%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG109+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 02:05:00 PM UTC 2026
% Result : Theorem 0.07s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 12 unt; 0 def)
% Number of atoms : 155 ( 65 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 178 ( 58 ~; 48 |; 61 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 65 ( 45 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [W0] :
( aElement0(W0)
=> ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,hypothesis,
( xb != sz00
| xa != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
( aElementOf0(xb,slsdtgt0(xb))
& ? [W0] :
( sdtasdt0(xb,W0) = xb
& aElement0(W0) )
& aElementOf0(sz00,slsdtgt0(xb))
& ? [W0] :
( sdtasdt0(xb,W0) = sz00
& aElement0(W0) )
& aElementOf0(xa,slsdtgt0(xa))
& ? [W0] :
( sdtasdt0(xa,W0) = xa
& aElement0(W0) )
& aElementOf0(sz00,slsdtgt0(xa))
& ? [W0] :
( sdtasdt0(xa,W0) = sz00
& aElement0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,conjecture,
? [W0] :
( W0 != sz00
& ( ! [W1] :
( aElementOf0(W1,slsdtgt0(xa))
<=> ? [W2] :
( sdtasdt0(xa,W2) = W1
& aElement0(W2) ) )
=> ( ! [W1] :
( aElementOf0(W1,slsdtgt0(xb))
<=> ? [W2] :
( sdtasdt0(xb,W2) = W1
& aElement0(W2) ) )
=> ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ ? [W0] :
( W0 != sz00
& ( ! [W1] :
( aElementOf0(W1,slsdtgt0(xa))
<=> ? [W2] :
( sdtasdt0(xa,W2) = W1
& aElement0(W2) ) )
=> ( ! [W1] :
( aElementOf0(W1,slsdtgt0(xb))
<=> ? [W2] :
( sdtasdt0(xb,W2) = W1
& aElement0(W2) ) )
=> ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f61,plain,
! [W0] :
( ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 )
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f62,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
! [X0] :
( X0 = sdtpldt0(sz00,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f198,plain,
aElement0(xa),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f199,plain,
aElement0(xb),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f200,plain,
( xb != sz00
| xa != sz00 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f238,plain,
( aElementOf0(xb,slsdtgt0(xb))
& sdtasdt0(xb,sK30_skl) = xb
& aElement0(sK30_skl)
& aElementOf0(sz00,slsdtgt0(xb))
& sdtasdt0(xb,sK29_skl) = sz00
& aElement0(sK29_skl)
& aElementOf0(xa,slsdtgt0(xa))
& sdtasdt0(xa,sK28_skl) = xa
& aElement0(sK28_skl)
& aElementOf0(sz00,slsdtgt0(xa))
& sdtasdt0(xa,sK27_skl) = sz00
& aElement0(sK27_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27_skl,sK28_skl,sK29_skl,sK30_skl]),skolemize(W0,sK27_skl),skolemize(W0,sK28_skl),skolemize(W0,sK29_skl),skolemize(W0,sK30_skl)],[f43]) ).
fof(f241,plain,
aElementOf0(sz00,slsdtgt0(xa)),
inference(cnf_transformation,[status(thm)],[f238]) ).
fof(f244,plain,
aElementOf0(xa,slsdtgt0(xa)),
inference(cnf_transformation,[status(thm)],[f238]) ).
fof(f250,plain,
aElementOf0(xb,slsdtgt0(xb)),
inference(cnf_transformation,[status(thm)],[f238]) ).
fof(f251,plain,
! [W0] :
( W0 = sz00
| ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) )
& ! [W1] :
( aElementOf0(W1,slsdtgt0(xb))
<=> ? [W2] :
( sdtasdt0(xb,W2) = W1
& aElement0(W2) ) )
& ! [W1] :
( aElementOf0(W1,slsdtgt0(xa))
<=> ? [W2] :
( sdtasdt0(xa,W2) = W1
& aElement0(W2) ) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f252,plain,
! [W0] :
( W0 = sz00
| ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) )
& ! [W1] :
( ( ! [W2] :
( sdtasdt0(xb,W2) != W1
| ~ aElement0(W2) )
| aElementOf0(W1,slsdtgt0(xb)) )
& ( ? [W2] :
( sdtasdt0(xb,W2) = W1
& aElement0(W2) )
| ~ aElementOf0(W1,slsdtgt0(xb)) ) )
& ! [W1] :
( ( ! [W2] :
( sdtasdt0(xa,W2) != W1
| ~ aElement0(W2) )
| aElementOf0(W1,slsdtgt0(xa)) )
& ( ? [W2] :
( sdtasdt0(xa,W2) = W1
& aElement0(W2) )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ) ),
inference(NNF_transformation,[status(thm)],[f251]) ).
fof(f253,plain,
! [W0] :
( W0 = sz00
| ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) )
& ! [W1] :
( ! [W2] :
( sdtasdt0(xb,W2) != W1
| ~ aElement0(W2) )
| aElementOf0(W1,slsdtgt0(xb)) )
& ! [W1] :
( ? [W2] :
( sdtasdt0(xb,W2) = W1
& aElement0(W2) )
| ~ aElementOf0(W1,slsdtgt0(xb)) )
& ! [W1] :
( ! [W2] :
( sdtasdt0(xa,W2) != W1
| ~ aElement0(W2) )
| aElementOf0(W1,slsdtgt0(xa)) )
& ! [W1] :
( ? [W2] :
( sdtasdt0(xa,W2) = W1
& aElement0(W2) )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ),
inference(miniscoping,[status(thm)],[f252]) ).
fof(f254,plain,
! [W0] :
( W0 = sz00
| ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) )
& ! [W1] :
( ! [W2] :
( sdtasdt0(xb,W2) != W1
| ~ aElement0(W2) )
| aElementOf0(W1,slsdtgt0(xb)) )
& ! [W1] :
( ( sdtasdt0(xb,sK32_skl(W1,W0)) = W1
& aElement0(sK32_skl(W1,W0)) )
| ~ aElementOf0(W1,slsdtgt0(xb)) )
& ! [W1] :
( ! [W2] :
( sdtasdt0(xa,W2) != W1
| ~ aElement0(W2) )
| aElementOf0(W1,slsdtgt0(xa)) )
& ! [W1] :
( ( sdtasdt0(xa,sK31_skl(W1,W0)) = W1
& aElement0(sK31_skl(W1,W0)) )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31_skl,sK32_skl]),skolemize(W2,sK31_skl(W1,W0)),skolemize(W2,sK32_skl(W1,W0))],[f253]) ).
fof(f261,plain,
! [X0,X1,X2] :
( X2 = sz00
| sdtpldt0(X0,X1) != X2
| ~ aElementOf0(X1,slsdtgt0(xb))
| ~ aElementOf0(X0,slsdtgt0(xa)) ),
inference(cnf_transformation,[status(thm)],[f254]) ).
fof(f317,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sz00
| ~ aElementOf0(X1,slsdtgt0(xb))
| ~ aElementOf0(X0,slsdtgt0(xa)) ),
inference(destructive_equality_resolution,[status(thm)],[f261]) ).
fof(f326,plain,
! [X0] :
( sdtpldt0(X0,xb) = sz00
| ~ aElementOf0(X0,slsdtgt0(xa)) ),
inference(resolution,[status(thm)],[f317,f250]) ).
fof(f393,plain,
sdtpldt0(xa,xb) = sz00,
inference(resolution,[status(thm)],[f326,f244]) ).
fof(f395,plain,
sdtpldt0(sz00,xb) = sz00,
inference(resolution,[status(thm)],[f326,f241]) ).
fof(f399,plain,
( xb = sz00
| ~ aElement0(xb) ),
inference(paramodulation,[status(thm)],[f395,f63]) ).
fof(f404,plain,
xb = sz00,
inference(forward_subsumption_resolution,[status(thm)],[f399,f199]) ).
fof(f412,plain,
sdtpldt0(xa,xb) = xb,
inference(backward_demodulation,[status(thm)],[f404,f393]) ).
fof(f426,plain,
! [X0] :
( sdtpldt0(X0,xb) = X0
| ~ aElement0(X0) ),
inference(backward_demodulation,[status(thm)],[f404,f62]) ).
fof(f434,plain,
( xb != xb
| xa != sz00 ),
inference(backward_demodulation,[status(thm)],[f404,f200]) ).
fof(f445,plain,
( xb != xb
| xa != xb ),
inference(forward_demodulation,[status(thm)],[f404,f434]) ).
fof(f446,plain,
xa != xb,
inference(trivial_equality_resolution,[status(thm)],[f445]) ).
fof(f527,plain,
( xb = xa
| ~ aElement0(xa) ),
inference(paramodulation,[status(thm)],[f412,f426]) ).
fof(f529,plain,
xb = xa,
inference(forward_subsumption_resolution,[status(thm)],[f527,f198]) ).
fof(f530,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f529,f446]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG109+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n009.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 04:20:27 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.37 % Drodi V4.1.1
% 0.07/0.40 % Refutation found
% 0.07/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.44 % Elapsed time: 0.078907 seconds
% 0.12/0.44 % CPU time: 0.246175 seconds
% 0.12/0.44 % Total memory used: 58.618 MB
% 0.12/0.44 % Net memory used: 58.435 MB
%------------------------------------------------------------------------------