TSTP Solution File: GEO002-2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO002-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n006.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 05:23:25 EDT 2022
% Result : Unsatisfiable 0.19s 0.52s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of clauses : 44 ( 24 unt; 0 nHn; 19 RR)
% Number of literals : 71 ( 22 equ; 28 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-5 aty)
% Number of variables : 113 ( 21 sgn)
% Comments :
%------------------------------------------------------------------------------
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(prove_a_between_a_and_b,negated_conjecture,
~ between(a,a,b) ).
cnf(refute_0_0,plain,
between(X,Y,extension(X,Y,V,V)),
inference(subst,[],[segment_construction1:[bind(W,$fot(V))]]) ).
cnf(refute_0_1,plain,
equidistant(X_12,extension(X,X_12,X_14,X_14),X_14,X_14),
inference(subst,[],[segment_construction2:[bind(V,$fot(X_14)),bind(W,$fot(X_14)),bind(Y,$fot(X_12))]]) ).
cnf(refute_0_2,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,$fot(X_14))]]) ).
cnf(refute_0_3,plain,
X_12 = extension(X,X_12,X_14,X_14),
inference(resolve,[$cnf( equidistant(X_12,extension(X,X_12,X_14,X_14),X_14,X_14) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
Y = extension(X,Y,V,V),
inference(subst,[],[refute_0_3:[bind(X_12,$fot(Y)),bind(X_14,$fot(V))]]) ).
cnf(refute_0_5,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_6,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_7,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( Y != extension(X,Y,V,V)
| extension(X,Y,V,V) = Y ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(Y)),bind(Y0,$fot(extension(X,Y,V,V)))]]) ).
cnf(refute_0_9,plain,
extension(X,Y,V,V) = Y,
inference(resolve,[$cnf( $equal(Y,extension(X,Y,V,V)) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
( extension(X,Y,V,V) != Y
| ~ between(X,Y,extension(X,Y,V,V))
| between(X,Y,Y) ),
introduced(tautology,[equality,[$cnf( between(X,Y,extension(X,Y,V,V)) ),[2],$fot(Y)]]) ).
cnf(refute_0_11,plain,
( ~ between(X,Y,extension(X,Y,V,V))
| between(X,Y,Y) ),
inference(resolve,[$cnf( $equal(extension(X,Y,V,V),Y) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
between(X,Y,Y),
inference(resolve,[$cnf( between(X,Y,extension(X,Y,V,V)) )],[refute_0_0,refute_0_11]) ).
cnf(refute_0_13,plain,
between(X_180,X_182,X_182),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_180)),bind(Y,$fot(X_182))]]) ).
cnf(refute_0_14,plain,
between(X_179,X_177,X_177),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_179)),bind(Y,$fot(X_177))]]) ).
cnf(refute_0_15,plain,
( ~ between(X_175,X_176,X_177)
| ~ between(X_179,X_177,X_177)
| between(X_176,inner_pasch(X_175,X_176,X_177,X_177,X_179),X_179) ),
inference(subst,[],[inner_pasch1:[bind(U,$fot(X_175)),bind(V,$fot(X_176)),bind(W,$fot(X_177)),bind(X,$fot(X_177)),bind(Y,$fot(X_179))]]) ).
cnf(refute_0_16,plain,
( ~ between(X_175,X_176,X_177)
| between(X_176,inner_pasch(X_175,X_176,X_177,X_177,X_179),X_179) ),
inference(resolve,[$cnf( between(X_179,X_177,X_177) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ between(X_180,X_182,X_182)
| between(X_182,inner_pasch(X_180,X_182,X_182,X_182,X_183),X_183) ),
inference(subst,[],[refute_0_16:[bind(X_175,$fot(X_180)),bind(X_176,$fot(X_182)),bind(X_177,$fot(X_182)),bind(X_179,$fot(X_183))]]) ).
cnf(refute_0_18,plain,
between(X_182,inner_pasch(X_180,X_182,X_182,X_182,X_183),X_183),
inference(resolve,[$cnf( between(X_180,X_182,X_182) )],[refute_0_13,refute_0_17]) ).
cnf(refute_0_19,plain,
between(X_185,inner_pasch(X_185,X_185,X_185,X_185,X_186),X_186),
inference(subst,[],[refute_0_18:[bind(X_180,$fot(X_185)),bind(X_182,$fot(X_185)),bind(X_183,$fot(X_186))]]) ).
cnf(refute_0_20,plain,
( ~ between(X_94,inner_pasch(X_94,X_94,X_94,X_94,X_96),X_94)
| X_94 = inner_pasch(X_94,X_94,X_94,X_94,X_96) ),
inference(subst,[],[identity_for_betweeness:[bind(X,$fot(X_94)),bind(Y,$fot(inner_pasch(X_94,X_94,X_94,X_94,X_96)))]]) ).
cnf(refute_0_21,plain,
between(X_90,X_92,X_92),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_90)),bind(Y,$fot(X_92))]]) ).
cnf(refute_0_22,plain,
between(X_79,X_77,X_77),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_79)),bind(Y,$fot(X_77))]]) ).
cnf(refute_0_23,plain,
( ~ between(X_75,X_76,X_77)
| ~ between(X_79,X_77,X_77)
| between(X_77,inner_pasch(X_75,X_76,X_77,X_77,X_79),X_75) ),
inference(subst,[],[inner_pasch2:[bind(U,$fot(X_75)),bind(V,$fot(X_76)),bind(W,$fot(X_77)),bind(X,$fot(X_77)),bind(Y,$fot(X_79))]]) ).
cnf(refute_0_24,plain,
( ~ between(X_75,X_76,X_77)
| between(X_77,inner_pasch(X_75,X_76,X_77,X_77,X_79),X_75) ),
inference(resolve,[$cnf( between(X_79,X_77,X_77) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ between(X_90,X_92,X_92)
| between(X_92,inner_pasch(X_90,X_92,X_92,X_92,X_93),X_90) ),
inference(subst,[],[refute_0_24:[bind(X_75,$fot(X_90)),bind(X_76,$fot(X_92)),bind(X_77,$fot(X_92)),bind(X_79,$fot(X_93))]]) ).
cnf(refute_0_26,plain,
between(X_92,inner_pasch(X_90,X_92,X_92,X_92,X_93),X_90),
inference(resolve,[$cnf( between(X_90,X_92,X_92) )],[refute_0_21,refute_0_25]) ).
cnf(refute_0_27,plain,
between(X_94,inner_pasch(X_94,X_94,X_94,X_94,X_96),X_94),
inference(subst,[],[refute_0_26:[bind(X_90,$fot(X_94)),bind(X_92,$fot(X_94)),bind(X_93,$fot(X_96))]]) ).
cnf(refute_0_28,plain,
X_94 = inner_pasch(X_94,X_94,X_94,X_94,X_96),
inference(resolve,[$cnf( between(X_94,inner_pasch(X_94,X_94,X_94,X_94,X_96),X_94) )],[refute_0_27,refute_0_20]) ).
cnf(refute_0_29,plain,
X_185 = inner_pasch(X_185,X_185,X_185,X_185,X_186),
inference(subst,[],[refute_0_28:[bind(X_94,$fot(X_185)),bind(X_96,$fot(X_186))]]) ).
cnf(refute_0_30,plain,
( X_185 != inner_pasch(X_185,X_185,X_185,X_185,X_186)
| inner_pasch(X_185,X_185,X_185,X_185,X_186) = X_185 ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(X_185)),bind(Y0,$fot(inner_pasch(X_185,X_185,X_185,X_185,X_186)))]]) ).
cnf(refute_0_31,plain,
inner_pasch(X_185,X_185,X_185,X_185,X_186) = X_185,
inference(resolve,[$cnf( $equal(X_185,inner_pasch(X_185,X_185,X_185,X_185,X_186)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( inner_pasch(X_185,X_185,X_185,X_185,X_186) != X_185
| ~ between(X_185,inner_pasch(X_185,X_185,X_185,X_185,X_186),X_186)
| between(X_185,X_185,X_186) ),
introduced(tautology,[equality,[$cnf( between(X_185,inner_pasch(X_185,X_185,X_185,X_185,X_186),X_186) ),[1],$fot(X_185)]]) ).
cnf(refute_0_33,plain,
( ~ between(X_185,inner_pasch(X_185,X_185,X_185,X_185,X_186),X_186)
| between(X_185,X_185,X_186) ),
inference(resolve,[$cnf( $equal(inner_pasch(X_185,X_185,X_185,X_185,X_186),X_185) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
between(X_185,X_185,X_186),
inference(resolve,[$cnf( between(X_185,inner_pasch(X_185,X_185,X_185,X_185,X_186),X_186) )],[refute_0_19,refute_0_33]) ).
cnf(refute_0_35,plain,
between(a,a,b),
inference(subst,[],[refute_0_34:[bind(X_185,$fot(a)),bind(X_186,$fot(b))]]) ).
cnf(refute_0_36,plain,
$false,
inference(resolve,[$cnf( between(a,a,b) )],[refute_0_35,prove_a_between_a_and_b]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO002-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jun 18 05:55:10 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.52 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.52
% 0.19/0.52 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.52
%------------------------------------------------------------------------------