TSTP Solution File: LAT382+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LAT382+1 : TPTP v8.1.0. Released v4.0.0.
% 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 06:03:38 EDT 2022
% Result : Theorem 1.77s 1.97s
% Output : CNFRefutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 76 ( 25 unt; 1 def)
% Number of atoms : 228 ( 14 equ)
% Maximal formula atoms : 25 ( 3 avg)
% Number of connectives : 288 ( 136 ~; 130 |; 12 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 62 ( 0 sgn 38 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mEOfElem,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ) ).
fof(mASymm,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> W0 = W1 ) ) ).
fof(mDefInf,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
=> ! [W2] :
( aInfimumOfIn0(W2,W1,W0)
<=> ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3] :
( aLowerBoundOfIn0(W3,W1,W0)
=> sdtlseqdt0(W3,W2) ) ) ) ) ) ).
fof(m__773,hypothesis,
aSet0(xT) ).
fof(m__773_01,hypothesis,
aSubsetOf0(xS,xT) ).
fof(m__792,hypothesis,
( aInfimumOfIn0(xu,xS,xT)
& aInfimumOfIn0(xv,xS,xT) ) ).
fof(m__,conjecture,
xu = xv ).
fof(subgoal_0,plain,
xu = xv,
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
xu != xv,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [W0,W1] :
( ~ aElement0(W0)
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| W0 = W1 ),
inference(canonicalize,[],[mASymm]) ).
fof(normalize_0_1,plain,
! [W0,W1] :
( ~ aElement0(W0)
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| W0 = W1 ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( aInfimumOfIn0(xu,xS,xT)
& aInfimumOfIn0(xv,xS,xT) ),
inference(canonicalize,[],[m__792]) ).
fof(normalize_0_3,plain,
aInfimumOfIn0(xu,xS,xT),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
aInfimumOfIn0(xv,xS,xT),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_5,plain,
! [W0] :
( ~ aSet0(W0)
| ! [W1] :
( ~ aSubsetOf0(W1,W0)
| ! [W2] :
( ~ aInfimumOfIn0(W2,W1,W0)
<=> ( ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ? [W3] :
( ~ sdtlseqdt0(W3,W2)
& aLowerBoundOfIn0(W3,W1,W0) ) ) ) ) ),
inference(canonicalize,[],[mDefInf]) ).
fof(normalize_0_6,plain,
! [W0] :
( ~ aSet0(W0)
| ! [W1] :
( ~ aSubsetOf0(W1,W0)
| ! [W2] :
( ~ aInfimumOfIn0(W2,W1,W0)
<=> ( ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ? [W3] :
( ~ sdtlseqdt0(W3,W2)
& aLowerBoundOfIn0(W3,W1,W0) ) ) ) ) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [W0,W1,W2,W3] :
( ( ~ aInfimumOfIn0(W2,W1,W0)
| ~ aSet0(W0)
| ~ aSubsetOf0(W1,W0)
| aElementOf0(W2,W0) )
& ( ~ aInfimumOfIn0(W2,W1,W0)
| ~ aSet0(W0)
| ~ aSubsetOf0(W1,W0)
| aLowerBoundOfIn0(W2,W1,W0) )
& ( ~ aInfimumOfIn0(W2,W1,W0)
| ~ aLowerBoundOfIn0(W3,W1,W0)
| ~ aSet0(W0)
| ~ aSubsetOf0(W1,W0)
| sdtlseqdt0(W3,W2) )
& ( ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ aSet0(W0)
| ~ aSubsetOf0(W1,W0)
| ~ sdtlseqdt0(skolemFOFtoCNF_W3_2(W0,W1,W2),W2)
| aInfimumOfIn0(W2,W1,W0) )
& ( ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ aSet0(W0)
| ~ aSubsetOf0(W1,W0)
| aInfimumOfIn0(W2,W1,W0)
| aLowerBoundOfIn0(skolemFOFtoCNF_W3_2(W0,W1,W2),W1,W0) ) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [W0,W1,W2] :
( ~ aInfimumOfIn0(W2,W1,W0)
| ~ aSet0(W0)
| ~ aSubsetOf0(W1,W0)
| aLowerBoundOfIn0(W2,W1,W0) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
aSet0(xT),
inference(canonicalize,[],[m__773]) ).
fof(normalize_0_10,plain,
aSubsetOf0(xS,xT),
inference(canonicalize,[],[m__773_01]) ).
fof(normalize_0_11,plain,
! [W0,W1,W2,W3] :
( ~ aInfimumOfIn0(W2,W1,W0)
| ~ aLowerBoundOfIn0(W3,W1,W0)
| ~ aSet0(W0)
| ~ aSubsetOf0(W1,W0)
| sdtlseqdt0(W3,W2) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_12,plain,
! [W0] :
( ~ aSet0(W0)
| ! [W1] :
( ~ aElementOf0(W1,W0)
| aElement0(W1) ) ),
inference(canonicalize,[],[mEOfElem]) ).
fof(normalize_0_13,plain,
! [W0] :
( ~ aSet0(W0)
| ! [W1] :
( ~ aElementOf0(W1,W0)
| aElement0(W1) ) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [W0,W1] :
( ~ aElementOf0(W1,W0)
| ~ aSet0(W0)
| aElement0(W1) ),
inference(clausify,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [W0,W1,W2] :
( ~ aInfimumOfIn0(W2,W1,W0)
| ~ aSet0(W0)
| ~ aSubsetOf0(W1,W0)
| aElementOf0(W2,W0) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_16,plain,
xu != xv,
inference(canonicalize,[],[negate_0_0]) ).
cnf(refute_0_0,plain,
( ~ aElement0(W0)
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| W0 = W1 ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ aElement0(xu)
| ~ aElement0(xv)
| ~ sdtlseqdt0(xu,xv)
| ~ sdtlseqdt0(xv,xu)
| xu = xv ),
inference(subst,[],[refute_0_0:[bind(W0,$fot(xu)),bind(W1,$fot(xv))]]) ).
cnf(refute_0_2,plain,
aInfimumOfIn0(xu,xS,xT),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
aInfimumOfIn0(xv,xS,xT),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_4,plain,
( ~ aInfimumOfIn0(W2,W1,W0)
| ~ aSet0(W0)
| ~ aSubsetOf0(W1,W0)
| aLowerBoundOfIn0(W2,W1,W0) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( ~ aInfimumOfIn0(xv,xS,xT)
| ~ aSet0(xT)
| ~ aSubsetOf0(xS,xT)
| aLowerBoundOfIn0(xv,xS,xT) ),
inference(subst,[],[refute_0_4:[bind(W0,$fot(xT)),bind(W1,$fot(xS)),bind(W2,$fot(xv))]]) ).
cnf(refute_0_6,plain,
( ~ aSet0(xT)
| ~ aSubsetOf0(xS,xT)
| aLowerBoundOfIn0(xv,xS,xT) ),
inference(resolve,[$cnf( aInfimumOfIn0(xv,xS,xT) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
aSet0(xT),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_8,plain,
( ~ aSubsetOf0(xS,xT)
| aLowerBoundOfIn0(xv,xS,xT) ),
inference(resolve,[$cnf( aSet0(xT) )],[refute_0_7,refute_0_6]) ).
cnf(refute_0_9,plain,
aSubsetOf0(xS,xT),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_10,plain,
aLowerBoundOfIn0(xv,xS,xT),
inference(resolve,[$cnf( aSubsetOf0(xS,xT) )],[refute_0_9,refute_0_8]) ).
cnf(refute_0_11,plain,
( ~ aInfimumOfIn0(W2,W1,W0)
| ~ aLowerBoundOfIn0(W3,W1,W0)
| ~ aSet0(W0)
| ~ aSubsetOf0(W1,W0)
| sdtlseqdt0(W3,W2) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_12,plain,
( ~ aInfimumOfIn0(X_148,xS,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| ~ aSet0(xT)
| ~ aSubsetOf0(xS,xT)
| sdtlseqdt0(xv,X_148) ),
inference(subst,[],[refute_0_11:[bind(W0,$fot(xT)),bind(W1,$fot(xS)),bind(W2,$fot(X_148)),bind(W3,$fot(xv))]]) ).
cnf(refute_0_13,plain,
( ~ aInfimumOfIn0(X_148,xS,xT)
| ~ aSet0(xT)
| ~ aSubsetOf0(xS,xT)
| sdtlseqdt0(xv,X_148) ),
inference(resolve,[$cnf( aLowerBoundOfIn0(xv,xS,xT) )],[refute_0_10,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ aInfimumOfIn0(X_148,xS,xT)
| ~ aSubsetOf0(xS,xT)
| sdtlseqdt0(xv,X_148) ),
inference(resolve,[$cnf( aSet0(xT) )],[refute_0_7,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ aInfimumOfIn0(X_148,xS,xT)
| sdtlseqdt0(xv,X_148) ),
inference(resolve,[$cnf( aSubsetOf0(xS,xT) )],[refute_0_9,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ aInfimumOfIn0(xu,xS,xT)
| sdtlseqdt0(xv,xu) ),
inference(subst,[],[refute_0_15:[bind(X_148,$fot(xu))]]) ).
cnf(refute_0_17,plain,
sdtlseqdt0(xv,xu),
inference(resolve,[$cnf( aInfimumOfIn0(xu,xS,xT) )],[refute_0_2,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ aElement0(xu)
| ~ aElement0(xv)
| ~ sdtlseqdt0(xu,xv)
| xu = xv ),
inference(resolve,[$cnf( sdtlseqdt0(xv,xu) )],[refute_0_17,refute_0_1]) ).
cnf(refute_0_19,plain,
( ~ aElementOf0(W1,W0)
| ~ aSet0(W0)
| aElement0(W1) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_20,plain,
( ~ aElementOf0(xu,xT)
| ~ aSet0(xT)
| aElement0(xu) ),
inference(subst,[],[refute_0_19:[bind(W0,$fot(xT)),bind(W1,$fot(xu))]]) ).
cnf(refute_0_21,plain,
( ~ aInfimumOfIn0(W2,W1,W0)
| ~ aSet0(W0)
| ~ aSubsetOf0(W1,W0)
| aElementOf0(W2,W0) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_22,plain,
( ~ aInfimumOfIn0(xu,xS,xT)
| ~ aSet0(xT)
| ~ aSubsetOf0(xS,xT)
| aElementOf0(xu,xT) ),
inference(subst,[],[refute_0_21:[bind(W0,$fot(xT)),bind(W1,$fot(xS)),bind(W2,$fot(xu))]]) ).
cnf(refute_0_23,plain,
( ~ aSet0(xT)
| ~ aSubsetOf0(xS,xT)
| aElementOf0(xu,xT) ),
inference(resolve,[$cnf( aInfimumOfIn0(xu,xS,xT) )],[refute_0_2,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ aSubsetOf0(xS,xT)
| aElementOf0(xu,xT) ),
inference(resolve,[$cnf( aSet0(xT) )],[refute_0_7,refute_0_23]) ).
cnf(refute_0_25,plain,
aElementOf0(xu,xT),
inference(resolve,[$cnf( aSubsetOf0(xS,xT) )],[refute_0_9,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ aSet0(xT)
| aElement0(xu) ),
inference(resolve,[$cnf( aElementOf0(xu,xT) )],[refute_0_25,refute_0_20]) ).
cnf(refute_0_27,plain,
aElement0(xu),
inference(resolve,[$cnf( aSet0(xT) )],[refute_0_7,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ aElement0(xv)
| ~ sdtlseqdt0(xu,xv)
| xu = xv ),
inference(resolve,[$cnf( aElement0(xu) )],[refute_0_27,refute_0_18]) ).
cnf(refute_0_29,plain,
( ~ aElementOf0(xv,xT)
| ~ aSet0(xT)
| aElement0(xv) ),
inference(subst,[],[refute_0_19:[bind(W0,$fot(xT)),bind(W1,$fot(xv))]]) ).
cnf(refute_0_30,plain,
( ~ aInfimumOfIn0(xv,xS,xT)
| ~ aSet0(xT)
| ~ aSubsetOf0(xS,xT)
| aElementOf0(xv,xT) ),
inference(subst,[],[refute_0_21:[bind(W0,$fot(xT)),bind(W1,$fot(xS)),bind(W2,$fot(xv))]]) ).
cnf(refute_0_31,plain,
( ~ aSet0(xT)
| ~ aSubsetOf0(xS,xT)
| aElementOf0(xv,xT) ),
inference(resolve,[$cnf( aInfimumOfIn0(xv,xS,xT) )],[refute_0_3,refute_0_30]) ).
cnf(refute_0_32,plain,
( ~ aSubsetOf0(xS,xT)
| aElementOf0(xv,xT) ),
inference(resolve,[$cnf( aSet0(xT) )],[refute_0_7,refute_0_31]) ).
cnf(refute_0_33,plain,
aElementOf0(xv,xT),
inference(resolve,[$cnf( aSubsetOf0(xS,xT) )],[refute_0_9,refute_0_32]) ).
cnf(refute_0_34,plain,
( ~ aSet0(xT)
| aElement0(xv) ),
inference(resolve,[$cnf( aElementOf0(xv,xT) )],[refute_0_33,refute_0_29]) ).
cnf(refute_0_35,plain,
aElement0(xv),
inference(resolve,[$cnf( aSet0(xT) )],[refute_0_7,refute_0_34]) ).
cnf(refute_0_36,plain,
( ~ sdtlseqdt0(xu,xv)
| xu = xv ),
inference(resolve,[$cnf( aElement0(xv) )],[refute_0_35,refute_0_28]) ).
cnf(refute_0_37,plain,
( ~ aInfimumOfIn0(xu,xS,xT)
| ~ aSet0(xT)
| ~ aSubsetOf0(xS,xT)
| aLowerBoundOfIn0(xu,xS,xT) ),
inference(subst,[],[refute_0_4:[bind(W0,$fot(xT)),bind(W1,$fot(xS)),bind(W2,$fot(xu))]]) ).
cnf(refute_0_38,plain,
( ~ aSet0(xT)
| ~ aSubsetOf0(xS,xT)
| aLowerBoundOfIn0(xu,xS,xT) ),
inference(resolve,[$cnf( aInfimumOfIn0(xu,xS,xT) )],[refute_0_2,refute_0_37]) ).
cnf(refute_0_39,plain,
( ~ aSubsetOf0(xS,xT)
| aLowerBoundOfIn0(xu,xS,xT) ),
inference(resolve,[$cnf( aSet0(xT) )],[refute_0_7,refute_0_38]) ).
cnf(refute_0_40,plain,
aLowerBoundOfIn0(xu,xS,xT),
inference(resolve,[$cnf( aSubsetOf0(xS,xT) )],[refute_0_9,refute_0_39]) ).
cnf(refute_0_41,plain,
( ~ aInfimumOfIn0(X_148,xS,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| ~ aSet0(xT)
| ~ aSubsetOf0(xS,xT)
| sdtlseqdt0(xu,X_148) ),
inference(subst,[],[refute_0_11:[bind(W0,$fot(xT)),bind(W1,$fot(xS)),bind(W2,$fot(X_148)),bind(W3,$fot(xu))]]) ).
cnf(refute_0_42,plain,
( ~ aInfimumOfIn0(X_148,xS,xT)
| ~ aSet0(xT)
| ~ aSubsetOf0(xS,xT)
| sdtlseqdt0(xu,X_148) ),
inference(resolve,[$cnf( aLowerBoundOfIn0(xu,xS,xT) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
( ~ aInfimumOfIn0(X_148,xS,xT)
| ~ aSubsetOf0(xS,xT)
| sdtlseqdt0(xu,X_148) ),
inference(resolve,[$cnf( aSet0(xT) )],[refute_0_7,refute_0_42]) ).
cnf(refute_0_44,plain,
( ~ aInfimumOfIn0(X_148,xS,xT)
| sdtlseqdt0(xu,X_148) ),
inference(resolve,[$cnf( aSubsetOf0(xS,xT) )],[refute_0_9,refute_0_43]) ).
cnf(refute_0_45,plain,
( ~ aInfimumOfIn0(xv,xS,xT)
| sdtlseqdt0(xu,xv) ),
inference(subst,[],[refute_0_44:[bind(X_148,$fot(xv))]]) ).
cnf(refute_0_46,plain,
sdtlseqdt0(xu,xv),
inference(resolve,[$cnf( aInfimumOfIn0(xv,xS,xT) )],[refute_0_3,refute_0_45]) ).
cnf(refute_0_47,plain,
xu = xv,
inference(resolve,[$cnf( sdtlseqdt0(xu,xv) )],[refute_0_46,refute_0_36]) ).
cnf(refute_0_48,plain,
xu != xv,
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_49,plain,
$false,
inference(resolve,[$cnf( $equal(xu,xv) )],[refute_0_47,refute_0_48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LAT382+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % 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 28 19:06:56 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.77/1.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.77/1.97
% 1.77/1.97 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.77/1.97
%------------------------------------------------------------------------------