%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG095+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 02:04:57 PM UTC 2026
% Result : Theorem 0.22s 0.48s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 39 ( 8 unt; 5 def)
% Number of atoms : 109 ( 8 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 103 ( 33 ~; 31 |; 27 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 22 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
aElement0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
( aIdeal0(xJ)
& ! [W0] :
( aElementOf0(W0,xJ)
=> ( ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xJ) )
& ! [W1] :
( aElementOf0(W1,xJ)
=> aElementOf0(sdtpldt0(W0,W1),xJ) ) ) )
& aSet0(xJ)
& 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(f29,hypothesis,
! [W0] :
( aElement0(W0)
=> ( aElementOf0(W0,sdtpldt1(xI,xJ))
& ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,xJ)
& aElementOf0(W1,xI) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,conjecture,
? [W0,W1] :
( sdtpldt0(W0,W1) = sz10
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
~ ? [W0,W1] :
( sdtpldt0(W0,W1) = sz10
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f37,plain,
aElement0(sz10),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f126,plain,
( aIdeal0(xJ)
& ! [W0] :
( ( ! [W1] :
( aElementOf0(sdtasdt0(W1,W0),xJ)
| ~ aElement0(W1) )
& ! [W1] :
( aElementOf0(sdtpldt0(W0,W1),xJ)
| ~ aElementOf0(W1,xJ) ) )
| ~ aElementOf0(W0,xJ) )
& aSet0(xJ)
& 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)],[f28]) ).
fof(f127,plain,
aSet0(xI),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f131,plain,
aSet0(xJ),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f135,plain,
! [W0] :
( ( aElementOf0(W0,sdtpldt1(xI,xJ))
& ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,xJ)
& aElementOf0(W1,xI) ) )
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f136,plain,
! [W0] :
( ( aElementOf0(W0,sdtpldt1(xI,xJ))
& sdtpldt0(sK11_skl(W0),sK12_skl(W0)) = W0
& aElementOf0(sK12_skl(W0),xJ)
& aElementOf0(sK11_skl(W0),xI) )
| ~ aElement0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl]),skolemize(W1,sK11_skl(W0)),skolemize(W2,sK12_skl(W0))],[f135]) ).
fof(f137,plain,
! [X0] :
( aElementOf0(sK11_skl(X0),xI)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f138,plain,
! [X0] :
( aElementOf0(sK12_skl(X0),xJ)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f139,plain,
! [X0] :
( sdtpldt0(sK11_skl(X0),sK12_skl(X0)) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f143,plain,
! [W0,W1] :
( sdtpldt0(W0,W1) != sz10
| ~ aElementOf0(W1,xJ)
| ~ aElementOf0(W0,xI) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f144,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) != sz10
| ~ aElementOf0(X1,xJ)
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f167,definition,
( sQ0_spl
<=> aElement0(sz10) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f169,plain,
( sQ0_spl
| ~ aElement0(sz10) ),
inference(component_clause,[status(thm)],[f167]) ).
fof(f185,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f169,f37]) ).
fof(f186,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f185]) ).
fof(f191,definition,
( sQ5_spl
<=> aSet0(xJ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f193,plain,
( sQ5_spl
| ~ aSet0(xJ) ),
inference(component_clause,[status(thm)],[f191]) ).
fof(f198,definition,
( sQ7_spl
<=> aSet0(xI) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f200,plain,
( sQ7_spl
| ~ aSet0(xI) ),
inference(component_clause,[status(thm)],[f198]) ).
fof(f213,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f200,f127]) ).
fof(f214,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f213]) ).
fof(f215,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f193,f131]) ).
fof(f216,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f215]) ).
fof(f231,plain,
( ~ aElementOf0(sK12_skl(sz10),xJ)
| ~ aElementOf0(sK11_skl(sz10),xI)
| ~ aElement0(sz10) ),
inference(resolution,[status(thm)],[f139,f144]) ).
fof(f232,definition,
( sQ13_spl
<=> aElementOf0(sK11_skl(sz10),xI) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f234,plain,
( sQ13_spl
| ~ aElementOf0(sK11_skl(sz10),xI) ),
inference(component_clause,[status(thm)],[f232]) ).
fof(f235,definition,
( sQ14_spl
<=> aElementOf0(sK12_skl(sz10),xJ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f237,plain,
( sQ14_spl
| ~ aElementOf0(sK12_skl(sz10),xJ) ),
inference(component_clause,[status(thm)],[f235]) ).
fof(f238,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f231,f167,f232,f235]) ).
fof(f239,plain,
( sQ13_spl
| ~ aElement0(sz10) ),
inference(resolution,[status(thm)],[f234,f137]) ).
fof(f240,plain,
( sQ13_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f239,f167,f232]) ).
fof(f241,plain,
( sQ14_spl
| ~ aElement0(sz10) ),
inference(resolution,[status(thm)],[f237,f138]) ).
fof(f242,plain,
( sQ14_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f241,f167,f235]) ).
fof(f243,plain,
$false,
inference(sat_refutation,[status(thm)],[f186,f214,f216,f238,f240,f242]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG095+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n004.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 21 04:19:22 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.44 % Drodi V4.1.1
% 0.22/0.48 % Refutation found
% 0.22/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.22/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.51 % Elapsed time: 0.061129 seconds
% 0.22/0.51 % CPU time: 0.161288 seconds
% 0.22/0.51 % Total memory used: 83.513 MB
% 0.22/0.51 % Net memory used: 83.355 MB
%------------------------------------------------------------------------------