TSTP Solution File: GEO233+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO233+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 0.19s 0.36s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 76 ( 24 unt; 0 def)
% Number of atoms : 143 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 130 ( 63 ~; 52 |; 5 &)
% ( 9 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 126 ( 4 sgn 64 !; 1 ?)
% 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(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] : equally_directed_lines(reverse_line(reverse_line(L)),L) ).
fof(subgoal_0,plain,
! [L] : equally_directed_lines(reverse_line(reverse_line(L)),L),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [L] : equally_directed_lines(reverse_line(reverse_line(L)),L),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [L] : ~ equally_directed_lines(reverse_line(reverse_line(L)),L),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
~ equally_directed_lines(reverse_line(reverse_line(skolemFOFtoCNF_L)),skolemFOFtoCNF_L),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] :
( ~ equally_directed_lines(X,Y)
<=> unequally_directed_lines(X,Y) ),
inference(canonicalize,[],[a4_defns]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( ~ equally_directed_lines(X,Y)
<=> unequally_directed_lines(X,Y) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,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_3]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( equally_directed_lines(X,Y)
| unequally_directed_lines(X,Y) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ~ equally_directed_opposite_lines(X,Y)
<=> unequally_directed_opposite_lines(X,Y) ),
inference(canonicalize,[],[a5_defns]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ~ equally_directed_opposite_lines(X,Y)
<=> unequally_directed_opposite_lines(X,Y) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,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_7]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( equally_directed_opposite_lines(X,Y)
| unequally_directed_opposite_lines(X,Y) ),
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_opposite_lines(X,Y)
| unequally_directed_lines(X,reverse_line(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))
| left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[ax9_basics]) ).
fof(normalize_0_15,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_14]) ).
fof(normalize_0_16,plain,
( ! [L,M] : ~ left_convergent_lines(L,M)
& ! [L,M] : ~ left_convergent_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[ax11_basics]) ).
fof(normalize_0_17,plain,
! [L,M] : ~ left_convergent_lines(L,M),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [L,M] : ~ left_convergent_lines(L,M),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [X,Y] :
( ~ equally_directed_opposite_lines(X,Y)
| ~ unequally_directed_opposite_lines(X,Y) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_20,plain,
! [X,Y] :
( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_21,plain,
! [L] : equally_directed_lines(L,L),
inference(canonicalize,[],[ax5_basics]) ).
fof(normalize_0_22,plain,
! [L] : equally_directed_lines(L,L),
inference(specialize,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [L,M] :
( unequally_directed_lines(L,M)
| unequally_directed_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[ax8_basics]) ).
fof(normalize_0_24,plain,
! [L,M] :
( unequally_directed_lines(L,M)
| unequally_directed_lines(L,reverse_line(M)) ),
inference(specialize,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [X,Y] :
( ~ equally_directed_lines(X,Y)
| ~ unequally_directed_lines(X,Y) ),
inference(conjunct,[],[normalize_0_4]) ).
cnf(refute_0_0,plain,
~ equally_directed_lines(reverse_line(reverse_line(skolemFOFtoCNF_L)),skolemFOFtoCNF_L),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( equally_directed_lines(X,Y)
| unequally_directed_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( equally_directed_lines(X_47,X_48)
| unequally_directed_lines(X_47,X_48) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_47)),bind(Y,$fot(X_48))]]) ).
cnf(refute_0_3,plain,
( equally_directed_opposite_lines(X,Y)
| unequally_directed_opposite_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_4,plain,
( equally_directed_opposite_lines(X_36,X_37)
| unequally_directed_opposite_lines(X_36,X_37) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_36)),bind(Y,$fot(X_37))]]) ).
cnf(refute_0_5,plain,
( ~ unequally_directed_opposite_lines(X,Y)
| unequally_directed_lines(X,reverse_line(Y)) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_6,plain,
( ~ unequally_directed_opposite_lines(X_36,X_37)
| unequally_directed_lines(X_36,reverse_line(X_37)) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_36)),bind(Y,$fot(X_37))]]) ).
cnf(refute_0_7,plain,
( equally_directed_opposite_lines(X_36,X_37)
| unequally_directed_lines(X_36,reverse_line(X_37)) ),
inference(resolve,[$cnf( unequally_directed_opposite_lines(X_36,X_37) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( equally_directed_opposite_lines(X_45,X_46)
| unequally_directed_lines(X_45,reverse_line(X_46)) ),
inference(subst,[],[refute_0_7:[bind(X_36,$fot(X_45)),bind(X_37,$fot(X_46))]]) ).
cnf(refute_0_9,plain,
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_10,plain,
~ left_convergent_lines(L,M),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_11,plain,
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| left_convergent_lines(L,reverse_line(M)) ),
inference(resolve,[$cnf( left_convergent_lines(L,M) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
~ left_convergent_lines(L,reverse_line(M)),
inference(subst,[],[refute_0_10:[bind(M,$fot(reverse_line(M)))]]) ).
cnf(refute_0_13,plain,
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M)) ),
inference(resolve,[$cnf( left_convergent_lines(L,reverse_line(M)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ unequally_directed_lines(X_45,X_46)
| ~ unequally_directed_lines(X_45,reverse_line(X_46)) ),
inference(subst,[],[refute_0_13:[bind(L,$fot(X_45)),bind(M,$fot(X_46))]]) ).
cnf(refute_0_15,plain,
( ~ unequally_directed_lines(X_45,X_46)
| equally_directed_opposite_lines(X_45,X_46) ),
inference(resolve,[$cnf( unequally_directed_lines(X_45,reverse_line(X_46)) )],[refute_0_8,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ unequally_directed_lines(X_47,X_48)
| equally_directed_opposite_lines(X_47,X_48) ),
inference(subst,[],[refute_0_15:[bind(X_45,$fot(X_47)),bind(X_46,$fot(X_48))]]) ).
cnf(refute_0_17,plain,
( equally_directed_lines(X_47,X_48)
| equally_directed_opposite_lines(X_47,X_48) ),
inference(resolve,[$cnf( unequally_directed_lines(X_47,X_48) )],[refute_0_2,refute_0_16]) ).
cnf(refute_0_18,plain,
( equally_directed_lines(reverse_line(reverse_line(X_58)),X_58)
| equally_directed_opposite_lines(reverse_line(reverse_line(X_58)),X_58) ),
inference(subst,[],[refute_0_17:[bind(X_47,$fot(reverse_line(reverse_line(X_58)))),bind(X_48,$fot(X_58))]]) ).
cnf(refute_0_19,plain,
( ~ equally_directed_opposite_lines(X,Y)
| ~ unequally_directed_opposite_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_20,plain,
( ~ equally_directed_opposite_lines(reverse_line(reverse_line(X_57)),X_57)
| ~ unequally_directed_opposite_lines(reverse_line(reverse_line(X_57)),X_57) ),
inference(subst,[],[refute_0_19:[bind(X,$fot(reverse_line(reverse_line(X_57)))),bind(Y,$fot(X_57))]]) ).
cnf(refute_0_21,plain,
( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_22,plain,
( ~ unequally_directed_lines(reverse_line(reverse_line(Y)),reverse_line(Y))
| unequally_directed_opposite_lines(reverse_line(reverse_line(Y)),Y) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(reverse_line(reverse_line(Y))))]]) ).
cnf(refute_0_23,plain,
equally_directed_lines(L,L),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_24,plain,
equally_directed_lines(reverse_line(X_51),reverse_line(X_51)),
inference(subst,[],[refute_0_23:[bind(L,$fot(reverse_line(X_51)))]]) ).
cnf(refute_0_25,plain,
( unequally_directed_lines(L,M)
| unequally_directed_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_26,plain,
( unequally_directed_lines(X_30,M)
| unequally_directed_lines(X_30,reverse_line(M)) ),
inference(subst,[],[refute_0_25:[bind(L,$fot(X_30))]]) ).
cnf(refute_0_27,plain,
( ~ equally_directed_lines(X,Y)
| ~ unequally_directed_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_28,plain,
( ~ equally_directed_lines(X_30,reverse_line(M))
| ~ unequally_directed_lines(X_30,reverse_line(M)) ),
inference(subst,[],[refute_0_27:[bind(X,$fot(X_30)),bind(Y,$fot(reverse_line(M)))]]) ).
cnf(refute_0_29,plain,
( ~ equally_directed_lines(X_30,reverse_line(M))
| unequally_directed_lines(X_30,M) ),
inference(resolve,[$cnf( unequally_directed_lines(X_30,reverse_line(M)) )],[refute_0_26,refute_0_28]) ).
cnf(refute_0_30,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_29:[bind(M,$fot(X_51)),bind(X_30,$fot(reverse_line(X_51)))]]) ).
cnf(refute_0_31,plain,
unequally_directed_lines(reverse_line(X_51),X_51),
inference(resolve,[$cnf( equally_directed_lines(reverse_line(X_51),reverse_line(X_51)) )],[refute_0_24,refute_0_30]) ).
cnf(refute_0_32,plain,
unequally_directed_lines(reverse_line(reverse_line(Y)),reverse_line(Y)),
inference(subst,[],[refute_0_31:[bind(X_51,$fot(reverse_line(Y)))]]) ).
cnf(refute_0_33,plain,
unequally_directed_opposite_lines(reverse_line(reverse_line(Y)),Y),
inference(resolve,[$cnf( unequally_directed_lines(reverse_line(reverse_line(Y)),reverse_line(Y)) )],[refute_0_32,refute_0_22]) ).
cnf(refute_0_34,plain,
unequally_directed_opposite_lines(reverse_line(reverse_line(X_57)),X_57),
inference(subst,[],[refute_0_33:[bind(Y,$fot(X_57))]]) ).
cnf(refute_0_35,plain,
~ equally_directed_opposite_lines(reverse_line(reverse_line(X_57)),X_57),
inference(resolve,[$cnf( unequally_directed_opposite_lines(reverse_line(reverse_line(X_57)),X_57) )],[refute_0_34,refute_0_20]) ).
cnf(refute_0_36,plain,
~ equally_directed_opposite_lines(reverse_line(reverse_line(X_58)),X_58),
inference(subst,[],[refute_0_35:[bind(X_57,$fot(X_58))]]) ).
cnf(refute_0_37,plain,
equally_directed_lines(reverse_line(reverse_line(X_58)),X_58),
inference(resolve,[$cnf( equally_directed_opposite_lines(reverse_line(reverse_line(X_58)),X_58) )],[refute_0_18,refute_0_36]) ).
cnf(refute_0_38,plain,
equally_directed_lines(reverse_line(reverse_line(skolemFOFtoCNF_L)),skolemFOFtoCNF_L),
inference(subst,[],[refute_0_37:[bind(X_58,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_39,plain,
$false,
inference(resolve,[$cnf( equally_directed_lines(reverse_line(reverse_line(skolemFOFtoCNF_L)),skolemFOFtoCNF_L) )],[refute_0_38,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO233+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.14/0.33 % Computer : n028.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 17:38:28 EDT 2022
% 0.14/0.33 % CPUTime :
% 0.14/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.36
% 0.19/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.36
%------------------------------------------------------------------------------