%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO223+2 : TPTP v8.1.0. Released v3.3.0.
% 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 05:25:36 EDT 2022
% Result : Theorem 3.77s 3.96s
% Output : CNFRefutation 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 15
% Syntax : Number of formulae : 143 ( 55 unt; 0 def)
% Number of atoms : 354 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 321 ( 110 ~; 191 |; 13 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 277 ( 24 sgn 117 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X] : ~ distinct_points(X,X) ).
fof(apart2,axiom,
! [X] : ~ distinct_lines(X,X) ).
fof(apart3,axiom,
! [X] : ~ convergent_lines(X,X) ).
fof(apart5,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(X,Z)
| distinct_lines(Y,Z) ) ) ).
fof(apart6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| convergent_lines(Y,Z) ) ) ).
fof(con2,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( ( apart_point_and_line(Z,X)
| apart_point_and_line(Z,Y) )
=> distinct_points(Z,intersection_point(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(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,Z] :
( ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y))
| ( ~ apart_point_and_line(Z,X)
& ~ apart_point_and_line(Z,Y) ) ),
inference(canonicalize,[],[con2]) ).
fof(normalize_0_7,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y))
| ( ~ apart_point_and_line(Z,X)
& ~ apart_point_and_line(Z,Y) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X,Y,Z] :
( ( ~ apart_point_and_line(Z,X)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) )
& ( ~ apart_point_and_line(Z,Y)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(Z,X)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X] : ~ distinct_lines(X,X),
inference(canonicalize,[],[apart2]) ).
fof(normalize_0_11,plain,
! [X] : ~ distinct_lines(X,X),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
inference(canonicalize,[],[ooc2]) ).
fof(normalize_0_13,plain,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,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_15,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_14]) ).
fof(normalize_0_16,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[apart5]) ).
fof(normalize_0_17,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,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_19,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_18]) ).
fof(normalize_0_20,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(canonicalize,[],[cp2]) ).
fof(normalize_0_21,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [X] : ~ distinct_points(X,X),
inference(canonicalize,[],[apart1]) ).
fof(normalize_0_23,plain,
! [X] : ~ distinct_points(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,Y,Z] :
( ~ apart_point_and_line(Z,Y)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_27,plain,
! [X] : ~ convergent_lines(X,X),
inference(canonicalize,[],[apart3]) ).
fof(normalize_0_28,plain,
! [X] : ~ convergent_lines(X,X),
inference(specialize,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(canonicalize,[],[cp1]) ).
fof(normalize_0_30,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(specialize,[],[normalize_0_29]) ).
fof(normalize_0_31,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[apart6]) ).
fof(normalize_0_32,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(specialize,[],[normalize_0_31]) ).
fof(normalize_0_33,plain,
! [L,M] :
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(canonicalize,[],[occu1]) ).
fof(normalize_0_34,plain,
! [L,M] :
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(specialize,[],[normalize_0_33]) ).
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(Z,X)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_5,plain,
( ~ apart_point_and_line(Z,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))
| distinct_points(Z,intersection_point(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,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_7,plain,
~ distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),
inference(subst,[],[refute_0_6:[bind(X,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_8,plain,
~ apart_point_and_line(A,orthogonal_through_point(L,A)),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_9,plain,
~ apart_point_and_line(X_1290,orthogonal_through_point(L,X_1290)),
inference(subst,[],[refute_0_8:[bind(A,$fot(X_1290))]]) ).
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_15]) ).
cnf(refute_0_11,plain,
( ~ distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_620)
| apart_point_and_line(X,X_620)
| apart_point_and_line(X,parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_620) ),
inference(subst,[],[refute_0_10:[bind(Y,$fot(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))),bind(Z,$fot(X_620))]]) ).
cnf(refute_0_12,plain,
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_13,plain,
( ~ distinct_lines(X_73,X_72)
| distinct_lines(X_72,Z)
| distinct_lines(X_73,Z) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_73)),bind(Y,$fot(X_72))]]) ).
cnf(refute_0_14,plain,
( ~ distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_25)
| distinct_lines(X_25,Z)
| distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),Z) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))),bind(Y,$fot(X_25))]]) ).
cnf(refute_0_15,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_19]) ).
cnf(refute_0_16,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_24)
| distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_24) ),
inference(subst,[],[refute_0_12:[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,$fot(X_24))]]) ).
cnf(refute_0_17,plain,
( distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_24)
| distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_24) ),
inference(resolve,[$cnf( distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_25)
| distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_25) ),
inference(subst,[],[refute_0_17:[bind(X_24,$fot(X_25))]]) ).
cnf(refute_0_19,plain,
( distinct_lines(X_25,Z)
| distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),Z)
| distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_25) ),
inference(resolve,[$cnf( distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_25) )],[refute_0_18,refute_0_14]) ).
cnf(refute_0_20,plain,
( distinct_lines(X_73,X_72)
| distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_72)
| distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_73) ),
inference(subst,[],[refute_0_19:[bind(Z,$fot(X_72)),bind(X_25,$fot(X_73))]]) ).
cnf(refute_0_21,plain,
( distinct_lines(X_72,Z)
| distinct_lines(X_73,Z)
| distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_72)
| distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_73) ),
inference(resolve,[$cnf( distinct_lines(X_73,X_72) )],[refute_0_20,refute_0_13]) ).
cnf(refute_0_22,plain,
( distinct_lines(X_619,X_618)
| distinct_lines(X_620,X_618)
| distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_619)
| distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_620) ),
inference(subst,[],[refute_0_21:[bind(Z,$fot(X_618)),bind(X_72,$fot(X_619)),bind(X_73,$fot(X_620))]]) ).
cnf(refute_0_23,plain,
( apart_point_and_line(X,X_620)
| apart_point_and_line(X,parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_620)
| distinct_lines(X_619,X_618)
| distinct_lines(X_620,X_618)
| distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_619) ),
inference(resolve,[$cnf( distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_620) )],[refute_0_22,refute_0_11]) ).
cnf(refute_0_24,plain,
( apart_point_and_line(X,X_620)
| apart_point_and_line(X,parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_620)
| distinct_lines(X_620,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_23:[bind(X_618,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))),bind(X_619,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_25,plain,
( apart_point_and_line(X,X_620)
| apart_point_and_line(X,parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_620)
| distinct_lines(X_620,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( distinct_lines(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_24,refute_0_7]) ).
cnf(refute_0_26,plain,
( apart_point_and_line(X_1290,orthogonal_through_point(L,X_1290))
| apart_point_and_line(X_1290,parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(L,X_1290))
| distinct_lines(orthogonal_through_point(L,X_1290),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(X_1290)),bind(X_620,$fot(orthogonal_through_point(L,X_1290)))]]) ).
cnf(refute_0_27,plain,
( apart_point_and_line(X_1290,parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(L,X_1290))
| distinct_lines(orthogonal_through_point(L,X_1290),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( apart_point_and_line(X_1290,orthogonal_through_point(L,X_1290)) )],[refute_0_26,refute_0_9]) ).
cnf(refute_0_28,plain,
( apart_point_and_line(skolemFOFtoCNF_A,parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_27:[bind(L,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))),bind(X_1290,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_29,plain,
( apart_point_and_line(skolemFOFtoCNF_A,parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( distinct_lines(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_28,refute_0_7]) ).
cnf(refute_0_30,plain,
~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_31,plain,
~ apart_point_and_line(skolemFOFtoCNF_A,parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),
inference(subst,[],[refute_0_30:[bind(X,$fot(skolemFOFtoCNF_A)),bind(Y,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_32,plain,
convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_A,parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_29,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ apart_point_and_line(Z,parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| distinct_points(Z,intersection_point(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))) ),
inference(resolve,[$cnf( convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) )],[refute_0_32,refute_0_5]) ).
cnf(refute_0_34,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))
| distinct_points(intersection_point(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),intersection_point(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))) ),
inference(subst,[],[refute_0_33:[bind(Z,$fot(intersection_point(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))))]]) ).
cnf(refute_0_35,plain,
~ distinct_points(X,X),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_36,plain,
~ distinct_points(intersection_point(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),intersection_point(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))),
inference(subst,[],[refute_0_35:[bind(X,$fot(intersection_point(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))))]]) ).
cnf(refute_0_37,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_38,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_19:[bind(Z,$fot(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))),bind(X_25,$fot(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_39,plain,
~ distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),
inference(subst,[],[refute_0_6:[bind(X,$fot(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_40,plain,
distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),
inference(resolve,[$cnf( distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,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_42,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_277,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| apart_point_and_line(X_277,parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_280)
| unorthogonal_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_280) ),
inference(subst,[],[refute_0_41:[bind(A,$fot(X_277)),bind(L,$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_280))]]) ).
cnf(refute_0_43,plain,
( apart_point_and_line(X_277,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| apart_point_and_line(X_277,parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_280)
| unorthogonal_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_280) ),
inference(resolve,[$cnf( distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_40,refute_0_42]) ).
cnf(refute_0_44,plain,
( apart_point_and_line(X_735,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| apart_point_and_line(X_735,parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| unorthogonal_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_43:[bind(X_277,$fot(X_735)),bind(X_280,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_45,plain,
( apart_point_and_line(X_735,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| apart_point_and_line(X_735,parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| unorthogonal_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_44,refute_0_37]) ).
cnf(refute_0_46,plain,
( apart_point_and_line(X_1298,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| apart_point_and_line(X_1298,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_45:[bind(X_735,$fot(X_1298))]]) ).
cnf(refute_0_47,plain,
( ~ apart_point_and_line(Z,Y)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_48,plain,
( ~ apart_point_and_line(Z,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| ~ convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| distinct_points(Z,intersection_point(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))) ),
inference(subst,[],[refute_0_47:[bind(X,$fot(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))),bind(Y,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_49,plain,
( ~ apart_point_and_line(Z,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| distinct_points(Z,intersection_point(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))) ),
inference(resolve,[$cnf( convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) )],[refute_0_32,refute_0_48]) ).
cnf(refute_0_50,plain,
( ~ apart_point_and_line(X_1298,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| distinct_points(X_1298,intersection_point(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))) ),
inference(subst,[],[refute_0_49:[bind(Z,$fot(X_1298))]]) ).
cnf(refute_0_51,plain,
( apart_point_and_line(X_1298,parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| distinct_points(X_1298,intersection_point(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)))
| unorthogonal_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( apart_point_and_line(X_1298,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) )],[refute_0_46,refute_0_50]) ).
cnf(refute_0_52,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))
| distinct_points(intersection_point(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),intersection_point(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(subst,[],[refute_0_51:[bind(X_1298,$fot(intersection_point(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))))]]) ).
cnf(refute_0_53,plain,
( apart_point_and_line(intersection_point(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| unorthogonal_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( distinct_points(intersection_point(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),intersection_point(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))) )],[refute_0_52,refute_0_36]) ).
cnf(refute_0_54,plain,
( distinct_points(intersection_point(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),intersection_point(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,[$cnf( apart_point_and_line(intersection_point(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_53,refute_0_34]) ).
cnf(refute_0_55,plain,
unorthogonal_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),
inference(resolve,[$cnf( distinct_points(intersection_point(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),intersection_point(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))) )],[refute_0_54,refute_0_36]) ).
cnf(refute_0_56,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,[$cnf( unorthogonal_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_55,refute_0_3]) ).
cnf(refute_0_57,plain,
~ convergent_lines(X,X),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_58,plain,
~ convergent_lines(orthogonal_through_point(X_346,X_347),orthogonal_through_point(X_346,X_347)),
inference(subst,[],[refute_0_57:[bind(X,$fot(orthogonal_through_point(X_346,X_347)))]]) ).
cnf(refute_0_59,plain,
~ convergent_lines(parallel_through_point(Y,X),Y),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_60,plain,
~ convergent_lines(parallel_through_point(X_331,X),X_331),
inference(subst,[],[refute_0_59:[bind(Y,$fot(X_331))]]) ).
cnf(refute_0_61,plain,
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_62,plain,
( ~ convergent_lines(orthogonal_through_point(X_105,X_107),X_106)
| convergent_lines(X_106,Z)
| convergent_lines(orthogonal_through_point(X_105,X_107),Z) ),
inference(subst,[],[refute_0_61:[bind(X,$fot(orthogonal_through_point(X_105,X_107))),bind(Y,$fot(X_106))]]) ).
cnf(refute_0_63,plain,
( ~ convergent_lines(X_95,X_92)
| convergent_lines(X_92,Z)
| convergent_lines(X_95,Z) ),
inference(subst,[],[refute_0_61:[bind(X,$fot(X_95)),bind(Y,$fot(X_92))]]) ).
cnf(refute_0_64,plain,
( ~ convergent_lines(orthogonal_through_point(X_35,X_34),X_36)
| convergent_lines(X_36,Z)
| convergent_lines(orthogonal_through_point(X_35,X_34),Z) ),
inference(subst,[],[refute_0_61:[bind(X,$fot(orthogonal_through_point(X_35,X_34))),bind(Y,$fot(X_36))]]) ).
cnf(refute_0_65,plain,
~ unorthogonal_lines(orthogonal_through_point(X_14,A),X_14),
inference(subst,[],[refute_0_0:[bind(L,$fot(X_14))]]) ).
cnf(refute_0_66,plain,
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(canonicalize,[],[normalize_0_34]) ).
cnf(refute_0_67,plain,
( convergent_lines(orthogonal_through_point(X_14,A),X_14)
| unorthogonal_lines(orthogonal_through_point(X_14,A),X_14) ),
inference(subst,[],[refute_0_66:[bind(L,$fot(orthogonal_through_point(X_14,A))),bind(M,$fot(X_14))]]) ).
cnf(refute_0_68,plain,
convergent_lines(orthogonal_through_point(X_14,A),X_14),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(X_14,A),X_14) )],[refute_0_67,refute_0_65]) ).
cnf(refute_0_69,plain,
convergent_lines(orthogonal_through_point(X_32,A),X_32),
inference(subst,[],[refute_0_68:[bind(X_14,$fot(X_32))]]) ).
cnf(refute_0_70,plain,
( ~ convergent_lines(orthogonal_through_point(X_32,A),X_32)
| convergent_lines(X_32,X_33)
| convergent_lines(orthogonal_through_point(X_32,A),X_33) ),
inference(subst,[],[refute_0_61:[bind(X,$fot(orthogonal_through_point(X_32,A))),bind(Y,$fot(X_32)),bind(Z,$fot(X_33))]]) ).
cnf(refute_0_71,plain,
( convergent_lines(X_32,X_33)
| convergent_lines(orthogonal_through_point(X_32,A),X_33) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(X_32,A),X_32) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
( convergent_lines(X_35,X_36)
| convergent_lines(orthogonal_through_point(X_35,X_34),X_36) ),
inference(subst,[],[refute_0_71:[bind(A,$fot(X_34)),bind(X_32,$fot(X_35)),bind(X_33,$fot(X_36))]]) ).
cnf(refute_0_73,plain,
( convergent_lines(X_35,X_36)
| convergent_lines(X_36,Z)
| convergent_lines(orthogonal_through_point(X_35,X_34),Z) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(X_35,X_34),X_36) )],[refute_0_72,refute_0_64]) ).
cnf(refute_0_74,plain,
( convergent_lines(X_94,X_95)
| convergent_lines(X_95,X_92)
| convergent_lines(orthogonal_through_point(X_94,X_93),X_92) ),
inference(subst,[],[refute_0_73:[bind(Z,$fot(X_92)),bind(X_34,$fot(X_93)),bind(X_35,$fot(X_94)),bind(X_36,$fot(X_95))]]) ).
cnf(refute_0_75,plain,
( convergent_lines(X_92,Z)
| convergent_lines(X_94,X_95)
| convergent_lines(X_95,Z)
| convergent_lines(orthogonal_through_point(X_94,X_93),X_92) ),
inference(resolve,[$cnf( convergent_lines(X_95,X_92) )],[refute_0_74,refute_0_63]) ).
cnf(refute_0_76,plain,
( convergent_lines(Z,Z)
| convergent_lines(X_92,Z)
| convergent_lines(orthogonal_through_point(Z,X_93),X_92) ),
inference(subst,[],[refute_0_75:[bind(X_94,$fot(Z)),bind(X_95,$fot(Z))]]) ).
cnf(refute_0_77,plain,
~ convergent_lines(Z,Z),
inference(subst,[],[refute_0_57:[bind(X,$fot(Z))]]) ).
cnf(refute_0_78,plain,
( convergent_lines(X_92,Z)
| convergent_lines(orthogonal_through_point(Z,X_93),X_92) ),
inference(resolve,[$cnf( convergent_lines(Z,Z) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
( convergent_lines(X_106,X_105)
| convergent_lines(orthogonal_through_point(X_105,X_107),X_106) ),
inference(subst,[],[refute_0_78:[bind(Z,$fot(X_105)),bind(X_92,$fot(X_106)),bind(X_93,$fot(X_107))]]) ).
cnf(refute_0_80,plain,
( convergent_lines(X_106,Z)
| convergent_lines(X_106,X_105)
| convergent_lines(orthogonal_through_point(X_105,X_107),Z) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(X_105,X_107),X_106) )],[refute_0_79,refute_0_62]) ).
cnf(refute_0_81,plain,
( convergent_lines(orthogonal_through_point(X_331,X_333),X_330)
| convergent_lines(parallel_through_point(X_331,X),X_330)
| convergent_lines(parallel_through_point(X_331,X),X_331) ),
inference(subst,[],[refute_0_80:[bind(Z,$fot(X_330)),bind(X_105,$fot(X_331)),bind(X_106,$fot(parallel_through_point(X_331,X))),bind(X_107,$fot(X_333))]]) ).
cnf(refute_0_82,plain,
( convergent_lines(orthogonal_through_point(X_331,X_333),X_330)
| convergent_lines(parallel_through_point(X_331,X),X_330) ),
inference(resolve,[$cnf( convergent_lines(parallel_through_point(X_331,X),X_331) )],[refute_0_81,refute_0_60]) ).
cnf(refute_0_83,plain,
( convergent_lines(orthogonal_through_point(X_346,X_347),orthogonal_through_point(X_346,X_347))
| convergent_lines(parallel_through_point(X_346,X_344),orthogonal_through_point(X_346,X_347)) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(X_344)),bind(X_330,$fot(orthogonal_through_point(X_346,X_347))),bind(X_331,$fot(X_346)),bind(X_333,$fot(X_347))]]) ).
cnf(refute_0_84,plain,
convergent_lines(parallel_through_point(X_346,X_344),orthogonal_through_point(X_346,X_347)),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(X_346,X_347),orthogonal_through_point(X_346,X_347)) )],[refute_0_83,refute_0_58]) ).
cnf(refute_0_85,plain,
convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),
inference(subst,[],[refute_0_84:[bind(X_344,$fot(skolemFOFtoCNF_A)),bind(X_346,$fot(skolemFOFtoCNF_L)),bind(X_347,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_86,plain,
( convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),N)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),N) ),
inference(resolve,[$cnf( convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_85,refute_0_56]) ).
cnf(refute_0_87,plain,
( convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_86:[bind(N,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_88,plain,
convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L) )],[refute_0_87,refute_0_1]) ).
cnf(refute_0_89,plain,
~ convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L),
inference(subst,[],[refute_0_59:[bind(X,$fot(skolemFOFtoCNF_A)),bind(Y,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_90,plain,
$false,
inference(resolve,[$cnf( convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L) )],[refute_0_88,refute_0_89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO223+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jun 18 06:28:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 3.77/3.96 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.77/3.96
% 3.77/3.96 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.77/3.97
%------------------------------------------------------------------------------