TSTP Solution File: NUM597+3 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : NUM597+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %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 : 300s
% DateTime : Tue Apr 30 20:35:17 EDT 2024
% Result : Theorem 1.86s 0.60s
% Output : CNFRefutation 1.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 59 ( 10 unt; 1 def)
% Number of atoms : 211 ( 44 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 235 ( 83 ~; 75 |; 62 &)
% ( 10 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 8 con; 0-2 aty)
% Number of variables : 69 ( 57 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,definition,
! [W0] :
( W0 = slcrc0
<=> ( aSet0(W0)
& ~ ? [W1] : aElementOf0(W1,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f92,hypothesis,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1] :
( ( aSet0(W1)
& ( ( ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
& sbrdtbr0(W1) = xk )
| aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) )
=> sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f93,hypothesis,
( aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
& ! [W0] :
( aElementOf0(W0,sdtlcdtrc0(xd,szDzozmdt0(xd)))
<=> ? [W1] :
( aElementOf0(W1,szDzozmdt0(xd))
& sdtlpdtrp0(xd,W1) = W0 ) )
& ! [W0] :
( aElementOf0(W0,sdtlcdtrc0(xd,szDzozmdt0(xd)))
=> aElementOf0(W0,xT) )
& aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f94,hypothesis,
~ ( ( aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [W0] :
( aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
<=> ( aElementOf0(W0,szDzozmdt0(xd))
& sdtlpdtrp0(xd,W0) = szDzizrdt0(xd) ) ) )
=> ~ ? [W0] : aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f95,conjecture,
aElementOf0(szDzizrdt0(xd),xT),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ aElementOf0(szDzizrdt0(xd),xT),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f107,plain,
! [W0] :
( W0 = slcrc0
<=> ( aSet0(W0)
& ! [W1] : ~ aElementOf0(W1,W0) ) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f108,plain,
! [W0] :
( ( W0 != slcrc0
| ( aSet0(W0)
& ! [W1] : ~ aElementOf0(W1,W0) ) )
& ( W0 = slcrc0
| ~ aSet0(W0)
| ? [W1] : aElementOf0(W1,W0) ) ),
inference(NNF_transformation,[status(esa)],[f107]) ).
fof(f109,plain,
( ! [W0] :
( W0 != slcrc0
| ( aSet0(W0)
& ! [W1] : ~ aElementOf0(W1,W0) ) )
& ! [W0] :
( W0 = slcrc0
| ~ aSet0(W0)
| ? [W1] : aElementOf0(W1,W0) ) ),
inference(miniscoping,[status(esa)],[f108]) ).
fof(f110,plain,
( ! [W0] :
( W0 != slcrc0
| ( aSet0(W0)
& ! [W1] : ~ aElementOf0(W1,W0) ) )
& ! [W0] :
( W0 = slcrc0
| ~ aSet0(W0)
| aElementOf0(sk0_0(W0),W0) ) ),
inference(skolemization,[status(esa)],[f109]) ).
fof(f112,plain,
! [X0,X1] :
( X0 != slcrc0
| ~ aElementOf0(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f110]) ).
fof(f113,plain,
! [X0] :
( X0 = slcrc0
| ~ aSet0(X0)
| aElementOf0(sk0_0(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f110]) ).
fof(f534,plain,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [W0] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1] :
( ~ aSet0(W1)
| ( ( ( ? [W2] :
( aElementOf0(W2,W1)
& ~ aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
& ~ aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| sbrdtbr0(W1) != xk )
& ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) )
| sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f92]) ).
fof(f535,plain,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [W0] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1] :
( ~ aSet0(W1)
| ( ( ( aElementOf0(sk0_32(W1,W0),W1)
& ~ aElementOf0(sk0_32(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ~ aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| sbrdtbr0(W1) != xk )
& ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) )
| sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ),
inference(skolemization,[status(esa)],[f534]) ).
fof(f537,plain,
szDzozmdt0(xd) = szNzAzT0,
inference(cnf_transformation,[status(esa)],[f535]) ).
fof(f542,plain,
( aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
& ! [W0] :
( aElementOf0(W0,sdtlcdtrc0(xd,szDzozmdt0(xd)))
<=> ? [W1] :
( aElementOf0(W1,szDzozmdt0(xd))
& sdtlpdtrp0(xd,W1) = W0 ) )
& ! [W0] :
( ~ aElementOf0(W0,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(W0,xT) )
& aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT) ),
inference(pre_NNF_transformation,[status(esa)],[f93]) ).
fof(f543,plain,
( aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
& ! [W0] :
( ( ~ aElementOf0(W0,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ? [W1] :
( aElementOf0(W1,szDzozmdt0(xd))
& sdtlpdtrp0(xd,W1) = W0 ) )
& ( aElementOf0(W0,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W1] :
( ~ aElementOf0(W1,szDzozmdt0(xd))
| sdtlpdtrp0(xd,W1) != W0 ) ) )
& ! [W0] :
( ~ aElementOf0(W0,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(W0,xT) )
& aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT) ),
inference(NNF_transformation,[status(esa)],[f542]) ).
fof(f544,plain,
( aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
& ! [W0] :
( ~ aElementOf0(W0,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ? [W1] :
( aElementOf0(W1,szDzozmdt0(xd))
& sdtlpdtrp0(xd,W1) = W0 ) )
& ! [W0] :
( aElementOf0(W0,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W1] :
( ~ aElementOf0(W1,szDzozmdt0(xd))
| sdtlpdtrp0(xd,W1) != W0 ) )
& ! [W0] :
( ~ aElementOf0(W0,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(W0,xT) )
& aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT) ),
inference(miniscoping,[status(esa)],[f543]) ).
fof(f545,plain,
( aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
& ! [W0] :
( ~ aElementOf0(W0,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ( aElementOf0(sk0_33(W0),szDzozmdt0(xd))
& sdtlpdtrp0(xd,sk0_33(W0)) = W0 ) )
& ! [W0] :
( aElementOf0(W0,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [W1] :
( ~ aElementOf0(W1,szDzozmdt0(xd))
| sdtlpdtrp0(xd,W1) != W0 ) )
& ! [W0] :
( ~ aElementOf0(W0,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(W0,xT) )
& aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT) ),
inference(skolemization,[status(esa)],[f544]) ).
fof(f549,plain,
! [X0,X1] :
( aElementOf0(X0,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ aElementOf0(X1,szDzozmdt0(xd))
| sdtlpdtrp0(xd,X1) != X0 ),
inference(cnf_transformation,[status(esa)],[f545]) ).
fof(f550,plain,
! [X0] :
( ~ aElementOf0(X0,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(X0,xT) ),
inference(cnf_transformation,[status(esa)],[f545]) ).
fof(f552,plain,
( aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [W0] :
( aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
<=> ( aElementOf0(W0,szDzozmdt0(xd))
& sdtlpdtrp0(xd,W0) = szDzizrdt0(xd) ) )
& ? [W0] : aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(pre_NNF_transformation,[status(esa)],[f94]) ).
fof(f553,plain,
( aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [W0] :
( ( ~ aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( aElementOf0(W0,szDzozmdt0(xd))
& sdtlpdtrp0(xd,W0) = szDzizrdt0(xd) ) )
& ( aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aElementOf0(W0,szDzozmdt0(xd))
| sdtlpdtrp0(xd,W0) != szDzizrdt0(xd) ) )
& ? [W0] : aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(NNF_transformation,[status(esa)],[f552]) ).
fof(f554,plain,
( aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [W0] :
( ~ aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( aElementOf0(W0,szDzozmdt0(xd))
& sdtlpdtrp0(xd,W0) = szDzizrdt0(xd) ) )
& ! [W0] :
( aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aElementOf0(W0,szDzozmdt0(xd))
| sdtlpdtrp0(xd,W0) != szDzizrdt0(xd) )
& ? [W0] : aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(miniscoping,[status(esa)],[f553]) ).
fof(f555,plain,
( aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [W0] :
( ~ aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( aElementOf0(W0,szDzozmdt0(xd))
& sdtlpdtrp0(xd,W0) = szDzizrdt0(xd) ) )
& ! [W0] :
( aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aElementOf0(W0,szDzozmdt0(xd))
| sdtlpdtrp0(xd,W0) != szDzizrdt0(xd) )
& aElementOf0(sk0_34,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(skolemization,[status(esa)],[f554]) ).
fof(f556,plain,
aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(cnf_transformation,[status(esa)],[f555]) ).
fof(f557,plain,
! [X0] :
( ~ aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(X0,szDzozmdt0(xd)) ),
inference(cnf_transformation,[status(esa)],[f555]) ).
fof(f558,plain,
! [X0] :
( ~ aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| sdtlpdtrp0(xd,X0) = szDzizrdt0(xd) ),
inference(cnf_transformation,[status(esa)],[f555]) ).
fof(f560,plain,
aElementOf0(sk0_34,sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(cnf_transformation,[status(esa)],[f555]) ).
fof(f561,plain,
~ aElementOf0(szDzizrdt0(xd),xT),
inference(cnf_transformation,[status(esa)],[f96]) ).
fof(f662,plain,
! [X0] : ~ aElementOf0(X0,slcrc0),
inference(destructive_equality_resolution,[status(esa)],[f112]) ).
fof(f726,plain,
! [X0,X1] :
( aElementOf0(X0,sdtlcdtrc0(xd,szNzAzT0))
| ~ aElementOf0(X1,szDzozmdt0(xd))
| sdtlpdtrp0(xd,X1) != X0 ),
inference(forward_demodulation,[status(thm)],[f537,f549]) ).
fof(f727,plain,
! [X0,X1] :
( aElementOf0(X0,sdtlcdtrc0(xd,szNzAzT0))
| ~ aElementOf0(X1,szNzAzT0)
| sdtlpdtrp0(xd,X1) != X0 ),
inference(forward_demodulation,[status(thm)],[f537,f726]) ).
fof(f728,plain,
! [X0] :
( aElementOf0(sdtlpdtrp0(xd,X0),sdtlcdtrc0(xd,szNzAzT0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(destructive_equality_resolution,[status(esa)],[f727]) ).
fof(f729,plain,
! [X0] :
( ~ aElementOf0(X0,sdtlcdtrc0(xd,szNzAzT0))
| aElementOf0(X0,xT) ),
inference(forward_demodulation,[status(thm)],[f537,f550]) ).
fof(f731,plain,
! [X0] :
( ~ aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(X0,szNzAzT0) ),
inference(forward_demodulation,[status(thm)],[f537,f557]) ).
fof(f760,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(sdtlpdtrp0(xd,X0),xT) ),
inference(resolution,[status(thm)],[f728,f729]) ).
fof(f791,plain,
( spl0_11
<=> sdtlbdtrb0(xd,szDzizrdt0(xd)) = slcrc0 ),
introduced(split_symbol_definition) ).
fof(f792,plain,
( sdtlbdtrb0(xd,szDzizrdt0(xd)) = slcrc0
| ~ spl0_11 ),
inference(component_clause,[status(thm)],[f791]) ).
fof(f794,plain,
( spl0_12
<=> aElementOf0(sk0_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
introduced(split_symbol_definition) ).
fof(f795,plain,
( aElementOf0(sk0_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ spl0_12 ),
inference(component_clause,[status(thm)],[f794]) ).
fof(f797,plain,
( sdtlbdtrb0(xd,szDzizrdt0(xd)) = slcrc0
| aElementOf0(sk0_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(resolution,[status(thm)],[f113,f556]) ).
fof(f798,plain,
( spl0_11
| spl0_12 ),
inference(split_clause,[status(thm)],[f797,f791,f794]) ).
fof(f849,plain,
( aElementOf0(sk0_34,slcrc0)
| ~ spl0_11 ),
inference(backward_demodulation,[status(thm)],[f792,f560]) ).
fof(f850,plain,
( $false
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[status(thm)],[f849,f662]) ).
fof(f851,plain,
~ spl0_11,
inference(contradiction_clause,[status(thm)],[f850]) ).
fof(f905,plain,
( aElementOf0(sk0_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),szNzAzT0)
| ~ spl0_12 ),
inference(resolution,[status(thm)],[f731,f795]) ).
fof(f922,plain,
( sdtlpdtrp0(xd,sk0_0(sdtlbdtrb0(xd,szDzizrdt0(xd)))) = szDzizrdt0(xd)
| ~ spl0_12 ),
inference(resolution,[status(thm)],[f558,f795]) ).
fof(f926,plain,
( spl0_24
<=> aElementOf0(sk0_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),szNzAzT0) ),
introduced(split_symbol_definition) ).
fof(f928,plain,
( ~ aElementOf0(sk0_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),szNzAzT0)
| spl0_24 ),
inference(component_clause,[status(thm)],[f926]) ).
fof(f931,plain,
( spl0_25
<=> aElementOf0(szDzizrdt0(xd),xT) ),
introduced(split_symbol_definition) ).
fof(f932,plain,
( aElementOf0(szDzizrdt0(xd),xT)
| ~ spl0_25 ),
inference(component_clause,[status(thm)],[f931]) ).
fof(f934,plain,
( ~ aElementOf0(sk0_0(sdtlbdtrb0(xd,szDzizrdt0(xd))),szNzAzT0)
| aElementOf0(szDzizrdt0(xd),xT)
| ~ spl0_12 ),
inference(paramodulation,[status(thm)],[f922,f760]) ).
fof(f935,plain,
( ~ spl0_24
| spl0_25
| ~ spl0_12 ),
inference(split_clause,[status(thm)],[f934,f926,f931,f794]) ).
fof(f936,plain,
( $false
| ~ spl0_12
| spl0_24 ),
inference(forward_subsumption_resolution,[status(thm)],[f928,f905]) ).
fof(f937,plain,
( ~ spl0_12
| spl0_24 ),
inference(contradiction_clause,[status(thm)],[f936]) ).
fof(f938,plain,
( $false
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[status(thm)],[f932,f561]) ).
fof(f939,plain,
~ spl0_25,
inference(contradiction_clause,[status(thm)],[f938]) ).
fof(f940,plain,
$false,
inference(sat_refutation,[status(thm)],[f798,f851,f935,f937,f939]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM597+3 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32 % Computer : n029.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Apr 29 21:12:04 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.35 % Drodi V3.6.0
% 1.86/0.60 % Refutation found
% 1.86/0.60 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.86/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.86/0.62 % Elapsed time: 0.289295 seconds
% 1.86/0.62 % CPU time: 2.073576 seconds
% 1.86/0.62 % Total memory used: 96.588 MB
% 1.86/0.62 % Net memory used: 94.693 MB
%------------------------------------------------------------------------------