%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG112+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 02:05:00 PM UTC 2026
% Result : Theorem 0.16s 10.49s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 6 unt; 0 def)
% Number of atoms : 100 ( 45 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 122 ( 50 ~; 45 |; 23 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 31 ( 24 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f42,hypothesis,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& aIdeal0(xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,hypothesis,
? [W0] :
( W0 != sz00
& aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,hypothesis,
! [W0] :
( ( W0 != sz00
& aElementOf0(W0,xI) )
=> ? [W1] :
( ! [W2] :
( ( W2 != sz00
& aElementOf0(W2,xI) )
=> ~ iLess0(sbrdtbr0(W2),sbrdtbr0(W1)) )
& W1 != sz00
& aElementOf0(W1,xI) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,conjecture,
? [W0] :
( ! [W1] :
( ( W1 != sz00
& aElementOf0(W1,xI) )
=> ~ iLess0(sbrdtbr0(W1),sbrdtbr0(W0)) )
& W0 != sz00
& aElementOf0(W0,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
~ ? [W0] :
( ! [W1] :
( ( W1 != sz00
& aElementOf0(W1,xI) )
=> ~ iLess0(sbrdtbr0(W1),sbrdtbr0(W0)) )
& W0 != sz00
& aElementOf0(W0,xI) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f205,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f210,plain,
( sK20_skl != sz00
& aElementOf0(sK20_skl,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl]),skolemize(W0,sK20_skl)],[f44]) ).
fof(f211,plain,
aElementOf0(sK20_skl,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(cnf_transformation,[status(thm)],[f210]) ).
fof(f212,plain,
sK20_skl != sz00,
inference(cnf_transformation,[status(thm)],[f210]) ).
fof(f213,plain,
! [W0] :
( ? [W1] :
( ! [W2] :
( ~ iLess0(sbrdtbr0(W2),sbrdtbr0(W1))
| W2 = sz00
| ~ aElementOf0(W2,xI) )
& W1 != sz00
& aElementOf0(W1,xI) )
| W0 = sz00
| ~ aElementOf0(W0,xI) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f214,plain,
( ? [W1] :
( ! [W2] :
( ~ iLess0(sbrdtbr0(W2),sbrdtbr0(W1))
| W2 = sz00
| ~ aElementOf0(W2,xI) )
& W1 != sz00
& aElementOf0(W1,xI) )
| ! [W0] :
( W0 = sz00
| ~ aElementOf0(W0,xI) ) ),
inference(miniscoping,[status(thm)],[f213]) ).
fof(f215,plain,
( ( ! [W2] :
( ~ iLess0(sbrdtbr0(W2),sbrdtbr0(sK21_skl))
| W2 = sz00
| ~ aElementOf0(W2,xI) )
& sK21_skl != sz00
& aElementOf0(sK21_skl,xI) )
| ! [W0] :
( W0 = sz00
| ~ aElementOf0(W0,xI) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21_skl]),skolemize(W1,sK21_skl)],[f214]) ).
fof(f216,plain,
! [X0] :
( aElementOf0(sK21_skl,xI)
| X0 = sz00
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[status(thm)],[f215]) ).
fof(f217,plain,
! [X0] :
( sK21_skl != sz00
| X0 = sz00
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[status(thm)],[f215]) ).
fof(f218,plain,
! [X0,X1] :
( ~ iLess0(sbrdtbr0(X1),sbrdtbr0(sK21_skl))
| X1 = sz00
| ~ aElementOf0(X1,xI)
| X0 = sz00
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[status(thm)],[f215]) ).
fof(f219,plain,
! [W0] :
( ? [W1] :
( iLess0(sbrdtbr0(W1),sbrdtbr0(W0))
& W1 != sz00
& aElementOf0(W1,xI) )
| W0 = sz00
| ~ aElementOf0(W0,xI) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f220,plain,
! [W0] :
( ( iLess0(sbrdtbr0(sK22_skl(W0)),sbrdtbr0(W0))
& sK22_skl(W0) != sz00
& aElementOf0(sK22_skl(W0),xI) )
| W0 = sz00
| ~ aElementOf0(W0,xI) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22_skl]),skolemize(W1,sK22_skl(W0))],[f219]) ).
fof(f221,plain,
! [X0] :
( aElementOf0(sK22_skl(X0),xI)
| X0 = sz00
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[status(thm)],[f220]) ).
fof(f222,plain,
! [X0] :
( sK22_skl(X0) != sz00
| X0 = sz00
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[status(thm)],[f220]) ).
fof(f223,plain,
! [X0] :
( iLess0(sbrdtbr0(sK22_skl(X0)),sbrdtbr0(X0))
| X0 = sz00
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[status(thm)],[f220]) ).
fof(f256,plain,
! [X0] :
( sK21_skl = sz00
| ~ aElementOf0(sK21_skl,xI)
| sK22_skl(sK21_skl) = sz00
| ~ aElementOf0(sK22_skl(sK21_skl),xI)
| X0 = sz00
| ~ aElementOf0(X0,xI) ),
inference(resolution,[status(thm)],[f218,f223]) ).
fof(f257,plain,
! [X0] :
( sK21_skl = sz00
| ~ aElementOf0(sK21_skl,xI)
| sK22_skl(sK21_skl) = sz00
| X0 = sz00
| ~ aElementOf0(X0,xI) ),
inference(forward_subsumption_resolution,[status(thm)],[f256,f221]) ).
fof(f258,plain,
! [X0] :
( sK21_skl = sz00
| ~ aElementOf0(sK21_skl,xI)
| X0 = sz00
| ~ aElementOf0(X0,xI) ),
inference(forward_subsumption_resolution,[status(thm)],[f257,f222]) ).
fof(f280,plain,
! [X0] :
( ~ aElementOf0(sK21_skl,xI)
| X0 = sz00
| ~ aElementOf0(X0,xI) ),
inference(backward_subsumption_resolution,[status(thm)],[f258,f217]) ).
fof(f304,plain,
aElementOf0(sK20_skl,xI),
inference(forward_demodulation,[status(thm)],[f205,f211]) ).
fof(f313,plain,
! [X0] :
( X0 = sz00
| ~ aElementOf0(X0,xI) ),
inference(forward_subsumption_resolution,[status(thm)],[f216,f280]) ).
fof(f314,plain,
sK20_skl = sz00,
inference(resolution,[status(thm)],[f313,f304]) ).
fof(f316,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f314,f212]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG112+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/10.45 % Computer : n016.cluster.edu
% 0.16/10.45 % Model : x86_64 x86_64
% 0.16/10.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/10.45 % Memory : 8046.5625MB
% 0.16/10.45 % OS : Linux 6.8.0-71-generic
% 0.16/10.45 % CPULimit : 300
% 0.16/10.45 % WCLimit : 300
% 0.16/10.45 % DateTime : Mon Sep 21 04:25:33 UTC 2026
% 0.16/10.45 % CPUTime :
% 0.16/10.47 % Drodi V4.1.1
% 0.16/10.49 % Refutation found
% 0.16/10.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/10.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/10.52 % Elapsed time: 0.061575 seconds
% 0.21/10.52 % CPU time: 0.167464 seconds
% 0.21/10.52 % Total memory used: 50.163 MB
% 0.21/10.52 % Net memory used: 50.078 MB
%------------------------------------------------------------------------------