TSTP Solution File: GEO205+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO205+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n032.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 05:25:19 EDT 2022
% Result : Theorem 11.82s 12.01s
% Output : CNFRefutation 11.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 10
% Syntax : Number of formulae : 102 ( 26 unt; 0 def)
% Number of atoms : 257 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 239 ( 84 ~; 126 |; 17 &)
% ( 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 147 ( 0 sgn 87 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(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(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,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[ceq3]) ).
fof(normalize_0_2,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
$false,
inference(simplify,[],[normalize_0_0,normalize_0_2]) ).
cnf(refute_0_0,plain,
$false,
inference(canonicalize,[],[normalize_0_3]) ).
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] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(canonicalize,[],[ci3]) ).
fof(normalize_1_5,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(specialize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(canonicalize,[],[ci4]) ).
fof(normalize_1_7,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(specialize,[],[normalize_1_6]) ).
fof(normalize_1_8,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_9,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_1_8]) ).
fof(normalize_1_10,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_11,plain,
( ~ distinct_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
& convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
& convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)
& distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)) ),
inference(skolemize,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
~ distinct_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(conjunct,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[ax6]) ).
fof(normalize_1_14,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(specialize,[],[normalize_1_13]) ).
fof(normalize_1_15,plain,
convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(conjunct,[],[normalize_1_11]) ).
fof(normalize_1_16,plain,
! [X] : ~ convergent_lines(X,X),
inference(canonicalize,[],[apart3]) ).
fof(normalize_1_17,plain,
! [X] : ~ convergent_lines(X,X),
inference(specialize,[],[normalize_1_16]) ).
fof(normalize_1_18,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[ceq3]) ).
fof(normalize_1_19,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_1_18]) ).
fof(normalize_1_20,plain,
distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)),
inference(conjunct,[],[normalize_1_11]) ).
fof(normalize_1_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(canonicalize,[],[cu1]) ).
fof(normalize_1_22,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_21]) ).
fof(normalize_1_23,plain,
convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),
inference(conjunct,[],[normalize_1_11]) ).
cnf(refute_1_0,plain,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_1_1]) ).
cnf(refute_1_1,plain,
~ distinct_lines(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z),
inference(subst,[],[refute_1_0:[bind(X,$fot(skolemFOFtoCNF_Z))]]) ).
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,skolemFOFtoCNF_Y)
| distinct_lines(skolemFOFtoCNF_Y,Z)
| distinct_lines(skolemFOFtoCNF_Z,Z) ),
inference(subst,[],[refute_1_2:[bind(X,$fot(skolemFOFtoCNF_Z)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_1_4,plain,
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(canonicalize,[],[normalize_1_5]) ).
cnf(refute_1_5,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
| ~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_1_4:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_1_6,plain,
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_7,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Y)
| ~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_1_6:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_1_8,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_1_9]) ).
cnf(refute_1_9,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z)
| distinct_lines(skolemFOFtoCNF_Z,Z) ),
inference(subst,[],[refute_1_8:[bind(X,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Y,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_1_10,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),skolemFOFtoCNF_X)
| ~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_1_4:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_1_11,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),skolemFOFtoCNF_Z)
| ~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_1_6:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_1_12,plain,
~ distinct_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_13,plain,
( ~ distinct_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| distinct_lines(skolemFOFtoCNF_X,Z)
| distinct_lines(skolemFOFtoCNF_Y,Z) ),
inference(subst,[],[refute_1_2:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_1_14,plain,
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[normalize_1_14]) ).
cnf(refute_1_15,plain,
( ~ convergent_lines(X_24,X_23)
| convergent_lines(X_23,Z)
| convergent_lines(X_24,Z) ),
inference(subst,[],[refute_1_14:[bind(X,$fot(X_24)),bind(Y,$fot(X_23))]]) ).
cnf(refute_1_16,plain,
( ~ convergent_lines(skolemFOFtoCNF_Y,X_21)
| convergent_lines(X_21,Z)
| convergent_lines(skolemFOFtoCNF_Y,Z) ),
inference(subst,[],[refute_1_14:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(X_21))]]) ).
cnf(refute_1_17,plain,
convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_1_15]) ).
cnf(refute_1_18,plain,
( ~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| convergent_lines(skolemFOFtoCNF_X,X_20)
| convergent_lines(skolemFOFtoCNF_Y,X_20) ),
inference(subst,[],[refute_1_14:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(X_20))]]) ).
cnf(refute_1_19,plain,
( convergent_lines(skolemFOFtoCNF_X,X_20)
| convergent_lines(skolemFOFtoCNF_Y,X_20) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_1_17,refute_1_18]) ).
cnf(refute_1_20,plain,
( convergent_lines(skolemFOFtoCNF_X,X_21)
| convergent_lines(skolemFOFtoCNF_Y,X_21) ),
inference(subst,[],[refute_1_19:[bind(X_20,$fot(X_21))]]) ).
cnf(refute_1_21,plain,
( convergent_lines(X_21,Z)
| convergent_lines(skolemFOFtoCNF_X,X_21)
| convergent_lines(skolemFOFtoCNF_Y,Z) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_Y,X_21) )],[refute_1_20,refute_1_16]) ).
cnf(refute_1_22,plain,
( convergent_lines(X_24,X_23)
| convergent_lines(skolemFOFtoCNF_X,X_24)
| convergent_lines(skolemFOFtoCNF_Y,X_23) ),
inference(subst,[],[refute_1_21:[bind(Z,$fot(X_23)),bind(X_21,$fot(X_24))]]) ).
cnf(refute_1_23,plain,
( convergent_lines(X_23,Z)
| convergent_lines(X_24,Z)
| convergent_lines(skolemFOFtoCNF_X,X_24)
| convergent_lines(skolemFOFtoCNF_Y,X_23) ),
inference(resolve,[$cnf( convergent_lines(X_24,X_23) )],[refute_1_22,refute_1_15]) ).
cnf(refute_1_24,plain,
( convergent_lines(X_23,skolemFOFtoCNF_X)
| convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_X)
| convergent_lines(skolemFOFtoCNF_Y,X_23) ),
inference(subst,[],[refute_1_23:[bind(Z,$fot(skolemFOFtoCNF_X)),bind(X_24,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_1_25,plain,
~ convergent_lines(X,X),
inference(canonicalize,[],[normalize_1_17]) ).
cnf(refute_1_26,plain,
~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_X),
inference(subst,[],[refute_1_25:[bind(X,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_1_27,plain,
( convergent_lines(X_23,skolemFOFtoCNF_X)
| convergent_lines(skolemFOFtoCNF_Y,X_23) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_X) )],[refute_1_24,refute_1_26]) ).
cnf(refute_1_28,plain,
( convergent_lines(X_33,skolemFOFtoCNF_X)
| convergent_lines(skolemFOFtoCNF_Y,X_33) ),
inference(subst,[],[refute_1_27:[bind(X_23,$fot(X_33))]]) ).
cnf(refute_1_29,plain,
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_1_19]) ).
cnf(refute_1_30,plain,
( ~ convergent_lines(X_33,skolemFOFtoCNF_X)
| convergent_lines(X_33,X_35)
| distinct_lines(skolemFOFtoCNF_X,X_35) ),
inference(subst,[],[refute_1_29:[bind(X,$fot(X_33)),bind(Y,$fot(skolemFOFtoCNF_X)),bind(Z,$fot(X_35))]]) ).
cnf(refute_1_31,plain,
( convergent_lines(X_33,X_35)
| convergent_lines(skolemFOFtoCNF_Y,X_33)
| distinct_lines(skolemFOFtoCNF_X,X_35) ),
inference(resolve,[$cnf( convergent_lines(X_33,skolemFOFtoCNF_X) )],[refute_1_28,refute_1_30]) ).
cnf(refute_1_32,plain,
( convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y)
| distinct_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_1_31:[bind(X_33,$fot(skolemFOFtoCNF_Y)),bind(X_35,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_1_33,plain,
~ convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y),
inference(subst,[],[refute_1_25:[bind(X,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_1_34,plain,
distinct_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) )],[refute_1_32,refute_1_33]) ).
cnf(refute_1_35,plain,
( distinct_lines(skolemFOFtoCNF_X,Z)
| distinct_lines(skolemFOFtoCNF_Y,Z) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_1_34,refute_1_13]) ).
cnf(refute_1_36,plain,
( distinct_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)
| distinct_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_1_35:[bind(Z,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_1_37,plain,
distinct_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_1_36,refute_1_12]) ).
cnf(refute_1_38,plain,
distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)),
inference(canonicalize,[],[normalize_1_20]) ).
cnf(refute_1_39,plain,
( ~ distinct_lines(U,V)
| ~ distinct_points(X,Y)
| apart_point_and_line(X,U)
| apart_point_and_line(X,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(Y,V) ),
inference(canonicalize,[],[normalize_1_22]) ).
cnf(refute_1_40,plain,
( ~ distinct_lines(X_420,X_421)
| ~ distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_420)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_421)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),X_420)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),X_421) ),
inference(subst,[],[refute_1_39:[bind(U,$fot(X_420)),bind(V,$fot(X_421)),bind(X,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Y,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)))]]) ).
cnf(refute_1_41,plain,
( ~ distinct_lines(X_420,X_421)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_420)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_421)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),X_420)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),X_421) ),
inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)) )],[refute_1_38,refute_1_40]) ).
cnf(refute_1_42,plain,
( ~ distinct_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),skolemFOFtoCNF_X)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_1_41:[bind(X_420,$fot(skolemFOFtoCNF_X)),bind(X_421,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_1_43,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),skolemFOFtoCNF_X)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z) )],[refute_1_37,refute_1_42]) ).
cnf(refute_1_44,plain,
( ~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),skolemFOFtoCNF_Z) )],[refute_1_43,refute_1_11]) ).
cnf(refute_1_45,plain,
convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),
inference(canonicalize,[],[normalize_1_23]) ).
cnf(refute_1_46,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z) )],[refute_1_45,refute_1_44]) ).
cnf(refute_1_47,plain,
( ~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),skolemFOFtoCNF_X) )],[refute_1_46,refute_1_10]) ).
cnf(refute_1_48,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z) )],[refute_1_45,refute_1_47]) ).
cnf(refute_1_49,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
| distinct_lines(skolemFOFtoCNF_Z,Z) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z) )],[refute_1_48,refute_1_9]) ).
cnf(refute_1_50,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Y)
| distinct_lines(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_1_49:[bind(Z,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_1_51,plain,
( ~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
| distinct_lines(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Y) )],[refute_1_50,refute_1_7]) ).
cnf(refute_1_52,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
| distinct_lines(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_1_17,refute_1_51]) ).
cnf(refute_1_53,plain,
( ~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| distinct_lines(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X) )],[refute_1_52,refute_1_5]) ).
cnf(refute_1_54,plain,
distinct_lines(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_1_17,refute_1_53]) ).
cnf(refute_1_55,plain,
( distinct_lines(skolemFOFtoCNF_Y,Z)
| distinct_lines(skolemFOFtoCNF_Z,Z) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y) )],[refute_1_54,refute_1_3]) ).
cnf(refute_1_56,plain,
( distinct_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| distinct_lines(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_1_55:[bind(Z,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_1_57,plain,
distinct_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) )],[refute_1_56,refute_1_1]) ).
cnf(refute_1_58,plain,
$false,
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_1_57,refute_1_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : GEO205+1 : TPTP v8.1.0. Released v3.3.0.
% 0.02/0.10 % Command : metis --show proof --show saturation %s
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Sat Jun 18 16:20:02 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.09/0.30 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 11.82/12.01 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.82/12.01
% 11.82/12.01 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.82/12.02
%------------------------------------------------------------------------------