%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO186+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 05:25:04 EDT 2022
% Result : Theorem 248.27s 248.44s
% Output : CNFRefutation 248.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 18
% Syntax : Number of formulae : 252 ( 71 unt; 0 def)
% Number of atoms : 641 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 572 ( 183 ~; 332 |; 39 &)
% ( 6 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 556 ( 90 sgn 160 !; 4 ?)
% 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(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(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(occu1,axiom,
! [L,M] :
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ) ).
fof(oac1,axiom,
! [L,M,N] :
( ( convergent_lines(L,M)
& unorthogonal_lines(L,M) )
=> ( ( convergent_lines(L,N)
& unorthogonal_lines(L,N) )
| ( convergent_lines(M,N)
& unorthogonal_lines(M,N) ) ) ) ).
fof(ooc1,axiom,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L) ).
fof(cotno1,axiom,
! [L,M,N] :
( ( ( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M) )
& ( ~ convergent_lines(L,N)
| ~ unorthogonal_lines(L,N) ) )
=> ( ~ convergent_lines(M,N)
| ~ unorthogonal_lines(M,N) ) ) ).
fof(couo1,axiom,
! [L,M,N] :
( ( ~ unorthogonal_lines(L,M)
& ~ unorthogonal_lines(L,N) )
=> ~ convergent_lines(M,N) ) ).
fof(a4,axiom,
! [X,Y] :
( incident_point_and_line(X,Y)
<=> ~ apart_point_and_line(X,Y) ) ).
fof(a5,axiom,
! [X,Y] :
( orthogonal_lines(X,Y)
<=> ~ unorthogonal_lines(X,Y) ) ).
fof(con,conjecture,
! [X,Y,U,V] :
( ( distinct_points(X,Y)
& convergent_lines(U,V)
& incident_point_and_line(X,U)
& incident_point_and_line(X,V) )
=> equal_points(X,intersection_point(U,V)) ) ).
fof(subgoal_0,plain,
! [X,Y,U,V] :
( ( distinct_points(X,Y)
& convergent_lines(U,V)
& incident_point_and_line(X,U)
& incident_point_and_line(X,V) )
=> equal_points(X,intersection_point(U,V)) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [X,Y,U,V] :
( ( distinct_points(X,Y)
& convergent_lines(U,V)
& incident_point_and_line(X,U)
& incident_point_and_line(X,V) )
=> equal_points(X,intersection_point(U,V)) ),
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] :
( ~ orthogonal_lines(X,Y)
<=> unorthogonal_lines(X,Y) ),
inference(canonicalize,[],[a5]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( ~ orthogonal_lines(X,Y)
<=> unorthogonal_lines(X,Y) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X,Y] :
( ( ~ orthogonal_lines(X,Y)
| ~ unorthogonal_lines(X,Y) )
& ( orthogonal_lines(X,Y)
| unorthogonal_lines(X,Y) ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ~ orthogonal_lines(X,Y)
| ~ unorthogonal_lines(X,Y) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( orthogonal_lines(X,Y)
| unorthogonal_lines(X,Y) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_7,plain,
! [L,M,N] :
( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| ( convergent_lines(L,N)
& unorthogonal_lines(L,N) )
| ( convergent_lines(M,N)
& unorthogonal_lines(M,N) ) ),
inference(canonicalize,[],[oac1]) ).
fof(normalize_0_8,plain,
! [L,M,N] :
( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| ( convergent_lines(L,N)
& unorthogonal_lines(L,N) )
| ( convergent_lines(M,N)
& unorthogonal_lines(M,N) ) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [L,M,N] :
( ( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| convergent_lines(L,N)
| convergent_lines(M,N) )
& ( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| convergent_lines(L,N)
| unorthogonal_lines(M,N) )
& ( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| convergent_lines(M,N)
| unorthogonal_lines(L,N) )
& ( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| unorthogonal_lines(L,N)
| unorthogonal_lines(M,N) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [L,M,N] :
( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| convergent_lines(L,N)
| unorthogonal_lines(M,N) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [L,M,N] :
( ~ convergent_lines(M,N)
| unorthogonal_lines(L,M)
| unorthogonal_lines(L,N) ),
inference(canonicalize,[],[couo1]) ).
fof(normalize_0_12,plain,
! [L,M,N] :
( ~ convergent_lines(M,N)
| unorthogonal_lines(L,M)
| unorthogonal_lines(L,N) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[ax6]) ).
fof(normalize_0_14,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(canonicalize,[],[ooc1]) ).
fof(normalize_0_16,plain,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [L,M] :
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(canonicalize,[],[occu1]) ).
fof(normalize_0_18,plain,
! [L,M] :
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [X] : ~ convergent_lines(X,X),
inference(canonicalize,[],[apart3]) ).
fof(normalize_0_20,plain,
! [X] : ~ convergent_lines(X,X),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [L,M,N] :
( ~ convergent_lines(M,N)
| ~ unorthogonal_lines(M,N)
| ( convergent_lines(L,M)
& unorthogonal_lines(L,M) )
| ( convergent_lines(L,N)
& unorthogonal_lines(L,N) ) ),
inference(canonicalize,[],[cotno1]) ).
fof(normalize_0_22,plain,
! [L,M,N] :
( ~ convergent_lines(M,N)
| ~ unorthogonal_lines(M,N)
| ( convergent_lines(L,M)
& unorthogonal_lines(L,M) )
| ( convergent_lines(L,N)
& unorthogonal_lines(L,N) ) ),
inference(specialize,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [L,M,N] :
( ( ~ convergent_lines(M,N)
| ~ unorthogonal_lines(M,N)
| convergent_lines(L,M)
| convergent_lines(L,N) )
& ( ~ convergent_lines(M,N)
| ~ unorthogonal_lines(M,N)
| convergent_lines(L,M)
| unorthogonal_lines(L,N) )
& ( ~ convergent_lines(M,N)
| ~ unorthogonal_lines(M,N)
| convergent_lines(L,N)
| unorthogonal_lines(L,M) )
& ( ~ convergent_lines(M,N)
| ~ unorthogonal_lines(M,N)
| unorthogonal_lines(L,M)
| unorthogonal_lines(L,N) ) ),
inference(clausify,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [L,M,N] :
( ~ convergent_lines(M,N)
| ~ unorthogonal_lines(M,N)
| convergent_lines(L,N)
| unorthogonal_lines(L,M) ),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [X] : ~ distinct_lines(X,X),
inference(canonicalize,[],[apart2]) ).
fof(normalize_0_26,plain,
! [X] : ~ distinct_lines(X,X),
inference(specialize,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(canonicalize,[],[cp1]) ).
fof(normalize_0_28,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(specialize,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[ceq3]) ).
fof(normalize_0_30,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_29]) ).
fof(normalize_0_31,plain,
! [L,M,N] :
( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| unorthogonal_lines(L,N)
| unorthogonal_lines(M,N) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_32,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(canonicalize,[],[p1]) ).
fof(normalize_0_33,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(specialize,[],[normalize_0_32]) ).
fof(normalize_0_34,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_35,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_34]) ).
fof(normalize_0_36,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[apart5]) ).
fof(normalize_0_37,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_36]) ).
fof(normalize_0_38,plain,
? [U,V,X,Y] :
( ~ equal_points(X,intersection_point(U,V))
& convergent_lines(U,V)
& distinct_points(X,Y)
& incident_point_and_line(X,U)
& incident_point_and_line(X,V) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_39,plain,
( ~ equal_points(skolemFOFtoCNF_X,intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
& convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V)
& distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
& incident_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U)
& incident_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_V) ),
inference(skolemize,[],[normalize_0_38]) ).
fof(normalize_0_40,plain,
convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V),
inference(conjunct,[],[normalize_0_39]) ).
fof(normalize_0_41,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(conjunct,[],[normalize_0_39]) ).
fof(normalize_0_42,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_43,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_42]) ).
fof(normalize_0_44,plain,
incident_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U),
inference(conjunct,[],[normalize_0_39]) ).
fof(normalize_0_45,plain,
! [X,Y] :
( ~ apart_point_and_line(X,Y)
<=> incident_point_and_line(X,Y) ),
inference(canonicalize,[],[a4]) ).
fof(normalize_0_46,plain,
! [X,Y] :
( ~ apart_point_and_line(X,Y)
<=> incident_point_and_line(X,Y) ),
inference(specialize,[],[normalize_0_45]) ).
fof(normalize_0_47,plain,
! [X,Y] :
( ( ~ apart_point_and_line(X,Y)
| ~ incident_point_and_line(X,Y) )
& ( apart_point_and_line(X,Y)
| incident_point_and_line(X,Y) ) ),
inference(clausify,[],[normalize_0_46]) ).
fof(normalize_0_48,plain,
! [X,Y] :
( ~ apart_point_and_line(X,Y)
| ~ incident_point_and_line(X,Y) ),
inference(conjunct,[],[normalize_0_47]) ).
fof(normalize_0_49,plain,
incident_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_V),
inference(conjunct,[],[normalize_0_39]) ).
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_Y,parallel_through_point(skolemFOFtoCNF_U,skolemFOFtoCNF_Y)),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_2,plain,
( ~ orthogonal_lines(X,Y)
| ~ unorthogonal_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( ~ orthogonal_lines(X_4358,X_4359)
| ~ unorthogonal_lines(X_4358,X_4359) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_4358)),bind(Y,$fot(X_4359))]]) ).
cnf(refute_0_4,plain,
( ~ orthogonal_lines(X_4355,orthogonal_through_point(X_4355,X_4356))
| ~ unorthogonal_lines(X_4355,orthogonal_through_point(X_4355,X_4356)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_4355)),bind(Y,$fot(orthogonal_through_point(X_4355,X_4356)))]]) ).
cnf(refute_0_5,plain,
( orthogonal_lines(X,Y)
| unorthogonal_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_6,plain,
( orthogonal_lines(X_258,X_259)
| unorthogonal_lines(X_258,X_259) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_258)),bind(Y,$fot(X_259))]]) ).
cnf(refute_0_7,plain,
( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| convergent_lines(L,N)
| unorthogonal_lines(M,N) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
( ~ convergent_lines(X_258,X_259)
| ~ unorthogonal_lines(X_258,X_259)
| convergent_lines(X_258,X_260)
| unorthogonal_lines(X_259,X_260) ),
inference(subst,[],[refute_0_7:[bind(L,$fot(X_258)),bind(M,$fot(X_259)),bind(N,$fot(X_260))]]) ).
cnf(refute_0_9,plain,
( ~ convergent_lines(X_258,X_259)
| convergent_lines(X_258,X_260)
| orthogonal_lines(X_258,X_259)
| unorthogonal_lines(X_259,X_260) ),
inference(resolve,[$cnf( unorthogonal_lines(X_258,X_259) )],[refute_0_6,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ convergent_lines(X_2407,X_2406)
| convergent_lines(X_2407,X_260)
| orthogonal_lines(X_2407,X_2406)
| unorthogonal_lines(X_2406,X_260) ),
inference(subst,[],[refute_0_9:[bind(X_258,$fot(X_2407)),bind(X_259,$fot(X_2406))]]) ).
cnf(refute_0_11,plain,
( ~ convergent_lines(M,N)
| unorthogonal_lines(L,M)
| unorthogonal_lines(L,N) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_12,plain,
( ~ convergent_lines(orthogonal_through_point(X_360,X_362),X_361)
| unorthogonal_lines(L,X_361)
| unorthogonal_lines(L,orthogonal_through_point(X_360,X_362)) ),
inference(subst,[],[refute_0_11:[bind(M,$fot(orthogonal_through_point(X_360,X_362))),bind(N,$fot(X_361))]]) ).
cnf(refute_0_13,plain,
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_14,plain,
( ~ convergent_lines(X_350,X_347)
| convergent_lines(X_347,Z)
| convergent_lines(X_350,Z) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(X_350)),bind(Y,$fot(X_347))]]) ).
cnf(refute_0_15,plain,
( ~ convergent_lines(orthogonal_through_point(X_66,X_65),X_67)
| convergent_lines(X_67,Z)
| convergent_lines(orthogonal_through_point(X_66,X_65),Z) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(orthogonal_through_point(X_66,X_65))),bind(Y,$fot(X_67))]]) ).
cnf(refute_0_16,plain,
~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_17,plain,
~ unorthogonal_lines(orthogonal_through_point(X_16,A),X_16),
inference(subst,[],[refute_0_16:[bind(L,$fot(X_16))]]) ).
cnf(refute_0_18,plain,
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_19,plain,
( convergent_lines(orthogonal_through_point(X_16,A),X_16)
| unorthogonal_lines(orthogonal_through_point(X_16,A),X_16) ),
inference(subst,[],[refute_0_18:[bind(L,$fot(orthogonal_through_point(X_16,A))),bind(M,$fot(X_16))]]) ).
cnf(refute_0_20,plain,
convergent_lines(orthogonal_through_point(X_16,A),X_16),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(X_16,A),X_16) )],[refute_0_19,refute_0_17]) ).
cnf(refute_0_21,plain,
convergent_lines(orthogonal_through_point(X_62,A),X_62),
inference(subst,[],[refute_0_20:[bind(X_16,$fot(X_62))]]) ).
cnf(refute_0_22,plain,
( ~ convergent_lines(orthogonal_through_point(X_62,A),X_62)
| convergent_lines(X_62,X_63)
| convergent_lines(orthogonal_through_point(X_62,A),X_63) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(orthogonal_through_point(X_62,A))),bind(Y,$fot(X_62)),bind(Z,$fot(X_63))]]) ).
cnf(refute_0_23,plain,
( convergent_lines(X_62,X_63)
| convergent_lines(orthogonal_through_point(X_62,A),X_63) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(X_62,A),X_62) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( convergent_lines(X_66,X_67)
| convergent_lines(orthogonal_through_point(X_66,X_65),X_67) ),
inference(subst,[],[refute_0_23:[bind(A,$fot(X_65)),bind(X_62,$fot(X_66)),bind(X_63,$fot(X_67))]]) ).
cnf(refute_0_25,plain,
( convergent_lines(X_66,X_67)
| convergent_lines(X_67,Z)
| convergent_lines(orthogonal_through_point(X_66,X_65),Z) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(X_66,X_65),X_67) )],[refute_0_24,refute_0_15]) ).
cnf(refute_0_26,plain,
( convergent_lines(X_349,X_350)
| convergent_lines(X_350,X_347)
| convergent_lines(orthogonal_through_point(X_349,X_348),X_347) ),
inference(subst,[],[refute_0_25:[bind(Z,$fot(X_347)),bind(X_65,$fot(X_348)),bind(X_66,$fot(X_349)),bind(X_67,$fot(X_350))]]) ).
cnf(refute_0_27,plain,
( convergent_lines(X_347,Z)
| convergent_lines(X_349,X_350)
| convergent_lines(X_350,Z)
| convergent_lines(orthogonal_through_point(X_349,X_348),X_347) ),
inference(resolve,[$cnf( convergent_lines(X_350,X_347) )],[refute_0_26,refute_0_14]) ).
cnf(refute_0_28,plain,
( convergent_lines(Z,Z)
| convergent_lines(X_347,Z)
| convergent_lines(orthogonal_through_point(Z,X_348),X_347) ),
inference(subst,[],[refute_0_27:[bind(X_349,$fot(Z)),bind(X_350,$fot(Z))]]) ).
cnf(refute_0_29,plain,
~ convergent_lines(X,X),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_30,plain,
~ convergent_lines(Z,Z),
inference(subst,[],[refute_0_29:[bind(X,$fot(Z))]]) ).
cnf(refute_0_31,plain,
( convergent_lines(X_347,Z)
| convergent_lines(orthogonal_through_point(Z,X_348),X_347) ),
inference(resolve,[$cnf( convergent_lines(Z,Z) )],[refute_0_28,refute_0_30]) ).
cnf(refute_0_32,plain,
( convergent_lines(X_361,X_360)
| convergent_lines(orthogonal_through_point(X_360,X_362),X_361) ),
inference(subst,[],[refute_0_31:[bind(Z,$fot(X_360)),bind(X_347,$fot(X_361)),bind(X_348,$fot(X_362))]]) ).
cnf(refute_0_33,plain,
( convergent_lines(X_361,X_360)
| unorthogonal_lines(L,X_361)
| unorthogonal_lines(L,orthogonal_through_point(X_360,X_362)) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(X_360,X_362),X_361) )],[refute_0_32,refute_0_12]) ).
cnf(refute_0_34,plain,
( convergent_lines(X_2407,X_2406)
| unorthogonal_lines(X_2405,X_2407)
| unorthogonal_lines(X_2405,orthogonal_through_point(X_2406,X_2408)) ),
inference(subst,[],[refute_0_33:[bind(L,$fot(X_2405)),bind(X_360,$fot(X_2406)),bind(X_361,$fot(X_2407)),bind(X_362,$fot(X_2408))]]) ).
cnf(refute_0_35,plain,
( convergent_lines(X_2407,X_260)
| orthogonal_lines(X_2407,X_2406)
| unorthogonal_lines(X_2405,X_2407)
| unorthogonal_lines(X_2405,orthogonal_through_point(X_2406,X_2408))
| unorthogonal_lines(X_2406,X_260) ),
inference(resolve,[$cnf( convergent_lines(X_2407,X_2406) )],[refute_0_34,refute_0_10]) ).
cnf(refute_0_36,plain,
( convergent_lines(X_260,X_260)
| orthogonal_lines(X_260,X_2406)
| unorthogonal_lines(X_2406,X_260)
| unorthogonal_lines(X_2406,orthogonal_through_point(X_2406,X_2408)) ),
inference(subst,[],[refute_0_35:[bind(X_2405,$fot(X_2406)),bind(X_2407,$fot(X_260))]]) ).
cnf(refute_0_37,plain,
~ convergent_lines(X_260,X_260),
inference(subst,[],[refute_0_29:[bind(X,$fot(X_260))]]) ).
cnf(refute_0_38,plain,
( orthogonal_lines(X_260,X_2406)
| unorthogonal_lines(X_2406,X_260)
| unorthogonal_lines(X_2406,orthogonal_through_point(X_2406,X_2408)) ),
inference(resolve,[$cnf( convergent_lines(X_260,X_260) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
( orthogonal_lines(X_4357,X_4355)
| unorthogonal_lines(X_4355,X_4357)
| unorthogonal_lines(X_4355,orthogonal_through_point(X_4355,X_4356)) ),
inference(subst,[],[refute_0_38:[bind(X_2406,$fot(X_4355)),bind(X_2408,$fot(X_4356)),bind(X_260,$fot(X_4357))]]) ).
cnf(refute_0_40,plain,
( ~ orthogonal_lines(X_4355,orthogonal_through_point(X_4355,X_4356))
| orthogonal_lines(X_4357,X_4355)
| unorthogonal_lines(X_4355,X_4357) ),
inference(resolve,[$cnf( unorthogonal_lines(X_4355,orthogonal_through_point(X_4355,X_4356)) )],[refute_0_39,refute_0_4]) ).
cnf(refute_0_41,plain,
( convergent_lines(X_1032,X_1033)
| convergent_lines(X_1033,Z)
| convergent_lines(orthogonal_through_point(X_1032,X_65),Z) ),
inference(subst,[],[refute_0_25:[bind(X_66,$fot(X_1032)),bind(X_67,$fot(X_1033))]]) ).
cnf(refute_0_42,plain,
( orthogonal_lines(X_274,X_275)
| unorthogonal_lines(X_274,X_275) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_274)),bind(Y,$fot(X_275))]]) ).
cnf(refute_0_43,plain,
( ~ convergent_lines(M,N)
| ~ unorthogonal_lines(M,N)
| convergent_lines(L,N)
| unorthogonal_lines(L,M) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_44,plain,
( ~ convergent_lines(X_274,X_275)
| ~ unorthogonal_lines(X_274,X_275)
| convergent_lines(X_273,X_275)
| unorthogonal_lines(X_273,X_274) ),
inference(subst,[],[refute_0_43:[bind(L,$fot(X_273)),bind(M,$fot(X_274)),bind(N,$fot(X_275))]]) ).
cnf(refute_0_45,plain,
( ~ convergent_lines(X_274,X_275)
| convergent_lines(X_273,X_275)
| orthogonal_lines(X_274,X_275)
| unorthogonal_lines(X_273,X_274) ),
inference(resolve,[$cnf( unorthogonal_lines(X_274,X_275) )],[refute_0_42,refute_0_44]) ).
cnf(refute_0_46,plain,
( ~ convergent_lines(X_1032,X_1033)
| convergent_lines(X_1031,X_1033)
| orthogonal_lines(X_1032,X_1033)
| unorthogonal_lines(X_1031,X_1032) ),
inference(subst,[],[refute_0_45:[bind(X_273,$fot(X_1031)),bind(X_274,$fot(X_1032)),bind(X_275,$fot(X_1033))]]) ).
cnf(refute_0_47,plain,
( convergent_lines(X_1031,X_1033)
| convergent_lines(X_1033,Z)
| convergent_lines(orthogonal_through_point(X_1032,X_65),Z)
| orthogonal_lines(X_1032,X_1033)
| unorthogonal_lines(X_1031,X_1032) ),
inference(resolve,[$cnf( convergent_lines(X_1032,X_1033) )],[refute_0_41,refute_0_46]) ).
cnf(refute_0_48,plain,
( convergent_lines(orthogonal_through_point(X_1032,X_65),orthogonal_through_point(X_1032,X_65))
| orthogonal_lines(X_1032,orthogonal_through_point(X_1032,X_65))
| unorthogonal_lines(orthogonal_through_point(X_1032,X_65),X_1032) ),
inference(subst,[],[refute_0_47:[bind(Z,$fot(orthogonal_through_point(X_1032,X_65))),bind(X_1031,$fot(orthogonal_through_point(X_1032,X_65))),bind(X_1033,$fot(orthogonal_through_point(X_1032,X_65)))]]) ).
cnf(refute_0_49,plain,
~ convergent_lines(orthogonal_through_point(X_1032,X_65),orthogonal_through_point(X_1032,X_65)),
inference(subst,[],[refute_0_29:[bind(X,$fot(orthogonal_through_point(X_1032,X_65)))]]) ).
cnf(refute_0_50,plain,
( orthogonal_lines(X_1032,orthogonal_through_point(X_1032,X_65))
| unorthogonal_lines(orthogonal_through_point(X_1032,X_65),X_1032) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(X_1032,X_65),orthogonal_through_point(X_1032,X_65)) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
~ unorthogonal_lines(orthogonal_through_point(X_1032,X_65),X_1032),
inference(subst,[],[refute_0_16:[bind(A,$fot(X_65)),bind(L,$fot(X_1032))]]) ).
cnf(refute_0_52,plain,
orthogonal_lines(X_1032,orthogonal_through_point(X_1032,X_65)),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(X_1032,X_65),X_1032) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
orthogonal_lines(X_4355,orthogonal_through_point(X_4355,X_4356)),
inference(subst,[],[refute_0_52:[bind(X_1032,$fot(X_4355)),bind(X_65,$fot(X_4356))]]) ).
cnf(refute_0_54,plain,
( orthogonal_lines(X_4357,X_4355)
| unorthogonal_lines(X_4355,X_4357) ),
inference(resolve,[$cnf( orthogonal_lines(X_4355,orthogonal_through_point(X_4355,X_4356)) )],[refute_0_53,refute_0_40]) ).
cnf(refute_0_55,plain,
( orthogonal_lines(X_4359,X_4358)
| unorthogonal_lines(X_4358,X_4359) ),
inference(subst,[],[refute_0_54:[bind(X_4355,$fot(X_4358)),bind(X_4357,$fot(X_4359))]]) ).
cnf(refute_0_56,plain,
( ~ orthogonal_lines(X_4358,X_4359)
| orthogonal_lines(X_4359,X_4358) ),
inference(resolve,[$cnf( unorthogonal_lines(X_4358,X_4359) )],[refute_0_55,refute_0_3]) ).
cnf(refute_0_57,plain,
( ~ orthogonal_lines(parallel_through_point(X_11239,X_11237),orthogonal_through_point(X_11239,X_11238))
| orthogonal_lines(orthogonal_through_point(X_11239,X_11238),parallel_through_point(X_11239,X_11237)) ),
inference(subst,[],[refute_0_56:[bind(X_4358,$fot(parallel_through_point(X_11239,X_11237))),bind(X_4359,$fot(orthogonal_through_point(X_11239,X_11238)))]]) ).
cnf(refute_0_58,plain,
( ~ convergent_lines(parallel_through_point(X_11233,X_11232),orthogonal_through_point(X_11236,X_11235))
| convergent_lines(parallel_through_point(X_11233,X_11232),X_260)
| orthogonal_lines(parallel_through_point(X_11233,X_11232),orthogonal_through_point(X_11236,X_11235))
| unorthogonal_lines(orthogonal_through_point(X_11236,X_11235),X_260) ),
inference(subst,[],[refute_0_9:[bind(X_258,$fot(parallel_through_point(X_11233,X_11232))),bind(X_259,$fot(orthogonal_through_point(X_11236,X_11235)))]]) ).
cnf(refute_0_59,plain,
( ~ convergent_lines(orthogonal_through_point(X_2464,X_2465),parallel_through_point(X_2464,X_2463))
| convergent_lines(orthogonal_through_point(X_2464,X_2465),Z)
| convergent_lines(parallel_through_point(X_2464,X_2463),Z) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(orthogonal_through_point(X_2464,X_2465))),bind(Y,$fot(parallel_through_point(X_2464,X_2463)))]]) ).
cnf(refute_0_60,plain,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_61,plain,
~ distinct_lines(parallel_through_point(X_2455,X_2453),parallel_through_point(X_2455,X_2453)),
inference(subst,[],[refute_0_60:[bind(X,$fot(parallel_through_point(X_2455,X_2453)))]]) ).
cnf(refute_0_62,plain,
~ convergent_lines(parallel_through_point(Y,X),Y),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_63,plain,
~ convergent_lines(parallel_through_point(X_2450,X),X_2450),
inference(subst,[],[refute_0_62:[bind(Y,$fot(X_2450))]]) ).
cnf(refute_0_64,plain,
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_65,plain,
( ~ convergent_lines(orthogonal_through_point(X_360,X_362),X_361)
| convergent_lines(orthogonal_through_point(X_360,X_362),Z)
| distinct_lines(X_361,Z) ),
inference(subst,[],[refute_0_64:[bind(X,$fot(orthogonal_through_point(X_360,X_362))),bind(Y,$fot(X_361))]]) ).
cnf(refute_0_66,plain,
( convergent_lines(X_361,X_360)
| convergent_lines(orthogonal_through_point(X_360,X_362),Z)
| distinct_lines(X_361,Z) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(X_360,X_362),X_361) )],[refute_0_32,refute_0_65]) ).
cnf(refute_0_67,plain,
( convergent_lines(orthogonal_through_point(X_2450,X_2452),X_2449)
| convergent_lines(parallel_through_point(X_2450,X),X_2450)
| distinct_lines(parallel_through_point(X_2450,X),X_2449) ),
inference(subst,[],[refute_0_66:[bind(Z,$fot(X_2449)),bind(X_360,$fot(X_2450)),bind(X_361,$fot(parallel_through_point(X_2450,X))),bind(X_362,$fot(X_2452))]]) ).
cnf(refute_0_68,plain,
( convergent_lines(orthogonal_through_point(X_2450,X_2452),X_2449)
| distinct_lines(parallel_through_point(X_2450,X),X_2449) ),
inference(resolve,[$cnf( convergent_lines(parallel_through_point(X_2450,X),X_2450) )],[refute_0_67,refute_0_63]) ).
cnf(refute_0_69,plain,
( convergent_lines(orthogonal_through_point(X_2455,X_2456),parallel_through_point(X_2455,X_2453))
| distinct_lines(parallel_through_point(X_2455,X_2453),parallel_through_point(X_2455,X_2453)) ),
inference(subst,[],[refute_0_68:[bind(X,$fot(X_2453)),bind(X_2449,$fot(parallel_through_point(X_2455,X_2453))),bind(X_2450,$fot(X_2455)),bind(X_2452,$fot(X_2456))]]) ).
cnf(refute_0_70,plain,
convergent_lines(orthogonal_through_point(X_2455,X_2456),parallel_through_point(X_2455,X_2453)),
inference(resolve,[$cnf( distinct_lines(parallel_through_point(X_2455,X_2453),parallel_through_point(X_2455,X_2453)) )],[refute_0_69,refute_0_61]) ).
cnf(refute_0_71,plain,
convergent_lines(orthogonal_through_point(X_2464,X_2465),parallel_through_point(X_2464,X_2463)),
inference(subst,[],[refute_0_70:[bind(X_2453,$fot(X_2463)),bind(X_2455,$fot(X_2464)),bind(X_2456,$fot(X_2465))]]) ).
cnf(refute_0_72,plain,
( convergent_lines(orthogonal_through_point(X_2464,X_2465),Z)
| convergent_lines(parallel_through_point(X_2464,X_2463),Z) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(X_2464,X_2465),parallel_through_point(X_2464,X_2463)) )],[refute_0_71,refute_0_59]) ).
cnf(refute_0_73,plain,
( convergent_lines(orthogonal_through_point(X_2464,X_2465),orthogonal_through_point(X_9833,X_9830))
| convergent_lines(parallel_through_point(X_2464,X_2463),orthogonal_through_point(X_9833,X_9830)) ),
inference(subst,[],[refute_0_72:[bind(Z,$fot(orthogonal_through_point(X_9833,X_9830)))]]) ).
cnf(refute_0_74,plain,
convergent_lines(orthogonal_through_point(X_91,A),X_91),
inference(subst,[],[refute_0_20:[bind(X_16,$fot(X_91))]]) ).
cnf(refute_0_75,plain,
( ~ convergent_lines(orthogonal_through_point(X_91,A),X_91)
| unorthogonal_lines(X_89,X_91)
| unorthogonal_lines(X_89,orthogonal_through_point(X_91,A)) ),
inference(subst,[],[refute_0_11:[bind(L,$fot(X_89)),bind(M,$fot(orthogonal_through_point(X_91,A))),bind(N,$fot(X_91))]]) ).
cnf(refute_0_76,plain,
( unorthogonal_lines(X_89,X_91)
| unorthogonal_lines(X_89,orthogonal_through_point(X_91,A)) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(X_91,A),X_91) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
( unorthogonal_lines(X_264,X_91)
| unorthogonal_lines(X_264,orthogonal_through_point(X_91,A)) ),
inference(subst,[],[refute_0_76:[bind(X_89,$fot(X_264))]]) ).
cnf(refute_0_78,plain,
( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| unorthogonal_lines(L,N)
| unorthogonal_lines(M,N) ),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_79,plain,
( ~ convergent_lines(X_264,orthogonal_through_point(X_91,A))
| ~ unorthogonal_lines(X_264,orthogonal_through_point(X_91,A))
| unorthogonal_lines(X_264,X_266)
| unorthogonal_lines(orthogonal_through_point(X_91,A),X_266) ),
inference(subst,[],[refute_0_78:[bind(L,$fot(X_264)),bind(M,$fot(orthogonal_through_point(X_91,A))),bind(N,$fot(X_266))]]) ).
cnf(refute_0_80,plain,
( ~ convergent_lines(X_264,orthogonal_through_point(X_91,A))
| unorthogonal_lines(X_264,X_266)
| unorthogonal_lines(X_264,X_91)
| unorthogonal_lines(orthogonal_through_point(X_91,A),X_266) ),
inference(resolve,[$cnf( unorthogonal_lines(X_264,orthogonal_through_point(X_91,A)) )],[refute_0_77,refute_0_79]) ).
cnf(refute_0_81,plain,
( ~ convergent_lines(orthogonal_through_point(X_2464,X_2465),orthogonal_through_point(X_9833,X_9830))
| unorthogonal_lines(orthogonal_through_point(X_2464,X_2465),X_9832)
| unorthogonal_lines(orthogonal_through_point(X_2464,X_2465),X_9833)
| unorthogonal_lines(orthogonal_through_point(X_9833,X_9830),X_9832) ),
inference(subst,[],[refute_0_80:[bind(A,$fot(X_9830)),bind(X_264,$fot(orthogonal_through_point(X_2464,X_2465))),bind(X_266,$fot(X_9832)),bind(X_91,$fot(X_9833))]]) ).
cnf(refute_0_82,plain,
( convergent_lines(parallel_through_point(X_2464,X_2463),orthogonal_through_point(X_9833,X_9830))
| unorthogonal_lines(orthogonal_through_point(X_2464,X_2465),X_9832)
| unorthogonal_lines(orthogonal_through_point(X_2464,X_2465),X_9833)
| unorthogonal_lines(orthogonal_through_point(X_9833,X_9830),X_9832) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(X_2464,X_2465),orthogonal_through_point(X_9833,X_9830)) )],[refute_0_73,refute_0_81]) ).
cnf(refute_0_83,plain,
( convergent_lines(parallel_through_point(X_2464,X_2463),orthogonal_through_point(X_9833,X_9830))
| unorthogonal_lines(orthogonal_through_point(X_2464,X_2465),X_9833)
| unorthogonal_lines(orthogonal_through_point(X_9833,X_9830),X_9833) ),
inference(subst,[],[refute_0_82:[bind(X_9832,$fot(X_9833))]]) ).
cnf(refute_0_84,plain,
~ unorthogonal_lines(orthogonal_through_point(X_9833,X_9830),X_9833),
inference(subst,[],[refute_0_16:[bind(A,$fot(X_9830)),bind(L,$fot(X_9833))]]) ).
cnf(refute_0_85,plain,
( convergent_lines(parallel_through_point(X_2464,X_2463),orthogonal_through_point(X_9833,X_9830))
| unorthogonal_lines(orthogonal_through_point(X_2464,X_2465),X_9833) ),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(X_9833,X_9830),X_9833) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
( convergent_lines(parallel_through_point(X_11233,X_11232),orthogonal_through_point(X_11236,X_11235))
| unorthogonal_lines(orthogonal_through_point(X_11233,X_11234),X_11236) ),
inference(subst,[],[refute_0_85:[bind(X_2463,$fot(X_11232)),bind(X_2464,$fot(X_11233)),bind(X_2465,$fot(X_11234)),bind(X_9830,$fot(X_11235)),bind(X_9833,$fot(X_11236))]]) ).
cnf(refute_0_87,plain,
( convergent_lines(parallel_through_point(X_11233,X_11232),X_260)
| orthogonal_lines(parallel_through_point(X_11233,X_11232),orthogonal_through_point(X_11236,X_11235))
| unorthogonal_lines(orthogonal_through_point(X_11233,X_11234),X_11236)
| unorthogonal_lines(orthogonal_through_point(X_11236,X_11235),X_260) ),
inference(resolve,[$cnf( convergent_lines(parallel_through_point(X_11233,X_11232),orthogonal_through_point(X_11236,X_11235)) )],[refute_0_86,refute_0_58]) ).
cnf(refute_0_88,plain,
( convergent_lines(parallel_through_point(X_260,X_11232),X_260)
| orthogonal_lines(parallel_through_point(X_260,X_11232),orthogonal_through_point(X_260,X_11235))
| unorthogonal_lines(orthogonal_through_point(X_260,X_11235),X_260) ),
inference(subst,[],[refute_0_87:[bind(X_11233,$fot(X_260)),bind(X_11234,$fot(X_11235)),bind(X_11236,$fot(X_260))]]) ).
cnf(refute_0_89,plain,
~ convergent_lines(parallel_through_point(X_260,X_11232),X_260),
inference(subst,[],[refute_0_62:[bind(X,$fot(X_11232)),bind(Y,$fot(X_260))]]) ).
cnf(refute_0_90,plain,
( orthogonal_lines(parallel_through_point(X_260,X_11232),orthogonal_through_point(X_260,X_11235))
| unorthogonal_lines(orthogonal_through_point(X_260,X_11235),X_260) ),
inference(resolve,[$cnf( convergent_lines(parallel_through_point(X_260,X_11232),X_260) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
~ unorthogonal_lines(orthogonal_through_point(X_260,X_11235),X_260),
inference(subst,[],[refute_0_16:[bind(A,$fot(X_11235)),bind(L,$fot(X_260))]]) ).
cnf(refute_0_92,plain,
orthogonal_lines(parallel_through_point(X_260,X_11232),orthogonal_through_point(X_260,X_11235)),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(X_260,X_11235),X_260) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
orthogonal_lines(parallel_through_point(X_11239,X_11237),orthogonal_through_point(X_11239,X_11238)),
inference(subst,[],[refute_0_92:[bind(X_11232,$fot(X_11237)),bind(X_11235,$fot(X_11238)),bind(X_260,$fot(X_11239))]]) ).
cnf(refute_0_94,plain,
orthogonal_lines(orthogonal_through_point(X_11239,X_11238),parallel_through_point(X_11239,X_11237)),
inference(resolve,[$cnf( orthogonal_lines(parallel_through_point(X_11239,X_11237),orthogonal_through_point(X_11239,X_11238)) )],[refute_0_93,refute_0_57]) ).
cnf(refute_0_95,plain,
orthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_U,X_17768),parallel_through_point(skolemFOFtoCNF_U,X_11237)),
inference(subst,[],[refute_0_94:[bind(X_11238,$fot(X_17768)),bind(X_11239,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_96,plain,
( ~ orthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_U,X_17766),X_17767)
| ~ unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_U,X_17766),X_17767) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(orthogonal_through_point(skolemFOFtoCNF_U,X_17766))),bind(Y,$fot(X_17767))]]) ).
cnf(refute_0_97,plain,
~ unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_U,A),skolemFOFtoCNF_U),
inference(subst,[],[refute_0_16:[bind(L,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_98,plain,
( ~ convergent_lines(skolemFOFtoCNF_U,X_17590)
| unorthogonal_lines(L,X_17590)
| unorthogonal_lines(L,skolemFOFtoCNF_U) ),
inference(subst,[],[refute_0_11:[bind(M,$fot(skolemFOFtoCNF_U)),bind(N,$fot(X_17590))]]) ).
cnf(refute_0_99,plain,
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_33]) ).
cnf(refute_0_100,plain,
( ~ distinct_lines(skolemFOFtoCNF_U,X_17589)
| convergent_lines(skolemFOFtoCNF_U,X_17589) ),
inference(subst,[],[refute_0_99:[bind(X,$fot(skolemFOFtoCNF_U)),bind(Y,$fot(X_17589))]]) ).
cnf(refute_0_101,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_102,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Y,skolemFOFtoCNF_U)
| apart_point_and_line(skolemFOFtoCNF_Y,Z)
| distinct_lines(skolemFOFtoCNF_U,Z) ),
inference(subst,[],[refute_0_101:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_103,plain,
~ convergent_lines(parallel_through_point(skolemFOFtoCNF_V,skolemFOFtoCNF_Y),skolemFOFtoCNF_V),
inference(subst,[],[refute_0_62:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(skolemFOFtoCNF_V))]]) ).
cnf(refute_0_104,plain,
( ~ distinct_lines(parallel_through_point(skolemFOFtoCNF_V,skolemFOFtoCNF_Y),X_17582)
| convergent_lines(parallel_through_point(skolemFOFtoCNF_V,skolemFOFtoCNF_Y),X_17582) ),
inference(subst,[],[refute_0_99:[bind(X,$fot(parallel_through_point(skolemFOFtoCNF_V,skolemFOFtoCNF_Y))),bind(Y,$fot(X_17582))]]) ).
cnf(refute_0_105,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X,parallel_through_point(skolemFOFtoCNF_V,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,Z)
| distinct_lines(parallel_through_point(skolemFOFtoCNF_V,skolemFOFtoCNF_Y),Z) ),
inference(subst,[],[refute_0_101:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(parallel_through_point(skolemFOFtoCNF_V,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_106,plain,
~ apart_point_and_line(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_V,skolemFOFtoCNF_Y)),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(skolemFOFtoCNF_V))]]) ).
cnf(refute_0_107,plain,
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_37]) ).
cnf(refute_0_108,plain,
( ~ distinct_lines(parallel_through_point(skolemFOFtoCNF_V,X_189),X_188)
| distinct_lines(X_188,Z)
| distinct_lines(parallel_through_point(skolemFOFtoCNF_V,X_189),Z) ),
inference(subst,[],[refute_0_107:[bind(X,$fot(parallel_through_point(skolemFOFtoCNF_V,X_189))),bind(Y,$fot(X_188))]]) ).
cnf(refute_0_109,plain,
( ~ distinct_lines(skolemFOFtoCNF_U,parallel_through_point(skolemFOFtoCNF_V,X_179))
| distinct_lines(parallel_through_point(skolemFOFtoCNF_V,X_179),Z)
| distinct_lines(skolemFOFtoCNF_U,Z) ),
inference(subst,[],[refute_0_107:[bind(X,$fot(skolemFOFtoCNF_U)),bind(Y,$fot(parallel_through_point(skolemFOFtoCNF_V,X_179)))]]) ).
cnf(refute_0_110,plain,
~ convergent_lines(parallel_through_point(skolemFOFtoCNF_V,X_178),parallel_through_point(skolemFOFtoCNF_V,X_178)),
inference(subst,[],[refute_0_29:[bind(X,$fot(parallel_through_point(skolemFOFtoCNF_V,X_178)))]]) ).
cnf(refute_0_111,plain,
( ~ convergent_lines(parallel_through_point(skolemFOFtoCNF_V,X_153),skolemFOFtoCNF_U)
| convergent_lines(parallel_through_point(skolemFOFtoCNF_V,X_153),Z)
| distinct_lines(skolemFOFtoCNF_U,Z) ),
inference(subst,[],[refute_0_64:[bind(X,$fot(parallel_through_point(skolemFOFtoCNF_V,X_153))),bind(Y,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_112,plain,
( ~ convergent_lines(parallel_through_point(skolemFOFtoCNF_V,X_152),X_151)
| convergent_lines(X_151,Z)
| convergent_lines(parallel_through_point(skolemFOFtoCNF_V,X_152),Z) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(parallel_through_point(skolemFOFtoCNF_V,X_152))),bind(Y,$fot(X_151))]]) ).
cnf(refute_0_113,plain,
( ~ distinct_lines(parallel_through_point(skolemFOFtoCNF_V,X_142),X_141)
| convergent_lines(parallel_through_point(skolemFOFtoCNF_V,X_142),X_141) ),
inference(subst,[],[refute_0_99:[bind(X,$fot(parallel_through_point(skolemFOFtoCNF_V,X_142))),bind(Y,$fot(X_141))]]) ).
cnf(refute_0_114,plain,
( ~ convergent_lines(skolemFOFtoCNF_U,parallel_through_point(skolemFOFtoCNF_V,X_130))
| convergent_lines(skolemFOFtoCNF_U,Z)
| distinct_lines(parallel_through_point(skolemFOFtoCNF_V,X_130),Z) ),
inference(subst,[],[refute_0_64:[bind(X,$fot(skolemFOFtoCNF_U)),bind(Y,$fot(parallel_through_point(skolemFOFtoCNF_V,X_130)))]]) ).
cnf(refute_0_115,plain,
~ convergent_lines(parallel_through_point(skolemFOFtoCNF_V,X),skolemFOFtoCNF_V),
inference(subst,[],[refute_0_62:[bind(Y,$fot(skolemFOFtoCNF_V))]]) ).
cnf(refute_0_116,plain,
~ convergent_lines(skolemFOFtoCNF_V,skolemFOFtoCNF_V),
inference(subst,[],[refute_0_29:[bind(X,$fot(skolemFOFtoCNF_V))]]) ).
cnf(refute_0_117,plain,
( ~ convergent_lines(skolemFOFtoCNF_V,X_64)
| convergent_lines(X_64,Z)
| convergent_lines(skolemFOFtoCNF_V,Z) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(skolemFOFtoCNF_V)),bind(Y,$fot(X_64))]]) ).
cnf(refute_0_118,plain,
convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V),
inference(canonicalize,[],[normalize_0_40]) ).
cnf(refute_0_119,plain,
( ~ convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V)
| convergent_lines(skolemFOFtoCNF_U,X_63)
| convergent_lines(skolemFOFtoCNF_V,X_63) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(skolemFOFtoCNF_U)),bind(Y,$fot(skolemFOFtoCNF_V)),bind(Z,$fot(X_63))]]) ).
cnf(refute_0_120,plain,
( convergent_lines(skolemFOFtoCNF_U,X_63)
| convergent_lines(skolemFOFtoCNF_V,X_63) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
( convergent_lines(skolemFOFtoCNF_U,X_64)
| convergent_lines(skolemFOFtoCNF_V,X_64) ),
inference(subst,[],[refute_0_120:[bind(X_63,$fot(X_64))]]) ).
cnf(refute_0_122,plain,
( convergent_lines(X_64,Z)
| convergent_lines(skolemFOFtoCNF_U,X_64)
| convergent_lines(skolemFOFtoCNF_V,Z) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_V,X_64) )],[refute_0_121,refute_0_117]) ).
cnf(refute_0_123,plain,
( convergent_lines(X_128,skolemFOFtoCNF_V)
| convergent_lines(skolemFOFtoCNF_U,X_128)
| convergent_lines(skolemFOFtoCNF_V,skolemFOFtoCNF_V) ),
inference(subst,[],[refute_0_122:[bind(Z,$fot(skolemFOFtoCNF_V)),bind(X_64,$fot(X_128))]]) ).
cnf(refute_0_124,plain,
( convergent_lines(X_128,skolemFOFtoCNF_V)
| convergent_lines(skolemFOFtoCNF_U,X_128) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_V,skolemFOFtoCNF_V) )],[refute_0_123,refute_0_116]) ).
cnf(refute_0_125,plain,
( convergent_lines(parallel_through_point(skolemFOFtoCNF_V,X),skolemFOFtoCNF_V)
| convergent_lines(skolemFOFtoCNF_U,parallel_through_point(skolemFOFtoCNF_V,X)) ),
inference(subst,[],[refute_0_124:[bind(X_128,$fot(parallel_through_point(skolemFOFtoCNF_V,X)))]]) ).
cnf(refute_0_126,plain,
convergent_lines(skolemFOFtoCNF_U,parallel_through_point(skolemFOFtoCNF_V,X)),
inference(resolve,[$cnf( convergent_lines(parallel_through_point(skolemFOFtoCNF_V,X),skolemFOFtoCNF_V) )],[refute_0_125,refute_0_115]) ).
cnf(refute_0_127,plain,
convergent_lines(skolemFOFtoCNF_U,parallel_through_point(skolemFOFtoCNF_V,X_130)),
inference(subst,[],[refute_0_126:[bind(X,$fot(X_130))]]) ).
cnf(refute_0_128,plain,
( convergent_lines(skolemFOFtoCNF_U,Z)
| distinct_lines(parallel_through_point(skolemFOFtoCNF_V,X_130),Z) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_U,parallel_through_point(skolemFOFtoCNF_V,X_130)) )],[refute_0_127,refute_0_114]) ).
cnf(refute_0_129,plain,
( convergent_lines(skolemFOFtoCNF_U,X_141)
| distinct_lines(parallel_through_point(skolemFOFtoCNF_V,X_142),X_141) ),
inference(subst,[],[refute_0_128:[bind(Z,$fot(X_141)),bind(X_130,$fot(X_142))]]) ).
cnf(refute_0_130,plain,
( convergent_lines(parallel_through_point(skolemFOFtoCNF_V,X_142),X_141)
| convergent_lines(skolemFOFtoCNF_U,X_141) ),
inference(resolve,[$cnf( distinct_lines(parallel_through_point(skolemFOFtoCNF_V,X_142),X_141) )],[refute_0_129,refute_0_113]) ).
cnf(refute_0_131,plain,
( convergent_lines(parallel_through_point(skolemFOFtoCNF_V,X_152),X_151)
| convergent_lines(skolemFOFtoCNF_U,X_151) ),
inference(subst,[],[refute_0_130:[bind(X_141,$fot(X_151)),bind(X_142,$fot(X_152))]]) ).
cnf(refute_0_132,plain,
( convergent_lines(X_151,Z)
| convergent_lines(parallel_through_point(skolemFOFtoCNF_V,X_152),Z)
| convergent_lines(skolemFOFtoCNF_U,X_151) ),
inference(resolve,[$cnf( convergent_lines(parallel_through_point(skolemFOFtoCNF_V,X_152),X_151) )],[refute_0_131,refute_0_112]) ).
cnf(refute_0_133,plain,
( convergent_lines(parallel_through_point(skolemFOFtoCNF_V,X_152),skolemFOFtoCNF_U)
| convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_U) ),
inference(subst,[],[refute_0_132:[bind(Z,$fot(skolemFOFtoCNF_U)),bind(X_151,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_134,plain,
~ convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_U),
inference(subst,[],[refute_0_29:[bind(X,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_135,plain,
convergent_lines(parallel_through_point(skolemFOFtoCNF_V,X_152),skolemFOFtoCNF_U),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_U) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
convergent_lines(parallel_through_point(skolemFOFtoCNF_V,X_153),skolemFOFtoCNF_U),
inference(subst,[],[refute_0_135:[bind(X_152,$fot(X_153))]]) ).
cnf(refute_0_137,plain,
( convergent_lines(parallel_through_point(skolemFOFtoCNF_V,X_153),Z)
| distinct_lines(skolemFOFtoCNF_U,Z) ),
inference(resolve,[$cnf( convergent_lines(parallel_through_point(skolemFOFtoCNF_V,X_153),skolemFOFtoCNF_U) )],[refute_0_136,refute_0_111]) ).
cnf(refute_0_138,plain,
( convergent_lines(parallel_through_point(skolemFOFtoCNF_V,X_178),parallel_through_point(skolemFOFtoCNF_V,X_178))
| distinct_lines(skolemFOFtoCNF_U,parallel_through_point(skolemFOFtoCNF_V,X_178)) ),
inference(subst,[],[refute_0_137:[bind(Z,$fot(parallel_through_point(skolemFOFtoCNF_V,X_178))),bind(X_153,$fot(X_178))]]) ).
cnf(refute_0_139,plain,
distinct_lines(skolemFOFtoCNF_U,parallel_through_point(skolemFOFtoCNF_V,X_178)),
inference(resolve,[$cnf( convergent_lines(parallel_through_point(skolemFOFtoCNF_V,X_178),parallel_through_point(skolemFOFtoCNF_V,X_178)) )],[refute_0_138,refute_0_110]) ).
cnf(refute_0_140,plain,
distinct_lines(skolemFOFtoCNF_U,parallel_through_point(skolemFOFtoCNF_V,X_179)),
inference(subst,[],[refute_0_139:[bind(X_178,$fot(X_179))]]) ).
cnf(refute_0_141,plain,
( distinct_lines(parallel_through_point(skolemFOFtoCNF_V,X_179),Z)
| distinct_lines(skolemFOFtoCNF_U,Z) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_U,parallel_through_point(skolemFOFtoCNF_V,X_179)) )],[refute_0_140,refute_0_109]) ).
cnf(refute_0_142,plain,
( distinct_lines(parallel_through_point(skolemFOFtoCNF_V,X_189),X_188)
| distinct_lines(skolemFOFtoCNF_U,X_188) ),
inference(subst,[],[refute_0_141:[bind(Z,$fot(X_188)),bind(X_179,$fot(X_189))]]) ).
cnf(refute_0_143,plain,
( distinct_lines(X_188,Z)
| distinct_lines(parallel_through_point(skolemFOFtoCNF_V,X_189),Z)
| distinct_lines(skolemFOFtoCNF_U,X_188) ),
inference(resolve,[$cnf( distinct_lines(parallel_through_point(skolemFOFtoCNF_V,X_189),X_188) )],[refute_0_142,refute_0_108]) ).
cnf(refute_0_144,plain,
( distinct_lines(parallel_through_point(skolemFOFtoCNF_V,X_189),skolemFOFtoCNF_U)
| distinct_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_U) ),
inference(subst,[],[refute_0_143:[bind(Z,$fot(skolemFOFtoCNF_U)),bind(X_188,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_145,plain,
~ distinct_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_U),
inference(subst,[],[refute_0_60:[bind(X,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_146,plain,
distinct_lines(parallel_through_point(skolemFOFtoCNF_V,X_189),skolemFOFtoCNF_U),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_U) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_0_41]) ).
cnf(refute_0_148,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_43]) ).
cnf(refute_0_149,plain,
( ~ distinct_lines(X_8115,X_8116)
| ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| apart_point_and_line(skolemFOFtoCNF_X,X_8115)
| apart_point_and_line(skolemFOFtoCNF_X,X_8116)
| apart_point_and_line(skolemFOFtoCNF_Y,X_8115)
| apart_point_and_line(skolemFOFtoCNF_Y,X_8116) ),
inference(subst,[],[refute_0_148:[bind(U,$fot(X_8115)),bind(V,$fot(X_8116)),bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_150,plain,
( ~ distinct_lines(X_8115,X_8116)
| apart_point_and_line(skolemFOFtoCNF_X,X_8115)
| apart_point_and_line(skolemFOFtoCNF_X,X_8116)
| apart_point_and_line(skolemFOFtoCNF_Y,X_8115)
| apart_point_and_line(skolemFOFtoCNF_Y,X_8116) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_147,refute_0_149]) ).
cnf(refute_0_151,plain,
( ~ distinct_lines(parallel_through_point(skolemFOFtoCNF_V,X_189),skolemFOFtoCNF_U)
| apart_point_and_line(skolemFOFtoCNF_X,parallel_through_point(skolemFOFtoCNF_V,X_189))
| apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U)
| apart_point_and_line(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_V,X_189))
| apart_point_and_line(skolemFOFtoCNF_Y,skolemFOFtoCNF_U) ),
inference(subst,[],[refute_0_150:[bind(X_8115,$fot(parallel_through_point(skolemFOFtoCNF_V,X_189))),bind(X_8116,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_152,plain,
( apart_point_and_line(skolemFOFtoCNF_X,parallel_through_point(skolemFOFtoCNF_V,X_189))
| apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U)
| apart_point_and_line(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_V,X_189))
| apart_point_and_line(skolemFOFtoCNF_Y,skolemFOFtoCNF_U) ),
inference(resolve,[$cnf( distinct_lines(parallel_through_point(skolemFOFtoCNF_V,X_189),skolemFOFtoCNF_U) )],[refute_0_146,refute_0_151]) ).
cnf(refute_0_153,plain,
incident_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U),
inference(canonicalize,[],[normalize_0_44]) ).
cnf(refute_0_154,plain,
( ~ apart_point_and_line(X,Y)
| ~ incident_point_and_line(X,Y) ),
inference(canonicalize,[],[normalize_0_48]) ).
cnf(refute_0_155,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U)
| ~ incident_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U) ),
inference(subst,[],[refute_0_154:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_156,plain,
~ apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U),
inference(resolve,[$cnf( incident_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U) )],[refute_0_153,refute_0_155]) ).
cnf(refute_0_157,plain,
( apart_point_and_line(skolemFOFtoCNF_X,parallel_through_point(skolemFOFtoCNF_V,X_189))
| apart_point_and_line(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_V,X_189))
| apart_point_and_line(skolemFOFtoCNF_Y,skolemFOFtoCNF_U) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U) )],[refute_0_152,refute_0_156]) ).
cnf(refute_0_158,plain,
( apart_point_and_line(skolemFOFtoCNF_X,parallel_through_point(skolemFOFtoCNF_V,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_V,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,skolemFOFtoCNF_U) ),
inference(subst,[],[refute_0_157:[bind(X_189,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_159,plain,
( apart_point_and_line(skolemFOFtoCNF_X,parallel_through_point(skolemFOFtoCNF_V,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,skolemFOFtoCNF_U) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_V,skolemFOFtoCNF_Y)) )],[refute_0_158,refute_0_106]) ).
cnf(refute_0_160,plain,
( apart_point_and_line(skolemFOFtoCNF_X,Z)
| apart_point_and_line(skolemFOFtoCNF_Y,skolemFOFtoCNF_U)
| distinct_lines(parallel_through_point(skolemFOFtoCNF_V,skolemFOFtoCNF_Y),Z) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,parallel_through_point(skolemFOFtoCNF_V,skolemFOFtoCNF_Y)) )],[refute_0_159,refute_0_105]) ).
cnf(refute_0_161,plain,
( apart_point_and_line(skolemFOFtoCNF_X,X_17582)
| apart_point_and_line(skolemFOFtoCNF_Y,skolemFOFtoCNF_U)
| distinct_lines(parallel_through_point(skolemFOFtoCNF_V,skolemFOFtoCNF_Y),X_17582) ),
inference(subst,[],[refute_0_160:[bind(Z,$fot(X_17582))]]) ).
cnf(refute_0_162,plain,
( apart_point_and_line(skolemFOFtoCNF_X,X_17582)
| apart_point_and_line(skolemFOFtoCNF_Y,skolemFOFtoCNF_U)
| convergent_lines(parallel_through_point(skolemFOFtoCNF_V,skolemFOFtoCNF_Y),X_17582) ),
inference(resolve,[$cnf( distinct_lines(parallel_through_point(skolemFOFtoCNF_V,skolemFOFtoCNF_Y),X_17582) )],[refute_0_161,refute_0_104]) ).
cnf(refute_0_163,plain,
( apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_V)
| apart_point_and_line(skolemFOFtoCNF_Y,skolemFOFtoCNF_U)
| convergent_lines(parallel_through_point(skolemFOFtoCNF_V,skolemFOFtoCNF_Y),skolemFOFtoCNF_V) ),
inference(subst,[],[refute_0_162:[bind(X_17582,$fot(skolemFOFtoCNF_V))]]) ).
cnf(refute_0_164,plain,
( apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_V)
| apart_point_and_line(skolemFOFtoCNF_Y,skolemFOFtoCNF_U) ),
inference(resolve,[$cnf( convergent_lines(parallel_through_point(skolemFOFtoCNF_V,skolemFOFtoCNF_Y),skolemFOFtoCNF_V) )],[refute_0_163,refute_0_103]) ).
cnf(refute_0_165,plain,
incident_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_V),
inference(canonicalize,[],[normalize_0_49]) ).
cnf(refute_0_166,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_V)
| ~ incident_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_V) ),
inference(subst,[],[refute_0_154:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_V))]]) ).
cnf(refute_0_167,plain,
~ apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_V),
inference(resolve,[$cnf( incident_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_V) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
apart_point_and_line(skolemFOFtoCNF_Y,skolemFOFtoCNF_U),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_V) )],[refute_0_164,refute_0_167]) ).
cnf(refute_0_169,plain,
( apart_point_and_line(skolemFOFtoCNF_Y,Z)
| distinct_lines(skolemFOFtoCNF_U,Z) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y,skolemFOFtoCNF_U) )],[refute_0_168,refute_0_102]) ).
cnf(refute_0_170,plain,
( apart_point_and_line(skolemFOFtoCNF_Y,X_17589)
| distinct_lines(skolemFOFtoCNF_U,X_17589) ),
inference(subst,[],[refute_0_169:[bind(Z,$fot(X_17589))]]) ).
cnf(refute_0_171,plain,
( apart_point_and_line(skolemFOFtoCNF_Y,X_17589)
| convergent_lines(skolemFOFtoCNF_U,X_17589) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_U,X_17589) )],[refute_0_170,refute_0_100]) ).
cnf(refute_0_172,plain,
( apart_point_and_line(skolemFOFtoCNF_Y,X_17590)
| convergent_lines(skolemFOFtoCNF_U,X_17590) ),
inference(subst,[],[refute_0_171:[bind(X_17589,$fot(X_17590))]]) ).
cnf(refute_0_173,plain,
( apart_point_and_line(skolemFOFtoCNF_Y,X_17590)
| unorthogonal_lines(L,X_17590)
| unorthogonal_lines(L,skolemFOFtoCNF_U) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_U,X_17590) )],[refute_0_172,refute_0_98]) ).
cnf(refute_0_174,plain,
( apart_point_and_line(skolemFOFtoCNF_Y,X_17763)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_U,A),X_17763)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_U,A),skolemFOFtoCNF_U) ),
inference(subst,[],[refute_0_173:[bind(L,$fot(orthogonal_through_point(skolemFOFtoCNF_U,A))),bind(X_17590,$fot(X_17763))]]) ).
cnf(refute_0_175,plain,
( apart_point_and_line(skolemFOFtoCNF_Y,X_17763)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_U,A),X_17763) ),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_U,A),skolemFOFtoCNF_U) )],[refute_0_174,refute_0_97]) ).
cnf(refute_0_176,plain,
( apart_point_and_line(skolemFOFtoCNF_Y,X_17767)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_U,X_17766),X_17767) ),
inference(subst,[],[refute_0_175:[bind(A,$fot(X_17766)),bind(X_17763,$fot(X_17767))]]) ).
cnf(refute_0_177,plain,
( ~ orthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_U,X_17766),X_17767)
| apart_point_and_line(skolemFOFtoCNF_Y,X_17767) ),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_U,X_17766),X_17767) )],[refute_0_176,refute_0_96]) ).
cnf(refute_0_178,plain,
( ~ orthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_U,X_17768),parallel_through_point(skolemFOFtoCNF_U,X_11237))
| apart_point_and_line(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_U,X_11237)) ),
inference(subst,[],[refute_0_177:[bind(X_17766,$fot(X_17768)),bind(X_17767,$fot(parallel_through_point(skolemFOFtoCNF_U,X_11237)))]]) ).
cnf(refute_0_179,plain,
apart_point_and_line(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_U,X_11237)),
inference(resolve,[$cnf( orthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_U,X_17768),parallel_through_point(skolemFOFtoCNF_U,X_11237)) )],[refute_0_95,refute_0_178]) ).
cnf(refute_0_180,plain,
apart_point_and_line(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_U,skolemFOFtoCNF_Y)),
inference(subst,[],[refute_0_179:[bind(X_11237,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_181,plain,
$false,
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_U,skolemFOFtoCNF_Y)) )],[refute_0_180,refute_0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO186+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jun 17 15:33:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 248.27/248.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 248.27/248.44
% 248.27/248.44 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 248.27/248.45
%------------------------------------------------------------------------------