%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KRS180+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 03:19:05 EDT 2022
% Result : Theorem 0.19s 0.38s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 68 ( 16 unt; 0 def)
% Number of atoms : 183 ( 0 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 206 ( 91 ~; 69 |; 21 &)
% ( 20 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 168 ( 26 sgn 92 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mighta,axiom,
! [S1,S2] :
( ? [Ax,C] :
( status(Ax,C,S1)
& status(Ax,C,S2) )
<=> mighta(S1,S2) ) ).
fof(isa,axiom,
! [S1,S2] :
( ! [Ax,C] :
( status(Ax,C,S1)
=> status(Ax,C,S2) )
<=> isa(S1,S2) ) ).
fof(nota,axiom,
! [S1,S2] :
( ? [Ax,C] :
( status(Ax,C,S1)
& ~ status(Ax,C,S2) )
<=> nota(S1,S2) ) ).
fof(nevera,axiom,
! [S1,S2] :
( ! [Ax,C] :
( status(Ax,C,S1)
=> ~ status(Ax,C,S2) )
<=> nevera(S1,S2) ) ).
fof(xora,axiom,
! [S1,S2] :
( ! [Ax,C] :
~ ( status(Ax,C,S1)
<=> status(Ax,C,S2) )
<=> xora(S1,S2) ) ).
fof(isa_exclusive,conjecture,
! [S1,S2] :
? [Ax,C] :
( status(Ax,C,S1)
=> ~ ( isa(S1,S2)
& ( nota(S1,S2)
| nevera(S1,S2)
| xora(S1,S2) ) ) ) ).
fof(subgoal_0,plain,
! [S1,S2] :
? [Ax,C] :
( status(Ax,C,S1)
=> ~ ( isa(S1,S2)
& ( nota(S1,S2)
| nevera(S1,S2)
| xora(S1,S2) ) ) ),
inference(strip,[],[isa_exclusive]) ).
fof(negate_0_0,plain,
~ ! [S1,S2] :
? [Ax,C] :
( status(Ax,C,S1)
=> ~ ( isa(S1,S2)
& ( nota(S1,S2)
| nevera(S1,S2)
| xora(S1,S2) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [S1,S2] :
( ~ nevera(S1,S2)
<=> ? [Ax,C] :
( status(Ax,C,S1)
& status(Ax,C,S2) ) ),
inference(canonicalize,[],[nevera]) ).
fof(normalize_0_1,plain,
! [S1,S2] :
( ~ mighta(S1,S2)
<=> ! [Ax,C] :
( ~ status(Ax,C,S1)
| ~ status(Ax,C,S2) ) ),
inference(canonicalize,[],[mighta]) ).
fof(normalize_0_2,plain,
! [S1,S2] :
( ~ mighta(S1,S2)
<=> ! [Ax,C] :
( ~ status(Ax,C,S1)
| ~ status(Ax,C,S2) ) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [S1,S2] :
( ~ mighta(S1,S2)
<=> nevera(S1,S2) ),
inference(simplify,[],[normalize_0_0,normalize_0_2]) ).
fof(normalize_0_4,plain,
! [S1,S2] :
( ~ mighta(S1,S2)
<=> nevera(S1,S2) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [S1,S2] :
( ( ~ mighta(S1,S2)
| ~ nevera(S1,S2) )
& ( mighta(S1,S2)
| nevera(S1,S2) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [S1,S2] :
( ~ mighta(S1,S2)
| ~ nevera(S1,S2) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [S1,S2] :
( ~ nota(S1,S2)
<=> ! [Ax,C] :
( ~ status(Ax,C,S1)
| status(Ax,C,S2) ) ),
inference(canonicalize,[],[nota]) ).
fof(normalize_0_8,plain,
! [S1,S2] :
( ~ isa(S1,S2)
<=> ? [Ax,C] :
( ~ status(Ax,C,S2)
& status(Ax,C,S1) ) ),
inference(canonicalize,[],[isa]) ).
fof(normalize_0_9,plain,
! [S1,S2] :
( ~ isa(S1,S2)
<=> ? [Ax,C] :
( ~ status(Ax,C,S2)
& status(Ax,C,S1) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [S1,S2] :
( ~ isa(S1,S2)
<=> nota(S1,S2) ),
inference(simplify,[],[normalize_0_7,normalize_0_9]) ).
fof(normalize_0_11,plain,
! [S1,S2] :
( ~ isa(S1,S2)
<=> nota(S1,S2) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [S1,S2] :
( ( ~ isa(S1,S2)
| ~ nota(S1,S2) )
& ( isa(S1,S2)
| nota(S1,S2) ) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [S1,S2] :
( ~ isa(S1,S2)
| ~ nota(S1,S2) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
? [S1,S2] :
( isa(S1,S2)
& ( nevera(S1,S2)
| nota(S1,S2)
| xora(S1,S2) )
& ! [Ax,C] : status(Ax,C,S1) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_15,plain,
( isa(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2)
& ( nevera(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2)
| nota(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2)
| xora(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2) )
& ! [Ax,C] : status(Ax,C,skolemFOFtoCNF_S1) ),
inference(skolemize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
( nevera(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2)
| nota(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2)
| xora(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2) ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [Ax,C] : status(Ax,C,skolemFOFtoCNF_S1),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_18,plain,
! [Ax,C] : status(Ax,C,skolemFOFtoCNF_S1),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
isa(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_20,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_9]) ).
fof(normalize_0_21,plain,
! [Ax,C,S1,S2] :
( ~ isa(S1,S2)
| ~ status(Ax,C,S1)
| status(Ax,C,S2) ),
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [S1,S2] :
( ~ xora(S1,S2)
<=> ? [Ax,C] :
( ~ status(Ax,C,S1)
<=> ~ status(Ax,C,S2) ) ),
inference(canonicalize,[],[xora]) ).
fof(normalize_0_23,plain,
! [S1,S2] :
( ~ xora(S1,S2)
<=> ? [Ax,C] :
( ~ status(Ax,C,S1)
<=> ~ status(Ax,C,S2) ) ),
inference(specialize,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [Ax,C,S1,S2] :
( ( ~ status(Ax,C,S1)
| ~ status(Ax,C,S2)
| ~ xora(S1,S2) )
& ( ~ status(skolemFOFtoCNF_Ax_2(S1,S2),skolemFOFtoCNF_C_2(S1,S2),S1)
| status(skolemFOFtoCNF_Ax_2(S1,S2),skolemFOFtoCNF_C_2(S1,S2),S2)
| xora(S1,S2) )
& ( ~ status(skolemFOFtoCNF_Ax_2(S1,S2),skolemFOFtoCNF_C_2(S1,S2),S2)
| status(skolemFOFtoCNF_Ax_2(S1,S2),skolemFOFtoCNF_C_2(S1,S2),S1)
| xora(S1,S2) )
& ( ~ xora(S1,S2)
| status(Ax,C,S1)
| status(Ax,C,S2) ) ),
inference(clausify,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [Ax,C,S1,S2] :
( ~ status(Ax,C,S1)
| ~ status(Ax,C,S2)
| ~ xora(S1,S2) ),
inference(conjunct,[],[normalize_0_24]) ).
fof(normalize_0_26,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_2]) ).
fof(normalize_0_27,plain,
! [Ax,C,S1,S2] :
( ~ status(Ax,C,S1)
| ~ status(Ax,C,S2)
| mighta(S1,S2) ),
inference(conjunct,[],[normalize_0_26]) ).
cnf(refute_0_0,plain,
( ~ mighta(S1,S2)
| ~ nevera(S1,S2) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_1,plain,
( ~ mighta(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2)
| ~ nevera(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2) ),
inference(subst,[],[refute_0_0:[bind(S1,$fot(skolemFOFtoCNF_S1)),bind(S2,$fot(skolemFOFtoCNF_S2))]]) ).
cnf(refute_0_2,plain,
( ~ isa(S1,S2)
| ~ nota(S1,S2) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_3,plain,
( ~ isa(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2)
| ~ nota(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2) ),
inference(subst,[],[refute_0_2:[bind(S1,$fot(skolemFOFtoCNF_S1)),bind(S2,$fot(skolemFOFtoCNF_S2))]]) ).
cnf(refute_0_4,plain,
( nevera(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2)
| nota(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2)
| xora(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_5,plain,
status(Ax,C,skolemFOFtoCNF_S1),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_6,plain,
status(X_93,X_94,skolemFOFtoCNF_S1),
inference(subst,[],[refute_0_5:[bind(Ax,$fot(X_93)),bind(C,$fot(X_94))]]) ).
cnf(refute_0_7,plain,
isa(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_8,plain,
status(X_57,X_58,skolemFOFtoCNF_S1),
inference(subst,[],[refute_0_5:[bind(Ax,$fot(X_57)),bind(C,$fot(X_58))]]) ).
cnf(refute_0_9,plain,
( ~ isa(S1,S2)
| ~ status(Ax,C,S1)
| status(Ax,C,S2) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_10,plain,
( ~ isa(skolemFOFtoCNF_S1,X_60)
| ~ status(X_57,X_58,skolemFOFtoCNF_S1)
| status(X_57,X_58,X_60) ),
inference(subst,[],[refute_0_9:[bind(Ax,$fot(X_57)),bind(C,$fot(X_58)),bind(S1,$fot(skolemFOFtoCNF_S1)),bind(S2,$fot(X_60))]]) ).
cnf(refute_0_11,plain,
( ~ isa(skolemFOFtoCNF_S1,X_60)
| status(X_57,X_58,X_60) ),
inference(resolve,[$cnf( status(X_57,X_58,skolemFOFtoCNF_S1) )],[refute_0_8,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ isa(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2)
| status(X_61,X_62,skolemFOFtoCNF_S2) ),
inference(subst,[],[refute_0_11:[bind(X_57,$fot(X_61)),bind(X_58,$fot(X_62)),bind(X_60,$fot(skolemFOFtoCNF_S2))]]) ).
cnf(refute_0_13,plain,
status(X_61,X_62,skolemFOFtoCNF_S2),
inference(resolve,[$cnf( isa(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2) )],[refute_0_7,refute_0_12]) ).
cnf(refute_0_14,plain,
status(X_84,X_85,skolemFOFtoCNF_S2),
inference(subst,[],[refute_0_13:[bind(X_61,$fot(X_84)),bind(X_62,$fot(X_85))]]) ).
cnf(refute_0_15,plain,
( ~ status(Ax,C,S1)
| ~ status(Ax,C,S2)
| ~ xora(S1,S2) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_16,plain,
( ~ status(X_84,X_85,X_86)
| ~ status(X_84,X_85,skolemFOFtoCNF_S2)
| ~ xora(X_86,skolemFOFtoCNF_S2) ),
inference(subst,[],[refute_0_15:[bind(Ax,$fot(X_84)),bind(C,$fot(X_85)),bind(S1,$fot(X_86)),bind(S2,$fot(skolemFOFtoCNF_S2))]]) ).
cnf(refute_0_17,plain,
( ~ status(X_84,X_85,X_86)
| ~ xora(X_86,skolemFOFtoCNF_S2) ),
inference(resolve,[$cnf( status(X_84,X_85,skolemFOFtoCNF_S2) )],[refute_0_14,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ status(X_93,X_94,skolemFOFtoCNF_S1)
| ~ xora(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2) ),
inference(subst,[],[refute_0_17:[bind(X_84,$fot(X_93)),bind(X_85,$fot(X_94)),bind(X_86,$fot(skolemFOFtoCNF_S1))]]) ).
cnf(refute_0_19,plain,
~ xora(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2),
inference(resolve,[$cnf( status(X_93,X_94,skolemFOFtoCNF_S1) )],[refute_0_6,refute_0_18]) ).
cnf(refute_0_20,plain,
( nevera(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2)
| nota(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2) ),
inference(resolve,[$cnf( xora(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2) )],[refute_0_4,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ isa(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2)
| nevera(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2) ),
inference(resolve,[$cnf( nota(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2) )],[refute_0_20,refute_0_3]) ).
cnf(refute_0_22,plain,
nevera(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2),
inference(resolve,[$cnf( isa(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2) )],[refute_0_7,refute_0_21]) ).
cnf(refute_0_23,plain,
~ mighta(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2),
inference(resolve,[$cnf( nevera(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2) )],[refute_0_22,refute_0_1]) ).
cnf(refute_0_24,plain,
status(X_39,X_40,skolemFOFtoCNF_S1),
inference(subst,[],[refute_0_5:[bind(Ax,$fot(X_39)),bind(C,$fot(X_40))]]) ).
cnf(refute_0_25,plain,
( ~ status(Ax,C,S1)
| ~ status(Ax,C,S2)
| mighta(S1,S2) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_26,plain,
( ~ status(X_39,X_40,X_42)
| ~ status(X_39,X_40,skolemFOFtoCNF_S1)
| mighta(skolemFOFtoCNF_S1,X_42) ),
inference(subst,[],[refute_0_25:[bind(Ax,$fot(X_39)),bind(C,$fot(X_40)),bind(S1,$fot(skolemFOFtoCNF_S1)),bind(S2,$fot(X_42))]]) ).
cnf(refute_0_27,plain,
( ~ status(X_39,X_40,X_42)
| mighta(skolemFOFtoCNF_S1,X_42) ),
inference(resolve,[$cnf( status(X_39,X_40,skolemFOFtoCNF_S1) )],[refute_0_24,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ status(X_64,X_65,skolemFOFtoCNF_S2)
| mighta(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2) ),
inference(subst,[],[refute_0_27:[bind(X_39,$fot(X_64)),bind(X_40,$fot(X_65)),bind(X_42,$fot(skolemFOFtoCNF_S2))]]) ).
cnf(refute_0_29,plain,
status(X_64,X_65,skolemFOFtoCNF_S2),
inference(subst,[],[refute_0_13:[bind(X_61,$fot(X_64)),bind(X_62,$fot(X_65))]]) ).
cnf(refute_0_30,plain,
mighta(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2),
inference(resolve,[$cnf( status(X_64,X_65,skolemFOFtoCNF_S2) )],[refute_0_29,refute_0_28]) ).
cnf(refute_0_31,plain,
$false,
inference(resolve,[$cnf( mighta(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2) )],[refute_0_30,refute_0_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS180+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 7 11:31:46 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.38
% 0.19/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.39
%------------------------------------------------------------------------------