%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG123+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 : 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 02:05:03 PM UTC 2026
% Result : Theorem 0.12s 5.59s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 55 ( 16 unt; 7 def)
% Number of atoms : 234 ( 44 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 254 ( 75 ~; 76 |; 87 &)
% ( 13 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 8 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 12 con; 0-2 aty)
% Number of variables : 83 ( 57 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f42,hypothesis,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [W0] :
( aElementOf0(W0,xI)
<=> ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) ) )
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xb))
<=> ? [W1] :
( sdtasdt0(xb,W1) = W0
& aElement0(W1) ) )
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xa))
<=> ? [W1] :
( sdtasdt0(xa,W1) = W0
& aElement0(W1) ) )
& aIdeal0(xI)
& ! [W0] :
( aElementOf0(W0,xI)
=> ( ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) )
& ! [W1] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) ) ) )
& aSet0(xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,hypothesis,
( aElementOf0(smndt0(sdtasdt0(xq,xu)),xI)
& ? [W0,W1] :
( sdtpldt0(W0,W1) = smndt0(sdtasdt0(xq,xu))
& aElementOf0(W1,slsdtgt0(xb))
& aElementOf0(W0,slsdtgt0(xa)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,hypothesis,
( aElementOf0(xb,xI)
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xb
& aElementOf0(W1,slsdtgt0(xb))
& aElementOf0(W0,slsdtgt0(xa)) )
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xb
& aElementOf0(W1,slsdtgt0(xb))
& aElementOf0(W0,slsdtgt0(xa)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,hypothesis,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,conjecture,
( 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(f56,negated_conjecture,
~ ( aElementOf0(xr,xI)
| ? [W0,W1] :
( sdtpldt0(W0,W1) = xr
& aElementOf0(W1,slsdtgt0(xb))
& aElementOf0(W0,slsdtgt0(xa)) ) ),
inference(negated_conjecture,[status(cth)],[f55]) ).
fof(f230,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [W0] :
( aElementOf0(W0,xI)
<=> ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) ) )
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xb))
<=> ? [W1] :
( sdtasdt0(xb,W1) = W0
& aElement0(W1) ) )
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xa))
<=> ? [W1] :
( sdtasdt0(xa,W1) = W0
& aElement0(W1) ) )
& aIdeal0(xI)
& ! [W0] :
( ( ! [W1] :
( aElementOf0(sdtasdt0(W1,W0),xI)
| ~ aElement0(W1) )
& ! [W1] :
( aElementOf0(sdtpldt0(W0,W1),xI)
| ~ aElementOf0(W1,xI) ) )
| ~ aElementOf0(W0,xI) )
& aSet0(xI) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f231,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [W0] :
( ( ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) )
| aElementOf0(W0,xI) )
& ( ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) )
| ~ aElementOf0(W0,xI) ) )
& ! [W0] :
( ( ! [W1] :
( sdtasdt0(xb,W1) != W0
| ~ aElement0(W1) )
| aElementOf0(W0,slsdtgt0(xb)) )
& ( ? [W1] :
( sdtasdt0(xb,W1) = W0
& aElement0(W1) )
| ~ aElementOf0(W0,slsdtgt0(xb)) ) )
& ! [W0] :
( ( ! [W1] :
( sdtasdt0(xa,W1) != W0
| ~ aElement0(W1) )
| aElementOf0(W0,slsdtgt0(xa)) )
& ( ? [W1] :
( sdtasdt0(xa,W1) = W0
& aElement0(W1) )
| ~ aElementOf0(W0,slsdtgt0(xa)) ) )
& aIdeal0(xI)
& ! [W0] :
( ( ! [W1] :
( aElementOf0(sdtasdt0(W1,W0),xI)
| ~ aElement0(W1) )
& ! [W1] :
( aElementOf0(sdtpldt0(W0,W1),xI)
| ~ aElementOf0(W1,xI) ) )
| ~ aElementOf0(W0,xI) )
& aSet0(xI) ),
inference(NNF_transformation,[status(thm)],[f230]) ).
fof(f232,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [W0] :
( ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) )
| aElementOf0(W0,xI) )
& ! [W0] :
( ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) )
| ~ aElementOf0(W0,xI) )
& ! [W0] :
( ! [W1] :
( sdtasdt0(xb,W1) != W0
| ~ aElement0(W1) )
| aElementOf0(W0,slsdtgt0(xb)) )
& ! [W0] :
( ? [W1] :
( sdtasdt0(xb,W1) = W0
& aElement0(W1) )
| ~ aElementOf0(W0,slsdtgt0(xb)) )
& ! [W0] :
( ! [W1] :
( sdtasdt0(xa,W1) != W0
| ~ aElement0(W1) )
| aElementOf0(W0,slsdtgt0(xa)) )
& ! [W0] :
( ? [W1] :
( sdtasdt0(xa,W1) = W0
& aElement0(W1) )
| ~ aElementOf0(W0,slsdtgt0(xa)) )
& aIdeal0(xI)
& ! [W0] :
( ( ! [W1] :
( aElementOf0(sdtasdt0(W1,W0),xI)
| ~ aElement0(W1) )
& ! [W1] :
( aElementOf0(sdtpldt0(W0,W1),xI)
| ~ aElementOf0(W1,xI) ) )
| ~ aElementOf0(W0,xI) )
& aSet0(xI) ),
inference(miniscoping,[status(thm)],[f231]) ).
fof(f233,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [W0] :
( ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) )
| aElementOf0(W0,xI) )
& ! [W0] :
( ( sdtpldt0(sK25_skl(W0),sK26_skl(W0)) = W0
& aElementOf0(sK26_skl(W0),slsdtgt0(xb))
& aElementOf0(sK25_skl(W0),slsdtgt0(xa)) )
| ~ aElementOf0(W0,xI) )
& ! [W0] :
( ! [W1] :
( sdtasdt0(xb,W1) != W0
| ~ aElement0(W1) )
| aElementOf0(W0,slsdtgt0(xb)) )
& ! [W0] :
( ( sdtasdt0(xb,sK24_skl(W0)) = W0
& aElement0(sK24_skl(W0)) )
| ~ aElementOf0(W0,slsdtgt0(xb)) )
& ! [W0] :
( ! [W1] :
( sdtasdt0(xa,W1) != W0
| ~ aElement0(W1) )
| aElementOf0(W0,slsdtgt0(xa)) )
& ! [W0] :
( ( sdtasdt0(xa,sK23_skl(W0)) = W0
& aElement0(sK23_skl(W0)) )
| ~ aElementOf0(W0,slsdtgt0(xa)) )
& aIdeal0(xI)
& ! [W0] :
( ( ! [W1] :
( aElementOf0(sdtasdt0(W1,W0),xI)
| ~ aElement0(W1) )
& ! [W1] :
( aElementOf0(sdtpldt0(W0,W1),xI)
| ~ aElementOf0(W1,xI) ) )
| ~ aElementOf0(W0,xI) )
& aSet0(xI) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl,sK24_skl,sK25_skl,sK26_skl]),skolemize(W1,sK23_skl(W0)),skolemize(W1,sK24_skl(W0)),skolemize(W1,sK25_skl(W0)),skolemize(W2,sK26_skl(W0))],[f232]) ).
fof(f235,plain,
! [X0,X1] :
( aElementOf0(sdtpldt0(X0,X1),xI)
| ~ aElementOf0(X1,xI)
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[status(thm)],[f233]) ).
fof(f247,plain,
! [X0,X1,X2] :
( sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa))
| aElementOf0(X0,xI) ),
inference(cnf_transformation,[status(thm)],[f233]) ).
fof(f307,plain,
( aElementOf0(smndt0(sdtasdt0(xq,xu)),xI)
& sdtpldt0(sK41_skl,sK42_skl) = smndt0(sdtasdt0(xq,xu))
& aElementOf0(sK42_skl,slsdtgt0(xb))
& aElementOf0(sK41_skl,slsdtgt0(xa)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41_skl,sK42_skl]),skolemize(W0,sK41_skl),skolemize(W1,sK42_skl)],[f52]) ).
fof(f308,plain,
aElementOf0(sK41_skl,slsdtgt0(xa)),
inference(cnf_transformation,[status(thm)],[f307]) ).
fof(f309,plain,
aElementOf0(sK42_skl,slsdtgt0(xb)),
inference(cnf_transformation,[status(thm)],[f307]) ).
fof(f310,plain,
sdtpldt0(sK41_skl,sK42_skl) = smndt0(sdtasdt0(xq,xu)),
inference(cnf_transformation,[status(thm)],[f307]) ).
fof(f312,plain,
( aElementOf0(xb,xI)
& sdtpldt0(sK45_skl,sK46_skl) = xb
& aElementOf0(sK46_skl,slsdtgt0(xb))
& aElementOf0(sK45_skl,slsdtgt0(xa))
& sdtpldt0(sK43_skl,sK44_skl) = xb
& aElementOf0(sK44_skl,slsdtgt0(xb))
& aElementOf0(sK43_skl,slsdtgt0(xa)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43_skl,sK44_skl,sK45_skl,sK46_skl]),skolemize(W0,sK43_skl),skolemize(W1,sK44_skl),skolemize(W0,sK45_skl),skolemize(W1,sK46_skl)],[f53]) ).
fof(f316,plain,
aElementOf0(sK45_skl,slsdtgt0(xa)),
inference(cnf_transformation,[status(thm)],[f312]) ).
fof(f317,plain,
aElementOf0(sK46_skl,slsdtgt0(xb)),
inference(cnf_transformation,[status(thm)],[f312]) ).
fof(f318,plain,
sdtpldt0(sK45_skl,sK46_skl) = xb,
inference(cnf_transformation,[status(thm)],[f312]) ).
fof(f320,plain,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f321,plain,
( ~ aElementOf0(xr,xI)
& ! [W0,W1] :
( sdtpldt0(W0,W1) != xr
| ~ aElementOf0(W1,slsdtgt0(xb))
| ~ aElementOf0(W0,slsdtgt0(xa)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f56]) ).
fof(f323,plain,
~ aElementOf0(xr,xI),
inference(cnf_transformation,[status(thm)],[f321]) ).
fof(f431,plain,
! [X0,X1] :
( ~ aElementOf0(X1,slsdtgt0(xb))
| ~ aElementOf0(X0,slsdtgt0(xa))
| aElementOf0(sdtpldt0(X0,X1),xI) ),
inference(destructive_equality_resolution,[status(thm)],[f247]) ).
fof(f560,definition,
( sQ36_spl
<=> aElementOf0(xb,xI) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f591,plain,
( ~ aElementOf0(sK46_skl,slsdtgt0(xb))
| ~ aElementOf0(sK45_skl,slsdtgt0(xa))
| aElementOf0(xb,xI) ),
inference(paramodulation,[status(thm)],[f318,f431]) ).
fof(f595,definition,
( sQ44_spl
<=> aElementOf0(sK45_skl,slsdtgt0(xa)) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f597,plain,
( sQ44_spl
| ~ aElementOf0(sK45_skl,slsdtgt0(xa)) ),
inference(component_clause,[status(thm)],[f595]) ).
fof(f598,definition,
( sQ45_spl
<=> aElementOf0(sK46_skl,slsdtgt0(xb)) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f600,plain,
( sQ45_spl
| ~ aElementOf0(sK46_skl,slsdtgt0(xb)) ),
inference(component_clause,[status(thm)],[f598]) ).
fof(f601,plain,
( ~ sQ45_spl
| ~ sQ44_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f591,f560,f595,f598]) ).
fof(f714,plain,
( sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f600,f317]) ).
fof(f715,plain,
sQ45_spl,
inference(contradiction_clause,[status(thm)],[f714]) ).
fof(f716,plain,
( sQ44_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f597,f316]) ).
fof(f717,plain,
sQ44_spl,
inference(contradiction_clause,[status(thm)],[f716]) ).
fof(f955,definition,
( sQ90_spl
<=> aElementOf0(xr,xI) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f956,plain,
( ~ sQ90_spl
| aElementOf0(xr,xI) ),
inference(component_clause,[status(thm)],[f955]) ).
fof(f984,plain,
xr = sdtpldt0(sdtpldt0(sK41_skl,sK42_skl),xb),
inference(forward_demodulation,[status(thm)],[f310,f320]) ).
fof(f992,plain,
( aElementOf0(xr,xI)
| ~ aElementOf0(xb,xI)
| ~ aElementOf0(sdtpldt0(sK41_skl,sK42_skl),xI) ),
inference(paramodulation,[status(thm)],[f984,f235]) ).
fof(f1001,definition,
( sQ98_spl
<=> aElementOf0(sdtpldt0(sK41_skl,sK42_skl),xI) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f1003,plain,
( sQ98_spl
| ~ aElementOf0(sdtpldt0(sK41_skl,sK42_skl),xI) ),
inference(component_clause,[status(thm)],[f1001]) ).
fof(f1025,plain,
( sQ90_spl
| ~ sQ36_spl
| ~ sQ98_spl ),
inference(split_clause,[status(thm)],[f992,f1001,f560,f955]) ).
fof(f1027,plain,
( sQ98_spl
| ~ aElementOf0(sK42_skl,slsdtgt0(xb))
| ~ aElementOf0(sK41_skl,slsdtgt0(xa)) ),
inference(resolution,[status(thm)],[f1003,f431]) ).
fof(f1029,definition,
( sQ104_spl
<=> aElementOf0(sK41_skl,slsdtgt0(xa)) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f1031,plain,
( sQ104_spl
| ~ aElementOf0(sK41_skl,slsdtgt0(xa)) ),
inference(component_clause,[status(thm)],[f1029]) ).
fof(f1032,definition,
( sQ105_spl
<=> aElementOf0(sK42_skl,slsdtgt0(xb)) ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f1034,plain,
( sQ105_spl
| ~ aElementOf0(sK42_skl,slsdtgt0(xb)) ),
inference(component_clause,[status(thm)],[f1032]) ).
fof(f1035,plain,
( sQ98_spl
| ~ sQ105_spl
| ~ sQ104_spl ),
inference(split_clause,[status(thm)],[f1027,f1029,f1032,f1001]) ).
fof(f1043,plain,
( sQ104_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1031,f308]) ).
fof(f1044,plain,
sQ104_spl,
inference(contradiction_clause,[status(thm)],[f1043]) ).
fof(f1045,plain,
( sQ105_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1034,f309]) ).
fof(f1046,plain,
sQ105_spl,
inference(contradiction_clause,[status(thm)],[f1045]) ).
fof(f1047,plain,
( ~ sQ90_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f956,f323]) ).
fof(f1048,plain,
~ sQ90_spl,
inference(contradiction_clause,[status(thm)],[f1047]) ).
fof(f1049,plain,
$false,
inference(sat_refutation,[status(thm)],[f601,f715,f717,f1025,f1035,f1044,f1046,f1048]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG123+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n014.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Mon Sep 21 04:21:56 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.38 % Drodi V4.1.1
% 0.12/5.59 % Refutation found
% 0.12/5.59 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/5.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/5.59 % Elapsed time: 0.228196 seconds
% 0.12/5.59 % CPU time: 1.537234 seconds
% 0.12/5.59 % Total memory used: 135.614 MB
% 0.12/5.59 % Net memory used: 133.613 MB
%------------------------------------------------------------------------------