TSTP Solution File: GEO223+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO223+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n011.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 05:25:35 EDT 2022
% Result : Theorem 1.37s 1.56s
% Output : CNFRefutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 16
% Syntax : Number of formulae : 151 ( 53 unt; 0 def)
% Number of atoms : 358 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 319 ( 112 ~; 189 |; 10 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 289 ( 31 sgn 117 !; 2 ?)
% 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(ceq3,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( distinct_lines(Y,Z)
| convergent_lines(X,Z) ) ) ).
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(cup1,axiom,
! [X,Y,Z] :
( distinct_lines(Y,Z)
=> ( apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| convergent_lines(Y,Z) ) ) ).
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(ooc2,axiom,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)) ).
fof(ouo1,axiom,
! [A,L,M,N] :
( distinct_lines(L,M)
=> ( apart_point_and_line(A,L)
| apart_point_and_line(A,M)
| unorthogonal_lines(L,N)
| unorthogonal_lines(M,N) ) ) ).
fof(con,conjecture,
! [A,L] : ~ distinct_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)) ).
fof(subgoal_0,plain,
! [A,L] : ~ distinct_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [A,L] : ~ distinct_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(canonicalize,[],[ooc1]) ).
fof(normalize_0_1,plain,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,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_3,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_2]) ).
fof(normalize_0_4,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_3]) ).
fof(normalize_0_5,plain,
! [L,M,N] :
( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| convergent_lines(L,N)
| unorthogonal_lines(M,N) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(canonicalize,[],[ci3]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(canonicalize,[],[ci4]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
? [A,L] : distinct_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_11,plain,
distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),
inference(skolemize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X,Y,Z] :
( ~ distinct_lines(Y,Z)
| apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[cup1]) ).
fof(normalize_0_13,plain,
! [X,Y,Z] :
( ~ distinct_lines(Y,Z)
| apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| convergent_lines(Y,Z) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[ceq3]) ).
fof(normalize_0_15,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(canonicalize,[],[cp2]) ).
fof(normalize_0_17,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[apart5]) ).
fof(normalize_0_19,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
inference(canonicalize,[],[ooc2]) ).
fof(normalize_0_21,plain,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [X] : ~ distinct_lines(X,X),
inference(canonicalize,[],[apart2]) ).
fof(normalize_0_23,plain,
! [X] : ~ distinct_lines(X,X),
inference(specialize,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [A,L,M,N] :
( ~ distinct_lines(L,M)
| apart_point_and_line(A,L)
| apart_point_and_line(A,M)
| unorthogonal_lines(L,N)
| unorthogonal_lines(M,N) ),
inference(canonicalize,[],[ouo1]) ).
fof(normalize_0_25,plain,
! [A,L,M,N] :
( ~ distinct_lines(L,M)
| apart_point_and_line(A,L)
| apart_point_and_line(A,M)
| unorthogonal_lines(L,N)
| unorthogonal_lines(M,N) ),
inference(specialize,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [X] : ~ convergent_lines(X,X),
inference(canonicalize,[],[apart3]) ).
fof(normalize_0_27,plain,
! [X] : ~ convergent_lines(X,X),
inference(specialize,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[ax6]) ).
fof(normalize_0_29,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(specialize,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(canonicalize,[],[cp1]) ).
fof(normalize_0_31,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(specialize,[],[normalize_0_30]) ).
fof(normalize_0_32,plain,
! [L,M] :
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(canonicalize,[],[occu1]) ).
fof(normalize_0_33,plain,
! [L,M] :
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(specialize,[],[normalize_0_32]) ).
cnf(refute_0_0,plain,
~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
~ unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A)),bind(L,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_2,plain,
( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| convergent_lines(L,N)
| unorthogonal_lines(M,N) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( ~ convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| ~ unorthogonal_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),N)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),N) ),
inference(subst,[],[refute_0_2:[bind(L,$fot(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))),bind(M,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_4,plain,
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ apart_point_and_line(intersection_point(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| ~ convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))),bind(Y,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_6,plain,
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_7,plain,
( ~ apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))),bind(Y,$fot(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_8,plain,
( ~ apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),Y),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),Y) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_9,plain,
distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_10,plain,
( ~ distinct_lines(Y,Z)
| apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_11,plain,
( ~ distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| apart_point_and_line(X_125,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| apart_point_and_line(X_125,parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(X_125)),bind(Y,$fot(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))),bind(Z,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_12,plain,
( apart_point_and_line(X_125,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| apart_point_and_line(X_125,parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
( apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),Y),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),Y),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_12:[bind(X_125,$fot(intersection_point(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),Y)))]]) ).
cnf(refute_0_14,plain,
( ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),Y)
| apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),Y),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),Y),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) )],[refute_0_13,refute_0_8]) ).
cnf(refute_0_15,plain,
( ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_14:[bind(Y,$fot(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_16,plain,
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_17,plain,
( ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),parallel_through_point(X_862,X_863))
| convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),Z)
| distinct_lines(parallel_through_point(X_862,X_863),Z) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))),bind(Y,$fot(parallel_through_point(X_862,X_863)))]]) ).
cnf(refute_0_18,plain,
~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_19,plain,
~ apart_point_and_line(X_487,parallel_through_point(Y,X_487)),
inference(subst,[],[refute_0_18:[bind(X,$fot(X_487))]]) ).
cnf(refute_0_20,plain,
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_21,plain,
( ~ distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_36)
| distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_36) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))),bind(Y,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))),bind(Z,$fot(X_36))]]) ).
cnf(refute_0_22,plain,
( distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_36)
| distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_36) ),
inference(resolve,[$cnf( distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) )],[refute_0_9,refute_0_21]) ).
cnf(refute_0_23,plain,
( distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_127)
| distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_127) ),
inference(subst,[],[refute_0_22:[bind(X_36,$fot(X_127))]]) ).
cnf(refute_0_24,plain,
( ~ distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_127)
| apart_point_and_line(X_125,X_127)
| apart_point_and_line(X_125,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_127) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(X_125)),bind(Y,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))),bind(Z,$fot(X_127))]]) ).
cnf(refute_0_25,plain,
( apart_point_and_line(X_125,X_127)
| apart_point_and_line(X_125,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_127)
| distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_127) ),
inference(resolve,[$cnf( distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_127) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( apart_point_and_line(X_487,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| apart_point_and_line(X_487,parallel_through_point(Y,X_487))
| convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),parallel_through_point(Y,X_487))
| distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),parallel_through_point(Y,X_487)) ),
inference(subst,[],[refute_0_25:[bind(X_125,$fot(X_487)),bind(X_127,$fot(parallel_through_point(Y,X_487)))]]) ).
cnf(refute_0_27,plain,
( apart_point_and_line(X_487,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),parallel_through_point(Y,X_487))
| distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),parallel_through_point(Y,X_487)) ),
inference(resolve,[$cnf( apart_point_and_line(X_487,parallel_through_point(Y,X_487)) )],[refute_0_26,refute_0_19]) ).
cnf(refute_0_28,plain,
( apart_point_and_line(X_863,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),parallel_through_point(X_862,X_863))
| distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),parallel_through_point(X_862,X_863)) ),
inference(subst,[],[refute_0_27:[bind(Y,$fot(X_862)),bind(X_487,$fot(X_863))]]) ).
cnf(refute_0_29,plain,
( apart_point_and_line(X_863,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),Z)
| distinct_lines(parallel_through_point(X_862,X_863),Z)
| distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),parallel_through_point(X_862,X_863)) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),parallel_through_point(X_862,X_863)) )],[refute_0_28,refute_0_17]) ).
cnf(refute_0_30,plain,
( apart_point_and_line(skolemFOFtoCNF_A,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_29:[bind(Z,$fot(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))),bind(X_862,$fot(skolemFOFtoCNF_L)),bind(X_863,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_31,plain,
~ apart_point_and_line(A,orthogonal_through_point(L,A)),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_32,plain,
~ apart_point_and_line(skolemFOFtoCNF_A,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),
inference(subst,[],[refute_0_31:[bind(A,$fot(skolemFOFtoCNF_A)),bind(L,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_33,plain,
( convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_A,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) )],[refute_0_30,refute_0_32]) ).
cnf(refute_0_34,plain,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_35,plain,
~ distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),
inference(subst,[],[refute_0_34:[bind(X,$fot(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_36,plain,
convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),
inference(resolve,[$cnf( distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_33,refute_0_35]) ).
cnf(refute_0_37,plain,
( apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_36,refute_0_15]) ).
cnf(refute_0_38,plain,
( ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_37,refute_0_7]) ).
cnf(refute_0_39,plain,
convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_36,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ apart_point_and_line(intersection_point(X,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| ~ convergent_lines(X,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_6:[bind(Y,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_41,plain,
~ unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A)),bind(L,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_42,plain,
( ~ distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_37)
| distinct_lines(X_37,Z)
| distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),Z) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))),bind(Y,$fot(X_37))]]) ).
cnf(refute_0_43,plain,
( distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_37)
| distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_37) ),
inference(subst,[],[refute_0_22:[bind(X_36,$fot(X_37))]]) ).
cnf(refute_0_44,plain,
( distinct_lines(X_37,Z)
| distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),Z)
| distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_37) ),
inference(resolve,[$cnf( distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_37) )],[refute_0_43,refute_0_42]) ).
cnf(refute_0_45,plain,
( distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_44:[bind(Z,$fot(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))),bind(X_37,$fot(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_46,plain,
distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),
inference(resolve,[$cnf( distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_45,refute_0_35]) ).
cnf(refute_0_47,plain,
( ~ distinct_lines(L,M)
| apart_point_and_line(A,L)
| apart_point_and_line(A,M)
| unorthogonal_lines(L,N)
| unorthogonal_lines(M,N) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_48,plain,
( ~ distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| apart_point_and_line(X_329,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| apart_point_and_line(X_329,parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_332)
| unorthogonal_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_332) ),
inference(subst,[],[refute_0_47:[bind(A,$fot(X_329)),bind(L,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))),bind(M,$fot(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))),bind(N,$fot(X_332))]]) ).
cnf(refute_0_49,plain,
( apart_point_and_line(X_329,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| apart_point_and_line(X_329,parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_332)
| unorthogonal_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_332) ),
inference(resolve,[$cnf( distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_46,refute_0_48]) ).
cnf(refute_0_50,plain,
( apart_point_and_line(X_1047,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| apart_point_and_line(X_1047,parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| unorthogonal_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_49:[bind(X_329,$fot(X_1047)),bind(X_332,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_51,plain,
( apart_point_and_line(X_1047,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| apart_point_and_line(X_1047,parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| unorthogonal_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_50,refute_0_41]) ).
cnf(refute_0_52,plain,
( apart_point_and_line(intersection_point(X,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| apart_point_and_line(intersection_point(X,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| unorthogonal_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_51:[bind(X_1047,$fot(intersection_point(X,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))))]]) ).
cnf(refute_0_53,plain,
( ~ convergent_lines(X,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| apart_point_and_line(intersection_point(X,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| unorthogonal_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(X,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) )],[refute_0_52,refute_0_40]) ).
cnf(refute_0_54,plain,
( ~ convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| apart_point_and_line(intersection_point(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| unorthogonal_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_53:[bind(X,$fot(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_55,plain,
( apart_point_and_line(intersection_point(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| unorthogonal_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) )],[refute_0_39,refute_0_54]) ).
cnf(refute_0_56,plain,
( ~ convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| unorthogonal_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_55,refute_0_5]) ).
cnf(refute_0_57,plain,
unorthogonal_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),
inference(resolve,[$cnf( convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) )],[refute_0_39,refute_0_56]) ).
cnf(refute_0_58,plain,
( ~ convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),N)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),N) ),
inference(resolve,[$cnf( unorthogonal_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_57,refute_0_3]) ).
cnf(refute_0_59,plain,
~ convergent_lines(X,X),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_60,plain,
~ convergent_lines(orthogonal_through_point(X_271,X_272),orthogonal_through_point(X_271,X_272)),
inference(subst,[],[refute_0_59:[bind(X,$fot(orthogonal_through_point(X_271,X_272)))]]) ).
cnf(refute_0_61,plain,
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_62,plain,
( ~ convergent_lines(orthogonal_through_point(X_264,X_265),parallel_through_point(X_264,X_263))
| convergent_lines(orthogonal_through_point(X_264,X_265),Z)
| convergent_lines(parallel_through_point(X_264,X_263),Z) ),
inference(subst,[],[refute_0_61:[bind(X,$fot(orthogonal_through_point(X_264,X_265))),bind(Y,$fot(parallel_through_point(X_264,X_263)))]]) ).
cnf(refute_0_63,plain,
~ distinct_lines(parallel_through_point(X_261,X_259),parallel_through_point(X_261,X_259)),
inference(subst,[],[refute_0_34:[bind(X,$fot(parallel_through_point(X_261,X_259)))]]) ).
cnf(refute_0_64,plain,
~ convergent_lines(parallel_through_point(Y,X),Y),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_65,plain,
~ convergent_lines(parallel_through_point(X_253,X),X_253),
inference(subst,[],[refute_0_64:[bind(Y,$fot(X_253))]]) ).
cnf(refute_0_66,plain,
( ~ convergent_lines(orthogonal_through_point(X_154,X_156),X_155)
| convergent_lines(orthogonal_through_point(X_154,X_156),Z)
| distinct_lines(X_155,Z) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(orthogonal_through_point(X_154,X_156))),bind(Y,$fot(X_155))]]) ).
cnf(refute_0_67,plain,
( ~ convergent_lines(X_140,X_137)
| convergent_lines(X_137,Z)
| convergent_lines(X_140,Z) ),
inference(subst,[],[refute_0_61:[bind(X,$fot(X_140)),bind(Y,$fot(X_137))]]) ).
cnf(refute_0_68,plain,
( ~ convergent_lines(orthogonal_through_point(X_27,X_26),X_28)
| convergent_lines(X_28,Z)
| convergent_lines(orthogonal_through_point(X_27,X_26),Z) ),
inference(subst,[],[refute_0_61:[bind(X,$fot(orthogonal_through_point(X_27,X_26))),bind(Y,$fot(X_28))]]) ).
cnf(refute_0_69,plain,
~ unorthogonal_lines(orthogonal_through_point(X_12,A),X_12),
inference(subst,[],[refute_0_0:[bind(L,$fot(X_12))]]) ).
cnf(refute_0_70,plain,
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(canonicalize,[],[normalize_0_33]) ).
cnf(refute_0_71,plain,
( convergent_lines(orthogonal_through_point(X_12,A),X_12)
| unorthogonal_lines(orthogonal_through_point(X_12,A),X_12) ),
inference(subst,[],[refute_0_70:[bind(L,$fot(orthogonal_through_point(X_12,A))),bind(M,$fot(X_12))]]) ).
cnf(refute_0_72,plain,
convergent_lines(orthogonal_through_point(X_12,A),X_12),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(X_12,A),X_12) )],[refute_0_71,refute_0_69]) ).
cnf(refute_0_73,plain,
convergent_lines(orthogonal_through_point(X_24,A),X_24),
inference(subst,[],[refute_0_72:[bind(X_12,$fot(X_24))]]) ).
cnf(refute_0_74,plain,
( ~ convergent_lines(orthogonal_through_point(X_24,A),X_24)
| convergent_lines(X_24,X_25)
| convergent_lines(orthogonal_through_point(X_24,A),X_25) ),
inference(subst,[],[refute_0_61:[bind(X,$fot(orthogonal_through_point(X_24,A))),bind(Y,$fot(X_24)),bind(Z,$fot(X_25))]]) ).
cnf(refute_0_75,plain,
( convergent_lines(X_24,X_25)
| convergent_lines(orthogonal_through_point(X_24,A),X_25) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(X_24,A),X_24) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
( convergent_lines(X_27,X_28)
| convergent_lines(orthogonal_through_point(X_27,X_26),X_28) ),
inference(subst,[],[refute_0_75:[bind(A,$fot(X_26)),bind(X_24,$fot(X_27)),bind(X_25,$fot(X_28))]]) ).
cnf(refute_0_77,plain,
( convergent_lines(X_27,X_28)
| convergent_lines(X_28,Z)
| convergent_lines(orthogonal_through_point(X_27,X_26),Z) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(X_27,X_26),X_28) )],[refute_0_76,refute_0_68]) ).
cnf(refute_0_78,plain,
( convergent_lines(X_139,X_140)
| convergent_lines(X_140,X_137)
| convergent_lines(orthogonal_through_point(X_139,X_138),X_137) ),
inference(subst,[],[refute_0_77:[bind(Z,$fot(X_137)),bind(X_26,$fot(X_138)),bind(X_27,$fot(X_139)),bind(X_28,$fot(X_140))]]) ).
cnf(refute_0_79,plain,
( convergent_lines(X_137,Z)
| convergent_lines(X_139,X_140)
| convergent_lines(X_140,Z)
| convergent_lines(orthogonal_through_point(X_139,X_138),X_137) ),
inference(resolve,[$cnf( convergent_lines(X_140,X_137) )],[refute_0_78,refute_0_67]) ).
cnf(refute_0_80,plain,
( convergent_lines(Z,Z)
| convergent_lines(X_137,Z)
| convergent_lines(orthogonal_through_point(Z,X_138),X_137) ),
inference(subst,[],[refute_0_79:[bind(X_139,$fot(Z)),bind(X_140,$fot(Z))]]) ).
cnf(refute_0_81,plain,
~ convergent_lines(Z,Z),
inference(subst,[],[refute_0_59:[bind(X,$fot(Z))]]) ).
cnf(refute_0_82,plain,
( convergent_lines(X_137,Z)
| convergent_lines(orthogonal_through_point(Z,X_138),X_137) ),
inference(resolve,[$cnf( convergent_lines(Z,Z) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
( convergent_lines(X_155,X_154)
| convergent_lines(orthogonal_through_point(X_154,X_156),X_155) ),
inference(subst,[],[refute_0_82:[bind(Z,$fot(X_154)),bind(X_137,$fot(X_155)),bind(X_138,$fot(X_156))]]) ).
cnf(refute_0_84,plain,
( convergent_lines(X_155,X_154)
| convergent_lines(orthogonal_through_point(X_154,X_156),Z)
| distinct_lines(X_155,Z) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(X_154,X_156),X_155) )],[refute_0_83,refute_0_66]) ).
cnf(refute_0_85,plain,
( convergent_lines(orthogonal_through_point(X_253,X_255),X_252)
| convergent_lines(parallel_through_point(X_253,X),X_253)
| distinct_lines(parallel_through_point(X_253,X),X_252) ),
inference(subst,[],[refute_0_84:[bind(Z,$fot(X_252)),bind(X_154,$fot(X_253)),bind(X_155,$fot(parallel_through_point(X_253,X))),bind(X_156,$fot(X_255))]]) ).
cnf(refute_0_86,plain,
( convergent_lines(orthogonal_through_point(X_253,X_255),X_252)
| distinct_lines(parallel_through_point(X_253,X),X_252) ),
inference(resolve,[$cnf( convergent_lines(parallel_through_point(X_253,X),X_253) )],[refute_0_85,refute_0_65]) ).
cnf(refute_0_87,plain,
( convergent_lines(orthogonal_through_point(X_261,X_262),parallel_through_point(X_261,X_259))
| distinct_lines(parallel_through_point(X_261,X_259),parallel_through_point(X_261,X_259)) ),
inference(subst,[],[refute_0_86:[bind(X,$fot(X_259)),bind(X_252,$fot(parallel_through_point(X_261,X_259))),bind(X_253,$fot(X_261)),bind(X_255,$fot(X_262))]]) ).
cnf(refute_0_88,plain,
convergent_lines(orthogonal_through_point(X_261,X_262),parallel_through_point(X_261,X_259)),
inference(resolve,[$cnf( distinct_lines(parallel_through_point(X_261,X_259),parallel_through_point(X_261,X_259)) )],[refute_0_87,refute_0_63]) ).
cnf(refute_0_89,plain,
convergent_lines(orthogonal_through_point(X_264,X_265),parallel_through_point(X_264,X_263)),
inference(subst,[],[refute_0_88:[bind(X_259,$fot(X_263)),bind(X_261,$fot(X_264)),bind(X_262,$fot(X_265))]]) ).
cnf(refute_0_90,plain,
( convergent_lines(orthogonal_through_point(X_264,X_265),Z)
| convergent_lines(parallel_through_point(X_264,X_263),Z) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(X_264,X_265),parallel_through_point(X_264,X_263)) )],[refute_0_89,refute_0_62]) ).
cnf(refute_0_91,plain,
( convergent_lines(orthogonal_through_point(X_271,X_272),orthogonal_through_point(X_271,X_272))
| convergent_lines(parallel_through_point(X_271,X_270),orthogonal_through_point(X_271,X_272)) ),
inference(subst,[],[refute_0_90:[bind(Z,$fot(orthogonal_through_point(X_271,X_272))),bind(X_263,$fot(X_270)),bind(X_264,$fot(X_271)),bind(X_265,$fot(X_272))]]) ).
cnf(refute_0_92,plain,
convergent_lines(parallel_through_point(X_271,X_270),orthogonal_through_point(X_271,X_272)),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(X_271,X_272),orthogonal_through_point(X_271,X_272)) )],[refute_0_91,refute_0_60]) ).
cnf(refute_0_93,plain,
convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),
inference(subst,[],[refute_0_92:[bind(X_270,$fot(skolemFOFtoCNF_A)),bind(X_271,$fot(skolemFOFtoCNF_L)),bind(X_272,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_94,plain,
( convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),N)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),N) ),
inference(resolve,[$cnf( convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_93,refute_0_58]) ).
cnf(refute_0_95,plain,
( convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_94:[bind(N,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_96,plain,
convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L) )],[refute_0_95,refute_0_1]) ).
cnf(refute_0_97,plain,
~ convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L),
inference(subst,[],[refute_0_64:[bind(X,$fot(skolemFOFtoCNF_A)),bind(Y,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_98,plain,
$false,
inference(resolve,[$cnf( convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L) )],[refute_0_96,refute_0_97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO223+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 18 11:52:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.37/1.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.37/1.56
% 1.37/1.56 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.41/1.57
%------------------------------------------------------------------------------