%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG123+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 : n011.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 02:05:03 PM UTC 2026
% Result : Theorem 0.10s 0.43s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 37 ( 16 unt; 1 def)
% Number of atoms : 116 ( 9 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 127 ( 48 ~; 46 |; 25 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 45 ( 39 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(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(f52,hypothesis,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,hypothesis,
aElementOf0(xb,xI),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,hypothesis,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,conjecture,
aElementOf0(xr,xI),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,negated_conjecture,
~ aElementOf0(xr,xI),
inference(negated_conjecture,[status(cth)],[f55]) ).
fof(f68,plain,
! [W0,W1] :
( sdtpldt0(W0,W1) = sdtpldt0(W1,W0)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f69,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f100,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f101,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f130,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(f131,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)],[f130]) ).
fof(f132,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)],[f131]) ).
fof(f133,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))],[f132]) ).
fof(f134,plain,
! [X0] :
( aSet0(X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f135,plain,
! [X0,X1,X2] :
( aElementOf0(sdtpldt0(X1,X2),X0)
| ~ aElementOf0(X2,X0)
| ~ aElementOf0(X1,X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f210,plain,
aElement0(xb),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f213,plain,
aIdeal0(xI),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f239,plain,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f240,plain,
aElementOf0(xb,xI),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f241,plain,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f242,plain,
~ aElementOf0(xr,xI),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f273,plain,
aSet0(xI),
inference(resolution,[status(thm)],[f134,f213]) ).
fof(f297,plain,
( aElement0(smndt0(sdtasdt0(xq,xu)))
| ~ aSet0(xI) ),
inference(resolution,[status(thm)],[f239,f101]) ).
fof(f298,plain,
aElement0(smndt0(sdtasdt0(xq,xu))),
inference(forward_subsumption_resolution,[status(thm)],[f297,f273]) ).
fof(f333,plain,
( xr = sdtpldt0(xb,smndt0(sdtasdt0(xq,xu)))
| ~ aElement0(xb)
| ~ aElement0(smndt0(sdtasdt0(xq,xu))) ),
inference(paramodulation,[status(thm)],[f241,f69]) ).
fof(f337,plain,
( xr = sdtpldt0(xb,smndt0(sdtasdt0(xq,xu)))
| ~ aElement0(xb) ),
inference(forward_subsumption_resolution,[status(thm)],[f333,f298]) ).
fof(f356,plain,
xr = sdtpldt0(xb,smndt0(sdtasdt0(xq,xu))),
inference(forward_subsumption_resolution,[status(thm)],[f337,f210]) ).
fof(f440,plain,
! [X0] :
( aElementOf0(xr,X0)
| ~ aElementOf0(smndt0(sdtasdt0(xq,xu)),X0)
| ~ aElementOf0(xb,X0)
| ~ aIdeal0(X0) ),
inference(paramodulation,[status(thm)],[f356,f135]) ).
fof(f482,plain,
( aElementOf0(xr,xI)
| ~ aElementOf0(xb,xI)
| ~ aIdeal0(xI) ),
inference(resolution,[status(thm)],[f440,f239]) ).
fof(f484,plain,
( aElementOf0(xr,xI)
| ~ aElementOf0(xb,xI) ),
inference(forward_subsumption_resolution,[status(thm)],[f482,f213]) ).
fof(f486,plain,
aElementOf0(xr,xI),
inference(forward_subsumption_resolution,[status(thm)],[f484,f240]) ).
fof(f487,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f242,f486]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG123+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 04:21:55 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.43 % Refutation found
% 0.10/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.46 % Elapsed time: 0.084456 seconds
% 0.10/0.46 % CPU time: 0.302709 seconds
% 0.10/0.46 % Total memory used: 110.157 MB
% 0.10/0.46 % Net memory used: 109.781 MB
%------------------------------------------------------------------------------