TSTP Solution File: GEO177+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO177+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 0.47s 0.71s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 9
% Syntax : Number of formulae : 75 ( 25 unt; 0 def)
% Number of atoms : 173 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 145 ( 47 ~; 75 |; 15 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 116 ( 5 sgn 63 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart2,axiom,
! [X] : ~ distinct_lines(X,X) ).
fof(apart3,axiom,
! [X] : ~ convergent_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(ceq3,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( distinct_lines(Y,Z)
| convergent_lines(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] :
( ( 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,parallel_through_point(Y,X)),
inference(canonicalize,[],[cp2]) ).
fof(normalize_0_1,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(canonicalize,[],[cp1]) ).
fof(normalize_0_3,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(canonicalize,[],[p1]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X] : ~ convergent_lines(X,X),
inference(canonicalize,[],[apart3]) ).
fof(normalize_0_7,plain,
! [X] : ~ convergent_lines(X,X),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[ceq3]) ).
fof(normalize_0_9,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[ceq2]) ).
fof(normalize_0_11,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X] : ~ distinct_lines(X,X),
inference(canonicalize,[],[apart2]) ).
fof(normalize_0_13,plain,
! [X] : ~ distinct_lines(X,X),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[apart5]) ).
fof(normalize_0_15,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,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_17,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_16]) ).
fof(normalize_0_18,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_17]) ).
cnf(refute_0_0,plain,
~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
~ apart_point_and_line(skolemFOFtoCNF_X,parallel_through_point(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_X)),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)))]]) ).
cnf(refute_0_2,plain,
~ convergent_lines(parallel_through_point(Y,X),Y),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
~ convergent_lines(parallel_through_point(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X),line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)),
inference(subst,[],[refute_0_2:[bind(Y,$fot(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)))]]) ).
cnf(refute_0_4,plain,
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_5,plain,
( ~ distinct_lines(X_536,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| convergent_lines(X_536,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_536)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)))]]) ).
cnf(refute_0_6,plain,
~ convergent_lines(X,X),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_7,plain,
~ convergent_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)),
inference(subst,[],[refute_0_6:[bind(X,$fot(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)))]]) ).
cnf(refute_0_8,plain,
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_9,plain,
( ~ convergent_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_489)
| convergent_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),Z)
| distinct_lines(X_489,Z) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))),bind(Y,$fot(X_489))]]) ).
cnf(refute_0_10,plain,
( ~ distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_488)
| convergent_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_488) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))),bind(Y,$fot(X_488))]]) ).
cnf(refute_0_11,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_12,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_X,Z)
| distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),Z) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)))]]) ).
cnf(refute_0_13,plain,
~ apart_point_and_line(skolemFOFtoCNF_Y,parallel_through_point(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_Y)),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)))]]) ).
cnf(refute_0_14,plain,
( ~ distinct_lines(X_482,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| convergent_lines(X_482,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_482)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)))]]) ).
cnf(refute_0_15,plain,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_16,plain,
~ distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)),
inference(subst,[],[refute_0_15:[bind(X,$fot(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)))]]) ).
cnf(refute_0_17,plain,
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_18,plain,
( ~ distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_83)
| distinct_lines(X_83,Z)
| distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),Z) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))),bind(Y,$fot(X_83))]]) ).
cnf(refute_0_19,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_20,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_Y,X_82)
| distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_82) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))),bind(Z,$fot(X_82))]]) ).
cnf(refute_0_21,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_Y,X_82)
| distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_82) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_Y,X_83)
| distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_83) ),
inference(subst,[],[refute_0_21:[bind(X_82,$fot(X_83))]]) ).
cnf(refute_0_23,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_Y,X_83)
| distinct_lines(X_83,Z)
| distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),Z) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_83) )],[refute_0_22,refute_0_18]) ).
cnf(refute_0_24,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_Y,X_481)
| distinct_lines(X_481,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(subst,[],[refute_0_23:[bind(Z,$fot(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))),bind(X_83,$fot(X_481))]]) ).
cnf(refute_0_25,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_Y,X_481)
| distinct_lines(X_481,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_24,refute_0_16]) ).
cnf(refute_0_26,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_Y,X_482)
| distinct_lines(X_482,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(subst,[],[refute_0_25:[bind(X_481,$fot(X_482))]]) ).
cnf(refute_0_27,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_Y,X_482)
| convergent_lines(X_482,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(resolve,[$cnf( distinct_lines(X_482,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_26,refute_0_14]) ).
cnf(refute_0_28,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_Y,parallel_through_point(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X))
| convergent_lines(parallel_through_point(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X),line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(subst,[],[refute_0_27:[bind(X_482,$fot(parallel_through_point(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X)))]]) ).
cnf(refute_0_29,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_Y,parallel_through_point(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X)) ),
inference(resolve,[$cnf( convergent_lines(parallel_through_point(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X),line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_28,refute_0_3]) ).
cnf(refute_0_30,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_Y,parallel_through_point(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_29:[bind(X,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_31,plain,
apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y,parallel_through_point(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_Y)) )],[refute_0_30,refute_0_13]) ).
cnf(refute_0_32,plain,
( apart_point_and_line(skolemFOFtoCNF_X,Z)
| distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),Z) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_31,refute_0_12]) ).
cnf(refute_0_33,plain,
( apart_point_and_line(skolemFOFtoCNF_X,X_488)
| distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_488) ),
inference(subst,[],[refute_0_32:[bind(Z,$fot(X_488))]]) ).
cnf(refute_0_34,plain,
( apart_point_and_line(skolemFOFtoCNF_X,X_488)
| convergent_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_488) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_488) )],[refute_0_33,refute_0_10]) ).
cnf(refute_0_35,plain,
( apart_point_and_line(skolemFOFtoCNF_X,X_489)
| convergent_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_489) ),
inference(subst,[],[refute_0_34:[bind(X_488,$fot(X_489))]]) ).
cnf(refute_0_36,plain,
( apart_point_and_line(skolemFOFtoCNF_X,X_489)
| convergent_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),Z)
| distinct_lines(X_489,Z) ),
inference(resolve,[$cnf( convergent_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_489) )],[refute_0_35,refute_0_9]) ).
cnf(refute_0_37,plain,
( apart_point_and_line(skolemFOFtoCNF_X,X_535)
| convergent_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| distinct_lines(X_535,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(subst,[],[refute_0_36:[bind(Z,$fot(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))),bind(X_489,$fot(X_535))]]) ).
cnf(refute_0_38,plain,
( apart_point_and_line(skolemFOFtoCNF_X,X_535)
| distinct_lines(X_535,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(resolve,[$cnf( convergent_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_37,refute_0_7]) ).
cnf(refute_0_39,plain,
( apart_point_and_line(skolemFOFtoCNF_X,X_536)
| distinct_lines(X_536,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(subst,[],[refute_0_38:[bind(X_535,$fot(X_536))]]) ).
cnf(refute_0_40,plain,
( apart_point_and_line(skolemFOFtoCNF_X,X_536)
| convergent_lines(X_536,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(resolve,[$cnf( distinct_lines(X_536,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_39,refute_0_5]) ).
cnf(refute_0_41,plain,
( apart_point_and_line(skolemFOFtoCNF_X,parallel_through_point(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X))
| convergent_lines(parallel_through_point(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X),line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(subst,[],[refute_0_40:[bind(X_536,$fot(parallel_through_point(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X)))]]) ).
cnf(refute_0_42,plain,
apart_point_and_line(skolemFOFtoCNF_X,parallel_through_point(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X)),
inference(resolve,[$cnf( convergent_lines(parallel_through_point(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X),line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_41,refute_0_3]) ).
cnf(refute_0_43,plain,
apart_point_and_line(skolemFOFtoCNF_X,parallel_through_point(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_X)),
inference(subst,[],[refute_0_42:[bind(X,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_44,plain,
$false,
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,parallel_through_point(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_X)) )],[refute_0_43,refute_0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEO177+3 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jun 18 03:34:58 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.47/0.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.47/0.71
% 0.47/0.71 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.47/0.72
%------------------------------------------------------------------------------