TSTP Solution File: GEO067-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO067-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.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 05:24:01 EDT 2022
% Result : Unsatisfiable 0.15s 0.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of clauses : 54 ( 24 unt; 0 nHn; 39 RR)
% Number of literals : 99 ( 25 equ; 51 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 72 ( 14 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(colinearity1,axiom,
( ~ between(X,Y,Z)
| colinear(X,Y,Z) ) ).
cnf(colinearity2,axiom,
( ~ between(Y,Z,X)
| colinear(X,Y,Z) ) ).
cnf(colinearity3,axiom,
( ~ between(Z,X,Y)
| colinear(X,Y,Z) ) ).
cnf(part_1,negated_conjecture,
( ~ colinear(x,x,y)
| ~ colinear(x,y,x)
| ~ colinear(y,x,x)
| x = y ) ).
cnf(part_2,negated_conjecture,
( ~ colinear(x,x,y)
| ~ colinear(x,y,x)
| ~ colinear(y,x,x)
| ~ colinear(x,z,y) ) ).
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_28,X_30,X_30),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_28)),bind(Y,$fot(X_30))]]) ).
cnf(refute_0_14,plain,
( ~ between(X_28,X_30,X_30)
| colinear(X_28,X_30,X_30) ),
inference(subst,[],[colinearity1:[bind(X,$fot(X_28)),bind(Y,$fot(X_30)),bind(Z,$fot(X_30))]]) ).
cnf(refute_0_15,plain,
colinear(X_28,X_30,X_30),
inference(resolve,[$cnf( between(X_28,X_30,X_30) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
colinear(y,x,x),
inference(subst,[],[refute_0_15:[bind(X_28,$fot(y)),bind(X_30,$fot(x))]]) ).
cnf(refute_0_17,plain,
( ~ colinear(x,x,y)
| ~ colinear(x,y,x)
| x = y ),
inference(resolve,[$cnf( colinear(y,x,x) )],[refute_0_16,part_1]) ).
cnf(refute_0_18,plain,
between(X_38,X_37,X_37),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_38)),bind(Y,$fot(X_37))]]) ).
cnf(refute_0_19,plain,
( ~ between(X_38,X_37,X_37)
| colinear(X_37,X_38,X_37) ),
inference(subst,[],[colinearity2:[bind(X,$fot(X_37)),bind(Y,$fot(X_38)),bind(Z,$fot(X_37))]]) ).
cnf(refute_0_20,plain,
colinear(X_37,X_38,X_37),
inference(resolve,[$cnf( between(X_38,X_37,X_37) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
colinear(x,y,x),
inference(subst,[],[refute_0_20:[bind(X_37,$fot(x)),bind(X_38,$fot(y))]]) ).
cnf(refute_0_22,plain,
( ~ colinear(x,x,y)
| x = y ),
inference(resolve,[$cnf( colinear(x,y,x) )],[refute_0_21,refute_0_17]) ).
cnf(refute_0_23,plain,
between(X_48,X_47,X_47),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_48)),bind(Y,$fot(X_47))]]) ).
cnf(refute_0_24,plain,
( ~ between(X_48,X_47,X_47)
| colinear(X_47,X_47,X_48) ),
inference(subst,[],[colinearity3:[bind(X,$fot(X_47)),bind(Y,$fot(X_47)),bind(Z,$fot(X_48))]]) ).
cnf(refute_0_25,plain,
colinear(X_47,X_47,X_48),
inference(resolve,[$cnf( between(X_48,X_47,X_47) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
colinear(x,x,y),
inference(subst,[],[refute_0_25:[bind(X_47,$fot(x)),bind(X_48,$fot(y))]]) ).
cnf(refute_0_27,plain,
x = y,
inference(resolve,[$cnf( colinear(x,x,y) )],[refute_0_26,refute_0_22]) ).
cnf(refute_0_28,plain,
( x != y
| y = x ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(x)),bind(Y0,$fot(y))]]) ).
cnf(refute_0_29,plain,
y = x,
inference(resolve,[$cnf( $equal(x,y) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( y != x
| ~ colinear(x,x,x)
| colinear(x,x,y) ),
introduced(tautology,[equality,[$cnf( ~ colinear(x,x,y) ),[2],$fot(x)]]) ).
cnf(refute_0_31,plain,
( ~ colinear(x,x,x)
| colinear(x,x,y) ),
inference(resolve,[$cnf( $equal(y,x) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( ~ colinear(x,x,x)
| ~ colinear(x,y,x)
| ~ colinear(x,z,y)
| ~ colinear(y,x,x) ),
inference(resolve,[$cnf( colinear(x,x,y) )],[refute_0_31,part_2]) ).
cnf(refute_0_33,plain,
( y != x
| ~ colinear(x,x,x)
| colinear(x,y,x) ),
introduced(tautology,[equality,[$cnf( ~ colinear(x,y,x) ),[1],$fot(x)]]) ).
cnf(refute_0_34,plain,
( ~ colinear(x,x,x)
| colinear(x,y,x) ),
inference(resolve,[$cnf( $equal(y,x) )],[refute_0_29,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ colinear(x,x,x)
| ~ colinear(x,z,y)
| ~ colinear(y,x,x) ),
inference(resolve,[$cnf( colinear(x,y,x) )],[refute_0_34,refute_0_32]) ).
cnf(refute_0_36,plain,
( y != x
| ~ colinear(x,z,x)
| colinear(x,z,y) ),
introduced(tautology,[equality,[$cnf( ~ colinear(x,z,y) ),[2],$fot(x)]]) ).
cnf(refute_0_37,plain,
( ~ colinear(x,z,x)
| colinear(x,z,y) ),
inference(resolve,[$cnf( $equal(y,x) )],[refute_0_29,refute_0_36]) ).
cnf(refute_0_38,plain,
( ~ colinear(x,x,x)
| ~ colinear(x,z,x)
| ~ colinear(y,x,x) ),
inference(resolve,[$cnf( colinear(x,z,y) )],[refute_0_37,refute_0_35]) ).
cnf(refute_0_39,plain,
( y != x
| ~ colinear(x,x,x)
| colinear(y,x,x) ),
introduced(tautology,[equality,[$cnf( ~ colinear(y,x,x) ),[0],$fot(x)]]) ).
cnf(refute_0_40,plain,
( ~ colinear(x,x,x)
| colinear(y,x,x) ),
inference(resolve,[$cnf( $equal(y,x) )],[refute_0_29,refute_0_39]) ).
cnf(refute_0_41,plain,
( ~ colinear(x,x,x)
| ~ colinear(x,z,x) ),
inference(resolve,[$cnf( colinear(y,x,x) )],[refute_0_40,refute_0_38]) ).
cnf(refute_0_42,plain,
colinear(x,x,x),
inference(subst,[],[refute_0_25:[bind(X_47,$fot(x)),bind(X_48,$fot(x))]]) ).
cnf(refute_0_43,plain,
~ colinear(x,z,x),
inference(resolve,[$cnf( colinear(x,x,x) )],[refute_0_42,refute_0_41]) ).
cnf(refute_0_44,plain,
colinear(x,z,x),
inference(subst,[],[refute_0_20:[bind(X_37,$fot(x)),bind(X_38,$fot(z))]]) ).
cnf(refute_0_45,plain,
$false,
inference(resolve,[$cnf( colinear(x,z,x) )],[refute_0_44,refute_0_43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GEO067-2 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.14 % Command : metis --show proof --show saturation %s
% 0.15/0.36 % Computer : n007.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Sat Jun 18 15:41:28 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.15/0.40 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.40
% 0.15/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.15/0.40
%------------------------------------------------------------------------------