%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG115+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 : n001.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 0.14s 0.68s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 7 unt; 3 def)
% Number of atoms : 253 ( 52 equ)
% Maximal formula atoms : 17 ( 5 avg)
% Number of connectives : 347 ( 142 ~; 130 |; 61 &)
% ( 11 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-5 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-4 aty)
% Number of variables : 157 ( 129 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f22,definition,
! [W0,W1] :
( ( aSet0(W1)
& aSet0(W0) )
=> ! [W2] :
( W2 = sdtpldt1(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ? [W4,W5] :
( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) ) )
& aSet0(W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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(f42,hypothesis,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& aIdeal0(xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,hypothesis,
( ! [W0] :
( ( W0 != sz00
& aElementOf0(W0,xI) )
=> ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,conjecture,
? [W0,W1] :
( xu = sdtpldt0(W0,W1)
& aElementOf0(W1,slsdtgt0(xb))
& aElementOf0(W0,slsdtgt0(xa)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
~ ? [W0,W1] :
( xu = sdtpldt0(W0,W1)
& aElementOf0(W1,slsdtgt0(xb))
& aElementOf0(W0,slsdtgt0(xa)) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f100,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtpldt1(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ? [W4,W5] :
( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) ) )
& aSet0(W2) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f101,definition,
! [W0,W1,W3,W4,W5] :
( sP1_prd(W5,W4,W3,W1,W0)
<=> ( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f102,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtpldt1(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ? [W4,W5] : sP1_prd(W5,W4,W3,W1,W0) )
& aSet0(W2) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(formula_renaming,[status(thm)],[f100,f101]) ).
fof(f103,plain,
! [W0,W1] :
( ! [W2] :
( ( ? [W3] :
( ( ? [W4,W5] : sP1_prd(W5,W4,W3,W1,W0)
| aElementOf0(W3,W2) )
& ( ! [W4,W5] : ~ sP1_prd(W5,W4,W3,W1,W0)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtpldt1(W0,W1) )
& ( ( ! [W3] :
( ( ! [W4,W5] : ~ sP1_prd(W5,W4,W3,W1,W0)
| aElementOf0(W3,W2) )
& ( ? [W4,W5] : sP1_prd(W5,W4,W3,W1,W0)
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != sdtpldt1(W0,W1) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f102]) ).
fof(f104,plain,
! [W0,W1] :
( ( ! [W2] :
( ? [W3] :
( ( ? [W4,W5] : sP1_prd(W5,W4,W3,W1,W0)
| aElementOf0(W3,W2) )
& ( ! [W4,W5] : ~ sP1_prd(W5,W4,W3,W1,W0)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtpldt1(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ! [W4,W5] : ~ sP1_prd(W5,W4,W3,W1,W0)
| aElementOf0(W3,W2) )
& ! [W3] :
( ? [W4,W5] : sP1_prd(W5,W4,W3,W1,W0)
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtpldt1(W0,W1) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(miniscoping,[status(thm)],[f103]) ).
fof(f105,plain,
! [W0,W1] :
( ( ! [W2] :
( ( ( sP1_prd(sK6_skl(W2,W1,W0),sK5_skl(W2,W1,W0),sK4_skl(W2,W1,W0),W1,W0)
| aElementOf0(sK4_skl(W2,W1,W0),W2) )
& ( ! [W4,W5] : ~ sP1_prd(W5,W4,sK4_skl(W2,W1,W0),W1,W0)
| ~ aElementOf0(sK4_skl(W2,W1,W0),W2) ) )
| ~ aSet0(W2)
| W2 = sdtpldt1(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ! [W4,W5] : ~ sP1_prd(W5,W4,W3,W1,W0)
| aElementOf0(W3,W2) )
& ! [W3] :
( sP1_prd(sK3_skl(W3,W2,W1,W0),sK2_skl(W3,W2,W1,W0),W3,W1,W0)
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtpldt1(W0,W1) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl,sK5_skl,sK6_skl]),skolemize(W4,sK2_skl(W3,W2,W1,W0)),skolemize(W5,sK3_skl(W3,W2,W1,W0)),skolemize(W3,sK4_skl(W2,W1,W0)),skolemize(W4,sK5_skl(W2,W1,W0)),skolemize(W5,sK6_skl(W2,W1,W0))],[f104]) ).
fof(f107,plain,
! [X0,X1,X2,X3] :
( sP1_prd(sK3_skl(X3,X2,X1,X0),sK2_skl(X3,X2,X1,X0),X3,X1,X0)
| ~ aElementOf0(X3,X2)
| X2 != sdtpldt1(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f188,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(f189,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)],[f188]) ).
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) )
& ! [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)],[f189]) ).
fof(f191,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))],[f190]) ).
fof(f192,plain,
! [X0,X1] :
( aSet0(X1)
| X1 != slsdtgt0(X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f201,plain,
aElement0(xa),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f202,plain,
aElement0(xb),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f206,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f214,plain,
( ! [W0] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| W0 = sz00
| ~ aElementOf0(W0,xI) )
& xu != sz00
& aElementOf0(xu,xI) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f215,plain,
aElementOf0(xu,xI),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f220,plain,
! [W0,W1] :
( xu != sdtpldt0(W0,W1)
| ~ aElementOf0(W1,slsdtgt0(xb))
| ~ aElementOf0(W0,slsdtgt0(xa)) ),
inference(pre_NNF_transformation,[status(thm)],[f48]) ).
fof(f221,plain,
! [X0,X1] :
( xu != sdtpldt0(X0,X1)
| ~ aElementOf0(X1,slsdtgt0(xb))
| ~ aElementOf0(X0,slsdtgt0(xa)) ),
inference(cnf_transformation,[status(thm)],[f220]) ).
fof(f227,plain,
! [W0,W1,W3,W4,W5] :
( ( sdtpldt0(W4,W5) != W3
| ~ aElementOf0(W5,W1)
| ~ aElementOf0(W4,W0)
| sP1_prd(W5,W4,W3,W1,W0) )
& ( ( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) )
| ~ sP1_prd(W5,W4,W3,W1,W0) ) ),
inference(NNF_transformation,[status(thm)],[f101]) ).
fof(f228,plain,
( ! [W0,W1,W3,W4,W5] :
( sdtpldt0(W4,W5) != W3
| ~ aElementOf0(W5,W1)
| ~ aElementOf0(W4,W0)
| sP1_prd(W5,W4,W3,W1,W0) )
& ! [W0,W1,W3,W4,W5] :
( ( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) )
| ~ sP1_prd(W5,W4,W3,W1,W0) ) ),
inference(miniscoping,[status(thm)],[f227]) ).
fof(f229,plain,
! [X0,X1,X2,X3,X4] :
( aElementOf0(X1,X4)
| ~ sP1_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f228]) ).
fof(f230,plain,
! [X0,X1,X2,X3,X4] :
( aElementOf0(X0,X3)
| ~ sP1_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f228]) ).
fof(f231,plain,
! [X0,X1,X2,X3,X4] :
( sdtpldt0(X1,X0) = X2
| ~ sP1_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f228]) ).
fof(f240,plain,
! [X0,X1,X2] :
( sP1_prd(sK3_skl(X2,sdtpldt1(X0,X1),X1,X0),sK2_skl(X2,sdtpldt1(X0,X1),X1,X0),X2,X1,X0)
| ~ aElementOf0(X2,sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f107]) ).
fof(f247,plain,
! [X0] :
( aSet0(slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f192]) ).
fof(f307,plain,
! [X0,X1,X2] :
( sdtpldt0(sK2_skl(X2,sdtpldt1(X0,X1),X1,X0),sK3_skl(X2,sdtpldt1(X0,X1),X1,X0)) = X2
| ~ aElementOf0(X2,sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f240,f231]) ).
fof(f308,plain,
! [X0,X1,X2] :
( aElementOf0(sK3_skl(X2,sdtpldt1(X0,X1),X1,X0),X1)
| ~ aElementOf0(X2,sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f240,f230]) ).
fof(f309,plain,
! [X0,X1,X2] :
( aElementOf0(sK2_skl(X2,sdtpldt1(X0,X1),X1,X0),X0)
| ~ aElementOf0(X2,sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f240,f229]) ).
fof(f575,plain,
! [X0,X1] :
( ~ aElementOf0(sK3_skl(xu,sdtpldt1(X0,X1),X1,X0),slsdtgt0(xb))
| ~ aElementOf0(sK2_skl(xu,sdtpldt1(X0,X1),X1,X0),slsdtgt0(xa))
| ~ aElementOf0(xu,sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f307,f221]) ).
fof(f582,plain,
! [X0] :
( ~ aElementOf0(xu,sdtpldt1(slsdtgt0(xa),X0))
| ~ aSet0(X0)
| ~ aSet0(slsdtgt0(xa))
| ~ aElementOf0(sK3_skl(xu,sdtpldt1(slsdtgt0(xa),X0),X0,slsdtgt0(xa)),slsdtgt0(xb))
| ~ aElementOf0(xu,sdtpldt1(slsdtgt0(xa),X0))
| ~ aSet0(X0)
| ~ aSet0(slsdtgt0(xa)) ),
inference(resolution,[status(thm)],[f575,f309]) ).
fof(f584,plain,
! [X0] :
( ~ aElementOf0(sK3_skl(xu,sdtpldt1(slsdtgt0(xa),X0),X0,slsdtgt0(xa)),slsdtgt0(xb))
| ~ aElementOf0(xu,sdtpldt1(slsdtgt0(xa),X0))
| ~ aSet0(X0)
| ~ aSet0(slsdtgt0(xa)) ),
inference(duplicate_literals_removal,[status(thm)],[f582]) ).
fof(f588,plain,
( ~ aElementOf0(xu,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ aSet0(slsdtgt0(xb))
| ~ aSet0(slsdtgt0(xa))
| ~ aElementOf0(xu,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ aSet0(slsdtgt0(xb))
| ~ aSet0(slsdtgt0(xa)) ),
inference(resolution,[status(thm)],[f584,f308]) ).
fof(f590,plain,
( ~ aElementOf0(xu,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ aSet0(slsdtgt0(xb))
| ~ aSet0(slsdtgt0(xa))
| ~ aElementOf0(xu,xI)
| ~ aSet0(slsdtgt0(xb))
| ~ aSet0(slsdtgt0(xa)) ),
inference(forward_demodulation,[status(thm)],[f206,f588]) ).
fof(f591,plain,
( ~ aElementOf0(xu,xI)
| ~ aSet0(slsdtgt0(xb))
| ~ aSet0(slsdtgt0(xa))
| ~ aElementOf0(xu,xI)
| ~ aSet0(slsdtgt0(xb))
| ~ aSet0(slsdtgt0(xa)) ),
inference(forward_demodulation,[status(thm)],[f206,f590]) ).
fof(f592,plain,
( ~ aElementOf0(xu,xI)
| ~ aSet0(slsdtgt0(xb))
| ~ aSet0(slsdtgt0(xa)) ),
inference(duplicate_literals_removal,[status(thm)],[f591]) ).
fof(f593,plain,
( ~ aSet0(slsdtgt0(xb))
| ~ aSet0(slsdtgt0(xa)) ),
inference(forward_subsumption_resolution,[status(thm)],[f592,f215]) ).
fof(f596,plain,
( ~ aElement0(xa)
| ~ aSet0(slsdtgt0(xb)) ),
inference(resolution,[status(thm)],[f593,f247]) ).
fof(f597,plain,
~ aSet0(slsdtgt0(xb)),
inference(forward_subsumption_resolution,[status(thm)],[f596,f201]) ).
fof(f598,plain,
~ aElement0(xb),
inference(resolution,[status(thm)],[f597,f247]) ).
fof(f599,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f598,f202]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG115+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.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 04:26:43 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.14/0.68 % Refutation found
% 0.14/0.68 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.72 % Elapsed time: 0.343921 seconds
% 0.14/0.72 % CPU time: 2.063334 seconds
% 0.14/0.72 % Total memory used: 123.764 MB
% 0.14/0.72 % Net memory used: 122.303 MB
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