%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO230+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n011.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 05:25:40 EDT 2022
% Result : Theorem 0.19s 0.49s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 107 ( 40 unt; 0 def)
% Number of atoms : 257 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 256 ( 106 ~; 123 |; 16 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 195 ( 33 sgn 86 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con_def,axiom,
! [L,M] :
( convergent_lines(L,M)
<=> ( unequally_directed_lines(L,M)
& unequally_directed_lines(L,reverse_line(M)) ) ) ).
fof(oag5,axiom,
! [L] : ~ unequally_directed_lines(L,L) ).
fof(oag6,axiom,
! [L,M,N] :
( unequally_directed_lines(L,M)
=> ( unequally_directed_lines(L,N)
| unequally_directed_lines(M,N) ) ) ).
fof(oag9,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(oag10,axiom,
! [A,L] :
~ ( left_apart_point(A,L)
| left_apart_point(A,reverse_line(L)) ) ).
fof(oag11,axiom,
! [L,M] :
~ ( left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ) ).
fof(oagco9,axiom,
! [A,B] : ~ unequally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))) ).
fof(oaguc1,axiom,
! [A,B,L,M] :
( ( distinct_points(A,B)
& distinct_lines(L,M) )
=> ( left_apart_point(A,L)
| left_apart_point(B,L)
| left_apart_point(A,M)
| left_apart_point(B,M)
| left_apart_point(A,reverse_line(L))
| left_apart_point(B,reverse_line(L))
| left_apart_point(A,reverse_line(M))
| left_apart_point(B,reverse_line(M)) ) ) ).
fof(con,conjecture,
! [A,B] :
( distinct_points(A,B)
=> ( ~ distinct_lines(line_connecting(A,B),line_connecting(B,A))
& ~ unequally_directed_lines(line_connecting(B,A),line_connecting(A,B)) ) ) ).
fof(subgoal_0,plain,
! [A,B] :
( distinct_points(A,B)
=> ~ distinct_lines(line_connecting(A,B),line_connecting(B,A)) ),
inference(strip,[],[con]) ).
fof(subgoal_1,plain,
! [A,B] :
( ( distinct_points(A,B)
& ~ distinct_lines(line_connecting(A,B),line_connecting(B,A)) )
=> ~ unequally_directed_lines(line_connecting(B,A),line_connecting(A,B)) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( distinct_points(A,B)
=> ~ distinct_lines(line_connecting(A,B),line_connecting(B,A)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B] :
( distinct_lines(line_connecting(A,B),line_connecting(B,A))
& distinct_points(A,B) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( distinct_lines(line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B),line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A))
& distinct_points(skolemFOFtoCNF_A,skolemFOFtoCNF_B) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
distinct_points(skolemFOFtoCNF_A,skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
distinct_lines(line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B),line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_4,plain,
! [A,B,L,M] :
( ~ distinct_lines(L,M)
| ~ distinct_points(A,B)
| left_apart_point(A,L)
| left_apart_point(A,M)
| left_apart_point(A,reverse_line(L))
| left_apart_point(A,reverse_line(M))
| left_apart_point(B,L)
| left_apart_point(B,M)
| left_apart_point(B,reverse_line(L))
| left_apart_point(B,reverse_line(M)) ),
inference(canonicalize,[],[oaguc1]) ).
fof(normalize_0_5,plain,
( ! [A,L] : ~ left_apart_point(A,L)
& ! [A,L] : ~ left_apart_point(A,reverse_line(L)) ),
inference(canonicalize,[],[oag10]) ).
fof(normalize_0_6,plain,
! [A,L] : ~ left_apart_point(A,L),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,L] : ~ left_apart_point(A,L),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,L] : ~ left_apart_point(A,reverse_line(L)),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_9,plain,
! [A,L] : ~ left_apart_point(A,reverse_line(L)),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B,L,M] :
( ~ distinct_lines(L,M)
| ~ distinct_points(A,B)
| left_apart_point(A,M)
| left_apart_point(A,reverse_line(M))
| left_apart_point(B,L)
| left_apart_point(B,M)
| left_apart_point(B,reverse_line(L))
| left_apart_point(B,reverse_line(M)) ),
inference(simplify,[],[normalize_0_4,normalize_0_7,normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B,L,M] :
( ~ distinct_lines(L,M)
| ~ distinct_points(A,B)
| left_apart_point(A,M)
| left_apart_point(A,reverse_line(M))
| left_apart_point(B,L)
| left_apart_point(B,M)
| left_apart_point(B,reverse_line(L))
| left_apart_point(B,reverse_line(M)) ),
inference(specialize,[],[normalize_0_10]) ).
cnf(refute_0_0,plain,
distinct_points(skolemFOFtoCNF_A,skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
distinct_lines(line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B),line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
( ~ distinct_lines(L,M)
| ~ distinct_points(A,B)
| left_apart_point(A,M)
| left_apart_point(A,reverse_line(M))
| left_apart_point(B,L)
| left_apart_point(B,M)
| left_apart_point(B,reverse_line(L))
| left_apart_point(B,reverse_line(M)) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_3,plain,
~ left_apart_point(A,L),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_4,plain,
~ left_apart_point(A,M),
inference(subst,[],[refute_0_3:[bind(L,$fot(M))]]) ).
cnf(refute_0_5,plain,
( ~ distinct_lines(L,M)
| ~ distinct_points(A,B)
| left_apart_point(A,reverse_line(M))
| left_apart_point(B,L)
| left_apart_point(B,M)
| left_apart_point(B,reverse_line(L))
| left_apart_point(B,reverse_line(M)) ),
inference(resolve,[$cnf( left_apart_point(A,M) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
~ left_apart_point(A,reverse_line(M)),
inference(subst,[],[refute_0_3:[bind(L,$fot(reverse_line(M)))]]) ).
cnf(refute_0_7,plain,
( ~ distinct_lines(L,M)
| ~ distinct_points(A,B)
| left_apart_point(B,L)
| left_apart_point(B,M)
| left_apart_point(B,reverse_line(L))
| left_apart_point(B,reverse_line(M)) ),
inference(resolve,[$cnf( left_apart_point(A,reverse_line(M)) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
~ left_apart_point(B,L),
inference(subst,[],[refute_0_3:[bind(A,$fot(B))]]) ).
cnf(refute_0_9,plain,
( ~ distinct_lines(L,M)
| ~ distinct_points(A,B)
| left_apart_point(B,M)
| left_apart_point(B,reverse_line(L))
| left_apart_point(B,reverse_line(M)) ),
inference(resolve,[$cnf( left_apart_point(B,L) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
~ left_apart_point(B,M),
inference(subst,[],[refute_0_3:[bind(A,$fot(B)),bind(L,$fot(M))]]) ).
cnf(refute_0_11,plain,
( ~ distinct_lines(L,M)
| ~ distinct_points(A,B)
| left_apart_point(B,reverse_line(L))
| left_apart_point(B,reverse_line(M)) ),
inference(resolve,[$cnf( left_apart_point(B,M) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
~ left_apart_point(B,reverse_line(L)),
inference(subst,[],[refute_0_3:[bind(A,$fot(B)),bind(L,$fot(reverse_line(L)))]]) ).
cnf(refute_0_13,plain,
( ~ distinct_lines(L,M)
| ~ distinct_points(A,B)
| left_apart_point(B,reverse_line(M)) ),
inference(resolve,[$cnf( left_apart_point(B,reverse_line(L)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
~ left_apart_point(B,reverse_line(M)),
inference(subst,[],[refute_0_3:[bind(A,$fot(B)),bind(L,$fot(reverse_line(M)))]]) ).
cnf(refute_0_15,plain,
( ~ distinct_lines(L,M)
| ~ distinct_points(A,B) ),
inference(resolve,[$cnf( left_apart_point(B,reverse_line(M)) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ distinct_lines(line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B),line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A))
| ~ distinct_points(X_26,X_27) ),
inference(subst,[],[refute_0_15:[bind(A,$fot(X_26)),bind(B,$fot(X_27)),bind(L,$fot(line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B))),bind(M,$fot(line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_17,plain,
~ distinct_points(X_26,X_27),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B),line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A)) )],[refute_0_1,refute_0_16]) ).
cnf(refute_0_18,plain,
~ distinct_points(skolemFOFtoCNF_A,skolemFOFtoCNF_B),
inference(subst,[],[refute_0_17:[bind(X_26,$fot(skolemFOFtoCNF_A)),bind(X_27,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_19,plain,
$false,
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_A,skolemFOFtoCNF_B) )],[refute_0_0,refute_0_18]) ).
fof(negate_1_0,plain,
~ ! [A,B] :
( ( distinct_points(A,B)
& ~ distinct_lines(line_connecting(A,B),line_connecting(B,A)) )
=> ~ unequally_directed_lines(line_connecting(B,A),line_connecting(A,B)) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [A,B] : ~ unequally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))),
inference(canonicalize,[],[oagco9]) ).
fof(normalize_1_1,plain,
! [A,B] : ~ unequally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
! [L] : ~ unequally_directed_lines(L,L),
inference(canonicalize,[],[oag5]) ).
fof(normalize_1_3,plain,
! [L] : ~ unequally_directed_lines(L,L),
inference(specialize,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
! [L,M,N] :
( ~ unequally_directed_lines(L,M)
| unequally_directed_lines(L,N)
| unequally_directed_lines(M,N) ),
inference(canonicalize,[],[oag6]) ).
fof(normalize_1_5,plain,
! [L,M,N] :
( ~ unequally_directed_lines(L,M)
| unequally_directed_lines(L,N)
| unequally_directed_lines(M,N) ),
inference(specialize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
? [A,B] :
( ~ distinct_lines(line_connecting(A,B),line_connecting(B,A))
& distinct_points(A,B)
& unequally_directed_lines(line_connecting(B,A),line_connecting(A,B)) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_7,plain,
( ~ distinct_lines(line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),line_connecting(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_1))
& distinct_points(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1)
& unequally_directed_lines(line_connecting(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_1),line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1)) ),
inference(skolemize,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
unequally_directed_lines(line_connecting(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_1),line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1)),
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [L,M] :
( ~ convergent_lines(L,M)
<=> ( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M)) ) ),
inference(canonicalize,[],[con_def]) ).
fof(normalize_1_10,plain,
! [L,M] :
( ~ convergent_lines(L,M)
<=> ( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M)) ) ),
inference(specialize,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
! [L,M] :
( ( ~ convergent_lines(L,M)
| unequally_directed_lines(L,M) )
& ( ~ convergent_lines(L,M)
| unequally_directed_lines(L,reverse_line(M)) )
& ( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| convergent_lines(L,M) ) ),
inference(clausify,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
! [L,M] :
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| convergent_lines(L,M) ),
inference(conjunct,[],[normalize_1_11]) ).
fof(normalize_1_13,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,[],[oag9]) ).
fof(normalize_1_14,plain,
! [L,M] :
( ~ convergent_lines(L,M)
| left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ),
inference(simplify,[],[normalize_1_13,normalize_1_10]) ).
fof(normalize_1_15,plain,
! [L,M] :
( ~ convergent_lines(L,M)
| left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ),
inference(specialize,[],[normalize_1_14]) ).
fof(normalize_1_16,plain,
( ! [L,M] : ~ left_convergent_lines(L,M)
& ! [L,M] : ~ left_convergent_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[oag11]) ).
fof(normalize_1_17,plain,
! [L,M] : ~ left_convergent_lines(L,M),
inference(conjunct,[],[normalize_1_16]) ).
fof(normalize_1_18,plain,
! [L,M] : ~ left_convergent_lines(L,M),
inference(specialize,[],[normalize_1_17]) ).
cnf(refute_1_0,plain,
~ unequally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))),
inference(canonicalize,[],[normalize_1_1]) ).
cnf(refute_1_1,plain,
~ unequally_directed_lines(line_connecting(A,A),reverse_line(line_connecting(A,A))),
inference(subst,[],[refute_1_0:[bind(B,$fot(A))]]) ).
cnf(refute_1_2,plain,
~ unequally_directed_lines(L,L),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_3,plain,
~ unequally_directed_lines(reverse_line(X_379),reverse_line(X_379)),
inference(subst,[],[refute_1_2:[bind(L,$fot(reverse_line(X_379)))]]) ).
cnf(refute_1_4,plain,
( ~ unequally_directed_lines(L,M)
| unequally_directed_lines(L,N)
| unequally_directed_lines(M,N) ),
inference(canonicalize,[],[normalize_1_5]) ).
cnf(refute_1_5,plain,
( ~ unequally_directed_lines(reverse_line(X_115),X_115)
| unequally_directed_lines(X_115,N)
| unequally_directed_lines(reverse_line(X_115),N) ),
inference(subst,[],[refute_1_4:[bind(L,$fot(reverse_line(X_115))),bind(M,$fot(X_115))]]) ).
cnf(refute_1_6,plain,
( ~ unequally_directed_lines(line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),reverse_line(X_88))
| unequally_directed_lines(line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),N)
| unequally_directed_lines(reverse_line(X_88),N) ),
inference(subst,[],[refute_1_4:[bind(L,$fot(line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1))),bind(M,$fot(reverse_line(X_88)))]]) ).
cnf(refute_1_7,plain,
unequally_directed_lines(line_connecting(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_1),line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1)),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_8,plain,
( ~ unequally_directed_lines(line_connecting(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_1),line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1))
| unequally_directed_lines(line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),X_84)
| unequally_directed_lines(line_connecting(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_1),X_84) ),
inference(subst,[],[refute_1_4:[bind(L,$fot(line_connecting(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_1))),bind(M,$fot(line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1))),bind(N,$fot(X_84))]]) ).
cnf(refute_1_9,plain,
( unequally_directed_lines(line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),X_84)
| unequally_directed_lines(line_connecting(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_1),X_84) ),
inference(resolve,[$cnf( unequally_directed_lines(line_connecting(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_1),line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1)) )],[refute_1_7,refute_1_8]) ).
cnf(refute_1_10,plain,
( unequally_directed_lines(line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),X_86)
| unequally_directed_lines(line_connecting(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_1),X_86) ),
inference(subst,[],[refute_1_9:[bind(X_84,$fot(X_86))]]) ).
cnf(refute_1_11,plain,
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| convergent_lines(L,M) ),
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_12,plain,
( ~ convergent_lines(L,M)
| left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[normalize_1_15]) ).
cnf(refute_1_13,plain,
~ left_convergent_lines(L,M),
inference(canonicalize,[],[normalize_1_18]) ).
cnf(refute_1_14,plain,
( ~ convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ),
inference(resolve,[$cnf( left_convergent_lines(L,M) )],[refute_1_12,refute_1_13]) ).
cnf(refute_1_15,plain,
~ left_convergent_lines(L,reverse_line(M)),
inference(subst,[],[refute_1_13:[bind(M,$fot(reverse_line(M)))]]) ).
cnf(refute_1_16,plain,
~ convergent_lines(L,M),
inference(resolve,[$cnf( left_convergent_lines(L,reverse_line(M)) )],[refute_1_14,refute_1_15]) ).
cnf(refute_1_17,plain,
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M)) ),
inference(resolve,[$cnf( convergent_lines(L,M) )],[refute_1_11,refute_1_16]) ).
cnf(refute_1_18,plain,
( ~ unequally_directed_lines(line_connecting(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_1),M)
| ~ unequally_directed_lines(line_connecting(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_1),reverse_line(M)) ),
inference(subst,[],[refute_1_17:[bind(L,$fot(line_connecting(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_1)))]]) ).
cnf(refute_1_19,plain,
( unequally_directed_lines(line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),reverse_line(M))
| unequally_directed_lines(line_connecting(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_1),reverse_line(M)) ),
inference(subst,[],[refute_1_9:[bind(X_84,$fot(reverse_line(M)))]]) ).
cnf(refute_1_20,plain,
( ~ unequally_directed_lines(line_connecting(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_1),M)
| unequally_directed_lines(line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),reverse_line(M)) ),
inference(resolve,[$cnf( unequally_directed_lines(line_connecting(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_1),reverse_line(M)) )],[refute_1_19,refute_1_18]) ).
cnf(refute_1_21,plain,
( ~ unequally_directed_lines(line_connecting(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_1),X_86)
| unequally_directed_lines(line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),reverse_line(X_86)) ),
inference(subst,[],[refute_1_20:[bind(M,$fot(X_86))]]) ).
cnf(refute_1_22,plain,
( unequally_directed_lines(line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),X_86)
| unequally_directed_lines(line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),reverse_line(X_86)) ),
inference(resolve,[$cnf( unequally_directed_lines(line_connecting(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_1),X_86) )],[refute_1_10,refute_1_21]) ).
cnf(refute_1_23,plain,
( unequally_directed_lines(line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),X_88)
| unequally_directed_lines(line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),reverse_line(X_88)) ),
inference(subst,[],[refute_1_22:[bind(X_86,$fot(X_88))]]) ).
cnf(refute_1_24,plain,
( unequally_directed_lines(line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),N)
| unequally_directed_lines(line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),X_88)
| unequally_directed_lines(reverse_line(X_88),N) ),
inference(resolve,[$cnf( unequally_directed_lines(line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),reverse_line(X_88)) )],[refute_1_23,refute_1_6]) ).
cnf(refute_1_25,plain,
( unequally_directed_lines(line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),X_114)
| unequally_directed_lines(reverse_line(X_114),X_114) ),
inference(subst,[],[refute_1_24:[bind(N,$fot(X_114)),bind(X_88,$fot(X_114))]]) ).
cnf(refute_1_26,plain,
( ~ unequally_directed_lines(line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),X_108)
| ~ unequally_directed_lines(line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),reverse_line(X_108)) ),
inference(subst,[],[refute_1_17:[bind(L,$fot(line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1))),bind(M,$fot(X_108))]]) ).
cnf(refute_1_27,plain,
( ~ unequally_directed_lines(line_connecting(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_1),X_103)
| unequally_directed_lines(line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),reverse_line(X_103)) ),
inference(subst,[],[refute_1_20:[bind(M,$fot(X_103))]]) ).
cnf(refute_1_28,plain,
( ~ unequally_directed_lines(line_connecting(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_1),X_85)
| unequally_directed_lines(X_85,N)
| unequally_directed_lines(line_connecting(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_1),N) ),
inference(subst,[],[refute_1_4:[bind(L,$fot(line_connecting(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_1))),bind(M,$fot(X_85))]]) ).
cnf(refute_1_29,plain,
( unequally_directed_lines(line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),X_85)
| unequally_directed_lines(line_connecting(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_1),X_85) ),
inference(subst,[],[refute_1_9:[bind(X_84,$fot(X_85))]]) ).
cnf(refute_1_30,plain,
( unequally_directed_lines(X_85,N)
| unequally_directed_lines(line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),X_85)
| unequally_directed_lines(line_connecting(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_1),N) ),
inference(resolve,[$cnf( unequally_directed_lines(line_connecting(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_1),X_85) )],[refute_1_29,refute_1_28]) ).
cnf(refute_1_31,plain,
( unequally_directed_lines(X_104,X_103)
| unequally_directed_lines(line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),X_104)
| unequally_directed_lines(line_connecting(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_1),X_103) ),
inference(subst,[],[refute_1_30:[bind(N,$fot(X_103)),bind(X_85,$fot(X_104))]]) ).
cnf(refute_1_32,plain,
( unequally_directed_lines(X_104,X_103)
| unequally_directed_lines(line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),X_104)
| unequally_directed_lines(line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),reverse_line(X_103)) ),
inference(resolve,[$cnf( unequally_directed_lines(line_connecting(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_1),X_103) )],[refute_1_31,refute_1_27]) ).
cnf(refute_1_33,plain,
( unequally_directed_lines(line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),reverse_line(X_108))
| unequally_directed_lines(reverse_line(X_108),X_108) ),
inference(subst,[],[refute_1_32:[bind(X_103,$fot(X_108)),bind(X_104,$fot(reverse_line(X_108)))]]) ).
cnf(refute_1_34,plain,
( ~ unequally_directed_lines(line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),X_108)
| unequally_directed_lines(reverse_line(X_108),X_108) ),
inference(resolve,[$cnf( unequally_directed_lines(line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),reverse_line(X_108)) )],[refute_1_33,refute_1_26]) ).
cnf(refute_1_35,plain,
( ~ unequally_directed_lines(line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),X_114)
| unequally_directed_lines(reverse_line(X_114),X_114) ),
inference(subst,[],[refute_1_34:[bind(X_108,$fot(X_114))]]) ).
cnf(refute_1_36,plain,
unequally_directed_lines(reverse_line(X_114),X_114),
inference(resolve,[$cnf( unequally_directed_lines(line_connecting(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),X_114) )],[refute_1_25,refute_1_35]) ).
cnf(refute_1_37,plain,
unequally_directed_lines(reverse_line(X_115),X_115),
inference(subst,[],[refute_1_36:[bind(X_114,$fot(X_115))]]) ).
cnf(refute_1_38,plain,
( unequally_directed_lines(X_115,N)
| unequally_directed_lines(reverse_line(X_115),N) ),
inference(resolve,[$cnf( unequally_directed_lines(reverse_line(X_115),X_115) )],[refute_1_37,refute_1_5]) ).
cnf(refute_1_39,plain,
( unequally_directed_lines(X_379,reverse_line(X_379))
| unequally_directed_lines(reverse_line(X_379),reverse_line(X_379)) ),
inference(subst,[],[refute_1_38:[bind(N,$fot(reverse_line(X_379))),bind(X_115,$fot(X_379))]]) ).
cnf(refute_1_40,plain,
unequally_directed_lines(X_379,reverse_line(X_379)),
inference(resolve,[$cnf( unequally_directed_lines(reverse_line(X_379),reverse_line(X_379)) )],[refute_1_39,refute_1_3]) ).
cnf(refute_1_41,plain,
unequally_directed_lines(line_connecting(A,A),reverse_line(line_connecting(A,A))),
inference(subst,[],[refute_1_40:[bind(X_379,$fot(line_connecting(A,A)))]]) ).
cnf(refute_1_42,plain,
$false,
inference(resolve,[$cnf( unequally_directed_lines(line_connecting(A,A),reverse_line(line_connecting(A,A))) )],[refute_1_41,refute_1_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO230+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n011.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 18:25:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.49
% 0.19/0.49 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.50
%------------------------------------------------------------------------------