%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG114+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 : 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 02:05:01 PM UTC 2026
% Result : Theorem 65.15s 8.67s
% Output : CNFRefutation 28.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 9 unt; 0 def)
% Number of atoms : 191 ( 54 equ)
% Maximal formula atoms : 28 ( 6 avg)
% Number of connectives : 240 ( 78 ~; 64 |; 88 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-2 aty)
% Number of variables : 91 ( 65 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f42,hypothesis,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [W0] :
( aElementOf0(W0,xI)
<=> ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) ) )
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xb))
<=> ? [W1] :
( sdtasdt0(xb,W1) = W0
& aElement0(W1) ) )
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xa))
<=> ? [W1] :
( sdtasdt0(xa,W1) = W0
& aElement0(W1) ) )
& aIdeal0(xI)
& ! [W0] :
( aElementOf0(W0,xI)
=> ( ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) )
& ! [W1] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) ) ) )
& aSet0(xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,hypothesis,
( ! [W0] :
( ( W0 != sz00
& ( aElementOf0(W0,xI)
| ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) ) ) )
=> ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI)
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xu
& aElementOf0(W1,slsdtgt0(xb))
& aElementOf0(W0,slsdtgt0(xa)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,conjecture,
? [W0,W1] :
( xu = sdtpldt0(sdtasdt0(xa,W0),sdtasdt0(xb,W1))
& aElement0(W1)
& aElement0(W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
~ ? [W0,W1] :
( xu = sdtpldt0(sdtasdt0(xa,W0),sdtasdt0(xb,W1))
& aElement0(W1)
& aElement0(W0) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f222,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [W0] :
( aElementOf0(W0,xI)
<=> ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) ) )
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xb))
<=> ? [W1] :
( sdtasdt0(xb,W1) = W0
& aElement0(W1) ) )
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xa))
<=> ? [W1] :
( sdtasdt0(xa,W1) = W0
& aElement0(W1) ) )
& aIdeal0(xI)
& ! [W0] :
( ( ! [W1] :
( aElementOf0(sdtasdt0(W1,W0),xI)
| ~ aElement0(W1) )
& ! [W1] :
( aElementOf0(sdtpldt0(W0,W1),xI)
| ~ aElementOf0(W1,xI) ) )
| ~ aElementOf0(W0,xI) )
& aSet0(xI) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f223,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [W0] :
( ( ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) )
| aElementOf0(W0,xI) )
& ( ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) )
| ~ aElementOf0(W0,xI) ) )
& ! [W0] :
( ( ! [W1] :
( sdtasdt0(xb,W1) != W0
| ~ aElement0(W1) )
| aElementOf0(W0,slsdtgt0(xb)) )
& ( ? [W1] :
( sdtasdt0(xb,W1) = W0
& aElement0(W1) )
| ~ aElementOf0(W0,slsdtgt0(xb)) ) )
& ! [W0] :
( ( ! [W1] :
( sdtasdt0(xa,W1) != W0
| ~ aElement0(W1) )
| aElementOf0(W0,slsdtgt0(xa)) )
& ( ? [W1] :
( sdtasdt0(xa,W1) = W0
& aElement0(W1) )
| ~ aElementOf0(W0,slsdtgt0(xa)) ) )
& aIdeal0(xI)
& ! [W0] :
( ( ! [W1] :
( aElementOf0(sdtasdt0(W1,W0),xI)
| ~ aElement0(W1) )
& ! [W1] :
( aElementOf0(sdtpldt0(W0,W1),xI)
| ~ aElementOf0(W1,xI) ) )
| ~ aElementOf0(W0,xI) )
& aSet0(xI) ),
inference(NNF_transformation,[status(thm)],[f222]) ).
fof(f224,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [W0] :
( ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) )
| aElementOf0(W0,xI) )
& ! [W0] :
( ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) )
| ~ aElementOf0(W0,xI) )
& ! [W0] :
( ! [W1] :
( sdtasdt0(xb,W1) != W0
| ~ aElement0(W1) )
| aElementOf0(W0,slsdtgt0(xb)) )
& ! [W0] :
( ? [W1] :
( sdtasdt0(xb,W1) = W0
& aElement0(W1) )
| ~ aElementOf0(W0,slsdtgt0(xb)) )
& ! [W0] :
( ! [W1] :
( sdtasdt0(xa,W1) != W0
| ~ aElement0(W1) )
| aElementOf0(W0,slsdtgt0(xa)) )
& ! [W0] :
( ? [W1] :
( sdtasdt0(xa,W1) = W0
& aElement0(W1) )
| ~ aElementOf0(W0,slsdtgt0(xa)) )
& aIdeal0(xI)
& ! [W0] :
( ( ! [W1] :
( aElementOf0(sdtasdt0(W1,W0),xI)
| ~ aElement0(W1) )
& ! [W1] :
( aElementOf0(sdtpldt0(W0,W1),xI)
| ~ aElementOf0(W1,xI) ) )
| ~ aElementOf0(W0,xI) )
& aSet0(xI) ),
inference(miniscoping,[status(thm)],[f223]) ).
fof(f225,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [W0] :
( ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) )
| aElementOf0(W0,xI) )
& ! [W0] :
( ( sdtpldt0(sK25_skl(W0),sK26_skl(W0)) = W0
& aElementOf0(sK26_skl(W0),slsdtgt0(xb))
& aElementOf0(sK25_skl(W0),slsdtgt0(xa)) )
| ~ aElementOf0(W0,xI) )
& ! [W0] :
( ! [W1] :
( sdtasdt0(xb,W1) != W0
| ~ aElement0(W1) )
| aElementOf0(W0,slsdtgt0(xb)) )
& ! [W0] :
( ( sdtasdt0(xb,sK24_skl(W0)) = W0
& aElement0(sK24_skl(W0)) )
| ~ aElementOf0(W0,slsdtgt0(xb)) )
& ! [W0] :
( ! [W1] :
( sdtasdt0(xa,W1) != W0
| ~ aElement0(W1) )
| aElementOf0(W0,slsdtgt0(xa)) )
& ! [W0] :
( ( sdtasdt0(xa,sK23_skl(W0)) = W0
& aElement0(sK23_skl(W0)) )
| ~ aElementOf0(W0,slsdtgt0(xa)) )
& aIdeal0(xI)
& ! [W0] :
( ( ! [W1] :
( aElementOf0(sdtasdt0(W1,W0),xI)
| ~ aElement0(W1) )
& ! [W1] :
( aElementOf0(sdtpldt0(W0,W1),xI)
| ~ aElementOf0(W1,xI) ) )
| ~ aElementOf0(W0,xI) )
& aSet0(xI) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl,sK24_skl,sK25_skl,sK26_skl]),skolemize(W1,sK23_skl(W0)),skolemize(W1,sK24_skl(W0)),skolemize(W1,sK25_skl(W0)),skolemize(W2,sK26_skl(W0))],[f224]) ).
fof(f230,plain,
! [X0] :
( aElement0(sK23_skl(X0))
| ~ aElementOf0(X0,slsdtgt0(xa)) ),
inference(cnf_transformation,[status(thm)],[f225]) ).
fof(f231,plain,
! [X0] :
( sdtasdt0(xa,sK23_skl(X0)) = X0
| ~ aElementOf0(X0,slsdtgt0(xa)) ),
inference(cnf_transformation,[status(thm)],[f225]) ).
fof(f233,plain,
! [X0] :
( aElement0(sK24_skl(X0))
| ~ aElementOf0(X0,slsdtgt0(xb)) ),
inference(cnf_transformation,[status(thm)],[f225]) ).
fof(f234,plain,
! [X0] :
( sdtasdt0(xb,sK24_skl(X0)) = X0
| ~ aElementOf0(X0,slsdtgt0(xb)) ),
inference(cnf_transformation,[status(thm)],[f225]) ).
fof(f268,plain,
( ! [W0] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| W0 = sz00
| ( ~ aElementOf0(W0,xI)
& ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
& xu != sz00
& aElementOf0(xu,xI)
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xu
& aElementOf0(W1,slsdtgt0(xb))
& aElementOf0(W0,slsdtgt0(xa)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f269,plain,
( ! [W0] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| W0 = sz00
| ( ~ aElementOf0(W0,xI)
& ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
& xu != sz00
& aElementOf0(xu,xI)
& sdtpldt0(sK36_skl,sK37_skl) = xu
& aElementOf0(sK37_skl,slsdtgt0(xb))
& aElementOf0(sK36_skl,slsdtgt0(xa)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36_skl,sK37_skl]),skolemize(W0,sK36_skl),skolemize(W1,sK37_skl)],[f268]) ).
fof(f270,plain,
aElementOf0(sK36_skl,slsdtgt0(xa)),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f271,plain,
aElementOf0(sK37_skl,slsdtgt0(xb)),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f272,plain,
sdtpldt0(sK36_skl,sK37_skl) = xu,
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f283,plain,
! [W0,W1] :
( xu != sdtpldt0(sdtasdt0(xa,W0),sdtasdt0(xb,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f48]) ).
fof(f284,plain,
! [X0,X1] :
( xu != sdtpldt0(sdtasdt0(xa,X0),sdtasdt0(xb,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f283]) ).
fof(f8076,plain,
aElement0(sK23_skl(sK36_skl)),
inference(resolution,[status(thm)],[f230,f270]) ).
fof(f8995,plain,
sdtasdt0(xa,sK23_skl(sK36_skl)) = sK36_skl,
inference(resolution,[status(thm)],[f231,f270]) ).
fof(f9023,plain,
aElement0(sK24_skl(sK37_skl)),
inference(resolution,[status(thm)],[f233,f271]) ).
fof(f10236,plain,
sdtasdt0(xb,sK24_skl(sK37_skl)) = sK37_skl,
inference(resolution,[status(thm)],[f234,f271]) ).
fof(f24693,plain,
! [X0] :
( xu != sdtpldt0(sK36_skl,sdtasdt0(xb,X0))
| ~ aElement0(X0)
| ~ aElement0(sK23_skl(sK36_skl)) ),
inference(paramodulation,[status(thm)],[f8995,f284]) ).
fof(f24710,plain,
! [X0] :
( xu != sdtpldt0(sK36_skl,sdtasdt0(xb,X0))
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f24693,f8076]) ).
fof(f29448,plain,
( xu != sdtpldt0(sK36_skl,sK37_skl)
| ~ aElement0(sK24_skl(sK37_skl)) ),
inference(paramodulation,[status(thm)],[f10236,f24710]) ).
fof(f29471,plain,
( xu != xu
| ~ aElement0(sK24_skl(sK37_skl)) ),
inference(forward_demodulation,[status(thm)],[f272,f29448]) ).
fof(f29472,plain,
~ aElement0(sK24_skl(sK37_skl)),
inference(trivial_equality_resolution,[status(thm)],[f29471]) ).
fof(f29473,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f29472,f9023]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG114+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.35 % Computer : n016.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Mon Sep 21 04:25:53 UTC 2026
% 0.11/0.35 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 65.15/8.67 % Refutation found
% 65.15/8.67 % SZS status Theorem for theBenchmark: Theorem is valid
% 65.15/8.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 28.77/8.76 % Elapsed time: 8.397774 seconds
% 28.77/8.76 % CPU time: 66.077311 seconds
% 28.77/8.76 % Total memory used: 447.591 MB
% 28.77/8.76 % Net memory used: 416.118 MB
%------------------------------------------------------------------------------