TSTP Solution File: KRS191+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KRS191+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 : Sun Jul 17 03:19:06 EDT 2022
% Result : Theorem 215.88s 216.14s
% Output : CNFRefutation 215.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 77 ( 7 unt; 0 def)
% Number of atoms : 191 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 197 ( 83 ~; 76 |; 18 &)
% ( 18 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 170 ( 23 sgn 89 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thm,axiom,
! [Ax,C] :
( ! [I1] :
( model(I1,Ax)
=> model(I1,C) )
<=> status(Ax,C,thm) ) ).
fof(wtc,axiom,
! [Ax,C] :
( ( ? [I1] : model(I1,Ax)
& ? [I2] : ~ model(I2,Ax)
& ! [I3] : model(I3,C) )
<=> status(Ax,C,wtc) ) ).
fof(cax,axiom,
! [Ax,C] :
( ~ ? [I1] : model(I1,Ax)
<=> status(Ax,C,cax) ) ).
fof(csa,axiom,
! [Ax,C] :
( ? [I1] :
( model(I1,Ax)
& model(I1,not(C)) )
<=> status(Ax,C,csa) ) ).
fof(isa,axiom,
! [S1,S2] :
( ! [Ax,C] :
( status(Ax,C,S1)
=> status(Ax,C,S2) )
<=> isa(S1,S2) ) ).
fof(completeness,axiom,
! [I,F] :
~ ( model(I,F)
<=> model(I,not(F)) ) ).
fof(isa_wtc_thm,conjecture,
isa(wtc,thm) ).
fof(subgoal_0,plain,
isa(wtc,thm),
inference(strip,[],[isa_wtc_thm]) ).
fof(negate_0_0,plain,
~ isa(wtc,thm),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [S1,S2] :
( ~ isa(S1,S2)
<=> ? [Ax,C] :
( ~ status(Ax,C,S2)
& status(Ax,C,S1) ) ),
inference(canonicalize,[],[isa]) ).
fof(normalize_0_1,plain,
! [S1,S2] :
( ~ isa(S1,S2)
<=> ? [Ax,C] :
( ~ status(Ax,C,S2)
& status(Ax,C,S1) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [Ax,C,S1,S2] :
( ( ~ status(skolemFOFtoCNF_Ax_1(S1,S2),skolemFOFtoCNF_C_1(S1,S2),S2)
| isa(S1,S2) )
& ( isa(S1,S2)
| status(skolemFOFtoCNF_Ax_1(S1,S2),skolemFOFtoCNF_C_1(S1,S2),S1) )
& ( ~ isa(S1,S2)
| ~ status(Ax,C,S1)
| status(Ax,C,S2) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [S1,S2] :
( ~ status(skolemFOFtoCNF_Ax_1(S1,S2),skolemFOFtoCNF_C_1(S1,S2),S2)
| isa(S1,S2) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [Ax,C] :
( ~ status(Ax,C,cax)
<=> ? [I1] : model(I1,Ax) ),
inference(canonicalize,[],[cax]) ).
fof(normalize_0_5,plain,
! [Ax,C] :
( ~ status(Ax,C,cax)
<=> ? [I1] : model(I1,Ax) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [Ax,C,I1] :
( ( ~ model(I1,Ax)
| ~ status(Ax,C,cax) )
& ( model(skolemFOFtoCNF_I1_13(Ax),Ax)
| status(Ax,C,cax) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [Ax,C,I1] :
( ~ model(I1,Ax)
| ~ status(Ax,C,cax) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [F,I] :
( ~ model(I,F)
<=> model(I,not(F)) ),
inference(canonicalize,[],[completeness]) ).
fof(normalize_0_9,plain,
! [F,I] :
( ~ model(I,F)
<=> model(I,not(F)) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [F,I] :
( ( ~ model(I,F)
| ~ model(I,not(F)) )
& ( model(I,F)
| model(I,not(F)) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [F,I] :
( ~ model(I,F)
| ~ model(I,not(F)) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [Ax,C] :
( model(skolemFOFtoCNF_I1_13(Ax),Ax)
| status(Ax,C,cax) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_13,plain,
! [Ax,C] :
( ~ status(Ax,C,wtc)
<=> ( ? [I3] : ~ model(I3,C)
| ! [I1] : ~ model(I1,Ax)
| ! [I2] : model(I2,Ax) ) ),
inference(canonicalize,[],[wtc]) ).
fof(normalize_0_14,plain,
! [Ax,C] :
( ~ status(Ax,C,wtc)
<=> ( ? [I3] : ~ model(I3,C)
| ! [I1] : ~ model(I1,Ax)
| ! [I2] : model(I2,Ax) ) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [Ax,C,I1,I2,I3] :
( ( ~ model(skolemFOFtoCNF_I2_8(Ax),Ax)
| ~ status(Ax,C,wtc) )
& ( ~ status(Ax,C,wtc)
| model(I3,C) )
& ( ~ status(Ax,C,wtc)
| model(skolemFOFtoCNF_I1_12(Ax),Ax) )
& ( ~ model(I1,Ax)
| ~ model(skolemFOFtoCNF_I3_2(C),C)
| model(I2,Ax)
| status(Ax,C,wtc) ) ),
inference(clausify,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [Ax,C,I3] :
( ~ status(Ax,C,wtc)
| model(I3,C) ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [S1,S2] :
( isa(S1,S2)
| status(skolemFOFtoCNF_Ax_1(S1,S2),skolemFOFtoCNF_C_1(S1,S2),S1) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_18,plain,
! [Ax,C] :
( ~ status(Ax,C,csa)
<=> ! [I1] :
( ~ model(I1,Ax)
| ~ model(I1,not(C)) ) ),
inference(canonicalize,[],[csa]) ).
fof(normalize_0_19,plain,
! [Ax,C] :
( ~ status(Ax,C,csa)
<=> ! [I1] :
( ~ model(I1,Ax)
| ~ model(I1,not(C)) ) ),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [Ax,C,I1] :
( ( ~ status(Ax,C,csa)
| model(skolemFOFtoCNF_I1_14(Ax,C),Ax) )
& ( ~ status(Ax,C,csa)
| model(skolemFOFtoCNF_I1_14(Ax,C),not(C)) )
& ( ~ model(I1,Ax)
| ~ model(I1,not(C))
| status(Ax,C,csa) ) ),
inference(clausify,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [Ax,C] :
( ~ status(Ax,C,csa)
| model(skolemFOFtoCNF_I1_14(Ax,C),not(C)) ),
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [Ax,C] :
( ~ status(Ax,C,thm)
<=> ? [I1] :
( ~ model(I1,C)
& model(I1,Ax) ) ),
inference(canonicalize,[],[thm]) ).
fof(normalize_0_23,plain,
! [Ax,C] :
( ~ status(Ax,C,thm)
<=> ? [I1] :
( ~ model(I1,C)
& model(I1,Ax) ) ),
inference(specialize,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [Ax,C,I1] :
( ( ~ model(skolemFOFtoCNF_I1_5(Ax,C),C)
| status(Ax,C,thm) )
& ( model(skolemFOFtoCNF_I1_5(Ax,C),Ax)
| status(Ax,C,thm) )
& ( ~ model(I1,Ax)
| ~ status(Ax,C,thm)
| model(I1,C) ) ),
inference(clausify,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [Ax,C] :
( ~ model(skolemFOFtoCNF_I1_5(Ax,C),C)
| status(Ax,C,thm) ),
inference(conjunct,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [F,I] :
( model(I,F)
| model(I,not(F)) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_27,plain,
! [Ax,C,I1] :
( ~ model(I1,Ax)
| ~ model(I1,not(C))
| status(Ax,C,csa) ),
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_28,plain,
~ isa(wtc,thm),
inference(canonicalize,[],[negate_0_0]) ).
cnf(refute_0_0,plain,
( ~ status(skolemFOFtoCNF_Ax_1(S1,S2),skolemFOFtoCNF_C_1(S1,S2),S2)
| isa(S1,S2) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ status(skolemFOFtoCNF_Ax_1(wtc,thm),skolemFOFtoCNF_C_1(wtc,thm),thm)
| isa(wtc,thm) ),
inference(subst,[],[refute_0_0:[bind(S1,$fot(wtc)),bind(S2,$fot(thm))]]) ).
cnf(refute_0_2,plain,
( ~ model(I1,Ax)
| ~ status(Ax,C,cax) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( ~ model(I1,not(skolemFOFtoCNF_C_1(wtc,X_2262)))
| ~ status(not(skolemFOFtoCNF_C_1(wtc,X_2262)),X_2261,cax) ),
inference(subst,[],[refute_0_2:[bind(Ax,$fot(not(skolemFOFtoCNF_C_1(wtc,X_2262)))),bind(C,$fot(X_2261))]]) ).
cnf(refute_0_4,plain,
( ~ model(I,F)
| ~ model(I,not(F)) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_5,plain,
( ~ model(skolemFOFtoCNF_I1_13(not(F)),F)
| ~ model(skolemFOFtoCNF_I1_13(not(F)),not(F)) ),
inference(subst,[],[refute_0_4:[bind(I,$fot(skolemFOFtoCNF_I1_13(not(F))))]]) ).
cnf(refute_0_6,plain,
( model(skolemFOFtoCNF_I1_13(Ax),Ax)
| status(Ax,C,cax) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_7,plain,
( model(skolemFOFtoCNF_I1_13(not(F)),not(F))
| status(not(F),X_55,cax) ),
inference(subst,[],[refute_0_6:[bind(Ax,$fot(not(F))),bind(C,$fot(X_55))]]) ).
cnf(refute_0_8,plain,
( ~ model(skolemFOFtoCNF_I1_13(not(F)),F)
| status(not(F),X_55,cax) ),
inference(resolve,[$cnf( model(skolemFOFtoCNF_I1_13(not(F)),not(F)) )],[refute_0_7,refute_0_5]) ).
cnf(refute_0_9,plain,
( ~ model(skolemFOFtoCNF_I1_13(not(skolemFOFtoCNF_C_1(wtc,X_687))),skolemFOFtoCNF_C_1(wtc,X_687))
| status(not(skolemFOFtoCNF_C_1(wtc,X_687)),X_55,cax) ),
inference(subst,[],[refute_0_8:[bind(F,$fot(skolemFOFtoCNF_C_1(wtc,X_687)))]]) ).
cnf(refute_0_10,plain,
( ~ status(Ax,C,wtc)
| model(I3,C) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_11,plain,
( ~ status(skolemFOFtoCNF_Ax_1(wtc,X_279),skolemFOFtoCNF_C_1(wtc,X_279),wtc)
| model(I3,skolemFOFtoCNF_C_1(wtc,X_279)) ),
inference(subst,[],[refute_0_10:[bind(Ax,$fot(skolemFOFtoCNF_Ax_1(wtc,X_279))),bind(C,$fot(skolemFOFtoCNF_C_1(wtc,X_279)))]]) ).
cnf(refute_0_12,plain,
( isa(S1,S2)
| status(skolemFOFtoCNF_Ax_1(S1,S2),skolemFOFtoCNF_C_1(S1,S2),S1) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_13,plain,
( isa(wtc,X_279)
| status(skolemFOFtoCNF_Ax_1(wtc,X_279),skolemFOFtoCNF_C_1(wtc,X_279),wtc) ),
inference(subst,[],[refute_0_12:[bind(S1,$fot(wtc)),bind(S2,$fot(X_279))]]) ).
cnf(refute_0_14,plain,
( isa(wtc,X_279)
| model(I3,skolemFOFtoCNF_C_1(wtc,X_279)) ),
inference(resolve,[$cnf( status(skolemFOFtoCNF_Ax_1(wtc,X_279),skolemFOFtoCNF_C_1(wtc,X_279),wtc) )],[refute_0_13,refute_0_11]) ).
cnf(refute_0_15,plain,
( isa(wtc,X_687)
| model(skolemFOFtoCNF_I1_13(not(skolemFOFtoCNF_C_1(wtc,X_687))),skolemFOFtoCNF_C_1(wtc,X_687)) ),
inference(subst,[],[refute_0_14:[bind(I3,$fot(skolemFOFtoCNF_I1_13(not(skolemFOFtoCNF_C_1(wtc,X_687))))),bind(X_279,$fot(X_687))]]) ).
cnf(refute_0_16,plain,
( isa(wtc,X_687)
| status(not(skolemFOFtoCNF_C_1(wtc,X_687)),X_55,cax) ),
inference(resolve,[$cnf( model(skolemFOFtoCNF_I1_13(not(skolemFOFtoCNF_C_1(wtc,X_687))),skolemFOFtoCNF_C_1(wtc,X_687)) )],[refute_0_15,refute_0_9]) ).
cnf(refute_0_17,plain,
( isa(wtc,X_2262)
| status(not(skolemFOFtoCNF_C_1(wtc,X_2262)),X_2261,cax) ),
inference(subst,[],[refute_0_16:[bind(X_55,$fot(X_2261)),bind(X_687,$fot(X_2262))]]) ).
cnf(refute_0_18,plain,
( ~ model(I1,not(skolemFOFtoCNF_C_1(wtc,X_2262)))
| isa(wtc,X_2262) ),
inference(resolve,[$cnf( status(not(skolemFOFtoCNF_C_1(wtc,X_2262)),X_2261,cax) )],[refute_0_17,refute_0_3]) ).
cnf(refute_0_19,plain,
( ~ model(skolemFOFtoCNF_I1_14(not(skolemFOFtoCNF_C_1(wtc,X_2262)),skolemFOFtoCNF_C_1(wtc,X_2262)),not(skolemFOFtoCNF_C_1(wtc,X_2262)))
| isa(wtc,X_2262) ),
inference(subst,[],[refute_0_18:[bind(I1,$fot(skolemFOFtoCNF_I1_14(not(skolemFOFtoCNF_C_1(wtc,X_2262)),skolemFOFtoCNF_C_1(wtc,X_2262))))]]) ).
cnf(refute_0_20,plain,
( ~ status(Ax,C,csa)
| model(skolemFOFtoCNF_I1_14(Ax,C),not(C)) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_21,plain,
( ~ status(not(X_1638),X_1638,csa)
| model(skolemFOFtoCNF_I1_14(not(X_1638),X_1638),not(X_1638)) ),
inference(subst,[],[refute_0_20:[bind(Ax,$fot(not(X_1638))),bind(C,$fot(X_1638))]]) ).
cnf(refute_0_22,plain,
( ~ model(skolemFOFtoCNF_I1_5(Ax,C),C)
| status(Ax,C,thm) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_23,plain,
( ~ model(skolemFOFtoCNF_I1_5(Ax,X_324),X_324)
| status(Ax,X_324,thm) ),
inference(subst,[],[refute_0_22:[bind(C,$fot(X_324))]]) ).
cnf(refute_0_24,plain,
( model(I,F)
| model(I,not(F)) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_25,plain,
( model(X_109,X_108)
| model(X_109,not(X_108)) ),
inference(subst,[],[refute_0_24:[bind(F,$fot(X_108)),bind(I,$fot(X_109))]]) ).
cnf(refute_0_26,plain,
( ~ model(I1,Ax)
| ~ model(I1,not(C))
| status(Ax,C,csa) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_27,plain,
( ~ model(X_109,not(X_108))
| status(not(X_108),X_108,csa) ),
inference(subst,[],[refute_0_26:[bind(Ax,$fot(not(X_108))),bind(C,$fot(X_108)),bind(I1,$fot(X_109))]]) ).
cnf(refute_0_28,plain,
( model(X_109,X_108)
| status(not(X_108),X_108,csa) ),
inference(resolve,[$cnf( model(X_109,not(X_108)) )],[refute_0_25,refute_0_27]) ).
cnf(refute_0_29,plain,
( model(skolemFOFtoCNF_I1_5(Ax,X_324),X_324)
| status(not(X_324),X_324,csa) ),
inference(subst,[],[refute_0_28:[bind(X_108,$fot(X_324)),bind(X_109,$fot(skolemFOFtoCNF_I1_5(Ax,X_324)))]]) ).
cnf(refute_0_30,plain,
( status(Ax,X_324,thm)
| status(not(X_324),X_324,csa) ),
inference(resolve,[$cnf( model(skolemFOFtoCNF_I1_5(Ax,X_324),X_324) )],[refute_0_29,refute_0_23]) ).
cnf(refute_0_31,plain,
( status(X_1637,X_1638,thm)
| status(not(X_1638),X_1638,csa) ),
inference(subst,[],[refute_0_30:[bind(Ax,$fot(X_1637)),bind(X_324,$fot(X_1638))]]) ).
cnf(refute_0_32,plain,
( model(skolemFOFtoCNF_I1_14(not(X_1638),X_1638),not(X_1638))
| status(X_1637,X_1638,thm) ),
inference(resolve,[$cnf( status(not(X_1638),X_1638,csa) )],[refute_0_31,refute_0_21]) ).
cnf(refute_0_33,plain,
( model(skolemFOFtoCNF_I1_14(not(skolemFOFtoCNF_C_1(wtc,X_2262)),skolemFOFtoCNF_C_1(wtc,X_2262)),not(skolemFOFtoCNF_C_1(wtc,X_2262)))
| status(X_9042,skolemFOFtoCNF_C_1(wtc,X_2262),thm) ),
inference(subst,[],[refute_0_32:[bind(X_1637,$fot(X_9042)),bind(X_1638,$fot(skolemFOFtoCNF_C_1(wtc,X_2262)))]]) ).
cnf(refute_0_34,plain,
( isa(wtc,X_2262)
| status(X_9042,skolemFOFtoCNF_C_1(wtc,X_2262),thm) ),
inference(resolve,[$cnf( model(skolemFOFtoCNF_I1_14(not(skolemFOFtoCNF_C_1(wtc,X_2262)),skolemFOFtoCNF_C_1(wtc,X_2262)),not(skolemFOFtoCNF_C_1(wtc,X_2262))) )],[refute_0_33,refute_0_19]) ).
cnf(refute_0_35,plain,
( isa(wtc,thm)
| status(skolemFOFtoCNF_Ax_1(wtc,thm),skolemFOFtoCNF_C_1(wtc,thm),thm) ),
inference(subst,[],[refute_0_34:[bind(X_2262,$fot(thm)),bind(X_9042,$fot(skolemFOFtoCNF_Ax_1(wtc,thm)))]]) ).
cnf(refute_0_36,plain,
isa(wtc,thm),
inference(resolve,[$cnf( status(skolemFOFtoCNF_Ax_1(wtc,thm),skolemFOFtoCNF_C_1(wtc,thm),thm) )],[refute_0_35,refute_0_1]) ).
cnf(refute_0_37,plain,
~ isa(wtc,thm),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_38,plain,
$false,
inference(resolve,[$cnf( isa(wtc,thm) )],[refute_0_36,refute_0_37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS191+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 7 10:26:06 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 215.88/216.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 215.88/216.14
% 215.88/216.14 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 215.88/216.15
%------------------------------------------------------------------------------