TSTP Solution File: GEO177+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO177+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.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 05:24:55 EDT 2022
% Result : Theorem 2.91s 3.15s
% Output : CNFRefutation 2.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 7
% Syntax : Number of formulae : 68 ( 16 unt; 0 def)
% Number of atoms : 199 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 193 ( 62 ~; 106 |; 16 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 98 ( 0 sgn 57 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X] : ~ distinct_points(X,X) ).
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)) )
=> 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)) )
=> apart_point_and_line(V,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,
? [U,V,X,Y] :
( ~ apart_point_and_line(U,line_connecting(X,Y))
& ~ apart_point_and_line(V,line_connecting(X,Y))
& distinct_points(U,V)
& distinct_points(X,Y)
& ( apart_point_and_line(X,line_connecting(U,V))
| apart_point_and_line(Y,line_connecting(U,V)) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
& ~ apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
& distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V)
& distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
& ( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,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_8,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_7]) ).
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)) ),
inference(conjunct,[],[normalize_0_5]) ).
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] : ~ 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_U,skolemFOFtoCNF_V),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_15,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_16,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_15]) ).
fof(normalize_0_17,plain,
~ apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_18,plain,
~ apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(conjunct,[],[normalize_0_5]) ).
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_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| ~ distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_U)),bind(Y,$fot(skolemFOFtoCNF_V))]]) ).
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_V,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| ~ distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_U)),bind(Y,$fot(skolemFOFtoCNF_V))]]) ).
cnf(refute_0_4,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_5,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_6,plain,
( ~ apart_point_and_line(X_99,line_connecting(X,X_99))
| ~ distinct_points(X,X_99) ),
inference(subst,[],[refute_0_2:[bind(Y,$fot(X_99))]]) ).
cnf(refute_0_7,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_8,plain,
( ~ apart_point_and_line(X_58,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(X_58,Z)
| distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),Z) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(X_58)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)))]]) ).
cnf(refute_0_9,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_10,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_11,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(X_24,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| distinct_points(skolemFOFtoCNF_Y,X_24) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))),bind(Z,$fot(X_24))]]) ).
cnf(refute_0_12,plain,
( apart_point_and_line(X_24,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| distinct_points(skolemFOFtoCNF_Y,X_24) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_X,X_29)
| distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_29) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))),bind(Z,$fot(X_29))]]) ).
cnf(refute_0_14,plain,
( apart_point_and_line(X_24,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_X,X_29)
| distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_29)
| distinct_points(skolemFOFtoCNF_Y,X_24) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( apart_point_and_line(X_58,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_X,X_59)
| distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_59)
| distinct_points(skolemFOFtoCNF_Y,X_58) ),
inference(subst,[],[refute_0_14:[bind(X_24,$fot(X_58)),bind(X_29,$fot(X_59))]]) ).
cnf(refute_0_16,plain,
( apart_point_and_line(X_58,Z)
| apart_point_and_line(skolemFOFtoCNF_X,X_59)
| distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),Z)
| distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_59)
| distinct_points(skolemFOFtoCNF_Y,X_58) ),
inference(resolve,[$cnf( apart_point_and_line(X_58,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_15,refute_0_8]) ).
cnf(refute_0_17,plain,
( apart_point_and_line(X_99,line_connecting(X,X_99))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(X,X_99))
| distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(X,X_99))
| distinct_points(skolemFOFtoCNF_Y,X_99) ),
inference(subst,[],[refute_0_16:[bind(Z,$fot(line_connecting(X,X_99))),bind(X_58,$fot(X_99)),bind(X_59,$fot(line_connecting(X,X_99)))]]) ).
cnf(refute_0_18,plain,
( ~ distinct_points(X,X_99)
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(X,X_99))
| distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(X,X_99))
| distinct_points(skolemFOFtoCNF_Y,X_99) ),
inference(resolve,[$cnf( apart_point_and_line(X_99,line_connecting(X,X_99)) )],[refute_0_17,refute_0_6]) ).
cnf(refute_0_19,plain,
( ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(skolemFOFtoCNF_X)),bind(X_99,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_20,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_5,refute_0_19]) ).
cnf(refute_0_21,plain,
~ distinct_points(X,X),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_22,plain,
~ distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y),
inference(subst,[],[refute_0_21:[bind(X,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_23,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) )],[refute_0_20,refute_0_22]) ).
cnf(refute_0_24,plain,
distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_25,plain,
( ~ distinct_lines(U,V)
| ~ distinct_points(X,Y)
| apart_point_and_line(X,U)
| apart_point_and_line(X,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(Y,V) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_26,plain,
( ~ distinct_lines(X_332,X_333)
| ~ distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V)
| apart_point_and_line(skolemFOFtoCNF_U,X_332)
| apart_point_and_line(skolemFOFtoCNF_U,X_333)
| apart_point_and_line(skolemFOFtoCNF_V,X_332)
| apart_point_and_line(skolemFOFtoCNF_V,X_333) ),
inference(subst,[],[refute_0_25:[bind(U,$fot(X_332)),bind(V,$fot(X_333)),bind(X,$fot(skolemFOFtoCNF_U)),bind(Y,$fot(skolemFOFtoCNF_V))]]) ).
cnf(refute_0_27,plain,
( ~ distinct_lines(X_332,X_333)
| apart_point_and_line(skolemFOFtoCNF_U,X_332)
| apart_point_and_line(skolemFOFtoCNF_U,X_333)
| apart_point_and_line(skolemFOFtoCNF_V,X_332)
| apart_point_and_line(skolemFOFtoCNF_V,X_333) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V) )],[refute_0_24,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_27:[bind(X_332,$fot(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))),bind(X_333,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_29,plain,
( apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_23,refute_0_28]) ).
cnf(refute_0_30,plain,
~ apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_31,plain,
( apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
~ apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_33,plain,
( apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
( ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_33,refute_0_4]) ).
cnf(refute_0_35,plain,
( apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_5,refute_0_34]) ).
cnf(refute_0_36,plain,
( ~ distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V)
| apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_35,refute_0_3]) ).
cnf(refute_0_37,plain,
apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V) )],[refute_0_24,refute_0_36]) ).
cnf(refute_0_38,plain,
~ distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_37,refute_0_1]) ).
cnf(refute_0_39,plain,
$false,
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V) )],[refute_0_24,refute_0_38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.21 % Problem : GEO177+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.21 % Command : metis --show proof --show saturation %s
% 0.13/0.42 % Computer : n007.cluster.edu
% 0.13/0.42 % Model : x86_64 x86_64
% 0.13/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.42 % Memory : 8042.1875MB
% 0.13/0.42 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.42 % CPULimit : 300
% 0.13/0.42 % WCLimit : 600
% 0.13/0.42 % DateTime : Fri Jun 17 23:11:13 EDT 2022
% 0.13/0.42 % CPUTime :
% 0.13/0.43 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.91/3.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.91/3.15
% 2.91/3.15 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.91/3.15
%------------------------------------------------------------------------------