thm)],[c_0_153,c_0_42]) ).
cnf(c_0_159,hypothesis,
( c = b
| between(a,c,extension(a,b,X1,X2)) ),
inference(spm,[status(thm)],[c_0_154,c_0_48]) ).
cnf(c_0_160,hypothesis,
( between(extension(b,a,X1,X2),c,b)
| between(a,b,c) ),
inference(spm,[status(thm)],[c_0_155,c_0_48]) ).
cnf(c_0_161,plain,
( X1 = X2
| ~ between(X3,X1,X2)
| ~ between(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_156,c_0_63]) ).
cnf(c_0_162,hypothesis,
( c = b
| between(extension(a,b,X1,X2),b,c) ),
inference(spm,[status(thm)],[c_0_157,c_0_42]) ).
cnf(c_0_163,hypothesis,
( between(d,b,extension(a,b,X1,X2))
| between(a,b,d) ),
inference(spm,[status(thm)],[c_0_36,c_0_158]) ).
cnf(c_0_164,negated_conjecture,
( ~ between(c,b,d)
| ~ between(a,c,d) ),
inference(spm,[status(thm)],[c_0_61,c_0_129]) ).
cnf(c_0_165,hypothesis,
( c = b
| between(c,b,X1)
| ~ between(a,b,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_152]) ).
cnf(c_0_166,hypothesis,
( c = b
| between(a,c,X1)
| ~ between(a,b,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_63]),c_0_41]) ).
cnf(c_0_167,hypothesis,
( c = b
| between(X1,c,b)
| ~ between(X1,a,b) ),
inference(spm,[status(thm)],[c_0_109,c_0_142]) ).
cnf(c_0_168,hypothesis,
( c = b
| between(a,d,b)
| between(b,a,d)
| between(a,c,d) ),
inference(spm,[status(thm)],[c_0_154,c_0_37]) ).
cnf(c_0_169,hypothesis,
( between(b,c,extension(b,a,X1,X2))
| between(a,b,c) ),
inference(spm,[status(thm)],[c_0_36,c_0_160]) ).
cnf(c_0_170,hypothesis,
( c = b
| ~ between(b,c,extension(a,b,X1,X2)) ),
inference(spm,[status(thm)],[c_0_161,c_0_162]) ).
cnf(c_0_171,hypothesis,
( extension(a,b,b,X1) = X1
| d = b
| between(a,b,d)
| ~ between(d,b,X1) ),
inference(spm,[status(thm)],[c_0_148,c_0_163]) ).
cnf(c_0_172,negated_conjecture,
( c = b
| ~ between(a,b,d) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_165]),c_0_166]) ).
cnf(c_0_173,axiom,
( between(X2,X4,X3)
| between(X4,X2,X3)
| ~ between(X1,X2,X3)
| ~ between(X1,X4,X3) ),
b14 ).
cnf(c_0_174,hypothesis,
( c = b
| between(b,c,X1)
| ~ between(X1,a,b) ),
inference(spm,[status(thm)],[c_0_36,c_0_167]) ).
cnf(c_0_175,hypothesis,
( c = b
| between(a,c,d)
| between(a,d,b)
| between(d,a,b) ),
inference(spm,[status(thm)],[c_0_36,c_0_168]) ).
cnf(c_0_176,negated_conjecture,
( c = b
| ~ between(c,a,d)
| ~ between(d,a,b) ),
inference(spm,[status(thm)],[c_0_102,c_0_167]) ).
cnf(c_0_177,negated_conjecture,
( ~ between(b,c,d)
| ~ between(a,c,d) ),
inference(spm,[status(thm)],[c_0_131,c_0_129]) ).
cnf(c_0_178,hypothesis,
( between(a,b,c)
| between(b,c,X1)
| ~ between(b,a,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_63]),c_0_41]) ).
cnf(c_0_179,negated_conjecture,
( ~ between(b,a,d)
| ~ between(a,b,c) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_124]),c_0_41]) ).
cnf(c_0_180,hypothesis,
( d = b
| c = b
| ~ between(b,c,X1)
| ~ between(d,b,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_171]),c_0_172]) ).
cnf(c_0_181,hypothesis,
( between(a,d,b)
| between(X1,a,d)
| between(a,X1,d)
| ~ between(b,X1,d) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_40]),c_0_109]) ).
cnf(c_0_182,hypothesis,
( c = b
| between(a,d,b)
| between(a,c,d)
| between(b,c,d) ),
inference(spm,[status(thm)],[c_0_174,c_0_175]) ).
cnf(c_0_183,negated_conjecture,
( c = b
| between(a,d,b)
| between(a,c,d)
| ~ between(c,a,d) ),
inference(spm,[status(thm)],[c_0_176,c_0_175]) ).
cnf(c_0_184,negated_conjecture,
( ~ between(a,c,d)
| ~ between(b,a,d) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_178]),c_0_179]) ).
cnf(c_0_185,hypothesis,
( c = b
| d = b
| between(a,d,b)
| between(b,a,d) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_37]),c_0_143]) ).
cnf(c_0_186,hypothesis,
( c = b
| between(a,c,d)
| between(a,d,b) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_182]),c_0_183]) ).
cnf(c_0_187,negated_conjecture,
( d = b
| c = b
| between(a,d,b) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_185]),c_0_186]) ).
cnf(c_0_188,negated_conjecture,
( c = b
| d = b
| between(b,d,a) ),
inference(spm,[status(thm)],[c_0_36,c_0_187]) ).
cnf(c_0_189,negated_conjecture,
( d = b
| c = b
| between(X1,d,a)
| ~ between(X1,b,a) ),
inference(spm,[status(thm)],[c_0_109,c_0_188]) ).
cnf(c_0_190,axiom,
( between(X1,X2,X4)
| between(X1,X4,X2)
| ~ between(X1,X2,X3)
| ~ between(X1,X4,X3) ),
t9 ).
cnf(c_0_191,plain,
( X1 = X2
| between(X3,X1,extension(X1,X2,X4,X5))
| ~ between(X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_46,c_0_42]) ).
cnf(c_0_192,negated_conjecture,
( c = b
| d = b
| between(a,d,X1)
| ~ between(X1,b,a) ),
inference(spm,[status(thm)],[c_0_36,c_0_189]) ).
cnf(c_0_193,plain,
( X1 = X2
| between(X3,X4,X1)
| between(X3,X1,X4)
| ~ between(X3,X4,extension(X1,X2,X5,X6))
| ~ between(X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_190,c_0_191]) ).
cnf(c_0_194,hypothesis,
( d = b
| c = b
| between(a,d,extension(c,b,X1,X2)) ),
inference(spm,[status(thm)],[c_0_192,c_0_147]) ).
cnf(c_0_195,hypothesis,
( c = b
| between(X1,c,b)
| ~ between(a,X1,c) ),
inference(spm,[status(thm)],[c_0_98,c_0_142]) ).
cnf(c_0_196,hypothesis,
( d = b
| c = b
| between(a,c,d)
| between(a,d,c) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_194]),c_0_142]) ).
cnf(c_0_197,negated_conjecture,
( ~ between(d,c,b)
| ~ between(c,d,a) ),
inference(spm,[status(thm)],[c_0_76,c_0_71]) ).
cnf(c_0_198,hypothesis,
( d = b
| c = b
| between(a,c,d)
| between(d,c,b) ),
inference(spm,[status(thm)],[c_0_195,c_0_196]) ).
cnf(c_0_199,hypothesis,
( c = b
| d = b
| between(a,c,d)
| between(c,d,a) ),
inference(spm,[status(thm)],[c_0_36,c_0_196]) ).
cnf(c_0_200,negated_conjecture,
( c = b
| d = b
| between(a,c,d) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_198]),c_0_199]) ).
cnf(c_0_201,negated_conjecture,
( d = b
| c = b
| between(d,c,a) ),
inference(spm,[status(thm)],[c_0_36,c_0_200]) ).
cnf(c_0_202,negated_conjecture,
( c = b
| d = b
| between(X1,d,b)
| ~ between(a,X1,d) ),
inference(spm,[status(thm)],[c_0_98,c_0_187]) ).
cnf(c_0_203,negated_conjecture,
( c = b
| d = b
| ~ between(c,d,b) ),
inference(spm,[status(thm)],[c_0_137,c_0_201]) ).
cnf(c_0_204,negated_conjecture,
( d = b
| c = b ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_200]),c_0_203]) ).
cnf(c_0_205,hypothesis,
colinear(a,c,b),
inference(spm,[status(thm)],[c_0_55,c_0_35]) ).
cnf(c_0_206,axiom,
colinear(X1,X2,X1),
c3_2 ).
cnf(c_0_207,negated_conjecture,
c = b,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_204]),c_0_205]),c_0_206])]) ).
cnf(c_0_208,axiom,
between(X1,X1,X2),
t2 ).
cnf(c_0_209,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_131,c_0_207]),c_0_31]),c_0_207]),c_0_208])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO012-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.13/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n013.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 23:30:46 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.55 start to proof: theBenchmark
% 1.64/1.69 % Version : CSE_E---1.5
% 1.64/1.69 % Problem : theBenchmark.p
% 1.64/1.69 % Proof found
% 1.64/1.69 % SZS status Theorem for theBenchmark.p
% 1.64/1.69 % SZS output start Proof
% See solution above
% 1.64/1.71 % Total time : 1.134000 s
% 1.64/1.71 % SZS output end Proof
% 1.64/1.71 % Total time : 1.139000 s
%------------------------------------------------------------------------------