%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG088+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 : n014.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 02:04:55 PM UTC 2026
% Result : Theorem 0.20s 0.49s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 8 unt; 1 def)
% Number of atoms : 102 ( 2 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 126 ( 51 ~; 41 |; 29 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 31 ( 25 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,hypothesis,
( aIdeal0(xJ)
& aIdeal0(xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
( xx = sdtpldt0(xk,xl)
& aElementOf0(xl,xJ)
& aElementOf0(xk,xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
( xy = sdtpldt0(xm,xn)
& aElementOf0(xn,xJ)
& aElementOf0(xm,xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
( aElementOf0(sdtpldt0(xl,xn),xJ)
& aElementOf0(sdtpldt0(xk,xm),xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ( aElementOf0(sdtpldt0(xl,xn),xJ)
& aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f104,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(f105,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)],[f104]) ).
fof(f106,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)],[f105]) ).
fof(f107,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))],[f106]) ).
fof(f109,plain,
! [X0,X1,X2] :
( aElementOf0(sdtpldt0(X1,X2),X0)
| ~ aElementOf0(X2,X0)
| ~ aElementOf0(X1,X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f116,plain,
aIdeal0(xI),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f117,plain,
aIdeal0(xJ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f121,plain,
aElementOf0(xk,xI),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f122,plain,
aElementOf0(xl,xJ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f124,plain,
aElementOf0(xm,xI),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f125,plain,
aElementOf0(xn,xJ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f127,plain,
( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| ~ aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f128,plain,
( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| ~ aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f194,plain,
( ~ aElementOf0(sdtpldt0(xk,xm),xI)
| ~ aElementOf0(xn,xJ)
| ~ aElementOf0(xl,xJ)
| ~ aIdeal0(xJ) ),
inference(resolution,[status(thm)],[f109,f128]) ).
fof(f200,plain,
( ~ aElementOf0(sdtpldt0(xk,xm),xI)
| ~ aElementOf0(xn,xJ)
| ~ aElementOf0(xl,xJ) ),
inference(forward_subsumption_resolution,[status(thm)],[f194,f117]) ).
fof(f211,plain,
( ~ aElementOf0(sdtpldt0(xk,xm),xI)
| ~ aElementOf0(xn,xJ) ),
inference(forward_subsumption_resolution,[status(thm)],[f200,f122]) ).
fof(f212,plain,
( ~ aElementOf0(xm,xI)
| ~ aElementOf0(xk,xI)
| ~ aIdeal0(xI)
| ~ aElementOf0(xn,xJ) ),
inference(resolution,[status(thm)],[f211,f109]) ).
fof(f213,plain,
( ~ aElementOf0(xm,xI)
| ~ aElementOf0(xk,xI)
| ~ aIdeal0(xI) ),
inference(forward_subsumption_resolution,[status(thm)],[f212,f125]) ).
fof(f214,plain,
( ~ aElementOf0(xm,xI)
| ~ aElementOf0(xk,xI) ),
inference(forward_subsumption_resolution,[status(thm)],[f213,f116]) ).
fof(f215,plain,
~ aElementOf0(xk,xI),
inference(resolution,[status(thm)],[f214,f124]) ).
fof(f216,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f215,f121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG088+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n014.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Mon Sep 21 04:18:52 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.47 % Drodi V4.1.1
% 0.20/0.49 % Refutation found
% 0.20/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.51 % Elapsed time: 0.052362 seconds
% 0.23/0.51 % CPU time: 0.155731 seconds
% 0.23/0.51 % Total memory used: 88.480 MB
% 0.23/0.51 % Net memory used: 88.362 MB
%------------------------------------------------------------------------------