TSTP Solution File: GEO187+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO187+1 : TPTP v8.1.0. Released v3.3.0.
% 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 05:25:04 EDT 2022
% Result : Theorem 19.43s 19.63s
% Output : CNFRefutation 19.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 9
% Syntax : Number of formulae : 143 ( 48 unt; 0 def)
% Number of atoms : 359 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 362 ( 146 ~; 168 |; 37 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 199 ( 0 sgn 115 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X] : ~ distinct_points(X,X) ).
fof(apart2,axiom,
! [X] : ~ distinct_lines(X,X) ).
fof(apart5,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(X,Z)
| distinct_lines(Y,Z) ) ) ).
fof(ci1,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ) ).
fof(ci2,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,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,U,V] :
( ( distinct_points(X,Y)
& distinct_points(U,V)
& ~ apart_point_and_line(X,line_connecting(U,V))
& ~ apart_point_and_line(Y,line_connecting(U,V)) )
=> ( ~ apart_point_and_line(U,line_connecting(X,Y))
& ~ apart_point_and_line(V,line_connecting(X,Y)) ) ) ).
fof(subgoal_0,plain,
! [X,Y,U,V] :
( ( distinct_points(X,Y)
& distinct_points(U,V)
& ~ apart_point_and_line(X,line_connecting(U,V))
& ~ apart_point_and_line(Y,line_connecting(U,V)) )
=> ~ apart_point_and_line(U,line_connecting(X,Y)) ),
inference(strip,[],[con]) ).
fof(subgoal_1,plain,
! [X,Y,U,V] :
( ( distinct_points(X,Y)
& distinct_points(U,V)
& ~ apart_point_and_line(X,line_connecting(U,V))
& ~ apart_point_and_line(Y,line_connecting(U,V))
& ~ apart_point_and_line(U,line_connecting(X,Y)) )
=> ~ apart_point_and_line(V,line_connecting(X,Y)) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [X,Y,U,V] :
( ( distinct_points(X,Y)
& distinct_points(U,V)
& ~ apart_point_and_line(X,line_connecting(U,V))
& ~ apart_point_and_line(Y,line_connecting(U,V)) )
=> ~ apart_point_and_line(U,line_connecting(X,Y)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[ci1]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[ci2]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X] : ~ distinct_lines(X,X),
inference(canonicalize,[],[apart2]) ).
fof(normalize_0_5,plain,
! [X] : ~ distinct_lines(X,X),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[apart5]) ).
fof(normalize_0_7,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
? [U,V,X,Y] :
( ~ apart_point_and_line(X,line_connecting(U,V))
& ~ apart_point_and_line(Y,line_connecting(U,V))
& apart_point_and_line(U,line_connecting(X,Y))
& distinct_points(U,V)
& distinct_points(X,Y) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_9,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
& ~ apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
& apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
& distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V)
& distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) ),
inference(skolemize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_12,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_13,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,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_15,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_14]) ).
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,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(conjunct,[],[normalize_0_9]) ).
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(canonicalize,[],[cu1]) ).
fof(normalize_0_20,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_19]) ).
fof(normalize_0_21,plain,
~ apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_22,plain,
~ apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)),
inference(conjunct,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_2,plain,
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_4,plain,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_5,plain,
~ distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(subst,[],[refute_0_4:[bind(X,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_6,plain,
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_7,plain,
( ~ distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),Z)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Y,$fot(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)))]]) ).
cnf(refute_0_8,plain,
distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_9,plain,
( ~ apart_point_and_line(X_38,line_connecting(X_38,Y))
| ~ distinct_points(X_38,Y) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(X_38))]]) ).
cnf(refute_0_10,plain,
apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_11,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_12,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(X_28,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_U,X_28) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(skolemFOFtoCNF_U)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Z,$fot(X_28))]]) ).
cnf(refute_0_13,plain,
( apart_point_and_line(X_28,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_U,X_28) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_10,refute_0_12]) ).
cnf(refute_0_14,plain,
( apart_point_and_line(X_34,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_U,X_34) ),
inference(subst,[],[refute_0_13:[bind(X_28,$fot(X_34))]]) ).
cnf(refute_0_15,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_16,plain,
( ~ apart_point_and_line(X_34,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(X_34,X_36)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_36) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(X_34)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Z,$fot(X_36))]]) ).
cnf(refute_0_17,plain,
( apart_point_and_line(X_34,X_36)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_36)
| distinct_points(skolemFOFtoCNF_U,X_34) ),
inference(resolve,[$cnf( apart_point_and_line(X_34,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_14,refute_0_16]) ).
cnf(refute_0_18,plain,
( apart_point_and_line(X_38,line_connecting(X_38,Y))
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(X_38,Y))
| distinct_points(skolemFOFtoCNF_U,X_38) ),
inference(subst,[],[refute_0_17:[bind(X_34,$fot(X_38)),bind(X_36,$fot(line_connecting(X_38,Y)))]]) ).
cnf(refute_0_19,plain,
( ~ distinct_points(X_38,Y)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(X_38,Y))
| distinct_points(skolemFOFtoCNF_U,X_38) ),
inference(resolve,[$cnf( apart_point_and_line(X_38,line_connecting(X_38,Y)) )],[refute_0_18,refute_0_9]) ).
cnf(refute_0_20,plain,
( ~ distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_U) ),
inference(subst,[],[refute_0_19:[bind(Y,$fot(skolemFOFtoCNF_V)),bind(X_38,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_21,plain,
( distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_U) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V) )],[refute_0_8,refute_0_20]) ).
cnf(refute_0_22,plain,
~ distinct_points(X,X),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_23,plain,
~ distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_U),
inference(subst,[],[refute_0_22:[bind(X,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_24,plain,
distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_U) )],[refute_0_21,refute_0_23]) ).
cnf(refute_0_25,plain,
( distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),Z)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_24,refute_0_7]) ).
cnf(refute_0_26,plain,
( distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_25:[bind(Z,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_27,plain,
distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_26,refute_0_5]) ).
cnf(refute_0_28,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_29,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_20]) ).
cnf(refute_0_30,plain,
( ~ distinct_lines(X_713,X_714)
| ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| apart_point_and_line(skolemFOFtoCNF_X,X_713)
| apart_point_and_line(skolemFOFtoCNF_X,X_714)
| apart_point_and_line(skolemFOFtoCNF_Y,X_713)
| apart_point_and_line(skolemFOFtoCNF_Y,X_714) ),
inference(subst,[],[refute_0_29:[bind(U,$fot(X_713)),bind(V,$fot(X_714)),bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_31,plain,
( ~ distinct_lines(X_713,X_714)
| apart_point_and_line(skolemFOFtoCNF_X,X_713)
| apart_point_and_line(skolemFOFtoCNF_X,X_714)
| apart_point_and_line(skolemFOFtoCNF_Y,X_713)
| apart_point_and_line(skolemFOFtoCNF_Y,X_714) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_28,refute_0_30]) ).
cnf(refute_0_32,plain,
( ~ distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_31:[bind(X_713,$fot(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))),bind(X_714,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_33,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_27,refute_0_32]) ).
cnf(refute_0_34,plain,
~ apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_35,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
~ apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_37,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_37,refute_0_3]) ).
cnf(refute_0_39,plain,
apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_28,refute_0_38]) ).
cnf(refute_0_40,plain,
~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_39,refute_0_1]) ).
cnf(refute_0_41,plain,
$false,
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_28,refute_0_40]) ).
fof(negate_1_0,plain,
~ ! [X,Y,U,V] :
( ( distinct_points(X,Y)
& distinct_points(U,V)
& ~ apart_point_and_line(X,line_connecting(U,V))
& ~ apart_point_and_line(Y,line_connecting(U,V))
& ~ apart_point_and_line(U,line_connecting(X,Y)) )
=> ~ apart_point_and_line(V,line_connecting(X,Y)) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[ci1]) ).
fof(normalize_1_1,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[ci2]) ).
fof(normalize_1_3,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(specialize,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
! [X] : ~ distinct_lines(X,X),
inference(canonicalize,[],[apart2]) ).
fof(normalize_1_5,plain,
! [X] : ~ distinct_lines(X,X),
inference(specialize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[apart5]) ).
fof(normalize_1_7,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
? [U,V,X,Y] :
( ~ apart_point_and_line(U,line_connecting(X,Y))
& ~ apart_point_and_line(X,line_connecting(U,V))
& ~ apart_point_and_line(Y,line_connecting(U,V))
& apart_point_and_line(V,line_connecting(X,Y))
& distinct_points(U,V)
& distinct_points(X,Y) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_9,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_U_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
& ~ apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1))
& ~ apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1))
& apart_point_and_line(skolemFOFtoCNF_V_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
& distinct_points(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)
& distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) ),
inference(skolemize,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
distinct_points(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1),
inference(conjunct,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
apart_point_and_line(skolemFOFtoCNF_V_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)),
inference(conjunct,[],[normalize_1_9]) ).
fof(normalize_1_12,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_1_13,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(specialize,[],[normalize_1_12]) ).
fof(normalize_1_14,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_1_15,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_1_14]) ).
fof(normalize_1_16,plain,
! [X] : ~ distinct_points(X,X),
inference(canonicalize,[],[apart1]) ).
fof(normalize_1_17,plain,
! [X] : ~ distinct_points(X,X),
inference(specialize,[],[normalize_1_16]) ).
fof(normalize_1_18,plain,
distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),
inference(conjunct,[],[normalize_1_9]) ).
fof(normalize_1_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(canonicalize,[],[cu1]) ).
fof(normalize_1_20,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_1_19]) ).
fof(normalize_1_21,plain,
~ apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)),
inference(conjunct,[],[normalize_1_9]) ).
fof(normalize_1_22,plain,
~ apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)),
inference(conjunct,[],[normalize_1_9]) ).
cnf(refute_1_0,plain,
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[normalize_1_1]) ).
cnf(refute_1_1,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| ~ distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) ),
inference(subst,[],[refute_1_0:[bind(X,$fot(skolemFOFtoCNF_X_1)),bind(Y,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_1_2,plain,
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_3,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| ~ distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) ),
inference(subst,[],[refute_1_2:[bind(X,$fot(skolemFOFtoCNF_X_1)),bind(Y,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_1_4,plain,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_1_5]) ).
cnf(refute_1_5,plain,
~ distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)),
inference(subst,[],[refute_1_4:[bind(X,$fot(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)))]]) ).
cnf(refute_1_6,plain,
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_7,plain,
( ~ distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1))
| distinct_lines(line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1),Z)
| distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),Z) ),
inference(subst,[],[refute_1_6:[bind(X,$fot(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))),bind(Y,$fot(line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)))]]) ).
cnf(refute_1_8,plain,
distinct_points(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_9,plain,
( ~ apart_point_and_line(X_1473,line_connecting(X,X_1473))
| ~ distinct_points(X,X_1473) ),
inference(subst,[],[refute_1_2:[bind(Y,$fot(X_1473))]]) ).
cnf(refute_1_10,plain,
apart_point_and_line(skolemFOFtoCNF_V_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_11,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(canonicalize,[],[normalize_1_13]) ).
cnf(refute_1_12,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_V_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| apart_point_and_line(X_1456,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| distinct_points(skolemFOFtoCNF_V_1,X_1456) ),
inference(subst,[],[refute_1_11:[bind(X,$fot(skolemFOFtoCNF_V_1)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))),bind(Z,$fot(X_1456))]]) ).
cnf(refute_1_13,plain,
( apart_point_and_line(X_1456,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| distinct_points(skolemFOFtoCNF_V_1,X_1456) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_V_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) )],[refute_1_10,refute_1_12]) ).
cnf(refute_1_14,plain,
( apart_point_and_line(X_1462,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| distinct_points(skolemFOFtoCNF_V_1,X_1462) ),
inference(subst,[],[refute_1_13:[bind(X_1456,$fot(X_1462))]]) ).
cnf(refute_1_15,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_1_15]) ).
cnf(refute_1_16,plain,
( ~ apart_point_and_line(X_1462,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| apart_point_and_line(X_1462,X_1464)
| distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X_1464) ),
inference(subst,[],[refute_1_15:[bind(X,$fot(X_1462)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))),bind(Z,$fot(X_1464))]]) ).
cnf(refute_1_17,plain,
( apart_point_and_line(X_1462,X_1464)
| distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X_1464)
| distinct_points(skolemFOFtoCNF_V_1,X_1462) ),
inference(resolve,[$cnf( apart_point_and_line(X_1462,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) )],[refute_1_14,refute_1_16]) ).
cnf(refute_1_18,plain,
( apart_point_and_line(X_1473,line_connecting(X,X_1473))
| distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(X,X_1473))
| distinct_points(skolemFOFtoCNF_V_1,X_1473) ),
inference(subst,[],[refute_1_17:[bind(X_1462,$fot(X_1473)),bind(X_1464,$fot(line_connecting(X,X_1473)))]]) ).
cnf(refute_1_19,plain,
( ~ distinct_points(X,X_1473)
| distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(X,X_1473))
| distinct_points(skolemFOFtoCNF_V_1,X_1473) ),
inference(resolve,[$cnf( apart_point_and_line(X_1473,line_connecting(X,X_1473)) )],[refute_1_18,refute_1_9]) ).
cnf(refute_1_20,plain,
( ~ distinct_points(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)
| distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1))
| distinct_points(skolemFOFtoCNF_V_1,skolemFOFtoCNF_V_1) ),
inference(subst,[],[refute_1_19:[bind(X,$fot(skolemFOFtoCNF_U_1)),bind(X_1473,$fot(skolemFOFtoCNF_V_1))]]) ).
cnf(refute_1_21,plain,
( distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1))
| distinct_points(skolemFOFtoCNF_V_1,skolemFOFtoCNF_V_1) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1) )],[refute_1_8,refute_1_20]) ).
cnf(refute_1_22,plain,
~ distinct_points(X,X),
inference(canonicalize,[],[normalize_1_17]) ).
cnf(refute_1_23,plain,
~ distinct_points(skolemFOFtoCNF_V_1,skolemFOFtoCNF_V_1),
inference(subst,[],[refute_1_22:[bind(X,$fot(skolemFOFtoCNF_V_1))]]) ).
cnf(refute_1_24,plain,
distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_V_1,skolemFOFtoCNF_V_1) )],[refute_1_21,refute_1_23]) ).
cnf(refute_1_25,plain,
( distinct_lines(line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1),Z)
| distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),Z) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)) )],[refute_1_24,refute_1_7]) ).
cnf(refute_1_26,plain,
( distinct_lines(line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1),line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) ),
inference(subst,[],[refute_1_25:[bind(Z,$fot(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)))]]) ).
cnf(refute_1_27,plain,
distinct_lines(line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1),line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) )],[refute_1_26,refute_1_5]) ).
cnf(refute_1_28,plain,
distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),
inference(canonicalize,[],[normalize_1_18]) ).
cnf(refute_1_29,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_1_20]) ).
cnf(refute_1_30,plain,
( ~ distinct_lines(X_2184,X_2185)
| ~ distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)
| apart_point_and_line(skolemFOFtoCNF_X_1,X_2184)
| apart_point_and_line(skolemFOFtoCNF_X_1,X_2185)
| apart_point_and_line(skolemFOFtoCNF_Y_1,X_2184)
| apart_point_and_line(skolemFOFtoCNF_Y_1,X_2185) ),
inference(subst,[],[refute_1_29:[bind(U,$fot(X_2184)),bind(V,$fot(X_2185)),bind(X,$fot(skolemFOFtoCNF_X_1)),bind(Y,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_1_31,plain,
( ~ distinct_lines(X_2184,X_2185)
| apart_point_and_line(skolemFOFtoCNF_X_1,X_2184)
| apart_point_and_line(skolemFOFtoCNF_X_1,X_2185)
| apart_point_and_line(skolemFOFtoCNF_Y_1,X_2184)
| apart_point_and_line(skolemFOFtoCNF_Y_1,X_2185) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) )],[refute_1_28,refute_1_30]) ).
cnf(refute_1_32,plain,
( ~ distinct_lines(line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1),line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1))
| apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1))
| apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) ),
inference(subst,[],[refute_1_31:[bind(X_2184,$fot(line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1))),bind(X_2185,$fot(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)))]]) ).
cnf(refute_1_33,plain,
( apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1))
| apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1))
| apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1),line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) )],[refute_1_27,refute_1_32]) ).
cnf(refute_1_34,plain,
~ apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)),
inference(canonicalize,[],[normalize_1_21]) ).
cnf(refute_1_35,plain,
( apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1))
| apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)) )],[refute_1_33,refute_1_34]) ).
cnf(refute_1_36,plain,
~ apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)),
inference(canonicalize,[],[normalize_1_22]) ).
cnf(refute_1_37,plain,
( apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)) )],[refute_1_35,refute_1_36]) ).
cnf(refute_1_38,plain,
( ~ distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)
| apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) )],[refute_1_37,refute_1_3]) ).
cnf(refute_1_39,plain,
apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) )],[refute_1_28,refute_1_38]) ).
cnf(refute_1_40,plain,
~ distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) )],[refute_1_39,refute_1_1]) ).
cnf(refute_1_41,plain,
$false,
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) )],[refute_1_28,refute_1_40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : GEO187+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.10 % Command : metis --show proof --show saturation %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 600
% 0.10/0.29 % DateTime : Fri Jun 17 20:43:46 EDT 2022
% 0.10/0.29 % CPUTime :
% 0.10/0.30 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 19.43/19.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.43/19.63
% 19.43/19.63 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 19.43/19.64
%------------------------------------------------------------------------------