TSTP Solution File: GEO001-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO001-2 : 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 05:23:24 EDT 2022
% Result : Unsatisfiable 2.15s 2.32s
% Output : CNFRefutation 2.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of clauses : 41 ( 21 unt; 0 nHn; 28 RR)
% Number of literals : 68 ( 21 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 : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 71 ( 11 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(b_between_a_and_c,hypothesis,
between(a,b,c) ).
cnf(prove_b_between_c_and_a,negated_conjecture,
~ between(c,b,a) ).
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_166,c,c),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_166)),bind(Y,$fot(c))]]) ).
cnf(refute_0_14,plain,
( ~ between(X_164,X_163,c)
| ~ between(a,b,c)
| between(X_163,inner_pasch(a,b,c,X_163,X_164),a) ),
inference(subst,[],[inner_pasch2:[bind(U,$fot(a)),bind(V,$fot(b)),bind(W,$fot(c)),bind(X,$fot(X_163)),bind(Y,$fot(X_164))]]) ).
cnf(refute_0_15,plain,
( ~ between(X_164,X_163,c)
| between(X_163,inner_pasch(a,b,c,X_163,X_164),a) ),
inference(resolve,[$cnf( between(a,b,c) )],[b_between_a_and_c,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ between(X_166,c,c)
| between(c,inner_pasch(a,b,c,c,X_166),a) ),
inference(subst,[],[refute_0_15:[bind(X_163,$fot(c)),bind(X_164,$fot(X_166))]]) ).
cnf(refute_0_17,plain,
between(c,inner_pasch(a,b,c,c,X_166),a),
inference(resolve,[$cnf( between(X_166,c,c) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
between(c,inner_pasch(a,b,c,c,b),a),
inference(subst,[],[refute_0_17:[bind(X_166,$fot(b))]]) ).
cnf(refute_0_19,plain,
( ~ between(b,inner_pasch(a,b,c,c,b),b)
| b = inner_pasch(a,b,c,c,b) ),
inference(subst,[],[identity_for_betweeness:[bind(X,$fot(b)),bind(Y,$fot(inner_pasch(a,b,c,c,b)))]]) ).
cnf(refute_0_20,plain,
between(X_108,c,c),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_108)),bind(Y,$fot(c))]]) ).
cnf(refute_0_21,plain,
( ~ between(X_106,X_105,c)
| ~ between(a,b,c)
| between(b,inner_pasch(a,b,c,X_105,X_106),X_106) ),
inference(subst,[],[inner_pasch1:[bind(U,$fot(a)),bind(V,$fot(b)),bind(W,$fot(c)),bind(X,$fot(X_105)),bind(Y,$fot(X_106))]]) ).
cnf(refute_0_22,plain,
( ~ between(X_106,X_105,c)
| between(b,inner_pasch(a,b,c,X_105,X_106),X_106) ),
inference(resolve,[$cnf( between(a,b,c) )],[b_between_a_and_c,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ between(X_108,c,c)
| between(b,inner_pasch(a,b,c,c,X_108),X_108) ),
inference(subst,[],[refute_0_22:[bind(X_105,$fot(c)),bind(X_106,$fot(X_108))]]) ).
cnf(refute_0_24,plain,
between(b,inner_pasch(a,b,c,c,X_108),X_108),
inference(resolve,[$cnf( between(X_108,c,c) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
between(b,inner_pasch(a,b,c,c,b),b),
inference(subst,[],[refute_0_24:[bind(X_108,$fot(b))]]) ).
cnf(refute_0_26,plain,
b = inner_pasch(a,b,c,c,b),
inference(resolve,[$cnf( between(b,inner_pasch(a,b,c,c,b),b) )],[refute_0_25,refute_0_19]) ).
cnf(refute_0_27,plain,
( b != inner_pasch(a,b,c,c,b)
| inner_pasch(a,b,c,c,b) = b ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(b)),bind(Y0,$fot(inner_pasch(a,b,c,c,b)))]]) ).
cnf(refute_0_28,plain,
inner_pasch(a,b,c,c,b) = b,
inference(resolve,[$cnf( $equal(b,inner_pasch(a,b,c,c,b)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( inner_pasch(a,b,c,c,b) != b
| ~ between(c,inner_pasch(a,b,c,c,b),a)
| between(c,b,a) ),
introduced(tautology,[equality,[$cnf( between(c,inner_pasch(a,b,c,c,b),a) ),[1],$fot(b)]]) ).
cnf(refute_0_30,plain,
( ~ between(c,inner_pasch(a,b,c,c,b),a)
| between(c,b,a) ),
inference(resolve,[$cnf( $equal(inner_pasch(a,b,c,c,b),b) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
between(c,b,a),
inference(resolve,[$cnf( between(c,inner_pasch(a,b,c,c,b),a) )],[refute_0_18,refute_0_30]) ).
cnf(refute_0_32,plain,
$false,
inference(resolve,[$cnf( between(c,b,a) )],[refute_0_31,prove_b_between_c_and_a]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GEO001-2 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n007.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 13:05:43 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.15/2.32 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.15/2.32
% 2.15/2.32 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.15/2.32
%------------------------------------------------------------------------------