%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG124+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 6 unt; 3 def)
% Number of atoms : 77 ( 22 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 80 ( 27 ~; 20 |; 29 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 11 con; 0-2 aty)
% Number of variables : 16 ( 8 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f45,hypothesis,
( ! [W0] :
( ( W0 != sz00
& ( aElementOf0(W0,xI)
| ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) ) ) )
=> ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI)
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xu
& aElementOf0(W1,slsdtgt0(xb))
& aElementOf0(W0,slsdtgt0(xa)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,hypothesis,
( ( iLess0(sbrdtbr0(xr),sbrdtbr0(xu))
| xr = sz00 )
& xb = sdtpldt0(sdtasdt0(xq,xu),xr)
& aElement0(xr)
& aElement0(xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,hypothesis,
xr != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,hypothesis,
( aElementOf0(xr,xI)
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xr
& aElementOf0(W1,slsdtgt0(xb))
& aElementOf0(W0,slsdtgt0(xa)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f277,plain,
( ! [W0] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| W0 = sz00
| ( ~ aElementOf0(W0,xI)
& ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
& xu != sz00
& aElementOf0(xu,xI)
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xu
& aElementOf0(W1,slsdtgt0(xb))
& aElementOf0(W0,slsdtgt0(xa)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f278,plain,
( ! [W0] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| W0 = sz00
| ( ~ aElementOf0(W0,xI)
& ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
& xu != sz00
& aElementOf0(xu,xI)
& sdtpldt0(sK36_skl,sK37_skl) = xu
& aElementOf0(sK37_skl,slsdtgt0(xb))
& aElementOf0(sK36_skl,slsdtgt0(xa)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36_skl,sK37_skl]),skolemize(W0,sK36_skl),skolemize(W1,sK37_skl)],[f277]) ).
fof(f285,plain,
! [X0] :
( ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu))
| X0 = sz00
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[status(thm)],[f278]) ).
fof(f306,plain,
( iLess0(sbrdtbr0(xr),sbrdtbr0(xu))
| xr = sz00 ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f307,plain,
xr != sz00,
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f322,plain,
( aElementOf0(xr,xI)
& sdtpldt0(sK47_skl,sK48_skl) = xr
& aElementOf0(sK48_skl,slsdtgt0(xb))
& aElementOf0(sK47_skl,slsdtgt0(xa)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl]),skolemize(W0,sK47_skl),skolemize(W1,sK48_skl)],[f55]) ).
fof(f326,plain,
aElementOf0(xr,xI),
inference(cnf_transformation,[status(thm)],[f322]) ).
fof(f393,definition,
( sQ6_spl
<=> xr = sz00 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f394,plain,
( ~ sQ6_spl
| xr = sz00 ),
inference(component_clause,[status(thm)],[f393]) ).
fof(f396,definition,
( sQ7_spl
<=> iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f399,plain,
( sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f306,f393,f396]) ).
fof(f443,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f394,f307]) ).
fof(f444,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f443]) ).
fof(f1068,plain,
( ~ iLess0(sbrdtbr0(xr),sbrdtbr0(xu))
| ~ aElementOf0(xr,xI) ),
inference(resolution,[status(thm)],[f285,f307]) ).
fof(f1076,definition,
( sQ133_spl
<=> aElementOf0(xr,xI) ),
introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition]) ).
fof(f1078,plain,
( sQ133_spl
| ~ aElementOf0(xr,xI) ),
inference(component_clause,[status(thm)],[f1076]) ).
fof(f1079,plain,
( ~ sQ7_spl
| ~ sQ133_spl ),
inference(split_clause,[status(thm)],[f1068,f1076,f396]) ).
fof(f1095,plain,
( sQ133_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1078,f326]) ).
fof(f1096,plain,
sQ133_spl,
inference(contradiction_clause,[status(thm)],[f1095]) ).
fof(f1097,plain,
$false,
inference(sat_refutation,[status(thm)],[f399,f444,f1079,f1096]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG124+4 : 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 : n007.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 04:19:35 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.064270 seconds
% 0.13/0.43 % CPU time: 0.227396 seconds
% 0.13/0.43 % Total memory used: 91.477 MB
% 0.13/0.43 % Net memory used: 91.226 MB
%------------------------------------------------------------------------------