TSTP Solution File: GEO222+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO222+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 0.41s 0.59s
% Output : CNFRefutation 0.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 12
% Syntax : Number of formulae : 103 ( 35 unt; 0 def)
% Number of atoms : 247 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 226 ( 82 ~; 127 |; 10 &)
% ( 0 <=>; 7 =>; 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 166 ( 6 sgn 90 !; 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(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(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] : ~ convergent_lines(L,orthogonal_through_point(orthogonal_through_point(L,A),A)) ).
fof(subgoal_0,plain,
! [A,L] : ~ convergent_lines(L,orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [A,L] : ~ convergent_lines(L,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),Y)
| ~ convergent_lines(X,Y) ),
inference(canonicalize,[],[ci4]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[ax6]) ).
fof(normalize_0_9,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
? [A,L] : convergent_lines(L,orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_11,plain,
convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),
inference(skolemize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X] : ~ convergent_lines(X,X),
inference(canonicalize,[],[apart3]) ).
fof(normalize_0_13,plain,
! [X] : ~ convergent_lines(X,X),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(canonicalize,[],[ci3]) ).
fof(normalize_0_15,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
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,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[ceq3]) ).
fof(normalize_0_19,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [X] : ~ distinct_lines(X,X),
inference(canonicalize,[],[apart2]) ).
fof(normalize_0_21,plain,
! [X] : ~ distinct_lines(X,X),
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,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_23,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_22]) ).
fof(normalize_0_24,plain,
! [L,M] :
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(canonicalize,[],[occu1]) ).
fof(normalize_0_25,plain,
! [L,M] :
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(specialize,[],[normalize_0_24]) ).
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(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| ~ unorthogonal_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| convergent_lines(skolemFOFtoCNF_L,N)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),N) ),
inference(subst,[],[refute_0_2:[bind(L,$fot(skolemFOFtoCNF_L)),bind(M,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_4,plain,
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),skolemFOFtoCNF_L),skolemFOFtoCNF_L)
| ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))),bind(Y,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_6,plain,
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_7,plain,
( ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_32)
| convergent_lines(X_32,Z)
| convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),Z) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))),bind(Y,$fot(X_32))]]) ).
cnf(refute_0_8,plain,
convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_9,plain,
( ~ convergent_lines(skolemFOFtoCNF_L,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_31)
| convergent_lines(skolemFOFtoCNF_L,X_31) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_10,plain,
( convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_31)
| convergent_lines(skolemFOFtoCNF_L,X_31) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_32)
| convergent_lines(skolemFOFtoCNF_L,X_32) ),
inference(subst,[],[refute_0_10:[bind(X_31,$fot(X_32))]]) ).
cnf(refute_0_12,plain,
( convergent_lines(X_32,Z)
| convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),Z)
| convergent_lines(skolemFOFtoCNF_L,X_32) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_32) )],[refute_0_11,refute_0_7]) ).
cnf(refute_0_13,plain,
( convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),skolemFOFtoCNF_L)
| convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_12:[bind(Z,$fot(skolemFOFtoCNF_L)),bind(X_32,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_14,plain,
~ convergent_lines(X,X),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_15,plain,
~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L),
inference(subst,[],[refute_0_14:[bind(X,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_16,plain,
convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),skolemFOFtoCNF_L),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L) )],[refute_0_13,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_18,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_17:[bind(X,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_19,plain,
~ unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A)),bind(L,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_20,plain,
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_21,plain,
( ~ distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_49)
| distinct_lines(X_49,Z)
| distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),Z) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))),bind(Y,$fot(X_49))]]) ).
cnf(refute_0_22,plain,
( ~ distinct_lines(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),Z)
| distinct_lines(skolemFOFtoCNF_L,Z) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_23,plain,
~ convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),
inference(subst,[],[refute_0_14:[bind(X,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_24,plain,
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_25,plain,
( ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),skolemFOFtoCNF_L)
| convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_46)
| distinct_lines(skolemFOFtoCNF_L,X_46) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))),bind(Y,$fot(skolemFOFtoCNF_L)),bind(Z,$fot(X_46))]]) ).
cnf(refute_0_26,plain,
( convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_46)
| distinct_lines(skolemFOFtoCNF_L,X_46) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),skolemFOFtoCNF_L) )],[refute_0_16,refute_0_25]) ).
cnf(refute_0_27,plain,
( convergent_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))
| distinct_lines(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_26:[bind(X_46,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_28,plain,
distinct_lines(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) )],[refute_0_27,refute_0_23]) ).
cnf(refute_0_29,plain,
( distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),Z)
| distinct_lines(skolemFOFtoCNF_L,Z) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) )],[refute_0_28,refute_0_22]) ).
cnf(refute_0_30,plain,
( distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_49)
| distinct_lines(skolemFOFtoCNF_L,X_49) ),
inference(subst,[],[refute_0_29:[bind(Z,$fot(X_49))]]) ).
cnf(refute_0_31,plain,
( distinct_lines(X_49,Z)
| distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),Z)
| distinct_lines(skolemFOFtoCNF_L,X_49) ),
inference(resolve,[$cnf( distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_49) )],[refute_0_30,refute_0_21]) ).
cnf(refute_0_32,plain,
( distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),skolemFOFtoCNF_L)
| distinct_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_31:[bind(Z,$fot(skolemFOFtoCNF_L)),bind(X_49,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_33,plain,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_34,plain,
~ distinct_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L),
inference(subst,[],[refute_0_33:[bind(X,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_35,plain,
distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),skolemFOFtoCNF_L),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L) )],[refute_0_32,refute_0_34]) ).
cnf(refute_0_36,plain,
( ~ distinct_lines(L,M)
| apart_point_and_line(A,L)
| apart_point_and_line(A,M)
| unorthogonal_lines(L,N)
| unorthogonal_lines(M,N) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_37,plain,
( ~ distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),skolemFOFtoCNF_L)
| apart_point_and_line(X_310,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| apart_point_and_line(X_310,skolemFOFtoCNF_L)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_313)
| unorthogonal_lines(skolemFOFtoCNF_L,X_313) ),
inference(subst,[],[refute_0_36:[bind(A,$fot(X_310)),bind(L,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))),bind(M,$fot(skolemFOFtoCNF_L)),bind(N,$fot(X_313))]]) ).
cnf(refute_0_38,plain,
( apart_point_and_line(X_310,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| apart_point_and_line(X_310,skolemFOFtoCNF_L)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_313)
| unorthogonal_lines(skolemFOFtoCNF_L,X_313) ),
inference(resolve,[$cnf( distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),skolemFOFtoCNF_L) )],[refute_0_35,refute_0_37]) ).
cnf(refute_0_39,plain,
( apart_point_and_line(X_395,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| apart_point_and_line(X_395,skolemFOFtoCNF_L)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| unorthogonal_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_38:[bind(X_310,$fot(X_395)),bind(X_313,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_40,plain,
( apart_point_and_line(X_395,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| apart_point_and_line(X_395,skolemFOFtoCNF_L)
| unorthogonal_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_39,refute_0_19]) ).
cnf(refute_0_41,plain,
( apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),Y),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),Y),skolemFOFtoCNF_L)
| unorthogonal_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_40:[bind(X_395,$fot(intersection_point(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),Y)))]]) ).
cnf(refute_0_42,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),skolemFOFtoCNF_L)
| unorthogonal_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),Y),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) )],[refute_0_41,refute_0_18]) ).
cnf(refute_0_43,plain,
( ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),skolemFOFtoCNF_L)
| apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),skolemFOFtoCNF_L),skolemFOFtoCNF_L)
| unorthogonal_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_42:[bind(Y,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_44,plain,
( apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),skolemFOFtoCNF_L),skolemFOFtoCNF_L)
| unorthogonal_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),skolemFOFtoCNF_L) )],[refute_0_16,refute_0_43]) ).
cnf(refute_0_45,plain,
( ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),skolemFOFtoCNF_L)
| unorthogonal_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),skolemFOFtoCNF_L),skolemFOFtoCNF_L) )],[refute_0_44,refute_0_5]) ).
cnf(refute_0_46,plain,
unorthogonal_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),skolemFOFtoCNF_L) )],[refute_0_16,refute_0_45]) ).
cnf(refute_0_47,plain,
( ~ convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| convergent_lines(skolemFOFtoCNF_L,N)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),N) ),
inference(resolve,[$cnf( unorthogonal_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_46,refute_0_3]) ).
cnf(refute_0_48,plain,
~ convergent_lines(orthogonal_through_point(X_34,X_33),orthogonal_through_point(X_34,X_33)),
inference(subst,[],[refute_0_14:[bind(X,$fot(orthogonal_through_point(X_34,X_33)))]]) ).
cnf(refute_0_49,plain,
~ unorthogonal_lines(orthogonal_through_point(X_14,A),X_14),
inference(subst,[],[refute_0_0:[bind(L,$fot(X_14))]]) ).
cnf(refute_0_50,plain,
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_51,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_50:[bind(L,$fot(orthogonal_through_point(X_14,A))),bind(M,$fot(X_14))]]) ).
cnf(refute_0_52,plain,
convergent_lines(orthogonal_through_point(X_14,A),X_14),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(X_14,A),X_14) )],[refute_0_51,refute_0_49]) ).
cnf(refute_0_53,plain,
convergent_lines(orthogonal_through_point(X_30,A),X_30),
inference(subst,[],[refute_0_52:[bind(X_14,$fot(X_30))]]) ).
cnf(refute_0_54,plain,
( ~ convergent_lines(orthogonal_through_point(X_30,A),X_30)
| convergent_lines(X_30,X_31)
| convergent_lines(orthogonal_through_point(X_30,A),X_31) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(orthogonal_through_point(X_30,A))),bind(Y,$fot(X_30)),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_55,plain,
( convergent_lines(X_30,X_31)
| convergent_lines(orthogonal_through_point(X_30,A),X_31) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(X_30,A),X_30) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
( convergent_lines(X_34,orthogonal_through_point(X_34,X_33))
| convergent_lines(orthogonal_through_point(X_34,X_33),orthogonal_through_point(X_34,X_33)) ),
inference(subst,[],[refute_0_55:[bind(A,$fot(X_33)),bind(X_30,$fot(X_34)),bind(X_31,$fot(orthogonal_through_point(X_34,X_33)))]]) ).
cnf(refute_0_57,plain,
convergent_lines(X_34,orthogonal_through_point(X_34,X_33)),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(X_34,X_33),orthogonal_through_point(X_34,X_33)) )],[refute_0_56,refute_0_48]) ).
cnf(refute_0_58,plain,
convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),
inference(subst,[],[refute_0_57:[bind(X_33,$fot(skolemFOFtoCNF_A)),bind(X_34,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_59,plain,
( convergent_lines(skolemFOFtoCNF_L,N)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),N) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_58,refute_0_47]) ).
cnf(refute_0_60,plain,
( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_59:[bind(N,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_61,plain,
convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L) )],[refute_0_60,refute_0_1]) ).
cnf(refute_0_62,plain,
$false,
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L) )],[refute_0_61,refute_0_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GEO222+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Fri Jun 17 21:02:24 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.41/0.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.41/0.59
% 0.41/0.59 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.44/0.60
%------------------------------------------------------------------------------