%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM565+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 : n016.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 01:41:01 PM UTC 2026
% Result : Theorem 0.19s 0.87s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 52 ( 17 unt; 2 def)
% Number of atoms : 195 ( 53 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 233 ( 90 ~; 88 |; 41 &)
% ( 8 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-3 aty)
% Number of variables : 71 ( 66 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
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(f23,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [W0] :
( aSet0(W0)
=> ( sbrdtbr0(W0) = sz00
<=> W0 = slcrc0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,definition,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aSet0(W0) )
=> ! [W2] :
( W2 = slbdtsldtrb0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) ) )
& aSet0(W2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f75,hypothesis,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f76,hypothesis,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aFunction0(xc) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f78,hypothesis,
xK = sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f80,conjecture,
! [W0] :
( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
=> sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f81,negated_conjecture,
~ ! [W0] :
( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
=> sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ),
inference(negated_conjecture,[status(cth)],[f80]) ).
fof(f106,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(f107,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)],[f106]) ).
fof(f108,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)],[f107]) ).
fof(f109,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))],[f108]) ).
fof(f110,plain,
! [X0,X1] :
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f158,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f160,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f202,plain,
! [W0] :
( ( sbrdtbr0(W0) = sz00
<=> W0 = slcrc0 )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f203,plain,
! [W0] :
( ( ( W0 != slcrc0
| sbrdtbr0(W0) = sz00 )
& ( W0 = slcrc0
| sbrdtbr0(W0) != sz00 ) )
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f202]) ).
fof(f204,plain,
! [X0] :
( X0 = slcrc0
| sbrdtbr0(X0) != sz00
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f263,plain,
! [W0,W1] :
( ! [W2] :
( W2 = slbdtsldtrb0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) ) )
& aSet0(W2) ) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f57]) ).
fof(f264,plain,
! [W0,W1] :
( ! [W2] :
( ( ? [W3] :
( ( ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) )
| aElementOf0(W3,W2) )
& ( sbrdtbr0(W3) != W1
| ~ aSubsetOf0(W3,W0)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = slbdtsldtrb0(W0,W1) )
& ( ( ! [W3] :
( ( sbrdtbr0(W3) != W1
| ~ aSubsetOf0(W3,W0)
| aElementOf0(W3,W2) )
& ( ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != slbdtsldtrb0(W0,W1) ) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f263]) ).
fof(f265,plain,
! [W0,W1] :
( ( ! [W2] :
( ? [W3] :
( ( ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) )
| aElementOf0(W3,W2) )
& ( sbrdtbr0(W3) != W1
| ~ aSubsetOf0(W3,W0)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = slbdtsldtrb0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( sbrdtbr0(W3) != W1
| ~ aSubsetOf0(W3,W0)
| aElementOf0(W3,W2) )
& ! [W3] :
( ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) )
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != slbdtsldtrb0(W0,W1) ) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0) ),
inference(miniscoping,[status(thm)],[f264]) ).
fof(f266,plain,
! [W0,W1] :
( ( ! [W2] :
( ( ( ( sbrdtbr0(sK10_skl(W2,W1,W0)) = W1
& aSubsetOf0(sK10_skl(W2,W1,W0),W0) )
| aElementOf0(sK10_skl(W2,W1,W0),W2) )
& ( sbrdtbr0(sK10_skl(W2,W1,W0)) != W1
| ~ aSubsetOf0(sK10_skl(W2,W1,W0),W0)
| ~ aElementOf0(sK10_skl(W2,W1,W0),W2) ) )
| ~ aSet0(W2)
| W2 = slbdtsldtrb0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( sbrdtbr0(W3) != W1
| ~ aSubsetOf0(W3,W0)
| aElementOf0(W3,W2) )
& ! [W3] :
( ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) )
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != slbdtsldtrb0(W0,W1) ) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(W3,sK10_skl(W2,W1,W0))],[f265]) ).
fof(f268,plain,
! [X0,X1,X2,X3] :
( aSubsetOf0(X3,X0)
| ~ aElementOf0(X3,X2)
| X2 != slbdtsldtrb0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f269,plain,
! [X0,X1,X2,X3] :
( sbrdtbr0(X3) = X1
| ~ aElementOf0(X3,X2)
| X2 != slbdtsldtrb0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f341,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f344,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f352,plain,
xK = sz00,
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f354,plain,
? [W0] :
( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0)
& aElementOf0(W0,slbdtsldtrb0(xS,sz00)) ),
inference(pre_NNF_transformation,[status(thm)],[f81]) ).
fof(f355,plain,
( sdtlpdtrp0(xc,sK21_skl) != sdtlpdtrp0(xc,slcrc0)
& aElementOf0(sK21_skl,slbdtsldtrb0(xS,sz00)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21_skl]),skolemize(W0,sK21_skl)],[f354]) ).
fof(f356,plain,
aElementOf0(sK21_skl,slbdtsldtrb0(xS,sz00)),
inference(cnf_transformation,[status(thm)],[f355]) ).
fof(f357,plain,
sdtlpdtrp0(xc,sK21_skl) != sdtlpdtrp0(xc,slcrc0),
inference(cnf_transformation,[status(thm)],[f355]) ).
fof(f388,plain,
! [X0,X1,X2] :
( aSubsetOf0(X2,X0)
| ~ aElementOf0(X2,slbdtsldtrb0(X0,X1))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f268]) ).
fof(f389,plain,
! [X0,X1,X2] :
( sbrdtbr0(X2) = X1
| ~ aElementOf0(X2,slbdtsldtrb0(X0,X1))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f269]) ).
fof(f412,plain,
( aSubsetOf0(sK21_skl,xS)
| ~ aElementOf0(sz00,szNzAzT0)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f388,f356]) ).
fof(f415,plain,
( aSubsetOf0(sK21_skl,xS)
| ~ aSet0(xS) ),
inference(forward_subsumption_resolution,[status(thm)],[f412,f160]) ).
fof(f416,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,sz00),
inference(backward_demodulation,[status(thm)],[f352,f344]) ).
fof(f439,plain,
( aSet0(xS)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[status(thm)],[f110,f341]) ).
fof(f441,plain,
aSet0(xS),
inference(forward_subsumption_resolution,[status(thm)],[f439,f158]) ).
fof(f442,plain,
( aSet0(sK21_skl)
| ~ aSet0(xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f415,f110]) ).
fof(f443,plain,
( aSet0(sK21_skl)
| ~ aSet0(xS) ),
inference(duplicate_literals_removal,[status(thm)],[f442]) ).
fof(f449,plain,
aSet0(sK21_skl),
inference(backward_subsumption_resolution,[status(thm)],[f443,f441]) ).
fof(f455,plain,
aElementOf0(sK21_skl,szDzozmdt0(xc)),
inference(backward_demodulation,[status(thm)],[f416,f356]) ).
fof(f1452,plain,
! [X0] :
( sbrdtbr0(X0) = sz00
| ~ aElementOf0(X0,szDzozmdt0(xc))
| ~ aElementOf0(sz00,szNzAzT0)
| ~ aSet0(xS) ),
inference(paramodulation,[status(thm)],[f416,f389]) ).
fof(f1459,plain,
! [X0] :
( sbrdtbr0(X0) = sz00
| ~ aElementOf0(X0,szDzozmdt0(xc))
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1452,f441]) ).
fof(f1460,plain,
! [X0] :
( sbrdtbr0(X0) = sz00
| ~ aElementOf0(X0,szDzozmdt0(xc)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1459,f160]) ).
fof(f1468,plain,
sbrdtbr0(sK21_skl) = sz00,
inference(resolution,[status(thm)],[f1460,f455]) ).
fof(f1477,plain,
( sK21_skl = slcrc0
| ~ aSet0(sK21_skl) ),
inference(resolution,[status(thm)],[f1468,f204]) ).
fof(f1492,plain,
sK21_skl = slcrc0,
inference(forward_subsumption_resolution,[status(thm)],[f1477,f449]) ).
fof(f1723,plain,
sdtlpdtrp0(xc,slcrc0) != sdtlpdtrp0(xc,slcrc0),
inference(backward_demodulation,[status(thm)],[f1492,f357]) ).
fof(f1778,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1723]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM565+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.52 % Computer : n016.cluster.edu
% 0.09/0.52 % Model : x86_64 x86_64
% 0.09/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.52 % Memory : 8046.5625MB
% 0.09/0.52 % OS : Linux 6.8.0-71-generic
% 0.09/0.52 % CPULimit : 300
% 0.09/0.52 % WCLimit : 300
% 0.09/0.52 % DateTime : Mon Sep 21 02:44:54 UTC 2026
% 0.09/0.52 % CPUTime :
% 0.09/0.54 % Drodi V4.1.1
% 0.19/0.87 % Refutation found
% 0.19/0.87 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.87 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.90 % Elapsed time: 0.356413 seconds
% 0.19/0.90 % CPU time: 2.527718 seconds
% 0.19/0.90 % Total memory used: 145.059 MB
% 0.19/0.90 % Net memory used: 141.222 MB
%------------------------------------------------------------------------------