%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG121+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 0.19s 0.54s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 39 ( 8 unt; 4 def)
% Number of atoms : 221 ( 51 equ)
% Maximal formula atoms : 28 ( 5 avg)
% Number of connectives : 251 ( 69 ~; 69 |; 99 &)
% ( 10 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 8 con; 0-2 aty)
% Number of variables : 88 ( 60 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [W0] :
( aElement0(W0)
=> ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = 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))
& ! [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/sandbox/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
( aElementOf0(xb,slsdtgt0(xb))
& ? [W0] :
( sdtasdt0(xb,W0) = xb
& aElement0(W0) )
& aElementOf0(sz00,slsdtgt0(xb))
& ? [W0] :
( sdtasdt0(xb,W0) = sz00
& aElement0(W0) )
& aElementOf0(xa,slsdtgt0(xa))
& ? [W0] :
( sdtasdt0(xa,W0) = xa
& aElement0(W0) )
& aElementOf0(sz00,slsdtgt0(xa))
& ? [W0] :
( sdtasdt0(xa,W0) = sz00
& aElement0(W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,conjecture,
( 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/sandbox/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
~ ( 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)) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f70,plain,
! [W0] :
( ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 )
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f72,plain,
! [X0] :
( X0 = sdtpldt0(sz00,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f208,plain,
aElement0(xb),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f228,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(f229,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)],[f228]) ).
fof(f230,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)],[f229]) ).
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) )
& ! [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))],[f230]) ).
fof(f238,plain,
! [X0,X1] :
( sdtasdt0(xa,X1) != X0
| ~ aElement0(X1)
| aElementOf0(X0,slsdtgt0(xa)) ),
inference(cnf_transformation,[status(thm)],[f231]) ).
fof(f247,plain,
( aElementOf0(xb,slsdtgt0(xb))
& sdtasdt0(xb,sK30_skl) = xb
& aElement0(sK30_skl)
& aElementOf0(sz00,slsdtgt0(xb))
& sdtasdt0(xb,sK29_skl) = sz00
& aElement0(sK29_skl)
& aElementOf0(xa,slsdtgt0(xa))
& sdtasdt0(xa,sK28_skl) = xa
& aElement0(sK28_skl)
& aElementOf0(sz00,slsdtgt0(xa))
& sdtasdt0(xa,sK27_skl) = sz00
& aElement0(sK27_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27_skl,sK28_skl,sK29_skl,sK30_skl]),skolemize(W0,sK27_skl),skolemize(W0,sK28_skl),skolemize(W0,sK29_skl),skolemize(W0,sK30_skl)],[f43]) ).
fof(f248,plain,
aElement0(sK27_skl),
inference(cnf_transformation,[status(thm)],[f247]) ).
fof(f249,plain,
sdtasdt0(xa,sK27_skl) = sz00,
inference(cnf_transformation,[status(thm)],[f247]) ).
fof(f259,plain,
aElementOf0(xb,slsdtgt0(xb)),
inference(cnf_transformation,[status(thm)],[f247]) ).
fof(f310,plain,
( ~ 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)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f311,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) != xb
| ~ aElementOf0(X1,slsdtgt0(xb))
| ~ aElementOf0(X0,slsdtgt0(xa)) ),
inference(cnf_transformation,[status(thm)],[f310]) ).
fof(f419,plain,
! [X0] :
( ~ aElement0(X0)
| aElementOf0(sdtasdt0(xa,X0),slsdtgt0(xa)) ),
inference(destructive_equality_resolution,[status(thm)],[f238]) ).
fof(f427,definition,
( sQ13_spl
<=> aElement0(xb) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f429,plain,
( sQ13_spl
| ~ aElement0(xb) ),
inference(component_clause,[status(thm)],[f427]) ).
fof(f440,plain,
( ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElementOf0(sz00,slsdtgt0(xa))
| ~ aElement0(xb) ),
inference(resolution,[status(thm)],[f72,f311]) ).
fof(f441,definition,
( sQ16_spl
<=> aElementOf0(sz00,slsdtgt0(xa)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f444,definition,
( sQ17_spl
<=> aElementOf0(xb,slsdtgt0(xb)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f446,plain,
( sQ17_spl
| ~ aElementOf0(xb,slsdtgt0(xb)) ),
inference(component_clause,[status(thm)],[f444]) ).
fof(f447,plain,
( ~ sQ17_spl
| ~ sQ16_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f440,f427,f441,f444]) ).
fof(f448,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f429,f208]) ).
fof(f449,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f448]) ).
fof(f726,plain,
( ~ aElement0(sK27_skl)
| aElementOf0(sz00,slsdtgt0(xa)) ),
inference(paramodulation,[status(thm)],[f249,f419]) ).
fof(f736,definition,
( sQ71_spl
<=> aElement0(sK27_skl) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f738,plain,
( sQ71_spl
| ~ aElement0(sK27_skl) ),
inference(component_clause,[status(thm)],[f736]) ).
fof(f739,plain,
( ~ sQ71_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f726,f441,f736]) ).
fof(f773,plain,
( sQ71_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f738,f248]) ).
fof(f774,plain,
sQ71_spl,
inference(contradiction_clause,[status(thm)],[f773]) ).
fof(f775,plain,
( sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f446,f259]) ).
fof(f776,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f775]) ).
fof(f777,plain,
$false,
inference(sat_refutation,[status(thm)],[f447,f449,f739,f774,f776]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG121+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n002.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 04:24:02 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.51 % Drodi V4.1.1
% 0.19/0.54 % Refutation found
% 0.19/0.54 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.59 % Elapsed time: 0.116888 seconds
% 0.22/0.59 % CPU time: 0.145132 seconds
% 0.22/0.59 % Total memory used: 17.794 MB
% 0.22/0.59 % Net memory used: 17.725 MB
%------------------------------------------------------------------------------