TSTP Solution File: KRS196+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KRS196+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 03:19:07 EDT 2022
% Result : Theorem 0.92s 1.11s
% Output : CNFRefutation 0.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 69 ( 7 unt; 0 def)
% Number of atoms : 179 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 192 ( 82 ~; 69 |; 19 &)
% ( 20 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 147 ( 6 sgn 89 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sat,axiom,
! [Ax,C] :
( ? [I1] :
( model(I1,Ax)
& model(I1,C) )
<=> status(Ax,C,sat) ) ).
fof(thm,axiom,
! [Ax,C] :
( ! [I1] :
( model(I1,Ax)
=> model(I1,C) )
<=> status(Ax,C,thm) ) ).
fof(cax,axiom,
! [Ax,C] :
( ~ ? [I1] : model(I1,Ax)
<=> status(Ax,C,cax) ) ).
fof(sca,axiom,
! [Ax,C] :
( ( ~ ? [I1] : model(I1,Ax)
& ? [I2] : model(I2,C) )
<=> status(Ax,C,sca) ) ).
fof(wca,axiom,
! [Ax,C] :
( ( ~ ? [I1] : model(I1,Ax)
& ? [I2] : model(I2,C)
& ? [I3] : ~ model(I3,C) )
<=> status(Ax,C,wca) ) ).
fof(isa,axiom,
! [S1,S2] :
( ! [Ax,C] :
( status(Ax,C,S1)
=> status(Ax,C,S2) )
<=> isa(S1,S2) ) ).
fof(isa_wca_thm,conjecture,
isa(wca,thm) ).
fof(subgoal_0,plain,
isa(wca,thm),
inference(strip,[],[isa_wca_thm]) ).
fof(negate_0_0,plain,
~ isa(wca,thm),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [Ax,C] :
( ~ status(Ax,C,sca)
<=> ( ? [I1] : model(I1,Ax)
| ! [I2] : ~ model(I2,C) ) ),
inference(canonicalize,[],[sca]) ).
fof(normalize_0_1,plain,
! [Ax,C] :
( ~ status(Ax,C,cax)
<=> ? [I1] : model(I1,Ax) ),
inference(canonicalize,[],[cax]) ).
fof(normalize_0_2,plain,
! [Ax,C] :
( ~ status(Ax,C,cax)
<=> ? [I1] : model(I1,Ax) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [Ax,C] :
( ~ status(Ax,C,sca)
<=> ( ~ status(Ax,C,cax)
| ! [I2] : ~ model(I2,C) ) ),
inference(simplify,[],[normalize_0_0,normalize_0_2]) ).
fof(normalize_0_4,plain,
! [Ax,C] :
( ~ status(Ax,C,sca)
<=> ( ~ status(Ax,C,cax)
| ! [I2] : ~ model(I2,C) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [Ax,C,I2] :
( ( ~ status(Ax,C,sca)
| model(skolemFOFtoCNF_I2_9(C),C) )
& ( ~ status(Ax,C,sca)
| status(Ax,C,cax) )
& ( ~ model(I2,C)
| ~ status(Ax,C,cax)
| status(Ax,C,sca) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [Ax,C] :
( ~ status(Ax,C,sca)
| status(Ax,C,cax) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [Ax,C] :
( ~ status(Ax,C,wca)
<=> ( ? [I1] : model(I1,Ax)
| ! [I2] : ~ model(I2,C)
| ! [I3] : model(I3,C) ) ),
inference(canonicalize,[],[wca]) ).
fof(normalize_0_8,plain,
! [Ax,C] :
( ~ status(Ax,C,wca)
<=> ( ~ status(Ax,C,sca)
| ! [I3] : model(I3,C) ) ),
inference(simplify,[],[normalize_0_7,normalize_0_4,normalize_0_2]) ).
fof(normalize_0_9,plain,
! [Ax,C] :
( ~ status(Ax,C,wca)
<=> ( ~ status(Ax,C,sca)
| ! [I3] : model(I3,C) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [Ax,C,I3] :
( ( ~ model(skolemFOFtoCNF_I3_3(C),C)
| ~ status(Ax,C,wca) )
& ( ~ status(Ax,C,wca)
| status(Ax,C,sca) )
& ( ~ status(Ax,C,sca)
| model(I3,C)
| status(Ax,C,wca) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [Ax,C] :
( ~ status(Ax,C,wca)
| status(Ax,C,sca) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [S1,S2] :
( ~ isa(S1,S2)
<=> ? [Ax,C] :
( ~ status(Ax,C,S2)
& status(Ax,C,S1) ) ),
inference(canonicalize,[],[isa]) ).
fof(normalize_0_13,plain,
! [S1,S2] :
( ~ isa(S1,S2)
<=> ? [Ax,C] :
( ~ status(Ax,C,S2)
& status(Ax,C,S1) ) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,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_13]) ).
fof(normalize_0_15,plain,
! [S1,S2] :
( isa(S1,S2)
| status(skolemFOFtoCNF_Ax_1(S1,S2),skolemFOFtoCNF_C_1(S1,S2),S1) ),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_16,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_2]) ).
fof(normalize_0_17,plain,
! [Ax,C,I1] :
( ~ model(I1,Ax)
| ~ status(Ax,C,cax) ),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [Ax,C] :
( ~ status(Ax,C,sat)
<=> ! [I1] :
( ~ model(I1,Ax)
| ~ model(I1,C) ) ),
inference(canonicalize,[],[sat]) ).
fof(normalize_0_19,plain,
! [Ax,C] :
( ~ status(Ax,C,sat)
<=> ! [I1] :
( ~ model(I1,Ax)
| ~ model(I1,C) ) ),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [Ax,C,I1] :
( ( ~ status(Ax,C,sat)
| model(skolemFOFtoCNF_I1_4(Ax,C),Ax) )
& ( ~ status(Ax,C,sat)
| model(skolemFOFtoCNF_I1_4(Ax,C),C) )
& ( ~ model(I1,Ax)
| ~ model(I1,C)
| status(Ax,C,sat) ) ),
inference(clausify,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [Ax,C] :
( ~ status(Ax,C,sat)
| model(skolemFOFtoCNF_I1_4(Ax,C),Ax) ),
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [Ax,C,I1] :
( ~ model(I1,Ax)
| ~ model(I1,C)
| status(Ax,C,sat) ),
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_23,plain,
! [Ax,C] :
( ~ status(Ax,C,thm)
<=> ? [I1] :
( ~ model(I1,C)
& model(I1,Ax) ) ),
inference(canonicalize,[],[thm]) ).
fof(normalize_0_24,plain,
! [Ax,C] :
( ~ status(Ax,C,thm)
<=> ? [I1] :
( ~ model(I1,C)
& model(I1,Ax) ) ),
inference(specialize,[],[normalize_0_23]) ).
fof(normalize_0_25,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_24]) ).
fof(normalize_0_26,plain,
! [Ax,C] :
( model(skolemFOFtoCNF_I1_5(Ax,C),Ax)
| status(Ax,C,thm) ),
inference(conjunct,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
! [S1,S2] :
( ~ status(skolemFOFtoCNF_Ax_1(S1,S2),skolemFOFtoCNF_C_1(S1,S2),S2)
| isa(S1,S2) ),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_28,plain,
~ isa(wca,thm),
inference(canonicalize,[],[negate_0_0]) ).
cnf(refute_0_0,plain,
( ~ status(Ax,C,sca)
| status(Ax,C,cax) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_1,plain,
( ~ status(skolemFOFtoCNF_Ax_1(wca,X_446),skolemFOFtoCNF_C_1(wca,X_446),sca)
| status(skolemFOFtoCNF_Ax_1(wca,X_446),skolemFOFtoCNF_C_1(wca,X_446),cax) ),
inference(subst,[],[refute_0_0:[bind(Ax,$fot(skolemFOFtoCNF_Ax_1(wca,X_446))),bind(C,$fot(skolemFOFtoCNF_C_1(wca,X_446)))]]) ).
cnf(refute_0_2,plain,
( ~ status(Ax,C,wca)
| status(Ax,C,sca) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_3,plain,
( ~ status(skolemFOFtoCNF_Ax_1(wca,X_407),skolemFOFtoCNF_C_1(wca,X_407),wca)
| status(skolemFOFtoCNF_Ax_1(wca,X_407),skolemFOFtoCNF_C_1(wca,X_407),sca) ),
inference(subst,[],[refute_0_2:[bind(Ax,$fot(skolemFOFtoCNF_Ax_1(wca,X_407))),bind(C,$fot(skolemFOFtoCNF_C_1(wca,X_407)))]]) ).
cnf(refute_0_4,plain,
( isa(S1,S2)
| status(skolemFOFtoCNF_Ax_1(S1,S2),skolemFOFtoCNF_C_1(S1,S2),S1) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_5,plain,
( isa(wca,X_407)
| status(skolemFOFtoCNF_Ax_1(wca,X_407),skolemFOFtoCNF_C_1(wca,X_407),wca) ),
inference(subst,[],[refute_0_4:[bind(S1,$fot(wca)),bind(S2,$fot(X_407))]]) ).
cnf(refute_0_6,plain,
( isa(wca,X_407)
| status(skolemFOFtoCNF_Ax_1(wca,X_407),skolemFOFtoCNF_C_1(wca,X_407),sca) ),
inference(resolve,[$cnf( status(skolemFOFtoCNF_Ax_1(wca,X_407),skolemFOFtoCNF_C_1(wca,X_407),wca) )],[refute_0_5,refute_0_3]) ).
cnf(refute_0_7,plain,
( isa(wca,X_446)
| status(skolemFOFtoCNF_Ax_1(wca,X_446),skolemFOFtoCNF_C_1(wca,X_446),sca) ),
inference(subst,[],[refute_0_6:[bind(X_407,$fot(X_446))]]) ).
cnf(refute_0_8,plain,
( isa(wca,X_446)
| status(skolemFOFtoCNF_Ax_1(wca,X_446),skolemFOFtoCNF_C_1(wca,X_446),cax) ),
inference(resolve,[$cnf( status(skolemFOFtoCNF_Ax_1(wca,X_446),skolemFOFtoCNF_C_1(wca,X_446),sca) )],[refute_0_7,refute_0_1]) ).
cnf(refute_0_9,plain,
( isa(wca,thm)
| status(skolemFOFtoCNF_Ax_1(wca,thm),skolemFOFtoCNF_C_1(wca,thm),cax) ),
inference(subst,[],[refute_0_8:[bind(X_446,$fot(thm))]]) ).
cnf(refute_0_10,plain,
( ~ model(I1,Ax)
| ~ status(Ax,C,cax) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_11,plain,
( ~ model(skolemFOFtoCNF_I1_4(skolemFOFtoCNF_Ax_1(X_529,thm),skolemFOFtoCNF_Ax_1(X_529,thm)),skolemFOFtoCNF_Ax_1(X_529,thm))
| ~ status(skolemFOFtoCNF_Ax_1(X_529,thm),C,cax) ),
inference(subst,[],[refute_0_10:[bind(Ax,$fot(skolemFOFtoCNF_Ax_1(X_529,thm))),bind(I1,$fot(skolemFOFtoCNF_I1_4(skolemFOFtoCNF_Ax_1(X_529,thm),skolemFOFtoCNF_Ax_1(X_529,thm))))]]) ).
cnf(refute_0_12,plain,
( ~ status(Ax,C,sat)
| model(skolemFOFtoCNF_I1_4(Ax,C),Ax) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_13,plain,
( ~ status(skolemFOFtoCNF_Ax_1(X_404,thm),skolemFOFtoCNF_Ax_1(X_404,thm),sat)
| model(skolemFOFtoCNF_I1_4(skolemFOFtoCNF_Ax_1(X_404,thm),skolemFOFtoCNF_Ax_1(X_404,thm)),skolemFOFtoCNF_Ax_1(X_404,thm)) ),
inference(subst,[],[refute_0_12:[bind(Ax,$fot(skolemFOFtoCNF_Ax_1(X_404,thm))),bind(C,$fot(skolemFOFtoCNF_Ax_1(X_404,thm)))]]) ).
cnf(refute_0_14,plain,
( ~ model(I1,Ax)
| ~ model(I1,C)
| status(Ax,C,sat) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_15,plain,
( ~ model(skolemFOFtoCNF_I1_5(X_112,X_113),X_112)
| status(X_112,X_112,sat) ),
inference(subst,[],[refute_0_14:[bind(Ax,$fot(X_112)),bind(C,$fot(X_112)),bind(I1,$fot(skolemFOFtoCNF_I1_5(X_112,X_113)))]]) ).
cnf(refute_0_16,plain,
( model(skolemFOFtoCNF_I1_5(Ax,C),Ax)
| status(Ax,C,thm) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_17,plain,
( model(skolemFOFtoCNF_I1_5(X_112,X_113),X_112)
| status(X_112,X_113,thm) ),
inference(subst,[],[refute_0_16:[bind(Ax,$fot(X_112)),bind(C,$fot(X_113))]]) ).
cnf(refute_0_18,plain,
( status(X_112,X_112,sat)
| status(X_112,X_113,thm) ),
inference(resolve,[$cnf( model(skolemFOFtoCNF_I1_5(X_112,X_113),X_112) )],[refute_0_17,refute_0_15]) ).
cnf(refute_0_19,plain,
( status(skolemFOFtoCNF_Ax_1(X_394,thm),skolemFOFtoCNF_Ax_1(X_394,thm),sat)
| status(skolemFOFtoCNF_Ax_1(X_394,thm),skolemFOFtoCNF_C_1(X_394,thm),thm) ),
inference(subst,[],[refute_0_18:[bind(X_112,$fot(skolemFOFtoCNF_Ax_1(X_394,thm))),bind(X_113,$fot(skolemFOFtoCNF_C_1(X_394,thm)))]]) ).
cnf(refute_0_20,plain,
( ~ status(skolemFOFtoCNF_Ax_1(S1,S2),skolemFOFtoCNF_C_1(S1,S2),S2)
| isa(S1,S2) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_21,plain,
( ~ status(skolemFOFtoCNF_Ax_1(X_394,thm),skolemFOFtoCNF_C_1(X_394,thm),thm)
| isa(X_394,thm) ),
inference(subst,[],[refute_0_20:[bind(S1,$fot(X_394)),bind(S2,$fot(thm))]]) ).
cnf(refute_0_22,plain,
( isa(X_394,thm)
| status(skolemFOFtoCNF_Ax_1(X_394,thm),skolemFOFtoCNF_Ax_1(X_394,thm),sat) ),
inference(resolve,[$cnf( status(skolemFOFtoCNF_Ax_1(X_394,thm),skolemFOFtoCNF_C_1(X_394,thm),thm) )],[refute_0_19,refute_0_21]) ).
cnf(refute_0_23,plain,
( isa(X_404,thm)
| status(skolemFOFtoCNF_Ax_1(X_404,thm),skolemFOFtoCNF_Ax_1(X_404,thm),sat) ),
inference(subst,[],[refute_0_22:[bind(X_394,$fot(X_404))]]) ).
cnf(refute_0_24,plain,
( isa(X_404,thm)
| model(skolemFOFtoCNF_I1_4(skolemFOFtoCNF_Ax_1(X_404,thm),skolemFOFtoCNF_Ax_1(X_404,thm)),skolemFOFtoCNF_Ax_1(X_404,thm)) ),
inference(resolve,[$cnf( status(skolemFOFtoCNF_Ax_1(X_404,thm),skolemFOFtoCNF_Ax_1(X_404,thm),sat) )],[refute_0_23,refute_0_13]) ).
cnf(refute_0_25,plain,
( isa(X_529,thm)
| model(skolemFOFtoCNF_I1_4(skolemFOFtoCNF_Ax_1(X_529,thm),skolemFOFtoCNF_Ax_1(X_529,thm)),skolemFOFtoCNF_Ax_1(X_529,thm)) ),
inference(subst,[],[refute_0_24:[bind(X_404,$fot(X_529))]]) ).
cnf(refute_0_26,plain,
( ~ status(skolemFOFtoCNF_Ax_1(X_529,thm),C,cax)
| isa(X_529,thm) ),
inference(resolve,[$cnf( model(skolemFOFtoCNF_I1_4(skolemFOFtoCNF_Ax_1(X_529,thm),skolemFOFtoCNF_Ax_1(X_529,thm)),skolemFOFtoCNF_Ax_1(X_529,thm)) )],[refute_0_25,refute_0_11]) ).
cnf(refute_0_27,plain,
( ~ status(skolemFOFtoCNF_Ax_1(wca,thm),skolemFOFtoCNF_C_1(wca,thm),cax)
| isa(wca,thm) ),
inference(subst,[],[refute_0_26:[bind(C,$fot(skolemFOFtoCNF_C_1(wca,thm))),bind(X_529,$fot(wca))]]) ).
cnf(refute_0_28,plain,
isa(wca,thm),
inference(resolve,[$cnf( status(skolemFOFtoCNF_Ax_1(wca,thm),skolemFOFtoCNF_C_1(wca,thm),cax) )],[refute_0_9,refute_0_27]) ).
cnf(refute_0_29,plain,
~ isa(wca,thm),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_30,plain,
$false,
inference(resolve,[$cnf( isa(wca,thm) )],[refute_0_28,refute_0_29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS196+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n025.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 : Tue Jun 7 13:38:34 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.92/1.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.92/1.11
% 0.92/1.11 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.92/1.12
%------------------------------------------------------------------------------