%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO234+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 05:25:43 EDT 2022
% Result : Theorem 0.20s 0.47s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 9
% Syntax : Number of formulae : 123 ( 27 unt; 0 def)
% Number of atoms : 246 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 221 ( 98 ~; 98 |; 11 &)
% ( 9 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 171 ( 4 sgn 79 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(a1_defns,axiom,
! [X,Y] :
( unequally_directed_opposite_lines(X,Y)
<=> unequally_directed_lines(X,reverse_line(Y)) ) ).
fof(a4_defns,axiom,
! [X,Y] :
( equally_directed_lines(X,Y)
<=> ~ unequally_directed_lines(X,Y) ) ).
fof(a5_defns,axiom,
! [X,Y] :
( equally_directed_opposite_lines(X,Y)
<=> ~ unequally_directed_opposite_lines(X,Y) ) ).
fof(ax5_basics,axiom,
! [L] : equally_directed_lines(L,L) ).
fof(ax6_basics,axiom,
! [L,M,N] :
( unequally_directed_lines(L,M)
=> ( unequally_directed_lines(L,N)
| unequally_directed_lines(M,N) ) ) ).
fof(ax8_basics,axiom,
! [L,M] :
( unequally_directed_lines(L,M)
| unequally_directed_lines(L,reverse_line(M)) ) ).
fof(ax9_basics,axiom,
! [L,M] :
( ( unequally_directed_lines(L,M)
& unequally_directed_lines(L,reverse_line(M)) )
=> ( left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ) ) ).
fof(ax11_basics,axiom,
! [L,M] :
~ ( left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ) ).
fof(con,conjecture,
! [L,M,N] :
( unequally_directed_opposite_lines(L,M)
=> ( unequally_directed_lines(L,N)
| unequally_directed_opposite_lines(M,N) ) ) ).
fof(subgoal_0,plain,
! [L,M,N] :
( ( unequally_directed_opposite_lines(L,M)
& ~ unequally_directed_lines(L,N) )
=> unequally_directed_opposite_lines(M,N) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [L,M,N] :
( ( unequally_directed_opposite_lines(L,M)
& ~ unequally_directed_lines(L,N) )
=> unequally_directed_opposite_lines(M,N) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y] :
( ~ equally_directed_opposite_lines(X,Y)
<=> unequally_directed_opposite_lines(X,Y) ),
inference(canonicalize,[],[a5_defns]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ~ equally_directed_opposite_lines(X,Y)
<=> unequally_directed_opposite_lines(X,Y) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] :
( ( ~ equally_directed_opposite_lines(X,Y)
| ~ unequally_directed_opposite_lines(X,Y) )
& ( equally_directed_opposite_lines(X,Y)
| unequally_directed_opposite_lines(X,Y) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( ~ equally_directed_opposite_lines(X,Y)
| ~ unequally_directed_opposite_lines(X,Y) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X,Y] :
( ~ unequally_directed_lines(X,reverse_line(Y))
<=> ~ unequally_directed_opposite_lines(X,Y) ),
inference(canonicalize,[],[a1_defns]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ~ unequally_directed_lines(X,reverse_line(Y))
<=> ~ unequally_directed_opposite_lines(X,Y) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) )
& ( ~ unequally_directed_opposite_lines(X,Y)
| unequally_directed_lines(X,reverse_line(Y)) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [L,M] :
( unequally_directed_lines(L,M)
| unequally_directed_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[ax8_basics]) ).
fof(normalize_0_9,plain,
! [L,M] :
( unequally_directed_lines(L,M)
| unequally_directed_lines(L,reverse_line(M)) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [L,M] :
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[ax9_basics]) ).
fof(normalize_0_11,plain,
! [L,M] :
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
( ! [L,M] : ~ left_convergent_lines(L,M)
& ! [L,M] : ~ left_convergent_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[ax11_basics]) ).
fof(normalize_0_13,plain,
! [L,M] : ~ left_convergent_lines(L,M),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [L,M] : ~ left_convergent_lines(L,M),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [X,Y] :
( ~ equally_directed_lines(X,Y)
<=> unequally_directed_lines(X,Y) ),
inference(canonicalize,[],[a4_defns]) ).
fof(normalize_0_16,plain,
! [X,Y] :
( ~ equally_directed_lines(X,Y)
<=> unequally_directed_lines(X,Y) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [X,Y] :
( ( ~ equally_directed_lines(X,Y)
| ~ unequally_directed_lines(X,Y) )
& ( equally_directed_lines(X,Y)
| unequally_directed_lines(X,Y) ) ),
inference(clausify,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [X,Y] :
( ~ equally_directed_lines(X,Y)
| ~ unequally_directed_lines(X,Y) ),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
? [L,M,N] :
( ~ unequally_directed_lines(L,N)
& ~ unequally_directed_opposite_lines(M,N)
& unequally_directed_opposite_lines(L,M) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_20,plain,
( ~ unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N)
& ~ unequally_directed_opposite_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
& unequally_directed_opposite_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
inference(skolemize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
~ unequally_directed_opposite_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N),
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [L,M,N] :
( ~ unequally_directed_lines(L,M)
| unequally_directed_lines(L,N)
| unequally_directed_lines(M,N) ),
inference(canonicalize,[],[ax6_basics]) ).
fof(normalize_0_23,plain,
! [L,M,N] :
( ~ unequally_directed_lines(L,M)
| unequally_directed_lines(L,N)
| unequally_directed_lines(M,N) ),
inference(specialize,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [X,Y] :
( equally_directed_lines(X,Y)
| unequally_directed_lines(X,Y) ),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_25,plain,
! [X,Y] :
( ~ unequally_directed_opposite_lines(X,Y)
| unequally_directed_lines(X,reverse_line(Y)) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_26,plain,
! [X,Y] :
( equally_directed_opposite_lines(X,Y)
| unequally_directed_opposite_lines(X,Y) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_27,plain,
unequally_directed_opposite_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_28,plain,
! [L] : equally_directed_lines(L,L),
inference(canonicalize,[],[ax5_basics]) ).
fof(normalize_0_29,plain,
! [L] : equally_directed_lines(L,L),
inference(specialize,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
~ unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N),
inference(conjunct,[],[normalize_0_20]) ).
cnf(refute_0_0,plain,
( ~ equally_directed_opposite_lines(X,Y)
| ~ unequally_directed_opposite_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ equally_directed_opposite_lines(X_42,X_43)
| ~ unequally_directed_opposite_lines(X_42,X_43) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(X_42)),bind(Y,$fot(X_43))]]) ).
cnf(refute_0_2,plain,
( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( ~ unequally_directed_lines(X_38,reverse_line(X_39))
| unequally_directed_opposite_lines(X_38,X_39) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_38)),bind(Y,$fot(X_39))]]) ).
cnf(refute_0_4,plain,
( unequally_directed_lines(L,M)
| unequally_directed_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_5,plain,
( unequally_directed_lines(X_38,X_39)
| unequally_directed_lines(X_38,reverse_line(X_39)) ),
inference(subst,[],[refute_0_4:[bind(L,$fot(X_38)),bind(M,$fot(X_39))]]) ).
cnf(refute_0_6,plain,
( unequally_directed_lines(X_38,X_39)
| unequally_directed_opposite_lines(X_38,X_39) ),
inference(resolve,[$cnf( unequally_directed_lines(X_38,reverse_line(X_39)) )],[refute_0_5,refute_0_3]) ).
cnf(refute_0_7,plain,
( unequally_directed_lines(X_42,X_43)
| unequally_directed_opposite_lines(X_42,X_43) ),
inference(subst,[],[refute_0_6:[bind(X_38,$fot(X_42)),bind(X_39,$fot(X_43))]]) ).
cnf(refute_0_8,plain,
( ~ equally_directed_opposite_lines(X_42,X_43)
| unequally_directed_lines(X_42,X_43) ),
inference(resolve,[$cnf( unequally_directed_opposite_lines(X_42,X_43) )],[refute_0_7,refute_0_1]) ).
cnf(refute_0_9,plain,
( ~ equally_directed_opposite_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N)
| unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_8:[bind(X_42,$fot(skolemFOFtoCNF_L)),bind(X_43,$fot(skolemFOFtoCNF_N))]]) ).
cnf(refute_0_10,plain,
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_11,plain,
~ left_convergent_lines(L,M),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_12,plain,
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| left_convergent_lines(L,reverse_line(M)) ),
inference(resolve,[$cnf( left_convergent_lines(L,M) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
~ left_convergent_lines(L,reverse_line(M)),
inference(subst,[],[refute_0_11:[bind(M,$fot(reverse_line(M)))]]) ).
cnf(refute_0_14,plain,
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M)) ),
inference(resolve,[$cnf( left_convergent_lines(L,reverse_line(M)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(reverse_line(skolemFOFtoCNF_N)))
| ~ unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(skolemFOFtoCNF_N)) ),
inference(subst,[],[refute_0_14:[bind(L,$fot(skolemFOFtoCNF_M)),bind(M,$fot(reverse_line(skolemFOFtoCNF_N)))]]) ).
cnf(refute_0_16,plain,
( ~ equally_directed_lines(X,Y)
| ~ unequally_directed_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_17,plain,
( ~ equally_directed_lines(skolemFOFtoCNF_N,X_243)
| ~ unequally_directed_lines(skolemFOFtoCNF_N,X_243) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(skolemFOFtoCNF_N)),bind(Y,$fot(X_243))]]) ).
cnf(refute_0_18,plain,
~ unequally_directed_opposite_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_19,plain,
( unequally_directed_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
| unequally_directed_opposite_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_6:[bind(X_38,$fot(skolemFOFtoCNF_M)),bind(X_39,$fot(skolemFOFtoCNF_N))]]) ).
cnf(refute_0_20,plain,
unequally_directed_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N),
inference(resolve,[$cnf( unequally_directed_opposite_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) )],[refute_0_19,refute_0_18]) ).
cnf(refute_0_21,plain,
( ~ unequally_directed_lines(L,M)
| unequally_directed_lines(L,N)
| unequally_directed_lines(M,N) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_22,plain,
( ~ unequally_directed_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
| unequally_directed_lines(skolemFOFtoCNF_M,X_242)
| unequally_directed_lines(skolemFOFtoCNF_N,X_242) ),
inference(subst,[],[refute_0_21:[bind(L,$fot(skolemFOFtoCNF_M)),bind(M,$fot(skolemFOFtoCNF_N)),bind(N,$fot(X_242))]]) ).
cnf(refute_0_23,plain,
( unequally_directed_lines(skolemFOFtoCNF_M,X_242)
| unequally_directed_lines(skolemFOFtoCNF_N,X_242) ),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) )],[refute_0_20,refute_0_22]) ).
cnf(refute_0_24,plain,
( unequally_directed_lines(skolemFOFtoCNF_M,X_243)
| unequally_directed_lines(skolemFOFtoCNF_N,X_243) ),
inference(subst,[],[refute_0_23:[bind(X_242,$fot(X_243))]]) ).
cnf(refute_0_25,plain,
( ~ equally_directed_lines(skolemFOFtoCNF_N,X_243)
| unequally_directed_lines(skolemFOFtoCNF_M,X_243) ),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_N,X_243) )],[refute_0_24,refute_0_17]) ).
cnf(refute_0_26,plain,
( ~ equally_directed_lines(skolemFOFtoCNF_N,reverse_line(reverse_line(skolemFOFtoCNF_N)))
| unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(reverse_line(skolemFOFtoCNF_N))) ),
inference(subst,[],[refute_0_25:[bind(X_243,$fot(reverse_line(reverse_line(skolemFOFtoCNF_N))))]]) ).
cnf(refute_0_27,plain,
( equally_directed_lines(X,Y)
| unequally_directed_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_28,plain,
( equally_directed_lines(X_40,reverse_line(X_41))
| unequally_directed_lines(X_40,reverse_line(X_41)) ),
inference(subst,[],[refute_0_27:[bind(X,$fot(X_40)),bind(Y,$fot(reverse_line(X_41)))]]) ).
cnf(refute_0_29,plain,
( ~ unequally_directed_lines(X_40,X_41)
| ~ unequally_directed_lines(X_40,reverse_line(X_41)) ),
inference(subst,[],[refute_0_14:[bind(L,$fot(X_40)),bind(M,$fot(X_41))]]) ).
cnf(refute_0_30,plain,
( ~ unequally_directed_lines(X_40,X_41)
| equally_directed_lines(X_40,reverse_line(X_41)) ),
inference(resolve,[$cnf( unequally_directed_lines(X_40,reverse_line(X_41)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( ~ unequally_directed_lines(skolemFOFtoCNF_N,reverse_line(skolemFOFtoCNF_N))
| equally_directed_lines(skolemFOFtoCNF_N,reverse_line(reverse_line(skolemFOFtoCNF_N))) ),
inference(subst,[],[refute_0_30:[bind(X_40,$fot(skolemFOFtoCNF_N)),bind(X_41,$fot(reverse_line(skolemFOFtoCNF_N)))]]) ).
cnf(refute_0_32,plain,
( ~ unequally_directed_opposite_lines(X,Y)
| unequally_directed_lines(X,reverse_line(Y)) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_33,plain,
( ~ unequally_directed_opposite_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_N)
| unequally_directed_lines(skolemFOFtoCNF_N,reverse_line(skolemFOFtoCNF_N)) ),
inference(subst,[],[refute_0_32:[bind(X,$fot(skolemFOFtoCNF_N)),bind(Y,$fot(skolemFOFtoCNF_N))]]) ).
cnf(refute_0_34,plain,
( ~ unequally_directed_lines(skolemFOFtoCNF_M,X_248)
| ~ unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(X_248)) ),
inference(subst,[],[refute_0_14:[bind(L,$fot(skolemFOFtoCNF_M)),bind(M,$fot(X_248))]]) ).
cnf(refute_0_35,plain,
( ~ unequally_directed_lines(skolemFOFtoCNF_N,reverse_line(Y))
| unequally_directed_opposite_lines(skolemFOFtoCNF_N,Y) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_N))]]) ).
cnf(refute_0_36,plain,
( unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(Y))
| unequally_directed_lines(skolemFOFtoCNF_N,reverse_line(Y)) ),
inference(subst,[],[refute_0_23:[bind(X_242,$fot(reverse_line(Y)))]]) ).
cnf(refute_0_37,plain,
( unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(Y))
| unequally_directed_opposite_lines(skolemFOFtoCNF_N,Y) ),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_N,reverse_line(Y)) )],[refute_0_36,refute_0_35]) ).
cnf(refute_0_38,plain,
( unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(X_248))
| unequally_directed_opposite_lines(skolemFOFtoCNF_N,X_248) ),
inference(subst,[],[refute_0_37:[bind(Y,$fot(X_248))]]) ).
cnf(refute_0_39,plain,
( ~ unequally_directed_lines(skolemFOFtoCNF_M,X_248)
| unequally_directed_opposite_lines(skolemFOFtoCNF_N,X_248) ),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(X_248)) )],[refute_0_38,refute_0_34]) ).
cnf(refute_0_40,plain,
( ~ unequally_directed_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
| unequally_directed_opposite_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_39:[bind(X_248,$fot(skolemFOFtoCNF_N))]]) ).
cnf(refute_0_41,plain,
unequally_directed_opposite_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_N),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) )],[refute_0_20,refute_0_40]) ).
cnf(refute_0_42,plain,
unequally_directed_lines(skolemFOFtoCNF_N,reverse_line(skolemFOFtoCNF_N)),
inference(resolve,[$cnf( unequally_directed_opposite_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_N) )],[refute_0_41,refute_0_33]) ).
cnf(refute_0_43,plain,
equally_directed_lines(skolemFOFtoCNF_N,reverse_line(reverse_line(skolemFOFtoCNF_N))),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_N,reverse_line(skolemFOFtoCNF_N)) )],[refute_0_42,refute_0_31]) ).
cnf(refute_0_44,plain,
unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(reverse_line(skolemFOFtoCNF_N))),
inference(resolve,[$cnf( equally_directed_lines(skolemFOFtoCNF_N,reverse_line(reverse_line(skolemFOFtoCNF_N))) )],[refute_0_43,refute_0_26]) ).
cnf(refute_0_45,plain,
~ unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(skolemFOFtoCNF_N)),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(reverse_line(skolemFOFtoCNF_N))) )],[refute_0_44,refute_0_15]) ).
cnf(refute_0_46,plain,
( equally_directed_opposite_lines(X,Y)
| unequally_directed_opposite_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_47,plain,
( equally_directed_opposite_lines(X_36,X_37)
| unequally_directed_opposite_lines(X_36,X_37) ),
inference(subst,[],[refute_0_46:[bind(X,$fot(X_36)),bind(Y,$fot(X_37))]]) ).
cnf(refute_0_48,plain,
( ~ unequally_directed_opposite_lines(X_36,X_37)
| unequally_directed_lines(X_36,reverse_line(X_37)) ),
inference(subst,[],[refute_0_32:[bind(X,$fot(X_36)),bind(Y,$fot(X_37))]]) ).
cnf(refute_0_49,plain,
( equally_directed_opposite_lines(X_36,X_37)
| unequally_directed_lines(X_36,reverse_line(X_37)) ),
inference(resolve,[$cnf( unequally_directed_opposite_lines(X_36,X_37) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
( equally_directed_opposite_lines(skolemFOFtoCNF_L,X_37)
| unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(X_37)) ),
inference(subst,[],[refute_0_49:[bind(X_36,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_51,plain,
( ~ unequally_directed_lines(skolemFOFtoCNF_L,X_292)
| ~ unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(X_292)) ),
inference(subst,[],[refute_0_14:[bind(L,$fot(skolemFOFtoCNF_L)),bind(M,$fot(X_292))]]) ).
cnf(refute_0_52,plain,
( ~ unequally_directed_lines(reverse_line(skolemFOFtoCNF_M),M)
| ~ unequally_directed_lines(reverse_line(skolemFOFtoCNF_M),reverse_line(M)) ),
inference(subst,[],[refute_0_14:[bind(L,$fot(reverse_line(skolemFOFtoCNF_M)))]]) ).
cnf(refute_0_53,plain,
unequally_directed_opposite_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_54,plain,
( ~ unequally_directed_opposite_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
| unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M)) ),
inference(subst,[],[refute_0_32:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_55,plain,
unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M)),
inference(resolve,[$cnf( unequally_directed_opposite_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
( ~ unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M))
| unequally_directed_lines(reverse_line(skolemFOFtoCNF_M),X_242)
| unequally_directed_lines(skolemFOFtoCNF_L,X_242) ),
inference(subst,[],[refute_0_21:[bind(L,$fot(skolemFOFtoCNF_L)),bind(M,$fot(reverse_line(skolemFOFtoCNF_M))),bind(N,$fot(X_242))]]) ).
cnf(refute_0_57,plain,
( unequally_directed_lines(reverse_line(skolemFOFtoCNF_M),X_242)
| unequally_directed_lines(skolemFOFtoCNF_L,X_242) ),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M)) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
( unequally_directed_lines(reverse_line(skolemFOFtoCNF_M),reverse_line(M))
| unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(M)) ),
inference(subst,[],[refute_0_57:[bind(X_242,$fot(reverse_line(M)))]]) ).
cnf(refute_0_59,plain,
( ~ unequally_directed_lines(reverse_line(skolemFOFtoCNF_M),M)
| unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(M)) ),
inference(resolve,[$cnf( unequally_directed_lines(reverse_line(skolemFOFtoCNF_M),reverse_line(M)) )],[refute_0_58,refute_0_52]) ).
cnf(refute_0_60,plain,
( ~ unequally_directed_lines(reverse_line(skolemFOFtoCNF_M),X_291)
| unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(X_291)) ),
inference(subst,[],[refute_0_59:[bind(M,$fot(X_291))]]) ).
cnf(refute_0_61,plain,
equally_directed_lines(L,L),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_62,plain,
equally_directed_lines(reverse_line(X_51),reverse_line(X_51)),
inference(subst,[],[refute_0_61:[bind(L,$fot(reverse_line(X_51)))]]) ).
cnf(refute_0_63,plain,
( ~ equally_directed_lines(X_38,reverse_line(X_39))
| ~ unequally_directed_lines(X_38,reverse_line(X_39)) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(X_38)),bind(Y,$fot(reverse_line(X_39)))]]) ).
cnf(refute_0_64,plain,
( ~ equally_directed_lines(X_38,reverse_line(X_39))
| unequally_directed_lines(X_38,X_39) ),
inference(resolve,[$cnf( unequally_directed_lines(X_38,reverse_line(X_39)) )],[refute_0_5,refute_0_63]) ).
cnf(refute_0_65,plain,
( ~ equally_directed_lines(reverse_line(X_51),reverse_line(X_51))
| unequally_directed_lines(reverse_line(X_51),X_51) ),
inference(subst,[],[refute_0_64:[bind(X_38,$fot(reverse_line(X_51))),bind(X_39,$fot(X_51))]]) ).
cnf(refute_0_66,plain,
unequally_directed_lines(reverse_line(X_51),X_51),
inference(resolve,[$cnf( equally_directed_lines(reverse_line(X_51),reverse_line(X_51)) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
unequally_directed_lines(reverse_line(X_241),X_241),
inference(subst,[],[refute_0_66:[bind(X_51,$fot(X_241))]]) ).
cnf(refute_0_68,plain,
( ~ unequally_directed_lines(reverse_line(X_241),X_241)
| unequally_directed_lines(X_241,X_242)
| unequally_directed_lines(reverse_line(X_241),X_242) ),
inference(subst,[],[refute_0_21:[bind(L,$fot(reverse_line(X_241))),bind(M,$fot(X_241)),bind(N,$fot(X_242))]]) ).
cnf(refute_0_69,plain,
( unequally_directed_lines(X_241,X_242)
| unequally_directed_lines(reverse_line(X_241),X_242) ),
inference(resolve,[$cnf( unequally_directed_lines(reverse_line(X_241),X_241) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
( unequally_directed_lines(reverse_line(skolemFOFtoCNF_M),X_291)
| unequally_directed_lines(skolemFOFtoCNF_M,X_291) ),
inference(subst,[],[refute_0_69:[bind(X_241,$fot(skolemFOFtoCNF_M)),bind(X_242,$fot(X_291))]]) ).
cnf(refute_0_71,plain,
( unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(X_291))
| unequally_directed_lines(skolemFOFtoCNF_M,X_291) ),
inference(resolve,[$cnf( unequally_directed_lines(reverse_line(skolemFOFtoCNF_M),X_291) )],[refute_0_70,refute_0_60]) ).
cnf(refute_0_72,plain,
( unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(X_292))
| unequally_directed_lines(skolemFOFtoCNF_M,X_292) ),
inference(subst,[],[refute_0_71:[bind(X_291,$fot(X_292))]]) ).
cnf(refute_0_73,plain,
( ~ unequally_directed_lines(skolemFOFtoCNF_L,X_292)
| unequally_directed_lines(skolemFOFtoCNF_M,X_292) ),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(X_292)) )],[refute_0_72,refute_0_51]) ).
cnf(refute_0_74,plain,
( ~ unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(X_37))
| unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(X_37)) ),
inference(subst,[],[refute_0_73:[bind(X_292,$fot(reverse_line(X_37)))]]) ).
cnf(refute_0_75,plain,
( equally_directed_opposite_lines(skolemFOFtoCNF_L,X_37)
| unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(X_37)) ),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(X_37)) )],[refute_0_50,refute_0_74]) ).
cnf(refute_0_76,plain,
( equally_directed_opposite_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N)
| unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(skolemFOFtoCNF_N)) ),
inference(subst,[],[refute_0_75:[bind(X_37,$fot(skolemFOFtoCNF_N))]]) ).
cnf(refute_0_77,plain,
equally_directed_opposite_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(skolemFOFtoCNF_N)) )],[refute_0_76,refute_0_45]) ).
cnf(refute_0_78,plain,
unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N),
inference(resolve,[$cnf( equally_directed_opposite_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N) )],[refute_0_77,refute_0_9]) ).
cnf(refute_0_79,plain,
~ unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_80,plain,
$false,
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N) )],[refute_0_78,refute_0_79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO234+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.33 % Computer : n025.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Fri Jun 17 21:23:27 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.47
% 0.20/0.47 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.48
%------------------------------------------------------------------------------