TSTP Solution File: GEO180+2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO180+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 05:24:58 EDT 2022
% Result : Theorem 4.99s 5.19s
% Output : CNFRefutation 4.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 7
% Syntax : Number of formulae : 98 ( 18 unt; 0 def)
% Number of atoms : 283 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 258 ( 73 ~; 164 |; 11 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 165 ( 0 sgn 69 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X] : ~ distinct_points(X,X) ).
fof(apart4,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( distinct_points(X,Z)
| distinct_points(Y,Z) ) ) ).
fof(con1,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( apart_point_and_line(Z,line_connecting(X,Y))
=> ( distinct_points(Z,X)
& distinct_points(Z,Y) ) ) ) ).
fof(cu1,axiom,
! [X,Y,U,V] :
( ( distinct_points(X,Y)
& distinct_lines(U,V) )
=> ( apart_point_and_line(X,U)
| apart_point_and_line(X,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(Y,V) ) ) ).
fof(ceq1,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( distinct_points(X,Z)
| apart_point_and_line(Z,Y) ) ) ).
fof(ceq2,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( distinct_lines(Y,Z)
| apart_point_and_line(X,Z) ) ) ).
fof(con,conjecture,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( apart_point_and_line(Z,line_connecting(X,Y))
=> apart_point_and_line(X,line_connecting(Z,Y)) ) ) ).
fof(subgoal_0,plain,
! [X,Y,Z] :
( ( distinct_points(X,Y)
& apart_point_and_line(Z,line_connecting(X,Y)) )
=> apart_point_and_line(X,line_connecting(Z,Y)) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [X,Y,Z] :
( ( distinct_points(X,Y)
& apart_point_and_line(Z,line_connecting(X,Y)) )
=> apart_point_and_line(X,line_connecting(Z,Y)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| ( distinct_points(Z,X)
& distinct_points(Z,Y) ) ),
inference(canonicalize,[],[con1]) ).
fof(normalize_0_1,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| ( distinct_points(Z,X)
& distinct_points(Z,Y) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y,Z] :
( ( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(Z,X) )
& ( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(Z,Y) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(Z,X) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(Z,Y) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_5,plain,
! [X,Y,Z] :
( ~ distinct_points(X,Y)
| distinct_points(X,Z)
| distinct_points(Y,Z) ),
inference(canonicalize,[],[apart4]) ).
fof(normalize_0_6,plain,
! [X,Y,Z] :
( ~ distinct_points(X,Y)
| distinct_points(X,Z)
| distinct_points(Y,Z) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(canonicalize,[],[ceq1]) ).
fof(normalize_0_8,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
? [X,Y,Z] :
( ~ apart_point_and_line(X,line_connecting(Z,Y))
& apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(X,Y) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_10,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
& apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
& distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) ),
inference(skolemize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X] : ~ distinct_points(X,X),
inference(canonicalize,[],[apart1]) ).
fof(normalize_0_13,plain,
! [X] : ~ distinct_points(X,X),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_15,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[ceq2]) ).
fof(normalize_0_16,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [U,V,X,Y] :
( ~ distinct_lines(U,V)
| ~ distinct_points(X,Y)
| apart_point_and_line(X,U)
| apart_point_and_line(X,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(Y,V) ),
inference(canonicalize,[],[cu1]) ).
fof(normalize_0_18,plain,
! [U,V,X,Y] :
( ~ distinct_lines(U,V)
| ~ distinct_points(X,Y)
| apart_point_and_line(X,U)
| apart_point_and_line(X,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(Y,V) ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
~ apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)),
inference(conjunct,[],[normalize_0_10]) ).
cnf(refute_0_0,plain,
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(Z,X) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_2,plain,
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(Z,Y) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_4,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| ~ distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_Z)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_5,plain,
( ~ distinct_points(X,Y)
| distinct_points(X,Z)
| distinct_points(Y,Z) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_6,plain,
( ~ distinct_points(X_115,X_114)
| distinct_points(X_114,Z)
| distinct_points(X_115,Z) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_115)),bind(Y,$fot(X_114))]]) ).
cnf(refute_0_7,plain,
( ~ distinct_points(X_54,X_53)
| distinct_points(X_53,Z)
| distinct_points(X_54,Z) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_54)),bind(Y,$fot(X_53))]]) ).
cnf(refute_0_8,plain,
( ~ distinct_points(X_50,skolemFOFtoCNF_Z)
| distinct_points(X_50,Z)
| distinct_points(skolemFOFtoCNF_Z,Z) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_50)),bind(Y,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_9,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_10,plain,
( ~ apart_point_and_line(X_8,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(X_8,Z) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_8)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_11,plain,
apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_12,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(X_7,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Z,X_7) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(skolemFOFtoCNF_Z)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Z,$fot(X_7))]]) ).
cnf(refute_0_13,plain,
( apart_point_and_line(X_7,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Z,X_7) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( apart_point_and_line(X_8,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Z,X_8) ),
inference(subst,[],[refute_0_13:[bind(X_7,$fot(X_8))]]) ).
cnf(refute_0_15,plain,
( apart_point_and_line(Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(X_8,Z)
| distinct_points(skolemFOFtoCNF_Z,X_8) ),
inference(resolve,[$cnf( apart_point_and_line(X_8,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_14,refute_0_10]) ).
cnf(refute_0_16,plain,
( apart_point_and_line(X_12,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(X_11,X_12)
| distinct_points(skolemFOFtoCNF_Z,X_11) ),
inference(subst,[],[refute_0_15:[bind(Z,$fot(X_12)),bind(X_8,$fot(X_11))]]) ).
cnf(refute_0_17,plain,
( ~ distinct_points(X_11,X_12)
| distinct_points(X_11,X_13)
| distinct_points(X_12,X_13) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_11)),bind(Y,$fot(X_12)),bind(Z,$fot(X_13))]]) ).
cnf(refute_0_18,plain,
( apart_point_and_line(X_12,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(X_11,X_13)
| distinct_points(X_12,X_13)
| distinct_points(skolemFOFtoCNF_Z,X_11) ),
inference(resolve,[$cnf( distinct_points(X_11,X_12) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( apart_point_and_line(X_12,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(X_12,skolemFOFtoCNF_Z)
| distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_18:[bind(X_11,$fot(skolemFOFtoCNF_Z)),bind(X_13,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_20,plain,
~ distinct_points(X,X),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_21,plain,
~ distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z),
inference(subst,[],[refute_0_20:[bind(X,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_22,plain,
( apart_point_and_line(X_12,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(X_12,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) )],[refute_0_19,refute_0_21]) ).
cnf(refute_0_23,plain,
( apart_point_and_line(X_49,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(X_49,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_22:[bind(X_12,$fot(X_49))]]) ).
cnf(refute_0_24,plain,
( ~ apart_point_and_line(X_49,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| distinct_points(X_49,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(X_49))]]) ).
cnf(refute_0_25,plain,
( ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| distinct_points(X_49,skolemFOFtoCNF_Y)
| distinct_points(X_49,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( apart_point_and_line(X_49,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_27,plain,
( distinct_points(X_49,skolemFOFtoCNF_Y)
| distinct_points(X_49,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_26,refute_0_25]) ).
cnf(refute_0_28,plain,
( distinct_points(X_50,skolemFOFtoCNF_Y)
| distinct_points(X_50,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_27:[bind(X_49,$fot(X_50))]]) ).
cnf(refute_0_29,plain,
( distinct_points(X_50,Z)
| distinct_points(X_50,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_Z,Z) ),
inference(resolve,[$cnf( distinct_points(X_50,skolemFOFtoCNF_Z) )],[refute_0_28,refute_0_8]) ).
cnf(refute_0_30,plain,
( distinct_points(X_54,X_53)
| distinct_points(X_54,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_Z,X_53) ),
inference(subst,[],[refute_0_29:[bind(Z,$fot(X_53)),bind(X_50,$fot(X_54))]]) ).
cnf(refute_0_31,plain,
( distinct_points(X_53,Z)
| distinct_points(X_54,Z)
| distinct_points(X_54,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_Z,X_53) ),
inference(resolve,[$cnf( distinct_points(X_54,X_53) )],[refute_0_30,refute_0_7]) ).
cnf(refute_0_32,plain,
( distinct_points(X_115,X_114)
| distinct_points(X_116,X_114)
| distinct_points(X_116,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_Z,X_115) ),
inference(subst,[],[refute_0_31:[bind(Z,$fot(X_114)),bind(X_53,$fot(X_115)),bind(X_54,$fot(X_116))]]) ).
cnf(refute_0_33,plain,
( distinct_points(X_114,Z)
| distinct_points(X_115,Z)
| distinct_points(X_116,X_114)
| distinct_points(X_116,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_Z,X_115) ),
inference(resolve,[$cnf( distinct_points(X_115,X_114) )],[refute_0_32,refute_0_6]) ).
cnf(refute_0_34,plain,
( distinct_points(X_114,skolemFOFtoCNF_Z)
| distinct_points(X_116,X_114)
| distinct_points(X_116,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_33:[bind(Z,$fot(skolemFOFtoCNF_Z)),bind(X_115,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_35,plain,
( distinct_points(X_114,skolemFOFtoCNF_Z)
| distinct_points(X_116,X_114)
| distinct_points(X_116,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) )],[refute_0_34,refute_0_21]) ).
cnf(refute_0_36,plain,
( distinct_points(X_114,skolemFOFtoCNF_Z)
| distinct_points(X_451,X_114)
| distinct_points(X_451,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_35:[bind(X_116,$fot(X_451))]]) ).
cnf(refute_0_37,plain,
( ~ apart_point_and_line(X_79,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(X_79,X) ),
inference(subst,[],[refute_0_0:[bind(Z,$fot(X_79))]]) ).
cnf(refute_0_38,plain,
( apart_point_and_line(X_24,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(X_24,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_22:[bind(X_12,$fot(X_24))]]) ).
cnf(refute_0_39,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_40,plain,
( ~ apart_point_and_line(X_24,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(X_24,X_26)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_26) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(X_24)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Z,$fot(X_26))]]) ).
cnf(refute_0_41,plain,
( apart_point_and_line(X_24,X_26)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_26)
| distinct_points(X_24,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( apart_point_and_line(X_24,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_38,refute_0_40]) ).
cnf(refute_0_42,plain,
( apart_point_and_line(X_79,line_connecting(X,Y))
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(X,Y))
| distinct_points(X_79,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_41:[bind(X_24,$fot(X_79)),bind(X_26,$fot(line_connecting(X,Y)))]]) ).
cnf(refute_0_43,plain,
( ~ distinct_points(X,Y)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(X,Y))
| distinct_points(X_79,X)
| distinct_points(X_79,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( apart_point_and_line(X_79,line_connecting(X,Y)) )],[refute_0_42,refute_0_37]) ).
cnf(refute_0_44,plain,
( ~ distinct_points(X_451,skolemFOFtoCNF_Y)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(X_451,skolemFOFtoCNF_Y))
| distinct_points(X_453,X_451)
| distinct_points(X_453,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_43:[bind(X,$fot(X_451)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(X_79,$fot(X_453))]]) ).
cnf(refute_0_45,plain,
( distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(X_451,skolemFOFtoCNF_Y))
| distinct_points(X_114,skolemFOFtoCNF_Z)
| distinct_points(X_451,X_114)
| distinct_points(X_453,X_451)
| distinct_points(X_453,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( distinct_points(X_451,skolemFOFtoCNF_Y) )],[refute_0_36,refute_0_44]) ).
cnf(refute_0_46,plain,
( distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_45:[bind(X_114,$fot(skolemFOFtoCNF_Z)),bind(X_451,$fot(skolemFOFtoCNF_Z)),bind(X_453,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_47,plain,
distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) )],[refute_0_46,refute_0_21]) ).
cnf(refute_0_48,plain,
( ~ distinct_lines(U,V)
| ~ distinct_points(X,Y)
| apart_point_and_line(X,U)
| apart_point_and_line(X,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(Y,V) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_49,plain,
( ~ distinct_lines(X_329,X_330)
| ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| apart_point_and_line(skolemFOFtoCNF_X,X_329)
| apart_point_and_line(skolemFOFtoCNF_X,X_330)
| apart_point_and_line(skolemFOFtoCNF_Y,X_329)
| apart_point_and_line(skolemFOFtoCNF_Y,X_330) ),
inference(subst,[],[refute_0_48:[bind(U,$fot(X_329)),bind(V,$fot(X_330)),bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_50,plain,
( ~ distinct_lines(X_329,X_330)
| apart_point_and_line(skolemFOFtoCNF_X,X_329)
| apart_point_and_line(skolemFOFtoCNF_X,X_330)
| apart_point_and_line(skolemFOFtoCNF_Y,X_329)
| apart_point_and_line(skolemFOFtoCNF_Y,X_330) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_26,refute_0_49]) ).
cnf(refute_0_51,plain,
( ~ distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_50:[bind(X_329,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(X_330,$fot(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_52,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) )],[refute_0_47,refute_0_51]) ).
cnf(refute_0_53,plain,
~ apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_54,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
( ~ distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) )],[refute_0_54,refute_0_4]) ).
cnf(refute_0_56,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_57,plain,
( ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_11,refute_0_56]) ).
cnf(refute_0_58,plain,
distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_26,refute_0_57]) ).
cnf(refute_0_59,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y) )],[refute_0_58,refute_0_55]) ).
cnf(refute_0_60,plain,
~ distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y),
inference(subst,[],[refute_0_20:[bind(X,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_61,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
( ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_61,refute_0_3]) ).
cnf(refute_0_63,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_26,refute_0_62]) ).
cnf(refute_0_64,plain,
apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) )],[refute_0_63,refute_0_60]) ).
cnf(refute_0_65,plain,
( ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_64,refute_0_1]) ).
cnf(refute_0_66,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_26,refute_0_65]) ).
cnf(refute_0_67,plain,
~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X),
inference(subst,[],[refute_0_20:[bind(X,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_68,plain,
$false,
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X) )],[refute_0_66,refute_0_67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GEO180+2 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 18 06:02:03 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 4.99/5.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.99/5.19
% 4.99/5.19 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.99/5.19
%------------------------------------------------------------------------------