TSTP Solution File: GEO037-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO037-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 : 600s
% DateTime : Sat Jul 16 05:23:46 EDT 2022
% Result : Unsatisfiable 0.84s 1.08s
% Output : CNFRefutation 0.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 20
% Syntax : Number of clauses : 127 ( 68 unt; 0 nHn; 60 RR)
% Number of literals : 207 ( 57 equ; 82 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-5 aty)
% Number of variables : 455 ( 82 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(reflexivity_for_equidistance,axiom,
equidistant(X,Y,Y,X) ).
cnf(transitivity_for_equidistance,axiom,
( ~ equidistant(X,Y,Z,V)
| ~ equidistant(X,Y,V2,W)
| equidistant(Z,V,V2,W) ) ).
cnf(identity_for_equidistance,axiom,
( ~ equidistant(X,Y,Z,Z)
| X = Y ) ).
cnf(segment_construction1,axiom,
between(X,Y,extension(X,Y,W,V)) ).
cnf(segment_construction2,axiom,
equidistant(Y,extension(X,Y,W,V),W,V) ).
cnf(identity_for_betweeness,axiom,
( ~ between(X,Y,X)
| X = Y ) ).
cnf(inner_pasch1,axiom,
( ~ between(U,V,W)
| ~ between(Y,X,W)
| between(V,inner_pasch(U,V,W,X,Y),Y) ) ).
cnf(inner_pasch2,axiom,
( ~ between(U,V,W)
| ~ between(Y,X,W)
| between(X,inner_pasch(U,V,W,X,Y),U) ) ).
cnf(lower_dimension1,axiom,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ).
cnf(prove_lengthen,negated_conjecture,
( v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2)
| ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| ~ between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2)) ) ).
cnf(refute_0_0,plain,
( ~ equidistant(lower_dimension_point_2,lower_dimension_point_1,X_986,X_986)
| lower_dimension_point_2 = lower_dimension_point_1 ),
inference(subst,[],[identity_for_equidistance:[bind(X,$fot(lower_dimension_point_2)),bind(Y,$fot(lower_dimension_point_1)),bind(Z,$fot(X_986))]]) ).
cnf(refute_0_1,plain,
equidistant(X_390,X_395,X_395,X_390),
inference(subst,[],[reflexivity_for_equidistance:[bind(X,$fot(X_390)),bind(Y,$fot(X_395))]]) ).
cnf(refute_0_2,plain,
( ~ equidistant(X_390,X_395,X_391,X_392)
| ~ equidistant(X_390,X_395,X_395,X_390)
| equidistant(X_395,X_390,X_391,X_392) ),
inference(subst,[],[transitivity_for_equidistance:[bind(V,$fot(X_390)),bind(V2,$fot(X_391)),bind(W,$fot(X_392)),bind(X,$fot(X_390)),bind(Y,$fot(X_395)),bind(Z,$fot(X_395))]]) ).
cnf(refute_0_3,plain,
( ~ equidistant(X_390,X_395,X_391,X_392)
| equidistant(X_395,X_390,X_391,X_392) ),
inference(resolve,[$cnf( equidistant(X_390,X_395,X_395,X_390) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ equidistant(X_660,X_659,X_663,extension(X_661,X_663,extension(X_662,X_664,X_665,extension(X_658,X_665,X_660,X_659)),X_664))
| equidistant(X_659,X_660,X_663,extension(X_661,X_663,extension(X_662,X_664,X_665,extension(X_658,X_665,X_660,X_659)),X_664)) ),
inference(subst,[],[refute_0_3:[bind(X_390,$fot(X_660)),bind(X_391,$fot(X_663)),bind(X_392,$fot(extension(X_661,X_663,extension(X_662,X_664,X_665,extension(X_658,X_665,X_660,X_659)),X_664))),bind(X_395,$fot(X_659))]]) ).
cnf(refute_0_5,plain,
equidistant(X_23,extension(X,X_23,X_25,X_22),X_25,X_22),
inference(subst,[],[segment_construction2:[bind(V,$fot(X_22)),bind(W,$fot(X_25)),bind(Y,$fot(X_23))]]) ).
cnf(refute_0_6,plain,
( ~ equidistant(X_23,extension(X,X_23,X_25,X_22),X_25,X_22)
| equidistant(X_25,X_22,X_25,X_22) ),
inference(subst,[],[transitivity_for_equidistance:[bind(V,$fot(X_22)),bind(V2,$fot(X_25)),bind(W,$fot(X_22)),bind(X,$fot(X_23)),bind(Y,$fot(extension(X,X_23,X_25,X_22))),bind(Z,$fot(X_25))]]) ).
cnf(refute_0_7,plain,
equidistant(X_25,X_22,X_25,X_22),
inference(resolve,[$cnf( equidistant(X_23,extension(X,X_23,X_25,X_22),X_25,X_22) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
equidistant(X_391,X_392,X_391,X_392),
inference(subst,[],[refute_0_7:[bind(X_22,$fot(X_392)),bind(X_25,$fot(X_391))]]) ).
cnf(refute_0_9,plain,
( ~ equidistant(X_391,X_392,X_391,X_392)
| ~ equidistant(X_391,X_392,X_395,X_390)
| equidistant(X_395,X_390,X_391,X_392) ),
inference(subst,[],[transitivity_for_equidistance:[bind(V,$fot(X_390)),bind(V2,$fot(X_391)),bind(W,$fot(X_392)),bind(X,$fot(X_391)),bind(Y,$fot(X_392)),bind(Z,$fot(X_395))]]) ).
cnf(refute_0_10,plain,
( ~ equidistant(X_391,X_392,X_395,X_390)
| equidistant(X_395,X_390,X_391,X_392) ),
inference(resolve,[$cnf( equidistant(X_391,X_392,X_391,X_392) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ equidistant(X_615,extension(X_613,X_615,extension(X_614,X_616,X_617,extension(X_610,X_617,X_612,X_611)),X_616),X_612,X_611)
| equidistant(X_612,X_611,X_615,extension(X_613,X_615,extension(X_614,X_616,X_617,extension(X_610,X_617,X_612,X_611)),X_616)) ),
inference(subst,[],[refute_0_10:[bind(X_390,$fot(X_611)),bind(X_391,$fot(X_615)),bind(X_392,$fot(extension(X_613,X_615,extension(X_614,X_616,X_617,extension(X_610,X_617,X_612,X_611)),X_616))),bind(X_395,$fot(X_612))]]) ).
cnf(refute_0_12,plain,
( ~ equidistant(extension(X_597,X_599,extension(X_598,X_600,X_601,extension(X_594,X_601,X_596,X_595)),X_600),X_599,X_596,X_595)
| equidistant(X_599,extension(X_597,X_599,extension(X_598,X_600,X_601,extension(X_594,X_601,X_596,X_595)),X_600),X_596,X_595) ),
inference(subst,[],[refute_0_3:[bind(X_390,$fot(extension(X_597,X_599,extension(X_598,X_600,X_601,extension(X_594,X_601,X_596,X_595)),X_600))),bind(X_391,$fot(X_596)),bind(X_392,$fot(X_595)),bind(X_395,$fot(X_599))]]) ).
cnf(refute_0_13,plain,
( ~ equidistant(X_548,X_547,extension(X_549,X_551,extension(X_550,X_552,X_553,extension(X_546,X_553,X_548,X_547)),X_552),X_551)
| equidistant(extension(X_549,X_551,extension(X_550,X_552,X_553,extension(X_546,X_553,X_548,X_547)),X_552),X_551,X_548,X_547) ),
inference(subst,[],[refute_0_10:[bind(X_390,$fot(X_551)),bind(X_391,$fot(X_548)),bind(X_392,$fot(X_547)),bind(X_395,$fot(extension(X_549,X_551,extension(X_550,X_552,X_553,extension(X_546,X_553,X_548,X_547)),X_552)))]]) ).
cnf(refute_0_14,plain,
equidistant(X_393,extension(X,X_393,X_395,X_390),X_395,X_390),
inference(subst,[],[segment_construction2:[bind(V,$fot(X_390)),bind(W,$fot(X_395)),bind(Y,$fot(X_393))]]) ).
cnf(refute_0_15,plain,
( ~ equidistant(X_393,extension(X,X_393,X_395,X_390),X_391,X_392)
| ~ equidistant(X_393,extension(X,X_393,X_395,X_390),X_395,X_390)
| equidistant(X_395,X_390,X_391,X_392) ),
inference(subst,[],[transitivity_for_equidistance:[bind(V,$fot(X_390)),bind(V2,$fot(X_391)),bind(W,$fot(X_392)),bind(X,$fot(X_393)),bind(Y,$fot(extension(X,X_393,X_395,X_390))),bind(Z,$fot(X_395))]]) ).
cnf(refute_0_16,plain,
( ~ equidistant(X_393,extension(X,X_393,X_395,X_390),X_391,X_392)
| equidistant(X_395,X_390,X_391,X_392) ),
inference(resolve,[$cnf( equidistant(X_393,extension(X,X_393,X_395,X_390),X_395,X_390) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ equidistant(X_455,extension(X,X_455,X_395,X_390),extension(X_450,X_453,extension(X_451,X_454,X_455,extension(X,X_455,X_395,X_390)),X_454),X_453)
| equidistant(X_395,X_390,extension(X_450,X_453,extension(X_451,X_454,X_455,extension(X,X_455,X_395,X_390)),X_454),X_453) ),
inference(subst,[],[refute_0_16:[bind(X_391,$fot(extension(X_450,X_453,extension(X_451,X_454,X_455,extension(X,X_455,X_395,X_390)),X_454))),bind(X_392,$fot(X_453)),bind(X_393,$fot(X_455))]]) ).
cnf(refute_0_18,plain,
equidistant(X_410,extension(X,X_410,X_411,X_408),X_411,X_408),
inference(subst,[],[segment_construction2:[bind(V,$fot(X_408)),bind(W,$fot(X_411)),bind(Y,$fot(X_410))]]) ).
cnf(refute_0_19,plain,
equidistant(X_392,X_391,X_391,X_392),
inference(subst,[],[reflexivity_for_equidistance:[bind(X,$fot(X_392)),bind(Y,$fot(X_391))]]) ).
cnf(refute_0_20,plain,
( ~ equidistant(X_392,X_391,X_391,X_392)
| ~ equidistant(X_392,X_391,X_395,X_390)
| equidistant(X_395,X_390,X_391,X_392) ),
inference(subst,[],[transitivity_for_equidistance:[bind(V,$fot(X_390)),bind(V2,$fot(X_391)),bind(W,$fot(X_392)),bind(X,$fot(X_392)),bind(Y,$fot(X_391)),bind(Z,$fot(X_395))]]) ).
cnf(refute_0_21,plain,
( ~ equidistant(X_392,X_391,X_395,X_390)
| equidistant(X_395,X_390,X_391,X_392) ),
inference(resolve,[$cnf( equidistant(X_392,X_391,X_391,X_392) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ equidistant(X_410,extension(X,X_410,X_411,X_408),X_411,X_408)
| equidistant(X_411,X_408,extension(X,X_410,X_411,X_408),X_410) ),
inference(subst,[],[refute_0_21:[bind(X_390,$fot(X_408)),bind(X_391,$fot(extension(X,X_410,X_411,X_408))),bind(X_392,$fot(X_410)),bind(X_395,$fot(X_411))]]) ).
cnf(refute_0_23,plain,
equidistant(X_411,X_408,extension(X,X_410,X_411,X_408),X_410),
inference(resolve,[$cnf( equidistant(X_410,extension(X,X_410,X_411,X_408),X_411,X_408) )],[refute_0_18,refute_0_22]) ).
cnf(refute_0_24,plain,
equidistant(X_424,X_427,extension(X,X_426,X_424,X_427),X_426),
inference(subst,[],[refute_0_23:[bind(X_408,$fot(X_427)),bind(X_410,$fot(X_426)),bind(X_411,$fot(X_424))]]) ).
cnf(refute_0_25,plain,
( ~ equidistant(X_424,X_427,extension(X,X_426,X_424,X_427),X_426)
| equidistant(X_427,X_424,extension(X,X_426,X_424,X_427),X_426) ),
inference(subst,[],[refute_0_3:[bind(X_390,$fot(X_424)),bind(X_391,$fot(extension(X,X_426,X_424,X_427))),bind(X_392,$fot(X_426)),bind(X_395,$fot(X_427))]]) ).
cnf(refute_0_26,plain,
equidistant(X_427,X_424,extension(X,X_426,X_424,X_427),X_426),
inference(resolve,[$cnf( equidistant(X_424,X_427,extension(X,X_426,X_424,X_427),X_426) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
equidistant(X_448,extension(X_444,X_448,X_449,X_445),extension(X,X_447,extension(X_444,X_448,X_449,X_445),X_448),X_447),
inference(subst,[],[refute_0_26:[bind(X_424,$fot(extension(X_444,X_448,X_449,X_445))),bind(X_426,$fot(X_447)),bind(X_427,$fot(X_448))]]) ).
cnf(refute_0_28,plain,
( ~ equidistant(X_448,extension(X_444,X_448,X_449,X_445),extension(X,X_447,extension(X_444,X_448,X_449,X_445),X_448),X_447)
| equidistant(X_449,X_445,extension(X,X_447,extension(X_444,X_448,X_449,X_445),X_448),X_447) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(X_444)),bind(X_390,$fot(X_445)),bind(X_391,$fot(extension(X,X_447,extension(X_444,X_448,X_449,X_445),X_448))),bind(X_392,$fot(X_447)),bind(X_393,$fot(X_448)),bind(X_395,$fot(X_449))]]) ).
cnf(refute_0_29,plain,
equidistant(X_449,X_445,extension(X,X_447,extension(X_444,X_448,X_449,X_445),X_448),X_447),
inference(resolve,[$cnf( equidistant(X_448,extension(X_444,X_448,X_449,X_445),extension(X,X_447,extension(X_444,X_448,X_449,X_445),X_448),X_447) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
equidistant(X_455,extension(X,X_455,X_395,X_390),extension(X_450,X_453,extension(X_451,X_454,X_455,extension(X,X_455,X_395,X_390)),X_454),X_453),
inference(subst,[],[refute_0_29:[bind(X,$fot(X_450)),bind(X_444,$fot(X_451)),bind(X_445,$fot(extension(X,X_455,X_395,X_390))),bind(X_447,$fot(X_453)),bind(X_448,$fot(X_454)),bind(X_449,$fot(X_455))]]) ).
cnf(refute_0_31,plain,
equidistant(X_395,X_390,extension(X_450,X_453,extension(X_451,X_454,X_455,extension(X,X_455,X_395,X_390)),X_454),X_453),
inference(resolve,[$cnf( equidistant(X_455,extension(X,X_455,X_395,X_390),extension(X_450,X_453,extension(X_451,X_454,X_455,extension(X,X_455,X_395,X_390)),X_454),X_453) )],[refute_0_30,refute_0_17]) ).
cnf(refute_0_32,plain,
equidistant(X_548,X_547,extension(X_549,X_551,extension(X_550,X_552,X_553,extension(X_546,X_553,X_548,X_547)),X_552),X_551),
inference(subst,[],[refute_0_31:[bind(X,$fot(X_546)),bind(X_390,$fot(X_547)),bind(X_395,$fot(X_548)),bind(X_450,$fot(X_549)),bind(X_451,$fot(X_550)),bind(X_453,$fot(X_551)),bind(X_454,$fot(X_552)),bind(X_455,$fot(X_553))]]) ).
cnf(refute_0_33,plain,
equidistant(extension(X_549,X_551,extension(X_550,X_552,X_553,extension(X_546,X_553,X_548,X_547)),X_552),X_551,X_548,X_547),
inference(resolve,[$cnf( equidistant(X_548,X_547,extension(X_549,X_551,extension(X_550,X_552,X_553,extension(X_546,X_553,X_548,X_547)),X_552),X_551) )],[refute_0_32,refute_0_13]) ).
cnf(refute_0_34,plain,
equidistant(extension(X_597,X_599,extension(X_598,X_600,X_601,extension(X_594,X_601,X_596,X_595)),X_600),X_599,X_596,X_595),
inference(subst,[],[refute_0_33:[bind(X_546,$fot(X_594)),bind(X_547,$fot(X_595)),bind(X_548,$fot(X_596)),bind(X_549,$fot(X_597)),bind(X_550,$fot(X_598)),bind(X_551,$fot(X_599)),bind(X_552,$fot(X_600)),bind(X_553,$fot(X_601))]]) ).
cnf(refute_0_35,plain,
equidistant(X_599,extension(X_597,X_599,extension(X_598,X_600,X_601,extension(X_594,X_601,X_596,X_595)),X_600),X_596,X_595),
inference(resolve,[$cnf( equidistant(extension(X_597,X_599,extension(X_598,X_600,X_601,extension(X_594,X_601,X_596,X_595)),X_600),X_599,X_596,X_595) )],[refute_0_34,refute_0_12]) ).
cnf(refute_0_36,plain,
equidistant(X_615,extension(X_613,X_615,extension(X_614,X_616,X_617,extension(X_610,X_617,X_612,X_611)),X_616),X_612,X_611),
inference(subst,[],[refute_0_35:[bind(X_594,$fot(X_610)),bind(X_595,$fot(X_611)),bind(X_596,$fot(X_612)),bind(X_597,$fot(X_613)),bind(X_598,$fot(X_614)),bind(X_599,$fot(X_615)),bind(X_600,$fot(X_616)),bind(X_601,$fot(X_617))]]) ).
cnf(refute_0_37,plain,
equidistant(X_612,X_611,X_615,extension(X_613,X_615,extension(X_614,X_616,X_617,extension(X_610,X_617,X_612,X_611)),X_616)),
inference(resolve,[$cnf( equidistant(X_615,extension(X_613,X_615,extension(X_614,X_616,X_617,extension(X_610,X_617,X_612,X_611)),X_616),X_612,X_611) )],[refute_0_36,refute_0_11]) ).
cnf(refute_0_38,plain,
equidistant(X_660,X_659,X_663,extension(X_661,X_663,extension(X_662,X_664,X_665,extension(X_658,X_665,X_660,X_659)),X_664)),
inference(subst,[],[refute_0_37:[bind(X_610,$fot(X_658)),bind(X_611,$fot(X_659)),bind(X_612,$fot(X_660)),bind(X_613,$fot(X_661)),bind(X_614,$fot(X_662)),bind(X_615,$fot(X_663)),bind(X_616,$fot(X_664)),bind(X_617,$fot(X_665))]]) ).
cnf(refute_0_39,plain,
equidistant(X_659,X_660,X_663,extension(X_661,X_663,extension(X_662,X_664,X_665,extension(X_658,X_665,X_660,X_659)),X_664)),
inference(resolve,[$cnf( equidistant(X_660,X_659,X_663,extension(X_661,X_663,extension(X_662,X_664,X_665,extension(X_658,X_665,X_660,X_659)),X_664)) )],[refute_0_38,refute_0_4]) ).
cnf(refute_0_40,plain,
equidistant(lower_dimension_point_2,lower_dimension_point_1,X_663,extension(X_661,X_663,extension(X_662,X_664,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2)),X_664)),
inference(subst,[],[refute_0_39:[bind(X_658,$fot(u)),bind(X_659,$fot(lower_dimension_point_2)),bind(X_660,$fot(lower_dimension_point_1)),bind(X_665,$fot(v))]]) ).
cnf(refute_0_41,plain,
between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2)),
inference(subst,[],[segment_construction1:[bind(V,$fot(lower_dimension_point_2)),bind(W,$fot(lower_dimension_point_1)),bind(X,$fot(u)),bind(Y,$fot(v))]]) ).
cnf(refute_0_42,plain,
( ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2) ),
inference(resolve,[$cnf( between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2)) )],[refute_0_41,prove_lengthen]) ).
cnf(refute_0_43,plain,
equidistant(X_397,extension(X,X_397,X_399,X_396),X_399,X_396),
inference(subst,[],[segment_construction2:[bind(V,$fot(X_396)),bind(W,$fot(X_399)),bind(Y,$fot(X_397))]]) ).
cnf(refute_0_44,plain,
( ~ equidistant(X_397,extension(X,X_397,X_399,X_396),X_399,X_396)
| equidistant(X_399,X_396,X_397,extension(X,X_397,X_399,X_396)) ),
inference(subst,[],[refute_0_10:[bind(X_390,$fot(X_396)),bind(X_391,$fot(X_397)),bind(X_392,$fot(extension(X,X_397,X_399,X_396))),bind(X_395,$fot(X_399))]]) ).
cnf(refute_0_45,plain,
equidistant(X_399,X_396,X_397,extension(X,X_397,X_399,X_396)),
inference(resolve,[$cnf( equidistant(X_397,extension(X,X_397,X_399,X_396),X_399,X_396) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
equidistant(X_960,X_958,X_955,extension(X,X_955,X_960,X_958)),
inference(subst,[],[refute_0_45:[bind(X_396,$fot(X_958)),bind(X_397,$fot(X_955)),bind(X_399,$fot(X_960))]]) ).
cnf(refute_0_47,plain,
( ~ equidistant(X_403,X_401,V2,W)
| ~ equidistant(X_403,X_401,X_402,extension(X_400,X_402,X_403,X_401))
| equidistant(X_402,extension(X_400,X_402,X_403,X_401),V2,W) ),
inference(subst,[],[transitivity_for_equidistance:[bind(V,$fot(extension(X_400,X_402,X_403,X_401))),bind(X,$fot(X_403)),bind(Y,$fot(X_401)),bind(Z,$fot(X_402))]]) ).
cnf(refute_0_48,plain,
equidistant(X_403,X_401,X_402,extension(X_400,X_402,X_403,X_401)),
inference(subst,[],[refute_0_45:[bind(X,$fot(X_400)),bind(X_396,$fot(X_401)),bind(X_397,$fot(X_402)),bind(X_399,$fot(X_403))]]) ).
cnf(refute_0_49,plain,
( ~ equidistant(X_403,X_401,V2,W)
| equidistant(X_402,extension(X_400,X_402,X_403,X_401),V2,W) ),
inference(resolve,[$cnf( equidistant(X_403,X_401,X_402,extension(X_400,X_402,X_403,X_401)) )],[refute_0_48,refute_0_47]) ).
cnf(refute_0_50,plain,
( ~ equidistant(X_960,X_958,X_955,extension(X,X_955,X_960,X_958))
| equidistant(X_959,extension(X_957,X_959,X_960,X_958),X_955,extension(X,X_955,X_960,X_958)) ),
inference(subst,[],[refute_0_49:[bind(V2,$fot(X_955)),bind(W,$fot(extension(X,X_955,X_960,X_958))),bind(X_400,$fot(X_957)),bind(X_401,$fot(X_958)),bind(X_402,$fot(X_959)),bind(X_403,$fot(X_960))]]) ).
cnf(refute_0_51,plain,
equidistant(X_959,extension(X_957,X_959,X_960,X_958),X_955,extension(X,X_955,X_960,X_958)),
inference(resolve,[$cnf( equidistant(X_960,X_958,X_955,extension(X,X_955,X_960,X_958)) )],[refute_0_46,refute_0_50]) ).
cnf(refute_0_52,plain,
equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2)),
inference(subst,[],[refute_0_51:[bind(X,$fot(w)),bind(X_955,$fot(x)),bind(X_957,$fot(u)),bind(X_958,$fot(lower_dimension_point_2)),bind(X_959,$fot(v)),bind(X_960,$fot(lower_dimension_point_1))]]) ).
cnf(refute_0_53,plain,
v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2),
inference(resolve,[$cnf( equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2)) )],[refute_0_52,refute_0_42]) ).
cnf(refute_0_54,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_55,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_56,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
( v != extension(u,v,lower_dimension_point_1,lower_dimension_point_2)
| extension(u,v,lower_dimension_point_1,lower_dimension_point_2) = v ),
inference(subst,[],[refute_0_56:[bind(X0,$fot(v)),bind(Y0,$fot(extension(u,v,lower_dimension_point_1,lower_dimension_point_2)))]]) ).
cnf(refute_0_58,plain,
extension(u,v,lower_dimension_point_1,lower_dimension_point_2) = v,
inference(resolve,[$cnf( $equal(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2)) )],[refute_0_53,refute_0_57]) ).
cnf(refute_0_59,plain,
( extension(u,v,lower_dimension_point_1,lower_dimension_point_2) != v
| ~ equidistant(lower_dimension_point_2,lower_dimension_point_1,X_663,extension(X_661,X_663,extension(X_662,X_664,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2)),X_664))
| equidistant(lower_dimension_point_2,lower_dimension_point_1,X_663,extension(X_661,X_663,extension(X_662,X_664,v,v),X_664)) ),
introduced(tautology,[equality,[$cnf( equidistant(lower_dimension_point_2,lower_dimension_point_1,X_663,extension(X_661,X_663,extension(X_662,X_664,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2)),X_664)) ),[3,2,3],$fot(v)]]) ).
cnf(refute_0_60,plain,
( ~ equidistant(lower_dimension_point_2,lower_dimension_point_1,X_663,extension(X_661,X_663,extension(X_662,X_664,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2)),X_664))
| equidistant(lower_dimension_point_2,lower_dimension_point_1,X_663,extension(X_661,X_663,extension(X_662,X_664,v,v),X_664)) ),
inference(resolve,[$cnf( $equal(extension(u,v,lower_dimension_point_1,lower_dimension_point_2),v) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
equidistant(lower_dimension_point_2,lower_dimension_point_1,X_663,extension(X_661,X_663,extension(X_662,X_664,v,v),X_664)),
inference(resolve,[$cnf( equidistant(lower_dimension_point_2,lower_dimension_point_1,X_663,extension(X_661,X_663,extension(X_662,X_664,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2)),X_664)) )],[refute_0_40,refute_0_60]) ).
cnf(refute_0_62,plain,
equidistant(X_12,extension(X,X_12,X_14,X_14),X_14,X_14),
inference(subst,[],[segment_construction2:[bind(V,$fot(X_14)),bind(W,$fot(X_14)),bind(Y,$fot(X_12))]]) ).
cnf(refute_0_63,plain,
( ~ equidistant(X_12,extension(X,X_12,X_14,X_14),X_14,X_14)
| X_12 = extension(X,X_12,X_14,X_14) ),
inference(subst,[],[identity_for_equidistance:[bind(X,$fot(X_12)),bind(Y,$fot(extension(X,X_12,X_14,X_14))),bind(Z,$fot(X_14))]]) ).
cnf(refute_0_64,plain,
X_12 = extension(X,X_12,X_14,X_14),
inference(resolve,[$cnf( equidistant(X_12,extension(X,X_12,X_14,X_14),X_14,X_14) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
( X_12 != extension(X,X_12,X_14,X_14)
| extension(X,X_12,X_14,X_14) = X_12 ),
inference(subst,[],[refute_0_56:[bind(X0,$fot(X_12)),bind(Y0,$fot(extension(X,X_12,X_14,X_14)))]]) ).
cnf(refute_0_66,plain,
extension(X,X_12,X_14,X_14) = X_12,
inference(resolve,[$cnf( $equal(X_12,extension(X,X_12,X_14,X_14)) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
extension(X_661,X_663,X_664,X_664) = X_663,
inference(subst,[],[refute_0_66:[bind(X,$fot(X_661)),bind(X_12,$fot(X_663)),bind(X_14,$fot(X_664))]]) ).
cnf(refute_0_68,plain,
extension(X_662,X_664,v,v) = X_664,
inference(subst,[],[refute_0_66:[bind(X,$fot(X_662)),bind(X_12,$fot(X_664)),bind(X_14,$fot(v))]]) ).
cnf(refute_0_69,plain,
extension(X_661,X_663,extension(X_662,X_664,v,v),X_664) = extension(X_661,X_663,extension(X_662,X_664,v,v),X_664),
introduced(tautology,[refl,[$fot(extension(X_661,X_663,extension(X_662,X_664,v,v),X_664))]]) ).
cnf(refute_0_70,plain,
( extension(X_661,X_663,extension(X_662,X_664,v,v),X_664) != extension(X_661,X_663,extension(X_662,X_664,v,v),X_664)
| extension(X_662,X_664,v,v) != X_664
| extension(X_661,X_663,extension(X_662,X_664,v,v),X_664) = extension(X_661,X_663,X_664,X_664) ),
introduced(tautology,[equality,[$cnf( $equal(extension(X_661,X_663,extension(X_662,X_664,v,v),X_664),extension(X_661,X_663,extension(X_662,X_664,v,v),X_664)) ),[1,2],$fot(X_664)]]) ).
cnf(refute_0_71,plain,
( extension(X_662,X_664,v,v) != X_664
| extension(X_661,X_663,extension(X_662,X_664,v,v),X_664) = extension(X_661,X_663,X_664,X_664) ),
inference(resolve,[$cnf( $equal(extension(X_661,X_663,extension(X_662,X_664,v,v),X_664),extension(X_661,X_663,extension(X_662,X_664,v,v),X_664)) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
extension(X_661,X_663,extension(X_662,X_664,v,v),X_664) = extension(X_661,X_663,X_664,X_664),
inference(resolve,[$cnf( $equal(extension(X_662,X_664,v,v),X_664) )],[refute_0_68,refute_0_71]) ).
cnf(refute_0_73,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_74,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_56,refute_0_73]) ).
cnf(refute_0_75,plain,
( extension(X_661,X_663,X_664,X_664) != X_663
| extension(X_661,X_663,extension(X_662,X_664,v,v),X_664) != extension(X_661,X_663,X_664,X_664)
| extension(X_661,X_663,extension(X_662,X_664,v,v),X_664) = X_663 ),
inference(subst,[],[refute_0_74:[bind(X0,$fot(extension(X_661,X_663,extension(X_662,X_664,v,v),X_664))),bind(Y0,$fot(extension(X_661,X_663,X_664,X_664))),bind(Z0,$fot(X_663))]]) ).
cnf(refute_0_76,plain,
( extension(X_661,X_663,X_664,X_664) != X_663
| extension(X_661,X_663,extension(X_662,X_664,v,v),X_664) = X_663 ),
inference(resolve,[$cnf( $equal(extension(X_661,X_663,extension(X_662,X_664,v,v),X_664),extension(X_661,X_663,X_664,X_664)) )],[refute_0_72,refute_0_75]) ).
cnf(refute_0_77,plain,
extension(X_661,X_663,extension(X_662,X_664,v,v),X_664) = X_663,
inference(resolve,[$cnf( $equal(extension(X_661,X_663,X_664,X_664),X_663) )],[refute_0_67,refute_0_76]) ).
cnf(refute_0_78,plain,
( extension(X_661,X_663,extension(X_662,X_664,v,v),X_664) != X_663
| ~ equidistant(lower_dimension_point_2,lower_dimension_point_1,X_663,extension(X_661,X_663,extension(X_662,X_664,v,v),X_664))
| equidistant(lower_dimension_point_2,lower_dimension_point_1,X_663,X_663) ),
introduced(tautology,[equality,[$cnf( equidistant(lower_dimension_point_2,lower_dimension_point_1,X_663,extension(X_661,X_663,extension(X_662,X_664,v,v),X_664)) ),[3],$fot(X_663)]]) ).
cnf(refute_0_79,plain,
( ~ equidistant(lower_dimension_point_2,lower_dimension_point_1,X_663,extension(X_661,X_663,extension(X_662,X_664,v,v),X_664))
| equidistant(lower_dimension_point_2,lower_dimension_point_1,X_663,X_663) ),
inference(resolve,[$cnf( $equal(extension(X_661,X_663,extension(X_662,X_664,v,v),X_664),X_663) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
equidistant(lower_dimension_point_2,lower_dimension_point_1,X_663,X_663),
inference(resolve,[$cnf( equidistant(lower_dimension_point_2,lower_dimension_point_1,X_663,extension(X_661,X_663,extension(X_662,X_664,v,v),X_664)) )],[refute_0_61,refute_0_79]) ).
cnf(refute_0_81,plain,
equidistant(lower_dimension_point_2,lower_dimension_point_1,X_986,X_986),
inference(subst,[],[refute_0_80:[bind(X_663,$fot(X_986))]]) ).
cnf(refute_0_82,plain,
lower_dimension_point_2 = lower_dimension_point_1,
inference(resolve,[$cnf( equidistant(lower_dimension_point_2,lower_dimension_point_1,X_986,X_986) )],[refute_0_81,refute_0_0]) ).
cnf(refute_0_83,plain,
( lower_dimension_point_2 != lower_dimension_point_1
| ~ between(lower_dimension_point_1,lower_dimension_point_1,lower_dimension_point_3)
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
introduced(tautology,[equality,[$cnf( ~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),[1],$fot(lower_dimension_point_1)]]) ).
cnf(refute_0_84,plain,
( ~ between(lower_dimension_point_1,lower_dimension_point_1,lower_dimension_point_3)
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
inference(resolve,[$cnf( $equal(lower_dimension_point_2,lower_dimension_point_1) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
~ between(lower_dimension_point_1,lower_dimension_point_1,lower_dimension_point_3),
inference(resolve,[$cnf( between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) )],[refute_0_84,lower_dimension1]) ).
cnf(refute_0_86,plain,
between(X,Y,extension(X,Y,V,V)),
inference(subst,[],[segment_construction1:[bind(W,$fot(V))]]) ).
cnf(refute_0_87,plain,
Y = extension(X,Y,V,V),
inference(subst,[],[refute_0_64:[bind(X_12,$fot(Y)),bind(X_14,$fot(V))]]) ).
cnf(refute_0_88,plain,
( Y != extension(X,Y,V,V)
| extension(X,Y,V,V) = Y ),
inference(subst,[],[refute_0_56:[bind(X0,$fot(Y)),bind(Y0,$fot(extension(X,Y,V,V)))]]) ).
cnf(refute_0_89,plain,
extension(X,Y,V,V) = Y,
inference(resolve,[$cnf( $equal(Y,extension(X,Y,V,V)) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
( extension(X,Y,V,V) != Y
| ~ between(X,Y,extension(X,Y,V,V))
| between(X,Y,Y) ),
introduced(tautology,[equality,[$cnf( between(X,Y,extension(X,Y,V,V)) ),[2],$fot(Y)]]) ).
cnf(refute_0_91,plain,
( ~ between(X,Y,extension(X,Y,V,V))
| between(X,Y,Y) ),
inference(resolve,[$cnf( $equal(extension(X,Y,V,V),Y) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
between(X,Y,Y),
inference(resolve,[$cnf( between(X,Y,extension(X,Y,V,V)) )],[refute_0_86,refute_0_91]) ).
cnf(refute_0_93,plain,
between(X_181,X_179,X_179),
inference(subst,[],[refute_0_92:[bind(X,$fot(X_181)),bind(Y,$fot(X_179))]]) ).
cnf(refute_0_94,plain,
between(X_173,X_175,X_175),
inference(subst,[],[refute_0_92:[bind(X,$fot(X_173)),bind(Y,$fot(X_175))]]) ).
cnf(refute_0_95,plain,
( ~ between(X_173,X_175,X_175)
| ~ between(X_177,X_176,X_175)
| between(X_176,inner_pasch(X_173,X_175,X_175,X_176,X_177),X_173) ),
inference(subst,[],[inner_pasch2:[bind(U,$fot(X_173)),bind(V,$fot(X_175)),bind(W,$fot(X_175)),bind(X,$fot(X_176)),bind(Y,$fot(X_177))]]) ).
cnf(refute_0_96,plain,
( ~ between(X_177,X_176,X_175)
| between(X_176,inner_pasch(X_173,X_175,X_175,X_176,X_177),X_173) ),
inference(resolve,[$cnf( between(X_173,X_175,X_175) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
( ~ between(X_181,X_179,X_179)
| between(X_179,inner_pasch(X_178,X_179,X_179,X_179,X_181),X_178) ),
inference(subst,[],[refute_0_96:[bind(X_173,$fot(X_178)),bind(X_175,$fot(X_179)),bind(X_176,$fot(X_179)),bind(X_177,$fot(X_181))]]) ).
cnf(refute_0_98,plain,
between(X_179,inner_pasch(X_178,X_179,X_179,X_179,X_181),X_178),
inference(resolve,[$cnf( between(X_181,X_179,X_179) )],[refute_0_93,refute_0_97]) ).
cnf(refute_0_99,plain,
between(X_184,inner_pasch(X_182,X_184,X_184,X_184,X_184),X_182),
inference(subst,[],[refute_0_98:[bind(X_178,$fot(X_182)),bind(X_179,$fot(X_184)),bind(X_181,$fot(X_184))]]) ).
cnf(refute_0_100,plain,
( ~ between(X_125,inner_pasch(X_123,X_125,X_125,X_125,X_125),X_125)
| X_125 = inner_pasch(X_123,X_125,X_125,X_125,X_125) ),
inference(subst,[],[identity_for_betweeness:[bind(X,$fot(X_125)),bind(Y,$fot(inner_pasch(X_123,X_125,X_125,X_125,X_125)))]]) ).
cnf(refute_0_101,plain,
between(X_122,X_120,X_120),
inference(subst,[],[refute_0_92:[bind(X,$fot(X_122)),bind(Y,$fot(X_120))]]) ).
cnf(refute_0_102,plain,
between(X_114,X_116,X_116),
inference(subst,[],[refute_0_92:[bind(X,$fot(X_114)),bind(Y,$fot(X_116))]]) ).
cnf(refute_0_103,plain,
( ~ between(X_114,X_116,X_116)
| ~ between(X_118,X_117,X_116)
| between(X_116,inner_pasch(X_114,X_116,X_116,X_117,X_118),X_118) ),
inference(subst,[],[inner_pasch1:[bind(U,$fot(X_114)),bind(V,$fot(X_116)),bind(W,$fot(X_116)),bind(X,$fot(X_117)),bind(Y,$fot(X_118))]]) ).
cnf(refute_0_104,plain,
( ~ between(X_118,X_117,X_116)
| between(X_116,inner_pasch(X_114,X_116,X_116,X_117,X_118),X_118) ),
inference(resolve,[$cnf( between(X_114,X_116,X_116) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
( ~ between(X_122,X_120,X_120)
| between(X_120,inner_pasch(X_119,X_120,X_120,X_120,X_122),X_122) ),
inference(subst,[],[refute_0_104:[bind(X_114,$fot(X_119)),bind(X_116,$fot(X_120)),bind(X_117,$fot(X_120)),bind(X_118,$fot(X_122))]]) ).
cnf(refute_0_106,plain,
between(X_120,inner_pasch(X_119,X_120,X_120,X_120,X_122),X_122),
inference(resolve,[$cnf( between(X_122,X_120,X_120) )],[refute_0_101,refute_0_105]) ).
cnf(refute_0_107,plain,
between(X_125,inner_pasch(X_123,X_125,X_125,X_125,X_125),X_125),
inference(subst,[],[refute_0_106:[bind(X_119,$fot(X_123)),bind(X_120,$fot(X_125)),bind(X_122,$fot(X_125))]]) ).
cnf(refute_0_108,plain,
X_125 = inner_pasch(X_123,X_125,X_125,X_125,X_125),
inference(resolve,[$cnf( between(X_125,inner_pasch(X_123,X_125,X_125,X_125,X_125),X_125) )],[refute_0_107,refute_0_100]) ).
cnf(refute_0_109,plain,
X_184 = inner_pasch(X_182,X_184,X_184,X_184,X_184),
inference(subst,[],[refute_0_108:[bind(X_123,$fot(X_182)),bind(X_125,$fot(X_184))]]) ).
cnf(refute_0_110,plain,
( X_184 != inner_pasch(X_182,X_184,X_184,X_184,X_184)
| inner_pasch(X_182,X_184,X_184,X_184,X_184) = X_184 ),
inference(subst,[],[refute_0_56:[bind(X0,$fot(X_184)),bind(Y0,$fot(inner_pasch(X_182,X_184,X_184,X_184,X_184)))]]) ).
cnf(refute_0_111,plain,
inner_pasch(X_182,X_184,X_184,X_184,X_184) = X_184,
inference(resolve,[$cnf( $equal(X_184,inner_pasch(X_182,X_184,X_184,X_184,X_184)) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
( inner_pasch(X_182,X_184,X_184,X_184,X_184) != X_184
| ~ between(X_184,inner_pasch(X_182,X_184,X_184,X_184,X_184),X_182)
| between(X_184,X_184,X_182) ),
introduced(tautology,[equality,[$cnf( between(X_184,inner_pasch(X_182,X_184,X_184,X_184,X_184),X_182) ),[1],$fot(X_184)]]) ).
cnf(refute_0_113,plain,
( ~ between(X_184,inner_pasch(X_182,X_184,X_184,X_184,X_184),X_182)
| between(X_184,X_184,X_182) ),
inference(resolve,[$cnf( $equal(inner_pasch(X_182,X_184,X_184,X_184,X_184),X_184) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
between(X_184,X_184,X_182),
inference(resolve,[$cnf( between(X_184,inner_pasch(X_182,X_184,X_184,X_184,X_184),X_182) )],[refute_0_99,refute_0_113]) ).
cnf(refute_0_115,plain,
between(lower_dimension_point_1,lower_dimension_point_1,lower_dimension_point_3),
inference(subst,[],[refute_0_114:[bind(X_182,$fot(lower_dimension_point_3)),bind(X_184,$fot(lower_dimension_point_1))]]) ).
cnf(refute_0_116,plain,
$false,
inference(resolve,[$cnf( between(lower_dimension_point_1,lower_dimension_point_1,lower_dimension_point_3) )],[refute_0_115,refute_0_85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO037-2 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Fri Jun 17 20:46:53 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.84/1.08 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.84/1.08
% 0.84/1.08 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.92/1.09
%------------------------------------------------------------------------------