TSTP Solution File: GEO059-3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO059-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n032.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 05:23:58 EDT 2022
% Result : Unsatisfiable 20.21s 20.37s
% Output : CNFRefutation 20.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 18
% Syntax : Number of clauses : 64 ( 29 unt; 11 nHn; 37 RR)
% Number of literals : 112 ( 61 equ; 39 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 116 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(segment_construction2,axiom,
equidistant(Y,extension(X,Y,W,V),W,V) ).
cnf(reflection,axiom,
reflection(U,V) = extension(U,V,U,V) ).
cnf(d2,axiom,
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) ) ).
cnf(d3,axiom,
( ~ equidistant(U,V,W,X)
| equidistant(V,U,W,X) ) ).
cnf(d4_1,axiom,
( ~ equidistant(U,V,W,X)
| equidistant(U,V,X,W) ) ).
cnf(r2_2,axiom,
equidistant(V,reflection(U,V),U,V) ).
cnf(r3_2,axiom,
U = reflection(U,U) ).
cnf(d10_2,axiom,
( ~ equidistant(W,X,Y,Z)
| extension(U,V,W,X) = extension(U,V,Y,Z)
| U = V ) ).
cnf(prove_congruence,negated_conjecture,
~ equidistant(v,u,v,reflection(reflection(u,v),v)) ).
cnf(refute_0_0,plain,
( ~ equidistant(X_52,X_53,reflection(X_52,X_53),X_53)
| equidistant(X_53,X_52,reflection(X_52,X_53),X_53) ),
inference(subst,[],[d3:[bind(U,$fot(X_52)),bind(V,$fot(X_53)),bind(W,$fot(reflection(X_52,X_53))),bind(X,$fot(X_53))]]) ).
cnf(refute_0_1,plain,
( ~ equidistant(reflection(X_48,X_49),X_49,X_48,X_49)
| equidistant(X_48,X_49,reflection(X_48,X_49),X_49) ),
inference(subst,[],[d2:[bind(U,$fot(reflection(X_48,X_49))),bind(V,$fot(X_49)),bind(W,$fot(X_48)),bind(X,$fot(X_49))]]) ).
cnf(refute_0_2,plain,
equidistant(X_47,reflection(X_46,X_47),X_46,X_47),
inference(subst,[],[r2_2:[bind(U,$fot(X_46)),bind(V,$fot(X_47))]]) ).
cnf(refute_0_3,plain,
( ~ equidistant(X_47,reflection(X_46,X_47),X_46,X_47)
| equidistant(reflection(X_46,X_47),X_47,X_46,X_47) ),
inference(subst,[],[d3:[bind(U,$fot(X_47)),bind(V,$fot(reflection(X_46,X_47))),bind(W,$fot(X_46)),bind(X,$fot(X_47))]]) ).
cnf(refute_0_4,plain,
equidistant(reflection(X_46,X_47),X_47,X_46,X_47),
inference(resolve,[$cnf( equidistant(X_47,reflection(X_46,X_47),X_46,X_47) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
equidistant(reflection(X_48,X_49),X_49,X_48,X_49),
inference(subst,[],[refute_0_4:[bind(X_46,$fot(X_48)),bind(X_47,$fot(X_49))]]) ).
cnf(refute_0_6,plain,
equidistant(X_48,X_49,reflection(X_48,X_49),X_49),
inference(resolve,[$cnf( equidistant(reflection(X_48,X_49),X_49,X_48,X_49) )],[refute_0_5,refute_0_1]) ).
cnf(refute_0_7,plain,
equidistant(X_52,X_53,reflection(X_52,X_53),X_53),
inference(subst,[],[refute_0_6:[bind(X_48,$fot(X_52)),bind(X_49,$fot(X_53))]]) ).
cnf(refute_0_8,plain,
equidistant(X_53,X_52,reflection(X_52,X_53),X_53),
inference(resolve,[$cnf( equidistant(X_52,X_53,reflection(X_52,X_53),X_53) )],[refute_0_7,refute_0_0]) ).
cnf(refute_0_9,plain,
equidistant(v,u,reflection(u,v),v),
inference(subst,[],[refute_0_8:[bind(X_52,$fot(u)),bind(X_53,$fot(v))]]) ).
cnf(refute_0_10,plain,
( ~ equidistant(X_65,extension(X_64,X_65,X_66,X_67),X_67,X_66)
| equidistant(X_67,X_66,X_65,extension(X_64,X_65,X_66,X_67)) ),
inference(subst,[],[d2:[bind(U,$fot(X_65)),bind(V,$fot(extension(X_64,X_65,X_66,X_67))),bind(W,$fot(X_67)),bind(X,$fot(X_66))]]) ).
cnf(refute_0_11,plain,
equidistant(X_60,extension(X,X_60,X_62,X_63),X_62,X_63),
inference(subst,[],[segment_construction2:[bind(V,$fot(X_63)),bind(W,$fot(X_62)),bind(Y,$fot(X_60))]]) ).
cnf(refute_0_12,plain,
( ~ equidistant(X_60,extension(X,X_60,X_62,X_63),X_62,X_63)
| equidistant(X_60,extension(X,X_60,X_62,X_63),X_63,X_62) ),
inference(subst,[],[d4_1:[bind(U,$fot(X_60)),bind(V,$fot(extension(X,X_60,X_62,X_63))),bind(W,$fot(X_62)),bind(X,$fot(X_63))]]) ).
cnf(refute_0_13,plain,
equidistant(X_60,extension(X,X_60,X_62,X_63),X_63,X_62),
inference(resolve,[$cnf( equidistant(X_60,extension(X,X_60,X_62,X_63),X_62,X_63) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
equidistant(X_65,extension(X_64,X_65,X_66,X_67),X_67,X_66),
inference(subst,[],[refute_0_13:[bind(X,$fot(X_64)),bind(X_60,$fot(X_65)),bind(X_62,$fot(X_66)),bind(X_63,$fot(X_67))]]) ).
cnf(refute_0_15,plain,
equidistant(X_67,X_66,X_65,extension(X_64,X_65,X_66,X_67)),
inference(resolve,[$cnf( equidistant(X_65,extension(X_64,X_65,X_66,X_67),X_67,X_66) )],[refute_0_14,refute_0_10]) ).
cnf(refute_0_16,plain,
equidistant(X_67,X_66,X_67,extension(reflection(X_66,X_67),X_67,X_66,X_67)),
inference(subst,[],[refute_0_15:[bind(X_64,$fot(reflection(X_66,X_67))),bind(X_65,$fot(X_67))]]) ).
cnf(refute_0_17,plain,
reflection(reflection(X_497,V),V) = extension(reflection(X_497,V),V,reflection(X_497,V),V),
inference(subst,[],[reflection:[bind(U,$fot(reflection(X_497,V)))]]) ).
cnf(refute_0_18,plain,
equidistant(reflection(X_477,X_478),X_478,X_477,X_478),
inference(subst,[],[refute_0_4:[bind(X_46,$fot(X_477)),bind(X_47,$fot(X_478))]]) ).
cnf(refute_0_19,plain,
( ~ equidistant(reflection(X_477,X_478),X_478,X_477,X_478)
| X_473 = X_474
| extension(X_473,X_474,reflection(X_477,X_478),X_478) = extension(X_473,X_474,X_477,X_478) ),
inference(subst,[],[d10_2:[bind(U,$fot(X_473)),bind(V,$fot(X_474)),bind(W,$fot(reflection(X_477,X_478))),bind(X,$fot(X_478)),bind(Y,$fot(X_477)),bind(Z,$fot(X_478))]]) ).
cnf(refute_0_20,plain,
( X_473 = X_474
| extension(X_473,X_474,reflection(X_477,X_478),X_478) = extension(X_473,X_474,X_477,X_478) ),
inference(resolve,[$cnf( equidistant(reflection(X_477,X_478),X_478,X_477,X_478) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( extension(reflection(X_497,V),V,reflection(X_497,V),V) = extension(reflection(X_497,V),V,X_497,V)
| reflection(X_497,V) = V ),
inference(subst,[],[refute_0_20:[bind(X_473,$fot(reflection(X_497,V))),bind(X_474,$fot(V)),bind(X_477,$fot(X_497)),bind(X_478,$fot(V))]]) ).
cnf(refute_0_22,plain,
( extension(reflection(X_497,V),V,reflection(X_497,V),V) != extension(reflection(X_497,V),V,X_497,V)
| reflection(reflection(X_497,V),V) != extension(reflection(X_497,V),V,reflection(X_497,V),V)
| reflection(reflection(X_497,V),V) = extension(reflection(X_497,V),V,X_497,V) ),
introduced(tautology,[equality,[$cnf( $equal(reflection(reflection(X_497,V),V),extension(reflection(X_497,V),V,reflection(X_497,V),V)) ),[1],$fot(extension(reflection(X_497,V),V,X_497,V))]]) ).
cnf(refute_0_23,plain,
( reflection(reflection(X_497,V),V) != extension(reflection(X_497,V),V,reflection(X_497,V),V)
| reflection(X_497,V) = V
| reflection(reflection(X_497,V),V) = extension(reflection(X_497,V),V,X_497,V) ),
inference(resolve,[$cnf( $equal(extension(reflection(X_497,V),V,reflection(X_497,V),V),extension(reflection(X_497,V),V,X_497,V)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( reflection(X_497,V) = V
| reflection(reflection(X_497,V),V) = extension(reflection(X_497,V),V,X_497,V) ),
inference(resolve,[$cnf( $equal(reflection(reflection(X_497,V),V),extension(reflection(X_497,V),V,reflection(X_497,V),V)) )],[refute_0_17,refute_0_23]) ).
cnf(refute_0_25,plain,
( reflection(X_66,X_67) = X_67
| reflection(reflection(X_66,X_67),X_67) = extension(reflection(X_66,X_67),X_67,X_66,X_67) ),
inference(subst,[],[refute_0_24:[bind(V,$fot(X_67)),bind(X_497,$fot(X_66))]]) ).
cnf(refute_0_26,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_27,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_28,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( reflection(reflection(X_66,X_67),X_67) != extension(reflection(X_66,X_67),X_67,X_66,X_67)
| extension(reflection(X_66,X_67),X_67,X_66,X_67) = reflection(reflection(X_66,X_67),X_67) ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(reflection(reflection(X_66,X_67),X_67))),bind(Y0,$fot(extension(reflection(X_66,X_67),X_67,X_66,X_67)))]]) ).
cnf(refute_0_30,plain,
( extension(reflection(X_66,X_67),X_67,X_66,X_67) = reflection(reflection(X_66,X_67),X_67)
| reflection(X_66,X_67) = X_67 ),
inference(resolve,[$cnf( $equal(reflection(reflection(X_66,X_67),X_67),extension(reflection(X_66,X_67),X_67,X_66,X_67)) )],[refute_0_25,refute_0_29]) ).
cnf(refute_0_31,plain,
( extension(reflection(X_66,X_67),X_67,X_66,X_67) != reflection(reflection(X_66,X_67),X_67)
| ~ equidistant(X_67,X_66,X_67,extension(reflection(X_66,X_67),X_67,X_66,X_67))
| equidistant(X_67,X_66,X_67,reflection(reflection(X_66,X_67),X_67)) ),
introduced(tautology,[equality,[$cnf( equidistant(X_67,X_66,X_67,extension(reflection(X_66,X_67),X_67,X_66,X_67)) ),[3],$fot(reflection(reflection(X_66,X_67),X_67))]]) ).
cnf(refute_0_32,plain,
( ~ equidistant(X_67,X_66,X_67,extension(reflection(X_66,X_67),X_67,X_66,X_67))
| reflection(X_66,X_67) = X_67
| equidistant(X_67,X_66,X_67,reflection(reflection(X_66,X_67),X_67)) ),
inference(resolve,[$cnf( $equal(extension(reflection(X_66,X_67),X_67,X_66,X_67),reflection(reflection(X_66,X_67),X_67)) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( reflection(X_66,X_67) = X_67
| equidistant(X_67,X_66,X_67,reflection(reflection(X_66,X_67),X_67)) ),
inference(resolve,[$cnf( equidistant(X_67,X_66,X_67,extension(reflection(X_66,X_67),X_67,X_66,X_67)) )],[refute_0_16,refute_0_32]) ).
cnf(refute_0_34,plain,
( reflection(u,v) = v
| equidistant(v,u,v,reflection(reflection(u,v),v)) ),
inference(subst,[],[refute_0_33:[bind(X_66,$fot(u)),bind(X_67,$fot(v))]]) ).
cnf(refute_0_35,plain,
reflection(u,v) = v,
inference(resolve,[$cnf( equidistant(v,u,v,reflection(reflection(u,v),v)) )],[refute_0_34,prove_congruence]) ).
cnf(refute_0_36,plain,
( reflection(u,v) != v
| ~ equidistant(v,u,reflection(u,v),v)
| equidistant(v,u,v,v) ),
introduced(tautology,[equality,[$cnf( equidistant(v,u,reflection(u,v),v) ),[2],$fot(v)]]) ).
cnf(refute_0_37,plain,
( ~ equidistant(v,u,reflection(u,v),v)
| equidistant(v,u,v,v) ),
inference(resolve,[$cnf( $equal(reflection(u,v),v) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
equidistant(v,u,v,v),
inference(resolve,[$cnf( equidistant(v,u,reflection(u,v),v) )],[refute_0_9,refute_0_37]) ).
cnf(refute_0_39,plain,
( U != reflection(U,U)
| reflection(U,U) = U ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(U)),bind(Y0,$fot(reflection(U,U)))]]) ).
cnf(refute_0_40,plain,
reflection(U,U) = U,
inference(resolve,[$cnf( $equal(U,reflection(U,U)) )],[r3_2,refute_0_39]) ).
cnf(refute_0_41,plain,
reflection(v,v) = v,
inference(subst,[],[refute_0_40:[bind(U,$fot(v))]]) ).
cnf(refute_0_42,plain,
reflection(reflection(u,v),v) = reflection(reflection(u,v),v),
introduced(tautology,[refl,[$fot(reflection(reflection(u,v),v))]]) ).
cnf(refute_0_43,plain,
( reflection(reflection(u,v),v) != reflection(reflection(u,v),v)
| reflection(u,v) != v
| reflection(reflection(u,v),v) = reflection(v,v) ),
introduced(tautology,[equality,[$cnf( $equal(reflection(reflection(u,v),v),reflection(reflection(u,v),v)) ),[1,0],$fot(v)]]) ).
cnf(refute_0_44,plain,
( reflection(u,v) != v
| reflection(reflection(u,v),v) = reflection(v,v) ),
inference(resolve,[$cnf( $equal(reflection(reflection(u,v),v),reflection(reflection(u,v),v)) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
reflection(reflection(u,v),v) = reflection(v,v),
inference(resolve,[$cnf( $equal(reflection(u,v),v) )],[refute_0_35,refute_0_44]) ).
cnf(refute_0_46,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_47,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_28,refute_0_46]) ).
cnf(refute_0_48,plain,
( reflection(reflection(u,v),v) != reflection(v,v)
| reflection(v,v) != v
| reflection(reflection(u,v),v) = v ),
inference(subst,[],[refute_0_47:[bind(X0,$fot(reflection(reflection(u,v),v))),bind(Y0,$fot(reflection(v,v))),bind(Z0,$fot(v))]]) ).
cnf(refute_0_49,plain,
( reflection(v,v) != v
| reflection(reflection(u,v),v) = v ),
inference(resolve,[$cnf( $equal(reflection(reflection(u,v),v),reflection(v,v)) )],[refute_0_45,refute_0_48]) ).
cnf(refute_0_50,plain,
reflection(reflection(u,v),v) = v,
inference(resolve,[$cnf( $equal(reflection(v,v),v) )],[refute_0_41,refute_0_49]) ).
cnf(refute_0_51,plain,
( reflection(reflection(u,v),v) != v
| ~ equidistant(v,u,v,v)
| equidistant(v,u,v,reflection(reflection(u,v),v)) ),
introduced(tautology,[equality,[$cnf( ~ equidistant(v,u,v,reflection(reflection(u,v),v)) ),[3],$fot(v)]]) ).
cnf(refute_0_52,plain,
( ~ equidistant(v,u,v,v)
| equidistant(v,u,v,reflection(reflection(u,v),v)) ),
inference(resolve,[$cnf( $equal(reflection(reflection(u,v),v),v) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
~ equidistant(v,u,v,v),
inference(resolve,[$cnf( equidistant(v,u,v,reflection(reflection(u,v),v)) )],[refute_0_52,prove_congruence]) ).
cnf(refute_0_54,plain,
$false,
inference(resolve,[$cnf( equidistant(v,u,v,v) )],[refute_0_38,refute_0_53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : GEO059-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.11 % Command : metis --show proof --show saturation %s
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 600
% 0.10/0.30 % DateTime : Sat Jun 18 14:13:47 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.10/0.30 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 20.21/20.37 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.21/20.37
% 20.21/20.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 20.21/20.37
%------------------------------------------------------------------------------