%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO070-3 : TPTP v9.2.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n028.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 04:19:13 PM UTC 2026
% Result : Unsatisfiable 19.26s 13.09s
% Output : CNFRefutation 19.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 37
% Syntax : Number of clauses : 168 ( 50 unt; 22 nHn; 154 RR)
% Number of literals : 373 ( 25 equ; 185 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-4 aty)
% Number of variables : 289 ( 19 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(d4_4,axiom,
( equidistant(X4,X3,X1,X2)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_4) ).
cnf(u_to_v_equals_w_to_x,hypothesis,
equidistant(u,v,w,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_v_equals_w_to_x) ).
cnf(d4_2,axiom,
( equidistant(X2,X1,X4,X3)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_2) ).
cnf(v_to_w_equals_x_to_u,hypothesis,
equidistant(v,w,x,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_to_w_equals_x_to_u) ).
cnf(t10_1,axiom,
( colinear(X3,X2,X1)
| ~ colinear(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_1) ).
cnf(prove_uvw_not_colinear,negated_conjecture,
colinear(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_uvw_not_colinear) ).
cnf(d3,axiom,
( equidistant(X2,X1,X3,X4)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3) ).
cnf(u_to_w_equals_v_to_x,hypothesis,
equidistant(u,w,v,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_w_equals_v_to_x) ).
cnf(c4,axiom,
( colinear(X3,X4,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X2,X5,X4,X6)
| ~ equidistant(X1,X5,X3,X6)
| ~ colinear(X1,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c4) ).
cnf(d4_1,axiom,
( equidistant(X1,X2,X4,X3)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_1) ).
cnf(t10_4,axiom,
( colinear(X3,X1,X2)
| ~ colinear(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_4) ).
cnf(b0,axiom,
( between(X2,X3,X1)
| X1 != extension(X2,X3,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b0) ).
cnf(b11,axiom,
( between(X3,X4,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X2,X5,X4,X6)
| ~ equidistant(X1,X5,X3,X6)
| ~ between(X1,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b11) ).
cnf(reflexivity_for_equidistance,axiom,
equidistant(X1,X2,X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',reflexivity_for_equidistance) ).
cnf(t1,axiom,
( between(X3,X2,X1)
| ~ between(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1) ).
cnf(d4_3,axiom,
( equidistant(X3,X4,X2,X1)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_3) ).
cnf(d4_5,axiom,
( equidistant(X4,X3,X2,X1)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_5) ).
cnf(t12_2,axiom,
( colinear(X2,X3,X4)
| X1 = X2
| ~ colinear(X1,X2,X3)
| ~ colinear(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_2) ).
cnf(u_not_v,hypothesis,
u != v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_not_v) ).
cnf(t10_2,axiom,
( colinear(X2,X3,X1)
| ~ colinear(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_2) ).
cnf(y_between_v_and_x,hypothesis,
between(v,y,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',y_between_v_and_x) ).
cnf(b3,axiom,
( X2 = X3
| ~ between(X1,X2,X3)
| ~ between(X1,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b3) ).
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(x_not_u,hypothesis,
x != u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_not_u) ).
cnf(b9,axiom,
( between(X1,X2,X4)
| ~ between(X1,X2,X3)
| ~ between(X1,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b9) ).
cnf(t2,axiom,
between(X1,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2) ).
cnf(b5,axiom,
( between(X2,X3,X4)
| ~ between(X1,X2,X3)
| ~ between(X1,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b5) ).
cnf(c5_2,axiom,
( colinear(X4,X1,X2)
| X3 = X2
| ~ colinear(X1,X2,X3)
| ~ colinear(X4,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c5_2) ).
cnf(colinearity1,axiom,
( colinear(X1,X2,X3)
| ~ between(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-1.ax',colinearity1) ).
cnf(b8,axiom,
( between(X1,X4,X3)
| ~ between(X1,X2,X3)
| ~ between(X2,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b8) ).
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(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(y_between_u_and_w,hypothesis,
between(u,y,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',y_between_u_and_w) ).
cnf(d7,axiom,
equidistant(X1,X1,X2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7) ).
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(identity_for_betweeness,axiom,
( X1 = X2
| ~ between(X1,X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',identity_for_betweeness) ).
cnf(c_0_37,axiom,
( equidistant(X4,X3,X1,X2)
| ~ equidistant(X1,X2,X3,X4) ),
d4_4 ).
cnf(c_0_38,hypothesis,
equidistant(u,v,w,x),
u_to_v_equals_w_to_x ).
cnf(c_0_39,axiom,
( equidistant(X2,X1,X4,X3)
| ~ equidistant(X1,X2,X3,X4) ),
d4_2 ).
cnf(c_0_40,hypothesis,
equidistant(v,w,x,u),
v_to_w_equals_x_to_u ).
cnf(c_0_41,axiom,
( colinear(X3,X2,X1)
| ~ colinear(X1,X2,X3) ),
t10_1 ).
cnf(c_0_42,negated_conjecture,
colinear(u,v,w),
prove_uvw_not_colinear ).
cnf(c_0_43,axiom,
( equidistant(X2,X1,X3,X4)
| ~ equidistant(X1,X2,X3,X4) ),
d3 ).
cnf(c_0_44,hypothesis,
equidistant(u,w,v,x),
u_to_w_equals_v_to_x ).
cnf(c_0_45,axiom,
( colinear(X3,X4,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X2,X5,X4,X6)
| ~ equidistant(X1,X5,X3,X6)
| ~ colinear(X1,X2,X5) ),
c4 ).
cnf(c_0_46,hypothesis,
equidistant(x,w,u,v),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_47,axiom,
( equidistant(X1,X2,X4,X3)
| ~ equidistant(X1,X2,X3,X4) ),
d4_1 ).
cnf(c_0_48,hypothesis,
equidistant(w,v,u,x),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_49,axiom,
( colinear(X3,X1,X2)
| ~ colinear(X1,X2,X3) ),
t10_4 ).
cnf(c_0_50,negated_conjecture,
colinear(w,v,u),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_51,axiom,
( between(X2,X3,X1)
| X1 != extension(X2,X3,X4,X5) ),
b0 ).
cnf(c_0_52,axiom,
( between(X3,X4,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X2,X5,X4,X6)
| ~ equidistant(X1,X5,X3,X6)
| ~ between(X1,X2,X5) ),
b11 ).
cnf(c_0_53,axiom,
equidistant(X1,X2,X2,X1),
reflexivity_for_equidistance ).
cnf(c_0_54,hypothesis,
equidistant(w,u,v,x),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_55,hypothesis,
( colinear(X1,u,v)
| ~ colinear(X2,x,w)
| ~ equidistant(X2,w,X1,v)
| ~ equidistant(X2,x,X1,u) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_56,hypothesis,
equidistant(u,w,x,v),
inference(spm,[status(thm)],[c_0_47,c_0_44]) ).
cnf(c_0_57,hypothesis,
( colinear(X1,u,x)
| ~ colinear(X2,w,v)
| ~ equidistant(X2,v,X1,x)
| ~ equidistant(X2,w,X1,u) ),
inference(spm,[status(thm)],[c_0_45,c_0_48]) ).
cnf(c_0_58,negated_conjecture,
colinear(u,w,v),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_59,axiom,
( between(X3,X2,X1)
| ~ between(X1,X2,X3) ),
t1 ).
cnf(c_0_60,plain,
between(X1,X2,extension(X1,X2,X3,X4)),
inference(er,[status(thm)],[c_0_51]) ).
cnf(c_0_61,plain,
( between(X1,X2,X3)
| ~ between(X4,X3,X2)
| ~ equidistant(X4,X2,X1,X3)
| ~ equidistant(X4,X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_62,hypothesis,
equidistant(w,u,x,v),
inference(spm,[status(thm)],[c_0_39,c_0_44]) ).
cnf(c_0_63,hypothesis,
equidistant(w,v,x,u),
inference(spm,[status(thm)],[c_0_43,c_0_40]) ).
cnf(c_0_64,axiom,
( equidistant(X3,X4,X2,X1)
| ~ equidistant(X1,X2,X3,X4) ),
d4_3 ).
cnf(c_0_65,axiom,
( equidistant(X4,X3,X2,X1)
| ~ equidistant(X1,X2,X3,X4) ),
d4_5 ).
cnf(c_0_66,hypothesis,
( between(X1,v,x)
| ~ between(X2,w,u)
| ~ equidistant(X2,u,X1,x)
| ~ equidistant(X2,w,X1,v) ),
inference(spm,[status(thm)],[c_0_52,c_0_54]) ).
cnf(c_0_67,hypothesis,
equidistant(v,u,w,x),
inference(spm,[status(thm)],[c_0_43,c_0_38]) ).
cnf(c_0_68,axiom,
( colinear(X2,X3,X4)
| X1 = X2
| ~ colinear(X1,X2,X3)
| ~ colinear(X1,X2,X4) ),
t12_2 ).
cnf(c_0_69,hypothesis,
u != v,
u_not_v ).
cnf(c_0_70,hypothesis,
( colinear(x,u,v)
| ~ colinear(u,x,w) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_53])]) ).
cnf(c_0_71,axiom,
( colinear(X2,X3,X1)
| ~ colinear(X1,X2,X3) ),
t10_2 ).
cnf(c_0_72,hypothesis,
colinear(w,u,x),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_38]),c_0_58]),c_0_53])]) ).
cnf(c_0_73,hypothesis,
between(v,y,x),
y_between_v_and_x ).
cnf(c_0_74,hypothesis,
equidistant(u,x,v,w),
inference(spm,[status(thm)],[c_0_37,c_0_40]) ).
cnf(c_0_75,axiom,
( X2 = X3
| ~ between(X1,X2,X3)
| ~ between(X1,X3,X2) ),
b3 ).
cnf(c_0_76,plain,
between(extension(X1,X2,X3,X4),X2,X1),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_77,axiom,
( X1 = X2
| X3 = extension(X1,X2,X2,X3)
| ~ between(X1,X2,X3) ),
d10_1 ).
cnf(c_0_78,hypothesis,
( between(x,u,v)
| ~ between(w,v,u) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63])]) ).
cnf(c_0_79,hypothesis,
x != u,
x_not_u ).
cnf(c_0_80,hypothesis,
equidistant(w,x,v,u),
inference(spm,[status(thm)],[c_0_64,c_0_38]) ).
cnf(c_0_81,hypothesis,
equidistant(u,x,w,v),
inference(spm,[status(thm)],[c_0_65,c_0_40]) ).
cnf(c_0_82,axiom,
( between(X1,X2,X4)
| ~ between(X1,X2,X3)
| ~ between(X1,X3,X4) ),
b9 ).
cnf(c_0_83,axiom,
between(X1,X1,X2),
t2 ).
cnf(c_0_84,axiom,
( between(X2,X3,X4)
| ~ between(X1,X2,X3)
| ~ between(X1,X3,X4) ),
b5 ).
cnf(c_0_85,hypothesis,
equidistant(v,u,x,w),
inference(spm,[status(thm)],[c_0_39,c_0_38]) ).
cnf(c_0_86,hypothesis,
( between(X1,x,u)
| ~ between(X2,v,w)
| ~ equidistant(X2,w,X1,u)
| ~ equidistant(X2,v,X1,x) ),
inference(spm,[status(thm)],[c_0_52,c_0_40]) ).
cnf(c_0_87,hypothesis,
equidistant(x,w,v,u),
inference(spm,[status(thm)],[c_0_65,c_0_38]) ).
cnf(c_0_88,hypothesis,
( between(w,v,x)
| ~ between(v,w,u) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_53]),c_0_67])]) ).
cnf(c_0_89,negated_conjecture,
( colinear(v,X1,w)
| ~ colinear(u,v,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_42]),c_0_69]) ).
cnf(c_0_90,axiom,
( colinear(X4,X1,X2)
| X3 = X2
| ~ colinear(X1,X2,X3)
| ~ colinear(X4,X2,X3) ),
c5_2 ).
cnf(c_0_91,axiom,
( colinear(X1,X2,X3)
| ~ between(X1,X2,X3) ),
colinearity1 ).
cnf(c_0_92,hypothesis,
( colinear(v,u,x)
| ~ colinear(u,x,w) ),
inference(spm,[status(thm)],[c_0_41,c_0_70]) ).
cnf(c_0_93,hypothesis,
colinear(u,x,w),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_94,axiom,
( between(X1,X4,X3)
| ~ between(X1,X2,X3)
| ~ between(X2,X4,X3) ),
b8 ).
cnf(c_0_95,hypothesis,
between(x,y,v),
inference(spm,[status(thm)],[c_0_59,c_0_73]) ).
cnf(c_0_96,hypothesis,
equidistant(v,x,w,u),
inference(spm,[status(thm)],[c_0_64,c_0_44]) ).
cnf(c_0_97,hypothesis,
( between(X1,v,w)
| ~ between(X2,u,x)
| ~ equidistant(X2,x,X1,w)
| ~ equidistant(X2,u,X1,v) ),
inference(spm,[status(thm)],[c_0_52,c_0_74]) ).
cnf(c_0_98,plain,
( X1 = X2
| ~ between(extension(X1,X2,X3,X4),X1,X2) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_99,hypothesis,
( extension(x,u,u,v) = v
| ~ between(w,v,u) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79]) ).
cnf(c_0_100,hypothesis,
( between(X1,v,u)
| ~ between(X2,w,x)
| ~ equidistant(X2,x,X1,u)
| ~ equidistant(X2,w,X1,v) ),
inference(spm,[status(thm)],[c_0_52,c_0_80]) ).
cnf(c_0_101,hypothesis,
equidistant(x,u,w,v),
inference(spm,[status(thm)],[c_0_64,c_0_40]) ).
cnf(c_0_102,hypothesis,
equidistant(v,w,u,x),
inference(spm,[status(thm)],[c_0_37,c_0_81]) ).
cnf(c_0_103,plain,
( between(X1,X2,X3)
| ~ between(X1,X2,X1) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_104,plain,
( between(X1,X2,extension(X3,X2,X4,X5))
| ~ between(X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_84,c_0_60]) ).
cnf(c_0_105,hypothesis,
( between(x,u,w)
| ~ between(v,w,u) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_85]),c_0_40])]) ).
cnf(c_0_106,axiom,
( between(X1,X2,X4)
| X2 = X3
| ~ between(X1,X2,X3)
| ~ between(X2,X3,X4) ),
b7 ).
cnf(c_0_107,hypothesis,
( between(v,x,u)
| ~ between(x,v,w) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_53])]) ).
cnf(c_0_108,hypothesis,
( between(x,v,w)
| ~ between(v,w,u) ),
inference(spm,[status(thm)],[c_0_59,c_0_88]) ).
cnf(c_0_109,axiom,
( between(X1,X2,X3)
| between(X2,X3,X1)
| between(X3,X1,X2)
| ~ colinear(X1,X2,X3) ),
colinearity4 ).
cnf(c_0_110,negated_conjecture,
( colinear(w,X1,v)
| ~ colinear(u,v,X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_89]) ).
cnf(c_0_111,plain,
( X1 = X2
| colinear(X3,X4,X1)
| ~ colinear(X4,X1,X2)
| ~ between(X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_112,hypothesis,
colinear(v,u,x),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_93])]) ).
cnf(c_0_113,plain,
( between(X1,X2,X3)
| ~ between(X2,X1,X2) ),
inference(spm,[status(thm)],[c_0_84,c_0_83]) ).
cnf(c_0_114,hypothesis,
( between(X1,y,v)
| ~ between(X1,x,v) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_115,negated_conjecture,
colinear(w,u,v),
inference(spm,[status(thm)],[c_0_49,c_0_42]) ).
cnf(c_0_116,hypothesis,
( between(X1,w,u)
| ~ between(X2,v,x)
| ~ equidistant(X2,x,X1,u)
| ~ equidistant(X2,v,X1,w) ),
inference(spm,[status(thm)],[c_0_52,c_0_96]) ).
cnf(c_0_117,hypothesis,
( between(x,v,w)
| ~ between(w,u,x) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_53]),c_0_62])]) ).
cnf(c_0_118,hypothesis,
( between(X1,w,v)
| ~ between(X2,u,x)
| ~ equidistant(X2,x,X1,v)
| ~ equidistant(X2,u,X1,w) ),
inference(spm,[status(thm)],[c_0_52,c_0_81]) ).
cnf(c_0_119,hypothesis,
( ~ between(v,x,u)
| ~ between(w,v,u) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_79]) ).
cnf(c_0_120,hypothesis,
( between(w,v,u)
| ~ between(v,w,x) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_96]),c_0_53])]) ).
cnf(c_0_121,hypothesis,
( between(X1,w,v)
| ~ between(X2,x,u)
| ~ equidistant(X2,u,X1,v)
| ~ equidistant(X2,x,X1,w) ),
inference(spm,[status(thm)],[c_0_52,c_0_101]) ).
cnf(c_0_122,hypothesis,
equidistant(u,v,x,w),
inference(spm,[status(thm)],[c_0_47,c_0_38]) ).
cnf(c_0_123,hypothesis,
between(u,y,w),
y_between_u_and_w ).
cnf(c_0_124,hypothesis,
( between(X1,u,x)
| ~ between(X2,v,w)
| ~ equidistant(X2,w,X1,x)
| ~ equidistant(X2,v,X1,u) ),
inference(spm,[status(thm)],[c_0_52,c_0_102]) ).
cnf(c_0_125,axiom,
equidistant(X1,X1,X2,X2),
d7 ).
cnf(c_0_126,plain,
( between(extension(X1,X2,X3,X4),X2,X5)
| ~ between(X1,extension(X1,X2,X3,X4),X2) ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_127,hypothesis,
( extension(x,u,u,w) = w
| ~ between(v,w,u) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_105]),c_0_79]) ).
cnf(c_0_128,plain,
( extension(X1,X2,X3,X4) = X2
| between(X5,extension(X1,X2,X3,X4),X1)
| ~ between(X5,extension(X1,X2,X3,X4),X2) ),
inference(spm,[status(thm)],[c_0_106,c_0_76]) ).
cnf(c_0_129,axiom,
( between(X2,X4,X3)
| between(X4,X2,X3)
| ~ between(X1,X2,X3)
| ~ between(X1,X4,X3) ),
b14 ).
cnf(c_0_130,hypothesis,
( between(v,x,u)
| ~ between(v,w,u) ),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_131,axiom,
( between(X1,X2,X4)
| between(X1,X4,X2)
| ~ between(X1,X2,X3)
| ~ between(X1,X4,X3) ),
t9 ).
cnf(c_0_132,hypothesis,
( between(x,v,u)
| ~ between(w,u,v) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_63]),c_0_62])]) ).
cnf(c_0_133,negated_conjecture,
( between(w,X1,v)
| between(X1,v,w)
| between(v,w,X1)
| ~ colinear(u,v,X1) ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_134,hypothesis,
( colinear(X1,v,u)
| ~ between(X1,u,x) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_79]) ).
cnf(c_0_135,hypothesis,
( between(y,v,X1)
| ~ between(v,x,v) ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_136,negated_conjecture,
( between(w,u,v)
| between(u,v,w)
| between(v,w,u) ),
inference(spm,[status(thm)],[c_0_109,c_0_115]) ).
cnf(c_0_137,hypothesis,
( between(v,w,u)
| ~ between(w,v,x) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_80]),c_0_53])]) ).
cnf(c_0_138,hypothesis,
( between(w,v,x)
| ~ between(w,u,x) ),
inference(spm,[status(thm)],[c_0_59,c_0_117]) ).
cnf(c_0_139,hypothesis,
( between(x,w,v)
| ~ between(v,u,x) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_53]),c_0_85])]) ).
cnf(c_0_140,hypothesis,
( ~ between(v,x,u)
| ~ between(v,w,x) ),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_141,hypothesis,
( between(x,w,v)
| ~ between(w,x,u) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_53]),c_0_62])]) ).
cnf(c_0_142,hypothesis,
equidistant(x,v,w,u),
inference(spm,[status(thm)],[c_0_65,c_0_44]) ).
cnf(c_0_143,hypothesis,
( between(X1,u,x)
| ~ between(X2,w,v)
| ~ equidistant(X2,v,X1,x)
| ~ equidistant(X2,w,X1,u) ),
inference(spm,[status(thm)],[c_0_52,c_0_48]) ).
cnf(c_0_144,hypothesis,
( between(x,w,v)
| ~ between(u,v,w) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_56]),c_0_122])]) ).
cnf(c_0_145,hypothesis,
( between(X1,x,v)
| ~ between(X2,u,w)
| ~ equidistant(X2,w,X1,v)
| ~ equidistant(X2,u,X1,x) ),
inference(spm,[status(thm)],[c_0_52,c_0_56]) ).
cnf(c_0_146,hypothesis,
( between(X1,y,w)
| ~ between(X1,u,w) ),
inference(spm,[status(thm)],[c_0_94,c_0_123]) ).
cnf(c_0_147,axiom,
( X1 = X2
| ~ between(X1,X2,X1) ),
identity_for_betweeness ).
cnf(c_0_148,hypothesis,
( between(x,u,x)
| ~ between(w,v,w) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_63])]) ).
cnf(c_0_149,hypothesis,
( between(w,u,X1)
| ~ between(x,w,u)
| ~ between(v,w,u) ),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_150,hypothesis,
( between(X1,v,x)
| ~ between(X1,v,u)
| ~ between(w,v,u) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_99]),c_0_69]) ).
cnf(c_0_151,hypothesis,
( between(x,X1,u)
| between(X1,x,u)
| ~ between(v,X1,u)
| ~ between(v,w,u) ),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_152,hypothesis,
( between(x,v,X1)
| between(x,X1,v)
| ~ between(x,X1,u)
| ~ between(w,u,v) ),
inference(spm,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_153,negated_conjecture,
( between(w,u,v)
| between(u,v,w)
| between(v,w,u) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_83])]) ).
cnf(c_0_154,hypothesis,
( between(X1,v,X2)
| ~ between(X1,y,X2)
| ~ between(v,x,v) ),
inference(spm,[status(thm)],[c_0_94,c_0_135]) ).
cnf(c_0_155,negated_conjecture,
( between(v,u,w)
| between(u,v,w)
| between(v,w,u) ),
inference(spm,[status(thm)],[c_0_59,c_0_136]) ).
cnf(c_0_156,hypothesis,
( between(v,w,u)
| ~ between(w,u,x) ),
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_157,hypothesis,
( between(v,w,x)
| ~ between(v,u,x) ),
inference(spm,[status(thm)],[c_0_59,c_0_139]) ).
cnf(c_0_158,hypothesis,
( ~ between(v,w,x)
| ~ between(v,w,u) ),
inference(spm,[status(thm)],[c_0_140,c_0_130]) ).
cnf(c_0_159,hypothesis,
( between(v,w,x)
| ~ between(w,x,u) ),
inference(spm,[status(thm)],[c_0_59,c_0_141]) ).
cnf(c_0_160,hypothesis,
( between(w,u,x)
| ~ between(x,v,w) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_53]),c_0_142])]) ).
cnf(c_0_161,hypothesis,
( between(v,u,x)
| ~ between(x,w,v) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_87]),c_0_53])]) ).
cnf(c_0_162,hypothesis,
( between(v,w,x)
| ~ between(u,v,w) ),
inference(spm,[status(thm)],[c_0_59,c_0_144]) ).
cnf(c_0_163,hypothesis,
( between(x,w,u)
| ~ between(v,u,w) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_40]),c_0_85])]) ).
cnf(c_0_164,hypothesis,
( between(v,x,v)
| ~ between(w,u,w) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_125]),c_0_54])]) ).
cnf(c_0_165,hypothesis,
( between(w,y,X1)
| ~ between(X1,u,w) ),
inference(spm,[status(thm)],[c_0_59,c_0_146]) ).
cnf(c_0_166,hypothesis,
~ between(w,v,w),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_79]) ).
cnf(c_0_167,plain,
$false,
inference(cdclpropres,[status(thm)],[c_0_149,c_0_150,c_0_151,c_0_152,c_0_153,c_0_154,c_0_155,c_0_156,c_0_157,c_0_158,c_0_159,c_0_160,c_0_161,c_0_162,c_0_163,c_0_137,c_0_164,c_0_120,c_0_165,c_0_166]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.20 % Problem : GEO070-3 : TPTP v9.2.1. Bugfixed v1.2.1.
% 0.04/0.20 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.13/0.44 % Computer : n028.cluster.edu
% 0.13/0.44 % Model : x86_64 x86_64
% 0.13/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.44 % Memory : 8042.1875MB
% 0.13/0.44 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.44 % CPULimit : 300
% 0.13/0.44 % WCLimit : 300
% 0.13/0.44 % DateTime : Mon May 4 17:42:16 EDT 2026
% 0.15/0.45 % CPUTime :
% 0.15/0.46 % start to proof: theBenchmark
% 19.26/13.09 % Version : CSE_E---1.7
% 19.26/13.09 % Problem : theBenchmark.p
% 19.26/13.09 % SZS status Unsatisfiable for theBenchmark.p
% 19.26/13.09 % SZS output start CNFRefutation
% See solution above
% 19.36/13.16 % Total time : 10.385s
%------------------------------------------------------------------------------