%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO191+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n016.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 05:25:08 EDT 2022
% Result : Theorem 41.97s 42.25s
% Output : CNFRefutation 41.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 12
% Syntax : Number of formulae : 116 ( 28 unt; 0 def)
% Number of atoms : 325 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 297 ( 88 ~; 181 |; 17 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 178 ( 0 sgn 90 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X] : ~ distinct_points(X,X) ).
fof(apart2,axiom,
! [X] : ~ distinct_lines(X,X) ).
fof(apart3,axiom,
! [X] : ~ convergent_lines(X,X) ).
fof(apart4,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( distinct_points(X,Z)
| distinct_points(Y,Z) ) ) ).
fof(ax6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| convergent_lines(Y,Z) ) ) ).
fof(ci3,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),X) ) ).
fof(ci4,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),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(ceq3,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( distinct_lines(Y,Z)
| convergent_lines(X,Z) ) ) ).
fof(con,conjecture,
! [X,Y,U,V] :
( ( convergent_lines(X,Y)
& convergent_lines(U,V)
& ( apart_point_and_line(intersection_point(X,Y),U)
| apart_point_and_line(intersection_point(X,Y),V) ) )
=> ( apart_point_and_line(intersection_point(U,V),X)
| apart_point_and_line(intersection_point(U,V),Y) ) ) ).
fof(subgoal_0,plain,
! [X,Y,U,V] :
( ( convergent_lines(X,Y)
& convergent_lines(U,V)
& ( apart_point_and_line(intersection_point(X,Y),U)
| apart_point_and_line(intersection_point(X,Y),V) )
& ~ apart_point_and_line(intersection_point(U,V),X) )
=> apart_point_and_line(intersection_point(U,V),Y) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [X,Y,U,V] :
( ( convergent_lines(X,Y)
& convergent_lines(U,V)
& ( apart_point_and_line(intersection_point(X,Y),U)
| apart_point_and_line(intersection_point(X,Y),V) )
& ~ apart_point_and_line(intersection_point(U,V),X) )
=> apart_point_and_line(intersection_point(U,V),Y) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(canonicalize,[],[ci3]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(canonicalize,[],[ci4]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X] : ~ distinct_points(X,X),
inference(canonicalize,[],[apart1]) ).
fof(normalize_0_5,plain,
! [X] : ~ distinct_points(X,X),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y,Z] :
( ~ distinct_points(X,Y)
| distinct_points(X,Z)
| distinct_points(Y,Z) ),
inference(canonicalize,[],[apart4]) ).
fof(normalize_0_7,plain,
! [X,Y,Z] :
( ~ distinct_points(X,Y)
| distinct_points(X,Z)
| distinct_points(Y,Z) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
? [U,V,X,Y] :
( ~ apart_point_and_line(intersection_point(U,V),X)
& ~ apart_point_and_line(intersection_point(U,V),Y)
& convergent_lines(U,V)
& convergent_lines(X,Y)
& ( apart_point_and_line(intersection_point(X,Y),U)
| apart_point_and_line(intersection_point(X,Y),V) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_9,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_X)
& ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_Y)
& convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V)
& convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
& ( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_V) ) ),
inference(skolemize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V),
inference(conjunct,[],[normalize_0_9]) ).
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(canonicalize,[],[ceq1]) ).
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(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_V) ),
inference(conjunct,[],[normalize_0_9]) ).
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_lines(X,X),
inference(canonicalize,[],[apart2]) ).
fof(normalize_0_17,plain,
! [X] : ~ distinct_lines(X,X),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[ceq3]) ).
fof(normalize_0_19,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [X] : ~ convergent_lines(X,X),
inference(canonicalize,[],[apart3]) ).
fof(normalize_0_21,plain,
! [X] : ~ convergent_lines(X,X),
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[ax6]) ).
fof(normalize_0_23,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(specialize,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_25,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_26,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_25]) ).
fof(normalize_0_27,plain,
~ apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_Y),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_28,plain,
~ apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_X),
inference(conjunct,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_U)
| ~ convergent_lines(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(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
| ~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_3,plain,
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_4,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Y)
| ~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_5,plain,
~ distinct_points(X,X),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_6,plain,
~ distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(subst,[],[refute_0_5:[bind(X,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_7,plain,
( ~ distinct_points(X,Y)
| distinct_points(X,Z)
| distinct_points(Y,Z) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_8,plain,
( ~ distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| distinct_points(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),Z)
| distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Y,$fot(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)))]]) ).
cnf(refute_0_9,plain,
convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_10,plain,
( ~ apart_point_and_line(intersection_point(X,X_386),X_386)
| ~ convergent_lines(X,X_386) ),
inference(subst,[],[refute_0_3:[bind(Y,$fot(X_386))]]) ).
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_12]) ).
cnf(refute_0_12,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_275)
| apart_point_and_line(Z,X_275)
| distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Y,$fot(X_275))]]) ).
cnf(refute_0_13,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
| apart_point_and_line(Z,skolemFOFtoCNF_U)
| distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Y,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_14,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_V) ),
inference(canonicalize,[],[normalize_0_13]) ).
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(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_V)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_32)
| distinct_lines(skolemFOFtoCNF_V,X_32) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Y,$fot(skolemFOFtoCNF_V)),bind(Z,$fot(X_32))]]) ).
cnf(refute_0_17,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_32)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
| distinct_lines(skolemFOFtoCNF_V,X_32) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_V) )],[refute_0_14,refute_0_16]) ).
cnf(refute_0_18,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_36)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
| distinct_lines(skolemFOFtoCNF_V,X_36) ),
inference(subst,[],[refute_0_17:[bind(X_32,$fot(X_36))]]) ).
cnf(refute_0_19,plain,
( apart_point_and_line(Z,skolemFOFtoCNF_U)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_36)
| distinct_lines(skolemFOFtoCNF_V,X_36)
| distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U) )],[refute_0_18,refute_0_13]) ).
cnf(refute_0_20,plain,
( apart_point_and_line(X_274,skolemFOFtoCNF_U)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_275)
| distinct_lines(skolemFOFtoCNF_V,X_275)
| distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_274) ),
inference(subst,[],[refute_0_19:[bind(Z,$fot(X_274)),bind(X_36,$fot(X_275))]]) ).
cnf(refute_0_21,plain,
( apart_point_and_line(Z,X_275)
| apart_point_and_line(X_274,skolemFOFtoCNF_U)
| distinct_lines(skolemFOFtoCNF_V,X_275)
| distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z)
| distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_274) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_275) )],[refute_0_20,refute_0_12]) ).
cnf(refute_0_22,plain,
( apart_point_and_line(intersection_point(X,X_386),X_386)
| apart_point_and_line(intersection_point(X,X_386),skolemFOFtoCNF_U)
| distinct_lines(skolemFOFtoCNF_V,X_386)
| distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(X,X_386)) ),
inference(subst,[],[refute_0_21:[bind(Z,$fot(intersection_point(X,X_386))),bind(X_274,$fot(intersection_point(X,X_386))),bind(X_275,$fot(X_386))]]) ).
cnf(refute_0_23,plain,
( ~ convergent_lines(X,X_386)
| apart_point_and_line(intersection_point(X,X_386),skolemFOFtoCNF_U)
| distinct_lines(skolemFOFtoCNF_V,X_386)
| distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(X,X_386)) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(X,X_386),X_386) )],[refute_0_22,refute_0_10]) ).
cnf(refute_0_24,plain,
( ~ convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_U)
| distinct_lines(skolemFOFtoCNF_V,skolemFOFtoCNF_V)
| distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(skolemFOFtoCNF_U)),bind(X_386,$fot(skolemFOFtoCNF_V))]]) ).
cnf(refute_0_25,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_U)
| distinct_lines(skolemFOFtoCNF_V,skolemFOFtoCNF_V)
| distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V) )],[refute_0_9,refute_0_24]) ).
cnf(refute_0_26,plain,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_27,plain,
~ distinct_lines(skolemFOFtoCNF_V,skolemFOFtoCNF_V),
inference(subst,[],[refute_0_26:[bind(X,$fot(skolemFOFtoCNF_V))]]) ).
cnf(refute_0_28,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_U)
| distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_V,skolemFOFtoCNF_V) )],[refute_0_25,refute_0_27]) ).
cnf(refute_0_29,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_U)
| distinct_points(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),Z)
| distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z) ),
inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_28,refute_0_8]) ).
cnf(refute_0_30,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_U)
| distinct_points(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_29:[bind(Z,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_31,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_U)
| distinct_points(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_30,refute_0_6]) ).
cnf(refute_0_32,plain,
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_33,plain,
( ~ convergent_lines(X_125,X_124)
| convergent_lines(X_125,Z)
| distinct_lines(X_124,Z) ),
inference(subst,[],[refute_0_32:[bind(X,$fot(X_125)),bind(Y,$fot(X_124))]]) ).
cnf(refute_0_34,plain,
( ~ convergent_lines(X_54,skolemFOFtoCNF_Y)
| convergent_lines(X_54,Z)
| distinct_lines(skolemFOFtoCNF_Y,Z) ),
inference(subst,[],[refute_0_32:[bind(X,$fot(X_54)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_35,plain,
~ convergent_lines(X,X),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_36,plain,
~ convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y),
inference(subst,[],[refute_0_35:[bind(X,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_37,plain,
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_38,plain,
( ~ convergent_lines(skolemFOFtoCNF_Y,X_21)
| convergent_lines(X_21,Z)
| convergent_lines(skolemFOFtoCNF_Y,Z) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(X_21))]]) ).
cnf(refute_0_39,plain,
convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_40,plain,
( ~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| convergent_lines(skolemFOFtoCNF_X,X_19)
| convergent_lines(skolemFOFtoCNF_Y,X_19) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(X_19))]]) ).
cnf(refute_0_41,plain,
( convergent_lines(skolemFOFtoCNF_X,X_19)
| convergent_lines(skolemFOFtoCNF_Y,X_19) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( convergent_lines(skolemFOFtoCNF_X,X_21)
| convergent_lines(skolemFOFtoCNF_Y,X_21) ),
inference(subst,[],[refute_0_41:[bind(X_19,$fot(X_21))]]) ).
cnf(refute_0_43,plain,
( convergent_lines(X_21,Z)
| convergent_lines(skolemFOFtoCNF_X,X_21)
| convergent_lines(skolemFOFtoCNF_Y,Z) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_Y,X_21) )],[refute_0_42,refute_0_38]) ).
cnf(refute_0_44,plain,
( convergent_lines(X_53,skolemFOFtoCNF_Y)
| convergent_lines(skolemFOFtoCNF_X,X_53)
| convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_43:[bind(Z,$fot(skolemFOFtoCNF_Y)),bind(X_21,$fot(X_53))]]) ).
cnf(refute_0_45,plain,
( convergent_lines(X_53,skolemFOFtoCNF_Y)
| convergent_lines(skolemFOFtoCNF_X,X_53) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) )],[refute_0_44,refute_0_36]) ).
cnf(refute_0_46,plain,
( convergent_lines(X_54,skolemFOFtoCNF_Y)
| convergent_lines(skolemFOFtoCNF_X,X_54) ),
inference(subst,[],[refute_0_45:[bind(X_53,$fot(X_54))]]) ).
cnf(refute_0_47,plain,
( convergent_lines(X_54,Z)
| convergent_lines(skolemFOFtoCNF_X,X_54)
| distinct_lines(skolemFOFtoCNF_Y,Z) ),
inference(resolve,[$cnf( convergent_lines(X_54,skolemFOFtoCNF_Y) )],[refute_0_46,refute_0_34]) ).
cnf(refute_0_48,plain,
( convergent_lines(X_125,X_124)
| convergent_lines(skolemFOFtoCNF_X,X_125)
| distinct_lines(skolemFOFtoCNF_Y,X_124) ),
inference(subst,[],[refute_0_47:[bind(Z,$fot(X_124)),bind(X_54,$fot(X_125))]]) ).
cnf(refute_0_49,plain,
( convergent_lines(X_125,Z)
| convergent_lines(skolemFOFtoCNF_X,X_125)
| distinct_lines(X_124,Z)
| distinct_lines(skolemFOFtoCNF_Y,X_124) ),
inference(resolve,[$cnf( convergent_lines(X_125,X_124) )],[refute_0_48,refute_0_33]) ).
cnf(refute_0_50,plain,
( convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_X)
| distinct_lines(X_124,skolemFOFtoCNF_X)
| distinct_lines(skolemFOFtoCNF_Y,X_124) ),
inference(subst,[],[refute_0_49:[bind(Z,$fot(skolemFOFtoCNF_X)),bind(X_125,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_51,plain,
~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_X),
inference(subst,[],[refute_0_35:[bind(X,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_52,plain,
( distinct_lines(X_124,skolemFOFtoCNF_X)
| distinct_lines(skolemFOFtoCNF_Y,X_124) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_X) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
( distinct_lines(X_147,skolemFOFtoCNF_X)
| distinct_lines(skolemFOFtoCNF_Y,X_147) ),
inference(subst,[],[refute_0_52:[bind(X_124,$fot(X_147))]]) ).
cnf(refute_0_54,plain,
( ~ distinct_lines(U,V)
| ~ distinct_points(X,Y)
| apart_point_and_line(X,U)
| apart_point_and_line(X,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(Y,V) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_55,plain,
( ~ distinct_lines(skolemFOFtoCNF_Y,X_147)
| ~ distinct_points(X_148,X_149)
| apart_point_and_line(X_148,X_147)
| apart_point_and_line(X_148,skolemFOFtoCNF_Y)
| apart_point_and_line(X_149,X_147)
| apart_point_and_line(X_149,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_54:[bind(U,$fot(skolemFOFtoCNF_Y)),bind(V,$fot(X_147)),bind(X,$fot(X_148)),bind(Y,$fot(X_149))]]) ).
cnf(refute_0_56,plain,
( ~ distinct_points(X_148,X_149)
| apart_point_and_line(X_148,X_147)
| apart_point_and_line(X_148,skolemFOFtoCNF_Y)
| apart_point_and_line(X_149,X_147)
| apart_point_and_line(X_149,skolemFOFtoCNF_Y)
| distinct_lines(X_147,skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_Y,X_147) )],[refute_0_53,refute_0_55]) ).
cnf(refute_0_57,plain,
( ~ distinct_points(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_2116)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_Y)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_2116)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Y)
| distinct_lines(X_2116,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_56:[bind(X_147,$fot(X_2116)),bind(X_148,$fot(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V))),bind(X_149,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_58,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_2116)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_U)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_Y)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_2116)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Y)
| distinct_lines(X_2116,skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_31,refute_0_57]) ).
cnf(refute_0_59,plain,
~ apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_60,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_2116)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_U)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_2116)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Y)
| distinct_lines(X_2116,skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_Y) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_2119)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_U)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_2119)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Y)
| distinct_lines(X_2119,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_60:[bind(X_2116,$fot(X_2119))]]) ).
cnf(refute_0_62,plain,
( ~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_2119)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_U)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_2119)
| distinct_lines(X_2119,skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Y) )],[refute_0_61,refute_0_4]) ).
cnf(refute_0_63,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_2119)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_U)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_2119)
| distinct_lines(X_2119,skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_39,refute_0_62]) ).
cnf(refute_0_64,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_U)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_X)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
| distinct_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_63:[bind(X_2119,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_65,plain,
( ~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_U)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_X)
| distinct_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X) )],[refute_0_64,refute_0_2]) ).
cnf(refute_0_66,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_U)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_X)
| distinct_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_39,refute_0_65]) ).
cnf(refute_0_67,plain,
~ apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_68,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_U)
| distinct_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_X) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
~ distinct_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_X),
inference(subst,[],[refute_0_26:[bind(X,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_70,plain,
apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_U),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_X) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
~ convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_U) )],[refute_0_70,refute_0_1]) ).
cnf(refute_0_72,plain,
$false,
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V) )],[refute_0_9,refute_0_71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GEO191+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Fri Jun 17 15:33:36 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 41.97/42.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 41.97/42.25
% 41.97/42.25 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 41.97/42.25
%------------------------------------------------------------------------------