TSTP Solution File: GEO043-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO043-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 05:23:49 EDT 2022
% Result : Unsatisfiable 8.95s 9.14s
% Output : CNFRefutation 8.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 17
% Syntax : Number of clauses : 116 ( 56 unt; 0 nHn; 82 RR)
% Number of literals : 195 ( 51 equ; 80 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 : 133 ( 29 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_w,hypothesis,
between(u,v,w) ).
cnf(w_between_u_and_x,hypothesis,
between(u,w,x) ).
cnf(prove_w_between_v_and_x,negated_conjecture,
~ between(v,w,x) ).
cnf(refute_0_0,plain,
( ~ between(U,V,u)
| ~ between(x,inner_pasch(X_121,x,x,w,u),u)
| between(V,inner_pasch(U,V,u,inner_pasch(X_121,x,x,w,u),x),x) ),
inference(subst,[],[inner_pasch1:[bind(W,$fot(u)),bind(X,$fot(inner_pasch(X_121,x,x,w,u))),bind(Y,$fot(x))]]) ).
cnf(refute_0_1,plain,
between(X,Y,extension(X,Y,V,V)),
inference(subst,[],[segment_construction1:[bind(W,$fot(V))]]) ).
cnf(refute_0_2,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,$fot(X_12))]]) ).
cnf(refute_0_3,plain,
( ~ equidistant(X_12,extension(X,X_12,X_14,X_14),X_14,X_14)
| X_12 = extension(X,X_12,X_14,X_14) ),
inference(subst,[],[identity_for_equidistance:[bind(X,$fot(X_12)),bind(Y,$fot(extension(X,X_12,X_14,X_14))),bind(Z,$fot(X_14))]]) ).
cnf(refute_0_4,plain,
X_12 = extension(X,X_12,X_14,X_14),
inference(resolve,[$cnf( equidistant(X_12,extension(X,X_12,X_14,X_14),X_14,X_14) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
Y = extension(X,Y,V,V),
inference(subst,[],[refute_0_4:[bind(X_12,$fot(Y)),bind(X_14,$fot(V))]]) ).
cnf(refute_0_6,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_7,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_8,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( Y != extension(X,Y,V,V)
| extension(X,Y,V,V) = Y ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(Y)),bind(Y0,$fot(extension(X,Y,V,V)))]]) ).
cnf(refute_0_10,plain,
extension(X,Y,V,V) = Y,
inference(resolve,[$cnf( $equal(Y,extension(X,Y,V,V)) )],[refute_0_5,refute_0_9]) ).
cnf(refute_0_11,plain,
( extension(X,Y,V,V) != Y
| ~ between(X,Y,extension(X,Y,V,V))
| between(X,Y,Y) ),
introduced(tautology,[equality,[$cnf( between(X,Y,extension(X,Y,V,V)) ),[2],$fot(Y)]]) ).
cnf(refute_0_12,plain,
( ~ between(X,Y,extension(X,Y,V,V))
| between(X,Y,Y) ),
inference(resolve,[$cnf( $equal(extension(X,Y,V,V),Y) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
between(X,Y,Y),
inference(resolve,[$cnf( between(X,Y,extension(X,Y,V,V)) )],[refute_0_1,refute_0_12]) ).
cnf(refute_0_14,plain,
between(X_119,x,x),
inference(subst,[],[refute_0_13:[bind(X,$fot(X_119)),bind(Y,$fot(x))]]) ).
cnf(refute_0_15,plain,
( ~ between(X_98,X_99,x)
| ~ between(u,w,x)
| between(X_99,inner_pasch(X_98,X_99,x,w,u),u) ),
inference(subst,[],[inner_pasch1:[bind(U,$fot(X_98)),bind(V,$fot(X_99)),bind(W,$fot(x)),bind(X,$fot(w)),bind(Y,$fot(u))]]) ).
cnf(refute_0_16,plain,
( ~ between(X_98,X_99,x)
| between(X_99,inner_pasch(X_98,X_99,x,w,u),u) ),
inference(resolve,[$cnf( between(u,w,x) )],[w_between_u_and_x,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ between(X_119,x,x)
| between(x,inner_pasch(X_119,x,x,w,u),u) ),
inference(subst,[],[refute_0_16:[bind(X_98,$fot(X_119)),bind(X_99,$fot(x))]]) ).
cnf(refute_0_18,plain,
between(x,inner_pasch(X_119,x,x,w,u),u),
inference(resolve,[$cnf( between(X_119,x,x) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
between(x,inner_pasch(X_121,x,x,w,u),u),
inference(subst,[],[refute_0_18:[bind(X_119,$fot(X_121))]]) ).
cnf(refute_0_20,plain,
( ~ between(U,V,u)
| between(V,inner_pasch(U,V,u,inner_pasch(X_121,x,x,w,u),x),x) ),
inference(resolve,[$cnf( between(x,inner_pasch(X_121,x,x,w,u),u) )],[refute_0_19,refute_0_0]) ).
cnf(refute_0_21,plain,
( ~ between(w,v,u)
| between(v,inner_pasch(w,v,u,inner_pasch(X_121,x,x,w,u),x),x) ),
inference(subst,[],[refute_0_20:[bind(U,$fot(w)),bind(V,$fot(v))]]) ).
cnf(refute_0_22,plain,
between(X_307,w,w),
inference(subst,[],[refute_0_13:[bind(X,$fot(X_307)),bind(Y,$fot(w))]]) ).
cnf(refute_0_23,plain,
( ~ between(X_224,X_223,w)
| ~ between(u,v,w)
| between(X_223,inner_pasch(u,v,w,X_223,X_224),u) ),
inference(subst,[],[inner_pasch2:[bind(U,$fot(u)),bind(V,$fot(v)),bind(W,$fot(w)),bind(X,$fot(X_223)),bind(Y,$fot(X_224))]]) ).
cnf(refute_0_24,plain,
( ~ between(X_224,X_223,w)
| between(X_223,inner_pasch(u,v,w,X_223,X_224),u) ),
inference(resolve,[$cnf( between(u,v,w) )],[v_between_u_and_w,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ between(X_307,w,w)
| between(w,inner_pasch(u,v,w,w,X_307),u) ),
inference(subst,[],[refute_0_24:[bind(X_223,$fot(w)),bind(X_224,$fot(X_307))]]) ).
cnf(refute_0_26,plain,
between(w,inner_pasch(u,v,w,w,X_307),u),
inference(resolve,[$cnf( between(X_307,w,w) )],[refute_0_22,refute_0_25]) ).
cnf(refute_0_27,plain,
between(w,inner_pasch(u,v,w,w,v),u),
inference(subst,[],[refute_0_26:[bind(X_307,$fot(v))]]) ).
cnf(refute_0_28,plain,
( ~ between(v,inner_pasch(u,v,w,w,v),v)
| v = inner_pasch(u,v,w,w,v) ),
inference(subst,[],[identity_for_betweeness:[bind(X,$fot(v)),bind(Y,$fot(inner_pasch(u,v,w,w,v)))]]) ).
cnf(refute_0_29,plain,
between(X_128,w,w),
inference(subst,[],[refute_0_13:[bind(X,$fot(X_128)),bind(Y,$fot(w))]]) ).
cnf(refute_0_30,plain,
( ~ between(X_102,X_101,w)
| ~ between(u,v,w)
| between(v,inner_pasch(u,v,w,X_101,X_102),X_102) ),
inference(subst,[],[inner_pasch1:[bind(U,$fot(u)),bind(V,$fot(v)),bind(W,$fot(w)),bind(X,$fot(X_101)),bind(Y,$fot(X_102))]]) ).
cnf(refute_0_31,plain,
( ~ between(X_102,X_101,w)
| between(v,inner_pasch(u,v,w,X_101,X_102),X_102) ),
inference(resolve,[$cnf( between(u,v,w) )],[v_between_u_and_w,refute_0_30]) ).
cnf(refute_0_32,plain,
( ~ between(X_128,w,w)
| between(v,inner_pasch(u,v,w,w,X_128),X_128) ),
inference(subst,[],[refute_0_31:[bind(X_101,$fot(w)),bind(X_102,$fot(X_128))]]) ).
cnf(refute_0_33,plain,
between(v,inner_pasch(u,v,w,w,X_128),X_128),
inference(resolve,[$cnf( between(X_128,w,w) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
between(v,inner_pasch(u,v,w,w,v),v),
inference(subst,[],[refute_0_33:[bind(X_128,$fot(v))]]) ).
cnf(refute_0_35,plain,
v = inner_pasch(u,v,w,w,v),
inference(resolve,[$cnf( between(v,inner_pasch(u,v,w,w,v),v) )],[refute_0_34,refute_0_28]) ).
cnf(refute_0_36,plain,
( v != inner_pasch(u,v,w,w,v)
| inner_pasch(u,v,w,w,v) = v ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(v)),bind(Y0,$fot(inner_pasch(u,v,w,w,v)))]]) ).
cnf(refute_0_37,plain,
inner_pasch(u,v,w,w,v) = v,
inference(resolve,[$cnf( $equal(v,inner_pasch(u,v,w,w,v)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( inner_pasch(u,v,w,w,v) != v
| ~ between(w,inner_pasch(u,v,w,w,v),u)
| between(w,v,u) ),
introduced(tautology,[equality,[$cnf( between(w,inner_pasch(u,v,w,w,v),u) ),[1],$fot(v)]]) ).
cnf(refute_0_39,plain,
( ~ between(w,inner_pasch(u,v,w,w,v),u)
| between(w,v,u) ),
inference(resolve,[$cnf( $equal(inner_pasch(u,v,w,w,v),v) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
between(w,v,u),
inference(resolve,[$cnf( between(w,inner_pasch(u,v,w,w,v),u) )],[refute_0_27,refute_0_39]) ).
cnf(refute_0_41,plain,
between(v,inner_pasch(w,v,u,inner_pasch(X_121,x,x,w,u),x),x),
inference(resolve,[$cnf( between(w,v,u) )],[refute_0_40,refute_0_21]) ).
cnf(refute_0_42,plain,
between(v,inner_pasch(w,v,u,inner_pasch(w,x,x,w,u),x),x),
inference(subst,[],[refute_0_41:[bind(X_121,$fot(w))]]) ).
cnf(refute_0_43,plain,
( ~ between(w,inner_pasch(w,x,x,w,u),w)
| w = inner_pasch(w,x,x,w,u) ),
inference(subst,[],[identity_for_betweeness:[bind(X,$fot(w)),bind(Y,$fot(inner_pasch(w,x,x,w,u)))]]) ).
cnf(refute_0_44,plain,
between(X_388,x,x),
inference(subst,[],[refute_0_13:[bind(X,$fot(X_388)),bind(Y,$fot(x))]]) ).
cnf(refute_0_45,plain,
( ~ between(X_220,X_221,x)
| ~ between(u,w,x)
| between(w,inner_pasch(X_220,X_221,x,w,u),X_220) ),
inference(subst,[],[inner_pasch2:[bind(U,$fot(X_220)),bind(V,$fot(X_221)),bind(W,$fot(x)),bind(X,$fot(w)),bind(Y,$fot(u))]]) ).
cnf(refute_0_46,plain,
( ~ between(X_220,X_221,x)
| between(w,inner_pasch(X_220,X_221,x,w,u),X_220) ),
inference(resolve,[$cnf( between(u,w,x) )],[w_between_u_and_x,refute_0_45]) ).
cnf(refute_0_47,plain,
( ~ between(X_388,x,x)
| between(w,inner_pasch(X_388,x,x,w,u),X_388) ),
inference(subst,[],[refute_0_46:[bind(X_220,$fot(X_388)),bind(X_221,$fot(x))]]) ).
cnf(refute_0_48,plain,
between(w,inner_pasch(X_388,x,x,w,u),X_388),
inference(resolve,[$cnf( between(X_388,x,x) )],[refute_0_44,refute_0_47]) ).
cnf(refute_0_49,plain,
between(w,inner_pasch(w,x,x,w,u),w),
inference(subst,[],[refute_0_48:[bind(X_388,$fot(w))]]) ).
cnf(refute_0_50,plain,
w = inner_pasch(w,x,x,w,u),
inference(resolve,[$cnf( between(w,inner_pasch(w,x,x,w,u),w) )],[refute_0_49,refute_0_43]) ).
cnf(refute_0_51,plain,
( w != inner_pasch(w,x,x,w,u)
| inner_pasch(w,x,x,w,u) = w ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(w)),bind(Y0,$fot(inner_pasch(w,x,x,w,u)))]]) ).
cnf(refute_0_52,plain,
inner_pasch(w,x,x,w,u) = w,
inference(resolve,[$cnf( $equal(w,inner_pasch(w,x,x,w,u)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
( inner_pasch(w,x,x,w,u) != w
| ~ between(v,inner_pasch(w,v,u,inner_pasch(w,x,x,w,u),x),x)
| between(v,inner_pasch(w,v,u,w,x),x) ),
introduced(tautology,[equality,[$cnf( between(v,inner_pasch(w,v,u,inner_pasch(w,x,x,w,u),x),x) ),[1,3],$fot(w)]]) ).
cnf(refute_0_54,plain,
( ~ between(v,inner_pasch(w,v,u,inner_pasch(w,x,x,w,u),x),x)
| between(v,inner_pasch(w,v,u,w,x),x) ),
inference(resolve,[$cnf( $equal(inner_pasch(w,x,x,w,u),w) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
between(v,inner_pasch(w,v,u,w,x),x),
inference(resolve,[$cnf( between(v,inner_pasch(w,v,u,inner_pasch(w,x,x,w,u),x),x) )],[refute_0_42,refute_0_54]) ).
cnf(refute_0_56,plain,
( ~ between(w,inner_pasch(w,inner_pasch(X_266,w,w,v,u),u,w,x),w)
| w = inner_pasch(w,inner_pasch(X_266,w,w,v,u),u,w,x) ),
inference(subst,[],[identity_for_betweeness:[bind(X,$fot(w)),bind(Y,$fot(inner_pasch(w,inner_pasch(X_266,w,w,v,u),u,w,x)))]]) ).
cnf(refute_0_57,plain,
between(X_226,x,x),
inference(subst,[],[refute_0_13:[bind(X,$fot(X_226)),bind(Y,$fot(x))]]) ).
cnf(refute_0_58,plain,
( ~ between(X_224,X_223,x)
| ~ between(u,w,x)
| between(X_223,inner_pasch(u,w,x,X_223,X_224),u) ),
inference(subst,[],[inner_pasch2:[bind(U,$fot(u)),bind(V,$fot(w)),bind(W,$fot(x)),bind(X,$fot(X_223)),bind(Y,$fot(X_224))]]) ).
cnf(refute_0_59,plain,
( ~ between(X_224,X_223,x)
| between(X_223,inner_pasch(u,w,x,X_223,X_224),u) ),
inference(resolve,[$cnf( between(u,w,x) )],[w_between_u_and_x,refute_0_58]) ).
cnf(refute_0_60,plain,
( ~ between(X_226,x,x)
| between(x,inner_pasch(u,w,x,x,X_226),u) ),
inference(subst,[],[refute_0_59:[bind(X_223,$fot(x)),bind(X_224,$fot(X_226))]]) ).
cnf(refute_0_61,plain,
between(x,inner_pasch(u,w,x,x,X_226),u),
inference(resolve,[$cnf( between(X_226,x,x) )],[refute_0_57,refute_0_60]) ).
cnf(refute_0_62,plain,
between(x,inner_pasch(u,w,x,x,w),u),
inference(subst,[],[refute_0_61:[bind(X_226,$fot(w))]]) ).
cnf(refute_0_63,plain,
( ~ between(w,inner_pasch(u,w,x,x,w),w)
| w = inner_pasch(u,w,x,x,w) ),
inference(subst,[],[identity_for_betweeness:[bind(X,$fot(w)),bind(Y,$fot(inner_pasch(u,w,x,x,w)))]]) ).
cnf(refute_0_64,plain,
between(X_104,x,x),
inference(subst,[],[refute_0_13:[bind(X,$fot(X_104)),bind(Y,$fot(x))]]) ).
cnf(refute_0_65,plain,
( ~ between(X_102,X_101,x)
| ~ between(u,w,x)
| between(w,inner_pasch(u,w,x,X_101,X_102),X_102) ),
inference(subst,[],[inner_pasch1:[bind(U,$fot(u)),bind(V,$fot(w)),bind(W,$fot(x)),bind(X,$fot(X_101)),bind(Y,$fot(X_102))]]) ).
cnf(refute_0_66,plain,
( ~ between(X_102,X_101,x)
| between(w,inner_pasch(u,w,x,X_101,X_102),X_102) ),
inference(resolve,[$cnf( between(u,w,x) )],[w_between_u_and_x,refute_0_65]) ).
cnf(refute_0_67,plain,
( ~ between(X_104,x,x)
| between(w,inner_pasch(u,w,x,x,X_104),X_104) ),
inference(subst,[],[refute_0_66:[bind(X_101,$fot(x)),bind(X_102,$fot(X_104))]]) ).
cnf(refute_0_68,plain,
between(w,inner_pasch(u,w,x,x,X_104),X_104),
inference(resolve,[$cnf( between(X_104,x,x) )],[refute_0_64,refute_0_67]) ).
cnf(refute_0_69,plain,
between(w,inner_pasch(u,w,x,x,w),w),
inference(subst,[],[refute_0_68:[bind(X_104,$fot(w))]]) ).
cnf(refute_0_70,plain,
w = inner_pasch(u,w,x,x,w),
inference(resolve,[$cnf( between(w,inner_pasch(u,w,x,x,w),w) )],[refute_0_69,refute_0_63]) ).
cnf(refute_0_71,plain,
( w != inner_pasch(u,w,x,x,w)
| inner_pasch(u,w,x,x,w) = w ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(w)),bind(Y0,$fot(inner_pasch(u,w,x,x,w)))]]) ).
cnf(refute_0_72,plain,
inner_pasch(u,w,x,x,w) = w,
inference(resolve,[$cnf( $equal(w,inner_pasch(u,w,x,x,w)) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
( inner_pasch(u,w,x,x,w) != w
| ~ between(x,inner_pasch(u,w,x,x,w),u)
| between(x,w,u) ),
introduced(tautology,[equality,[$cnf( between(x,inner_pasch(u,w,x,x,w),u) ),[1],$fot(w)]]) ).
cnf(refute_0_74,plain,
( ~ between(x,inner_pasch(u,w,x,x,w),u)
| between(x,w,u) ),
inference(resolve,[$cnf( $equal(inner_pasch(u,w,x,x,w),w) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
between(x,w,u),
inference(resolve,[$cnf( between(x,inner_pasch(u,w,x,x,w),u) )],[refute_0_62,refute_0_74]) ).
cnf(refute_0_76,plain,
between(X_142,w,w),
inference(subst,[],[refute_0_13:[bind(X,$fot(X_142)),bind(Y,$fot(w))]]) ).
cnf(refute_0_77,plain,
( ~ between(X_98,X_99,w)
| ~ between(u,v,w)
| between(X_99,inner_pasch(X_98,X_99,w,v,u),u) ),
inference(subst,[],[inner_pasch1:[bind(U,$fot(X_98)),bind(V,$fot(X_99)),bind(W,$fot(w)),bind(X,$fot(v)),bind(Y,$fot(u))]]) ).
cnf(refute_0_78,plain,
( ~ between(X_98,X_99,w)
| between(X_99,inner_pasch(X_98,X_99,w,v,u),u) ),
inference(resolve,[$cnf( between(u,v,w) )],[v_between_u_and_w,refute_0_77]) ).
cnf(refute_0_79,plain,
( ~ between(X_142,w,w)
| between(w,inner_pasch(X_142,w,w,v,u),u) ),
inference(subst,[],[refute_0_78:[bind(X_98,$fot(X_142)),bind(X_99,$fot(w))]]) ).
cnf(refute_0_80,plain,
between(w,inner_pasch(X_142,w,w,v,u),u),
inference(resolve,[$cnf( between(X_142,w,w) )],[refute_0_76,refute_0_79]) ).
cnf(refute_0_81,plain,
( ~ between(X_224,X_223,u)
| ~ between(w,inner_pasch(X_142,w,w,v,u),u)
| between(X_223,inner_pasch(w,inner_pasch(X_142,w,w,v,u),u,X_223,X_224),w) ),
inference(subst,[],[inner_pasch2:[bind(U,$fot(w)),bind(V,$fot(inner_pasch(X_142,w,w,v,u))),bind(W,$fot(u)),bind(X,$fot(X_223)),bind(Y,$fot(X_224))]]) ).
cnf(refute_0_82,plain,
( ~ between(X_224,X_223,u)
| between(X_223,inner_pasch(w,inner_pasch(X_142,w,w,v,u),u,X_223,X_224),w) ),
inference(resolve,[$cnf( between(w,inner_pasch(X_142,w,w,v,u),u) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
( ~ between(x,w,u)
| between(w,inner_pasch(w,inner_pasch(X_263,w,w,v,u),u,w,x),w) ),
inference(subst,[],[refute_0_82:[bind(X_142,$fot(X_263)),bind(X_223,$fot(w)),bind(X_224,$fot(x))]]) ).
cnf(refute_0_84,plain,
between(w,inner_pasch(w,inner_pasch(X_263,w,w,v,u),u,w,x),w),
inference(resolve,[$cnf( between(x,w,u) )],[refute_0_75,refute_0_83]) ).
cnf(refute_0_85,plain,
between(w,inner_pasch(w,inner_pasch(X_266,w,w,v,u),u,w,x),w),
inference(subst,[],[refute_0_84:[bind(X_263,$fot(X_266))]]) ).
cnf(refute_0_86,plain,
w = inner_pasch(w,inner_pasch(X_266,w,w,v,u),u,w,x),
inference(resolve,[$cnf( between(w,inner_pasch(w,inner_pasch(X_266,w,w,v,u),u,w,x),w) )],[refute_0_85,refute_0_56]) ).
cnf(refute_0_87,plain,
w = inner_pasch(w,inner_pasch(v,w,w,v,u),u,w,x),
inference(subst,[],[refute_0_86:[bind(X_266,$fot(v))]]) ).
cnf(refute_0_88,plain,
( ~ between(v,inner_pasch(v,w,w,v,u),v)
| v = inner_pasch(v,w,w,v,u) ),
inference(subst,[],[identity_for_betweeness:[bind(X,$fot(v)),bind(Y,$fot(inner_pasch(v,w,w,v,u)))]]) ).
cnf(refute_0_89,plain,
between(X_349,w,w),
inference(subst,[],[refute_0_13:[bind(X,$fot(X_349)),bind(Y,$fot(w))]]) ).
cnf(refute_0_90,plain,
( ~ between(X_220,X_221,w)
| ~ between(u,v,w)
| between(v,inner_pasch(X_220,X_221,w,v,u),X_220) ),
inference(subst,[],[inner_pasch2:[bind(U,$fot(X_220)),bind(V,$fot(X_221)),bind(W,$fot(w)),bind(X,$fot(v)),bind(Y,$fot(u))]]) ).
cnf(refute_0_91,plain,
( ~ between(X_220,X_221,w)
| between(v,inner_pasch(X_220,X_221,w,v,u),X_220) ),
inference(resolve,[$cnf( between(u,v,w) )],[v_between_u_and_w,refute_0_90]) ).
cnf(refute_0_92,plain,
( ~ between(X_349,w,w)
| between(v,inner_pasch(X_349,w,w,v,u),X_349) ),
inference(subst,[],[refute_0_91:[bind(X_220,$fot(X_349)),bind(X_221,$fot(w))]]) ).
cnf(refute_0_93,plain,
between(v,inner_pasch(X_349,w,w,v,u),X_349),
inference(resolve,[$cnf( between(X_349,w,w) )],[refute_0_89,refute_0_92]) ).
cnf(refute_0_94,plain,
between(v,inner_pasch(v,w,w,v,u),v),
inference(subst,[],[refute_0_93:[bind(X_349,$fot(v))]]) ).
cnf(refute_0_95,plain,
v = inner_pasch(v,w,w,v,u),
inference(resolve,[$cnf( between(v,inner_pasch(v,w,w,v,u),v) )],[refute_0_94,refute_0_88]) ).
cnf(refute_0_96,plain,
( v != inner_pasch(v,w,w,v,u)
| inner_pasch(v,w,w,v,u) = v ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(v)),bind(Y0,$fot(inner_pasch(v,w,w,v,u)))]]) ).
cnf(refute_0_97,plain,
inner_pasch(v,w,w,v,u) = v,
inference(resolve,[$cnf( $equal(v,inner_pasch(v,w,w,v,u)) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
( inner_pasch(v,w,w,v,u) != v
| w != inner_pasch(w,inner_pasch(v,w,w,v,u),u,w,x)
| w = inner_pasch(w,v,u,w,x) ),
introduced(tautology,[equality,[$cnf( $equal(w,inner_pasch(w,inner_pasch(v,w,w,v,u),u,w,x)) ),[1,1],$fot(v)]]) ).
cnf(refute_0_99,plain,
( w != inner_pasch(w,inner_pasch(v,w,w,v,u),u,w,x)
| w = inner_pasch(w,v,u,w,x) ),
inference(resolve,[$cnf( $equal(inner_pasch(v,w,w,v,u),v) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
w = inner_pasch(w,v,u,w,x),
inference(resolve,[$cnf( $equal(w,inner_pasch(w,inner_pasch(v,w,w,v,u),u,w,x)) )],[refute_0_87,refute_0_99]) ).
cnf(refute_0_101,plain,
( w != inner_pasch(w,v,u,w,x)
| inner_pasch(w,v,u,w,x) = w ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(w)),bind(Y0,$fot(inner_pasch(w,v,u,w,x)))]]) ).
cnf(refute_0_102,plain,
inner_pasch(w,v,u,w,x) = w,
inference(resolve,[$cnf( $equal(w,inner_pasch(w,v,u,w,x)) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
( inner_pasch(w,v,u,w,x) != w
| ~ between(v,inner_pasch(w,v,u,w,x),x)
| between(v,w,x) ),
introduced(tautology,[equality,[$cnf( between(v,inner_pasch(w,v,u,w,x),x) ),[1],$fot(w)]]) ).
cnf(refute_0_104,plain,
( ~ between(v,inner_pasch(w,v,u,w,x),x)
| between(v,w,x) ),
inference(resolve,[$cnf( $equal(inner_pasch(w,v,u,w,x),w) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
between(v,w,x),
inference(resolve,[$cnf( between(v,inner_pasch(w,v,u,w,x),x) )],[refute_0_55,refute_0_104]) ).
cnf(refute_0_106,plain,
$false,
inference(resolve,[$cnf( between(v,w,x) )],[refute_0_105,prove_w_between_v_and_x]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO043-2 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jun 18 16:15:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 8.95/9.14 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.95/9.14
% 8.95/9.14 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.95/9.15
%------------------------------------------------------------------------------