%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM620+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:41:13 PM UTC 2026
% Result : Theorem 7.62s 1.42s
% Output : CNFRefutation 7.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of formulae : 62 ( 12 unt; 2 def)
% Number of atoms : 210 ( 28 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 251 ( 103 ~; 97 |; 36 &)
% ( 4 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-2 aty)
% Number of variables : 75 ( 71 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
isFinite0(slcrc0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [W0] :
( ( isCountable0(W0)
& aSet0(W0) )
=> ~ isFinite0(W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& aSet0(W1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [W0,W1,W2] :
( ( aSet0(W2)
& aSet0(W1)
& aSet0(W0) )
=> ( ( aSubsetOf0(W1,W2)
& aSubsetOf0(W0,W1) )
=> aSubsetOf0(W0,W2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( szszuzczcdt0(W0) != sz00
& aElementOf0(szszuzczcdt0(W0),szNzAzT0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,definition,
! [W0] :
( ( W0 != slcrc0
& aSubsetOf0(W0,szNzAzT0) )
=> ! [W1] :
( W1 = szmzizndt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W0)
=> sdtlseqdt0(W1,W2) )
& aElementOf0(W1,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f82,hypothesis,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( isCountable0(sdtlpdtrp0(xN,W0))
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f111,hypothesis,
( sdtlpdtrp0(xe,xn) = xp
& aElementOf0(xn,szNzAzT0)
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f115,hypothesis,
( xx = sdtlpdtrp0(xe,xm)
& aElementOf0(xm,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f116,hypothesis,
xx = szmzizndt0(sdtlpdtrp0(xN,xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f117,conjecture,
( aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
=> aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f118,negated_conjecture,
~ ( aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
=> aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(negated_conjecture,[status(cth)],[f117]) ).
fof(f136,plain,
isFinite0(slcrc0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f139,plain,
! [W0] :
( ~ isFinite0(W0)
| ~ isCountable0(W0)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f140,plain,
! [X0] :
( ~ isFinite0(X0)
| ~ isCountable0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f143,plain,
! [W0] :
( ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) ) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f144,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f143]) ).
fof(f145,plain,
! [W0] :
( ( ! [W1] :
( ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ! [W1] :
( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(miniscoping,[status(thm)],[f144]) ).
fof(f146,plain,
! [W0] :
( ( ! [W1] :
( ( ~ aElementOf0(sK1_skl(W1,W0),W0)
& aElementOf0(sK1_skl(W1,W0),W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ! [W1] :
( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W2,sK1_skl(W1,W0))],[f145]) ).
fof(f147,plain,
! [X0,X1] :
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f148,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f157,plain,
! [W0,W1,W2] :
( aSubsetOf0(W0,W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W2)
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f158,plain,
! [X0,X1,X2] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f157]) ).
fof(f195,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f198,plain,
! [W0] :
( ( szszuzczcdt0(W0) != sz00
& aElementOf0(szszuzczcdt0(W0),szNzAzT0) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f199,plain,
! [X0] :
( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f253,plain,
! [W0] :
( ! [W1] :
( W1 = szmzizndt0(W0)
<=> ( ! [W2] :
( sdtlseqdt0(W1,W2)
| ~ aElementOf0(W2,W0) )
& aElementOf0(W1,W0) ) )
| W0 = slcrc0
| ~ aSubsetOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f254,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ~ sdtlseqdt0(W1,W2)
& aElementOf0(W2,W0) )
| ~ aElementOf0(W1,W0)
| W1 = szmzizndt0(W0) )
& ( ( ! [W2] :
( sdtlseqdt0(W1,W2)
| ~ aElementOf0(W2,W0) )
& aElementOf0(W1,W0) )
| W1 != szmzizndt0(W0) ) )
| W0 = slcrc0
| ~ aSubsetOf0(W0,szNzAzT0) ),
inference(NNF_transformation,[status(thm)],[f253]) ).
fof(f255,plain,
! [W0] :
( ( ! [W1] :
( ? [W2] :
( ~ sdtlseqdt0(W1,W2)
& aElementOf0(W2,W0) )
| ~ aElementOf0(W1,W0)
| W1 = szmzizndt0(W0) )
& ! [W1] :
( ( ! [W2] :
( sdtlseqdt0(W1,W2)
| ~ aElementOf0(W2,W0) )
& aElementOf0(W1,W0) )
| W1 != szmzizndt0(W0) ) )
| W0 = slcrc0
| ~ aSubsetOf0(W0,szNzAzT0) ),
inference(miniscoping,[status(thm)],[f254]) ).
fof(f256,plain,
! [W0] :
( ( ! [W1] :
( ( ~ sdtlseqdt0(W1,sK6_skl(W1,W0))
& aElementOf0(sK6_skl(W1,W0),W0) )
| ~ aElementOf0(W1,W0)
| W1 = szmzizndt0(W0) )
& ! [W1] :
( ( ! [W2] :
( sdtlseqdt0(W1,W2)
| ~ aElementOf0(W2,W0) )
& aElementOf0(W1,W0) )
| W1 != szmzizndt0(W0) ) )
| W0 = slcrc0
| ~ aSubsetOf0(W0,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(W2,sK6_skl(W1,W0))],[f255]) ).
fof(f257,plain,
! [X0,X1] :
( aElementOf0(X1,X0)
| X1 != szmzizndt0(X0)
| X0 = slcrc0
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f256]) ).
fof(f399,plain,
! [W0] :
( ( isCountable0(sdtlpdtrp0(xN,W0))
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f82]) ).
fof(f400,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f399]) ).
fof(f401,plain,
! [X0] :
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f399]) ).
fof(f464,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f470,plain,
aElementOf0(xm,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f472,plain,
xx = szmzizndt0(sdtlpdtrp0(xN,xm)),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f473,plain,
( ~ aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
& aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(pre_NNF_transformation,[status(thm)],[f118]) ).
fof(f474,plain,
aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(cnf_transformation,[status(thm)],[f473]) ).
fof(f475,plain,
~ aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(cnf_transformation,[status(thm)],[f473]) ).
fof(f495,plain,
! [X0] :
( aElementOf0(szmzizndt0(X0),X0)
| X0 = slcrc0
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(destructive_equality_resolution,[status(thm)],[f257]) ).
fof(f525,plain,
! [X0] :
( aSet0(sdtlpdtrp0(xN,X0))
| ~ aSet0(szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[status(thm)],[f400,f147]) ).
fof(f526,plain,
! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xm))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(resolution,[status(thm)],[f148,f474]) ).
fof(f533,plain,
! [X0,X1,X2] :
( aSubsetOf0(X2,X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X2,X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f158,f147]) ).
fof(f534,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,xm),X0)
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),X0)
| ~ aSet0(X0)
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(resolution,[status(thm)],[f533,f474]) ).
fof(f537,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,xm),X0)
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),X0)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f534,f147]) ).
fof(f555,plain,
( ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[status(thm)],[f537,f400]) ).
fof(f557,plain,
( ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[f555,f195]) ).
fof(f571,plain,
( ~ aElementOf0(xx,sdtlpdtrp0(xN,xm))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(resolution,[status(thm)],[f526,f475]) ).
fof(f677,plain,
! [X0] :
( aSet0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[f525,f195]) ).
fof(f1198,plain,
! [X0] :
( ~ isFinite0(sdtlpdtrp0(xN,X0))
| ~ aSet0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[status(thm)],[f401,f140]) ).
fof(f1203,plain,
! [X0] :
( ~ isFinite0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1198,f677]) ).
fof(f2005,plain,
( aElementOf0(xx,sdtlpdtrp0(xN,xm))
| sdtlpdtrp0(xN,xm) = slcrc0
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0) ),
inference(paramodulation,[status(thm)],[f472,f495]) ).
fof(f3538,plain,
( ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| aElementOf0(xx,sdtlpdtrp0(xN,xm))
| sdtlpdtrp0(xN,xm) = slcrc0 ),
inference(resolution,[status(thm)],[f2005,f557]) ).
fof(f3748,plain,
( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| sdtlpdtrp0(xN,xm) = slcrc0 ),
inference(resolution,[status(thm)],[f3538,f571]) ).
fof(f3757,plain,
( ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| sdtlpdtrp0(xN,xm) = slcrc0 ),
inference(forward_subsumption_resolution,[status(thm)],[f3748,f677]) ).
fof(f3763,plain,
( ~ aElementOf0(xn,szNzAzT0)
| sdtlpdtrp0(xN,xm) = slcrc0 ),
inference(resolution,[status(thm)],[f3757,f199]) ).
fof(f3764,plain,
sdtlpdtrp0(xN,xm) = slcrc0,
inference(forward_subsumption_resolution,[status(thm)],[f3763,f464]) ).
fof(f3829,plain,
( ~ isFinite0(slcrc0)
| ~ aElementOf0(xm,szNzAzT0) ),
inference(paramodulation,[status(thm)],[f3764,f1203]) ).
fof(f3873,plain,
~ isFinite0(slcrc0),
inference(forward_subsumption_resolution,[status(thm)],[f3829,f470]) ).
fof(f3878,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3873,f136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM620+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 02:47:51 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.39 % Drodi V4.1.1
% 7.62/1.42 % Refutation found
% 7.62/1.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 7.62/1.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.62/1.44 % Elapsed time: 1.061029 seconds
% 7.62/1.44 % CPU time: 7.948268 seconds
% 7.62/1.44 % Total memory used: 168.973 MB
% 7.62/1.44 % Net memory used: 163.176 MB
%------------------------------------------------------------------------------