TSTP Solution File: GEO002-4 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO002-4 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 05:23:26 EDT 2022
% Result : Unsatisfiable 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of clauses : 44 ( 24 unt; 0 nHn; 22 RR)
% Number of literals : 72 ( 0 equ; 29 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-5 aty)
% Number of variables : 115 ( 18 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(transitivity_for_betweeness,axiom,
( ~ between(X,Y,V)
| ~ between(Y,Z,V)
| between(X,Y,Z) ) ).
cnf(identity_for_equidistance,axiom,
( ~ equidistant(X,Y,Z,Z)
| equalish(X,Y) ) ).
cnf(outer_pasch1,axiom,
( ~ between(X,W,V)
| ~ between(Y,V,Z)
| between(X,outer_pasch(W,X,Y,Z,V),Y) ) ).
cnf(outer_pasch2,axiom,
( ~ between(X,W,V)
| ~ between(Y,V,Z)
| between(Z,W,outer_pasch(W,X,Y,Z,V)) ) ).
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(between_substitution3,axiom,
( ~ equalish(X,Y)
| ~ between(W,Z,X)
| between(W,Z,Y) ) ).
cnf(prove_a_between_a_and_b,negated_conjecture,
~ between(a,a,b) ).
cnf(refute_0_0,plain,
( ~ between(X,X_72,X_72)
| ~ between(X_72,outer_pasch(X_73,X_72,X_72,X_73,X_73),X_72)
| between(X,X_72,outer_pasch(X_73,X_72,X_72,X_73,X_73)) ),
inference(subst,[],[transitivity_for_betweeness:[bind(V,$fot(X_72)),bind(Y,$fot(X_72)),bind(Z,$fot(outer_pasch(X_73,X_72,X_72,X_73,X_73)))]]) ).
cnf(refute_0_1,plain,
( ~ between(X_67,X_68,X_68)
| between(X_67,outer_pasch(X_68,X_67,X_67,X_68,X_68),X_67) ),
inference(subst,[],[outer_pasch1:[bind(V,$fot(X_68)),bind(W,$fot(X_68)),bind(X,$fot(X_67)),bind(Y,$fot(X_67)),bind(Z,$fot(X_68))]]) ).
cnf(refute_0_2,plain,
between(X_63,X_66,extension(X_63,X_66,X_64,X_64)),
inference(subst,[],[segment_construction1:[bind(V,$fot(X_64)),bind(W,$fot(X_64)),bind(X,$fot(X_63)),bind(Y,$fot(X_66))]]) ).
cnf(refute_0_3,plain,
equidistant(X_8,extension(X,X_8,X_10,X_10),X_10,X_10),
inference(subst,[],[segment_construction2:[bind(V,$fot(X_10)),bind(W,$fot(X_10)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_4,plain,
( ~ equidistant(X_8,extension(X,X_8,X_10,X_10),X_10,X_10)
| equalish(X_8,extension(X,X_8,X_10,X_10)) ),
inference(subst,[],[identity_for_equidistance:[bind(X,$fot(X_8)),bind(Y,$fot(extension(X,X_8,X_10,X_10))),bind(Z,$fot(X_10))]]) ).
cnf(refute_0_5,plain,
equalish(X_8,extension(X,X_8,X_10,X_10)),
inference(resolve,[$cnf( equidistant(X_8,extension(X,X_8,X_10,X_10),X_10,X_10) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
equalish(X_27,extension(X,X_27,X_10,X_10)),
inference(subst,[],[refute_0_5:[bind(X_8,$fot(X_27))]]) ).
cnf(refute_0_7,plain,
between(X_15,X_15,extension(X_15,X_15,W,V)),
inference(subst,[],[segment_construction1:[bind(X,$fot(X_15)),bind(Y,$fot(X_15))]]) ).
cnf(refute_0_8,plain,
( ~ between(X_15,X_15,extension(X_15,X_15,W,V))
| between(X_15,X_15,X_15) ),
inference(subst,[],[transitivity_for_betweeness:[bind(V,$fot(extension(X_15,X_15,W,V))),bind(X,$fot(X_15)),bind(Y,$fot(X_15)),bind(Z,$fot(X_15))]]) ).
cnf(refute_0_9,plain,
between(X_15,X_15,X_15),
inference(resolve,[$cnf( between(X_15,X_15,extension(X_15,X_15,W,V)) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
between(X_24,X_24,X_24),
inference(subst,[],[refute_0_9:[bind(X_15,$fot(X_24))]]) ).
cnf(refute_0_11,plain,
( ~ equalish(X_24,X_25)
| ~ between(X_24,X_24,X_24)
| between(X_24,X_24,X_25) ),
inference(subst,[],[between_substitution3:[bind(W,$fot(X_24)),bind(X,$fot(X_24)),bind(Y,$fot(X_25)),bind(Z,$fot(X_24))]]) ).
cnf(refute_0_12,plain,
( ~ equalish(X_24,X_25)
| between(X_24,X_24,X_25) ),
inference(resolve,[$cnf( between(X_24,X_24,X_24) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ equalish(X_27,extension(X,X_27,X_10,X_10))
| between(X_27,X_27,extension(X,X_27,X_10,X_10)) ),
inference(subst,[],[refute_0_12:[bind(X_24,$fot(X_27)),bind(X_25,$fot(extension(X,X_27,X_10,X_10)))]]) ).
cnf(refute_0_14,plain,
between(X_27,X_27,extension(X,X_27,X_10,X_10)),
inference(resolve,[$cnf( equalish(X_27,extension(X,X_27,X_10,X_10)) )],[refute_0_6,refute_0_13]) ).
cnf(refute_0_15,plain,
between(X_54,X_54,extension(X,X_54,X_10,X_10)),
inference(subst,[],[refute_0_14:[bind(X_27,$fot(X_54))]]) ).
cnf(refute_0_16,plain,
( ~ between(X_52,X_54,extension(X,X_54,X_10,X_10))
| ~ between(X_54,X_54,extension(X,X_54,X_10,X_10))
| between(X_52,X_54,X_54) ),
inference(subst,[],[transitivity_for_betweeness:[bind(V,$fot(extension(X,X_54,X_10,X_10))),bind(X,$fot(X_52)),bind(Y,$fot(X_54)),bind(Z,$fot(X_54))]]) ).
cnf(refute_0_17,plain,
( ~ between(X_52,X_54,extension(X,X_54,X_10,X_10))
| between(X_52,X_54,X_54) ),
inference(resolve,[$cnf( between(X_54,X_54,extension(X,X_54,X_10,X_10)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ between(X_63,X_66,extension(X_63,X_66,X_64,X_64))
| between(X_63,X_66,X_66) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(X_63)),bind(X_10,$fot(X_64)),bind(X_52,$fot(X_63)),bind(X_54,$fot(X_66))]]) ).
cnf(refute_0_19,plain,
between(X_63,X_66,X_66),
inference(resolve,[$cnf( between(X_63,X_66,extension(X_63,X_66,X_64,X_64)) )],[refute_0_2,refute_0_18]) ).
cnf(refute_0_20,plain,
between(X_67,X_68,X_68),
inference(subst,[],[refute_0_19:[bind(X_63,$fot(X_67)),bind(X_66,$fot(X_68))]]) ).
cnf(refute_0_21,plain,
between(X_67,outer_pasch(X_68,X_67,X_67,X_68,X_68),X_67),
inference(resolve,[$cnf( between(X_67,X_68,X_68) )],[refute_0_20,refute_0_1]) ).
cnf(refute_0_22,plain,
between(X_72,outer_pasch(X_73,X_72,X_72,X_73,X_73),X_72),
inference(subst,[],[refute_0_21:[bind(X_67,$fot(X_72)),bind(X_68,$fot(X_73))]]) ).
cnf(refute_0_23,plain,
( ~ between(X,X_72,X_72)
| between(X,X_72,outer_pasch(X_73,X_72,X_72,X_73,X_73)) ),
inference(resolve,[$cnf( between(X_72,outer_pasch(X_73,X_72,X_72,X_73,X_73),X_72) )],[refute_0_22,refute_0_0]) ).
cnf(refute_0_24,plain,
between(X,X_72,X_72),
inference(subst,[],[refute_0_19:[bind(X_63,$fot(X)),bind(X_66,$fot(X_72))]]) ).
cnf(refute_0_25,plain,
between(X,X_72,outer_pasch(X_73,X_72,X_72,X_73,X_73)),
inference(resolve,[$cnf( between(X,X_72,X_72) )],[refute_0_24,refute_0_23]) ).
cnf(refute_0_26,plain,
between(X_229,X_228,outer_pasch(X_229,X_228,X_228,X_229,X_229)),
inference(subst,[],[refute_0_25:[bind(X,$fot(X_229)),bind(X_72,$fot(X_228)),bind(X_73,$fot(X_229))]]) ).
cnf(refute_0_27,plain,
( ~ between(X_75,Z,outer_pasch(X_75,X_74,X_74,X_75,X_75))
| ~ between(X_75,X_75,outer_pasch(X_75,X_74,X_74,X_75,X_75))
| between(X_75,X_75,Z) ),
inference(subst,[],[transitivity_for_betweeness:[bind(V,$fot(outer_pasch(X_75,X_74,X_74,X_75,X_75))),bind(X,$fot(X_75)),bind(Y,$fot(X_75))]]) ).
cnf(refute_0_28,plain,
( ~ between(X_67,X_68,X_68)
| between(X_68,X_68,outer_pasch(X_68,X_67,X_67,X_68,X_68)) ),
inference(subst,[],[outer_pasch2:[bind(V,$fot(X_68)),bind(W,$fot(X_68)),bind(X,$fot(X_67)),bind(Y,$fot(X_67)),bind(Z,$fot(X_68))]]) ).
cnf(refute_0_29,plain,
between(X_68,X_68,outer_pasch(X_68,X_67,X_67,X_68,X_68)),
inference(resolve,[$cnf( between(X_67,X_68,X_68) )],[refute_0_20,refute_0_28]) ).
cnf(refute_0_30,plain,
between(X_75,X_75,outer_pasch(X_75,X_74,X_74,X_75,X_75)),
inference(subst,[],[refute_0_29:[bind(X_67,$fot(X_74)),bind(X_68,$fot(X_75))]]) ).
cnf(refute_0_31,plain,
( ~ between(X_75,Z,outer_pasch(X_75,X_74,X_74,X_75,X_75))
| between(X_75,X_75,Z) ),
inference(resolve,[$cnf( between(X_75,X_75,outer_pasch(X_75,X_74,X_74,X_75,X_75)) )],[refute_0_30,refute_0_27]) ).
cnf(refute_0_32,plain,
( ~ between(X_229,X_228,outer_pasch(X_229,X_228,X_228,X_229,X_229))
| between(X_229,X_229,X_228) ),
inference(subst,[],[refute_0_31:[bind(Z,$fot(X_228)),bind(X_74,$fot(X_228)),bind(X_75,$fot(X_229))]]) ).
cnf(refute_0_33,plain,
between(X_229,X_229,X_228),
inference(resolve,[$cnf( between(X_229,X_228,outer_pasch(X_229,X_228,X_228,X_229,X_229)) )],[refute_0_26,refute_0_32]) ).
cnf(refute_0_34,plain,
between(a,a,b),
inference(subst,[],[refute_0_33:[bind(X_228,$fot(b)),bind(X_229,$fot(a))]]) ).
cnf(refute_0_35,plain,
$false,
inference(resolve,[$cnf( between(a,a,b) )],[refute_0_34,prove_a_between_a_and_b]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.13 % Problem : GEO002-4 : TPTP v8.1.0. Released v1.1.0.
% 0.12/0.14 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % 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 : Sat Jun 18 09:06:53 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.41 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.41
% 0.13/0.41 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.42
%------------------------------------------------------------------------------