TSTP Solution File: GEO192+2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO192+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 05:25:09 EDT 2022
% Result : Theorem 0.22s 0.44s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 98 ( 34 unt; 0 def)
% Number of atoms : 230 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 214 ( 82 ~; 99 |; 23 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 148 ( 0 sgn 82 !; 6 ?)
% 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(con2,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( ( apart_point_and_line(Z,X)
| apart_point_and_line(Z,Y) )
=> distinct_points(Z,intersection_point(X,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,Z] :
( convergent_lines(X,Y)
=> ( apart_point_and_line(intersection_point(X,Y),Z)
=> ( distinct_lines(X,Z)
& distinct_lines(Y,Z) ) ) ) ).
fof(subgoal_0,plain,
! [X,Y,Z] :
( ( convergent_lines(X,Y)
& apart_point_and_line(intersection_point(X,Y),Z) )
=> distinct_lines(X,Z) ),
inference(strip,[],[con]) ).
fof(subgoal_1,plain,
! [X,Y,Z] :
( ( convergent_lines(X,Y)
& apart_point_and_line(intersection_point(X,Y),Z)
& distinct_lines(X,Z) )
=> distinct_lines(Y,Z) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [X,Y,Z] :
( ( convergent_lines(X,Y)
& apart_point_and_line(intersection_point(X,Y),Z) )
=> distinct_lines(X,Z) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[apart5]) ).
fof(normalize_0_1,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,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_3,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [X,Y,Z] :
( ~ distinct_lines(X,Z)
& apart_point_and_line(intersection_point(X,Y),Z)
& convergent_lines(X,Y) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( ~ distinct_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)
& apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z)
& convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X] : ~ distinct_lines(X,X),
inference(canonicalize,[],[apart2]) ).
fof(normalize_0_8,plain,
! [X] : ~ distinct_lines(X,X),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_10,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y))
| ( ~ apart_point_and_line(Z,X)
& ~ apart_point_and_line(Z,Y) ) ),
inference(canonicalize,[],[con2]) ).
fof(normalize_0_11,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y))
| ( ~ apart_point_and_line(Z,X)
& ~ apart_point_and_line(Z,Y) ) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X,Y,Z] :
( ( ~ apart_point_and_line(Z,X)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) )
& ( ~ apart_point_and_line(Z,Y)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(Z,X)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
~ distinct_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_15,plain,
! [X] : ~ distinct_points(X,X),
inference(canonicalize,[],[apart1]) ).
fof(normalize_0_16,plain,
! [X] : ~ distinct_points(X,X),
inference(specialize,[],[normalize_0_15]) ).
cnf(refute_0_0,plain,
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ distinct_lines(X_33,X_32)
| distinct_lines(X_32,Z)
| distinct_lines(X_33,Z) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(X_33)),bind(Y,$fot(X_32))]]) ).
cnf(refute_0_2,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_31)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z)
| distinct_lines(X_31,Z) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Y,$fot(X_31))]]) ).
cnf(refute_0_4,plain,
apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_5,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_30)
| distinct_lines(skolemFOFtoCNF_Z,X_30) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Y,$fot(skolemFOFtoCNF_Z)),bind(Z,$fot(X_30))]]) ).
cnf(refute_0_6,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_30)
| distinct_lines(skolemFOFtoCNF_Z,X_30) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_31)
| distinct_lines(skolemFOFtoCNF_Z,X_31) ),
inference(subst,[],[refute_0_6:[bind(X_30,$fot(X_31))]]) ).
cnf(refute_0_8,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z)
| distinct_lines(X_31,Z)
| distinct_lines(skolemFOFtoCNF_Z,X_31) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_31) )],[refute_0_7,refute_0_3]) ).
cnf(refute_0_9,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_32)
| distinct_lines(X_33,X_32)
| distinct_lines(skolemFOFtoCNF_Z,X_33) ),
inference(subst,[],[refute_0_8:[bind(Z,$fot(X_32)),bind(X_31,$fot(X_33))]]) ).
cnf(refute_0_10,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_32)
| distinct_lines(X_32,Z)
| distinct_lines(X_33,Z)
| distinct_lines(skolemFOFtoCNF_Z,X_33) ),
inference(resolve,[$cnf( distinct_lines(X_33,X_32) )],[refute_0_9,refute_0_1]) ).
cnf(refute_0_11,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_32)
| distinct_lines(X_32,skolemFOFtoCNF_Z)
| distinct_lines(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_10:[bind(Z,$fot(skolemFOFtoCNF_Z)),bind(X_33,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_12,plain,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_13,plain,
~ distinct_lines(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z),
inference(subst,[],[refute_0_12:[bind(X,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_14,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_32)
| distinct_lines(X_32,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
| distinct_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_14:[bind(X_32,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_16,plain,
convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_17,plain,
( ~ apart_point_and_line(Z,X)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_18,plain,
( ~ apart_point_and_line(X_63,skolemFOFtoCNF_X)
| ~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| distinct_points(X_63,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(X_63))]]) ).
cnf(refute_0_19,plain,
( ~ apart_point_and_line(X_63,skolemFOFtoCNF_X)
| distinct_points(X_63,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_16,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
| distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_19:[bind(X_63,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_21,plain,
( distinct_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)
| distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X) )],[refute_0_15,refute_0_20]) ).
cnf(refute_0_22,plain,
~ distinct_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_23,plain,
distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
~ distinct_points(X,X),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_25,plain,
~ distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(subst,[],[refute_0_24:[bind(X,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_26,plain,
$false,
inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_23,refute_0_25]) ).
fof(negate_1_0,plain,
~ ! [X,Y,Z] :
( ( convergent_lines(X,Y)
& apart_point_and_line(intersection_point(X,Y),Z)
& distinct_lines(X,Z) )
=> distinct_lines(Y,Z) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[apart5]) ).
fof(normalize_1_1,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_2,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_3,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
? [X,Y,Z] :
( ~ distinct_lines(Y,Z)
& apart_point_and_line(intersection_point(X,Y),Z)
& convergent_lines(X,Y)
& distinct_lines(X,Z) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_5,plain,
( ~ distinct_lines(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Z_1)
& apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_Z_1)
& convergent_lines(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)
& distinct_lines(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1) ),
inference(skolemize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_Z_1),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [X] : ~ distinct_lines(X,X),
inference(canonicalize,[],[apart2]) ).
fof(normalize_1_8,plain,
! [X] : ~ distinct_lines(X,X),
inference(specialize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
convergent_lines(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_10,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y))
| ( ~ apart_point_and_line(Z,X)
& ~ apart_point_and_line(Z,Y) ) ),
inference(canonicalize,[],[con2]) ).
fof(normalize_1_11,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y))
| ( ~ apart_point_and_line(Z,X)
& ~ apart_point_and_line(Z,Y) ) ),
inference(specialize,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
! [X,Y,Z] :
( ( ~ apart_point_and_line(Z,X)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) )
& ( ~ apart_point_and_line(Z,Y)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ) ),
inference(clausify,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(Z,Y)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ),
inference(conjunct,[],[normalize_1_12]) ).
fof(normalize_1_14,plain,
~ distinct_lines(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Z_1),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_15,plain,
! [X] : ~ distinct_points(X,X),
inference(canonicalize,[],[apart1]) ).
fof(normalize_1_16,plain,
! [X] : ~ distinct_points(X,X),
inference(specialize,[],[normalize_1_15]) ).
cnf(refute_1_0,plain,
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_1_1]) ).
cnf(refute_1_1,plain,
( ~ distinct_lines(X_126,X_125)
| distinct_lines(X_125,Z)
| distinct_lines(X_126,Z) ),
inference(subst,[],[refute_1_0:[bind(X,$fot(X_126)),bind(Y,$fot(X_125))]]) ).
cnf(refute_1_2,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_3,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X_100)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),Z)
| distinct_lines(X_100,Z) ),
inference(subst,[],[refute_1_2:[bind(X,$fot(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))),bind(Y,$fot(X_100))]]) ).
cnf(refute_1_4,plain,
apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_Z_1),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_5,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_Z_1)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X_99)
| distinct_lines(skolemFOFtoCNF_Z_1,X_99) ),
inference(subst,[],[refute_1_2:[bind(X,$fot(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))),bind(Y,$fot(skolemFOFtoCNF_Z_1)),bind(Z,$fot(X_99))]]) ).
cnf(refute_1_6,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X_99)
| distinct_lines(skolemFOFtoCNF_Z_1,X_99) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_Z_1) )],[refute_1_4,refute_1_5]) ).
cnf(refute_1_7,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X_100)
| distinct_lines(skolemFOFtoCNF_Z_1,X_100) ),
inference(subst,[],[refute_1_6:[bind(X_99,$fot(X_100))]]) ).
cnf(refute_1_8,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),Z)
| distinct_lines(X_100,Z)
| distinct_lines(skolemFOFtoCNF_Z_1,X_100) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X_100) )],[refute_1_7,refute_1_3]) ).
cnf(refute_1_9,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X_125)
| distinct_lines(X_126,X_125)
| distinct_lines(skolemFOFtoCNF_Z_1,X_126) ),
inference(subst,[],[refute_1_8:[bind(Z,$fot(X_125)),bind(X_100,$fot(X_126))]]) ).
cnf(refute_1_10,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X_125)
| distinct_lines(X_125,Z)
| distinct_lines(X_126,Z)
| distinct_lines(skolemFOFtoCNF_Z_1,X_126) ),
inference(resolve,[$cnf( distinct_lines(X_126,X_125) )],[refute_1_9,refute_1_1]) ).
cnf(refute_1_11,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X_125)
| distinct_lines(X_125,skolemFOFtoCNF_Z_1)
| distinct_lines(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Z_1) ),
inference(subst,[],[refute_1_10:[bind(Z,$fot(skolemFOFtoCNF_Z_1)),bind(X_126,$fot(skolemFOFtoCNF_Z_1))]]) ).
cnf(refute_1_12,plain,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_13,plain,
~ distinct_lines(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Z_1),
inference(subst,[],[refute_1_12:[bind(X,$fot(skolemFOFtoCNF_Z_1))]]) ).
cnf(refute_1_14,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X_125)
| distinct_lines(X_125,skolemFOFtoCNF_Z_1) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Z_1) )],[refute_1_11,refute_1_13]) ).
cnf(refute_1_15,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_Y_1)
| distinct_lines(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Z_1) ),
inference(subst,[],[refute_1_14:[bind(X_125,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_1_16,plain,
convergent_lines(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),
inference(canonicalize,[],[normalize_1_9]) ).
cnf(refute_1_17,plain,
( ~ apart_point_and_line(Z,Y)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ),
inference(canonicalize,[],[normalize_1_13]) ).
cnf(refute_1_18,plain,
( ~ apart_point_and_line(X_152,skolemFOFtoCNF_Y_1)
| ~ convergent_lines(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)
| distinct_points(X_152,intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) ),
inference(subst,[],[refute_1_17:[bind(X,$fot(skolemFOFtoCNF_X_1)),bind(Y,$fot(skolemFOFtoCNF_Y_1)),bind(Z,$fot(X_152))]]) ).
cnf(refute_1_19,plain,
( ~ apart_point_and_line(X_152,skolemFOFtoCNF_Y_1)
| distinct_points(X_152,intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) )],[refute_1_16,refute_1_18]) ).
cnf(refute_1_20,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_Y_1)
| distinct_points(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) ),
inference(subst,[],[refute_1_19:[bind(X_152,$fot(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)))]]) ).
cnf(refute_1_21,plain,
( distinct_lines(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Z_1)
| distinct_points(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_Y_1) )],[refute_1_15,refute_1_20]) ).
cnf(refute_1_22,plain,
~ distinct_lines(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Z_1),
inference(canonicalize,[],[normalize_1_14]) ).
cnf(refute_1_23,plain,
distinct_points(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Z_1) )],[refute_1_21,refute_1_22]) ).
cnf(refute_1_24,plain,
~ distinct_points(X,X),
inference(canonicalize,[],[normalize_1_16]) ).
cnf(refute_1_25,plain,
~ distinct_points(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)),
inference(subst,[],[refute_1_24:[bind(X,$fot(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)))]]) ).
cnf(refute_1_26,plain,
$false,
inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) )],[refute_1_23,refute_1_25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : GEO192+2 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.15 % Command : metis --show proof --show saturation %s
% 0.15/0.37 % Computer : n017.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 600
% 0.15/0.37 % DateTime : Fri Jun 17 15:23:26 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.22/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.22/0.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.44
% 0.22/0.44 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.22/0.45
%------------------------------------------------------------------------------