%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG118+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 : 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 02:05:02 PM UTC 2026
% Result : Theorem 0.22s 0.60s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 7
% Syntax : Number of formulae : 55 ( 9 unt; 1 def)
% Number of atoms : 244 ( 63 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 314 ( 125 ~; 128 |; 51 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-2 aty)
% Number of variables : 71 ( 55 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f20,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,definition,
! [W0] :
( aIdeal0(W0)
<=> ( ! [W1] :
( aElementOf0(W1,W0)
=> ( ! [W2] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) )
& ! [W2] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) ) ) )
& aSet0(W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [W0,W1] :
( ( W1 != sz00
& aElement0(W1)
& aElement0(W0) )
=> ? [W2,W3] :
( ( W3 != sz00
=> iLess0(sbrdtbr0(W3),sbrdtbr0(W1)) )
& W0 = sdtpldt0(sdtasdt0(W2,W1),W3)
& aElement0(W3)
& aElement0(W2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,hypothesis,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& aIdeal0(xI) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f50,conjecture,
? [W0,W1] :
( ( iLess0(sbrdtbr0(W1),sbrdtbr0(xu))
| W1 = sz00 )
& xb = sdtpldt0(sdtasdt0(W0,xu),W1)
& aElement0(W1)
& aElement0(W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,negated_conjecture,
~ ? [W0,W1] :
( ( iLess0(sbrdtbr0(W1),sbrdtbr0(xu))
| W1 = sz00 )
& xb = sdtpldt0(sdtasdt0(W0,xu),W1)
& aElement0(W1)
& aElement0(W0) ),
inference(negated_conjecture,[status(cth)],[f50]) ).
fof(f95,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f96,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f125,plain,
! [W0] :
( aIdeal0(W0)
<=> ( ! [W1] :
( ( ! [W2] :
( aElementOf0(sdtasdt0(W2,W1),W0)
| ~ aElement0(W2) )
& ! [W2] :
( aElementOf0(sdtpldt0(W1,W2),W0)
| ~ aElementOf0(W2,W0) ) )
| ~ aElementOf0(W1,W0) )
& aSet0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f126,plain,
! [W0] :
( ( ? [W1] :
( ( ? [W2] :
( ~ aElementOf0(sdtasdt0(W2,W1),W0)
& aElement0(W2) )
| ? [W2] :
( ~ aElementOf0(sdtpldt0(W1,W2),W0)
& aElementOf0(W2,W0) ) )
& aElementOf0(W1,W0) )
| ~ aSet0(W0)
| aIdeal0(W0) )
& ( ( ! [W1] :
( ( ! [W2] :
( aElementOf0(sdtasdt0(W2,W1),W0)
| ~ aElement0(W2) )
& ! [W2] :
( aElementOf0(sdtpldt0(W1,W2),W0)
| ~ aElementOf0(W2,W0) ) )
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aIdeal0(W0) ) ),
inference(NNF_transformation,[status(thm)],[f125]) ).
fof(f127,plain,
( ! [W0] :
( ? [W1] :
( ( ? [W2] :
( ~ aElementOf0(sdtasdt0(W2,W1),W0)
& aElement0(W2) )
| ? [W2] :
( ~ aElementOf0(sdtpldt0(W1,W2),W0)
& aElementOf0(W2,W0) ) )
& aElementOf0(W1,W0) )
| ~ aSet0(W0)
| aIdeal0(W0) )
& ! [W0] :
( ( ! [W1] :
( ( ! [W2] :
( aElementOf0(sdtasdt0(W2,W1),W0)
| ~ aElement0(W2) )
& ! [W2] :
( aElementOf0(sdtpldt0(W1,W2),W0)
| ~ aElementOf0(W2,W0) ) )
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aIdeal0(W0) ) ),
inference(miniscoping,[status(thm)],[f126]) ).
fof(f128,plain,
( ! [W0] :
( ( ( ( ~ aElementOf0(sdtasdt0(sK10_skl(W0),sK8_skl(W0)),W0)
& aElement0(sK10_skl(W0)) )
| ( ~ aElementOf0(sdtpldt0(sK8_skl(W0),sK9_skl(W0)),W0)
& aElementOf0(sK9_skl(W0),W0) ) )
& aElementOf0(sK8_skl(W0),W0) )
| ~ aSet0(W0)
| aIdeal0(W0) )
& ! [W0] :
( ( ! [W1] :
( ( ! [W2] :
( aElementOf0(sdtasdt0(W2,W1),W0)
| ~ aElement0(W2) )
& ! [W2] :
( aElementOf0(sdtpldt0(W1,W2),W0)
| ~ aElementOf0(W2,W0) ) )
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aIdeal0(W0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl,sK10_skl]),skolemize(W1,sK8_skl(W0)),skolemize(W2,sK9_skl(W0)),skolemize(W2,sK10_skl(W0))],[f127]) ).
fof(f129,plain,
! [X0] :
( aSet0(X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f158,plain,
! [W0,W1] :
( ? [W2,W3] :
( ( iLess0(sbrdtbr0(W3),sbrdtbr0(W1))
| W3 = sz00 )
& W0 = sdtpldt0(sdtasdt0(W2,W1),W3)
& aElement0(W3)
& aElement0(W2) )
| W1 = sz00
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f159,plain,
! [W0,W1] :
( ? [W3] :
( ( iLess0(sbrdtbr0(W3),sbrdtbr0(W1))
| W3 = sz00 )
& ? [W2] :
( W0 = sdtpldt0(sdtasdt0(W2,W1),W3)
& aElement0(W3)
& aElement0(W2) ) )
| W1 = sz00
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(miniscoping,[status(thm)],[f158]) ).
fof(f160,plain,
! [W0,W1] :
( ( ( iLess0(sbrdtbr0(sK13_skl(W1,W0)),sbrdtbr0(W1))
| sK13_skl(W1,W0) = sz00 )
& W0 = sdtpldt0(sdtasdt0(sK14_skl(W1,W0),W1),sK13_skl(W1,W0))
& aElement0(sK13_skl(W1,W0))
& aElement0(sK14_skl(W1,W0)) )
| W1 = sz00
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl]),skolemize(W3,sK13_skl(W1,W0)),skolemize(W2,sK14_skl(W1,W0))],[f159]) ).
fof(f161,plain,
! [X0,X1] :
( aElement0(sK14_skl(X1,X0))
| X1 = sz00
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f162,plain,
! [X0,X1] :
( aElement0(sK13_skl(X1,X0))
| X1 = sz00
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f163,plain,
! [X0,X1] :
( X0 = sdtpldt0(sdtasdt0(sK14_skl(X1,X0),X1),sK13_skl(X1,X0))
| X1 = sz00
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f164,plain,
! [X0,X1] :
( iLess0(sbrdtbr0(sK13_skl(X1,X0)),sbrdtbr0(X1))
| sK13_skl(X1,X0) = sz00
| X1 = sz00
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f205,plain,
aElement0(xb),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f208,plain,
aIdeal0(xI),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f217,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(f218,plain,
aElementOf0(xu,xI),
inference(cnf_transformation,[status(thm)],[f217]) ).
fof(f219,plain,
xu != sz00,
inference(cnf_transformation,[status(thm)],[f217]) ).
fof(f229,plain,
! [W0,W1] :
( ( ~ iLess0(sbrdtbr0(W1),sbrdtbr0(xu))
& W1 != sz00 )
| xb != sdtpldt0(sdtasdt0(W0,xu),W1)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f51]) ).
fof(f230,plain,
! [W1] :
( ( ~ iLess0(sbrdtbr0(W1),sbrdtbr0(xu))
& W1 != sz00 )
| ! [W0] :
( xb != sdtpldt0(sdtasdt0(W0,xu),W1)
| ~ aElement0(W1)
| ~ aElement0(W0) ) ),
inference(miniscoping,[status(thm)],[f229]) ).
fof(f231,plain,
! [X0,X1] :
( X1 != sz00
| xb != sdtpldt0(sdtasdt0(X0,xu),X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f230]) ).
fof(f232,plain,
! [X0,X1] :
( ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu))
| xb != sdtpldt0(sdtasdt0(X0,xu),X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f230]) ).
fof(f252,plain,
( aElement0(xu)
| ~ aSet0(xI) ),
inference(resolution,[status(thm)],[f96,f218]) ).
fof(f256,plain,
( ~ iLess0(sbrdtbr0(sK13_skl(xu,xb)),sbrdtbr0(xu))
| ~ aElement0(sK13_skl(xu,xb))
| ~ aElement0(sK14_skl(xu,xb))
| xu = sz00
| ~ aElement0(xu)
| ~ aElement0(xb) ),
inference(resolution,[status(thm)],[f163,f232]) ).
fof(f257,plain,
( sK13_skl(xu,xb) != sz00
| ~ aElement0(sK13_skl(xu,xb))
| ~ aElement0(sK14_skl(xu,xb))
| xu = sz00
| ~ aElement0(xu)
| ~ aElement0(xb) ),
inference(resolution,[status(thm)],[f163,f231]) ).
fof(f258,plain,
( ~ iLess0(sbrdtbr0(sK13_skl(xu,xb)),sbrdtbr0(xu))
| ~ aElement0(sK13_skl(xu,xb))
| ~ aElement0(sK14_skl(xu,xb))
| xu = sz00
| ~ aElement0(xu) ),
inference(forward_subsumption_resolution,[status(thm)],[f256,f205]) ).
fof(f259,plain,
( sK13_skl(xu,xb) != sz00
| ~ aElement0(sK13_skl(xu,xb))
| ~ aElement0(sK14_skl(xu,xb))
| xu = sz00
| ~ aElement0(xu) ),
inference(forward_subsumption_resolution,[status(thm)],[f257,f205]) ).
fof(f260,plain,
aSet0(xI),
inference(resolution,[status(thm)],[f129,f208]) ).
fof(f261,plain,
aElement0(xu),
inference(backward_subsumption_resolution,[status(thm)],[f252,f260]) ).
fof(f262,plain,
( sK13_skl(xu,xb) != sz00
| ~ aElement0(sK13_skl(xu,xb))
| ~ aElement0(sK14_skl(xu,xb))
| xu = sz00 ),
inference(forward_subsumption_resolution,[status(thm)],[f259,f261]) ).
fof(f263,plain,
( ~ iLess0(sbrdtbr0(sK13_skl(xu,xb)),sbrdtbr0(xu))
| ~ aElement0(sK13_skl(xu,xb))
| ~ aElement0(sK14_skl(xu,xb))
| xu = sz00 ),
inference(forward_subsumption_resolution,[status(thm)],[f258,f261]) ).
fof(f264,plain,
( ~ aElement0(sK13_skl(xu,xb))
| ~ aElement0(sK14_skl(xu,xb))
| xu = sz00
| sK13_skl(xu,xb) = sz00
| xu = sz00
| ~ aElement0(xu)
| ~ aElement0(xb) ),
inference(resolution,[status(thm)],[f164,f263]) ).
fof(f266,plain,
( ~ aElement0(sK13_skl(xu,xb))
| ~ aElement0(sK14_skl(xu,xb))
| sK13_skl(xu,xb) = sz00
| xu = sz00
| ~ aElement0(xu)
| ~ aElement0(xb) ),
inference(duplicate_literals_removal,[status(thm)],[f264]) ).
fof(f267,plain,
( ~ aElement0(sK13_skl(xu,xb))
| ~ aElement0(sK14_skl(xu,xb))
| sK13_skl(xu,xb) = sz00
| xu = sz00
| ~ aElement0(xu) ),
inference(forward_subsumption_resolution,[status(thm)],[f266,f205]) ).
fof(f270,plain,
( ~ aElement0(sK13_skl(xu,xb))
| ~ aElement0(sK14_skl(xu,xb))
| xu = sz00 ),
inference(backward_subsumption_resolution,[status(thm)],[f262,f271]) ).
fof(f271,plain,
( ~ aElement0(sK13_skl(xu,xb))
| ~ aElement0(sK14_skl(xu,xb))
| sK13_skl(xu,xb) = sz00
| xu = sz00 ),
inference(forward_subsumption_resolution,[status(thm)],[f267,f261]) ).
fof(f272,plain,
( ~ aElement0(sK13_skl(xu,xb))
| ~ aElement0(sK14_skl(xu,xb)) ),
inference(forward_subsumption_resolution,[status(thm)],[f270,f219]) ).
fof(f324,plain,
( ~ aElement0(sK13_skl(xu,xb))
| xu = sz00
| ~ aElement0(xu)
| ~ aElement0(xb) ),
inference(resolution,[status(thm)],[f161,f272]) ).
fof(f325,plain,
( ~ aElement0(sK13_skl(xu,xb))
| xu = sz00
| ~ aElement0(xu) ),
inference(forward_subsumption_resolution,[status(thm)],[f324,f205]) ).
fof(f326,plain,
( ~ aElement0(sK13_skl(xu,xb))
| xu = sz00 ),
inference(forward_subsumption_resolution,[status(thm)],[f325,f261]) ).
fof(f327,plain,
( xu = sz00
| xu = sz00
| ~ aElement0(xu)
| ~ aElement0(xb) ),
inference(resolution,[status(thm)],[f162,f326]) ).
fof(f328,plain,
( xu = sz00
| ~ aElement0(xu)
| ~ aElement0(xb) ),
inference(duplicate_literals_removal,[status(thm)],[f327]) ).
fof(f329,plain,
( xu = sz00
| ~ aElement0(xu) ),
inference(forward_subsumption_resolution,[status(thm)],[f328,f205]) ).
fof(f339,plain,
sz00 != sz00,
inference(backward_demodulation,[status(thm)],[f342,f219]) ).
fof(f342,plain,
xu = sz00,
inference(forward_subsumption_resolution,[status(thm)],[f329,f261]) ).
fof(f346,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f339]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG118+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n016.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 04:25:37 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.47 % Drodi V4.1.1
% 0.22/0.60 % Refutation found
% 0.22/0.60 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.22/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.63 % Elapsed time: 0.168355 seconds
% 0.22/0.63 % CPU time: 1.025483 seconds
% 0.22/0.63 % Total memory used: 117.109 MB
% 0.22/0.63 % Net memory used: 116.208 MB
%------------------------------------------------------------------------------