%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO059-3 : TPTP v9.2.1. Released v1.0.0.
% 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 04:19:11 PM UTC 2026
% Result : Unsatisfiable 0.31s 1.62s
% Output : CNFRefutation 0.41s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_43)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_congruence,negated_conjecture,
~ equidistant(v,u,v,reflection(reflection(u,v),v)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_congruence) ).
cnf(reflection,axiom,
reflection(X1,X2) = extension(X1,X2,X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-2.ax',reflection) ).
cnf(r2_2,axiom,
equidistant(X1,reflection(X2,X1),X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_2) ).
cnf(r2_1,axiom,
between(X1,X2,reflection(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_1) ).
cnf(r4,axiom,
( X2 = X1
| X1 != reflection(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r4) ).
cnf(r3_1,axiom,
( X2 = reflection(X1,X2)
| X1 != X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_1) ).
cnf(r3_2,axiom,
X1 = reflection(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_2) ).
cnf(continuity2,axiom,
( equidistant(X1,X6,X1,continuous(X1,X2,X3,X6,X4,X5))
| ~ equidistant(X1,X2,X1,X3)
| ~ equidistant(X1,X4,X1,X5)
| ~ between(X1,X2,X4)
| ~ between(X2,X6,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',continuity2) ).
cnf(continuity1,axiom,
( between(X3,continuous(X1,X2,X3,X6,X4,X5),X5)
| ~ equidistant(X1,X2,X1,X3)
| ~ equidistant(X1,X4,X1,X5)
| ~ between(X1,X2,X4)
| ~ between(X2,X6,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',continuity1) ).
cnf(euclid3,axiom,
( X1 = X2
| between(euclid1(X1,X4,X2,X5,X3),X3,euclid2(X1,X4,X2,X5,X3))
| ~ between(X1,X2,X3)
| ~ between(X4,X2,X5) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',euclid3) ).
cnf(euclid1,axiom,
( X1 = X2
| between(X1,X4,euclid1(X1,X4,X2,X5,X3))
| ~ between(X1,X2,X3)
| ~ between(X4,X2,X5) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',euclid1) ).
cnf(euclid2,axiom,
( X1 = X2
| between(X1,X5,euclid2(X1,X4,X2,X5,X3))
| ~ between(X1,X2,X3)
| ~ between(X4,X2,X5) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',euclid2) ).
cnf(inner_pasch1,axiom,
( between(X2,inner_pasch(X1,X2,X3,X5,X4),X4)
| ~ between(X1,X2,X3)
| ~ between(X4,X5,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',inner_pasch1) ).
cnf(inner_pasch2,axiom,
( between(X5,inner_pasch(X1,X2,X3,X5,X4),X1)
| ~ between(X1,X2,X3)
| ~ between(X4,X5,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',inner_pasch2) ).
cnf(outer_five_segment,axiom,
( X1 = X2
| equidistant(X5,X7,X6,X8)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X2,X5,X4,X6)
| ~ equidistant(X1,X7,X3,X8)
| ~ equidistant(X2,X7,X4,X8)
| ~ between(X1,X2,X5)
| ~ between(X3,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',outer_five_segment) ).
cnf(upper_dimension,axiom,
( between(X1,X4,X5)
| between(X4,X5,X1)
| between(X5,X1,X4)
| X2 = X3
| ~ equidistant(X1,X2,X1,X3)
| ~ equidistant(X4,X2,X4,X3)
| ~ equidistant(X5,X2,X5,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',upper_dimension) ).
cnf(d8,axiom,
( equidistant(X1,X5,X3,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X2,X5,X4,X6)
| ~ between(X1,X2,X5)
| ~ between(X3,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8) ).
cnf(d5,axiom,
( equidistant(X1,X2,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X3,X4,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5) ).
cnf(transitivity_for_equidistance,axiom,
( equidistant(X3,X4,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X1,X2,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',transitivity_for_equidistance) ).
cnf(d10_2,axiom,
( extension(X5,X6,X1,X2) = extension(X5,X6,X3,X4)
| X5 = X6
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_2) ).
cnf(segment_construction2,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',segment_construction2) ).
cnf(d4_1,axiom,
( equidistant(X1,X2,X4,X3)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_1) ).
cnf(d3,axiom,
( equidistant(X2,X1,X3,X4)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3) ).
cnf(d4_2,axiom,
( equidistant(X2,X1,X4,X3)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_2) ).
cnf(d2,axiom,
( equidistant(X3,X4,X1,X2)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).
cnf(d4_3,axiom,
( equidistant(X3,X4,X2,X1)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_3) ).
cnf(d4_4,axiom,
( equidistant(X4,X3,X1,X2)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_4) ).
cnf(d4_5,axiom,
( equidistant(X4,X3,X2,X1)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_5) ).
cnf(d9,axiom,
( X1 = X2
| X3 = X4
| ~ between(X1,X2,X3)
| ~ between(X1,X2,X4)
| ~ equidistant(X2,X3,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9) ).
cnf(segment_construction1,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',segment_construction1) ).
cnf(d10_3,axiom,
( extension(X1,X2,X1,X2) = extension(X1,X2,X2,X1)
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_3) ).
cnf(b0,axiom,
( between(X2,X3,X1)
| X1 != extension(X2,X3,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b0) ).
cnf(identity_for_equidistance,axiom,
( X1 = X2
| ~ equidistant(X1,X2,X3,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',identity_for_equidistance) ).
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(e1,axiom,
X1 = extension(X2,X1,X3,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e1) ).
cnf(d7,axiom,
equidistant(X1,X1,X2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7) ).
cnf(d1,axiom,
equidistant(X1,X2,X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
cnf(reflexivity_for_equidistance,axiom,
equidistant(X1,X2,X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',reflexivity_for_equidistance) ).
cnf(identity_for_betweeness,axiom,
( X1 = X2
| ~ between(X1,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',identity_for_betweeness) ).
cnf(lower_dimension3,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',lower_dimension3) ).
cnf(lower_dimension2,axiom,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',lower_dimension2) ).
cnf(lower_dimension1,axiom,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',lower_dimension1) ).
cnf(i_0_42,negated_conjecture,
~ equidistant(v,u,v,reflection(reflection(u,v),v)),
prove_congruence ).
cnf(i_0_43,axiom,
reflection(X1,X2) = extension(X1,X2,X1,X2),
reflection ).
cnf(i_0_44,axiom,
equidistant(X1,reflection(X2,X1),X2,X1),
r2_2 ).
cnf(i_0_45,axiom,
between(X1,X2,reflection(X1,X2)),
r2_1 ).
cnf(i_0_46,axiom,
( X2 = X1
| X1 != reflection(X2,X1) ),
r4 ).
cnf(i_0_47,axiom,
( X2 = reflection(X1,X2)
| X1 != X2 ),
r3_1 ).
cnf(i_0_48,axiom,
X1 = reflection(X1,X1),
r3_2 ).
cnf(i_0_49,axiom,
( equidistant(X1,X6,X1,continuous(X1,X2,X3,X6,X4,X5))
| ~ equidistant(X1,X2,X1,X3)
| ~ equidistant(X1,X4,X1,X5)
| ~ between(X1,X2,X4)
| ~ between(X2,X6,X4) ),
continuity2,
[final] ).
cnf(i_0_50,axiom,
( between(X3,continuous(X1,X2,X3,X6,X4,X5),X5)
| ~ equidistant(X1,X2,X1,X3)
| ~ equidistant(X1,X4,X1,X5)
| ~ between(X1,X2,X4)
| ~ between(X2,X6,X4) ),
continuity1,
[final] ).
cnf(i_0_51,axiom,
( X1 = X2
| between(euclid1(X1,X4,X2,X5,X3),X3,euclid2(X1,X4,X2,X5,X3))
| ~ between(X1,X2,X3)
| ~ between(X4,X2,X5) ),
euclid3,
[final] ).
cnf(i_0_52,negated_conjecture,
~ equidistant(v,u,v,extension(extension(u,v,u,v),v,extension(u,v,u,v),v)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_42,c_0_43]),c_0_43]),
[final] ).
cnf(i_0_53,axiom,
( X1 = X2
| between(X1,X4,euclid1(X1,X4,X2,X5,X3))
| ~ between(X1,X2,X3)
| ~ between(X4,X2,X5) ),
euclid1,
[final] ).
cnf(i_0_54,axiom,
( X1 = X2
| between(X1,X5,euclid2(X1,X4,X2,X5,X3))
| ~ between(X1,X2,X3)
| ~ between(X4,X2,X5) ),
euclid2,
[final] ).
cnf(i_0_55,axiom,
( between(X2,inner_pasch(X1,X2,X3,X5,X4),X4)
| ~ between(X1,X2,X3)
| ~ between(X4,X5,X3) ),
inner_pasch1,
[final] ).
cnf(i_0_56,axiom,
( between(X5,inner_pasch(X1,X2,X3,X5,X4),X1)
| ~ between(X1,X2,X3)
| ~ between(X4,X5,X3) ),
inner_pasch2,
[final] ).
cnf(i_0_57,axiom,
( X1 = X2
| equidistant(X5,X7,X6,X8)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X2,X5,X4,X6)
| ~ equidistant(X1,X7,X3,X8)
| ~ equidistant(X2,X7,X4,X8)
| ~ between(X1,X2,X5)
| ~ between(X3,X4,X6) ),
outer_five_segment,
[final] ).
cnf(i_0_58,axiom,
( between(X1,X4,X5)
| between(X4,X5,X1)
| between(X5,X1,X4)
| X2 = X3
| ~ equidistant(X1,X2,X1,X3)
| ~ equidistant(X4,X2,X4,X3)
| ~ equidistant(X5,X2,X5,X3) ),
upper_dimension,
[final] ).
cnf(i_0_59,axiom,
( equidistant(X1,X5,X3,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X2,X5,X4,X6)
| ~ between(X1,X2,X5)
| ~ between(X3,X4,X6) ),
d8,
[final] ).
cnf(i_0_60,axiom,
( equidistant(X1,X2,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X3,X4,X5,X6) ),
d5,
[final] ).
cnf(i_0_61,axiom,
( equidistant(X3,X4,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X1,X2,X5,X6) ),
transitivity_for_equidistance,
[final] ).
cnf(i_0_62,axiom,
( extension(X5,X6,X1,X2) = extension(X5,X6,X3,X4)
| X5 = X6
| ~ equidistant(X1,X2,X3,X4) ),
d10_2,
[final] ).
cnf(i_0_63,plain,
equidistant(X1,extension(X2,X1,X2,X1),X2,X1),
inference(rw,[status(thm)],[i_0_44,c_0_43]),
[final] ).
cnf(i_0_64,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
segment_construction2,
[final] ).
cnf(i_0_65,axiom,
( equidistant(X1,X2,X4,X3)
| ~ equidistant(X1,X2,X3,X4) ),
d4_1,
[final] ).
cnf(i_0_66,axiom,
( equidistant(X2,X1,X3,X4)
| ~ equidistant(X1,X2,X3,X4) ),
d3,
[final] ).
cnf(i_0_67,axiom,
( equidistant(X2,X1,X4,X3)
| ~ equidistant(X1,X2,X3,X4) ),
d4_2,
[final] ).
cnf(i_0_68,axiom,
( equidistant(X3,X4,X1,X2)
| ~ equidistant(X1,X2,X3,X4) ),
d2,
[final] ).
cnf(i_0_69,axiom,
( equidistant(X3,X4,X2,X1)
| ~ equidistant(X1,X2,X3,X4) ),
d4_3,
[final] ).
cnf(i_0_70,axiom,
( equidistant(X4,X3,X1,X2)
| ~ equidistant(X1,X2,X3,X4) ),
d4_4,
[final] ).
cnf(i_0_71,axiom,
( equidistant(X4,X3,X2,X1)
| ~ equidistant(X1,X2,X3,X4) ),
d4_5,
[final] ).
cnf(i_0_72,axiom,
( X1 = X2
| X3 = X4
| ~ between(X1,X2,X3)
| ~ between(X1,X2,X4)
| ~ equidistant(X2,X3,X2,X4) ),
d9,
[final] ).
cnf(i_0_73,plain,
between(X1,X2,extension(X1,X2,X1,X2)),
inference(rw,[status(thm)],[i_0_45,c_0_43]),
[final] ).
cnf(i_0_74,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
segment_construction1,
[final] ).
cnf(i_0_75,axiom,
( extension(X1,X2,X1,X2) = extension(X1,X2,X2,X1)
| X1 = X2 ),
d10_3,
[final] ).
cnf(i_0_76,axiom,
( between(X2,X3,X1)
| X1 != extension(X2,X3,X4,X5) ),
b0,
[final] ).
cnf(i_0_77,plain,
( X1 = X2
| X1 != extension(X2,X1,X2,X1) ),
inference(rw,[status(thm)],[i_0_46,c_0_43]),
[final] ).
cnf(i_0_78,axiom,
( X1 = X2
| ~ equidistant(X1,X2,X3,X3) ),
identity_for_equidistance,
[final] ).
cnf(i_0_79,axiom,
( X1 = X2
| X3 = extension(X1,X2,X2,X3)
| ~ between(X1,X2,X3) ),
d10_1,
[final] ).
cnf(i_0_80,plain,
( X2 = extension(X1,X2,X1,X2)
| X1 != X2 ),
inference(rw,[status(thm)],[i_0_47,c_0_43]),
[final] ).
cnf(i_0_81,plain,
X1 = extension(X1,X1,X1,X1),
inference(rw,[status(thm)],[i_0_48,c_0_43]),
[final] ).
cnf(i_0_82,axiom,
X1 = extension(X2,X1,X3,X3),
e1,
[final] ).
cnf(i_0_83,axiom,
equidistant(X1,X1,X2,X2),
d7,
[final] ).
cnf(i_0_84,axiom,
equidistant(X1,X2,X1,X2),
d1,
[final] ).
cnf(i_0_85,axiom,
equidistant(X1,X2,X2,X1),
reflexivity_for_equidistance,
[final] ).
cnf(i_0_86,axiom,
( X1 = X2
| ~ between(X1,X2,X1) ),
identity_for_betweeness,
[final] ).
cnf(i_0_87,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
lower_dimension3,
[final] ).
cnf(i_0_88,axiom,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
lower_dimension2,
[final] ).
cnf(i_0_89,axiom,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
lower_dimension1,
[final] ).
cnf(i_0_90,axiom,
X1 = X1 ).
cnf(i_0_91,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_92,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_93,axiom,
( X1 != X2
| extension(X1,X3,X4,X5) = extension(X2,X3,X4,X5) ) ).
cnf(i_0_94,axiom,
( X1 != X2
| extension(X3,X1,X4,X5) = extension(X3,X2,X4,X5) ) ).
cnf(i_0_95,axiom,
( X1 != X2
| extension(X3,X4,X1,X5) = extension(X3,X4,X2,X5) ) ).
cnf(i_0_96,axiom,
( X1 != X2
| extension(X3,X4,X5,X1) = extension(X3,X4,X5,X2) ) ).
cnf(i_0_97,axiom,
( X1 != X2
| ~ equidistant(X1,X3,X4,X5)
| equidistant(X2,X3,X4,X5) ) ).
cnf(i_0_98,axiom,
( X1 != X2
| ~ equidistant(X3,X1,X4,X5)
| equidistant(X3,X2,X4,X5) ) ).
cnf(i_0_99,axiom,
( X1 != X2
| ~ equidistant(X3,X4,X1,X5)
| equidistant(X3,X4,X2,X5) ) ).
cnf(i_0_100,axiom,
( X1 != X2
| ~ equidistant(X3,X4,X5,X1)
| equidistant(X3,X4,X5,X2) ) ).
cnf(i_0_101,axiom,
( X1 != X2
| ~ between(X1,X3,X4)
| between(X2,X3,X4) ) ).
cnf(i_0_102,axiom,
( X1 != X2
| ~ between(X3,X1,X4)
| between(X3,X2,X4) ) ).
cnf(i_0_103,axiom,
( X1 != X2
| ~ between(X3,X4,X1)
| between(X3,X4,X2) ) ).
cnf(i_0_90_001,axiom,
X1 = X1 ).
cnf(i_0_91_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_92_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_93_004,axiom,
( X1 != X2
| extension(X1,X3,X4,X5) = extension(X2,X3,X4,X5) ) ).
cnf(i_0_94_005,axiom,
( X1 != X2
| extension(X3,X1,X4,X5) = extension(X3,X2,X4,X5) ) ).
cnf(i_0_95_006,axiom,
( X1 != X2
| extension(X3,X4,X1,X5) = extension(X3,X4,X2,X5) ) ).
cnf(i_0_96_007,axiom,
( X1 != X2
| extension(X3,X4,X5,X1) = extension(X3,X4,X5,X2) ) ).
cnf(i_0_97_008,axiom,
( X1 != X2
| ~ equidistant(X1,X3,X4,X5)
| equidistant(X2,X3,X4,X5) ) ).
cnf(i_0_98_009,axiom,
( X1 != X2
| ~ equidistant(X3,X1,X4,X5)
| equidistant(X3,X2,X4,X5) ) ).
cnf(i_0_99_010,axiom,
( X1 != X2
| ~ equidistant(X3,X4,X1,X5)
| equidistant(X3,X4,X2,X5) ) ).
cnf(i_0_100_011,axiom,
( X1 != X2
| ~ equidistant(X3,X4,X5,X1)
| equidistant(X3,X4,X5,X2) ) ).
cnf(i_0_101_012,axiom,
( X1 != X2
| ~ between(X1,X3,X4)
| between(X2,X3,X4) ) ).
cnf(i_0_102_013,axiom,
( X1 != X2
| ~ between(X3,X1,X4)
| between(X3,X2,X4) ) ).
cnf(i_0_103_014,axiom,
( X1 != X2
| ~ between(X3,X4,X1)
| between(X3,X4,X2) ) ).
cnf(i_0_104,plain,
between(X1,X2,extension(X1,X2,X3,X4)),
inference(equality_inference,[],[76]) ).
cnf(i_0_105,plain,
X1 = extension(X1,X1,X1,X1),
inference(equality_inference,[],[80]) ).
cnf(i_0_106,plain,
equidistant(X1,extension(X2,X1,X3,X4),X4,X3),
inference(scs_inference,[],[i_0_64,i_0_65]) ).
cnf(i_0_107,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X1,X2,X4,X3) ),
inference(rename_variables,[],[i_0_65]) ).
cnf(i_0_108,plain,
equidistant(extension(X1,X2,X3,X4),X2,X3,X4),
inference(scs_inference,[],[i_0_64,i_0_65,i_0_66]) ).
cnf(i_0_109,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X2,X1,X3,X4) ),
inference(rename_variables,[],[i_0_66]) ).
cnf(i_0_110,plain,
equidistant(extension(X1,X2,X3,X4),X2,X4,X3),
inference(scs_inference,[],[i_0_64,i_0_65,i_0_66,i_0_67]) ).
cnf(i_0_111,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X2,X1,X4,X3) ),
inference(rename_variables,[],[i_0_67]) ).
cnf(i_0_112,plain,
equidistant(X1,X2,X3,extension(X4,X3,X1,X2)),
inference(scs_inference,[],[i_0_64,i_0_65,i_0_66,i_0_67,i_0_68]) ).
cnf(i_0_113,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X3,X4,X1,X2) ),
inference(rename_variables,[],[i_0_68]) ).
cnf(i_0_114,plain,
equidistant(X1,X2,extension(X3,X4,X1,X2),X4),
inference(scs_inference,[],[i_0_64,i_0_65,i_0_66,i_0_67,i_0_68,i_0_69]) ).
cnf(i_0_115,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X3,X4,X2,X1) ),
inference(rename_variables,[],[i_0_69]) ).
cnf(i_0_116,plain,
equidistant(X1,X2,X3,extension(X4,X3,X2,X1)),
inference(scs_inference,[],[i_0_64,i_0_65,i_0_66,i_0_67,i_0_68,i_0_69,i_0_70]) ).
cnf(i_0_117,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X4,X3,X1,X2) ),
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_118,plain,
equidistant(X1,X2,extension(X3,X4,X2,X1),X4),
inference(scs_inference,[],[i_0_64,i_0_65,i_0_66,i_0_67,i_0_68,i_0_69,i_0_70,i_0_71]) ).
cnf(i_0_119,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X4,X3,X2,X1) ),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_120,plain,
between(X1,X2,X2),
inference(scs_inference,[],[i_0_64,i_0_82,i_0_65,i_0_66,i_0_67,i_0_68,i_0_69,i_0_70,i_0_71,i_0_76]) ).
cnf(i_0_121,plain,
( X1 != extension(X2,X3,X4,X5)
| between(X2,X3,X1) ),
inference(rename_variables,[],[i_0_76]) ).
cnf(i_0_122,plain,
extension(X1,X2,X3,X3) = X2,
inference(scs_inference,[],[i_0_64,i_0_82,i_0_65,i_0_66,i_0_67,i_0_68,i_0_69,i_0_70,i_0_71,i_0_76,i_0_78]) ).
cnf(i_0_123,plain,
( ~ equidistant(X1,X2,X3,X3)
| X1 = X2 ),
inference(rename_variables,[],[i_0_78]) ).
cnf(i_0_124,plain,
~ equidistant(v,u,extension(extension(u,v,u,v),v,extension(u,v,u,v),v),v),
inference(scs_inference,[],[i_0_52,i_0_85,i_0_64,i_0_82,i_0_65,i_0_66,i_0_67,i_0_68,i_0_69,i_0_70,i_0_71,i_0_76,i_0_78,i_0_60]) ).
cnf(i_0_125,plain,
equidistant(X1,X2,X2,X1),
inference(rename_variables,[],[i_0_85]) ).
cnf(i_0_126,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X5,X6,X3,X4)
| ~ equidistant(X5,X6,X1,X2) ),
inference(rename_variables,[],[i_0_60]) ).
cnf(i_0_127,plain,
~ equidistant(v,extension(extension(u,v,u,v),v,extension(u,v,u,v),v),v,u),
inference(scs_inference,[],[i_0_52,i_0_84,i_0_85,i_0_64,i_0_82,i_0_65,i_0_66,i_0_67,i_0_68,i_0_69,i_0_70,i_0_71,i_0_76,i_0_78,i_0_60,i_0_61]) ).
cnf(i_0_128,plain,
equidistant(X1,X2,X1,X2),
inference(rename_variables,[],[i_0_84]) ).
cnf(i_0_129,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X5,X6,X3,X4)
| ~ equidistant(X1,X2,X5,X6) ),
inference(rename_variables,[],[i_0_61]) ).
cnf(i_0_130,plain,
~ equidistant(extension(X1,v,X2,X2),u,v,extension(extension(u,v,u,v),v,extension(u,v,u,v),v)),
inference(scs_inference,[],[i_0_52,i_0_84,i_0_85,i_0_64,i_0_82,i_0_65,i_0_66,i_0_67,i_0_68,i_0_69,i_0_70,i_0_71,i_0_76,i_0_78,i_0_60,i_0_61,i_0_97]) ).
cnf(i_0_131,plain,
extension(extension(u,v,u,v),v,extension(u,v,u,v),v) != u,
inference(scs_inference,[],[i_0_52,i_0_84,i_0_128,i_0_85,i_0_64,i_0_82,i_0_65,i_0_66,i_0_67,i_0_68,i_0_69,i_0_70,i_0_71,i_0_76,i_0_78,i_0_60,i_0_61,i_0_97,i_0_98]) ).
cnf(i_0_132,plain,
equidistant(X1,X2,X1,X2),
inference(rename_variables,[],[i_0_84]) ).
cnf(i_0_133,plain,
~ equidistant(v,u,extension(X1,v,X2,X2),extension(extension(u,v,u,v),v,extension(u,v,u,v),v)),
inference(scs_inference,[],[i_0_52,i_0_84,i_0_128,i_0_85,i_0_64,i_0_82,i_0_65,i_0_66,i_0_67,i_0_68,i_0_69,i_0_70,i_0_71,i_0_76,i_0_78,i_0_60,i_0_61,i_0_97,i_0_98,i_0_99]) ).
cnf(i_0_134,plain,
u != extension(extension(u,v,u,v),v,extension(u,v,u,v),v),
inference(scs_inference,[],[i_0_52,i_0_84,i_0_128,i_0_132,i_0_85,i_0_64,i_0_82,i_0_65,i_0_66,i_0_67,i_0_68,i_0_69,i_0_70,i_0_71,i_0_76,i_0_78,i_0_60,i_0_61,i_0_97,i_0_98,i_0_99,i_0_100]) ).
cnf(i_0_135,plain,
equidistant(X1,X2,X1,X2),
inference(rename_variables,[],[i_0_84]) ).
cnf(i_0_136,plain,
extension(X1,v,X2,X2) = extension(X3,v,X4,X4),
inference(scs_inference,[],[i_0_52,i_0_84,i_0_128,i_0_132,i_0_85,i_0_64,i_0_82,i_0_65,i_0_66,i_0_67,i_0_68,i_0_69,i_0_70,i_0_71,i_0_76,i_0_78,i_0_60,i_0_61,i_0_97,i_0_98,i_0_99,i_0_100,i_0_92]) ).
cnf(i_0_137,plain,
X1 = extension(X2,X1,X3,X3),
inference(rename_variables,[],[i_0_82]) ).
cnf(i_0_138,plain,
extension(lower_dimension_point_3,lower_dimension_point_1,X1,X2) != lower_dimension_point_2,
inference(scs_inference,[],[i_0_52,i_0_84,i_0_128,i_0_132,i_0_85,i_0_64,i_0_74,i_0_82,i_0_87,i_0_65,i_0_66,i_0_67,i_0_68,i_0_69,i_0_70,i_0_71,i_0_76,i_0_78,i_0_60,i_0_61,i_0_97,i_0_98,i_0_99,i_0_100,i_0_92,i_0_103]) ).
cnf(i_0_139,plain,
between(X1,X2,extension(X1,X2,X3,X4)),
inference(rename_variables,[],[i_0_74]) ).
cnf(i_0_140,plain,
( X1 != lower_dimension_point_3
| ~ between(X1,lower_dimension_point_1,lower_dimension_point_2) ),
inference(scs_inference,[],[i_0_52,i_0_84,i_0_128,i_0_132,i_0_85,i_0_64,i_0_74,i_0_82,i_0_87,i_0_65,i_0_66,i_0_67,i_0_68,i_0_69,i_0_70,i_0_71,i_0_76,i_0_78,i_0_60,i_0_61,i_0_97,i_0_98,i_0_99,i_0_100,i_0_92,i_0_103,i_0_101]) ).
cnf(i_0_141,plain,
( X1 != lower_dimension_point_1
| ~ between(lower_dimension_point_3,X1,lower_dimension_point_2) ),
inference(scs_inference,[],[i_0_52,i_0_84,i_0_128,i_0_132,i_0_85,i_0_64,i_0_74,i_0_82,i_0_87,i_0_65,i_0_66,i_0_67,i_0_68,i_0_69,i_0_70,i_0_71,i_0_76,i_0_78,i_0_60,i_0_61,i_0_97,i_0_98,i_0_99,i_0_100,i_0_92,i_0_103,i_0_101,i_0_102]) ).
cnf(i_0_142,plain,
equidistant(X1,X1,X2,X2),
inference(rename_variables,[],[i_0_83]) ).
cnf(i_0_143,plain,
equidistant(X1,X2,X1,X2),
inference(rename_variables,[],[i_0_84]) ).
cnf(i_0_144,plain,
( between(X1,continuous(X2,X3,X1,X4,X5,X6),X6)
| ~ equidistant(X2,X3,X2,X1)
| ~ equidistant(X2,X5,X2,X6)
| ~ between(X2,X3,X5)
| ~ between(X3,X4,X5) ),
inference(rename_variables,[],[i_0_50]) ).
cnf(i_0_145,plain,
between(X1,X2,extension(X1,X2,X3,X4)),
inference(rename_variables,[],[i_0_74]) ).
cnf(i_0_147,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
inference(equality_inference,[],[140]) ).
cnf(i_0_148,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
inference(equality_inference,[],[141]) ).
cnf(i_0_149,plain,
lower_dimension_point_2 != lower_dimension_point_1,
inference(scs_inference,[],[i_0_120,i_0_141]) ).
cnf(i_0_150,plain,
between(X1,X2,X2),
inference(rename_variables,[],[i_0_120]) ).
cnf(i_0_151,plain,
between(X1,X2,extension(X3,extension(X1,X2,X4,X5),X6,X6)),
inference(scs_inference,[],[i_0_120,i_0_122,i_0_141,i_0_76]) ).
cnf(i_0_152,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_122]) ).
cnf(i_0_153,plain,
( X1 != extension(X2,X3,X4,X5)
| between(X2,X3,X1) ),
inference(rename_variables,[],[i_0_76]) ).
cnf(i_0_154,plain,
$false,
inference(scs_inference,[],[i_0_52,i_0_120,i_0_110,i_0_112,i_0_122,i_0_141,i_0_76,i_0_61]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO059-3 : TPTP v9.2.1. Released v1.0.0.
% 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
% 0.15/0.33 % Computer : n014.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 17:38:36 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.31/1.62 % Version : CSE_E---1.7
% 0.31/1.62 % Problem : theBenchmark.p
% 0.31/1.62 % SZS status Unsatisfiable for theBenchmark.p
% 0.31/1.62 % SZS output start CNFRefutation
% See solution above
% 0.41/1.77 % Total time : 1.271s
%------------------------------------------------------------------------------