TSTP Solution File: GEO042-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO042-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n011.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 05:23:48 EDT 2022
% Result : Unsatisfiable 259.33s 259.58s
% Output : CNFRefutation 259.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 17
% Syntax : Number of clauses : 64 ( 29 unt; 0 nHn; 46 RR)
% Number of literals : 111 ( 35 equ; 48 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-5 aty)
% Number of variables : 98 ( 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(v_between_u_and_x,hypothesis,
between(u,v,x) ).
cnf(w_between_v_and_x,hypothesis,
between(v,w,x) ).
cnf(prove_v_between_u_and_w,negated_conjecture,
~ between(u,v,w) ).
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_2240,u,u),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_2240)),bind(Y,$fot(u))]]) ).
cnf(refute_0_14,plain,
( ~ between(X_108,X_107,x)
| ~ between(v,w,x)
| between(w,inner_pasch(v,w,x,X_107,X_108),X_108) ),
inference(subst,[],[inner_pasch1:[bind(U,$fot(v)),bind(V,$fot(w)),bind(W,$fot(x)),bind(X,$fot(X_107)),bind(Y,$fot(X_108))]]) ).
cnf(refute_0_15,plain,
( ~ between(X_108,X_107,x)
| between(w,inner_pasch(v,w,x,X_107,X_108),X_108) ),
inference(resolve,[$cnf( between(v,w,x) )],[w_between_v_and_x,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ between(u,v,x)
| between(w,inner_pasch(v,w,x,v,u),u) ),
inference(subst,[],[refute_0_15:[bind(X_107,$fot(v)),bind(X_108,$fot(u))]]) ).
cnf(refute_0_17,plain,
between(w,inner_pasch(v,w,x,v,u),u),
inference(resolve,[$cnf( between(u,v,x) )],[v_between_u_and_x,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ between(X_235,X_234,u)
| ~ between(w,inner_pasch(v,w,x,v,u),u)
| between(X_234,inner_pasch(w,inner_pasch(v,w,x,v,u),u,X_234,X_235),w) ),
inference(subst,[],[inner_pasch2:[bind(U,$fot(w)),bind(V,$fot(inner_pasch(v,w,x,v,u))),bind(W,$fot(u)),bind(X,$fot(X_234)),bind(Y,$fot(X_235))]]) ).
cnf(refute_0_19,plain,
( ~ between(X_235,X_234,u)
| between(X_234,inner_pasch(w,inner_pasch(v,w,x,v,u),u,X_234,X_235),w) ),
inference(resolve,[$cnf( between(w,inner_pasch(v,w,x,v,u),u) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ between(v,inner_pasch(v,w,x,v,u),v)
| v = inner_pasch(v,w,x,v,u) ),
inference(subst,[],[identity_for_betweeness:[bind(X,$fot(v)),bind(Y,$fot(inner_pasch(v,w,x,v,u)))]]) ).
cnf(refute_0_21,plain,
( ~ between(X_235,X_234,x)
| ~ between(v,w,x)
| between(X_234,inner_pasch(v,w,x,X_234,X_235),v) ),
inference(subst,[],[inner_pasch2:[bind(U,$fot(v)),bind(V,$fot(w)),bind(W,$fot(x)),bind(X,$fot(X_234)),bind(Y,$fot(X_235))]]) ).
cnf(refute_0_22,plain,
( ~ between(X_235,X_234,x)
| between(X_234,inner_pasch(v,w,x,X_234,X_235),v) ),
inference(resolve,[$cnf( between(v,w,x) )],[w_between_v_and_x,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ between(u,v,x)
| between(v,inner_pasch(v,w,x,v,u),v) ),
inference(subst,[],[refute_0_22:[bind(X_234,$fot(v)),bind(X_235,$fot(u))]]) ).
cnf(refute_0_24,plain,
between(v,inner_pasch(v,w,x,v,u),v),
inference(resolve,[$cnf( between(u,v,x) )],[v_between_u_and_x,refute_0_23]) ).
cnf(refute_0_25,plain,
v = inner_pasch(v,w,x,v,u),
inference(resolve,[$cnf( between(v,inner_pasch(v,w,x,v,u),v) )],[refute_0_24,refute_0_20]) ).
cnf(refute_0_26,plain,
( v != inner_pasch(v,w,x,v,u)
| inner_pasch(v,w,x,v,u) = v ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(v)),bind(Y0,$fot(inner_pasch(v,w,x,v,u)))]]) ).
cnf(refute_0_27,plain,
inner_pasch(v,w,x,v,u) = v,
inference(resolve,[$cnf( $equal(v,inner_pasch(v,w,x,v,u)) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
inner_pasch(w,inner_pasch(v,w,x,v,u),u,X_234,X_235) = inner_pasch(w,inner_pasch(v,w,x,v,u),u,X_234,X_235),
introduced(tautology,[refl,[$fot(inner_pasch(w,inner_pasch(v,w,x,v,u),u,X_234,X_235))]]) ).
cnf(refute_0_29,plain,
( inner_pasch(v,w,x,v,u) != v
| inner_pasch(w,inner_pasch(v,w,x,v,u),u,X_234,X_235) != inner_pasch(w,inner_pasch(v,w,x,v,u),u,X_234,X_235)
| inner_pasch(w,inner_pasch(v,w,x,v,u),u,X_234,X_235) = inner_pasch(w,v,u,X_234,X_235) ),
introduced(tautology,[equality,[$cnf( $equal(inner_pasch(w,inner_pasch(v,w,x,v,u),u,X_234,X_235),inner_pasch(w,inner_pasch(v,w,x,v,u),u,X_234,X_235)) ),[1,1],$fot(v)]]) ).
cnf(refute_0_30,plain,
( inner_pasch(v,w,x,v,u) != v
| inner_pasch(w,inner_pasch(v,w,x,v,u),u,X_234,X_235) = inner_pasch(w,v,u,X_234,X_235) ),
inference(resolve,[$cnf( $equal(inner_pasch(w,inner_pasch(v,w,x,v,u),u,X_234,X_235),inner_pasch(w,inner_pasch(v,w,x,v,u),u,X_234,X_235)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
inner_pasch(w,inner_pasch(v,w,x,v,u),u,X_234,X_235) = inner_pasch(w,v,u,X_234,X_235),
inference(resolve,[$cnf( $equal(inner_pasch(v,w,x,v,u),v) )],[refute_0_27,refute_0_30]) ).
cnf(refute_0_32,plain,
( inner_pasch(w,inner_pasch(v,w,x,v,u),u,X_234,X_235) != inner_pasch(w,v,u,X_234,X_235)
| ~ between(X_234,inner_pasch(w,inner_pasch(v,w,x,v,u),u,X_234,X_235),w)
| between(X_234,inner_pasch(w,v,u,X_234,X_235),w) ),
introduced(tautology,[equality,[$cnf( between(X_234,inner_pasch(w,inner_pasch(v,w,x,v,u),u,X_234,X_235),w) ),[1],$fot(inner_pasch(w,v,u,X_234,X_235))]]) ).
cnf(refute_0_33,plain,
( ~ between(X_234,inner_pasch(w,inner_pasch(v,w,x,v,u),u,X_234,X_235),w)
| between(X_234,inner_pasch(w,v,u,X_234,X_235),w) ),
inference(resolve,[$cnf( $equal(inner_pasch(w,inner_pasch(v,w,x,v,u),u,X_234,X_235),inner_pasch(w,v,u,X_234,X_235)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
( ~ between(X_235,X_234,u)
| between(X_234,inner_pasch(w,v,u,X_234,X_235),w) ),
inference(resolve,[$cnf( between(X_234,inner_pasch(w,inner_pasch(v,w,x,v,u),u,X_234,X_235),w) )],[refute_0_19,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ between(X_2240,u,u)
| between(u,inner_pasch(w,v,u,u,X_2240),w) ),
inference(subst,[],[refute_0_34:[bind(X_234,$fot(u)),bind(X_235,$fot(X_2240))]]) ).
cnf(refute_0_36,plain,
between(u,inner_pasch(w,v,u,u,X_2240),w),
inference(resolve,[$cnf( between(X_2240,u,u) )],[refute_0_13,refute_0_35]) ).
cnf(refute_0_37,plain,
between(u,inner_pasch(w,v,u,u,v),w),
inference(subst,[],[refute_0_36:[bind(X_2240,$fot(v))]]) ).
cnf(refute_0_38,plain,
( ~ between(v,inner_pasch(w,v,u,u,v),v)
| v = inner_pasch(w,v,u,u,v) ),
inference(subst,[],[identity_for_betweeness:[bind(X,$fot(v)),bind(Y,$fot(inner_pasch(w,v,u,u,v)))]]) ).
cnf(refute_0_39,plain,
( inner_pasch(v,w,x,v,u) != v
| ~ between(w,inner_pasch(v,w,x,v,u),u)
| between(w,v,u) ),
introduced(tautology,[equality,[$cnf( between(w,inner_pasch(v,w,x,v,u),u) ),[1],$fot(v)]]) ).
cnf(refute_0_40,plain,
( ~ between(w,inner_pasch(v,w,x,v,u),u)
| between(w,v,u) ),
inference(resolve,[$cnf( $equal(inner_pasch(v,w,x,v,u),v) )],[refute_0_27,refute_0_39]) ).
cnf(refute_0_41,plain,
between(w,v,u),
inference(resolve,[$cnf( between(w,inner_pasch(v,w,x,v,u),u) )],[refute_0_17,refute_0_40]) ).
cnf(refute_0_42,plain,
between(X_108,X_106,X_106),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_108)),bind(Y,$fot(X_106))]]) ).
cnf(refute_0_43,plain,
( ~ between(X_104,X_105,X_106)
| ~ between(X_108,X_106,X_106)
| between(X_105,inner_pasch(X_104,X_105,X_106,X_106,X_108),X_108) ),
inference(subst,[],[inner_pasch1:[bind(U,$fot(X_104)),bind(V,$fot(X_105)),bind(W,$fot(X_106)),bind(X,$fot(X_106)),bind(Y,$fot(X_108))]]) ).
cnf(refute_0_44,plain,
( ~ between(X_104,X_105,X_106)
| between(X_105,inner_pasch(X_104,X_105,X_106,X_106,X_108),X_108) ),
inference(resolve,[$cnf( between(X_108,X_106,X_106) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
( ~ between(w,v,u)
| between(v,inner_pasch(w,v,u,u,X_3119),X_3119) ),
inference(subst,[],[refute_0_44:[bind(X_104,$fot(w)),bind(X_105,$fot(v)),bind(X_106,$fot(u)),bind(X_108,$fot(X_3119))]]) ).
cnf(refute_0_46,plain,
between(v,inner_pasch(w,v,u,u,X_3119),X_3119),
inference(resolve,[$cnf( between(w,v,u) )],[refute_0_41,refute_0_45]) ).
cnf(refute_0_47,plain,
between(v,inner_pasch(w,v,u,u,v),v),
inference(subst,[],[refute_0_46:[bind(X_3119,$fot(v))]]) ).
cnf(refute_0_48,plain,
v = inner_pasch(w,v,u,u,v),
inference(resolve,[$cnf( between(v,inner_pasch(w,v,u,u,v),v) )],[refute_0_47,refute_0_38]) ).
cnf(refute_0_49,plain,
( v != inner_pasch(w,v,u,u,v)
| inner_pasch(w,v,u,u,v) = v ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(v)),bind(Y0,$fot(inner_pasch(w,v,u,u,v)))]]) ).
cnf(refute_0_50,plain,
inner_pasch(w,v,u,u,v) = v,
inference(resolve,[$cnf( $equal(v,inner_pasch(w,v,u,u,v)) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
( inner_pasch(w,v,u,u,v) != v
| ~ between(u,inner_pasch(w,v,u,u,v),w)
| between(u,v,w) ),
introduced(tautology,[equality,[$cnf( between(u,inner_pasch(w,v,u,u,v),w) ),[1],$fot(v)]]) ).
cnf(refute_0_52,plain,
( ~ between(u,inner_pasch(w,v,u,u,v),w)
| between(u,v,w) ),
inference(resolve,[$cnf( $equal(inner_pasch(w,v,u,u,v),v) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
between(u,v,w),
inference(resolve,[$cnf( between(u,inner_pasch(w,v,u,u,v),w) )],[refute_0_37,refute_0_52]) ).
cnf(refute_0_54,plain,
$false,
inference(resolve,[$cnf( between(u,v,w) )],[refute_0_53,prove_v_between_u_and_w]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO042-2 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Fri Jun 17 19:55:22 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 259.33/259.58 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 259.33/259.58
% 259.33/259.58 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 259.33/259.58
%------------------------------------------------------------------------------