%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM614+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 01:41:12 PM UTC 2026
% Result : Theorem 0.14s 0.52s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of formulae : 53 ( 14 unt; 7 def)
% Number of atoms : 197 ( 28 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 234 ( 90 ~; 92 |; 37 &)
% ( 11 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 6 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 62 ( 58 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& aSet0(W1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [W0] :
( aSet0(W0)
=> aSubsetOf0(W0,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f80,hypothesis,
( szszuzczcdt0(xk) = xK
& aElementOf0(xk,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f95,hypothesis,
( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aSet0(xO) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f108,hypothesis,
aSubsetOf0(xP,xO),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f109,hypothesis,
sbrdtbr0(xP) = xk,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f110,conjecture,
aElementOf0(xP,slbdtsldtrb0(xO,xk)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f111,negated_conjecture,
~ aElementOf0(xP,slbdtsldtrb0(xO,xk)),
inference(negated_conjecture,[status(cth)],[f110]) ).
fof(f136,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(f137,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)],[f136]) ).
fof(f138,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)],[f137]) ).
fof(f139,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))],[f138]) ).
fof(f141,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f146,plain,
! [W0] :
( aSubsetOf0(W0,W0)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f147,plain,
! [X0] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f188,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f293,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(f294,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)],[f293]) ).
fof(f295,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)],[f294]) ).
fof(f296,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))],[f295]) ).
fof(f300,plain,
! [X0,X1,X2,X3] :
( sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0)
| aElementOf0(X3,X2)
| X2 != slbdtsldtrb0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f296]) ).
fof(f384,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f432,plain,
aSet0(xO),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f453,plain,
aSubsetOf0(xP,xO),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f454,plain,
sbrdtbr0(xP) = xk,
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f455,plain,
~ aElementOf0(xP,slbdtsldtrb0(xO,xk)),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f488,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| aElementOf0(X1,slbdtsldtrb0(X0,sbrdtbr0(X1)))
| ~ aElementOf0(sbrdtbr0(X1),szNzAzT0)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f300]) ).
fof(f516,definition,
( sQ3_spl
<=> aSet0(szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f518,plain,
( sQ3_spl
| ~ aSet0(szNzAzT0) ),
inference(component_clause,[status(thm)],[f516]) ).
fof(f546,plain,
! [X0] :
( aElementOf0(xk,X0)
| ~ aSubsetOf0(szNzAzT0,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f141,f384]) ).
fof(f554,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f518,f188]) ).
fof(f555,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f554]) ).
fof(f570,definition,
( sQ9_spl
<=> aElementOf0(xk,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f579,plain,
( aElementOf0(xk,szNzAzT0)
| ~ aSet0(szNzAzT0)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[status(thm)],[f147,f546]) ).
fof(f581,plain,
( sQ9_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f579,f516,f570]) ).
fof(f587,definition,
( sQ11_spl
<=> aSet0(xO) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f589,plain,
( sQ11_spl
| ~ aSet0(xO) ),
inference(component_clause,[status(thm)],[f587]) ).
fof(f625,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f589,f432]) ).
fof(f626,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f625]) ).
fof(f2192,plain,
! [X0] :
( ~ aSubsetOf0(xP,X0)
| aElementOf0(xP,slbdtsldtrb0(X0,sbrdtbr0(xP)))
| ~ aElementOf0(xk,szNzAzT0)
| ~ aSet0(X0) ),
inference(paramodulation,[status(thm)],[f454,f488]) ).
fof(f2194,definition,
! [X0] :
( sQ226_spl
<=> ( ~ aSubsetOf0(xP,X0)
| aElementOf0(xP,slbdtsldtrb0(X0,sbrdtbr0(xP)))
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ226_spl])],[split_symbol_definition]) ).
fof(f2195,plain,
! [X0] :
( ~ sQ226_spl
| ~ aSubsetOf0(xP,X0)
| aElementOf0(xP,slbdtsldtrb0(X0,sbrdtbr0(xP)))
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f2194]) ).
fof(f2197,plain,
( ~ sQ9_spl
| sQ226_spl ),
inference(split_clause,[status(thm)],[f2192,f2194,f570]) ).
fof(f2202,plain,
! [X0] :
( ~ sQ226_spl
| ~ aSubsetOf0(xP,X0)
| aElementOf0(xP,slbdtsldtrb0(X0,xk))
| ~ aSet0(X0) ),
inference(forward_demodulation,[status(thm)],[f454,f2195]) ).
fof(f2565,plain,
( ~ sQ226_spl
| aElementOf0(xP,slbdtsldtrb0(xO,xk))
| ~ aSet0(xO) ),
inference(resolution,[status(thm)],[f2202,f453]) ).
fof(f2576,definition,
( sQ252_spl
<=> aElementOf0(xP,slbdtsldtrb0(xO,xk)) ),
introduced(definition,[new_symbols(definition,[sQ252_spl])],[split_symbol_definition]) ).
fof(f2577,plain,
( ~ sQ252_spl
| aElementOf0(xP,slbdtsldtrb0(xO,xk)) ),
inference(component_clause,[status(thm)],[f2576]) ).
fof(f2579,plain,
( ~ sQ226_spl
| sQ252_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2565,f587,f2576,f2194]) ).
fof(f2588,plain,
( ~ sQ252_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2577,f455]) ).
fof(f2589,plain,
~ sQ252_spl,
inference(contradiction_clause,[status(thm)],[f2588]) ).
fof(f2590,plain,
$false,
inference(sat_refutation,[status(thm)],[f555,f581,f626,f2197,f2579,f2589]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM614+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.33 % Computer : n002.cluster.edu
% 0.08/0.33 % Model : x86_64 x86_64
% 0.08/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.33 % Memory : 8046.5625MB
% 0.08/0.33 % OS : Linux 6.8.0-71-generic
% 0.08/0.33 % CPULimit : 300
% 0.08/0.33 % WCLimit : 300
% 0.08/0.33 % DateTime : Mon Sep 21 02:47:17 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 0.14/0.52 % Refutation found
% 0.14/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.55 % Elapsed time: 0.196760 seconds
% 0.21/0.55 % CPU time: 1.329768 seconds
% 0.21/0.55 % Total memory used: 135.046 MB
% 0.21/0.55 % Net memory used: 132.624 MB
%------------------------------------------------------------------------------