TSTP Solution File: GEO197+2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO197+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 05:25:13 EDT 2022
% Result : Theorem 139.68s 139.90s
% Output : CNFRefutation 139.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of formulae : 82 ( 26 unt; 0 def)
% Number of atoms : 211 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 207 ( 78 ~; 99 |; 21 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 108 ( 0 sgn 69 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X] : ~ distinct_points(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(apart6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| convergent_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(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(ceq3,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> distinct_lines(X,Y) ) ).
fof(con,conjecture,
! [X,Y,Z] :
( ( convergent_lines(X,Y)
& convergent_lines(Z,Y)
& convergent_lines(X,Z)
& ~ apart_point_and_line(intersection_point(X,Y),Z) )
=> ~ apart_point_and_line(intersection_point(Z,Y),X) ) ).
fof(subgoal_0,plain,
! [X,Y,Z] :
( ( convergent_lines(X,Y)
& convergent_lines(Z,Y)
& convergent_lines(X,Z)
& ~ apart_point_and_line(intersection_point(X,Y),Z) )
=> ~ apart_point_and_line(intersection_point(Z,Y),X) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [X,Y,Z] :
( ( convergent_lines(X,Y)
& convergent_lines(Z,Y)
& convergent_lines(X,Z)
& ~ apart_point_and_line(intersection_point(X,Y),Z) )
=> ~ apart_point_and_line(intersection_point(Z,Y),X) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X,Y,Z] :
( ~ apart_point_and_line(intersection_point(X,Y),Z)
& apart_point_and_line(intersection_point(Z,Y),X)
& convergent_lines(X,Y)
& convergent_lines(X,Z)
& convergent_lines(Z,Y) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z)
& apart_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
& convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
& convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)
& convergent_lines(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,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_4,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_3]) ).
fof(normalize_0_5,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_4]) ).
fof(normalize_0_6,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(Z,Y)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
convergent_lines(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_8,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_5]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ convergent_lines(X,Y)
| distinct_lines(X,Y) ),
inference(canonicalize,[],[ceq3]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ~ convergent_lines(X,Y)
| distinct_lines(X,Y) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X] : ~ convergent_lines(X,X),
inference(canonicalize,[],[apart3]) ).
fof(normalize_0_12,plain,
! [X] : ~ convergent_lines(X,X),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[apart6]) ).
fof(normalize_0_14,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(specialize,[],[normalize_0_13]) ).
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]) ).
fof(normalize_0_17,plain,
! [X,Y,Z] :
( ~ distinct_points(X,Y)
| distinct_points(X,Z)
| distinct_points(Y,Z) ),
inference(canonicalize,[],[apart4]) ).
fof(normalize_0_18,plain,
! [X,Y,Z] :
( ~ distinct_points(X,Y)
| distinct_points(X,Z)
| distinct_points(Y,Z) ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
apart_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),skolemFOFtoCNF_X),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_20,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_21,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_20]) ).
fof(normalize_0_22,plain,
~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ apart_point_and_line(Z,Y)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( ~ apart_point_and_line(X_103,skolemFOFtoCNF_Y)
| ~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| distinct_points(X_103,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(X_103))]]) ).
cnf(refute_0_3,plain,
( ~ apart_point_and_line(X_103,skolemFOFtoCNF_Y)
| distinct_points(X_103,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Y)
| distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_3:[bind(X_103,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_5,plain,
convergent_lines(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_6,plain,
( ~ apart_point_and_line(X_103,skolemFOFtoCNF_Y)
| ~ convergent_lines(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)
| distinct_points(X_103,intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(skolemFOFtoCNF_Z)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(X_103))]]) ).
cnf(refute_0_7,plain,
( ~ apart_point_and_line(X_103,skolemFOFtoCNF_Y)
| distinct_points(X_103,intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),skolemFOFtoCNF_Y)
| distinct_points(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_7:[bind(X_103,$fot(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_9,plain,
( ~ apart_point_and_line(Z,X)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_10,plain,
( ~ apart_point_and_line(X_88,skolemFOFtoCNF_Z)
| ~ convergent_lines(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)
| distinct_points(X_88,intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(skolemFOFtoCNF_Z)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(X_88))]]) ).
cnf(refute_0_11,plain,
( ~ apart_point_and_line(X_88,skolemFOFtoCNF_Z)
| distinct_points(X_88,intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y) )],[refute_0_5,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z)
| distinct_points(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_11:[bind(X_88,$fot(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_13,plain,
( ~ convergent_lines(X,Y)
| distinct_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_14,plain,
( ~ convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| distinct_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_15,plain,
~ convergent_lines(X,X),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_16,plain,
~ convergent_lines(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z),
inference(subst,[],[refute_0_15:[bind(X,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_17,plain,
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_18,plain,
( ~ convergent_lines(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)
| convergent_lines(skolemFOFtoCNF_Y,X_7)
| convergent_lines(skolemFOFtoCNF_Z,X_7) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(skolemFOFtoCNF_Z)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(X_7))]]) ).
cnf(refute_0_19,plain,
( convergent_lines(skolemFOFtoCNF_Y,X_7)
| convergent_lines(skolemFOFtoCNF_Z,X_7) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y) )],[refute_0_5,refute_0_18]) ).
cnf(refute_0_20,plain,
( convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| convergent_lines(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_19:[bind(X_7,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_21,plain,
convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) )],[refute_0_20,refute_0_16]) ).
cnf(refute_0_22,plain,
distinct_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_0_21,refute_0_14]) ).
cnf(refute_0_23,plain,
~ distinct_points(X,X),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_24,plain,
~ distinct_points(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)),
inference(subst,[],[refute_0_23:[bind(X,$fot(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_25,plain,
( ~ distinct_points(X,Y)
| distinct_points(X,Z)
| distinct_points(Y,Z) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_26,plain,
( ~ distinct_points(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z)
| distinct_points(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),Z) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))),bind(Y,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_27,plain,
apart_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_28,plain,
( ~ apart_point_and_line(X_88,skolemFOFtoCNF_X)
| ~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| distinct_points(X_88,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(X_88))]]) ).
cnf(refute_0_29,plain,
( ~ apart_point_and_line(X_88,skolemFOFtoCNF_X)
| distinct_points(X_88,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_0,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
| distinct_points(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_29:[bind(X_88,$fot(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_31,plain,
distinct_points(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),skolemFOFtoCNF_X) )],[refute_0_27,refute_0_30]) ).
cnf(refute_0_32,plain,
( distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z)
| distinct_points(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),Z) ),
inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_31,refute_0_26]) ).
cnf(refute_0_33,plain,
( distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| distinct_points(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_32:[bind(Z,$fot(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_34,plain,
distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)),
inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) )],[refute_0_33,refute_0_24]) ).
cnf(refute_0_35,plain,
( ~ distinct_lines(U,V)
| ~ distinct_points(X,Y)
| apart_point_and_line(X,U)
| apart_point_and_line(X,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(Y,V) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_36,plain,
( ~ distinct_lines(X_1919,X_1920)
| ~ distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_1919)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_1920)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),X_1919)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),X_1920) ),
inference(subst,[],[refute_0_35:[bind(U,$fot(X_1919)),bind(V,$fot(X_1920)),bind(X,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Y,$fot(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_37,plain,
( ~ distinct_lines(X_1919,X_1920)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_1919)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_1920)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),X_1919)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),X_1920) ),
inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) )],[refute_0_34,refute_0_36]) ).
cnf(refute_0_38,plain,
( ~ distinct_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Y)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),skolemFOFtoCNF_Y)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_37:[bind(X_1919,$fot(skolemFOFtoCNF_Y)),bind(X_1920,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_39,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Y)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),skolemFOFtoCNF_Y)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_0_22,refute_0_38]) ).
cnf(refute_0_40,plain,
~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_41,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Y)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),skolemFOFtoCNF_Y)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Y)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),skolemFOFtoCNF_Y)
| distinct_points(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z) )],[refute_0_41,refute_0_12]) ).
cnf(refute_0_43,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Y)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) )],[refute_0_42,refute_0_24]) ).
cnf(refute_0_44,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Y)
| distinct_points(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),skolemFOFtoCNF_Y) )],[refute_0_43,refute_0_8]) ).
cnf(refute_0_45,plain,
apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Y),
inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) )],[refute_0_44,refute_0_24]) ).
cnf(refute_0_46,plain,
distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Y) )],[refute_0_45,refute_0_4]) ).
cnf(refute_0_47,plain,
~ distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(subst,[],[refute_0_23:[bind(X,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_48,plain,
$false,
inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_46,refute_0_47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO197+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 18 09:58:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 139.68/139.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 139.68/139.90
% 139.68/139.90 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 139.68/139.90
%------------------------------------------------------------------------------