TSTP Solution File: GEO191+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO191+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 05:25:08 EDT 2022
% Result : Theorem 0.57s 0.77s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 7
% Syntax : Number of formulae : 70 ( 25 unt; 0 def)
% Number of atoms : 157 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 128 ( 41 ~; 65 |; 16 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 113 ( 21 sgn 51 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
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(ceq2,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( distinct_lines(Y,Z)
| apart_point_and_line(X,Z) ) ) ).
fof(p1,axiom,
! [X,Y] :
( distinct_lines(X,Y)
=> convergent_lines(X,Y) ) ).
fof(cp1,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y) ).
fof(cp2,axiom,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)) ).
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] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(canonicalize,[],[cp1]) ).
fof(normalize_0_1,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(canonicalize,[],[p1]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[apart5]) ).
fof(normalize_0_5,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(canonicalize,[],[cp2]) ).
fof(normalize_0_7,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(specialize,[],[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,
? [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_11,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_10]) ).
fof(normalize_0_12,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_11]) ).
fof(normalize_0_13,plain,
! [X] : ~ distinct_lines(X,X),
inference(canonicalize,[],[apart2]) ).
fof(normalize_0_14,plain,
! [X] : ~ distinct_lines(X,X),
inference(specialize,[],[normalize_0_13]) ).
cnf(refute_0_0,plain,
~ convergent_lines(parallel_through_point(Y,X),Y),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
~ convergent_lines(parallel_through_point(skolemFOFtoCNF_U,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_U),
inference(subst,[],[refute_0_0:[bind(X,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Y,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_2,plain,
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
( ~ distinct_lines(parallel_through_point(X_649,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_U)
| convergent_lines(parallel_through_point(X_649,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_U) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(parallel_through_point(X_649,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))),bind(Y,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_4,plain,
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_5,plain,
( ~ distinct_lines(parallel_through_point(X_648,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),X_647)
| distinct_lines(X_647,Z)
| distinct_lines(parallel_through_point(X_648,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),Z) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(parallel_through_point(X_648,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))),bind(Y,$fot(X_647))]]) ).
cnf(refute_0_6,plain,
( ~ distinct_lines(skolemFOFtoCNF_U,parallel_through_point(X_585,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))
| distinct_lines(parallel_through_point(X_585,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),Z)
| distinct_lines(skolemFOFtoCNF_U,Z) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_U)),bind(Y,$fot(parallel_through_point(X_585,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))))]]) ).
cnf(refute_0_7,plain,
~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_8,plain,
~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),parallel_through_point(Y,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),
inference(subst,[],[refute_0_7:[bind(X,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_9,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_10,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z)
| distinct_lines(skolemFOFtoCNF_U,Z) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Y,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_11,plain,
~ convergent_lines(parallel_through_point(skolemFOFtoCNF_V,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_V),
inference(subst,[],[refute_0_0:[bind(X,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Y,$fot(skolemFOFtoCNF_V))]]) ).
cnf(refute_0_12,plain,
( ~ distinct_lines(parallel_through_point(X_581,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_V)
| convergent_lines(parallel_through_point(X_581,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_V) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(parallel_through_point(X_581,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))),bind(Y,$fot(skolemFOFtoCNF_V))]]) ).
cnf(refute_0_13,plain,
( ~ distinct_lines(parallel_through_point(X_580,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),X_579)
| distinct_lines(X_579,Z)
| distinct_lines(parallel_through_point(X_580,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),Z) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(parallel_through_point(X_580,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))),bind(Y,$fot(X_579))]]) ).
cnf(refute_0_14,plain,
( ~ distinct_lines(skolemFOFtoCNF_V,parallel_through_point(X_92,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))
| distinct_lines(parallel_through_point(X_92,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),Z)
| distinct_lines(skolemFOFtoCNF_V,Z) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_V)),bind(Y,$fot(parallel_through_point(X_92,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))))]]) ).
cnf(refute_0_15,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_V) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_16,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_V)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_89)
| distinct_lines(skolemFOFtoCNF_V,X_89) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Y,$fot(skolemFOFtoCNF_V)),bind(Z,$fot(X_89))]]) ).
cnf(refute_0_17,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_89)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
| distinct_lines(skolemFOFtoCNF_V,X_89) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_V) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),parallel_through_point(Y,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
| distinct_lines(skolemFOFtoCNF_V,parallel_through_point(Y,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))) ),
inference(subst,[],[refute_0_17:[bind(X_89,$fot(parallel_through_point(Y,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))))]]) ).
cnf(refute_0_19,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
| distinct_lines(skolemFOFtoCNF_V,parallel_through_point(Y,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),parallel_through_point(Y,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))) )],[refute_0_18,refute_0_8]) ).
cnf(refute_0_20,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
| distinct_lines(skolemFOFtoCNF_V,parallel_through_point(X_92,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))) ),
inference(subst,[],[refute_0_19:[bind(Y,$fot(X_92))]]) ).
cnf(refute_0_21,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
| distinct_lines(parallel_through_point(X_92,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),Z)
| distinct_lines(skolemFOFtoCNF_V,Z) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_V,parallel_through_point(X_92,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))) )],[refute_0_20,refute_0_14]) ).
cnf(refute_0_22,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
| distinct_lines(parallel_through_point(X_580,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),X_579)
| distinct_lines(skolemFOFtoCNF_V,X_579) ),
inference(subst,[],[refute_0_21:[bind(Z,$fot(X_579)),bind(X_92,$fot(X_580))]]) ).
cnf(refute_0_23,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
| distinct_lines(X_579,Z)
| distinct_lines(parallel_through_point(X_580,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),Z)
| distinct_lines(skolemFOFtoCNF_V,X_579) ),
inference(resolve,[$cnf( distinct_lines(parallel_through_point(X_580,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),X_579) )],[refute_0_22,refute_0_13]) ).
cnf(refute_0_24,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
| distinct_lines(parallel_through_point(X_580,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_V)
| distinct_lines(skolemFOFtoCNF_V,skolemFOFtoCNF_V) ),
inference(subst,[],[refute_0_23:[bind(Z,$fot(skolemFOFtoCNF_V)),bind(X_579,$fot(skolemFOFtoCNF_V))]]) ).
cnf(refute_0_25,plain,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_26,plain,
~ distinct_lines(skolemFOFtoCNF_V,skolemFOFtoCNF_V),
inference(subst,[],[refute_0_25:[bind(X,$fot(skolemFOFtoCNF_V))]]) ).
cnf(refute_0_27,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
| distinct_lines(parallel_through_point(X_580,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_V) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_V,skolemFOFtoCNF_V) )],[refute_0_24,refute_0_26]) ).
cnf(refute_0_28,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
| distinct_lines(parallel_through_point(X_581,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_V) ),
inference(subst,[],[refute_0_27:[bind(X_580,$fot(X_581))]]) ).
cnf(refute_0_29,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
| convergent_lines(parallel_through_point(X_581,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_V) ),
inference(resolve,[$cnf( distinct_lines(parallel_through_point(X_581,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_V) )],[refute_0_28,refute_0_12]) ).
cnf(refute_0_30,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
| convergent_lines(parallel_through_point(skolemFOFtoCNF_V,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_V) ),
inference(subst,[],[refute_0_29:[bind(X_581,$fot(skolemFOFtoCNF_V))]]) ).
cnf(refute_0_31,plain,
apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U),
inference(resolve,[$cnf( convergent_lines(parallel_through_point(skolemFOFtoCNF_V,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_V) )],[refute_0_30,refute_0_11]) ).
cnf(refute_0_32,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z)
| distinct_lines(skolemFOFtoCNF_U,Z) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U) )],[refute_0_31,refute_0_10]) ).
cnf(refute_0_33,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),parallel_through_point(Y,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))
| distinct_lines(skolemFOFtoCNF_U,parallel_through_point(Y,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))) ),
inference(subst,[],[refute_0_32:[bind(Z,$fot(parallel_through_point(Y,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))))]]) ).
cnf(refute_0_34,plain,
distinct_lines(skolemFOFtoCNF_U,parallel_through_point(Y,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),parallel_through_point(Y,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))) )],[refute_0_33,refute_0_8]) ).
cnf(refute_0_35,plain,
distinct_lines(skolemFOFtoCNF_U,parallel_through_point(X_585,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),
inference(subst,[],[refute_0_34:[bind(Y,$fot(X_585))]]) ).
cnf(refute_0_36,plain,
( distinct_lines(parallel_through_point(X_585,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),Z)
| distinct_lines(skolemFOFtoCNF_U,Z) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_U,parallel_through_point(X_585,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))) )],[refute_0_35,refute_0_6]) ).
cnf(refute_0_37,plain,
( distinct_lines(parallel_through_point(X_648,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),X_647)
| distinct_lines(skolemFOFtoCNF_U,X_647) ),
inference(subst,[],[refute_0_36:[bind(Z,$fot(X_647)),bind(X_585,$fot(X_648))]]) ).
cnf(refute_0_38,plain,
( distinct_lines(X_647,Z)
| distinct_lines(parallel_through_point(X_648,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),Z)
| distinct_lines(skolemFOFtoCNF_U,X_647) ),
inference(resolve,[$cnf( distinct_lines(parallel_through_point(X_648,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),X_647) )],[refute_0_37,refute_0_5]) ).
cnf(refute_0_39,plain,
( distinct_lines(parallel_through_point(X_648,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_U)
| distinct_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_U) ),
inference(subst,[],[refute_0_38:[bind(Z,$fot(skolemFOFtoCNF_U)),bind(X_647,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_40,plain,
~ distinct_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_U),
inference(subst,[],[refute_0_25:[bind(X,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_41,plain,
distinct_lines(parallel_through_point(X_648,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_U),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_U) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
distinct_lines(parallel_through_point(X_649,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_U),
inference(subst,[],[refute_0_41:[bind(X_648,$fot(X_649))]]) ).
cnf(refute_0_43,plain,
convergent_lines(parallel_through_point(X_649,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_U),
inference(resolve,[$cnf( distinct_lines(parallel_through_point(X_649,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_U) )],[refute_0_42,refute_0_3]) ).
cnf(refute_0_44,plain,
convergent_lines(parallel_through_point(skolemFOFtoCNF_U,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_U),
inference(subst,[],[refute_0_43:[bind(X_649,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_45,plain,
$false,
inference(resolve,[$cnf( convergent_lines(parallel_through_point(skolemFOFtoCNF_U,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_U) )],[refute_0_44,refute_0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GEO191+3 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : metis --show proof --show saturation %s
% 0.15/0.36 % Computer : n020.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 06:06:49 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.57/0.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.57/0.77
% 0.57/0.77 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.57/0.78
%------------------------------------------------------------------------------