%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KRS235+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 03:19:13 EDT 2022
% Result : Theorem 63.56s 63.75s
% Output : CNFRefutation 63.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 61 ( 13 unt; 0 def)
% Number of atoms : 155 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 177 ( 83 ~; 55 |; 17 &)
% ( 20 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 108 ( 0 sgn 82 !; 9 ?)
% 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(noc,axiom,
! [Ax,C] :
( ( ? [I1] :
( model(I1,Ax)
& model(I1,C) )
& ? [I2] :
( model(I2,Ax)
& model(I2,not(C)) ) )
<=> status(Ax,C,noc) ) ).
fof(mighta,axiom,
! [S1,S2] :
( ? [Ax,C] :
( status(Ax,C,S1)
& status(Ax,C,S2) )
<=> mighta(S1,S2) ) ).
fof(nevera,axiom,
! [S1,S2] :
( ! [Ax,C] :
( status(Ax,C,S1)
=> ~ status(Ax,C,S2) )
<=> nevera(S1,S2) ) ).
fof(completeness,axiom,
! [I,F] :
~ ( model(I,F)
<=> model(I,not(F)) ) ).
fof(nevera_noc_thm,conjecture,
nevera(noc,thm) ).
fof(subgoal_0,plain,
nevera(noc,thm),
inference(strip,[],[nevera_noc_thm]) ).
fof(negate_0_0,plain,
~ nevera(noc,thm),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [Ax,C] :
( ~ status(Ax,C,noc)
<=> ( ! [I1] :
( ~ model(I1,Ax)
| ~ model(I1,C) )
| ! [I2] :
( ~ model(I2,Ax)
| ~ model(I2,not(C)) ) ) ),
inference(canonicalize,[],[noc]) ).
fof(normalize_0_1,plain,
! [Ax,C] :
( ~ status(Ax,C,sat)
<=> ! [I1] :
( ~ model(I1,Ax)
| ~ model(I1,C) ) ),
inference(canonicalize,[],[sat]) ).
fof(normalize_0_2,plain,
! [Ax,C] :
( ~ status(Ax,C,sat)
<=> ! [I1] :
( ~ model(I1,Ax)
| ~ model(I1,C) ) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [Ax,C] :
( ~ status(Ax,C,noc)
<=> ( ~ status(Ax,C,sat)
| ! [I2] :
( ~ model(I2,Ax)
| ~ model(I2,not(C)) ) ) ),
inference(simplify,[],[normalize_0_0,normalize_0_2]) ).
fof(normalize_0_4,plain,
! [Ax,C] :
( ~ status(Ax,C,noc)
<=> ( ~ status(Ax,C,sat)
| ! [I2] :
( ~ model(I2,Ax)
| ~ model(I2,not(C)) ) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [Ax,C,I2] :
( ( ~ status(Ax,C,noc)
| model(skolemFOFtoCNF_I2_12(Ax,C),Ax) )
& ( ~ status(Ax,C,noc)
| model(skolemFOFtoCNF_I2_12(Ax,C),not(C)) )
& ( ~ status(Ax,C,noc)
| status(Ax,C,sat) )
& ( ~ model(I2,Ax)
| ~ model(I2,not(C))
| ~ status(Ax,C,sat)
| status(Ax,C,noc) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [Ax,C] :
( ~ status(Ax,C,noc)
| model(skolemFOFtoCNF_I2_12(Ax,C),Ax) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
~ nevera(noc,thm),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_8,plain,
! [S1,S2] :
( ~ nevera(S1,S2)
<=> ? [Ax,C] :
( status(Ax,C,S1)
& status(Ax,C,S2) ) ),
inference(canonicalize,[],[nevera]) ).
fof(normalize_0_9,plain,
! [S1,S2] :
( ~ mighta(S1,S2)
<=> ! [Ax,C] :
( ~ status(Ax,C,S1)
| ~ status(Ax,C,S2) ) ),
inference(canonicalize,[],[mighta]) ).
fof(normalize_0_10,plain,
! [S1,S2] :
( ~ mighta(S1,S2)
<=> ! [Ax,C] :
( ~ status(Ax,C,S1)
| ~ status(Ax,C,S2) ) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [S1,S2] :
( ~ mighta(S1,S2)
<=> nevera(S1,S2) ),
inference(simplify,[],[normalize_0_8,normalize_0_10]) ).
fof(normalize_0_12,plain,
! [S1,S2] :
( ~ mighta(S1,S2)
<=> nevera(S1,S2) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [S1,S2] :
( ( ~ mighta(S1,S2)
| ~ nevera(S1,S2) )
& ( mighta(S1,S2)
| nevera(S1,S2) ) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [S1,S2] :
( mighta(S1,S2)
| nevera(S1,S2) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [Ax,C,S1,S2] :
( ( ~ mighta(S1,S2)
| status(skolemFOFtoCNF_Ax(S1,S2),skolemFOFtoCNF_C(S1,S2),S1) )
& ( ~ mighta(S1,S2)
| status(skolemFOFtoCNF_Ax(S1,S2),skolemFOFtoCNF_C(S1,S2),S2) )
& ( ~ status(Ax,C,S1)
| ~ status(Ax,C,S2)
| mighta(S1,S2) ) ),
inference(clausify,[],[normalize_0_10]) ).
fof(normalize_0_16,plain,
! [S1,S2] :
( ~ mighta(S1,S2)
| status(skolemFOFtoCNF_Ax(S1,S2),skolemFOFtoCNF_C(S1,S2),S1) ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [S1,S2] :
( ~ mighta(S1,S2)
| status(skolemFOFtoCNF_Ax(S1,S2),skolemFOFtoCNF_C(S1,S2),S2) ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_18,plain,
! [Ax,C] :
( ~ status(Ax,C,thm)
<=> ? [I1] :
( ~ model(I1,C)
& model(I1,Ax) ) ),
inference(canonicalize,[],[thm]) ).
fof(normalize_0_19,plain,
! [Ax,C] :
( ~ status(Ax,C,thm)
<=> ? [I1] :
( ~ model(I1,C)
& model(I1,Ax) ) ),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,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_19]) ).
fof(normalize_0_21,plain,
! [Ax,C,I1] :
( ~ model(I1,Ax)
| ~ status(Ax,C,thm)
| model(I1,C) ),
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [F,I] :
( ~ model(I,F)
<=> model(I,not(F)) ),
inference(canonicalize,[],[completeness]) ).
fof(normalize_0_23,plain,
! [F,I] :
( ~ model(I,F)
<=> model(I,not(F)) ),
inference(specialize,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [F,I] :
( ( ~ model(I,F)
| ~ model(I,not(F)) )
& ( model(I,F)
| model(I,not(F)) ) ),
inference(clausify,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [F,I] :
( ~ model(I,F)
| ~ model(I,not(F)) ),
inference(conjunct,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [Ax,C] :
( ~ status(Ax,C,noc)
| model(skolemFOFtoCNF_I2_12(Ax,C),not(C)) ),
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
( ~ status(Ax,C,noc)
| model(skolemFOFtoCNF_I2_12(Ax,C),Ax) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_1,plain,
( ~ status(skolemFOFtoCNF_Ax(noc,thm),skolemFOFtoCNF_C(noc,thm),noc)
| model(skolemFOFtoCNF_I2_12(skolemFOFtoCNF_Ax(noc,thm),skolemFOFtoCNF_C(noc,thm)),skolemFOFtoCNF_Ax(noc,thm)) ),
inference(subst,[],[refute_0_0:[bind(Ax,$fot(skolemFOFtoCNF_Ax(noc,thm))),bind(C,$fot(skolemFOFtoCNF_C(noc,thm)))]]) ).
cnf(refute_0_2,plain,
~ nevera(noc,thm),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( mighta(S1,S2)
| nevera(S1,S2) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_4,plain,
( mighta(noc,thm)
| nevera(noc,thm) ),
inference(subst,[],[refute_0_3:[bind(S1,$fot(noc)),bind(S2,$fot(thm))]]) ).
cnf(refute_0_5,plain,
mighta(noc,thm),
inference(resolve,[$cnf( nevera(noc,thm) )],[refute_0_4,refute_0_2]) ).
cnf(refute_0_6,plain,
( ~ mighta(S1,S2)
| status(skolemFOFtoCNF_Ax(S1,S2),skolemFOFtoCNF_C(S1,S2),S1) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_7,plain,
( ~ mighta(noc,thm)
| status(skolemFOFtoCNF_Ax(noc,thm),skolemFOFtoCNF_C(noc,thm),noc) ),
inference(subst,[],[refute_0_6:[bind(S1,$fot(noc)),bind(S2,$fot(thm))]]) ).
cnf(refute_0_8,plain,
status(skolemFOFtoCNF_Ax(noc,thm),skolemFOFtoCNF_C(noc,thm),noc),
inference(resolve,[$cnf( mighta(noc,thm) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
model(skolemFOFtoCNF_I2_12(skolemFOFtoCNF_Ax(noc,thm),skolemFOFtoCNF_C(noc,thm)),skolemFOFtoCNF_Ax(noc,thm)),
inference(resolve,[$cnf( status(skolemFOFtoCNF_Ax(noc,thm),skolemFOFtoCNF_C(noc,thm),noc) )],[refute_0_8,refute_0_1]) ).
cnf(refute_0_10,plain,
( ~ mighta(S1,S2)
| status(skolemFOFtoCNF_Ax(S1,S2),skolemFOFtoCNF_C(S1,S2),S2) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_11,plain,
( ~ mighta(noc,thm)
| status(skolemFOFtoCNF_Ax(noc,thm),skolemFOFtoCNF_C(noc,thm),thm) ),
inference(subst,[],[refute_0_10:[bind(S1,$fot(noc)),bind(S2,$fot(thm))]]) ).
cnf(refute_0_12,plain,
status(skolemFOFtoCNF_Ax(noc,thm),skolemFOFtoCNF_C(noc,thm),thm),
inference(resolve,[$cnf( mighta(noc,thm) )],[refute_0_5,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ model(I1,Ax)
| ~ status(Ax,C,thm)
| model(I1,C) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_14,plain,
( ~ model(X_5198,skolemFOFtoCNF_Ax(noc,thm))
| ~ status(skolemFOFtoCNF_Ax(noc,thm),skolemFOFtoCNF_C(noc,thm),thm)
| model(X_5198,skolemFOFtoCNF_C(noc,thm)) ),
inference(subst,[],[refute_0_13:[bind(Ax,$fot(skolemFOFtoCNF_Ax(noc,thm))),bind(C,$fot(skolemFOFtoCNF_C(noc,thm))),bind(I1,$fot(X_5198))]]) ).
cnf(refute_0_15,plain,
( ~ model(X_5198,skolemFOFtoCNF_Ax(noc,thm))
| model(X_5198,skolemFOFtoCNF_C(noc,thm)) ),
inference(resolve,[$cnf( status(skolemFOFtoCNF_Ax(noc,thm),skolemFOFtoCNF_C(noc,thm),thm) )],[refute_0_12,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ model(skolemFOFtoCNF_I2_12(skolemFOFtoCNF_Ax(noc,thm),skolemFOFtoCNF_C(noc,thm)),skolemFOFtoCNF_Ax(noc,thm))
| model(skolemFOFtoCNF_I2_12(skolemFOFtoCNF_Ax(noc,thm),skolemFOFtoCNF_C(noc,thm)),skolemFOFtoCNF_C(noc,thm)) ),
inference(subst,[],[refute_0_15:[bind(X_5198,$fot(skolemFOFtoCNF_I2_12(skolemFOFtoCNF_Ax(noc,thm),skolemFOFtoCNF_C(noc,thm))))]]) ).
cnf(refute_0_17,plain,
model(skolemFOFtoCNF_I2_12(skolemFOFtoCNF_Ax(noc,thm),skolemFOFtoCNF_C(noc,thm)),skolemFOFtoCNF_C(noc,thm)),
inference(resolve,[$cnf( model(skolemFOFtoCNF_I2_12(skolemFOFtoCNF_Ax(noc,thm),skolemFOFtoCNF_C(noc,thm)),skolemFOFtoCNF_Ax(noc,thm)) )],[refute_0_9,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ model(I,F)
| ~ model(I,not(F)) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_19,plain,
( ~ model(skolemFOFtoCNF_I2_12(skolemFOFtoCNF_Ax(noc,thm),skolemFOFtoCNF_C(noc,thm)),not(skolemFOFtoCNF_C(noc,thm)))
| ~ model(skolemFOFtoCNF_I2_12(skolemFOFtoCNF_Ax(noc,thm),skolemFOFtoCNF_C(noc,thm)),skolemFOFtoCNF_C(noc,thm)) ),
inference(subst,[],[refute_0_18:[bind(F,$fot(skolemFOFtoCNF_C(noc,thm))),bind(I,$fot(skolemFOFtoCNF_I2_12(skolemFOFtoCNF_Ax(noc,thm),skolemFOFtoCNF_C(noc,thm))))]]) ).
cnf(refute_0_20,plain,
( ~ status(Ax,C,noc)
| model(skolemFOFtoCNF_I2_12(Ax,C),not(C)) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_21,plain,
( ~ status(skolemFOFtoCNF_Ax(noc,thm),skolemFOFtoCNF_C(noc,thm),noc)
| model(skolemFOFtoCNF_I2_12(skolemFOFtoCNF_Ax(noc,thm),skolemFOFtoCNF_C(noc,thm)),not(skolemFOFtoCNF_C(noc,thm))) ),
inference(subst,[],[refute_0_20:[bind(Ax,$fot(skolemFOFtoCNF_Ax(noc,thm))),bind(C,$fot(skolemFOFtoCNF_C(noc,thm)))]]) ).
cnf(refute_0_22,plain,
model(skolemFOFtoCNF_I2_12(skolemFOFtoCNF_Ax(noc,thm),skolemFOFtoCNF_C(noc,thm)),not(skolemFOFtoCNF_C(noc,thm))),
inference(resolve,[$cnf( status(skolemFOFtoCNF_Ax(noc,thm),skolemFOFtoCNF_C(noc,thm),noc) )],[refute_0_8,refute_0_21]) ).
cnf(refute_0_23,plain,
~ model(skolemFOFtoCNF_I2_12(skolemFOFtoCNF_Ax(noc,thm),skolemFOFtoCNF_C(noc,thm)),skolemFOFtoCNF_C(noc,thm)),
inference(resolve,[$cnf( model(skolemFOFtoCNF_I2_12(skolemFOFtoCNF_Ax(noc,thm),skolemFOFtoCNF_C(noc,thm)),not(skolemFOFtoCNF_C(noc,thm))) )],[refute_0_22,refute_0_19]) ).
cnf(refute_0_24,plain,
$false,
inference(resolve,[$cnf( model(skolemFOFtoCNF_I2_12(skolemFOFtoCNF_Ax(noc,thm),skolemFOFtoCNF_C(noc,thm)),skolemFOFtoCNF_C(noc,thm)) )],[refute_0_17,refute_0_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : KRS235+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.10/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n029.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 15:39:50 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 63.56/63.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 63.56/63.75
% 63.56/63.75 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 63.56/63.76
%------------------------------------------------------------------------------