%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO202+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n006.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 1.53s 1.69s
% Output : CNFRefutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 8
% Syntax : Number of formulae : 74 ( 18 unt; 0 def)
% Number of atoms : 190 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 179 ( 63 ~; 94 |; 13 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 106 ( 0 sgn 60 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart3,axiom,
! [X] : ~ convergent_lines(X,X) ).
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(ci3,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),X) ) ).
fof(ci4,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),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,Z] :
( convergent_lines(X,Y)
=> ( distinct_lines(Y,Z)
| convergent_lines(X,Z) ) ) ).
fof(con,conjecture,
! [X,Y,Z] :
( ( distinct_points(X,Y)
& distinct_points(X,Z)
& convergent_lines(line_connecting(X,Y),line_connecting(X,Z)) )
=> ~ distinct_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)) )
=> ~ distinct_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)) )
=> ~ distinct_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,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[ci1]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(canonicalize,[],[ci3]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(canonicalize,[],[ci4]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [X,Y,Z] :
( convergent_lines(line_connecting(X,Y),line_connecting(X,Z))
& distinct_points(X,Y)
& distinct_points(X,Z)
& distinct_points(intersection_point(line_connecting(X,Y),line_connecting(X,Z)),X) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_7,plain,
( convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))
& distinct_points(intersection_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)),skolemFOFtoCNF_X)
& distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
& distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Z) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
distinct_points(intersection_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)),skolemFOFtoCNF_X),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[ceq3]) ).
fof(normalize_0_10,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[ax6]) ).
fof(normalize_0_12,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_14,plain,
! [X] : ~ convergent_lines(X,X),
inference(canonicalize,[],[apart3]) ).
fof(normalize_0_15,plain,
! [X] : ~ convergent_lines(X,X),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,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_17,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_16]) ).
fof(normalize_0_18,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_19,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(conjunct,[],[normalize_0_7]) ).
cnf(refute_0_0,plain,
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_2,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))
| ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_3,plain,
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_4,plain,
( ~ apart_point_and_line(intersection_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| ~ convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)))]]) ).
cnf(refute_0_5,plain,
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_6,plain,
( ~ apart_point_and_line(intersection_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))
| ~ convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)))]]) ).
cnf(refute_0_7,plain,
distinct_points(intersection_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)),skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_8,plain,
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_9,plain,
( ~ convergent_lines(X_49,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| convergent_lines(X_49,Z)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_49)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_10,plain,
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_11,plain,
( ~ convergent_lines(X_47,X_46)
| convergent_lines(X_46,Z)
| convergent_lines(X_47,Z) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(X_47)),bind(Y,$fot(X_46))]]) ).
cnf(refute_0_12,plain,
( ~ convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),X_27)
| convergent_lines(X_27,Z)
| convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),Z) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))),bind(Y,$fot(X_27))]]) ).
cnf(refute_0_13,plain,
convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_14,plain,
( ~ convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))
| convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_26)
| convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),X_26) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))),bind(Z,$fot(X_26))]]) ).
cnf(refute_0_15,plain,
( convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_26)
| convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),X_26) ),
inference(resolve,[$cnf( convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_27)
| convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),X_27) ),
inference(subst,[],[refute_0_15:[bind(X_26,$fot(X_27))]]) ).
cnf(refute_0_17,plain,
( convergent_lines(X_27,Z)
| convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_27)
| convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),Z) ),
inference(resolve,[$cnf( convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),X_27) )],[refute_0_16,refute_0_12]) ).
cnf(refute_0_18,plain,
( convergent_lines(X_47,X_46)
| convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_47)
| convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),X_46) ),
inference(subst,[],[refute_0_17:[bind(Z,$fot(X_46)),bind(X_27,$fot(X_47))]]) ).
cnf(refute_0_19,plain,
( convergent_lines(X_46,Z)
| convergent_lines(X_47,Z)
| convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_47)
| convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),X_46) ),
inference(resolve,[$cnf( convergent_lines(X_47,X_46) )],[refute_0_18,refute_0_11]) ).
cnf(refute_0_20,plain,
( convergent_lines(X_46,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),X_46) ),
inference(subst,[],[refute_0_19:[bind(Z,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(X_47,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_21,plain,
~ convergent_lines(X,X),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_22,plain,
~ convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(subst,[],[refute_0_21:[bind(X,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_23,plain,
( convergent_lines(X_46,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),X_46) ),
inference(resolve,[$cnf( convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_20,refute_0_22]) ).
cnf(refute_0_24,plain,
( convergent_lines(X_49,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),X_49) ),
inference(subst,[],[refute_0_23:[bind(X_46,$fot(X_49))]]) ).
cnf(refute_0_25,plain,
( convergent_lines(X_49,Z)
| convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),X_49)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z) ),
inference(resolve,[$cnf( convergent_lines(X_49,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_24,refute_0_9]) ).
cnf(refute_0_26,plain,
( convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)) ),
inference(subst,[],[refute_0_25:[bind(Z,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))),bind(X_49,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)))]]) ).
cnf(refute_0_27,plain,
~ convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)),
inference(subst,[],[refute_0_21:[bind(X,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)))]]) ).
cnf(refute_0_28,plain,
distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)),
inference(resolve,[$cnf( convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ distinct_lines(U,V)
| ~ distinct_points(X,Y)
| apart_point_and_line(X,U)
| apart_point_and_line(X,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(Y,V) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_30,plain,
( ~ distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))
| ~ distinct_points(X_277,X_278)
| apart_point_and_line(X_277,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(X_277,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))
| apart_point_and_line(X_278,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(X_278,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)) ),
inference(subst,[],[refute_0_29:[bind(U,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(V,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))),bind(X,$fot(X_277)),bind(Y,$fot(X_278))]]) ).
cnf(refute_0_31,plain,
( ~ distinct_points(X_277,X_278)
| apart_point_and_line(X_277,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(X_277,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))
| apart_point_and_line(X_278,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(X_278,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)) )],[refute_0_28,refute_0_30]) ).
cnf(refute_0_32,plain,
( ~ distinct_points(intersection_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)),skolemFOFtoCNF_X)
| apart_point_and_line(intersection_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(intersection_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)),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)) ),
inference(subst,[],[refute_0_31:[bind(X_277,$fot(intersection_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)))),bind(X_278,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_33,plain,
( apart_point_and_line(intersection_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(intersection_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)),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)) ),
inference(resolve,[$cnf( distinct_points(intersection_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)),skolemFOFtoCNF_X) )],[refute_0_7,refute_0_32]) ).
cnf(refute_0_34,plain,
( ~ convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))
| apart_point_and_line(intersection_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)) )],[refute_0_33,refute_0_6]) ).
cnf(refute_0_35,plain,
( apart_point_and_line(intersection_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_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)) ),
inference(resolve,[$cnf( convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)) )],[refute_0_13,refute_0_34]) ).
cnf(refute_0_36,plain,
( ~ convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_35,refute_0_4]) ).
cnf(refute_0_37,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)) ),
inference(resolve,[$cnf( convergent_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)) )],[refute_0_13,refute_0_36]) ).
cnf(refute_0_38,plain,
( ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)) )],[refute_0_37,refute_0_2]) ).
cnf(refute_0_39,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_40,plain,
apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Z) )],[refute_0_39,refute_0_38]) ).
cnf(refute_0_41,plain,
~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_40,refute_0_1]) ).
cnf(refute_0_42,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_43,plain,
$false,
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_42,refute_0_41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GEO202+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.14 % Command : metis --show proof --show saturation %s
% 0.15/0.36 % Computer : n006.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Fri Jun 17 21:02:41 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.53/1.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.53/1.69
% 1.53/1.69 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.53/1.69
%------------------------------------------------------------------------------