TSTP Solution File: GEO006-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO006-1 : TPTP v8.1.0. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 05:23:28 EDT 2022
% Result : Unsatisfiable 134.50s 134.69s
% Output : CNFRefutation 134.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 16
% Syntax : Number of clauses : 78 ( 35 unt; 3 nHn; 61 RR)
% Number of literals : 134 ( 36 equ; 56 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 : 93 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(identity_for_betweeness,axiom,
( ~ between(X,Y,X)
| X = Y ) ).
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)
| 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(a_not_c,hypothesis,
a != c ).
cnf(c_not_d,hypothesis,
c != d ).
cnf(c_between_a_and_d,hypothesis,
between(a,c,d) ).
cnf(prove_not_between_others,negated_conjecture,
( between(c,a,d)
| between(a,d,c) ) ).
cnf(refute_0_0,plain,
( ~ between(c,d,c)
| c = d ),
inference(subst,[],[identity_for_betweeness:[bind(X,$fot(c)),bind(Y,$fot(d))]]) ).
cnf(refute_0_1,plain,
( ~ between(X,d,a)
| ~ between(d,c,a)
| between(X,d,c) ),
inference(subst,[],[transitivity_for_betweeness:[bind(V,$fot(a)),bind(Y,$fot(d)),bind(Z,$fot(c))]]) ).
cnf(refute_0_2,plain,
between(X,Y,extension(X,Y,V,V)),
inference(subst,[],[segment_construction1:[bind(W,$fot(V))]]) ).
cnf(refute_0_3,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,$fot(X_12))]]) ).
cnf(refute_0_4,plain,
( ~ equidistant(X_12,extension(X,X_12,X_14,X_14),X_14,X_14)
| X_12 = extension(X,X_12,X_14,X_14) ),
inference(subst,[],[identity_for_equidistance:[bind(X,$fot(X_12)),bind(Y,$fot(extension(X,X_12,X_14,X_14))),bind(Z,$fot(X_14))]]) ).
cnf(refute_0_5,plain,
X_12 = extension(X,X_12,X_14,X_14),
inference(resolve,[$cnf( equidistant(X_12,extension(X,X_12,X_14,X_14),X_14,X_14) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
Y = extension(X,Y,V,V),
inference(subst,[],[refute_0_5:[bind(X_12,$fot(Y)),bind(X_14,$fot(V))]]) ).
cnf(refute_0_7,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_8,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_9,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( Y != extension(X,Y,V,V)
| extension(X,Y,V,V) = Y ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(Y)),bind(Y0,$fot(extension(X,Y,V,V)))]]) ).
cnf(refute_0_11,plain,
extension(X,Y,V,V) = Y,
inference(resolve,[$cnf( $equal(Y,extension(X,Y,V,V)) )],[refute_0_6,refute_0_10]) ).
cnf(refute_0_12,plain,
( extension(X,Y,V,V) != Y
| ~ between(X,Y,extension(X,Y,V,V))
| between(X,Y,Y) ),
introduced(tautology,[equality,[$cnf( between(X,Y,extension(X,Y,V,V)) ),[2],$fot(Y)]]) ).
cnf(refute_0_13,plain,
( ~ between(X,Y,extension(X,Y,V,V))
| between(X,Y,Y) ),
inference(resolve,[$cnf( $equal(extension(X,Y,V,V),Y) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
between(X,Y,Y),
inference(resolve,[$cnf( between(X,Y,extension(X,Y,V,V)) )],[refute_0_2,refute_0_13]) ).
cnf(refute_0_15,plain,
between(X_7865,c,c),
inference(subst,[],[refute_0_14:[bind(X,$fot(X_7865)),bind(Y,$fot(c))]]) ).
cnf(refute_0_16,plain,
( ~ between(X_7861,X_7860,c)
| ~ between(a,c,d)
| between(d,X_7860,outer_pasch(X_7860,X_7861,a,d,c)) ),
inference(subst,[],[outer_pasch2:[bind(V,$fot(c)),bind(W,$fot(X_7860)),bind(X,$fot(X_7861)),bind(Y,$fot(a)),bind(Z,$fot(d))]]) ).
cnf(refute_0_17,plain,
( ~ between(X_7861,X_7860,c)
| between(d,X_7860,outer_pasch(X_7860,X_7861,a,d,c)) ),
inference(resolve,[$cnf( between(a,c,d) )],[c_between_a_and_d,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ between(X_7865,c,c)
| between(d,c,outer_pasch(c,X_7865,a,d,c)) ),
inference(subst,[],[refute_0_17:[bind(X_7860,$fot(c)),bind(X_7861,$fot(X_7865))]]) ).
cnf(refute_0_19,plain,
between(d,c,outer_pasch(c,X_7865,a,d,c)),
inference(resolve,[$cnf( between(X_7865,c,c) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
between(d,c,outer_pasch(c,a,a,d,c)),
inference(subst,[],[refute_0_19:[bind(X_7865,$fot(a))]]) ).
cnf(refute_0_21,plain,
( ~ between(a,outer_pasch(c,a,a,d,c),a)
| a = outer_pasch(c,a,a,d,c) ),
inference(subst,[],[identity_for_betweeness:[bind(X,$fot(a)),bind(Y,$fot(outer_pasch(c,a,a,d,c)))]]) ).
cnf(refute_0_22,plain,
between(X_118,c,c),
inference(subst,[],[refute_0_14:[bind(X,$fot(X_118)),bind(Y,$fot(c))]]) ).
cnf(refute_0_23,plain,
( ~ between(X_93,X_92,c)
| ~ between(a,c,d)
| between(X_93,outer_pasch(X_92,X_93,a,d,c),a) ),
inference(subst,[],[outer_pasch1:[bind(V,$fot(c)),bind(W,$fot(X_92)),bind(X,$fot(X_93)),bind(Y,$fot(a)),bind(Z,$fot(d))]]) ).
cnf(refute_0_24,plain,
( ~ between(X_93,X_92,c)
| between(X_93,outer_pasch(X_92,X_93,a,d,c),a) ),
inference(resolve,[$cnf( between(a,c,d) )],[c_between_a_and_d,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ between(X_118,c,c)
| between(X_118,outer_pasch(c,X_118,a,d,c),a) ),
inference(subst,[],[refute_0_24:[bind(X_92,$fot(c)),bind(X_93,$fot(X_118))]]) ).
cnf(refute_0_26,plain,
between(X_118,outer_pasch(c,X_118,a,d,c),a),
inference(resolve,[$cnf( between(X_118,c,c) )],[refute_0_22,refute_0_25]) ).
cnf(refute_0_27,plain,
between(a,outer_pasch(c,a,a,d,c),a),
inference(subst,[],[refute_0_26:[bind(X_118,$fot(a))]]) ).
cnf(refute_0_28,plain,
a = outer_pasch(c,a,a,d,c),
inference(resolve,[$cnf( between(a,outer_pasch(c,a,a,d,c),a) )],[refute_0_27,refute_0_21]) ).
cnf(refute_0_29,plain,
( a != outer_pasch(c,a,a,d,c)
| outer_pasch(c,a,a,d,c) = a ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(a)),bind(Y0,$fot(outer_pasch(c,a,a,d,c)))]]) ).
cnf(refute_0_30,plain,
outer_pasch(c,a,a,d,c) = a,
inference(resolve,[$cnf( $equal(a,outer_pasch(c,a,a,d,c)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( outer_pasch(c,a,a,d,c) != a
| ~ between(d,c,outer_pasch(c,a,a,d,c))
| between(d,c,a) ),
introduced(tautology,[equality,[$cnf( between(d,c,outer_pasch(c,a,a,d,c)) ),[2],$fot(a)]]) ).
cnf(refute_0_32,plain,
( ~ between(d,c,outer_pasch(c,a,a,d,c))
| between(d,c,a) ),
inference(resolve,[$cnf( $equal(outer_pasch(c,a,a,d,c),a) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
between(d,c,a),
inference(resolve,[$cnf( between(d,c,outer_pasch(c,a,a,d,c)) )],[refute_0_20,refute_0_32]) ).
cnf(refute_0_34,plain,
( ~ between(X,d,a)
| between(X,d,c) ),
inference(resolve,[$cnf( between(d,c,a) )],[refute_0_33,refute_0_1]) ).
cnf(refute_0_35,plain,
( ~ between(c,d,a)
| between(c,d,c) ),
inference(subst,[],[refute_0_34:[bind(X,$fot(c))]]) ).
cnf(refute_0_36,plain,
between(X_8357,c,c),
inference(subst,[],[refute_0_14:[bind(X,$fot(X_8357)),bind(Y,$fot(c))]]) ).
cnf(refute_0_37,plain,
( ~ between(c,a,c)
| c = a ),
inference(subst,[],[identity_for_betweeness:[bind(X,$fot(c)),bind(Y,$fot(a))]]) ).
cnf(refute_0_38,plain,
( ~ between(X_41,a,d)
| ~ between(a,c,d)
| between(X_41,a,c) ),
inference(subst,[],[transitivity_for_betweeness:[bind(V,$fot(d)),bind(X,$fot(X_41)),bind(Y,$fot(a)),bind(Z,$fot(c))]]) ).
cnf(refute_0_39,plain,
( ~ between(X_41,a,d)
| between(X_41,a,c) ),
inference(resolve,[$cnf( between(a,c,d) )],[c_between_a_and_d,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ between(c,a,d)
| between(c,a,c) ),
inference(subst,[],[refute_0_39:[bind(X_41,$fot(c))]]) ).
cnf(refute_0_41,plain,
( between(a,d,c)
| between(c,a,c) ),
inference(resolve,[$cnf( between(c,a,d) )],[prove_not_between_others,refute_0_40]) ).
cnf(refute_0_42,plain,
( c = a
| between(a,d,c) ),
inference(resolve,[$cnf( between(c,a,c) )],[refute_0_41,refute_0_37]) ).
cnf(refute_0_43,plain,
( c != a
| a = c ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(c)),bind(Y0,$fot(a))]]) ).
cnf(refute_0_44,plain,
c != a,
inference(resolve,[$cnf( $equal(a,c) )],[refute_0_43,a_not_c]) ).
cnf(refute_0_45,plain,
between(a,d,c),
inference(resolve,[$cnf( $equal(c,a) )],[refute_0_42,refute_0_44]) ).
cnf(refute_0_46,plain,
( ~ between(X_7862,c,X_7863)
| ~ between(a,d,c)
| between(X_7863,d,outer_pasch(d,a,X_7862,X_7863,c)) ),
inference(subst,[],[outer_pasch2:[bind(V,$fot(c)),bind(W,$fot(d)),bind(X,$fot(a)),bind(Y,$fot(X_7862)),bind(Z,$fot(X_7863))]]) ).
cnf(refute_0_47,plain,
( ~ between(X_7862,c,X_7863)
| between(X_7863,d,outer_pasch(d,a,X_7862,X_7863,c)) ),
inference(resolve,[$cnf( between(a,d,c) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
( ~ between(X_8357,c,c)
| between(c,d,outer_pasch(d,a,X_8357,c,c)) ),
inference(subst,[],[refute_0_47:[bind(X_7862,$fot(X_8357)),bind(X_7863,$fot(c))]]) ).
cnf(refute_0_49,plain,
between(c,d,outer_pasch(d,a,X_8357,c,c)),
inference(resolve,[$cnf( between(X_8357,c,c) )],[refute_0_36,refute_0_48]) ).
cnf(refute_0_50,plain,
between(c,d,outer_pasch(d,a,a,c,c)),
inference(subst,[],[refute_0_49:[bind(X_8357,$fot(a))]]) ).
cnf(refute_0_51,plain,
( ~ between(a,outer_pasch(d,a,a,c,c),a)
| a = outer_pasch(d,a,a,c,c) ),
inference(subst,[],[identity_for_betweeness:[bind(X,$fot(a)),bind(Y,$fot(outer_pasch(d,a,a,c,c)))]]) ).
cnf(refute_0_52,plain,
between(X_131,c,c),
inference(subst,[],[refute_0_14:[bind(X,$fot(X_131)),bind(Y,$fot(c))]]) ).
cnf(refute_0_53,plain,
( ~ between(X_94,c,X_95)
| ~ between(a,d,c)
| between(a,outer_pasch(d,a,X_94,X_95,c),X_94) ),
inference(subst,[],[outer_pasch1:[bind(V,$fot(c)),bind(W,$fot(d)),bind(X,$fot(a)),bind(Y,$fot(X_94)),bind(Z,$fot(X_95))]]) ).
cnf(refute_0_54,plain,
( ~ between(X_94,c,X_95)
| between(a,outer_pasch(d,a,X_94,X_95,c),X_94) ),
inference(resolve,[$cnf( between(a,d,c) )],[refute_0_45,refute_0_53]) ).
cnf(refute_0_55,plain,
( ~ between(X_131,c,c)
| between(a,outer_pasch(d,a,X_131,c,c),X_131) ),
inference(subst,[],[refute_0_54:[bind(X_94,$fot(X_131)),bind(X_95,$fot(c))]]) ).
cnf(refute_0_56,plain,
between(a,outer_pasch(d,a,X_131,c,c),X_131),
inference(resolve,[$cnf( between(X_131,c,c) )],[refute_0_52,refute_0_55]) ).
cnf(refute_0_57,plain,
between(a,outer_pasch(d,a,a,c,c),a),
inference(subst,[],[refute_0_56:[bind(X_131,$fot(a))]]) ).
cnf(refute_0_58,plain,
a = outer_pasch(d,a,a,c,c),
inference(resolve,[$cnf( between(a,outer_pasch(d,a,a,c,c),a) )],[refute_0_57,refute_0_51]) ).
cnf(refute_0_59,plain,
( a != outer_pasch(d,a,a,c,c)
| outer_pasch(d,a,a,c,c) = a ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(a)),bind(Y0,$fot(outer_pasch(d,a,a,c,c)))]]) ).
cnf(refute_0_60,plain,
outer_pasch(d,a,a,c,c) = a,
inference(resolve,[$cnf( $equal(a,outer_pasch(d,a,a,c,c)) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
( outer_pasch(d,a,a,c,c) != a
| ~ between(c,d,outer_pasch(d,a,a,c,c))
| between(c,d,a) ),
introduced(tautology,[equality,[$cnf( between(c,d,outer_pasch(d,a,a,c,c)) ),[2],$fot(a)]]) ).
cnf(refute_0_62,plain,
( ~ between(c,d,outer_pasch(d,a,a,c,c))
| between(c,d,a) ),
inference(resolve,[$cnf( $equal(outer_pasch(d,a,a,c,c),a) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
between(c,d,a),
inference(resolve,[$cnf( between(c,d,outer_pasch(d,a,a,c,c)) )],[refute_0_50,refute_0_62]) ).
cnf(refute_0_64,plain,
between(c,d,c),
inference(resolve,[$cnf( between(c,d,a) )],[refute_0_63,refute_0_35]) ).
cnf(refute_0_65,plain,
c = d,
inference(resolve,[$cnf( between(c,d,c) )],[refute_0_64,refute_0_0]) ).
cnf(refute_0_66,plain,
$false,
inference(resolve,[$cnf( $equal(c,d) )],[refute_0_65,c_not_d]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO006-1 : TPTP v8.1.0. Bugfixed v2.5.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jun 17 15:47:47 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 134.50/134.69 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 134.50/134.69
% 134.50/134.69 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 134.51/134.69
%------------------------------------------------------------------------------