TSTP Solution File: GEO231+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO231+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n032.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 05:25:41 EDT 2022
% Result : Theorem 0.14s 0.35s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 7
% Syntax : Number of formulae : 108 ( 31 unt; 0 def)
% Number of atoms : 227 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 208 ( 89 ~; 99 |; 12 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 136 ( 12 sgn 55 !; 3 ?)
% 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(oag11,axiom,
! [L,M] :
~ ( left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ) ).
fof(oagco10,axiom,
! [A,L] : ~ unequally_directed_lines(parallel_through_point(L,A),L) ).
fof(con,conjecture,
! [L,M,N] :
( ( ~ unequally_directed_lines(L,reverse_line(M))
& ~ unequally_directed_lines(L,N) )
=> ~ unequally_directed_lines(M,reverse_line(N)) ) ).
fof(subgoal_0,plain,
! [L,M,N] :
( ( ~ unequally_directed_lines(L,reverse_line(M))
& ~ unequally_directed_lines(L,N) )
=> ~ unequally_directed_lines(M,reverse_line(N)) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [L,M,N] :
( ( ~ unequally_directed_lines(L,reverse_line(M))
& ~ unequally_directed_lines(L,N) )
=> ~ unequally_directed_lines(M,reverse_line(N)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [L] : ~ unequally_directed_lines(L,L),
inference(canonicalize,[],[oag5]) ).
fof(normalize_0_1,plain,
! [L] : ~ unequally_directed_lines(L,L),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [L,M,N] :
( ~ unequally_directed_lines(L,M)
| unequally_directed_lines(L,N)
| unequally_directed_lines(M,N) ),
inference(canonicalize,[],[oag6]) ).
fof(normalize_0_3,plain,
! [L,M,N] :
( ~ unequally_directed_lines(L,M)
| unequally_directed_lines(L,N)
| unequally_directed_lines(M,N) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,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_0_5,plain,
! [L,M] :
( ~ convergent_lines(L,M)
<=> ( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M)) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,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_0_5]) ).
fof(normalize_0_7,plain,
! [L,M] :
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| convergent_lines(L,M) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,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_0_9,plain,
! [L,M] :
( ~ convergent_lines(L,M)
| left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ),
inference(simplify,[],[normalize_0_8,normalize_0_5]) ).
fof(normalize_0_10,plain,
! [L,M] :
( ~ convergent_lines(L,M)
| left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
( ! [L,M] : ~ left_convergent_lines(L,M)
& ! [L,M] : ~ left_convergent_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[oag11]) ).
fof(normalize_0_12,plain,
! [L,M] : ~ left_convergent_lines(L,M),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [L,M] : ~ left_convergent_lines(L,M),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
? [L,M,N] :
( ~ unequally_directed_lines(L,N)
& ~ unequally_directed_lines(L,reverse_line(M))
& unequally_directed_lines(M,reverse_line(N)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_15,plain,
( ~ unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M))
& ~ unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N)
& unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(skolemFOFtoCNF_N)) ),
inference(skolemize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(skolemFOFtoCNF_N)),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [A,L] : ~ unequally_directed_lines(parallel_through_point(L,A),L),
inference(canonicalize,[],[oagco10]) ).
fof(normalize_0_18,plain,
! [A,L] : ~ unequally_directed_lines(parallel_through_point(L,A),L),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
~ unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M)),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_20,plain,
~ unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N),
inference(conjunct,[],[normalize_0_15]) ).
cnf(refute_0_0,plain,
~ unequally_directed_lines(L,L),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
~ unequally_directed_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_N),
inference(subst,[],[refute_0_0:[bind(L,$fot(skolemFOFtoCNF_N))]]) ).
cnf(refute_0_2,plain,
( ~ unequally_directed_lines(L,M)
| unequally_directed_lines(L,N)
| unequally_directed_lines(M,N) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
( ~ unequally_directed_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_L)
| unequally_directed_lines(skolemFOFtoCNF_L,N)
| unequally_directed_lines(skolemFOFtoCNF_N,N) ),
inference(subst,[],[refute_0_2:[bind(L,$fot(skolemFOFtoCNF_N)),bind(M,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_4,plain,
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| convergent_lines(L,M) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ convergent_lines(L,M)
| left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_6,plain,
~ left_convergent_lines(L,M),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_7,plain,
( ~ convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ),
inference(resolve,[$cnf( left_convergent_lines(L,M) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
~ left_convergent_lines(L,reverse_line(M)),
inference(subst,[],[refute_0_6:[bind(M,$fot(reverse_line(M)))]]) ).
cnf(refute_0_9,plain,
~ convergent_lines(L,M),
inference(resolve,[$cnf( left_convergent_lines(L,reverse_line(M)) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M)) ),
inference(resolve,[$cnf( convergent_lines(L,M) )],[refute_0_4,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ unequally_directed_lines(skolemFOFtoCNF_M,X_76)
| ~ unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(X_76)) ),
inference(subst,[],[refute_0_10:[bind(L,$fot(skolemFOFtoCNF_M)),bind(M,$fot(X_76))]]) ).
cnf(refute_0_12,plain,
( ~ unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),M)
| ~ unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),reverse_line(M)) ),
inference(subst,[],[refute_0_10:[bind(L,$fot(reverse_line(skolemFOFtoCNF_N)))]]) ).
cnf(refute_0_13,plain,
unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(skolemFOFtoCNF_N)),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_14,plain,
( ~ unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(skolemFOFtoCNF_N))
| unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),X_45)
| unequally_directed_lines(skolemFOFtoCNF_M,X_45) ),
inference(subst,[],[refute_0_2:[bind(L,$fot(skolemFOFtoCNF_M)),bind(M,$fot(reverse_line(skolemFOFtoCNF_N))),bind(N,$fot(X_45))]]) ).
cnf(refute_0_15,plain,
( unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),X_45)
| unequally_directed_lines(skolemFOFtoCNF_M,X_45) ),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(skolemFOFtoCNF_N)) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),reverse_line(M))
| unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(M)) ),
inference(subst,[],[refute_0_15:[bind(X_45,$fot(reverse_line(M)))]]) ).
cnf(refute_0_17,plain,
( ~ unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),M)
| unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(M)) ),
inference(resolve,[$cnf( unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),reverse_line(M)) )],[refute_0_16,refute_0_12]) ).
cnf(refute_0_18,plain,
( ~ unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),X_70)
| unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(X_70)) ),
inference(subst,[],[refute_0_17:[bind(M,$fot(X_70))]]) ).
cnf(refute_0_19,plain,
( ~ unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),skolemFOFtoCNF_N)
| unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),N)
| unequally_directed_lines(skolemFOFtoCNF_N,N) ),
inference(subst,[],[refute_0_2:[bind(L,$fot(reverse_line(skolemFOFtoCNF_N))),bind(M,$fot(skolemFOFtoCNF_N))]]) ).
cnf(refute_0_20,plain,
~ unequally_directed_lines(parallel_through_point(L,A),L),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_21,plain,
~ unequally_directed_lines(parallel_through_point(skolemFOFtoCNF_M,A),skolemFOFtoCNF_M),
inference(subst,[],[refute_0_20:[bind(L,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_22,plain,
( ~ unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),X_46)
| unequally_directed_lines(X_46,N)
| unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),N) ),
inference(subst,[],[refute_0_2:[bind(L,$fot(reverse_line(skolemFOFtoCNF_N))),bind(M,$fot(X_46))]]) ).
cnf(refute_0_23,plain,
( unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),X_46)
| unequally_directed_lines(skolemFOFtoCNF_M,X_46) ),
inference(subst,[],[refute_0_15:[bind(X_45,$fot(X_46))]]) ).
cnf(refute_0_24,plain,
( unequally_directed_lines(X_46,N)
| unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),N)
| unequally_directed_lines(skolemFOFtoCNF_M,X_46) ),
inference(resolve,[$cnf( unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),X_46) )],[refute_0_23,refute_0_22]) ).
cnf(refute_0_25,plain,
( unequally_directed_lines(X_63,skolemFOFtoCNF_N)
| unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),skolemFOFtoCNF_N)
| unequally_directed_lines(skolemFOFtoCNF_M,X_63) ),
inference(subst,[],[refute_0_24:[bind(N,$fot(skolemFOFtoCNF_N)),bind(X_46,$fot(X_63))]]) ).
cnf(refute_0_26,plain,
( ~ unequally_directed_lines(X_60,reverse_line(skolemFOFtoCNF_N))
| ~ unequally_directed_lines(X_60,skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_10:[bind(L,$fot(X_60)),bind(M,$fot(skolemFOFtoCNF_N))]]) ).
cnf(refute_0_27,plain,
~ unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),reverse_line(skolemFOFtoCNF_N)),
inference(subst,[],[refute_0_0:[bind(L,$fot(reverse_line(skolemFOFtoCNF_N)))]]) ).
cnf(refute_0_28,plain,
( unequally_directed_lines(X_59,reverse_line(skolemFOFtoCNF_N))
| unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),reverse_line(skolemFOFtoCNF_N))
| unequally_directed_lines(skolemFOFtoCNF_M,X_59) ),
inference(subst,[],[refute_0_24:[bind(N,$fot(reverse_line(skolemFOFtoCNF_N))),bind(X_46,$fot(X_59))]]) ).
cnf(refute_0_29,plain,
( unequally_directed_lines(X_59,reverse_line(skolemFOFtoCNF_N))
| unequally_directed_lines(skolemFOFtoCNF_M,X_59) ),
inference(resolve,[$cnf( unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),reverse_line(skolemFOFtoCNF_N)) )],[refute_0_28,refute_0_27]) ).
cnf(refute_0_30,plain,
( unequally_directed_lines(X_60,reverse_line(skolemFOFtoCNF_N))
| unequally_directed_lines(skolemFOFtoCNF_M,X_60) ),
inference(subst,[],[refute_0_29:[bind(X_59,$fot(X_60))]]) ).
cnf(refute_0_31,plain,
( ~ unequally_directed_lines(X_60,skolemFOFtoCNF_N)
| unequally_directed_lines(skolemFOFtoCNF_M,X_60) ),
inference(resolve,[$cnf( unequally_directed_lines(X_60,reverse_line(skolemFOFtoCNF_N)) )],[refute_0_30,refute_0_26]) ).
cnf(refute_0_32,plain,
( ~ unequally_directed_lines(X_63,skolemFOFtoCNF_N)
| unequally_directed_lines(skolemFOFtoCNF_M,X_63) ),
inference(subst,[],[refute_0_31:[bind(X_60,$fot(X_63))]]) ).
cnf(refute_0_33,plain,
( unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),skolemFOFtoCNF_N)
| unequally_directed_lines(skolemFOFtoCNF_M,X_63) ),
inference(resolve,[$cnf( unequally_directed_lines(X_63,skolemFOFtoCNF_N) )],[refute_0_25,refute_0_32]) ).
cnf(refute_0_34,plain,
( unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),skolemFOFtoCNF_N)
| unequally_directed_lines(skolemFOFtoCNF_M,X_67) ),
inference(subst,[],[refute_0_33:[bind(X_63,$fot(X_67))]]) ).
cnf(refute_0_35,plain,
( ~ unequally_directed_lines(skolemFOFtoCNF_M,X_66)
| ~ unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(X_66)) ),
inference(subst,[],[refute_0_10:[bind(L,$fot(skolemFOFtoCNF_M)),bind(M,$fot(X_66))]]) ).
cnf(refute_0_36,plain,
( ~ unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),X_62)
| unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(X_62)) ),
inference(subst,[],[refute_0_17:[bind(M,$fot(X_62))]]) ).
cnf(refute_0_37,plain,
( ~ unequally_directed_lines(X_59,X_58)
| unequally_directed_lines(X_58,N)
| unequally_directed_lines(X_59,N) ),
inference(subst,[],[refute_0_2:[bind(L,$fot(X_59)),bind(M,$fot(X_58))]]) ).
cnf(refute_0_38,plain,
( unequally_directed_lines(X_59,X_58)
| unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),X_58)
| unequally_directed_lines(skolemFOFtoCNF_M,X_59) ),
inference(subst,[],[refute_0_24:[bind(N,$fot(X_58)),bind(X_46,$fot(X_59))]]) ).
cnf(refute_0_39,plain,
( unequally_directed_lines(X_58,N)
| unequally_directed_lines(X_59,N)
| unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),X_58)
| unequally_directed_lines(skolemFOFtoCNF_M,X_59) ),
inference(resolve,[$cnf( unequally_directed_lines(X_59,X_58) )],[refute_0_38,refute_0_37]) ).
cnf(refute_0_40,plain,
( unequally_directed_lines(X_58,skolemFOFtoCNF_M)
| unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),X_58)
| unequally_directed_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_M) ),
inference(subst,[],[refute_0_39:[bind(N,$fot(skolemFOFtoCNF_M)),bind(X_59,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_41,plain,
~ unequally_directed_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_M),
inference(subst,[],[refute_0_0:[bind(L,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_42,plain,
( unequally_directed_lines(X_58,skolemFOFtoCNF_M)
| unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),X_58) ),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_M) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
( unequally_directed_lines(X_62,skolemFOFtoCNF_M)
| unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),X_62) ),
inference(subst,[],[refute_0_42:[bind(X_58,$fot(X_62))]]) ).
cnf(refute_0_44,plain,
( unequally_directed_lines(X_62,skolemFOFtoCNF_M)
| unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(X_62)) ),
inference(resolve,[$cnf( unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),X_62) )],[refute_0_43,refute_0_36]) ).
cnf(refute_0_45,plain,
( unequally_directed_lines(X_66,skolemFOFtoCNF_M)
| unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(X_66)) ),
inference(subst,[],[refute_0_44:[bind(X_62,$fot(X_66))]]) ).
cnf(refute_0_46,plain,
( ~ unequally_directed_lines(skolemFOFtoCNF_M,X_66)
| unequally_directed_lines(X_66,skolemFOFtoCNF_M) ),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(X_66)) )],[refute_0_45,refute_0_35]) ).
cnf(refute_0_47,plain,
( ~ unequally_directed_lines(skolemFOFtoCNF_M,X_67)
| unequally_directed_lines(X_67,skolemFOFtoCNF_M) ),
inference(subst,[],[refute_0_46:[bind(X_66,$fot(X_67))]]) ).
cnf(refute_0_48,plain,
( unequally_directed_lines(X_67,skolemFOFtoCNF_M)
| unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),skolemFOFtoCNF_N) ),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_M,X_67) )],[refute_0_34,refute_0_47]) ).
cnf(refute_0_49,plain,
( unequally_directed_lines(parallel_through_point(skolemFOFtoCNF_M,A),skolemFOFtoCNF_M)
| unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_48:[bind(X_67,$fot(parallel_through_point(skolemFOFtoCNF_M,A)))]]) ).
cnf(refute_0_50,plain,
unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),skolemFOFtoCNF_N),
inference(resolve,[$cnf( unequally_directed_lines(parallel_through_point(skolemFOFtoCNF_M,A),skolemFOFtoCNF_M) )],[refute_0_49,refute_0_21]) ).
cnf(refute_0_51,plain,
( unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),N)
| unequally_directed_lines(skolemFOFtoCNF_N,N) ),
inference(resolve,[$cnf( unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),skolemFOFtoCNF_N) )],[refute_0_50,refute_0_19]) ).
cnf(refute_0_52,plain,
( unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),X_70)
| unequally_directed_lines(skolemFOFtoCNF_N,X_70) ),
inference(subst,[],[refute_0_51:[bind(N,$fot(X_70))]]) ).
cnf(refute_0_53,plain,
( unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(X_70))
| unequally_directed_lines(skolemFOFtoCNF_N,X_70) ),
inference(resolve,[$cnf( unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),X_70) )],[refute_0_52,refute_0_18]) ).
cnf(refute_0_54,plain,
( unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(X_76))
| unequally_directed_lines(skolemFOFtoCNF_N,X_76) ),
inference(subst,[],[refute_0_53:[bind(X_70,$fot(X_76))]]) ).
cnf(refute_0_55,plain,
( ~ unequally_directed_lines(skolemFOFtoCNF_M,X_76)
| unequally_directed_lines(skolemFOFtoCNF_N,X_76) ),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(X_76)) )],[refute_0_54,refute_0_11]) ).
cnf(refute_0_56,plain,
( ~ unequally_directed_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L)
| unequally_directed_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_55:[bind(X_76,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_57,plain,
~ unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M)),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_58,plain,
~ unequally_directed_lines(reverse_line(skolemFOFtoCNF_M),reverse_line(skolemFOFtoCNF_M)),
inference(subst,[],[refute_0_0:[bind(L,$fot(reverse_line(skolemFOFtoCNF_M)))]]) ).
cnf(refute_0_59,plain,
( ~ unequally_directed_lines(reverse_line(skolemFOFtoCNF_M),X_49)
| unequally_directed_lines(X_49,N)
| unequally_directed_lines(reverse_line(skolemFOFtoCNF_M),N) ),
inference(subst,[],[refute_0_2:[bind(L,$fot(reverse_line(skolemFOFtoCNF_M))),bind(M,$fot(X_49))]]) ).
cnf(refute_0_60,plain,
( ~ unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(skolemFOFtoCNF_M))
| unequally_directed_lines(reverse_line(skolemFOFtoCNF_M),N)
| unequally_directed_lines(skolemFOFtoCNF_M,N) ),
inference(subst,[],[refute_0_2:[bind(L,$fot(skolemFOFtoCNF_M)),bind(M,$fot(reverse_line(skolemFOFtoCNF_M)))]]) ).
cnf(refute_0_61,plain,
( unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),skolemFOFtoCNF_M)
| unequally_directed_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_M) ),
inference(subst,[],[refute_0_24:[bind(N,$fot(skolemFOFtoCNF_M)),bind(X_46,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_62,plain,
unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),skolemFOFtoCNF_M),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_M) )],[refute_0_61,refute_0_41]) ).
cnf(refute_0_63,plain,
( ~ unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),skolemFOFtoCNF_M)
| unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(skolemFOFtoCNF_M)) ),
inference(subst,[],[refute_0_17:[bind(M,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_64,plain,
unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(skolemFOFtoCNF_M)),
inference(resolve,[$cnf( unequally_directed_lines(reverse_line(skolemFOFtoCNF_N),skolemFOFtoCNF_M) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
( unequally_directed_lines(reverse_line(skolemFOFtoCNF_M),N)
| unequally_directed_lines(skolemFOFtoCNF_M,N) ),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_M,reverse_line(skolemFOFtoCNF_M)) )],[refute_0_64,refute_0_60]) ).
cnf(refute_0_66,plain,
( unequally_directed_lines(reverse_line(skolemFOFtoCNF_M),X_49)
| unequally_directed_lines(skolemFOFtoCNF_M,X_49) ),
inference(subst,[],[refute_0_65:[bind(N,$fot(X_49))]]) ).
cnf(refute_0_67,plain,
( unequally_directed_lines(X_49,N)
| unequally_directed_lines(reverse_line(skolemFOFtoCNF_M),N)
| unequally_directed_lines(skolemFOFtoCNF_M,X_49) ),
inference(resolve,[$cnf( unequally_directed_lines(reverse_line(skolemFOFtoCNF_M),X_49) )],[refute_0_66,refute_0_59]) ).
cnf(refute_0_68,plain,
( unequally_directed_lines(X_110,reverse_line(skolemFOFtoCNF_M))
| unequally_directed_lines(reverse_line(skolemFOFtoCNF_M),reverse_line(skolemFOFtoCNF_M))
| unequally_directed_lines(skolemFOFtoCNF_M,X_110) ),
inference(subst,[],[refute_0_67:[bind(N,$fot(reverse_line(skolemFOFtoCNF_M))),bind(X_49,$fot(X_110))]]) ).
cnf(refute_0_69,plain,
( unequally_directed_lines(X_110,reverse_line(skolemFOFtoCNF_M))
| unequally_directed_lines(skolemFOFtoCNF_M,X_110) ),
inference(resolve,[$cnf( unequally_directed_lines(reverse_line(skolemFOFtoCNF_M),reverse_line(skolemFOFtoCNF_M)) )],[refute_0_68,refute_0_58]) ).
cnf(refute_0_70,plain,
( unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M))
| unequally_directed_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_69:[bind(X_110,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_71,plain,
unequally_directed_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M)) )],[refute_0_70,refute_0_57]) ).
cnf(refute_0_72,plain,
unequally_directed_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_L),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L) )],[refute_0_71,refute_0_56]) ).
cnf(refute_0_73,plain,
( unequally_directed_lines(skolemFOFtoCNF_L,N)
| unequally_directed_lines(skolemFOFtoCNF_N,N) ),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_L) )],[refute_0_72,refute_0_3]) ).
cnf(refute_0_74,plain,
( unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N)
| unequally_directed_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_73:[bind(N,$fot(skolemFOFtoCNF_N))]]) ).
cnf(refute_0_75,plain,
unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_N) )],[refute_0_74,refute_0_1]) ).
cnf(refute_0_76,plain,
~ unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_77,plain,
$false,
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N) )],[refute_0_75,refute_0_76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : GEO231+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.00/0.10 % Command : metis --show proof --show saturation %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 600
% 0.10/0.29 % DateTime : Sat Jun 18 01:33:31 EDT 2022
% 0.10/0.29 % CPUTime :
% 0.10/0.30 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35
% 0.14/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.14/0.35
%------------------------------------------------------------------------------