%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG116+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 : n026.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 02:05:01 PM UTC 2026
% Result : Theorem 138.55s 17.87s
% Output : CNFRefutation 26.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 13 unt; 1 def)
% Number of atoms : 120 ( 41 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 143 ( 57 ~; 52 |; 29 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 53 ( 41 !; 12 ?)
% 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/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,hypothesis,
( xu = sdtpldt0(xk,xl)
& aElementOf0(xl,slsdtgt0(xb))
& aElementOf0(xk,slsdtgt0(xa)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,conjecture,
? [W0,W1] :
( xu = sdtpldt0(sdtasdt0(xa,W0),sdtasdt0(xb,W1))
& aElement0(W1)
& aElement0(W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
~ ? [W0,W1] :
( xu = sdtpldt0(sdtasdt0(xa,W0),sdtasdt0(xb,W1))
& aElement0(W1)
& aElement0(W0) ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f189,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(f190,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)],[f189]) ).
fof(f191,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)],[f190]) ).
fof(f192,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))],[f191]) ).
fof(f194,plain,
! [X0,X1,X2] :
( aElement0(sK17_skl(X2,X1,X0))
| ~ aElementOf0(X2,X1)
| X1 != slsdtgt0(X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f195,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)],[f192]) ).
fof(f202,plain,
aElement0(xa),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f203,plain,
aElement0(xb),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f221,plain,
aElementOf0(xk,slsdtgt0(xa)),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f222,plain,
aElementOf0(xl,slsdtgt0(xb)),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f223,plain,
xu = sdtpldt0(xk,xl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f224,plain,
! [W0,W1] :
( xu != sdtpldt0(sdtasdt0(xa,W0),sdtasdt0(xb,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f49]) ).
fof(f225,plain,
! [X0,X1] :
( xu != sdtpldt0(sdtasdt0(xa,X0),sdtasdt0(xb,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f224]) ).
fof(f252,plain,
! [X0,X1] :
( aElement0(sK17_skl(X1,slsdtgt0(X0),X0))
| ~ aElementOf0(X1,slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f194]) ).
fof(f253,plain,
! [X0,X1] :
( sdtasdt0(X0,sK17_skl(X1,slsdtgt0(X0),X0)) = X1
| ~ aElementOf0(X1,slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f195]) ).
fof(f4951,plain,
( aElement0(sK17_skl(xl,slsdtgt0(xb),xb))
| ~ aElement0(xb) ),
inference(resolution,[status(thm)],[f252,f222]) ).
fof(f4952,plain,
( aElement0(sK17_skl(xk,slsdtgt0(xa),xa))
| ~ aElement0(xa) ),
inference(resolution,[status(thm)],[f252,f221]) ).
fof(f4966,plain,
aElement0(sK17_skl(xl,slsdtgt0(xb),xb)),
inference(forward_subsumption_resolution,[status(thm)],[f4951,f203]) ).
fof(f4967,plain,
aElement0(sK17_skl(xk,slsdtgt0(xa),xa)),
inference(forward_subsumption_resolution,[status(thm)],[f4952,f202]) ).
fof(f4981,plain,
( sdtasdt0(xb,sK17_skl(xl,slsdtgt0(xb),xb)) = xl
| ~ aElement0(xb) ),
inference(resolution,[status(thm)],[f253,f222]) ).
fof(f4982,plain,
( sdtasdt0(xa,sK17_skl(xk,slsdtgt0(xa),xa)) = xk
| ~ aElement0(xa) ),
inference(resolution,[status(thm)],[f253,f221]) ).
fof(f4996,plain,
sdtasdt0(xb,sK17_skl(xl,slsdtgt0(xb),xb)) = xl,
inference(forward_subsumption_resolution,[status(thm)],[f4981,f203]) ).
fof(f4997,plain,
sdtasdt0(xa,sK17_skl(xk,slsdtgt0(xa),xa)) = xk,
inference(forward_subsumption_resolution,[status(thm)],[f4982,f202]) ).
fof(f44999,plain,
! [X0] :
( xu != sdtpldt0(sdtasdt0(xa,X0),xl)
| ~ aElement0(sK17_skl(xl,slsdtgt0(xb),xb))
| ~ aElement0(X0) ),
inference(paramodulation,[status(thm)],[f4996,f225]) ).
fof(f45008,plain,
! [X0] :
( xu != sdtpldt0(sdtasdt0(xa,X0),xl)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f44999,f4966]) ).
fof(f45920,plain,
xu != sdtpldt0(sdtasdt0(xa,sK17_skl(xk,slsdtgt0(xa),xa)),xl),
inference(resolution,[status(thm)],[f45008,f4967]) ).
fof(f46072,plain,
xu != sdtpldt0(xk,xl),
inference(forward_demodulation,[status(thm)],[f4997,f45920]) ).
fof(f46073,plain,
xu != xu,
inference(forward_demodulation,[status(thm)],[f223,f46072]) ).
fof(f46074,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f46073]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG116+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n026.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 04:23:53 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 138.55/17.87 % Refutation found
% 138.55/17.87 % SZS status Theorem for theBenchmark: Theorem is valid
% 138.55/17.87 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 26.01/17.92 % Elapsed time: 17.548566 seconds
% 26.01/17.92 % CPU time: 138.951162 seconds
% 26.01/17.92 % Total memory used: 574.915 MB
% 26.01/17.92 % Net memory used: 518.920 MB
%------------------------------------------------------------------------------