%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG101+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 : n018.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 02:04:58 PM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 6 unt; 4 def)
% Number of atoms : 122 ( 30 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 146 ( 56 ~; 56 |; 26 &)
% ( 7 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 47 ( 37 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f37,definition,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( W1 = slsdtgt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) ) )
& aSet0(W1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,hypothesis,
aElement0(xc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aElement0(xz)
& aElementOf0(xy,slsdtgt0(xc))
& aElementOf0(xx,slsdtgt0(xc)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,conjecture,
? [W0] :
( sdtasdt0(xc,W0) = xx
& aElement0(W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
~ ? [W0] :
( sdtasdt0(xc,W0) = xx
& aElement0(W0) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f181,plain,
! [W0] :
( ! [W1] :
( W1 = slsdtgt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) ) )
& aSet0(W1) ) )
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f182,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ( ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) )
| aElementOf0(W2,W1) )
& ( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
| ~ aElementOf0(W2,W1) ) )
| ~ aSet0(W1)
| W1 = slsdtgt0(W0) )
& ( ( ! [W2] :
( ( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
| aElementOf0(W2,W1) )
& ( ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) )
| ~ aElementOf0(W2,W1) ) )
& aSet0(W1) )
| W1 != slsdtgt0(W0) ) )
| ~ aElement0(W0) ),
inference(NNF_transformation,[status(thm)],[f181]) ).
fof(f183,plain,
! [W0] :
( ( ! [W1] :
( ? [W2] :
( ( ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) )
| aElementOf0(W2,W1) )
& ( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
| ~ aElementOf0(W2,W1) ) )
| ~ aSet0(W1)
| W1 = slsdtgt0(W0) )
& ! [W1] :
( ( ! [W2] :
( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
| aElementOf0(W2,W1) )
& ! [W2] :
( ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) )
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| W1 != slsdtgt0(W0) ) )
| ~ aElement0(W0) ),
inference(miniscoping,[status(thm)],[f182]) ).
fof(f184,plain,
! [W0] :
( ( ! [W1] :
( ( ( ( sdtasdt0(W0,sK19_skl(W1,W0)) = sK18_skl(W1,W0)
& aElement0(sK19_skl(W1,W0)) )
| aElementOf0(sK18_skl(W1,W0),W1) )
& ( ! [W3] :
( sdtasdt0(W0,W3) != sK18_skl(W1,W0)
| ~ aElement0(W3) )
| ~ aElementOf0(sK18_skl(W1,W0),W1) ) )
| ~ aSet0(W1)
| W1 = slsdtgt0(W0) )
& ! [W1] :
( ( ! [W2] :
( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
| aElementOf0(W2,W1) )
& ! [W2] :
( ( sdtasdt0(W0,sK17_skl(W2,W1,W0)) = W2
& aElement0(sK17_skl(W2,W1,W0)) )
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| W1 != slsdtgt0(W0) ) )
| ~ aElement0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl,sK19_skl]),skolemize(W3,sK17_skl(W2,W1,W0)),skolemize(W2,sK18_skl(W1,W0)),skolemize(W3,sK19_skl(W1,W0))],[f183]) ).
fof(f186,plain,
! [X0,X1,X2] :
( aElement0(sK17_skl(X2,X1,X0))
| ~ aElementOf0(X2,X1)
| X1 != slsdtgt0(X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f184]) ).
fof(f187,plain,
! [X0,X1,X2] :
( sdtasdt0(X0,sK17_skl(X2,X1,X0)) = X2
| ~ aElementOf0(X2,X1)
| X1 != slsdtgt0(X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f184]) ).
fof(f192,plain,
aElement0(xc),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f193,plain,
aElementOf0(xx,slsdtgt0(xc)),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f196,plain,
! [W0] :
( sdtasdt0(xc,W0) != xx
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f197,plain,
! [X0] :
( sdtasdt0(xc,X0) != xx
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f224,plain,
! [X0,X1] :
( aElement0(sK17_skl(X1,slsdtgt0(X0),X0))
| ~ aElementOf0(X1,slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f186]) ).
fof(f225,plain,
! [X0,X1] :
( sdtasdt0(X0,sK17_skl(X1,slsdtgt0(X0),X0)) = X1
| ~ aElementOf0(X1,slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f187]) ).
fof(f301,definition,
( sQ8_spl
<=> aElement0(xc) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f303,plain,
( sQ8_spl
| ~ aElement0(xc) ),
inference(component_clause,[status(thm)],[f301]) ).
fof(f399,plain,
( ~ aElement0(sK17_skl(xx,slsdtgt0(xc),xc))
| ~ aElementOf0(xx,slsdtgt0(xc))
| ~ aElement0(xc) ),
inference(resolution,[status(thm)],[f225,f197]) ).
fof(f401,definition,
( sQ15_spl
<=> aElementOf0(xx,slsdtgt0(xc)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f403,plain,
( sQ15_spl
| ~ aElementOf0(xx,slsdtgt0(xc)) ),
inference(component_clause,[status(thm)],[f401]) ).
fof(f404,definition,
( sQ16_spl
<=> aElement0(sK17_skl(xx,slsdtgt0(xc),xc)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f406,plain,
( sQ16_spl
| ~ aElement0(sK17_skl(xx,slsdtgt0(xc),xc)) ),
inference(component_clause,[status(thm)],[f404]) ).
fof(f407,plain,
( ~ sQ16_spl
| ~ sQ15_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f399,f301,f401,f404]) ).
fof(f410,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f303,f192]) ).
fof(f411,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f410]) ).
fof(f412,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f403,f193]) ).
fof(f413,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f412]) ).
fof(f414,plain,
( sQ16_spl
| ~ aElementOf0(xx,slsdtgt0(xc))
| ~ aElement0(xc) ),
inference(resolution,[status(thm)],[f406,f224]) ).
fof(f415,plain,
( sQ16_spl
| ~ sQ15_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f414,f301,f401,f404]) ).
fof(f416,plain,
$false,
inference(sat_refutation,[status(thm)],[f407,f411,f413,f415]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG101+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 : n018.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 04:21:44 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.44 % Elapsed time: 0.059864 seconds
% 0.09/0.44 % CPU time: 0.201784 seconds
% 0.09/0.44 % Total memory used: 72.924 MB
% 0.09/0.44 % Net memory used: 72.642 MB
%------------------------------------------------------------------------------