TSTP Solution File: NUM602+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM602+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n006.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 : Mon Jul 18 12:28:08 EDT 2022
% Result : Theorem 0.52s 0.72s
% Output : CNFRefutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 8 unt; 0 def)
% Number of atoms : 124 ( 46 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 138 ( 54 ~; 31 |; 41 &)
% ( 11 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 25 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__4854,hypothesis,
( aElementOf0(szDzizrdt0(xd),xT)
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [W0] :
( aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
<=> ( aElementOf0(W0,szDzozmdt0(xd))
& sdtlpdtrp0(xd,W0) = szDzizrdt0(xd) ) ) ) ).
fof(m__4891,hypothesis,
( aSet0(xO)
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [W0] :
( aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
<=> ( aElementOf0(W0,szDzozmdt0(xd))
& sdtlpdtrp0(xd,W0) = szDzizrdt0(xd) ) )
& ! [W0] :
( aElementOf0(W0,xO)
<=> ? [W1] :
( aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,W1) = W0 ) )
& xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ).
fof(m__4982,hypothesis,
! [W0] :
( ( ? [W1] :
( aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,W1) = W0 )
| aElementOf0(W0,xO) )
=> ? [W1] :
( aElementOf0(W1,szNzAzT0)
& sdtlpdtrp0(xd,W1) = szDzizrdt0(xd)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,W1) = W0 ) ) ).
fof(m__5009,hypothesis,
( ? [W0] :
( aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,W0) = xx )
& aElementOf0(xx,xO) ) ).
fof(m__,conjecture,
? [W0] :
( aElementOf0(W0,szNzAzT0)
& sdtlpdtrp0(xe,W0) = xx ) ).
fof(subgoal_0,plain,
? [W0] :
( aElementOf0(W0,szNzAzT0)
& sdtlpdtrp0(xe,W0) = xx ),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ ? [W0] :
( aElementOf0(W0,szNzAzT0)
& sdtlpdtrp0(xe,W0) = xx ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [W0] :
( sdtlpdtrp0(xe,W0) != xx
| ~ aElementOf0(W0,szNzAzT0) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [W0] :
( sdtlpdtrp0(xe,W0) != xx
| ~ aElementOf0(W0,szNzAzT0) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( aElementOf0(xx,xO)
& ? [W0] :
( sdtlpdtrp0(xe,W0) = xx
& aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ),
inference(canonicalize,[],[m__5009]) ).
fof(normalize_0_3,plain,
aElementOf0(xx,xO),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [W0] :
( ( ~ aElementOf0(W0,xO)
& ! [W1] :
( sdtlpdtrp0(xe,W1) != W0
| ~ aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
| ? [W1] :
( sdtlpdtrp0(xd,W1) = szDzizrdt0(xd)
& sdtlpdtrp0(xe,W1) = W0
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(W1,szNzAzT0) ) ),
inference(canonicalize,[],[m__4982]) ).
fof(normalize_0_5,plain,
( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aSet0(xO)
& ! [W0] :
( ~ aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
<=> ( sdtlpdtrp0(xd,W0) != szDzizrdt0(xd)
| ~ aElementOf0(W0,szDzozmdt0(xd)) ) )
& ! [W0] :
( ~ aElementOf0(W0,xO)
<=> ! [W1] :
( sdtlpdtrp0(xe,W1) != W0
| ~ aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ) ),
inference(canonicalize,[],[m__4891]) ).
fof(normalize_0_6,plain,
( aElementOf0(szDzizrdt0(xd),xT)
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [W0] :
( ~ aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
<=> ( sdtlpdtrp0(xd,W0) != szDzizrdt0(xd)
| ~ aElementOf0(W0,szDzozmdt0(xd)) ) ) ),
inference(canonicalize,[],[m__4854]) ).
fof(normalize_0_7,plain,
aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [W0] :
( ~ aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
<=> ( sdtlpdtrp0(xd,W0) != szDzizrdt0(xd)
| ~ aElementOf0(W0,szDzozmdt0(xd)) ) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_9,plain,
! [W0] :
( ~ aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
<=> ( sdtlpdtrp0(xd,W0) != szDzizrdt0(xd)
| ~ aElementOf0(W0,szDzozmdt0(xd)) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aSet0(xO)
& ! [W0] :
( ~ aElementOf0(W0,xO)
<=> ! [W1] :
( sdtlpdtrp0(xe,W1) != W0
| ~ aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ) ),
inference(simplify,[],[normalize_0_5,normalize_0_7,normalize_0_9]) ).
fof(normalize_0_11,plain,
! [W0] :
( ~ aElementOf0(W0,xO)
<=> ! [W1] :
( sdtlpdtrp0(xe,W1) != W0
| ~ aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [W0] :
( ~ aElementOf0(W0,xO)
<=> ! [W1] :
( sdtlpdtrp0(xe,W1) != W0
| ~ aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [W0] :
( ~ aElementOf0(W0,xO)
| ? [W1] :
( sdtlpdtrp0(xd,W1) = szDzizrdt0(xd)
& sdtlpdtrp0(xe,W1) = W0
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(W1,szNzAzT0) ) ),
inference(simplify,[],[normalize_0_4,normalize_0_12]) ).
fof(normalize_0_14,plain,
! [W0] :
( ~ aElementOf0(W0,xO)
| ? [W1] :
( sdtlpdtrp0(xd,W1) = szDzizrdt0(xd)
& sdtlpdtrp0(xe,W1) = W0
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(W1,szNzAzT0) ) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [W0] :
( ( ~ aElementOf0(W0,xO)
| sdtlpdtrp0(xd,skolemFOFtoCNF_W1_10(W0)) = szDzizrdt0(xd) )
& ( ~ aElementOf0(W0,xO)
| sdtlpdtrp0(xe,skolemFOFtoCNF_W1_10(W0)) = W0 )
& ( ~ aElementOf0(W0,xO)
| aElementOf0(skolemFOFtoCNF_W1_10(W0),sdtlbdtrb0(xd,szDzizrdt0(xd))) )
& ( ~ aElementOf0(W0,xO)
| aElementOf0(skolemFOFtoCNF_W1_10(W0),szNzAzT0) ) ),
inference(clausify,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [W0] :
( ~ aElementOf0(W0,xO)
| sdtlpdtrp0(xe,skolemFOFtoCNF_W1_10(W0)) = W0 ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [W0] :
( ~ aElementOf0(W0,xO)
| aElementOf0(skolemFOFtoCNF_W1_10(W0),szNzAzT0) ),
inference(conjunct,[],[normalize_0_15]) ).
cnf(refute_0_0,plain,
( sdtlpdtrp0(xe,W0) != xx
| ~ aElementOf0(W0,szNzAzT0) ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( sdtlpdtrp0(xe,skolemFOFtoCNF_W1_10(xx)) != xx
| ~ aElementOf0(skolemFOFtoCNF_W1_10(xx),szNzAzT0) ),
inference(subst,[],[refute_0_0:[bind(W0,$fot(skolemFOFtoCNF_W1_10(xx)))]]) ).
cnf(refute_0_2,plain,
aElementOf0(xx,xO),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
( ~ aElementOf0(W0,xO)
| sdtlpdtrp0(xe,skolemFOFtoCNF_W1_10(W0)) = W0 ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_4,plain,
( ~ aElementOf0(xx,xO)
| sdtlpdtrp0(xe,skolemFOFtoCNF_W1_10(xx)) = xx ),
inference(subst,[],[refute_0_3:[bind(W0,$fot(xx))]]) ).
cnf(refute_0_5,plain,
sdtlpdtrp0(xe,skolemFOFtoCNF_W1_10(xx)) = xx,
inference(resolve,[$cnf( aElementOf0(xx,xO) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
( sdtlpdtrp0(xe,skolemFOFtoCNF_W1_10(xx)) != xx
| xx != xx
| sdtlpdtrp0(xe,skolemFOFtoCNF_W1_10(xx)) = xx ),
introduced(tautology,[equality,[$cnf( ~ $equal(sdtlpdtrp0(xe,skolemFOFtoCNF_W1_10(xx)),xx) ),[0],$fot(xx)]]) ).
cnf(refute_0_7,plain,
( xx != xx
| sdtlpdtrp0(xe,skolemFOFtoCNF_W1_10(xx)) = xx ),
inference(resolve,[$cnf( $equal(sdtlpdtrp0(xe,skolemFOFtoCNF_W1_10(xx)),xx) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( xx != xx
| ~ aElementOf0(skolemFOFtoCNF_W1_10(xx),szNzAzT0) ),
inference(resolve,[$cnf( $equal(sdtlpdtrp0(xe,skolemFOFtoCNF_W1_10(xx)),xx) )],[refute_0_7,refute_0_1]) ).
cnf(refute_0_9,plain,
xx = xx,
introduced(tautology,[refl,[$fot(xx)]]) ).
cnf(refute_0_10,plain,
~ aElementOf0(skolemFOFtoCNF_W1_10(xx),szNzAzT0),
inference(resolve,[$cnf( $equal(xx,xx) )],[refute_0_9,refute_0_8]) ).
cnf(refute_0_11,plain,
( ~ aElementOf0(W0,xO)
| aElementOf0(skolemFOFtoCNF_W1_10(W0),szNzAzT0) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_12,plain,
( ~ aElementOf0(xx,xO)
| aElementOf0(skolemFOFtoCNF_W1_10(xx),szNzAzT0) ),
inference(subst,[],[refute_0_11:[bind(W0,$fot(xx))]]) ).
cnf(refute_0_13,plain,
aElementOf0(skolemFOFtoCNF_W1_10(xx),szNzAzT0),
inference(resolve,[$cnf( aElementOf0(xx,xO) )],[refute_0_2,refute_0_12]) ).
cnf(refute_0_14,plain,
$false,
inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W1_10(xx),szNzAzT0) )],[refute_0_13,refute_0_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM602+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n006.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 Jul 5 04:38:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.52/0.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.52/0.72
% 0.52/0.72 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.52/0.73
%------------------------------------------------------------------------------