%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO266+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n014.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 05:26:02 EDT 2022
% Result : Theorem 0.21s 0.49s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 124 ( 35 unt; 0 def)
% Number of atoms : 246 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 223 ( 101 ~; 97 |; 10 &)
% ( 9 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 186 ( 13 sgn 100 !; 4 ?)
% 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(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] :
( unequally_directed_opposite_lines(L,M)
<=> unequally_directed_opposite_lines(M,L) ) ).
fof(subgoal_0,plain,
! [L,M] :
( unequally_directed_opposite_lines(L,M)
=> unequally_directed_opposite_lines(M,L) ),
inference(strip,[],[con]) ).
fof(subgoal_1,plain,
! [L,M] :
( unequally_directed_opposite_lines(M,L)
=> unequally_directed_opposite_lines(L,M) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [L,M] :
( unequally_directed_opposite_lines(L,M)
=> unequally_directed_opposite_lines(M,L) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,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_1,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_0]) ).
fof(normalize_0_2,plain,
( ! [L,M] : ~ left_convergent_lines(L,M)
& ! [L,M] : ~ left_convergent_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[ax11_basics]) ).
fof(normalize_0_3,plain,
! [L,M] : ~ left_convergent_lines(L,M),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [L,M] : ~ left_convergent_lines(L,M),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,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_6,plain,
! [L,M,N] :
( ~ unequally_directed_lines(L,M)
| unequally_directed_lines(L,N)
| unequally_directed_lines(M,N) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
? [L,M] :
( ~ unequally_directed_opposite_lines(M,L)
& unequally_directed_opposite_lines(L,M) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_8,plain,
( ~ unequally_directed_opposite_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L)
& unequally_directed_opposite_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
inference(skolemize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
~ unequally_directed_opposite_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ~ unequally_directed_lines(X,reverse_line(Y))
<=> ~ unequally_directed_opposite_lines(X,Y) ),
inference(canonicalize,[],[a1_defns]) ).
fof(normalize_0_11,plain,
! [X,Y] :
( ~ unequally_directed_lines(X,reverse_line(Y))
<=> ~ unequally_directed_opposite_lines(X,Y) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,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_11]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [L,M] :
( unequally_directed_lines(L,M)
| unequally_directed_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[ax8_basics]) ).
fof(normalize_0_15,plain,
! [L,M] :
( unequally_directed_lines(L,M)
| unequally_directed_lines(L,reverse_line(M)) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
unequally_directed_opposite_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_17,plain,
! [X,Y] :
( ~ unequally_directed_opposite_lines(X,Y)
| unequally_directed_lines(X,reverse_line(Y)) ),
inference(conjunct,[],[normalize_0_12]) ).
cnf(refute_0_0,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_1]) ).
cnf(refute_0_1,plain,
~ left_convergent_lines(L,M),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| left_convergent_lines(L,reverse_line(M)) ),
inference(resolve,[$cnf( left_convergent_lines(L,M) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
~ left_convergent_lines(L,reverse_line(M)),
inference(subst,[],[refute_0_1:[bind(M,$fot(reverse_line(M)))]]) ).
cnf(refute_0_4,plain,
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M)) ),
inference(resolve,[$cnf( left_convergent_lines(L,reverse_line(M)) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ unequally_directed_lines(skolemFOFtoCNF_M,M)
| ~ unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(M)) ),
inference(subst,[],[refute_0_4:[bind(L,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_6,plain,
( ~ unequally_directed_lines(L,M)
| unequally_directed_lines(L,N)
| unequally_directed_lines(M,N) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_7,plain,
( ~ unequally_directed_lines(skolemFOFtoCNF_M,X_240)
| unequally_directed_lines(X_240,N)
| unequally_directed_lines(skolemFOFtoCNF_M,N) ),
inference(subst,[],[refute_0_6:[bind(L,$fot(skolemFOFtoCNF_M)),bind(M,$fot(X_240))]]) ).
cnf(refute_0_8,plain,
~ unequally_directed_opposite_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_9,plain,
( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_10,plain,
( ~ unequally_directed_lines(X_41,reverse_line(X_42))
| unequally_directed_opposite_lines(X_41,X_42) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_41)),bind(Y,$fot(X_42))]]) ).
cnf(refute_0_11,plain,
( unequally_directed_lines(L,M)
| unequally_directed_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_12,plain,
( unequally_directed_lines(X_41,X_42)
| unequally_directed_lines(X_41,reverse_line(X_42)) ),
inference(subst,[],[refute_0_11:[bind(L,$fot(X_41)),bind(M,$fot(X_42))]]) ).
cnf(refute_0_13,plain,
( unequally_directed_lines(X_41,X_42)
| unequally_directed_opposite_lines(X_41,X_42) ),
inference(resolve,[$cnf( unequally_directed_lines(X_41,reverse_line(X_42)) )],[refute_0_12,refute_0_10]) ).
cnf(refute_0_14,plain,
( unequally_directed_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L)
| unequally_directed_opposite_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_13:[bind(X_41,$fot(skolemFOFtoCNF_M)),bind(X_42,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_15,plain,
unequally_directed_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L),
inference(resolve,[$cnf( unequally_directed_opposite_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L) )],[refute_0_14,refute_0_8]) ).
cnf(refute_0_16,plain,
( ~ unequally_directed_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L)
| unequally_directed_lines(skolemFOFtoCNF_L,X_239)
| unequally_directed_lines(skolemFOFtoCNF_M,X_239) ),
inference(subst,[],[refute_0_6:[bind(L,$fot(skolemFOFtoCNF_M)),bind(M,$fot(skolemFOFtoCNF_L)),bind(N,$fot(X_239))]]) ).
cnf(refute_0_17,plain,
( unequally_directed_lines(skolemFOFtoCNF_L,X_239)
| unequally_directed_lines(skolemFOFtoCNF_M,X_239) ),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( unequally_directed_lines(skolemFOFtoCNF_L,X_240)
| unequally_directed_lines(skolemFOFtoCNF_M,X_240) ),
inference(subst,[],[refute_0_17:[bind(X_239,$fot(X_240))]]) ).
cnf(refute_0_19,plain,
( unequally_directed_lines(X_240,N)
| unequally_directed_lines(skolemFOFtoCNF_L,X_240)
| unequally_directed_lines(skolemFOFtoCNF_M,N) ),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_M,X_240) )],[refute_0_18,refute_0_7]) ).
cnf(refute_0_20,plain,
( unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
| unequally_directed_lines(skolemFOFtoCNF_M,N) ),
inference(subst,[],[refute_0_19:[bind(X_240,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_21,plain,
unequally_directed_opposite_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_22,plain,
( ~ unequally_directed_opposite_lines(X,Y)
| unequally_directed_lines(X,reverse_line(Y)) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_23,plain,
( ~ unequally_directed_opposite_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
| unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M)) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_24,plain,
unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M)),
inference(resolve,[$cnf( unequally_directed_opposite_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_21,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M))
| ~ unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
inference(subst,[],[refute_0_4:[bind(L,$fot(skolemFOFtoCNF_L)),bind(M,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_26,plain,
~ unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
unequally_directed_lines(skolemFOFtoCNF_M,N),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_20,refute_0_26]) ).
cnf(refute_0_28,plain,
unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(M)),
inference(subst,[],[refute_0_27:[bind(N,$fot(reverse_line(M)))]]) ).
cnf(refute_0_29,plain,
~ unequally_directed_lines(skolemFOFtoCNF_M,M),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(M)) )],[refute_0_28,refute_0_5]) ).
cnf(refute_0_30,plain,
unequally_directed_lines(skolemFOFtoCNF_M,M),
inference(subst,[],[refute_0_27:[bind(N,$fot(M))]]) ).
cnf(refute_0_31,plain,
$false,
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_M,M) )],[refute_0_30,refute_0_29]) ).
fof(negate_1_0,plain,
~ ! [L,M] :
( unequally_directed_opposite_lines(M,L)
=> unequally_directed_opposite_lines(L,M) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [X,Y] :
( ~ equally_directed_lines(X,Y)
<=> unequally_directed_lines(X,Y) ),
inference(canonicalize,[],[a4_defns]) ).
fof(normalize_1_1,plain,
! [X,Y] :
( ~ equally_directed_lines(X,Y)
<=> unequally_directed_lines(X,Y) ),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_2,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_1_1]) ).
fof(normalize_1_3,plain,
! [X,Y] :
( ~ equally_directed_lines(X,Y)
| ~ unequally_directed_lines(X,Y) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
? [L,M] :
( ~ unequally_directed_opposite_lines(L,M)
& unequally_directed_opposite_lines(M,L) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_5,plain,
( ~ unequally_directed_opposite_lines(skolemFOFtoCNF_L_1,skolemFOFtoCNF_M_1)
& unequally_directed_opposite_lines(skolemFOFtoCNF_M_1,skolemFOFtoCNF_L_1) ),
inference(skolemize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
unequally_directed_opposite_lines(skolemFOFtoCNF_M_1,skolemFOFtoCNF_L_1),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [X,Y] :
( ~ unequally_directed_lines(X,reverse_line(Y))
<=> ~ unequally_directed_opposite_lines(X,Y) ),
inference(canonicalize,[],[a1_defns]) ).
fof(normalize_1_8,plain,
! [X,Y] :
( ~ unequally_directed_lines(X,reverse_line(Y))
<=> ~ unequally_directed_opposite_lines(X,Y) ),
inference(specialize,[],[normalize_1_7]) ).
fof(normalize_1_9,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_1_8]) ).
fof(normalize_1_10,plain,
! [X,Y] :
( ~ unequally_directed_opposite_lines(X,Y)
| unequally_directed_lines(X,reverse_line(Y)) ),
inference(conjunct,[],[normalize_1_9]) ).
fof(normalize_1_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(canonicalize,[],[ax9_basics]) ).
fof(normalize_1_12,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_1_11]) ).
fof(normalize_1_13,plain,
( ! [L,M] : ~ left_convergent_lines(L,M)
& ! [L,M] : ~ left_convergent_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[ax11_basics]) ).
fof(normalize_1_14,plain,
! [L,M] : ~ left_convergent_lines(L,M),
inference(conjunct,[],[normalize_1_13]) ).
fof(normalize_1_15,plain,
! [L,M] : ~ left_convergent_lines(L,M),
inference(specialize,[],[normalize_1_14]) ).
fof(normalize_1_16,plain,
~ unequally_directed_opposite_lines(skolemFOFtoCNF_L_1,skolemFOFtoCNF_M_1),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_17,plain,
! [L,M] :
( unequally_directed_lines(L,M)
| unequally_directed_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[ax8_basics]) ).
fof(normalize_1_18,plain,
! [L,M] :
( unequally_directed_lines(L,M)
| unequally_directed_lines(L,reverse_line(M)) ),
inference(specialize,[],[normalize_1_17]) ).
fof(normalize_1_19,plain,
! [X,Y] :
( equally_directed_lines(X,Y)
| unequally_directed_lines(X,Y) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_20,plain,
! [X,Y] :
( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) ),
inference(conjunct,[],[normalize_1_9]) ).
fof(normalize_1_21,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_1_22,plain,
! [L,M,N] :
( ~ unequally_directed_lines(L,M)
| unequally_directed_lines(L,N)
| unequally_directed_lines(M,N) ),
inference(specialize,[],[normalize_1_21]) ).
fof(normalize_1_23,plain,
! [L] : equally_directed_lines(L,L),
inference(canonicalize,[],[ax5_basics]) ).
fof(normalize_1_24,plain,
! [L] : equally_directed_lines(L,L),
inference(specialize,[],[normalize_1_23]) ).
cnf(refute_1_0,plain,
( ~ equally_directed_lines(X,Y)
| ~ unequally_directed_lines(X,Y) ),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_1,plain,
( ~ equally_directed_lines(skolemFOFtoCNF_L_1,skolemFOFtoCNF_L_1)
| ~ unequally_directed_lines(skolemFOFtoCNF_L_1,skolemFOFtoCNF_L_1) ),
inference(subst,[],[refute_1_0:[bind(X,$fot(skolemFOFtoCNF_L_1)),bind(Y,$fot(skolemFOFtoCNF_L_1))]]) ).
cnf(refute_1_2,plain,
unequally_directed_opposite_lines(skolemFOFtoCNF_M_1,skolemFOFtoCNF_L_1),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_3,plain,
( ~ unequally_directed_opposite_lines(X,Y)
| unequally_directed_lines(X,reverse_line(Y)) ),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_4,plain,
( ~ unequally_directed_opposite_lines(skolemFOFtoCNF_M_1,skolemFOFtoCNF_L_1)
| unequally_directed_lines(skolemFOFtoCNF_M_1,reverse_line(skolemFOFtoCNF_L_1)) ),
inference(subst,[],[refute_1_3:[bind(X,$fot(skolemFOFtoCNF_M_1)),bind(Y,$fot(skolemFOFtoCNF_L_1))]]) ).
cnf(refute_1_5,plain,
unequally_directed_lines(skolemFOFtoCNF_M_1,reverse_line(skolemFOFtoCNF_L_1)),
inference(resolve,[$cnf( unequally_directed_opposite_lines(skolemFOFtoCNF_M_1,skolemFOFtoCNF_L_1) )],[refute_1_2,refute_1_4]) ).
cnf(refute_1_6,plain,
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_7,plain,
~ left_convergent_lines(L,M),
inference(canonicalize,[],[normalize_1_15]) ).
cnf(refute_1_8,plain,
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| left_convergent_lines(L,reverse_line(M)) ),
inference(resolve,[$cnf( left_convergent_lines(L,M) )],[refute_1_6,refute_1_7]) ).
cnf(refute_1_9,plain,
~ left_convergent_lines(L,reverse_line(M)),
inference(subst,[],[refute_1_7:[bind(M,$fot(reverse_line(M)))]]) ).
cnf(refute_1_10,plain,
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M)) ),
inference(resolve,[$cnf( left_convergent_lines(L,reverse_line(M)) )],[refute_1_8,refute_1_9]) ).
cnf(refute_1_11,plain,
( ~ unequally_directed_lines(skolemFOFtoCNF_M_1,reverse_line(skolemFOFtoCNF_L_1))
| ~ unequally_directed_lines(skolemFOFtoCNF_M_1,skolemFOFtoCNF_L_1) ),
inference(subst,[],[refute_1_10:[bind(L,$fot(skolemFOFtoCNF_M_1)),bind(M,$fot(skolemFOFtoCNF_L_1))]]) ).
cnf(refute_1_12,plain,
~ unequally_directed_lines(skolemFOFtoCNF_M_1,skolemFOFtoCNF_L_1),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_M_1,reverse_line(skolemFOFtoCNF_L_1)) )],[refute_1_5,refute_1_11]) ).
cnf(refute_1_13,plain,
~ unequally_directed_opposite_lines(skolemFOFtoCNF_L_1,skolemFOFtoCNF_M_1),
inference(canonicalize,[],[normalize_1_16]) ).
cnf(refute_1_14,plain,
( ~ equally_directed_lines(X_278,reverse_line(X_279))
| ~ unequally_directed_lines(X_278,reverse_line(X_279)) ),
inference(subst,[],[refute_1_0:[bind(X,$fot(X_278)),bind(Y,$fot(reverse_line(X_279)))]]) ).
cnf(refute_1_15,plain,
( unequally_directed_lines(L,M)
| unequally_directed_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[normalize_1_18]) ).
cnf(refute_1_16,plain,
( unequally_directed_lines(X_278,X_279)
| unequally_directed_lines(X_278,reverse_line(X_279)) ),
inference(subst,[],[refute_1_15:[bind(L,$fot(X_278)),bind(M,$fot(X_279))]]) ).
cnf(refute_1_17,plain,
( ~ equally_directed_lines(X_278,reverse_line(X_279))
| unequally_directed_lines(X_278,X_279) ),
inference(resolve,[$cnf( unequally_directed_lines(X_278,reverse_line(X_279)) )],[refute_1_16,refute_1_14]) ).
cnf(refute_1_18,plain,
( ~ equally_directed_lines(X_326,reverse_line(X_327))
| unequally_directed_lines(X_326,X_327) ),
inference(subst,[],[refute_1_17:[bind(X_278,$fot(X_326)),bind(X_279,$fot(X_327))]]) ).
cnf(refute_1_19,plain,
( equally_directed_lines(X,Y)
| unequally_directed_lines(X,Y) ),
inference(canonicalize,[],[normalize_1_19]) ).
cnf(refute_1_20,plain,
( equally_directed_lines(X_274,reverse_line(X_275))
| unequally_directed_lines(X_274,reverse_line(X_275)) ),
inference(subst,[],[refute_1_19:[bind(X,$fot(X_274)),bind(Y,$fot(reverse_line(X_275)))]]) ).
cnf(refute_1_21,plain,
( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) ),
inference(canonicalize,[],[normalize_1_20]) ).
cnf(refute_1_22,plain,
( ~ unequally_directed_lines(X_274,reverse_line(X_275))
| unequally_directed_opposite_lines(X_274,X_275) ),
inference(subst,[],[refute_1_21:[bind(X,$fot(X_274)),bind(Y,$fot(X_275))]]) ).
cnf(refute_1_23,plain,
( equally_directed_lines(X_274,reverse_line(X_275))
| unequally_directed_opposite_lines(X_274,X_275) ),
inference(resolve,[$cnf( unequally_directed_lines(X_274,reverse_line(X_275)) )],[refute_1_20,refute_1_22]) ).
cnf(refute_1_24,plain,
( equally_directed_lines(X_326,reverse_line(X_327))
| unequally_directed_opposite_lines(X_326,X_327) ),
inference(subst,[],[refute_1_23:[bind(X_274,$fot(X_326)),bind(X_275,$fot(X_327))]]) ).
cnf(refute_1_25,plain,
( unequally_directed_lines(X_326,X_327)
| unequally_directed_opposite_lines(X_326,X_327) ),
inference(resolve,[$cnf( equally_directed_lines(X_326,reverse_line(X_327)) )],[refute_1_24,refute_1_18]) ).
cnf(refute_1_26,plain,
( unequally_directed_lines(skolemFOFtoCNF_L_1,skolemFOFtoCNF_M_1)
| unequally_directed_opposite_lines(skolemFOFtoCNF_L_1,skolemFOFtoCNF_M_1) ),
inference(subst,[],[refute_1_25:[bind(X_326,$fot(skolemFOFtoCNF_L_1)),bind(X_327,$fot(skolemFOFtoCNF_M_1))]]) ).
cnf(refute_1_27,plain,
unequally_directed_lines(skolemFOFtoCNF_L_1,skolemFOFtoCNF_M_1),
inference(resolve,[$cnf( unequally_directed_opposite_lines(skolemFOFtoCNF_L_1,skolemFOFtoCNF_M_1) )],[refute_1_26,refute_1_13]) ).
cnf(refute_1_28,plain,
( ~ unequally_directed_lines(L,M)
| unequally_directed_lines(L,N)
| unequally_directed_lines(M,N) ),
inference(canonicalize,[],[normalize_1_22]) ).
cnf(refute_1_29,plain,
( ~ unequally_directed_lines(skolemFOFtoCNF_L_1,skolemFOFtoCNF_M_1)
| unequally_directed_lines(skolemFOFtoCNF_L_1,X_494)
| unequally_directed_lines(skolemFOFtoCNF_M_1,X_494) ),
inference(subst,[],[refute_1_28:[bind(L,$fot(skolemFOFtoCNF_L_1)),bind(M,$fot(skolemFOFtoCNF_M_1)),bind(N,$fot(X_494))]]) ).
cnf(refute_1_30,plain,
( unequally_directed_lines(skolemFOFtoCNF_L_1,X_494)
| unequally_directed_lines(skolemFOFtoCNF_M_1,X_494) ),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_L_1,skolemFOFtoCNF_M_1) )],[refute_1_27,refute_1_29]) ).
cnf(refute_1_31,plain,
( unequally_directed_lines(skolemFOFtoCNF_L_1,skolemFOFtoCNF_L_1)
| unequally_directed_lines(skolemFOFtoCNF_M_1,skolemFOFtoCNF_L_1) ),
inference(subst,[],[refute_1_30:[bind(X_494,$fot(skolemFOFtoCNF_L_1))]]) ).
cnf(refute_1_32,plain,
unequally_directed_lines(skolemFOFtoCNF_L_1,skolemFOFtoCNF_L_1),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_M_1,skolemFOFtoCNF_L_1) )],[refute_1_31,refute_1_12]) ).
cnf(refute_1_33,plain,
~ equally_directed_lines(skolemFOFtoCNF_L_1,skolemFOFtoCNF_L_1),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_L_1,skolemFOFtoCNF_L_1) )],[refute_1_32,refute_1_1]) ).
cnf(refute_1_34,plain,
equally_directed_lines(L,L),
inference(canonicalize,[],[normalize_1_24]) ).
cnf(refute_1_35,plain,
equally_directed_lines(skolemFOFtoCNF_L_1,skolemFOFtoCNF_L_1),
inference(subst,[],[refute_1_34:[bind(L,$fot(skolemFOFtoCNF_L_1))]]) ).
cnf(refute_1_36,plain,
$false,
inference(resolve,[$cnf( equally_directed_lines(skolemFOFtoCNF_L_1,skolemFOFtoCNF_L_1) )],[refute_1_35,refute_1_33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO266+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sat Jun 18 05:27:34 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.49
% 0.21/0.49 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.21/0.49
%------------------------------------------------------------------------------