TSTP Solution File: GEO202+3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO202+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 05:25:17 EDT 2022
% Result : Theorem 48.14s 48.37s
% Output : CNFRefutation 48.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 15
% Syntax : Number of formulae : 124 ( 37 unt; 0 def)
% Number of atoms : 298 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 263 ( 89 ~; 149 |; 13 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 194 ( 4 sgn 105 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X] : ~ distinct_points(X,X) ).
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(ax6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| convergent_lines(Y,Z) ) ) ).
fof(ci1,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ) ).
fof(ci2,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(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(ceq1,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( distinct_points(X,Z)
| apart_point_and_line(Z,Y) ) ) ).
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,Z] :
( ( distinct_points(X,Y)
& distinct_points(X,Z)
& convergent_lines(line_connecting(X,Y),line_connecting(X,Z)) )
=> equal_points(intersection_point(line_connecting(X,Y),line_connecting(X,Z)),X) ) ).
fof(subgoal_0,plain,
! [X,Y,Z] :
( ( distinct_points(X,Y)
& distinct_points(X,Z)
& convergent_lines(line_connecting(X,Y),line_connecting(X,Z)) )
=> equal_points(intersection_point(line_connecting(X,Y),line_connecting(X,Z)),X) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [X,Y,Z] :
( ( distinct_points(X,Y)
& distinct_points(X,Z)
& convergent_lines(line_connecting(X,Y),line_connecting(X,Z)) )
=> equal_points(intersection_point(line_connecting(X,Y),line_connecting(X,Z)),X) ),
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] : ~ distinct_lines(X,X),
inference(canonicalize,[],[apart2]) ).
fof(normalize_0_7,plain,
! [X] : ~ distinct_lines(X,X),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[apart5]) ).
fof(normalize_0_9,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_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,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(canonicalize,[],[ceq1]) ).
fof(normalize_0_13,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[ci1]) ).
fof(normalize_0_15,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[ci2]) ).
fof(normalize_0_17,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[ceq3]) ).
fof(normalize_0_19,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[ax6]) ).
fof(normalize_0_21,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
? [X,Y,Z] :
( ~ equal_points(intersection_point(line_connecting(X,Y),line_connecting(X,Z)),X)
& convergent_lines(line_connecting(X,Y),line_connecting(X,Z))
& distinct_points(X,Y)
& distinct_points(X,Z) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_23,plain,
( ~ equal_points(intersection_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)),skolemFOFtoCNF_X)
& convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))
& distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
& distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Z) ),
inference(skolemize,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [X] : ~ convergent_lines(X,X),
inference(canonicalize,[],[apart3]) ).
fof(normalize_0_26,plain,
! [X] : ~ convergent_lines(X,X),
inference(specialize,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_28,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_29,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_28]) ).
fof(normalize_0_30,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_31,plain,
! [X] : ~ distinct_points(X,X),
inference(canonicalize,[],[apart1]) ).
fof(normalize_0_32,plain,
! [X] : ~ distinct_points(X,X),
inference(specialize,[],[normalize_0_31]) ).
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_Z,parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z)),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_Z)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
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_X,skolemFOFtoCNF_Y),X),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(subst,[],[refute_0_2:[bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_4,plain,
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_5,plain,
( ~ distinct_lines(X_12972,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| convergent_lines(X_12972,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_12972)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_6,plain,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_7,plain,
~ distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(subst,[],[refute_0_6:[bind(X,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_8,plain,
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_9,plain,
( ~ distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_12810)
| distinct_lines(X_12810,Z)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Y,$fot(X_12810))]]) ).
cnf(refute_0_10,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_11,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Z,Z)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(skolemFOFtoCNF_Z)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_12,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_13,plain,
( ~ apart_point_and_line(X_12809,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(X_12809,Z) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_12809)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_14,plain,
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_15,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_16,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))
| ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_17,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Z,Z) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(skolemFOFtoCNF_Z)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_18,plain,
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_19,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))
| ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_20,plain,
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_21,plain,
( ~ convergent_lines(X_172,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| convergent_lines(X_172,Z)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(X_172)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_22,plain,
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_23,plain,
( ~ convergent_lines(X_169,X_168)
| convergent_lines(X_168,Z)
| convergent_lines(X_169,Z) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(X_169)),bind(Y,$fot(X_168))]]) ).
cnf(refute_0_24,plain,
( ~ convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),X_69)
| convergent_lines(X_69,Z)
| convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),Z) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))),bind(Y,$fot(X_69))]]) ).
cnf(refute_0_25,plain,
convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_26,plain,
( ~ convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))
| convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_68)
| convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),X_68) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))),bind(Z,$fot(X_68))]]) ).
cnf(refute_0_27,plain,
( convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_68)
| convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),X_68) ),
inference(resolve,[$cnf( convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_69)
| convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),X_69) ),
inference(subst,[],[refute_0_27:[bind(X_68,$fot(X_69))]]) ).
cnf(refute_0_29,plain,
( convergent_lines(X_69,Z)
| convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_69)
| convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),Z) ),
inference(resolve,[$cnf( convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),X_69) )],[refute_0_28,refute_0_24]) ).
cnf(refute_0_30,plain,
( convergent_lines(X_169,X_168)
| convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_169)
| convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),X_168) ),
inference(subst,[],[refute_0_29:[bind(Z,$fot(X_168)),bind(X_69,$fot(X_169))]]) ).
cnf(refute_0_31,plain,
( convergent_lines(X_168,Z)
| convergent_lines(X_169,Z)
| convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_169)
| convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),X_168) ),
inference(resolve,[$cnf( convergent_lines(X_169,X_168) )],[refute_0_30,refute_0_23]) ).
cnf(refute_0_32,plain,
( convergent_lines(X_168,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),X_168) ),
inference(subst,[],[refute_0_31:[bind(Z,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(X_169,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_33,plain,
~ convergent_lines(X,X),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_34,plain,
~ convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(subst,[],[refute_0_33:[bind(X,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_35,plain,
( convergent_lines(X_168,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),X_168) ),
inference(resolve,[$cnf( convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_32,refute_0_34]) ).
cnf(refute_0_36,plain,
( convergent_lines(X_172,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),X_172) ),
inference(subst,[],[refute_0_35:[bind(X_168,$fot(X_172))]]) ).
cnf(refute_0_37,plain,
( convergent_lines(X_172,Z)
| convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),X_172)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z) ),
inference(resolve,[$cnf( convergent_lines(X_172,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_36,refute_0_21]) ).
cnf(refute_0_38,plain,
( convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)) ),
inference(subst,[],[refute_0_37:[bind(Z,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))),bind(X_172,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)))]]) ).
cnf(refute_0_39,plain,
~ convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)),
inference(subst,[],[refute_0_33:[bind(X,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)))]]) ).
cnf(refute_0_40,plain,
distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)),
inference(resolve,[$cnf( convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_42,plain,
( ~ distinct_lines(U,V)
| ~ distinct_points(X,Y)
| apart_point_and_line(X,U)
| apart_point_and_line(X,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(Y,V) ),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_43,plain,
( ~ distinct_lines(X_7310,X_7311)
| ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)
| apart_point_and_line(skolemFOFtoCNF_X,X_7310)
| apart_point_and_line(skolemFOFtoCNF_X,X_7311)
| apart_point_and_line(skolemFOFtoCNF_Z,X_7310)
| apart_point_and_line(skolemFOFtoCNF_Z,X_7311) ),
inference(subst,[],[refute_0_42:[bind(U,$fot(X_7310)),bind(V,$fot(X_7311)),bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_44,plain,
( ~ distinct_lines(X_7310,X_7311)
| apart_point_and_line(skolemFOFtoCNF_X,X_7310)
| apart_point_and_line(skolemFOFtoCNF_X,X_7311)
| apart_point_and_line(skolemFOFtoCNF_Z,X_7310)
| apart_point_and_line(skolemFOFtoCNF_Z,X_7311) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Z) )],[refute_0_41,refute_0_43]) ).
cnf(refute_0_45,plain,
( ~ distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))
| apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)) ),
inference(subst,[],[refute_0_44:[bind(X_7310,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(X_7311,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)))]]) ).
cnf(refute_0_46,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))
| apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)) )],[refute_0_40,refute_0_45]) ).
cnf(refute_0_47,plain,
( ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))
| apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)) )],[refute_0_46,refute_0_19]) ).
cnf(refute_0_48,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))
| apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Z) )],[refute_0_41,refute_0_47]) ).
cnf(refute_0_49,plain,
( apart_point_and_line(Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))
| distinct_points(skolemFOFtoCNF_Z,Z) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_48,refute_0_17]) ).
cnf(refute_0_50,plain,
( apart_point_and_line(X_12806,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))
| distinct_points(skolemFOFtoCNF_Z,X_12806) ),
inference(subst,[],[refute_0_49:[bind(Z,$fot(X_12806))]]) ).
cnf(refute_0_51,plain,
( ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)
| apart_point_and_line(X_12806,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Z,X_12806) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)) )],[refute_0_50,refute_0_16]) ).
cnf(refute_0_52,plain,
( apart_point_and_line(X_12806,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Z,X_12806) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Z) )],[refute_0_41,refute_0_51]) ).
cnf(refute_0_53,plain,
( apart_point_and_line(X_12808,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Z,X_12808) ),
inference(subst,[],[refute_0_52:[bind(X_12806,$fot(X_12808))]]) ).
cnf(refute_0_54,plain,
( ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| apart_point_and_line(X_12808,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Z,X_12808) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_53,refute_0_15]) ).
cnf(refute_0_55,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_56,plain,
( apart_point_and_line(X_12808,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Z,X_12808) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_55,refute_0_54]) ).
cnf(refute_0_57,plain,
( apart_point_and_line(X_12809,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Z,X_12809) ),
inference(subst,[],[refute_0_56:[bind(X_12808,$fot(X_12809))]]) ).
cnf(refute_0_58,plain,
( apart_point_and_line(Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(X_12809,Z)
| distinct_points(skolemFOFtoCNF_Z,X_12809) ),
inference(resolve,[$cnf( apart_point_and_line(X_12809,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_57,refute_0_13]) ).
cnf(refute_0_59,plain,
( apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_58:[bind(Z,$fot(skolemFOFtoCNF_Z)),bind(X_12809,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_60,plain,
~ distinct_points(X,X),
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_61,plain,
~ distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z),
inference(subst,[],[refute_0_60:[bind(X,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_62,plain,
apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) )],[refute_0_59,refute_0_61]) ).
cnf(refute_0_63,plain,
( apart_point_and_line(skolemFOFtoCNF_Z,Z)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_62,refute_0_11]) ).
cnf(refute_0_64,plain,
( apart_point_and_line(skolemFOFtoCNF_Z,X_12810)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_12810) ),
inference(subst,[],[refute_0_63:[bind(Z,$fot(X_12810))]]) ).
cnf(refute_0_65,plain,
( apart_point_and_line(skolemFOFtoCNF_Z,X_12810)
| distinct_lines(X_12810,Z)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_12810) )],[refute_0_64,refute_0_9]) ).
cnf(refute_0_66,plain,
( apart_point_and_line(skolemFOFtoCNF_Z,X_12971)
| distinct_lines(X_12971,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_65:[bind(Z,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(X_12810,$fot(X_12971))]]) ).
cnf(refute_0_67,plain,
( apart_point_and_line(skolemFOFtoCNF_Z,X_12971)
| distinct_lines(X_12971,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_66,refute_0_7]) ).
cnf(refute_0_68,plain,
( apart_point_and_line(skolemFOFtoCNF_Z,X_12972)
| distinct_lines(X_12972,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_67:[bind(X_12971,$fot(X_12972))]]) ).
cnf(refute_0_69,plain,
( apart_point_and_line(skolemFOFtoCNF_Z,X_12972)
| convergent_lines(X_12972,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( distinct_lines(X_12972,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_68,refute_0_5]) ).
cnf(refute_0_70,plain,
( apart_point_and_line(skolemFOFtoCNF_Z,parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X))
| convergent_lines(parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_69:[bind(X_12972,$fot(parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X)))]]) ).
cnf(refute_0_71,plain,
apart_point_and_line(skolemFOFtoCNF_Z,parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X)),
inference(resolve,[$cnf( convergent_lines(parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_70,refute_0_3]) ).
cnf(refute_0_72,plain,
apart_point_and_line(skolemFOFtoCNF_Z,parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z)),
inference(subst,[],[refute_0_71:[bind(X,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_73,plain,
$false,
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Z,parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z)) )],[refute_0_72,refute_0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO202+3 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n022.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 : Fri Jun 17 17:06:47 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 48.14/48.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 48.14/48.37
% 48.14/48.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 48.14/48.38
%------------------------------------------------------------------------------