TSTP Solution File: GEO218+3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO218+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 05:25:31 EDT 2022
% Result : Theorem 0.91s 1.12s
% Output : CNFRefutation 0.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 10
% Syntax : Number of formulae : 124 ( 20 unt; 0 def)
% Number of atoms : 346 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 335 ( 113 ~; 181 |; 27 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 201 ( 0 sgn 97 !; 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(ceq3,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( distinct_lines(Y,Z)
| convergent_lines(X,Z) ) ) ).
fof(p1,axiom,
! [X,Y] :
( distinct_lines(X,Y)
=> convergent_lines(X,Y) ) ).
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(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(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] :
( ( parallel_lines(L,M)
& orthogonal_lines(L,N) )
=> orthogonal_lines(M,N) ) ).
fof(subgoal_0,plain,
! [L,M,N] :
( ( parallel_lines(L,M)
& orthogonal_lines(L,N) )
=> orthogonal_lines(M,N) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [L,M,N] :
( ( parallel_lines(L,M)
& orthogonal_lines(L,N) )
=> orthogonal_lines(M,N) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [L,M,N] :
( ~ orthogonal_lines(M,N)
& orthogonal_lines(L,N)
& parallel_lines(L,M) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ orthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
& orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N)
& parallel_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( ~ orthogonal_lines(X,Y)
<=> unorthogonal_lines(X,Y) ),
inference(canonicalize,[],[a5]) ).
fof(normalize_0_4,plain,
! [X,Y] :
( ~ orthogonal_lines(X,Y)
<=> unorthogonal_lines(X,Y) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ( ~ orthogonal_lines(X,Y)
| ~ unorthogonal_lines(X,Y) )
& ( orthogonal_lines(X,Y)
| unorthogonal_lines(X,Y) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ~ orthogonal_lines(X,Y)
| ~ unorthogonal_lines(X,Y) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,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_8,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_7]) ).
fof(normalize_0_9,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_8]) ).
fof(normalize_0_10,plain,
! [L,M,N] :
( ~ convergent_lines(M,N)
| ~ unorthogonal_lines(M,N)
| convergent_lines(L,N)
| unorthogonal_lines(L,M) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(canonicalize,[],[p1]) ).
fof(normalize_0_12,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[ceq3]) ).
fof(normalize_0_14,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
parallel_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_16,plain,
! [X,Y] :
( ~ convergent_lines(X,Y)
<=> parallel_lines(X,Y) ),
inference(canonicalize,[],[a3]) ).
fof(normalize_0_17,plain,
! [X,Y] :
( ~ convergent_lines(X,Y)
<=> parallel_lines(X,Y) ),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [X,Y] :
( ( ~ convergent_lines(X,Y)
| ~ parallel_lines(X,Y) )
& ( convergent_lines(X,Y)
| parallel_lines(X,Y) ) ),
inference(clausify,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [X,Y] :
( ~ convergent_lines(X,Y)
| ~ parallel_lines(X,Y) ),
inference(conjunct,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[ax6]) ).
fof(normalize_0_21,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [X] : ~ convergent_lines(X,X),
inference(canonicalize,[],[apart3]) ).
fof(normalize_0_23,plain,
! [X] : ~ convergent_lines(X,X),
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]) ).
fof(normalize_0_26,plain,
! [X,Y] :
( orthogonal_lines(X,Y)
| unorthogonal_lines(X,Y) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_27,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_28,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_27]) ).
fof(normalize_0_29,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_28]) ).
fof(normalize_0_30,plain,
! [L,M,N] :
( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| convergent_lines(M,N)
| unorthogonal_lines(L,N) ),
inference(conjunct,[],[normalize_0_29]) ).
fof(normalize_0_31,plain,
! [L,M,N] :
( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| convergent_lines(L,N)
| unorthogonal_lines(M,N) ),
inference(conjunct,[],[normalize_0_29]) ).
fof(normalize_0_32,plain,
~ orthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ orthogonal_lines(X,Y)
| ~ unorthogonal_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( ~ orthogonal_lines(X_968,skolemFOFtoCNF_N)
| ~ unorthogonal_lines(X_968,skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_968)),bind(Y,$fot(skolemFOFtoCNF_N))]]) ).
cnf(refute_0_3,plain,
( ~ convergent_lines(M,N)
| ~ unorthogonal_lines(M,N)
| convergent_lines(L,N)
| unorthogonal_lines(L,M) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_4,plain,
( ~ convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_M)
| ~ unorthogonal_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_M)
| convergent_lines(L,skolemFOFtoCNF_M)
| unorthogonal_lines(L,skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_3:[bind(M,$fot(skolemFOFtoCNF_N)),bind(N,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_5,plain,
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_6,plain,
( ~ distinct_lines(skolemFOFtoCNF_N,X_477)
| convergent_lines(skolemFOFtoCNF_N,X_477) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(skolemFOFtoCNF_N)),bind(Y,$fot(X_477))]]) ).
cnf(refute_0_7,plain,
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_8,plain,
( ~ convergent_lines(X_402,skolemFOFtoCNF_N)
| convergent_lines(X_402,Z)
| distinct_lines(skolemFOFtoCNF_N,Z) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(X_402)),bind(Y,$fot(skolemFOFtoCNF_N))]]) ).
cnf(refute_0_9,plain,
parallel_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_10,plain,
( ~ convergent_lines(X,Y)
| ~ parallel_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_11,plain,
( ~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
| ~ parallel_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_12,plain,
~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(resolve,[$cnf( parallel_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_14,plain,
( ~ convergent_lines(skolemFOFtoCNF_L,X_116)
| convergent_lines(X_116,Z)
| convergent_lines(skolemFOFtoCNF_L,Z) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(X_116))]]) ).
cnf(refute_0_15,plain,
~ convergent_lines(X,X),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_16,plain,
~ convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_N),
inference(subst,[],[refute_0_15:[bind(X,$fot(skolemFOFtoCNF_N))]]) ).
cnf(refute_0_17,plain,
( ~ convergent_lines(skolemFOFtoCNF_N,X_65)
| convergent_lines(X_65,Z)
| convergent_lines(skolemFOFtoCNF_N,Z) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(skolemFOFtoCNF_N)),bind(Y,$fot(X_65))]]) ).
cnf(refute_0_18,plain,
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_19,plain,
( convergent_lines(X_35,X_36)
| unorthogonal_lines(X_35,X_36) ),
inference(subst,[],[refute_0_18:[bind(L,$fot(X_35)),bind(M,$fot(X_36))]]) ).
cnf(refute_0_20,plain,
( ~ orthogonal_lines(X_35,X_36)
| ~ unorthogonal_lines(X_35,X_36) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_35)),bind(Y,$fot(X_36))]]) ).
cnf(refute_0_21,plain,
( ~ orthogonal_lines(X_35,X_36)
| convergent_lines(X_35,X_36) ),
inference(resolve,[$cnf( unorthogonal_lines(X_35,X_36) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N)
| convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_21:[bind(X_35,$fot(skolemFOFtoCNF_L)),bind(X_36,$fot(skolemFOFtoCNF_N))]]) ).
cnf(refute_0_23,plain,
convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N),
inference(resolve,[$cnf( orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N) )],[refute_0_0,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N)
| convergent_lines(skolemFOFtoCNF_L,X_64)
| convergent_lines(skolemFOFtoCNF_N,X_64) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(skolemFOFtoCNF_N)),bind(Z,$fot(X_64))]]) ).
cnf(refute_0_25,plain,
( convergent_lines(skolemFOFtoCNF_L,X_64)
| convergent_lines(skolemFOFtoCNF_N,X_64) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( convergent_lines(skolemFOFtoCNF_L,X_65)
| convergent_lines(skolemFOFtoCNF_N,X_65) ),
inference(subst,[],[refute_0_25:[bind(X_64,$fot(X_65))]]) ).
cnf(refute_0_27,plain,
( convergent_lines(X_65,Z)
| convergent_lines(skolemFOFtoCNF_L,X_65)
| convergent_lines(skolemFOFtoCNF_N,Z) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_N,X_65) )],[refute_0_26,refute_0_17]) ).
cnf(refute_0_28,plain,
( convergent_lines(X_114,skolemFOFtoCNF_N)
| convergent_lines(skolemFOFtoCNF_L,X_114)
| convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_27:[bind(Z,$fot(skolemFOFtoCNF_N)),bind(X_65,$fot(X_114))]]) ).
cnf(refute_0_29,plain,
( convergent_lines(X_114,skolemFOFtoCNF_N)
| convergent_lines(skolemFOFtoCNF_L,X_114) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_N) )],[refute_0_28,refute_0_16]) ).
cnf(refute_0_30,plain,
( convergent_lines(X_116,skolemFOFtoCNF_N)
| convergent_lines(skolemFOFtoCNF_L,X_116) ),
inference(subst,[],[refute_0_29:[bind(X_114,$fot(X_116))]]) ).
cnf(refute_0_31,plain,
( convergent_lines(X_116,Z)
| convergent_lines(X_116,skolemFOFtoCNF_N)
| convergent_lines(skolemFOFtoCNF_L,Z) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,X_116) )],[refute_0_30,refute_0_14]) ).
cnf(refute_0_32,plain,
( convergent_lines(X_401,skolemFOFtoCNF_M)
| convergent_lines(X_401,skolemFOFtoCNF_N)
| convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
inference(subst,[],[refute_0_31:[bind(Z,$fot(skolemFOFtoCNF_M)),bind(X_116,$fot(X_401))]]) ).
cnf(refute_0_33,plain,
( convergent_lines(X_401,skolemFOFtoCNF_M)
| convergent_lines(X_401,skolemFOFtoCNF_N) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_32,refute_0_12]) ).
cnf(refute_0_34,plain,
( convergent_lines(X_402,skolemFOFtoCNF_M)
| convergent_lines(X_402,skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_33:[bind(X_401,$fot(X_402))]]) ).
cnf(refute_0_35,plain,
( convergent_lines(X_402,Z)
| convergent_lines(X_402,skolemFOFtoCNF_M)
| distinct_lines(skolemFOFtoCNF_N,Z) ),
inference(resolve,[$cnf( convergent_lines(X_402,skolemFOFtoCNF_N) )],[refute_0_34,refute_0_8]) ).
cnf(refute_0_36,plain,
( convergent_lines(X_478,X_477)
| convergent_lines(X_478,skolemFOFtoCNF_M)
| distinct_lines(skolemFOFtoCNF_N,X_477) ),
inference(subst,[],[refute_0_35:[bind(Z,$fot(X_477)),bind(X_402,$fot(X_478))]]) ).
cnf(refute_0_37,plain,
( convergent_lines(X_478,X_477)
| convergent_lines(X_478,skolemFOFtoCNF_M)
| convergent_lines(skolemFOFtoCNF_N,X_477) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_N,X_477) )],[refute_0_36,refute_0_6]) ).
cnf(refute_0_38,plain,
( convergent_lines(X_478,X_870)
| convergent_lines(X_478,skolemFOFtoCNF_M)
| convergent_lines(skolemFOFtoCNF_N,X_870) ),
inference(subst,[],[refute_0_37:[bind(X_477,$fot(X_870))]]) ).
cnf(refute_0_39,plain,
( orthogonal_lines(X,Y)
| unorthogonal_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_40,plain,
( orthogonal_lines(X_273,X_274)
| unorthogonal_lines(X_273,X_274) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(X_273)),bind(Y,$fot(X_274))]]) ).
cnf(refute_0_41,plain,
( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| convergent_lines(M,N)
| unorthogonal_lines(L,N) ),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_42,plain,
( ~ convergent_lines(X_273,X_274)
| ~ unorthogonal_lines(X_273,X_274)
| convergent_lines(X_274,X_275)
| unorthogonal_lines(X_273,X_275) ),
inference(subst,[],[refute_0_41:[bind(L,$fot(X_273)),bind(M,$fot(X_274)),bind(N,$fot(X_275))]]) ).
cnf(refute_0_43,plain,
( ~ convergent_lines(X_273,X_274)
| convergent_lines(X_274,X_275)
| orthogonal_lines(X_273,X_274)
| unorthogonal_lines(X_273,X_275) ),
inference(resolve,[$cnf( unorthogonal_lines(X_273,X_274) )],[refute_0_40,refute_0_42]) ).
cnf(refute_0_44,plain,
( ~ convergent_lines(skolemFOFtoCNF_N,X_870)
| convergent_lines(X_870,X_871)
| orthogonal_lines(skolemFOFtoCNF_N,X_870)
| unorthogonal_lines(skolemFOFtoCNF_N,X_871) ),
inference(subst,[],[refute_0_43:[bind(X_273,$fot(skolemFOFtoCNF_N)),bind(X_274,$fot(X_870)),bind(X_275,$fot(X_871))]]) ).
cnf(refute_0_45,plain,
( convergent_lines(X_478,X_870)
| convergent_lines(X_478,skolemFOFtoCNF_M)
| convergent_lines(X_870,X_871)
| orthogonal_lines(skolemFOFtoCNF_N,X_870)
| unorthogonal_lines(skolemFOFtoCNF_N,X_871) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_N,X_870) )],[refute_0_38,refute_0_44]) ).
cnf(refute_0_46,plain,
( convergent_lines(X_870,X_870)
| convergent_lines(X_870,skolemFOFtoCNF_M)
| orthogonal_lines(skolemFOFtoCNF_N,X_870)
| unorthogonal_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_M) ),
inference(subst,[],[refute_0_45:[bind(X_478,$fot(X_870)),bind(X_871,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_47,plain,
~ convergent_lines(X_870,X_870),
inference(subst,[],[refute_0_15:[bind(X,$fot(X_870))]]) ).
cnf(refute_0_48,plain,
( convergent_lines(X_870,skolemFOFtoCNF_M)
| orthogonal_lines(skolemFOFtoCNF_N,X_870)
| unorthogonal_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_M) ),
inference(resolve,[$cnf( convergent_lines(X_870,X_870) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( convergent_lines(X_967,skolemFOFtoCNF_M)
| orthogonal_lines(skolemFOFtoCNF_N,X_967)
| unorthogonal_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_M) ),
inference(subst,[],[refute_0_48:[bind(X_870,$fot(X_967))]]) ).
cnf(refute_0_50,plain,
( ~ orthogonal_lines(skolemFOFtoCNF_N,X_966)
| ~ unorthogonal_lines(skolemFOFtoCNF_N,X_966) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(skolemFOFtoCNF_N)),bind(Y,$fot(X_966))]]) ).
cnf(refute_0_51,plain,
( ~ convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_M)
| convergent_lines(skolemFOFtoCNF_M,Z)
| convergent_lines(skolemFOFtoCNF_N,Z) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(skolemFOFtoCNF_N)),bind(Y,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_52,plain,
( convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_M)
| convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_33:[bind(X_401,$fot(skolemFOFtoCNF_N))]]) ).
cnf(refute_0_53,plain,
convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_M),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_N) )],[refute_0_52,refute_0_16]) ).
cnf(refute_0_54,plain,
( convergent_lines(skolemFOFtoCNF_M,Z)
| convergent_lines(skolemFOFtoCNF_N,Z) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_M) )],[refute_0_53,refute_0_51]) ).
cnf(refute_0_55,plain,
( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
| convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_54:[bind(Z,$fot(skolemFOFtoCNF_N))]]) ).
cnf(refute_0_56,plain,
convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_N) )],[refute_0_55,refute_0_16]) ).
cnf(refute_0_57,plain,
( orthogonal_lines(X_270,X_271)
| unorthogonal_lines(X_270,X_271) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(X_270)),bind(Y,$fot(X_271))]]) ).
cnf(refute_0_58,plain,
( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| convergent_lines(L,N)
| unorthogonal_lines(M,N) ),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_59,plain,
( ~ convergent_lines(X_270,X_271)
| ~ unorthogonal_lines(X_270,X_271)
| convergent_lines(X_270,X_272)
| unorthogonal_lines(X_271,X_272) ),
inference(subst,[],[refute_0_58:[bind(L,$fot(X_270)),bind(M,$fot(X_271)),bind(N,$fot(X_272))]]) ).
cnf(refute_0_60,plain,
( ~ convergent_lines(X_270,X_271)
| convergent_lines(X_270,X_272)
| orthogonal_lines(X_270,X_271)
| unorthogonal_lines(X_271,X_272) ),
inference(resolve,[$cnf( unorthogonal_lines(X_270,X_271) )],[refute_0_57,refute_0_59]) ).
cnf(refute_0_61,plain,
( ~ convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
| convergent_lines(skolemFOFtoCNF_M,X_965)
| orthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
| unorthogonal_lines(skolemFOFtoCNF_N,X_965) ),
inference(subst,[],[refute_0_60:[bind(X_270,$fot(skolemFOFtoCNF_M)),bind(X_271,$fot(skolemFOFtoCNF_N)),bind(X_272,$fot(X_965))]]) ).
cnf(refute_0_62,plain,
( convergent_lines(skolemFOFtoCNF_M,X_965)
| orthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
| unorthogonal_lines(skolemFOFtoCNF_N,X_965) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) )],[refute_0_56,refute_0_61]) ).
cnf(refute_0_63,plain,
~ orthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N),
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_64,plain,
( convergent_lines(skolemFOFtoCNF_M,X_965)
| unorthogonal_lines(skolemFOFtoCNF_N,X_965) ),
inference(resolve,[$cnf( orthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
( convergent_lines(skolemFOFtoCNF_M,X_966)
| unorthogonal_lines(skolemFOFtoCNF_N,X_966) ),
inference(subst,[],[refute_0_64:[bind(X_965,$fot(X_966))]]) ).
cnf(refute_0_66,plain,
( ~ orthogonal_lines(skolemFOFtoCNF_N,X_966)
| convergent_lines(skolemFOFtoCNF_M,X_966) ),
inference(resolve,[$cnf( unorthogonal_lines(skolemFOFtoCNF_N,X_966) )],[refute_0_65,refute_0_50]) ).
cnf(refute_0_67,plain,
( ~ orthogonal_lines(skolemFOFtoCNF_N,X_967)
| convergent_lines(skolemFOFtoCNF_M,X_967) ),
inference(subst,[],[refute_0_66:[bind(X_966,$fot(X_967))]]) ).
cnf(refute_0_68,plain,
( convergent_lines(X_967,skolemFOFtoCNF_M)
| convergent_lines(skolemFOFtoCNF_M,X_967)
| unorthogonal_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_M) ),
inference(resolve,[$cnf( orthogonal_lines(skolemFOFtoCNF_N,X_967) )],[refute_0_49,refute_0_67]) ).
cnf(refute_0_69,plain,
( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_M)
| unorthogonal_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_M) ),
inference(subst,[],[refute_0_68:[bind(X_967,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_70,plain,
~ convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_M),
inference(subst,[],[refute_0_15:[bind(X,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_71,plain,
unorthogonal_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_M),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_M) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
( ~ convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_M)
| convergent_lines(L,skolemFOFtoCNF_M)
| unorthogonal_lines(L,skolemFOFtoCNF_N) ),
inference(resolve,[$cnf( unorthogonal_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_M) )],[refute_0_71,refute_0_4]) ).
cnf(refute_0_73,plain,
( convergent_lines(L,skolemFOFtoCNF_M)
| unorthogonal_lines(L,skolemFOFtoCNF_N) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_M) )],[refute_0_53,refute_0_72]) ).
cnf(refute_0_74,plain,
( convergent_lines(X_968,skolemFOFtoCNF_M)
| unorthogonal_lines(X_968,skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_73:[bind(L,$fot(X_968))]]) ).
cnf(refute_0_75,plain,
( ~ orthogonal_lines(X_968,skolemFOFtoCNF_N)
| convergent_lines(X_968,skolemFOFtoCNF_M) ),
inference(resolve,[$cnf( unorthogonal_lines(X_968,skolemFOFtoCNF_N) )],[refute_0_74,refute_0_2]) ).
cnf(refute_0_76,plain,
( ~ orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N)
| convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
inference(subst,[],[refute_0_75:[bind(X_968,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_77,plain,
convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(resolve,[$cnf( orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N) )],[refute_0_0,refute_0_76]) ).
cnf(refute_0_78,plain,
$false,
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_77,refute_0_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO218+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n022.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 04:25:02 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.91/1.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.91/1.12
% 0.91/1.12 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.91/1.13
%------------------------------------------------------------------------------