TSTP Solution File: GEO182+2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO182+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 05:25:00 EDT 2022
% Result : Theorem 5.44s 5.61s
% Output : CNFRefutation 5.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 7
% Syntax : Number of formulae : 144 ( 21 unt; 0 def)
% Number of atoms : 426 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 376 ( 94 ~; 261 |; 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 : 203 ( 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(Z,line_connecting(Y,X)) ) ) ).
fof(subgoal_0,plain,
! [X,Y,Z] :
( ( distinct_points(X,Y)
& apart_point_and_line(Z,line_connecting(X,Y)) )
=> apart_point_and_line(Z,line_connecting(Y,X)) ),
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(Z,line_connecting(Y,X)) ),
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,Y) ),
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,X) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_5,plain,
? [X,Y,Z] :
( ~ apart_point_and_line(Z,line_connecting(Y,X))
& apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(X,Y) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_6,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))
& apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
& distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) ),
inference(skolemize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
~ apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,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_9,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,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_11,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X,Y,Z] :
( ~ distinct_points(X,Y)
| distinct_points(X,Z)
| distinct_points(Y,Z) ),
inference(canonicalize,[],[apart4]) ).
fof(normalize_0_13,plain,
! [X,Y,Z] :
( ~ distinct_points(X,Y)
| distinct_points(X,Z)
| distinct_points(Y,Z) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_15,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_16,plain,
! [X] : ~ distinct_points(X,X),
inference(canonicalize,[],[apart1]) ).
fof(normalize_0_17,plain,
! [X] : ~ distinct_points(X,X),
inference(specialize,[],[normalize_0_16]) ).
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(canonicalize,[],[cu1]) ).
fof(normalize_0_19,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_18]) ).
cnf(refute_0_0,plain,
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(Z,Y) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))
| ~ distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)
| distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(skolemFOFtoCNF_X)),bind(Z,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_2,plain,
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(Z,X) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))
| ~ distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(skolemFOFtoCNF_X)),bind(Z,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_4,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z))
| ~ distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(skolemFOFtoCNF_Z)),bind(Z,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_5,plain,
~ apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_6,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z))
| ~ distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(skolemFOFtoCNF_Z)),bind(Z,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_7,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_8,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z))
| apart_point_and_line(skolemFOFtoCNF_X,Z)
| distinct_lines(line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),Z) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_Y,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_11]) ).
cnf(refute_0_10,plain,
( ~ apart_point_and_line(X_844,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z))
| apart_point_and_line(Z,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z))
| distinct_points(X_844,Z) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_844)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)))]]) ).
cnf(refute_0_11,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_2:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_12,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z))
| apart_point_and_line(Z,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z))
| distinct_points(skolemFOFtoCNF_X,Z) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)))]]) ).
cnf(refute_0_13,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_14,plain,
( ~ distinct_points(X,Y)
| distinct_points(X,Z)
| distinct_points(Y,Z) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_15,plain,
( ~ distinct_points(X_170,X_169)
| distinct_points(X_169,Z)
| distinct_points(X_170,Z) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(X_170)),bind(Y,$fot(X_169))]]) ).
cnf(refute_0_16,plain,
( ~ distinct_points(X_53,X_52)
| distinct_points(X_52,Z)
| distinct_points(X_53,Z) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(X_53)),bind(Y,$fot(X_52))]]) ).
cnf(refute_0_17,plain,
( ~ distinct_points(skolemFOFtoCNF_Z,X_45)
| distinct_points(X_45,Z)
| distinct_points(skolemFOFtoCNF_Z,Z) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(skolemFOFtoCNF_Z)),bind(Y,$fot(X_45))]]) ).
cnf(refute_0_18,plain,
( ~ distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_Y,Z)
| distinct_points(skolemFOFtoCNF_Z,Z) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(skolemFOFtoCNF_Z)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_19,plain,
apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_20,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_0:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_21,plain,
( ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_23,plain,
distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_22,refute_0_21]) ).
cnf(refute_0_24,plain,
( distinct_points(skolemFOFtoCNF_Y,Z)
| distinct_points(skolemFOFtoCNF_Z,Z) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y) )],[refute_0_23,refute_0_18]) ).
cnf(refute_0_25,plain,
( distinct_points(skolemFOFtoCNF_Y,X_45)
| distinct_points(skolemFOFtoCNF_Z,X_45) ),
inference(subst,[],[refute_0_24:[bind(Z,$fot(X_45))]]) ).
cnf(refute_0_26,plain,
( distinct_points(X_45,Z)
| distinct_points(skolemFOFtoCNF_Y,X_45)
| distinct_points(skolemFOFtoCNF_Z,Z) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Z,X_45) )],[refute_0_25,refute_0_17]) ).
cnf(refute_0_27,plain,
( distinct_points(X_53,X_52)
| distinct_points(skolemFOFtoCNF_Y,X_53)
| distinct_points(skolemFOFtoCNF_Z,X_52) ),
inference(subst,[],[refute_0_26:[bind(Z,$fot(X_52)),bind(X_45,$fot(X_53))]]) ).
cnf(refute_0_28,plain,
( distinct_points(X_52,Z)
| distinct_points(X_53,Z)
| distinct_points(skolemFOFtoCNF_Y,X_53)
| distinct_points(skolemFOFtoCNF_Z,X_52) ),
inference(resolve,[$cnf( distinct_points(X_53,X_52) )],[refute_0_27,refute_0_16]) ).
cnf(refute_0_29,plain,
( distinct_points(X_170,X_169)
| distinct_points(X_171,X_169)
| distinct_points(skolemFOFtoCNF_Y,X_171)
| distinct_points(skolemFOFtoCNF_Z,X_170) ),
inference(subst,[],[refute_0_28:[bind(Z,$fot(X_169)),bind(X_52,$fot(X_170)),bind(X_53,$fot(X_171))]]) ).
cnf(refute_0_30,plain,
( distinct_points(X_169,Z)
| distinct_points(X_170,Z)
| distinct_points(X_171,X_169)
| distinct_points(skolemFOFtoCNF_Y,X_171)
| distinct_points(skolemFOFtoCNF_Z,X_170) ),
inference(resolve,[$cnf( distinct_points(X_170,X_169) )],[refute_0_29,refute_0_15]) ).
cnf(refute_0_31,plain,
( distinct_points(X_169,skolemFOFtoCNF_Z)
| distinct_points(X_171,X_169)
| distinct_points(skolemFOFtoCNF_Y,X_171)
| distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_30:[bind(Z,$fot(skolemFOFtoCNF_Z)),bind(X_170,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_32,plain,
~ distinct_points(X,X),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_33,plain,
~ distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z),
inference(subst,[],[refute_0_32:[bind(X,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_34,plain,
( distinct_points(X_169,skolemFOFtoCNF_Z)
| distinct_points(X_171,X_169)
| distinct_points(skolemFOFtoCNF_Y,X_171) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) )],[refute_0_31,refute_0_33]) ).
cnf(refute_0_35,plain,
( distinct_points(X_169,skolemFOFtoCNF_Z)
| distinct_points(X_262,X_169)
| distinct_points(skolemFOFtoCNF_Y,X_262) ),
inference(subst,[],[refute_0_34:[bind(X_171,$fot(X_262))]]) ).
cnf(refute_0_36,plain,
( ~ apart_point_and_line(X_75,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(X_75,Y) ),
inference(subst,[],[refute_0_0:[bind(Z,$fot(X_75))]]) ).
cnf(refute_0_37,plain,
( ~ apart_point_and_line(X_11,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(X_11,Z) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_11)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_38,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(X_10,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Z,X_10) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(skolemFOFtoCNF_Z)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Z,$fot(X_10))]]) ).
cnf(refute_0_39,plain,
( apart_point_and_line(X_10,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Z,X_10) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_19,refute_0_38]) ).
cnf(refute_0_40,plain,
( apart_point_and_line(X_11,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Z,X_11) ),
inference(subst,[],[refute_0_39:[bind(X_10,$fot(X_11))]]) ).
cnf(refute_0_41,plain,
( apart_point_and_line(Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(X_11,Z)
| distinct_points(skolemFOFtoCNF_Z,X_11) ),
inference(resolve,[$cnf( apart_point_and_line(X_11,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_40,refute_0_37]) ).
cnf(refute_0_42,plain,
( apart_point_and_line(X_15,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(X_14,X_15)
| distinct_points(skolemFOFtoCNF_Z,X_14) ),
inference(subst,[],[refute_0_41:[bind(Z,$fot(X_15)),bind(X_11,$fot(X_14))]]) ).
cnf(refute_0_43,plain,
( ~ distinct_points(X_14,X_15)
| distinct_points(X_14,X_16)
| distinct_points(X_15,X_16) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(X_14)),bind(Y,$fot(X_15)),bind(Z,$fot(X_16))]]) ).
cnf(refute_0_44,plain,
( apart_point_and_line(X_15,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(X_14,X_16)
| distinct_points(X_15,X_16)
| distinct_points(skolemFOFtoCNF_Z,X_14) ),
inference(resolve,[$cnf( distinct_points(X_14,X_15) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
( apart_point_and_line(X_15,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(X_15,skolemFOFtoCNF_Z)
| distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_44:[bind(X_14,$fot(skolemFOFtoCNF_Z)),bind(X_16,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_46,plain,
( apart_point_and_line(X_15,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(X_15,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) )],[refute_0_45,refute_0_33]) ).
cnf(refute_0_47,plain,
( apart_point_and_line(X_22,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(X_22,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_46:[bind(X_15,$fot(X_22))]]) ).
cnf(refute_0_48,plain,
( ~ apart_point_and_line(X_22,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(X_22,X_24)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_24) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(X_22)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Z,$fot(X_24))]]) ).
cnf(refute_0_49,plain,
( apart_point_and_line(X_22,X_24)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_24)
| distinct_points(X_22,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( apart_point_and_line(X_22,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
( apart_point_and_line(X_75,line_connecting(X,Y))
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(X,Y))
| distinct_points(X_75,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_49:[bind(X_22,$fot(X_75)),bind(X_24,$fot(line_connecting(X,Y)))]]) ).
cnf(refute_0_51,plain,
( ~ distinct_points(X,Y)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(X,Y))
| distinct_points(X_75,Y)
| distinct_points(X_75,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( apart_point_and_line(X_75,line_connecting(X,Y)) )],[refute_0_50,refute_0_36]) ).
cnf(refute_0_52,plain,
( ~ distinct_points(skolemFOFtoCNF_Y,X_262)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_Y,X_262))
| distinct_points(X_263,X_262)
| distinct_points(X_263,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_51:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(X_262)),bind(X_75,$fot(X_263))]]) ).
cnf(refute_0_53,plain,
( distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_Y,X_262))
| distinct_points(X_169,skolemFOFtoCNF_Z)
| distinct_points(X_262,X_169)
| distinct_points(X_263,X_262)
| distinct_points(X_263,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Y,X_262) )],[refute_0_35,refute_0_52]) ).
cnf(refute_0_54,plain,
( distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z))
| distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_53:[bind(X_169,$fot(skolemFOFtoCNF_Z)),bind(X_262,$fot(skolemFOFtoCNF_Z)),bind(X_263,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_55,plain,
distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) )],[refute_0_54,refute_0_33]) ).
cnf(refute_0_56,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_19]) ).
cnf(refute_0_57,plain,
( ~ distinct_lines(X_385,X_386)
| ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| apart_point_and_line(skolemFOFtoCNF_X,X_385)
| apart_point_and_line(skolemFOFtoCNF_X,X_386)
| apart_point_and_line(skolemFOFtoCNF_Y,X_385)
| apart_point_and_line(skolemFOFtoCNF_Y,X_386) ),
inference(subst,[],[refute_0_56:[bind(U,$fot(X_385)),bind(V,$fot(X_386)),bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_58,plain,
( ~ distinct_lines(X_385,X_386)
| apart_point_and_line(skolemFOFtoCNF_X,X_385)
| apart_point_and_line(skolemFOFtoCNF_X,X_386)
| apart_point_and_line(skolemFOFtoCNF_Y,X_385)
| apart_point_and_line(skolemFOFtoCNF_Y,X_386) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_22,refute_0_57]) ).
cnf(refute_0_59,plain,
( ~ distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)) ),
inference(subst,[],[refute_0_58:[bind(X_385,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(X_386,$fot(line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)))]]) ).
cnf(refute_0_60,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)) )],[refute_0_55,refute_0_59]) ).
cnf(refute_0_61,plain,
( ~ distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)) )],[refute_0_60,refute_0_4]) ).
cnf(refute_0_62,plain,
( ~ distinct_points(X_44,skolemFOFtoCNF_Y)
| distinct_points(X_44,Z)
| distinct_points(skolemFOFtoCNF_Y,Z) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(X_44)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_63,plain,
( apart_point_and_line(X_43,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Z,X_43) ),
inference(subst,[],[refute_0_39:[bind(X_10,$fot(X_43))]]) ).
cnf(refute_0_64,plain,
( ~ apart_point_and_line(X_43,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| distinct_points(X_43,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(X_43))]]) ).
cnf(refute_0_65,plain,
( ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| distinct_points(X_43,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_Z,X_43) ),
inference(resolve,[$cnf( apart_point_and_line(X_43,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
( distinct_points(X_43,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_Z,X_43) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_22,refute_0_65]) ).
cnf(refute_0_67,plain,
( distinct_points(X_44,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_Z,X_44) ),
inference(subst,[],[refute_0_66:[bind(X_43,$fot(X_44))]]) ).
cnf(refute_0_68,plain,
( distinct_points(X_44,Z)
| distinct_points(skolemFOFtoCNF_Y,Z)
| distinct_points(skolemFOFtoCNF_Z,X_44) ),
inference(resolve,[$cnf( distinct_points(X_44,skolemFOFtoCNF_Y) )],[refute_0_67,refute_0_62]) ).
cnf(refute_0_69,plain,
( distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_68:[bind(Z,$fot(skolemFOFtoCNF_Z)),bind(X_44,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_70,plain,
distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) )],[refute_0_69,refute_0_33]) ).
cnf(refute_0_71,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_0_70,refute_0_61]) ).
cnf(refute_0_72,plain,
~ distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y),
inference(subst,[],[refute_0_32:[bind(X,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_73,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
( ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z))
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_73,refute_0_13]) ).
cnf(refute_0_75,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z))
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_22,refute_0_74]) ).
cnf(refute_0_76,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) )],[refute_0_75,refute_0_72]) ).
cnf(refute_0_77,plain,
( apart_point_and_line(Z,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_X,Z) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)) )],[refute_0_76,refute_0_12]) ).
cnf(refute_0_78,plain,
( apart_point_and_line(X_843,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_X,X_843) ),
inference(subst,[],[refute_0_77:[bind(Z,$fot(X_843))]]) ).
cnf(refute_0_79,plain,
( ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| apart_point_and_line(X_843,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z))
| distinct_points(skolemFOFtoCNF_X,X_843)
| distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_78,refute_0_11]) ).
cnf(refute_0_80,plain,
( apart_point_and_line(X_843,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z))
| distinct_points(skolemFOFtoCNF_X,X_843)
| distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_22,refute_0_79]) ).
cnf(refute_0_81,plain,
~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X),
inference(subst,[],[refute_0_32:[bind(X,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_82,plain,
( apart_point_and_line(X_843,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z))
| distinct_points(skolemFOFtoCNF_X,X_843) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
( apart_point_and_line(X_844,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z))
| distinct_points(skolemFOFtoCNF_X,X_844) ),
inference(subst,[],[refute_0_82:[bind(X_843,$fot(X_844))]]) ).
cnf(refute_0_84,plain,
( apart_point_and_line(Z,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z))
| distinct_points(X_844,Z)
| distinct_points(skolemFOFtoCNF_X,X_844) ),
inference(resolve,[$cnf( apart_point_and_line(X_844,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)) )],[refute_0_83,refute_0_10]) ).
cnf(refute_0_85,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z))
| distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_84:[bind(Z,$fot(skolemFOFtoCNF_X)),bind(X_844,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_86,plain,
apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X) )],[refute_0_85,refute_0_81]) ).
cnf(refute_0_87,plain,
( apart_point_and_line(skolemFOFtoCNF_X,Z)
| distinct_lines(line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),Z) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)) )],[refute_0_86,refute_0_8]) ).
cnf(refute_0_88,plain,
( apart_point_and_line(skolemFOFtoCNF_X,X_863)
| distinct_lines(line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),X_863) ),
inference(subst,[],[refute_0_87:[bind(Z,$fot(X_863))]]) ).
cnf(refute_0_89,plain,
( ~ distinct_lines(X_385,X_386)
| ~ distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| apart_point_and_line(skolemFOFtoCNF_Y,X_385)
| apart_point_and_line(skolemFOFtoCNF_Y,X_386)
| apart_point_and_line(skolemFOFtoCNF_Z,X_385)
| apart_point_and_line(skolemFOFtoCNF_Z,X_386) ),
inference(subst,[],[refute_0_56:[bind(U,$fot(X_385)),bind(V,$fot(X_386)),bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_90,plain,
( ~ distinct_lines(X_385,X_386)
| apart_point_and_line(skolemFOFtoCNF_Y,X_385)
| apart_point_and_line(skolemFOFtoCNF_Y,X_386)
| apart_point_and_line(skolemFOFtoCNF_Z,X_385)
| apart_point_and_line(skolemFOFtoCNF_Z,X_386) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_0_70,refute_0_89]) ).
cnf(refute_0_91,plain,
( ~ distinct_lines(line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),X_863)
| apart_point_and_line(skolemFOFtoCNF_Y,X_863)
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z))
| apart_point_and_line(skolemFOFtoCNF_Z,X_863)
| apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)) ),
inference(subst,[],[refute_0_90:[bind(X_385,$fot(line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z))),bind(X_386,$fot(X_863))]]) ).
cnf(refute_0_92,plain,
( apart_point_and_line(skolemFOFtoCNF_X,X_863)
| apart_point_and_line(skolemFOFtoCNF_Y,X_863)
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z))
| apart_point_and_line(skolemFOFtoCNF_Z,X_863)
| apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),X_863) )],[refute_0_88,refute_0_91]) ).
cnf(refute_0_93,plain,
( apart_point_and_line(skolemFOFtoCNF_X,X_864)
| apart_point_and_line(skolemFOFtoCNF_Y,X_864)
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z))
| apart_point_and_line(skolemFOFtoCNF_Z,X_864)
| apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)) ),
inference(subst,[],[refute_0_92:[bind(X_863,$fot(X_864))]]) ).
cnf(refute_0_94,plain,
( ~ distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| apart_point_and_line(skolemFOFtoCNF_X,X_864)
| apart_point_and_line(skolemFOFtoCNF_Y,X_864)
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z))
| apart_point_and_line(skolemFOFtoCNF_Z,X_864)
| distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)) )],[refute_0_93,refute_0_6]) ).
cnf(refute_0_95,plain,
( apart_point_and_line(skolemFOFtoCNF_X,X_864)
| apart_point_and_line(skolemFOFtoCNF_Y,X_864)
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z))
| apart_point_and_line(skolemFOFtoCNF_Z,X_864)
| distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_0_70,refute_0_94]) ).
cnf(refute_0_96,plain,
( apart_point_and_line(skolemFOFtoCNF_X,X_864)
| apart_point_and_line(skolemFOFtoCNF_Y,X_864)
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z))
| apart_point_and_line(skolemFOFtoCNF_Z,X_864) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) )],[refute_0_95,refute_0_33]) ).
cnf(refute_0_97,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z))
| apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_0_96:[bind(X_864,$fot(line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)))]]) ).
cnf(refute_0_98,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)) )],[refute_0_97,refute_0_5]) ).
cnf(refute_0_99,plain,
( ~ distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)) )],[refute_0_98,refute_0_4]) ).
cnf(refute_0_100,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_0_70,refute_0_99]) ).
cnf(refute_0_101,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) )],[refute_0_100,refute_0_72]) ).
cnf(refute_0_102,plain,
( ~ distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)) )],[refute_0_101,refute_0_3]) ).
cnf(refute_0_103,plain,
( ~ distinct_points(skolemFOFtoCNF_Y,X_17)
| distinct_points(X_17,Z)
| distinct_points(skolemFOFtoCNF_Y,Z) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(X_17))]]) ).
cnf(refute_0_104,plain,
( ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_X,X_16)
| distinct_points(skolemFOFtoCNF_Y,X_16) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(X_16))]]) ).
cnf(refute_0_105,plain,
( distinct_points(skolemFOFtoCNF_X,X_16)
| distinct_points(skolemFOFtoCNF_Y,X_16) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_22,refute_0_104]) ).
cnf(refute_0_106,plain,
( distinct_points(skolemFOFtoCNF_X,X_17)
| distinct_points(skolemFOFtoCNF_Y,X_17) ),
inference(subst,[],[refute_0_105:[bind(X_16,$fot(X_17))]]) ).
cnf(refute_0_107,plain,
( distinct_points(X_17,Z)
| distinct_points(skolemFOFtoCNF_X,X_17)
| distinct_points(skolemFOFtoCNF_Y,Z) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Y,X_17) )],[refute_0_106,refute_0_103]) ).
cnf(refute_0_108,plain,
( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X)
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_107:[bind(Z,$fot(skolemFOFtoCNF_X)),bind(X_17,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_109,plain,
distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X) )],[refute_0_108,refute_0_81]) ).
cnf(refute_0_110,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_X) )],[refute_0_109,refute_0_102]) ).
cnf(refute_0_111,plain,
apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) )],[refute_0_110,refute_0_72]) ).
cnf(refute_0_112,plain,
( ~ distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)
| distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)) )],[refute_0_111,refute_0_1]) ).
cnf(refute_0_113,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_X) )],[refute_0_109,refute_0_112]) ).
cnf(refute_0_114,plain,
$false,
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X) )],[refute_0_113,refute_0_81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : GEO182+2 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.14 % Command : metis --show proof --show saturation %s
% 0.15/0.36 % Computer : n027.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Sat Jun 18 01:18:52 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.22/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 5.44/5.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.44/5.61
% 5.44/5.61 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.44/5.62
%------------------------------------------------------------------------------