TSTP Solution File: GEO205+2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO205+2 : TPTP v8.1.0. Released v3.3.0.
% 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 05:25:20 EDT 2022
% Result : Theorem 17.15s 17.36s
% Output : CNFRefutation 17.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 9
% Syntax : Number of formulae : 107 ( 31 unt; 0 def)
% Number of atoms : 265 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 255 ( 97 ~; 124 |; 22 &)
% ( 0 <=>; 12 =>; 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 : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 140 ( 0 sgn 88 !; 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(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(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] :
( convergent_lines(X,Y)
=> distinct_lines(X,Y) ) ).
fof(con,conjecture,
! [X,Y,Z] :
( ( convergent_lines(X,Y)
& ~ distinct_lines(Y,Z) )
=> ( convergent_lines(X,Z)
& ~ distinct_points(intersection_point(X,Y),intersection_point(X,Z)) ) ) ).
fof(subgoal_0,plain,
! [X,Y,Z] :
( ( convergent_lines(X,Y)
& ~ distinct_lines(Y,Z) )
=> convergent_lines(X,Z) ),
inference(strip,[],[con]) ).
fof(subgoal_1,plain,
! [X,Y,Z] :
( ( convergent_lines(X,Y)
& ~ distinct_lines(Y,Z)
& convergent_lines(X,Z) )
=> ~ distinct_points(intersection_point(X,Y),intersection_point(X,Z)) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [X,Y,Z] :
( ( convergent_lines(X,Y)
& ~ distinct_lines(Y,Z) )
=> convergent_lines(X,Z) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X,Y,Z] :
( ~ convergent_lines(X,Z)
& ~ distinct_lines(Y,Z)
& convergent_lines(X,Y) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)
& ~ distinct_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
& convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ distinct_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( ~ convergent_lines(X,Y)
| distinct_lines(X,Y) ),
inference(canonicalize,[],[ceq3]) ).
fof(normalize_0_4,plain,
! [X,Y] :
( ~ convergent_lines(X,Y)
| distinct_lines(X,Y) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_6,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[apart6]) ).
fof(normalize_0_7,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
~ distinct_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ convergent_lines(X,Y)
| distinct_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( ~ convergent_lines(skolemFOFtoCNF_Y,X_8)
| distinct_lines(skolemFOFtoCNF_Y,X_8) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_3,plain,
convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| convergent_lines(skolemFOFtoCNF_X,X_7)
| convergent_lines(skolemFOFtoCNF_Y,X_7) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(X_7))]]) ).
cnf(refute_0_6,plain,
( convergent_lines(skolemFOFtoCNF_X,X_7)
| convergent_lines(skolemFOFtoCNF_Y,X_7) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
( convergent_lines(skolemFOFtoCNF_X,X_8)
| convergent_lines(skolemFOFtoCNF_Y,X_8) ),
inference(subst,[],[refute_0_6:[bind(X_7,$fot(X_8))]]) ).
cnf(refute_0_8,plain,
( convergent_lines(skolemFOFtoCNF_X,X_8)
| distinct_lines(skolemFOFtoCNF_Y,X_8) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_Y,X_8) )],[refute_0_7,refute_0_2]) ).
cnf(refute_0_9,plain,
( convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)
| distinct_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_8:[bind(X_8,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_10,plain,
convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_0_9,refute_0_0]) ).
cnf(refute_0_11,plain,
~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_12,plain,
$false,
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z) )],[refute_0_10,refute_0_11]) ).
fof(negate_1_0,plain,
~ ! [X,Y,Z] :
( ( convergent_lines(X,Y)
& ~ distinct_lines(Y,Z)
& convergent_lines(X,Z) )
=> ~ distinct_points(intersection_point(X,Y),intersection_point(X,Z)) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [X] : ~ distinct_lines(X,X),
inference(canonicalize,[],[apart2]) ).
fof(normalize_1_1,plain,
! [X] : ~ distinct_lines(X,X),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[apart5]) ).
fof(normalize_1_3,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
? [X,Y,Z] :
( ~ distinct_lines(Y,Z)
& convergent_lines(X,Y)
& convergent_lines(X,Z)
& distinct_points(intersection_point(X,Y),intersection_point(X,Z)) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_5,plain,
( ~ distinct_lines(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Z_1)
& convergent_lines(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)
& convergent_lines(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)
& distinct_points(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)) ),
inference(skolemize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
convergent_lines(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,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_8,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_7]) ).
fof(normalize_1_9,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_8]) ).
fof(normalize_1_10,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(Z,X)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ),
inference(conjunct,[],[normalize_1_9]) ).
fof(normalize_1_11,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_9]) ).
fof(normalize_1_12,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_13,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_1_12]) ).
fof(normalize_1_14,plain,
convergent_lines(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_15,plain,
! [X,Y] :
( ~ convergent_lines(X,Y)
| distinct_lines(X,Y) ),
inference(canonicalize,[],[ceq3]) ).
fof(normalize_1_16,plain,
! [X,Y] :
( ~ convergent_lines(X,Y)
| distinct_lines(X,Y) ),
inference(specialize,[],[normalize_1_15]) ).
fof(normalize_1_17,plain,
distinct_points(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_18,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_1_19,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_1_18]) ).
fof(normalize_1_20,plain,
! [X] : ~ distinct_points(X,X),
inference(canonicalize,[],[apart1]) ).
fof(normalize_1_21,plain,
! [X] : ~ distinct_points(X,X),
inference(specialize,[],[normalize_1_20]) ).
fof(normalize_1_22,plain,
~ distinct_lines(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Z_1),
inference(conjunct,[],[normalize_1_5]) ).
cnf(refute_1_0,plain,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_1_1]) ).
cnf(refute_1_1,plain,
~ distinct_lines(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Z_1),
inference(subst,[],[refute_1_0:[bind(X,$fot(skolemFOFtoCNF_Z_1))]]) ).
cnf(refute_1_2,plain,
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_3,plain,
( ~ distinct_lines(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1)
| distinct_lines(skolemFOFtoCNF_Y_1,Z)
| distinct_lines(skolemFOFtoCNF_Z_1,Z) ),
inference(subst,[],[refute_1_2:[bind(X,$fot(skolemFOFtoCNF_Z_1)),bind(Y,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_1_4,plain,
convergent_lines(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_5,plain,
( ~ apart_point_and_line(Z,X)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_6,plain,
( ~ apart_point_and_line(X_77,skolemFOFtoCNF_X_1)
| ~ convergent_lines(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)
| distinct_points(X_77,intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) ),
inference(subst,[],[refute_1_5:[bind(X,$fot(skolemFOFtoCNF_X_1)),bind(Y,$fot(skolemFOFtoCNF_Y_1)),bind(Z,$fot(X_77))]]) ).
cnf(refute_1_7,plain,
( ~ apart_point_and_line(X_77,skolemFOFtoCNF_X_1)
| distinct_points(X_77,intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) )],[refute_1_4,refute_1_6]) ).
cnf(refute_1_8,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_X_1)
| distinct_points(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) ),
inference(subst,[],[refute_1_7:[bind(X_77,$fot(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)))]]) ).
cnf(refute_1_9,plain,
( ~ apart_point_and_line(Z,Y)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_10,plain,
( ~ apart_point_and_line(X_84,skolemFOFtoCNF_Y_1)
| ~ convergent_lines(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)
| distinct_points(X_84,intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) ),
inference(subst,[],[refute_1_9:[bind(X,$fot(skolemFOFtoCNF_X_1)),bind(Y,$fot(skolemFOFtoCNF_Y_1)),bind(Z,$fot(X_84))]]) ).
cnf(refute_1_11,plain,
( ~ apart_point_and_line(X_84,skolemFOFtoCNF_Y_1)
| distinct_points(X_84,intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) )],[refute_1_4,refute_1_10]) ).
cnf(refute_1_12,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_11:[bind(X_84,$fot(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)))]]) ).
cnf(refute_1_13,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_1_13]) ).
cnf(refute_1_14,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_Z_1)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),Z)
| distinct_lines(skolemFOFtoCNF_Z_1,Z) ),
inference(subst,[],[refute_1_13:[bind(X,$fot(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))),bind(Y,$fot(skolemFOFtoCNF_Z_1))]]) ).
cnf(refute_1_15,plain,
convergent_lines(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1),
inference(canonicalize,[],[normalize_1_14]) ).
cnf(refute_1_16,plain,
( ~ apart_point_and_line(X_77,skolemFOFtoCNF_X_1)
| ~ convergent_lines(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)
| distinct_points(X_77,intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)) ),
inference(subst,[],[refute_1_5:[bind(X,$fot(skolemFOFtoCNF_X_1)),bind(Y,$fot(skolemFOFtoCNF_Z_1)),bind(Z,$fot(X_77))]]) ).
cnf(refute_1_17,plain,
( ~ apart_point_and_line(X_77,skolemFOFtoCNF_X_1)
| distinct_points(X_77,intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1) )],[refute_1_15,refute_1_16]) ).
cnf(refute_1_18,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1),skolemFOFtoCNF_X_1)
| distinct_points(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1),intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)) ),
inference(subst,[],[refute_1_17:[bind(X_77,$fot(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)))]]) ).
cnf(refute_1_19,plain,
( ~ apart_point_and_line(X_84,skolemFOFtoCNF_Z_1)
| ~ convergent_lines(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)
| distinct_points(X_84,intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)) ),
inference(subst,[],[refute_1_9:[bind(X,$fot(skolemFOFtoCNF_X_1)),bind(Y,$fot(skolemFOFtoCNF_Z_1)),bind(Z,$fot(X_84))]]) ).
cnf(refute_1_20,plain,
( ~ apart_point_and_line(X_84,skolemFOFtoCNF_Z_1)
| distinct_points(X_84,intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1) )],[refute_1_15,refute_1_19]) ).
cnf(refute_1_21,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1),skolemFOFtoCNF_Z_1)
| distinct_points(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1),intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)) ),
inference(subst,[],[refute_1_20:[bind(X_84,$fot(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)))]]) ).
cnf(refute_1_22,plain,
( ~ convergent_lines(X,Y)
| distinct_lines(X,Y) ),
inference(canonicalize,[],[normalize_1_16]) ).
cnf(refute_1_23,plain,
( ~ convergent_lines(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)
| distinct_lines(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1) ),
inference(subst,[],[refute_1_22:[bind(X,$fot(skolemFOFtoCNF_X_1)),bind(Y,$fot(skolemFOFtoCNF_Z_1))]]) ).
cnf(refute_1_24,plain,
distinct_lines(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1) )],[refute_1_15,refute_1_23]) ).
cnf(refute_1_25,plain,
distinct_points(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)),
inference(canonicalize,[],[normalize_1_17]) ).
cnf(refute_1_26,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_1_19]) ).
cnf(refute_1_27,plain,
( ~ distinct_lines(X_578,X_579)
| ~ distinct_points(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1))
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X_578)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X_579)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1),X_578)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1),X_579) ),
inference(subst,[],[refute_1_26:[bind(U,$fot(X_578)),bind(V,$fot(X_579)),bind(X,$fot(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))),bind(Y,$fot(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)))]]) ).
cnf(refute_1_28,plain,
( ~ distinct_lines(X_578,X_579)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X_578)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X_579)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1),X_578)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1),X_579) ),
inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)) )],[refute_1_25,refute_1_27]) ).
cnf(refute_1_29,plain,
( ~ distinct_lines(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_X_1)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_Z_1)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1),skolemFOFtoCNF_X_1)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1),skolemFOFtoCNF_Z_1) ),
inference(subst,[],[refute_1_28:[bind(X_578,$fot(skolemFOFtoCNF_X_1)),bind(X_579,$fot(skolemFOFtoCNF_Z_1))]]) ).
cnf(refute_1_30,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_X_1)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_Z_1)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1),skolemFOFtoCNF_X_1)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1),skolemFOFtoCNF_Z_1) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1) )],[refute_1_24,refute_1_29]) ).
cnf(refute_1_31,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_X_1)
| 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_Z_1),skolemFOFtoCNF_X_1)
| distinct_points(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1),intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1),skolemFOFtoCNF_Z_1) )],[refute_1_30,refute_1_21]) ).
cnf(refute_1_32,plain,
~ distinct_points(X,X),
inference(canonicalize,[],[normalize_1_21]) ).
cnf(refute_1_33,plain,
~ distinct_points(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1),intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)),
inference(subst,[],[refute_1_32:[bind(X,$fot(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)))]]) ).
cnf(refute_1_34,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_X_1)
| 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_Z_1),skolemFOFtoCNF_X_1) ),
inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1),intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)) )],[refute_1_31,refute_1_33]) ).
cnf(refute_1_35,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_X_1)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_Z_1)
| distinct_points(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1),intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1),skolemFOFtoCNF_X_1) )],[refute_1_34,refute_1_18]) ).
cnf(refute_1_36,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_X_1)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_Z_1) ),
inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1),intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)) )],[refute_1_35,refute_1_33]) ).
cnf(refute_1_37,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),Z)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_X_1)
| distinct_lines(skolemFOFtoCNF_Z_1,Z) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_Z_1) )],[refute_1_36,refute_1_14]) ).
cnf(refute_1_38,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_X_1)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_Y_1)
| distinct_lines(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1) ),
inference(subst,[],[refute_1_37:[bind(Z,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_1_39,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_X_1)
| distinct_lines(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1)
| distinct_points(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_Y_1) )],[refute_1_38,refute_1_12]) ).
cnf(refute_1_40,plain,
~ distinct_points(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)),
inference(subst,[],[refute_1_32:[bind(X,$fot(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)))]]) ).
cnf(refute_1_41,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_X_1)
| distinct_lines(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1) ),
inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) )],[refute_1_39,refute_1_40]) ).
cnf(refute_1_42,plain,
( distinct_lines(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1)
| distinct_points(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_X_1) )],[refute_1_41,refute_1_8]) ).
cnf(refute_1_43,plain,
distinct_lines(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1),
inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) )],[refute_1_42,refute_1_40]) ).
cnf(refute_1_44,plain,
( distinct_lines(skolemFOFtoCNF_Y_1,Z)
| distinct_lines(skolemFOFtoCNF_Z_1,Z) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1) )],[refute_1_43,refute_1_3]) ).
cnf(refute_1_45,plain,
( distinct_lines(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Z_1)
| distinct_lines(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Z_1) ),
inference(subst,[],[refute_1_44:[bind(Z,$fot(skolemFOFtoCNF_Z_1))]]) ).
cnf(refute_1_46,plain,
distinct_lines(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Z_1),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Z_1) )],[refute_1_45,refute_1_1]) ).
cnf(refute_1_47,plain,
~ distinct_lines(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Z_1),
inference(canonicalize,[],[normalize_1_22]) ).
cnf(refute_1_48,plain,
$false,
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Z_1) )],[refute_1_46,refute_1_47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO205+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 18 16:11:43 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 17.15/17.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.15/17.36
% 17.15/17.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 17.15/17.37
%------------------------------------------------------------------------------