TSTP Solution File: GEO219+3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO219+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.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 05:25:32 EDT 2022
% Result : Theorem 0.56s 0.76s
% Output : CNFRefutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 7
% Syntax : Number of formulae : 105 ( 22 unt; 0 def)
% Number of atoms : 259 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 233 ( 79 ~; 124 |; 19 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 132 ( 0 sgn 64 !; 3 ?)
% 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(a3,axiom,
! [X,Y] :
( parallel_lines(X,Y)
<=> ~ convergent_lines(X,Y) ) ).
fof(a5,axiom,
! [X,Y] :
( orthogonal_lines(X,Y)
<=> ~ unorthogonal_lines(X,Y) ) ).
fof(con,conjecture,
! [L,M,N] :
( ( orthogonal_lines(L,M)
& parallel_lines(L,N) )
=> orthogonal_lines(M,N) ) ).
fof(subgoal_0,plain,
! [L,M,N] :
( ( orthogonal_lines(L,M)
& parallel_lines(L,N) )
=> orthogonal_lines(M,N) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [L,M,N] :
( ( orthogonal_lines(L,M)
& parallel_lines(L,N) )
=> orthogonal_lines(M,N) ),
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,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[ax6]) ).
fof(normalize_0_3,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X,Y] :
( ~ orthogonal_lines(X,Y)
<=> unorthogonal_lines(X,Y) ),
inference(canonicalize,[],[a5]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ~ orthogonal_lines(X,Y)
<=> unorthogonal_lines(X,Y) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ( ~ orthogonal_lines(X,Y)
| ~ unorthogonal_lines(X,Y) )
& ( orthogonal_lines(X,Y)
| unorthogonal_lines(X,Y) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ~ orthogonal_lines(X,Y)
| ~ unorthogonal_lines(X,Y) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
? [L,M,N] :
( ~ orthogonal_lines(M,N)
& orthogonal_lines(L,M)
& parallel_lines(L,N) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_9,plain,
( ~ orthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
& orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
& parallel_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N) ),
inference(skolemize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
parallel_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X,Y] :
( ~ convergent_lines(X,Y)
<=> parallel_lines(X,Y) ),
inference(canonicalize,[],[a3]) ).
fof(normalize_0_12,plain,
! [X,Y] :
( ~ convergent_lines(X,Y)
<=> parallel_lines(X,Y) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( ( ~ convergent_lines(X,Y)
| ~ parallel_lines(X,Y) )
& ( convergent_lines(X,Y)
| parallel_lines(X,Y) ) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X,Y] :
( ~ convergent_lines(X,Y)
| ~ parallel_lines(X,Y) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_16,plain,
! [L,M] :
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(canonicalize,[],[occu1]) ).
fof(normalize_0_17,plain,
! [L,M] :
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [X,Y] :
( orthogonal_lines(X,Y)
| unorthogonal_lines(X,Y) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_19,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_20,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_19]) ).
fof(normalize_0_21,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_20]) ).
fof(normalize_0_22,plain,
! [L,M,N] :
( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| convergent_lines(L,N)
| unorthogonal_lines(M,N) ),
inference(conjunct,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
~ orthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N),
inference(conjunct,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
~ convergent_lines(X,X),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
~ convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_N),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_N))]]) ).
cnf(refute_0_2,plain,
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
( ~ convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_L)
| convergent_lines(skolemFOFtoCNF_L,Z)
| convergent_lines(skolemFOFtoCNF_N,Z) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_N)),bind(Y,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_4,plain,
( ~ orthogonal_lines(X,Y)
| ~ unorthogonal_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ orthogonal_lines(skolemFOFtoCNF_N,X_659)
| ~ unorthogonal_lines(skolemFOFtoCNF_N,X_659) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_N)),bind(Y,$fot(X_659))]]) ).
cnf(refute_0_6,plain,
( ~ convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_M)
| convergent_lines(skolemFOFtoCNF_M,Z)
| convergent_lines(skolemFOFtoCNF_N,Z) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_N)),bind(Y,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_7,plain,
parallel_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
( ~ convergent_lines(X,Y)
| ~ parallel_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_9,plain,
( ~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N)
| ~ parallel_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(skolemFOFtoCNF_N))]]) ).
cnf(refute_0_10,plain,
~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N),
inference(resolve,[$cnf( parallel_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ convergent_lines(skolemFOFtoCNF_L,X_116)
| convergent_lines(X_116,Z)
| convergent_lines(skolemFOFtoCNF_L,Z) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(X_116))]]) ).
cnf(refute_0_12,plain,
~ convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_M),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_13,plain,
( ~ convergent_lines(skolemFOFtoCNF_M,X_62)
| convergent_lines(X_62,Z)
| convergent_lines(skolemFOFtoCNF_M,Z) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_M)),bind(Y,$fot(X_62))]]) ).
cnf(refute_0_14,plain,
orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_15,plain,
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_16,plain,
( convergent_lines(X_33,X_34)
| unorthogonal_lines(X_33,X_34) ),
inference(subst,[],[refute_0_15:[bind(L,$fot(X_33)),bind(M,$fot(X_34))]]) ).
cnf(refute_0_17,plain,
( ~ orthogonal_lines(X_33,X_34)
| ~ unorthogonal_lines(X_33,X_34) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_33)),bind(Y,$fot(X_34))]]) ).
cnf(refute_0_18,plain,
( ~ orthogonal_lines(X_33,X_34)
| convergent_lines(X_33,X_34) ),
inference(resolve,[$cnf( unorthogonal_lines(X_33,X_34) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
| convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
inference(subst,[],[refute_0_18:[bind(X_33,$fot(skolemFOFtoCNF_L)),bind(X_34,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_20,plain,
convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(resolve,[$cnf( orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_14,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
| convergent_lines(skolemFOFtoCNF_L,X_61)
| convergent_lines(skolemFOFtoCNF_M,X_61) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(skolemFOFtoCNF_M)),bind(Z,$fot(X_61))]]) ).
cnf(refute_0_22,plain,
( convergent_lines(skolemFOFtoCNF_L,X_61)
| convergent_lines(skolemFOFtoCNF_M,X_61) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( convergent_lines(skolemFOFtoCNF_L,X_62)
| convergent_lines(skolemFOFtoCNF_M,X_62) ),
inference(subst,[],[refute_0_22:[bind(X_61,$fot(X_62))]]) ).
cnf(refute_0_24,plain,
( convergent_lines(X_62,Z)
| convergent_lines(skolemFOFtoCNF_L,X_62)
| convergent_lines(skolemFOFtoCNF_M,Z) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_M,X_62) )],[refute_0_23,refute_0_13]) ).
cnf(refute_0_25,plain,
( convergent_lines(X_112,skolemFOFtoCNF_M)
| convergent_lines(skolemFOFtoCNF_L,X_112)
| convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_M) ),
inference(subst,[],[refute_0_24:[bind(Z,$fot(skolemFOFtoCNF_M)),bind(X_62,$fot(X_112))]]) ).
cnf(refute_0_26,plain,
( convergent_lines(X_112,skolemFOFtoCNF_M)
| convergent_lines(skolemFOFtoCNF_L,X_112) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_M) )],[refute_0_25,refute_0_12]) ).
cnf(refute_0_27,plain,
( convergent_lines(X_116,skolemFOFtoCNF_M)
| convergent_lines(skolemFOFtoCNF_L,X_116) ),
inference(subst,[],[refute_0_26:[bind(X_112,$fot(X_116))]]) ).
cnf(refute_0_28,plain,
( convergent_lines(X_116,Z)
| convergent_lines(X_116,skolemFOFtoCNF_M)
| convergent_lines(skolemFOFtoCNF_L,Z) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,X_116) )],[refute_0_27,refute_0_11]) ).
cnf(refute_0_29,plain,
( convergent_lines(X_294,skolemFOFtoCNF_M)
| convergent_lines(X_294,skolemFOFtoCNF_N)
| convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_28:[bind(Z,$fot(skolemFOFtoCNF_N)),bind(X_116,$fot(X_294))]]) ).
cnf(refute_0_30,plain,
( convergent_lines(X_294,skolemFOFtoCNF_M)
| convergent_lines(X_294,skolemFOFtoCNF_N) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N) )],[refute_0_29,refute_0_10]) ).
cnf(refute_0_31,plain,
( convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_M)
| convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_30:[bind(X_294,$fot(skolemFOFtoCNF_N))]]) ).
cnf(refute_0_32,plain,
convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_M),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_N) )],[refute_0_31,refute_0_1]) ).
cnf(refute_0_33,plain,
( convergent_lines(skolemFOFtoCNF_M,Z)
| convergent_lines(skolemFOFtoCNF_N,Z) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_M) )],[refute_0_32,refute_0_6]) ).
cnf(refute_0_34,plain,
( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
| convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_33:[bind(Z,$fot(skolemFOFtoCNF_N))]]) ).
cnf(refute_0_35,plain,
convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_N) )],[refute_0_34,refute_0_1]) ).
cnf(refute_0_36,plain,
( orthogonal_lines(X,Y)
| unorthogonal_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_37,plain,
( orthogonal_lines(X_253,X_254)
| unorthogonal_lines(X_253,X_254) ),
inference(subst,[],[refute_0_36:[bind(X,$fot(X_253)),bind(Y,$fot(X_254))]]) ).
cnf(refute_0_38,plain,
( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| convergent_lines(L,N)
| unorthogonal_lines(M,N) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_39,plain,
( ~ convergent_lines(X_253,X_254)
| ~ unorthogonal_lines(X_253,X_254)
| convergent_lines(X_253,X_255)
| unorthogonal_lines(X_254,X_255) ),
inference(subst,[],[refute_0_38:[bind(L,$fot(X_253)),bind(M,$fot(X_254)),bind(N,$fot(X_255))]]) ).
cnf(refute_0_40,plain,
( ~ convergent_lines(X_253,X_254)
| convergent_lines(X_253,X_255)
| orthogonal_lines(X_253,X_254)
| unorthogonal_lines(X_254,X_255) ),
inference(resolve,[$cnf( unorthogonal_lines(X_253,X_254) )],[refute_0_37,refute_0_39]) ).
cnf(refute_0_41,plain,
( ~ convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
| convergent_lines(skolemFOFtoCNF_M,X_658)
| orthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
| unorthogonal_lines(skolemFOFtoCNF_N,X_658) ),
inference(subst,[],[refute_0_40:[bind(X_253,$fot(skolemFOFtoCNF_M)),bind(X_254,$fot(skolemFOFtoCNF_N)),bind(X_255,$fot(X_658))]]) ).
cnf(refute_0_42,plain,
( convergent_lines(skolemFOFtoCNF_M,X_658)
| orthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
| unorthogonal_lines(skolemFOFtoCNF_N,X_658) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) )],[refute_0_35,refute_0_41]) ).
cnf(refute_0_43,plain,
~ orthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_44,plain,
( convergent_lines(skolemFOFtoCNF_M,X_658)
| unorthogonal_lines(skolemFOFtoCNF_N,X_658) ),
inference(resolve,[$cnf( orthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
( convergent_lines(skolemFOFtoCNF_M,X_659)
| unorthogonal_lines(skolemFOFtoCNF_N,X_659) ),
inference(subst,[],[refute_0_44:[bind(X_658,$fot(X_659))]]) ).
cnf(refute_0_46,plain,
( ~ orthogonal_lines(skolemFOFtoCNF_N,X_659)
| convergent_lines(skolemFOFtoCNF_M,X_659) ),
inference(resolve,[$cnf( unorthogonal_lines(skolemFOFtoCNF_N,X_659) )],[refute_0_45,refute_0_5]) ).
cnf(refute_0_47,plain,
( ~ orthogonal_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_M)
| convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_M) ),
inference(subst,[],[refute_0_46:[bind(X_659,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_48,plain,
( ~ orthogonal_lines(skolemFOFtoCNF_L,X_661)
| ~ unorthogonal_lines(skolemFOFtoCNF_L,X_661) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(X_661))]]) ).
cnf(refute_0_49,plain,
( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L)
| convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_24:[bind(Z,$fot(skolemFOFtoCNF_L)),bind(X_62,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_50,plain,
~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_51,plain,
convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
( ~ convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L)
| convergent_lines(skolemFOFtoCNF_M,X_658)
| orthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L)
| unorthogonal_lines(skolemFOFtoCNF_L,X_658) ),
inference(subst,[],[refute_0_40:[bind(X_253,$fot(skolemFOFtoCNF_M)),bind(X_254,$fot(skolemFOFtoCNF_L)),bind(X_255,$fot(X_658))]]) ).
cnf(refute_0_53,plain,
( convergent_lines(skolemFOFtoCNF_M,X_658)
| orthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L)
| unorthogonal_lines(skolemFOFtoCNF_L,X_658) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
( convergent_lines(skolemFOFtoCNF_M,X_661)
| orthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L)
| unorthogonal_lines(skolemFOFtoCNF_L,X_661) ),
inference(subst,[],[refute_0_53:[bind(X_658,$fot(X_661))]]) ).
cnf(refute_0_55,plain,
( ~ orthogonal_lines(skolemFOFtoCNF_L,X_661)
| convergent_lines(skolemFOFtoCNF_M,X_661)
| orthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L) ),
inference(resolve,[$cnf( unorthogonal_lines(skolemFOFtoCNF_L,X_661) )],[refute_0_54,refute_0_48]) ).
cnf(refute_0_56,plain,
( ~ orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
| convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_M)
| orthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_55:[bind(X_661,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_57,plain,
( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_M)
| orthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L) ),
inference(resolve,[$cnf( orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_14,refute_0_56]) ).
cnf(refute_0_58,plain,
orthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_M) )],[refute_0_57,refute_0_12]) ).
cnf(refute_0_59,plain,
( ~ orthogonal_lines(skolemFOFtoCNF_M,X_662)
| ~ unorthogonal_lines(skolemFOFtoCNF_M,X_662) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_M)),bind(Y,$fot(X_662))]]) ).
cnf(refute_0_60,plain,
( ~ convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_M)
| convergent_lines(skolemFOFtoCNF_N,X_658)
| orthogonal_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_M)
| unorthogonal_lines(skolemFOFtoCNF_M,X_658) ),
inference(subst,[],[refute_0_40:[bind(X_253,$fot(skolemFOFtoCNF_N)),bind(X_254,$fot(skolemFOFtoCNF_M)),bind(X_255,$fot(X_658))]]) ).
cnf(refute_0_61,plain,
( convergent_lines(skolemFOFtoCNF_N,X_658)
| orthogonal_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_M)
| unorthogonal_lines(skolemFOFtoCNF_M,X_658) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_M) )],[refute_0_32,refute_0_60]) ).
cnf(refute_0_62,plain,
( convergent_lines(skolemFOFtoCNF_N,X_662)
| orthogonal_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_M)
| unorthogonal_lines(skolemFOFtoCNF_M,X_662) ),
inference(subst,[],[refute_0_61:[bind(X_658,$fot(X_662))]]) ).
cnf(refute_0_63,plain,
( ~ orthogonal_lines(skolemFOFtoCNF_M,X_662)
| convergent_lines(skolemFOFtoCNF_N,X_662)
| orthogonal_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_M) ),
inference(resolve,[$cnf( unorthogonal_lines(skolemFOFtoCNF_M,X_662) )],[refute_0_62,refute_0_59]) ).
cnf(refute_0_64,plain,
( ~ orthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L)
| convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_L)
| orthogonal_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_M) ),
inference(subst,[],[refute_0_63:[bind(X_662,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_65,plain,
( convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_L)
| orthogonal_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_M) ),
inference(resolve,[$cnf( orthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L) )],[refute_0_58,refute_0_64]) ).
cnf(refute_0_66,plain,
( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_M)
| convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_L) ),
inference(resolve,[$cnf( orthogonal_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_M) )],[refute_0_65,refute_0_47]) ).
cnf(refute_0_67,plain,
convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_L),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_M) )],[refute_0_66,refute_0_12]) ).
cnf(refute_0_68,plain,
( convergent_lines(skolemFOFtoCNF_L,Z)
| convergent_lines(skolemFOFtoCNF_N,Z) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_L) )],[refute_0_67,refute_0_3]) ).
cnf(refute_0_69,plain,
( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N)
| convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_68:[bind(Z,$fot(skolemFOFtoCNF_N))]]) ).
cnf(refute_0_70,plain,
convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_N) )],[refute_0_69,refute_0_1]) ).
cnf(refute_0_71,plain,
$false,
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N) )],[refute_0_70,refute_0_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEO219+3 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jun 18 10:27:49 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.56/0.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.56/0.76
% 0.56/0.76 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.61/0.77
%------------------------------------------------------------------------------