%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG106+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 02:04:59 PM UTC 2026
% Result : Theorem 0.11s 0.45s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 62 ( 10 unt; 9 def)
% Number of atoms : 353 ( 72 equ)
% Maximal formula atoms : 29 ( 5 avg)
% Number of connectives : 404 ( 113 ~; 106 |; 160 &)
% ( 13 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 8 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-3 aty)
% Number of variables : 154 ( 104 !; 50 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
aElement0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,hypothesis,
aElement0(xc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,conjecture,
( ! [W0,W1,W2] :
( ( aElement0(W2)
& ( aElementOf0(W1,slsdtgt0(xc))
| ? [W3] :
( sdtasdt0(xc,W3) = W1
& aElement0(W3) ) )
& ( aElementOf0(W0,slsdtgt0(xc))
| ? [W3] :
( sdtasdt0(xc,W3) = W0
& aElement0(W3) ) ) )
=> ? [W3] :
( ? [W4] :
( aElementOf0(sdtasdt0(W2,W0),slsdtgt0(xc))
& ? [W5] :
( sdtasdt0(xc,W5) = sdtasdt0(W2,W0)
& aElement0(W5) )
& aElementOf0(sdtpldt0(W0,W1),slsdtgt0(xc))
& ? [W5] :
( sdtasdt0(xc,W5) = sdtpldt0(W0,W1)
& aElement0(W5) )
& sdtasdt0(W2,W0) = sdtasdt0(xc,sdtasdt0(W3,W2))
& sdtpldt0(W0,W1) = sdtasdt0(xc,sdtpldt0(W3,W4))
& sdtasdt0(xc,W4) = W1
& aElement0(W4) )
& sdtasdt0(xc,W3) = W0
& aElement0(W3) ) )
=> ( ( ! [W0] :
( aElementOf0(W0,slsdtgt0(xc))
<=> ? [W1] :
( sdtasdt0(xc,W1) = W0
& aElement0(W1) ) )
& aSet0(slsdtgt0(xc)) )
=> ( aIdeal0(slsdtgt0(xc))
| ! [W0] :
( aElementOf0(W0,slsdtgt0(xc))
=> ( ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),slsdtgt0(xc)) )
& ! [W1] :
( aElementOf0(W1,slsdtgt0(xc))
=> aElementOf0(sdtpldt0(W0,W1),slsdtgt0(xc)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
~ ( ! [W0,W1,W2] :
( ( aElement0(W2)
& ( aElementOf0(W1,slsdtgt0(xc))
| ? [W3] :
( sdtasdt0(xc,W3) = W1
& aElement0(W3) ) )
& ( aElementOf0(W0,slsdtgt0(xc))
| ? [W3] :
( sdtasdt0(xc,W3) = W0
& aElement0(W3) ) ) )
=> ? [W3] :
( ? [W4] :
( aElementOf0(sdtasdt0(W2,W0),slsdtgt0(xc))
& ? [W5] :
( sdtasdt0(xc,W5) = sdtasdt0(W2,W0)
& aElement0(W5) )
& aElementOf0(sdtpldt0(W0,W1),slsdtgt0(xc))
& ? [W5] :
( sdtasdt0(xc,W5) = sdtpldt0(W0,W1)
& aElement0(W5) )
& sdtasdt0(W2,W0) = sdtasdt0(xc,sdtasdt0(W3,W2))
& sdtpldt0(W0,W1) = sdtasdt0(xc,sdtpldt0(W3,W4))
& sdtasdt0(xc,W4) = W1
& aElement0(W4) )
& sdtasdt0(xc,W3) = W0
& aElement0(W3) ) )
=> ( ( ! [W0] :
( aElementOf0(W0,slsdtgt0(xc))
<=> ? [W1] :
( sdtasdt0(xc,W1) = W0
& aElement0(W1) ) )
& aSet0(slsdtgt0(xc)) )
=> ( aIdeal0(slsdtgt0(xc))
| ! [W0] :
( aElementOf0(W0,slsdtgt0(xc))
=> ( ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),slsdtgt0(xc)) )
& ! [W1] :
( aElementOf0(W1,slsdtgt0(xc))
=> aElementOf0(sdtpldt0(W0,W1),slsdtgt0(xc)) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f45,plain,
aElement0(sz10),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f191,plain,
aElement0(xc),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f192,plain,
( ~ aIdeal0(slsdtgt0(xc))
& ? [W0] :
( ( ? [W1] :
( ~ aElementOf0(sdtasdt0(W1,W0),slsdtgt0(xc))
& aElement0(W1) )
| ? [W1] :
( ~ aElementOf0(sdtpldt0(W0,W1),slsdtgt0(xc))
& aElementOf0(W1,slsdtgt0(xc)) ) )
& aElementOf0(W0,slsdtgt0(xc)) )
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xc))
<=> ? [W1] :
( sdtasdt0(xc,W1) = W0
& aElement0(W1) ) )
& aSet0(slsdtgt0(xc))
& ! [W0,W1,W2] :
( ? [W3] :
( ? [W4] :
( aElementOf0(sdtasdt0(W2,W0),slsdtgt0(xc))
& ? [W5] :
( sdtasdt0(xc,W5) = sdtasdt0(W2,W0)
& aElement0(W5) )
& aElementOf0(sdtpldt0(W0,W1),slsdtgt0(xc))
& ? [W5] :
( sdtasdt0(xc,W5) = sdtpldt0(W0,W1)
& aElement0(W5) )
& sdtasdt0(W2,W0) = sdtasdt0(xc,sdtasdt0(W3,W2))
& sdtpldt0(W0,W1) = sdtasdt0(xc,sdtpldt0(W3,W4))
& sdtasdt0(xc,W4) = W1
& aElement0(W4) )
& sdtasdt0(xc,W3) = W0
& aElement0(W3) )
| ~ aElement0(W2)
| ( ~ aElementOf0(W1,slsdtgt0(xc))
& ! [W3] :
( sdtasdt0(xc,W3) != W1
| ~ aElement0(W3) ) )
| ( ~ aElementOf0(W0,slsdtgt0(xc))
& ! [W3] :
( sdtasdt0(xc,W3) != W0
| ~ aElement0(W3) ) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f193,definition,
! [W0,W1,W2] :
( sP3_prd(W2,W1,W0)
<=> ( ~ aElement0(W2)
| ( ~ aElementOf0(W1,slsdtgt0(xc))
& ! [W3] :
( sdtasdt0(xc,W3) != W1
| ~ aElement0(W3) ) )
| ( ~ aElementOf0(W0,slsdtgt0(xc))
& ! [W3] :
( sdtasdt0(xc,W3) != W0
| ~ aElement0(W3) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3_prd])],[]) ).
fof(f194,definition,
! [W0,W1] :
( sP4_prd(W1,W0)
<=> ( ~ aElementOf0(sdtpldt0(W0,W1),slsdtgt0(xc))
& aElementOf0(W1,slsdtgt0(xc)) ) ),
introduced(definition,[new_symbols(definition,[sP4_prd])],[]) ).
fof(f195,plain,
( ~ aIdeal0(slsdtgt0(xc))
& ? [W0] :
( ( ? [W1] :
( ~ aElementOf0(sdtasdt0(W1,W0),slsdtgt0(xc))
& aElement0(W1) )
| ? [W1] : sP4_prd(W1,W0) )
& aElementOf0(W0,slsdtgt0(xc)) )
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xc))
<=> ? [W1] :
( sdtasdt0(xc,W1) = W0
& aElement0(W1) ) )
& aSet0(slsdtgt0(xc))
& ! [W0,W1,W2] :
( ? [W3] :
( ? [W4] :
( aElementOf0(sdtasdt0(W2,W0),slsdtgt0(xc))
& ? [W5] :
( sdtasdt0(xc,W5) = sdtasdt0(W2,W0)
& aElement0(W5) )
& aElementOf0(sdtpldt0(W0,W1),slsdtgt0(xc))
& ? [W5] :
( sdtasdt0(xc,W5) = sdtpldt0(W0,W1)
& aElement0(W5) )
& sdtasdt0(W2,W0) = sdtasdt0(xc,sdtasdt0(W3,W2))
& sdtpldt0(W0,W1) = sdtasdt0(xc,sdtpldt0(W3,W4))
& sdtasdt0(xc,W4) = W1
& aElement0(W4) )
& sdtasdt0(xc,W3) = W0
& aElement0(W3) )
| sP3_prd(W2,W1,W0) ) ),
inference(formula_renaming,[status(thm)],[f192,f194,f193]) ).
fof(f196,plain,
( ~ aIdeal0(slsdtgt0(xc))
& ? [W0] :
( ( ? [W1] :
( ~ aElementOf0(sdtasdt0(W1,W0),slsdtgt0(xc))
& aElement0(W1) )
| ? [W1] : sP4_prd(W1,W0) )
& aElementOf0(W0,slsdtgt0(xc)) )
& ! [W0] :
( ( ! [W1] :
( sdtasdt0(xc,W1) != W0
| ~ aElement0(W1) )
| aElementOf0(W0,slsdtgt0(xc)) )
& ( ? [W1] :
( sdtasdt0(xc,W1) = W0
& aElement0(W1) )
| ~ aElementOf0(W0,slsdtgt0(xc)) ) )
& aSet0(slsdtgt0(xc))
& ! [W0,W1,W2] :
( ? [W3] :
( ? [W4] :
( aElementOf0(sdtasdt0(W2,W0),slsdtgt0(xc))
& ? [W5] :
( sdtasdt0(xc,W5) = sdtasdt0(W2,W0)
& aElement0(W5) )
& aElementOf0(sdtpldt0(W0,W1),slsdtgt0(xc))
& ? [W5] :
( sdtasdt0(xc,W5) = sdtpldt0(W0,W1)
& aElement0(W5) )
& sdtasdt0(W2,W0) = sdtasdt0(xc,sdtasdt0(W3,W2))
& sdtpldt0(W0,W1) = sdtasdt0(xc,sdtpldt0(W3,W4))
& sdtasdt0(xc,W4) = W1
& aElement0(W4) )
& sdtasdt0(xc,W3) = W0
& aElement0(W3) )
| sP3_prd(W2,W1,W0) ) ),
inference(NNF_transformation,[status(thm)],[f195]) ).
fof(f197,plain,
( ~ aIdeal0(slsdtgt0(xc))
& ? [W0] :
( ( ? [W1] :
( ~ aElementOf0(sdtasdt0(W1,W0),slsdtgt0(xc))
& aElement0(W1) )
| ? [W1] : sP4_prd(W1,W0) )
& aElementOf0(W0,slsdtgt0(xc)) )
& ! [W0] :
( ! [W1] :
( sdtasdt0(xc,W1) != W0
| ~ aElement0(W1) )
| aElementOf0(W0,slsdtgt0(xc)) )
& ! [W0] :
( ? [W1] :
( sdtasdt0(xc,W1) = W0
& aElement0(W1) )
| ~ aElementOf0(W0,slsdtgt0(xc)) )
& aSet0(slsdtgt0(xc))
& ! [W0,W1,W2] :
( ? [W3] :
( aElementOf0(sdtasdt0(W2,W0),slsdtgt0(xc))
& ? [W5] :
( sdtasdt0(xc,W5) = sdtasdt0(W2,W0)
& aElement0(W5) )
& aElementOf0(sdtpldt0(W0,W1),slsdtgt0(xc))
& ? [W5] :
( sdtasdt0(xc,W5) = sdtpldt0(W0,W1)
& aElement0(W5) )
& sdtasdt0(W2,W0) = sdtasdt0(xc,sdtasdt0(W3,W2))
& ? [W4] :
( sdtpldt0(W0,W1) = sdtasdt0(xc,sdtpldt0(W3,W4))
& sdtasdt0(xc,W4) = W1
& aElement0(W4) )
& sdtasdt0(xc,W3) = W0
& aElement0(W3) )
| sP3_prd(W2,W1,W0) ) ),
inference(miniscoping,[status(thm)],[f196]) ).
fof(f198,plain,
( ~ aIdeal0(slsdtgt0(xc))
& ( ( ~ aElementOf0(sdtasdt0(sK27_skl,sK25_skl),slsdtgt0(xc))
& aElement0(sK27_skl) )
| sP4_prd(sK26_skl,sK25_skl) )
& aElementOf0(sK25_skl,slsdtgt0(xc))
& ! [W0] :
( ! [W1] :
( sdtasdt0(xc,W1) != W0
| ~ aElement0(W1) )
| aElementOf0(W0,slsdtgt0(xc)) )
& ! [W0] :
( ( sdtasdt0(xc,sK24_skl(W0)) = W0
& aElement0(sK24_skl(W0)) )
| ~ aElementOf0(W0,slsdtgt0(xc)) )
& aSet0(slsdtgt0(xc))
& ! [W0,W1,W2] :
( ( aElementOf0(sdtasdt0(W2,W0),slsdtgt0(xc))
& sdtasdt0(xc,sK23_skl(W2,W1,W0)) = sdtasdt0(W2,W0)
& aElement0(sK23_skl(W2,W1,W0))
& aElementOf0(sdtpldt0(W0,W1),slsdtgt0(xc))
& sdtasdt0(xc,sK22_skl(W2,W1,W0)) = sdtpldt0(W0,W1)
& aElement0(sK22_skl(W2,W1,W0))
& sdtasdt0(W2,W0) = sdtasdt0(xc,sdtasdt0(sK20_skl(W2,W1,W0),W2))
& sdtpldt0(W0,W1) = sdtasdt0(xc,sdtpldt0(sK20_skl(W2,W1,W0),sK21_skl(W2,W1,W0)))
& sdtasdt0(xc,sK21_skl(W2,W1,W0)) = W1
& aElement0(sK21_skl(W2,W1,W0))
& sdtasdt0(xc,sK20_skl(W2,W1,W0)) = W0
& aElement0(sK20_skl(W2,W1,W0)) )
| sP3_prd(W2,W1,W0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl,sK22_skl,sK23_skl,sK24_skl,sK25_skl,sK26_skl,sK27_skl]),skolemize(W3,sK20_skl(W2,W1,W0)),skolemize(W4,sK21_skl(W2,W1,W0)),skolemize(W5,sK22_skl(W2,W1,W0)),skolemize(W5,sK23_skl(W2,W1,W0)),skolemize(W1,sK24_skl(W0)),skolemize(W0,sK25_skl),skolemize(W1,sK26_skl),skolemize(W1,sK27_skl)],[f197]) ).
fof(f207,plain,
! [X0,X1,X2] :
( aElementOf0(sdtpldt0(X2,X1),slsdtgt0(xc))
| sP3_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f210,plain,
! [X0,X1,X2] :
( aElementOf0(sdtasdt0(X0,X2),slsdtgt0(xc))
| sP3_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f211,plain,
aSet0(slsdtgt0(xc)),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f215,plain,
aElementOf0(sK25_skl,slsdtgt0(xc)),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f216,plain,
( aElement0(sK27_skl)
| sP4_prd(sK26_skl,sK25_skl) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f217,plain,
( ~ aElementOf0(sdtasdt0(sK27_skl,sK25_skl),slsdtgt0(xc))
| sP4_prd(sK26_skl,sK25_skl) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f236,plain,
! [W0,W1,W2] :
( ( ( aElement0(W2)
& ( aElementOf0(W1,slsdtgt0(xc))
| ? [W3] :
( sdtasdt0(xc,W3) = W1
& aElement0(W3) ) )
& ( aElementOf0(W0,slsdtgt0(xc))
| ? [W3] :
( sdtasdt0(xc,W3) = W0
& aElement0(W3) ) ) )
| sP3_prd(W2,W1,W0) )
& ( ~ aElement0(W2)
| ( ~ aElementOf0(W1,slsdtgt0(xc))
& ! [W3] :
( sdtasdt0(xc,W3) != W1
| ~ aElement0(W3) ) )
| ( ~ aElementOf0(W0,slsdtgt0(xc))
& ! [W3] :
( sdtasdt0(xc,W3) != W0
| ~ aElement0(W3) ) )
| ~ sP3_prd(W2,W1,W0) ) ),
inference(NNF_transformation,[status(thm)],[f193]) ).
fof(f237,plain,
( ! [W0,W1,W2] :
( ( aElement0(W2)
& ( aElementOf0(W1,slsdtgt0(xc))
| ? [W3] :
( sdtasdt0(xc,W3) = W1
& aElement0(W3) ) )
& ( aElementOf0(W0,slsdtgt0(xc))
| ? [W3] :
( sdtasdt0(xc,W3) = W0
& aElement0(W3) ) ) )
| sP3_prd(W2,W1,W0) )
& ! [W0,W1,W2] :
( ~ aElement0(W2)
| ( ~ aElementOf0(W1,slsdtgt0(xc))
& ! [W3] :
( sdtasdt0(xc,W3) != W1
| ~ aElement0(W3) ) )
| ( ~ aElementOf0(W0,slsdtgt0(xc))
& ! [W3] :
( sdtasdt0(xc,W3) != W0
| ~ aElement0(W3) ) )
| ~ sP3_prd(W2,W1,W0) ) ),
inference(miniscoping,[status(thm)],[f236]) ).
fof(f238,plain,
( ! [W0,W1,W2] :
( ( aElement0(W2)
& ( aElementOf0(W1,slsdtgt0(xc))
| ( sdtasdt0(xc,sK29_skl(W2,W1,W0)) = W1
& aElement0(sK29_skl(W2,W1,W0)) ) )
& ( aElementOf0(W0,slsdtgt0(xc))
| ( sdtasdt0(xc,sK28_skl(W2,W1,W0)) = W0
& aElement0(sK28_skl(W2,W1,W0)) ) ) )
| sP3_prd(W2,W1,W0) )
& ! [W0,W1,W2] :
( ~ aElement0(W2)
| ( ~ aElementOf0(W1,slsdtgt0(xc))
& ! [W3] :
( sdtasdt0(xc,W3) != W1
| ~ aElement0(W3) ) )
| ( ~ aElementOf0(W0,slsdtgt0(xc))
& ! [W3] :
( sdtasdt0(xc,W3) != W0
| ~ aElement0(W3) ) )
| ~ sP3_prd(W2,W1,W0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28_skl,sK29_skl]),skolemize(W3,sK28_skl(W2,W1,W0)),skolemize(W3,sK29_skl(W2,W1,W0))],[f237]) ).
fof(f242,plain,
! [X0,X1,X2] :
( ~ aElement0(X0)
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElementOf0(X2,slsdtgt0(xc))
| ~ sP3_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f238]) ).
fof(f248,plain,
! [W0,W1] :
( ( aElementOf0(sdtpldt0(W0,W1),slsdtgt0(xc))
| ~ aElementOf0(W1,slsdtgt0(xc))
| sP4_prd(W1,W0) )
& ( ( ~ aElementOf0(sdtpldt0(W0,W1),slsdtgt0(xc))
& aElementOf0(W1,slsdtgt0(xc)) )
| ~ sP4_prd(W1,W0) ) ),
inference(NNF_transformation,[status(thm)],[f194]) ).
fof(f249,plain,
( ! [W0,W1] :
( aElementOf0(sdtpldt0(W0,W1),slsdtgt0(xc))
| ~ aElementOf0(W1,slsdtgt0(xc))
| sP4_prd(W1,W0) )
& ! [W0,W1] :
( ( ~ aElementOf0(sdtpldt0(W0,W1),slsdtgt0(xc))
& aElementOf0(W1,slsdtgt0(xc)) )
| ~ sP4_prd(W1,W0) ) ),
inference(miniscoping,[status(thm)],[f248]) ).
fof(f250,plain,
! [X0,X1] :
( aElementOf0(X0,slsdtgt0(xc))
| ~ sP4_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f249]) ).
fof(f251,plain,
! [X0,X1] :
( ~ aElementOf0(sdtpldt0(X1,X0),slsdtgt0(xc))
| ~ sP4_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f249]) ).
fof(f253,definition,
( sQ0_spl
<=> sP4_prd(sK26_skl,sK25_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f254,plain,
( ~ sQ0_spl
| sP4_prd(sK26_skl,sK25_skl) ),
inference(component_clause,[status(thm)],[f253]) ).
fof(f256,definition,
( sQ1_spl
<=> aElement0(sK27_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f257,plain,
( ~ sQ1_spl
| aElement0(sK27_skl) ),
inference(component_clause,[status(thm)],[f256]) ).
fof(f259,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f216,f253,f256]) ).
fof(f260,definition,
( sQ2_spl
<=> aElementOf0(sdtasdt0(sK27_skl,sK25_skl),slsdtgt0(xc)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f262,plain,
( sQ2_spl
| ~ aElementOf0(sdtasdt0(sK27_skl,sK25_skl),slsdtgt0(xc)) ),
inference(component_clause,[status(thm)],[f260]) ).
fof(f263,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f217,f253,f260]) ).
fof(f284,plain,
! [X0,X1,X2] :
( ~ sP4_prd(X1,X2)
| sP3_prd(X0,X1,X2) ),
inference(resolution,[status(thm)],[f207,f251]) ).
fof(f289,definition,
! [X0,X1] :
( sQ4_spl
<=> ( ~ sP4_prd(X1,X0)
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElementOf0(X0,slsdtgt0(xc)) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f290,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ sP4_prd(X1,X0)
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElementOf0(X0,slsdtgt0(xc)) ),
inference(component_clause,[status(thm)],[f289]) ).
fof(f355,definition,
! [X1] :
( sQ14_spl
<=> ~ aElement0(X1) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f356,plain,
! [X0] :
( ~ sQ14_spl
| ~ aElement0(X0) ),
inference(component_clause,[status(thm)],[f355]) ).
fof(f376,plain,
( ~ sQ14_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f45,f356]) ).
fof(f382,plain,
~ sQ14_spl,
inference(contradiction_clause,[status(thm)],[f376]) ).
fof(f436,plain,
! [X0,X1,X2] :
( ~ sP4_prd(X1,X0)
| ~ aElement0(X2)
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElementOf0(X0,slsdtgt0(xc)) ),
inference(resolution,[status(thm)],[f242,f284]) ).
fof(f448,plain,
! [X0] :
( ~ aElement0(X0)
| ~ sP3_prd(X0,sK25_skl,sK25_skl) ),
inference(resolution,[status(thm)],[f242,f215]) ).
fof(f470,plain,
( sQ14_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f436,f289,f355]) ).
fof(f478,definition,
( sQ26_spl
<=> aSet0(slsdtgt0(xc)) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f480,plain,
( sQ26_spl
| ~ aSet0(slsdtgt0(xc)) ),
inference(component_clause,[status(thm)],[f478]) ).
fof(f502,plain,
( sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f480,f211]) ).
fof(f503,plain,
sQ26_spl,
inference(contradiction_clause,[status(thm)],[f502]) ).
fof(f504,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ sP4_prd(X1,X0)
| ~ aElementOf0(X0,slsdtgt0(xc)) ),
inference(forward_subsumption_resolution,[status(thm)],[f290,f250]) ).
fof(f509,plain,
! [X0] :
( aElementOf0(sdtasdt0(X0,sK25_skl),slsdtgt0(xc))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f448,f210]) ).
fof(f532,plain,
( ~ sQ0_spl
| ~ sQ4_spl
| ~ aElementOf0(sK25_skl,slsdtgt0(xc)) ),
inference(resolution,[status(thm)],[f504,f254]) ).
fof(f541,plain,
( ~ sQ0_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f532,f215]) ).
fof(f542,plain,
( ~ sQ0_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f541]) ).
fof(f858,definition,
( sQ74_spl
<=> aElement0(xc) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f860,plain,
( sQ74_spl
| ~ aElement0(xc) ),
inference(component_clause,[status(thm)],[f858]) ).
fof(f865,plain,
( sQ74_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f860,f191]) ).
fof(f866,plain,
sQ74_spl,
inference(contradiction_clause,[status(thm)],[f865]) ).
fof(f963,plain,
( sQ2_spl
| ~ aElement0(sK27_skl) ),
inference(resolution,[status(thm)],[f509,f262]) ).
fof(f965,plain,
( sQ2_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f963,f257]) ).
fof(f966,plain,
( sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f965]) ).
fof(f967,plain,
$false,
inference(sat_refutation,[status(thm)],[f259,f263,f382,f470,f503,f542,f866,f966]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG106+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n002.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 04:23:01 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.11/0.45 % Refutation found
% 0.11/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.48 % Elapsed time: 0.103035 seconds
% 0.11/0.48 % CPU time: 0.583365 seconds
% 0.11/0.48 % Total memory used: 95.216 MB
% 0.11/0.48 % Net memory used: 94.442 MB
%------------------------------------------------------------------------------