TSTP Solution File: GEO222+3 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO222+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n009.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 0.39s 0.56s
% Output : CNFRefutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 84 ( 29 unt; 0 def)
% Number of atoms : 228 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 225 ( 81 ~; 117 |; 20 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 166 ( 13 sgn 79 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart3,axiom,
! [X] : ~ convergent_lines(X,X) ).
fof(ax6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(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(cotno1,axiom,
! [L,M,N] :
( ( ( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M) )
& ( ~ convergent_lines(L,N)
| ~ unorthogonal_lines(L,N) ) )
=> ( ~ convergent_lines(M,N)
| ~ unorthogonal_lines(M,N) ) ) ).
fof(couo1,axiom,
! [L,M,N] :
( ( ~ unorthogonal_lines(L,M)
& ~ unorthogonal_lines(L,N) )
=> ~ convergent_lines(M,N) ) ).
fof(a3,axiom,
! [X,Y] :
( parallel_lines(X,Y)
<=> ~ convergent_lines(X,Y) ) ).
fof(con,conjecture,
! [A,L] : parallel_lines(L,orthogonal_through_point(orthogonal_through_point(L,A),A)) ).
fof(subgoal_0,plain,
! [A,L] : parallel_lines(L,orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [A,L] : parallel_lines(L,orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X] : ~ convergent_lines(X,X),
inference(canonicalize,[],[apart3]) ).
fof(normalize_0_1,plain,
! [X] : ~ convergent_lines(X,X),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [L,M,N] :
( ~ convergent_lines(M,N)
| ~ unorthogonal_lines(M,N)
| ( convergent_lines(L,M)
& unorthogonal_lines(L,M) )
| ( convergent_lines(L,N)
& unorthogonal_lines(L,N) ) ),
inference(canonicalize,[],[cotno1]) ).
fof(normalize_0_3,plain,
! [L,M,N] :
( ~ convergent_lines(M,N)
| ~ unorthogonal_lines(M,N)
| ( convergent_lines(L,M)
& unorthogonal_lines(L,M) )
| ( convergent_lines(L,N)
& unorthogonal_lines(L,N) ) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [L,M,N] :
( ( ~ convergent_lines(M,N)
| ~ unorthogonal_lines(M,N)
| convergent_lines(L,M)
| convergent_lines(L,N) )
& ( ~ convergent_lines(M,N)
| ~ unorthogonal_lines(M,N)
| convergent_lines(L,M)
| unorthogonal_lines(L,N) )
& ( ~ convergent_lines(M,N)
| ~ unorthogonal_lines(M,N)
| convergent_lines(L,N)
| unorthogonal_lines(L,M) )
& ( ~ convergent_lines(M,N)
| ~ unorthogonal_lines(M,N)
| unorthogonal_lines(L,M)
| unorthogonal_lines(L,N) ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [L,M,N] :
( ~ convergent_lines(M,N)
| ~ unorthogonal_lines(M,N)
| convergent_lines(L,N)
| unorthogonal_lines(L,M) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(canonicalize,[],[ooc1]) ).
fof(normalize_0_7,plain,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [L,M] :
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(canonicalize,[],[occu1]) ).
fof(normalize_0_9,plain,
! [L,M] :
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [L,M,N] :
( ~ convergent_lines(M,N)
| unorthogonal_lines(L,M)
| unorthogonal_lines(L,N) ),
inference(canonicalize,[],[couo1]) ).
fof(normalize_0_11,plain,
! [L,M,N] :
( ~ convergent_lines(M,N)
| unorthogonal_lines(L,M)
| unorthogonal_lines(L,N) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,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_13,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_12]) ).
fof(normalize_0_14,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_13]) ).
fof(normalize_0_15,plain,
! [L,M,N] :
( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| unorthogonal_lines(L,N)
| unorthogonal_lines(M,N) ),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
? [A,L] : ~ parallel_lines(L,orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_17,plain,
~ parallel_lines(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),
inference(skolemize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [X,Y] :
( ~ convergent_lines(X,Y)
<=> parallel_lines(X,Y) ),
inference(canonicalize,[],[a3]) ).
fof(normalize_0_19,plain,
! [X,Y] :
( ~ convergent_lines(X,Y)
<=> parallel_lines(X,Y) ),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [X,Y] :
( ( ~ convergent_lines(X,Y)
| ~ parallel_lines(X,Y) )
& ( convergent_lines(X,Y)
| parallel_lines(X,Y) ) ),
inference(clausify,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [X,Y] :
( convergent_lines(X,Y)
| parallel_lines(X,Y) ),
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[ax6]) ).
fof(normalize_0_23,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(specialize,[],[normalize_0_22]) ).
cnf(refute_0_0,plain,
~ convergent_lines(X,X),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
~ convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),
inference(subst,[],[refute_0_0:[bind(X,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_2,plain,
( ~ convergent_lines(M,N)
| ~ unorthogonal_lines(M,N)
| convergent_lines(L,N)
| unorthogonal_lines(L,M) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( ~ convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| ~ unorthogonal_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| convergent_lines(L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| unorthogonal_lines(L,skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_2:[bind(M,$fot(skolemFOFtoCNF_L)),bind(N,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_4,plain,
~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
~ unorthogonal_lines(orthogonal_through_point(X_14,A),X_14),
inference(subst,[],[refute_0_4:[bind(L,$fot(X_14))]]) ).
cnf(refute_0_6,plain,
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_7,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_6:[bind(L,$fot(orthogonal_through_point(X_14,A))),bind(M,$fot(X_14))]]) ).
cnf(refute_0_8,plain,
convergent_lines(orthogonal_through_point(X_14,A),X_14),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(X_14,A),X_14) )],[refute_0_7,refute_0_5]) ).
cnf(refute_0_9,plain,
convergent_lines(orthogonal_through_point(X_58,A),X_58),
inference(subst,[],[refute_0_8:[bind(X_14,$fot(X_58))]]) ).
cnf(refute_0_10,plain,
( ~ convergent_lines(M,N)
| unorthogonal_lines(L,M)
| unorthogonal_lines(L,N) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_11,plain,
( ~ convergent_lines(orthogonal_through_point(X_58,A),X_58)
| unorthogonal_lines(X_56,X_58)
| unorthogonal_lines(X_56,orthogonal_through_point(X_58,A)) ),
inference(subst,[],[refute_0_10:[bind(L,$fot(X_56)),bind(M,$fot(orthogonal_through_point(X_58,A))),bind(N,$fot(X_58))]]) ).
cnf(refute_0_12,plain,
( unorthogonal_lines(X_56,X_58)
| unorthogonal_lines(X_56,orthogonal_through_point(X_58,A)) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(X_58,A),X_58) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
( unorthogonal_lines(X_196,X_58)
| unorthogonal_lines(X_196,orthogonal_through_point(X_58,A)) ),
inference(subst,[],[refute_0_12:[bind(X_56,$fot(X_196))]]) ).
cnf(refute_0_14,plain,
( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| unorthogonal_lines(L,N)
| unorthogonal_lines(M,N) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_15,plain,
( ~ convergent_lines(X_196,orthogonal_through_point(X_58,A))
| ~ unorthogonal_lines(X_196,orthogonal_through_point(X_58,A))
| unorthogonal_lines(X_196,X_198)
| unorthogonal_lines(orthogonal_through_point(X_58,A),X_198) ),
inference(subst,[],[refute_0_14:[bind(L,$fot(X_196)),bind(M,$fot(orthogonal_through_point(X_58,A))),bind(N,$fot(X_198))]]) ).
cnf(refute_0_16,plain,
( ~ convergent_lines(X_196,orthogonal_through_point(X_58,A))
| unorthogonal_lines(X_196,X_198)
| unorthogonal_lines(X_196,X_58)
| unorthogonal_lines(orthogonal_through_point(X_58,A),X_198) ),
inference(resolve,[$cnf( unorthogonal_lines(X_196,orthogonal_through_point(X_58,A)) )],[refute_0_13,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(X_383,X_382))
| unorthogonal_lines(orthogonal_through_point(X_383,X_382),X_198)
| unorthogonal_lines(skolemFOFtoCNF_L,X_198)
| unorthogonal_lines(skolemFOFtoCNF_L,X_383) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(X_382)),bind(X_196,$fot(skolemFOFtoCNF_L)),bind(X_58,$fot(X_383))]]) ).
cnf(refute_0_18,plain,
~ parallel_lines(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_19,plain,
( convergent_lines(X,Y)
| parallel_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_20,plain,
( convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| parallel_lines(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_19:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_21,plain,
convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),
inference(resolve,[$cnf( parallel_lines(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) )],[refute_0_20,refute_0_18]) ).
cnf(refute_0_22,plain,
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_23,plain,
( ~ convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_80)
| convergent_lines(skolemFOFtoCNF_L,X_80) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))),bind(Z,$fot(X_80))]]) ).
cnf(refute_0_24,plain,
( convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_80)
| convergent_lines(skolemFOFtoCNF_L,X_80) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) )],[refute_0_21,refute_0_23]) ).
cnf(refute_0_25,plain,
( convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),orthogonal_through_point(X_332,X_329))
| convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(X_332,X_329)) ),
inference(subst,[],[refute_0_24:[bind(X_80,$fot(orthogonal_through_point(X_332,X_329)))]]) ).
cnf(refute_0_26,plain,
( ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),orthogonal_through_point(X_332,X_329))
| unorthogonal_lines(orthogonal_through_point(X_332,X_329),X_331)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_331)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_332) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(X_329)),bind(X_196,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))),bind(X_198,$fot(X_331)),bind(X_58,$fot(X_332))]]) ).
cnf(refute_0_27,plain,
( convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(X_332,X_329))
| unorthogonal_lines(orthogonal_through_point(X_332,X_329),X_331)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_331)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_332) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),orthogonal_through_point(X_332,X_329)) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(X_332,X_329))
| unorthogonal_lines(orthogonal_through_point(X_332,X_329),X_332)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_332) ),
inference(subst,[],[refute_0_27:[bind(X_331,$fot(X_332))]]) ).
cnf(refute_0_29,plain,
~ unorthogonal_lines(orthogonal_through_point(X_332,X_329),X_332),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_329)),bind(L,$fot(X_332))]]) ).
cnf(refute_0_30,plain,
( convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(X_332,X_329))
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_332) ),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(X_332,X_329),X_332) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(X_383,X_382))
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_383) ),
inference(subst,[],[refute_0_30:[bind(X_329,$fot(X_382)),bind(X_332,$fot(X_383))]]) ).
cnf(refute_0_32,plain,
( unorthogonal_lines(orthogonal_through_point(X_383,X_382),X_198)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_383)
| unorthogonal_lines(skolemFOFtoCNF_L,X_198)
| unorthogonal_lines(skolemFOFtoCNF_L,X_383) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(X_383,X_382)) )],[refute_0_31,refute_0_17]) ).
cnf(refute_0_33,plain,
( 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_32:[bind(X_198,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))),bind(X_382,$fot(skolemFOFtoCNF_A)),bind(X_383,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_34,plain,
~ unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_A)),bind(L,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_35,plain,
unorthogonal_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
( ~ convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| convergent_lines(L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| unorthogonal_lines(L,skolemFOFtoCNF_L) ),
inference(resolve,[$cnf( unorthogonal_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_35,refute_0_3]) ).
cnf(refute_0_37,plain,
~ convergent_lines(orthogonal_through_point(X_83,X_82),orthogonal_through_point(X_83,X_82)),
inference(subst,[],[refute_0_0:[bind(X,$fot(orthogonal_through_point(X_83,X_82)))]]) ).
cnf(refute_0_38,plain,
convergent_lines(orthogonal_through_point(X_79,A),X_79),
inference(subst,[],[refute_0_8:[bind(X_14,$fot(X_79))]]) ).
cnf(refute_0_39,plain,
( ~ convergent_lines(orthogonal_through_point(X_79,A),X_79)
| convergent_lines(X_79,X_80)
| convergent_lines(orthogonal_through_point(X_79,A),X_80) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(orthogonal_through_point(X_79,A))),bind(Y,$fot(X_79)),bind(Z,$fot(X_80))]]) ).
cnf(refute_0_40,plain,
( convergent_lines(X_79,X_80)
| convergent_lines(orthogonal_through_point(X_79,A),X_80) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(X_79,A),X_79) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( convergent_lines(X_83,orthogonal_through_point(X_83,X_82))
| convergent_lines(orthogonal_through_point(X_83,X_82),orthogonal_through_point(X_83,X_82)) ),
inference(subst,[],[refute_0_40:[bind(A,$fot(X_82)),bind(X_79,$fot(X_83)),bind(X_80,$fot(orthogonal_through_point(X_83,X_82)))]]) ).
cnf(refute_0_42,plain,
convergent_lines(X_83,orthogonal_through_point(X_83,X_82)),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(X_83,X_82),orthogonal_through_point(X_83,X_82)) )],[refute_0_41,refute_0_37]) ).
cnf(refute_0_43,plain,
convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),
inference(subst,[],[refute_0_42:[bind(X_82,$fot(skolemFOFtoCNF_A)),bind(X_83,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_44,plain,
( convergent_lines(L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| unorthogonal_lines(L,skolemFOFtoCNF_L) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_43,refute_0_36]) ).
cnf(refute_0_45,plain,
( convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_44:[bind(L,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_46,plain,
unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_45,refute_0_1]) ).
cnf(refute_0_47,plain,
~ unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_A)),bind(L,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_48,plain,
$false,
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L) )],[refute_0_46,refute_0_47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GEO222+3 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n009.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 : Sat Jun 18 10:53:22 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.39/0.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.39/0.56
% 0.39/0.56 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.39/0.56
%------------------------------------------------------------------------------