%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG109+1 : 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 02:05:00 PM UTC 2026
% Result : Theorem 3.82s 1.02s
% Output : CNFRefutation 3.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 30
% Syntax : Number of formulae : 132 ( 20 unt; 19 def)
% Number of atoms : 432 ( 82 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 498 ( 198 ~; 195 |; 68 &)
% ( 27 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 16 prp; 0-5 aty)
% Number of functors : 17 ( 17 usr; 5 con; 0-4 aty)
% Number of variables : 196 ( 168 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
aElement0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [W0] :
( aElement0(W0)
=> ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
sz10 != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [W0,W1] :
( ( aSet0(W1)
& aSet0(W0) )
=> ( ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& ! [W2] :
( aElementOf0(W2,W0)
=> aElementOf0(W2,W1) ) )
=> W0 = W1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,definition,
! [W0,W1] :
( ( aSet0(W1)
& aSet0(W0) )
=> ! [W2] :
( W2 = sdtpldt1(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ? [W4,W5] :
( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) ) )
& aSet0(W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,definition,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( W1 = slsdtgt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) ) )
& aSet0(W1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [W0] :
( aElement0(W0)
=> aIdeal0(slsdtgt0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,hypothesis,
( xb != sz00
| xa != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,hypothesis,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& aIdeal0(xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
( aElementOf0(xb,slsdtgt0(xb))
& aElementOf0(sz00,slsdtgt0(xb))
& aElementOf0(xa,slsdtgt0(xa))
& aElementOf0(sz00,slsdtgt0(xa)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,conjecture,
? [W0] :
( W0 != sz00
& aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ ? [W0] :
( W0 != sz00
& aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f50,plain,
aElement0(sz10),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f61,plain,
! [W0] :
( ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 )
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f62,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
! [X0] :
( X0 = sdtpldt0(sz00,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f85,plain,
sz10 != sz00,
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f89,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f90,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f91,plain,
! [W0,W1] :
( W0 = W1
| ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ? [W2] :
( ~ aElementOf0(W2,W1)
& aElementOf0(W2,W0) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f92,definition,
! [W0,W1,W2] :
( sP0_prd(W2,W1,W0)
<=> ( ~ aElementOf0(W2,W1)
& aElementOf0(W2,W0) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f97,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtpldt1(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ? [W4,W5] :
( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) ) )
& aSet0(W2) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f98,definition,
! [W0,W1,W3,W4,W5] :
( sP1_prd(W5,W4,W3,W1,W0)
<=> ( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f99,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtpldt1(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ? [W4,W5] : sP1_prd(W5,W4,W3,W1,W0) )
& aSet0(W2) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(formula_renaming,[status(thm)],[f97,f98]) ).
fof(f100,plain,
! [W0,W1] :
( ! [W2] :
( ( ? [W3] :
( ( ? [W4,W5] : sP1_prd(W5,W4,W3,W1,W0)
| aElementOf0(W3,W2) )
& ( ! [W4,W5] : ~ sP1_prd(W5,W4,W3,W1,W0)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtpldt1(W0,W1) )
& ( ( ! [W3] :
( ( ! [W4,W5] : ~ sP1_prd(W5,W4,W3,W1,W0)
| aElementOf0(W3,W2) )
& ( ? [W4,W5] : sP1_prd(W5,W4,W3,W1,W0)
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != sdtpldt1(W0,W1) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f99]) ).
fof(f101,plain,
! [W0,W1] :
( ( ! [W2] :
( ? [W3] :
( ( ? [W4,W5] : sP1_prd(W5,W4,W3,W1,W0)
| aElementOf0(W3,W2) )
& ( ! [W4,W5] : ~ sP1_prd(W5,W4,W3,W1,W0)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtpldt1(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ! [W4,W5] : ~ sP1_prd(W5,W4,W3,W1,W0)
| aElementOf0(W3,W2) )
& ! [W3] :
( ? [W4,W5] : sP1_prd(W5,W4,W3,W1,W0)
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtpldt1(W0,W1) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(miniscoping,[status(thm)],[f100]) ).
fof(f102,plain,
! [W0,W1] :
( ( ! [W2] :
( ( ( sP1_prd(sK6_skl(W2,W1,W0),sK5_skl(W2,W1,W0),sK4_skl(W2,W1,W0),W1,W0)
| aElementOf0(sK4_skl(W2,W1,W0),W2) )
& ( ! [W4,W5] : ~ sP1_prd(W5,W4,sK4_skl(W2,W1,W0),W1,W0)
| ~ aElementOf0(sK4_skl(W2,W1,W0),W2) ) )
| ~ aSet0(W2)
| W2 = sdtpldt1(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ! [W4,W5] : ~ sP1_prd(W5,W4,W3,W1,W0)
| aElementOf0(W3,W2) )
& ! [W3] :
( sP1_prd(sK3_skl(W3,W2,W1,W0),sK2_skl(W3,W2,W1,W0),W3,W1,W0)
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtpldt1(W0,W1) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl,sK5_skl,sK6_skl]),skolemize(W4,sK2_skl(W3,W2,W1,W0)),skolemize(W5,sK3_skl(W3,W2,W1,W0)),skolemize(W3,sK4_skl(W2,W1,W0)),skolemize(W4,sK5_skl(W2,W1,W0)),skolemize(W5,sK6_skl(W2,W1,W0))],[f101]) ).
fof(f105,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sP1_prd(X4,X5,X3,X1,X0)
| aElementOf0(X3,X2)
| X2 != sdtpldt1(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f185,plain,
! [W0] :
( ! [W1] :
( W1 = slsdtgt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) ) )
& aSet0(W1) ) )
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f186,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ( ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) )
| aElementOf0(W2,W1) )
& ( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
| ~ aElementOf0(W2,W1) ) )
| ~ aSet0(W1)
| W1 = slsdtgt0(W0) )
& ( ( ! [W2] :
( ( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
| aElementOf0(W2,W1) )
& ( ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) )
| ~ aElementOf0(W2,W1) ) )
& aSet0(W1) )
| W1 != slsdtgt0(W0) ) )
| ~ aElement0(W0) ),
inference(NNF_transformation,[status(thm)],[f185]) ).
fof(f187,plain,
! [W0] :
( ( ! [W1] :
( ? [W2] :
( ( ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) )
| aElementOf0(W2,W1) )
& ( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
| ~ aElementOf0(W2,W1) ) )
| ~ aSet0(W1)
| W1 = slsdtgt0(W0) )
& ! [W1] :
( ( ! [W2] :
( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
| aElementOf0(W2,W1) )
& ! [W2] :
( ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) )
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| W1 != slsdtgt0(W0) ) )
| ~ aElement0(W0) ),
inference(miniscoping,[status(thm)],[f186]) ).
fof(f188,plain,
! [W0] :
( ( ! [W1] :
( ( ( ( sdtasdt0(W0,sK19_skl(W1,W0)) = sK18_skl(W1,W0)
& aElement0(sK19_skl(W1,W0)) )
| aElementOf0(sK18_skl(W1,W0),W1) )
& ( ! [W3] :
( sdtasdt0(W0,W3) != sK18_skl(W1,W0)
| ~ aElement0(W3) )
| ~ aElementOf0(sK18_skl(W1,W0),W1) ) )
| ~ aSet0(W1)
| W1 = slsdtgt0(W0) )
& ! [W1] :
( ( ! [W2] :
( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
| aElementOf0(W2,W1) )
& ! [W2] :
( ( sdtasdt0(W0,sK17_skl(W2,W1,W0)) = W2
& aElement0(sK17_skl(W2,W1,W0)) )
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| W1 != slsdtgt0(W0) ) )
| ~ aElement0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl,sK19_skl]),skolemize(W3,sK17_skl(W2,W1,W0)),skolemize(W2,sK18_skl(W1,W0)),skolemize(W3,sK19_skl(W1,W0))],[f187]) ).
fof(f189,plain,
! [X0,X1] :
( aSet0(X1)
| X1 != slsdtgt0(X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f196,plain,
! [W0] :
( aIdeal0(slsdtgt0(W0))
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f197,plain,
! [X0] :
( aIdeal0(slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f198,plain,
aElement0(xa),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f199,plain,
aElement0(xb),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f200,plain,
( xb != sz00
| xa != sz00 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f203,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f204,plain,
aElementOf0(sz00,slsdtgt0(xa)),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f205,plain,
aElementOf0(xa,slsdtgt0(xa)),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f207,plain,
aElementOf0(xb,slsdtgt0(xb)),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f208,plain,
! [W0] :
( W0 = sz00
| ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f209,plain,
! [X0] :
( X0 = sz00
| ~ aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(cnf_transformation,[status(thm)],[f208]) ).
fof(f210,plain,
! [W0,W1,W2] :
( ( aElementOf0(W2,W1)
| ~ aElementOf0(W2,W0)
| sP0_prd(W2,W1,W0) )
& ( ( ~ aElementOf0(W2,W1)
& aElementOf0(W2,W0) )
| ~ sP0_prd(W2,W1,W0) ) ),
inference(NNF_transformation,[status(thm)],[f92]) ).
fof(f211,plain,
( ! [W0,W1,W2] :
( aElementOf0(W2,W1)
| ~ aElementOf0(W2,W0)
| sP0_prd(W2,W1,W0) )
& ! [W0,W1,W2] :
( ( ~ aElementOf0(W2,W1)
& aElementOf0(W2,W0) )
| ~ sP0_prd(W2,W1,W0) ) ),
inference(miniscoping,[status(thm)],[f210]) ).
fof(f213,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X0,X1)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f211]) ).
fof(f215,plain,
! [W0,W1,W3,W4,W5] :
( ( sdtpldt0(W4,W5) != W3
| ~ aElementOf0(W5,W1)
| ~ aElementOf0(W4,W0)
| sP1_prd(W5,W4,W3,W1,W0) )
& ( ( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) )
| ~ sP1_prd(W5,W4,W3,W1,W0) ) ),
inference(NNF_transformation,[status(thm)],[f98]) ).
fof(f216,plain,
( ! [W0,W1,W3,W4,W5] :
( sdtpldt0(W4,W5) != W3
| ~ aElementOf0(W5,W1)
| ~ aElementOf0(W4,W0)
| sP1_prd(W5,W4,W3,W1,W0) )
& ! [W0,W1,W3,W4,W5] :
( ( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) )
| ~ sP1_prd(W5,W4,W3,W1,W0) ) ),
inference(miniscoping,[status(thm)],[f215]) ).
fof(f220,plain,
! [X0,X1,X2,X3,X4] :
( sdtpldt0(X1,X0) != X2
| ~ aElementOf0(X0,X3)
| ~ aElementOf0(X1,X4)
| sP1_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f216]) ).
fof(f227,definition,
( sQ0_spl
<=> xa = sz00 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f229,plain,
( sQ0_spl
| xa != sz00 ),
inference(component_clause,[status(thm)],[f227]) ).
fof(f230,definition,
( sQ1_spl
<=> xb = sz00 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f231,plain,
( ~ sQ1_spl
| xb = sz00 ),
inference(component_clause,[status(thm)],[f230]) ).
fof(f233,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f200,f227,f230]) ).
fof(f236,plain,
! [X0,X1,X2,X3,X4] :
( ~ sP1_prd(X3,X4,X2,X1,X0)
| aElementOf0(X2,sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f105]) ).
fof(f242,plain,
! [X0] :
( aSet0(slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f189]) ).
fof(f246,plain,
! [X0,X1,X2,X3] :
( ~ aElementOf0(X0,X2)
| ~ aElementOf0(X1,X3)
| sP1_prd(X0,X1,sdtpldt0(X1,X0),X2,X3) ),
inference(destructive_equality_resolution,[status(thm)],[f220]) ).
fof(f249,definition,
! [X0] :
( sQ2_spl
<=> ( ~ aElement0(X0)
| X0 = sz00
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f250,plain,
! [X0] :
( ~ sQ2_spl
| ~ aElement0(X0)
| X0 = sz00
| ~ aElement0(X0) ),
inference(component_clause,[status(thm)],[f249]) ).
fof(f264,definition,
( sQ5_spl
<=> aElement0(sz10) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f266,plain,
( sQ5_spl
| ~ aElement0(sz10) ),
inference(component_clause,[status(thm)],[f264]) ).
fof(f274,plain,
( aElement0(xb)
| ~ aSet0(slsdtgt0(xb)) ),
inference(resolution,[status(thm)],[f90,f207]) ).
fof(f275,plain,
( aElement0(xa)
| ~ aSet0(slsdtgt0(xa)) ),
inference(resolution,[status(thm)],[f90,f205]) ).
fof(f279,definition,
( sQ7_spl
<=> aSet0(slsdtgt0(xb)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f281,plain,
( sQ7_spl
| ~ aSet0(slsdtgt0(xb)) ),
inference(component_clause,[status(thm)],[f279]) ).
fof(f282,definition,
( sQ8_spl
<=> aElement0(xb) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f285,plain,
( sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f274,f279,f282]) ).
fof(f286,definition,
( sQ9_spl
<=> aSet0(slsdtgt0(xa)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f288,plain,
( sQ9_spl
| ~ aSet0(slsdtgt0(xa)) ),
inference(component_clause,[status(thm)],[f286]) ).
fof(f289,definition,
( sQ10_spl
<=> aElement0(xa) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f292,plain,
( sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f275,f286,f289]) ).
fof(f295,plain,
( sQ9_spl
| ~ aElement0(xa) ),
inference(resolution,[status(thm)],[f288,f242]) ).
fof(f296,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f295,f198]) ).
fof(f297,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f296]) ).
fof(f298,plain,
( sQ7_spl
| ~ aElement0(xb) ),
inference(resolution,[status(thm)],[f281,f242]) ).
fof(f299,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f298,f199]) ).
fof(f300,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f299]) ).
fof(f321,definition,
( sQ15_spl
<=> aIdeal0(slsdtgt0(xa)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f323,plain,
( sQ15_spl
| ~ aIdeal0(slsdtgt0(xa)) ),
inference(component_clause,[status(thm)],[f321]) ).
fof(f324,definition,
( sQ16_spl
<=> aIdeal0(slsdtgt0(xb)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f326,plain,
( sQ16_spl
| ~ aIdeal0(slsdtgt0(xb)) ),
inference(component_clause,[status(thm)],[f324]) ).
fof(f332,plain,
! [X0] :
( X0 = sz00
| ~ aElementOf0(X0,xI) ),
inference(backward_demodulation,[status(thm)],[f203,f209]) ).
fof(f345,plain,
( sQ16_spl
| ~ aElement0(xb) ),
inference(resolution,[status(thm)],[f326,f197]) ).
fof(f346,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f345,f199]) ).
fof(f347,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f346]) ).
fof(f348,plain,
( sQ15_spl
| ~ aElement0(xa) ),
inference(resolution,[status(thm)],[f323,f197]) ).
fof(f349,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f348,f198]) ).
fof(f350,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f349]) ).
fof(f420,plain,
! [X0] :
( ~ sQ2_spl
| X0 = sz00
| ~ aElement0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f250]) ).
fof(f427,plain,
( ~ sQ2_spl
| sz10 = sz00 ),
inference(resolution,[status(thm)],[f420,f50]) ).
fof(f431,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f427,f85]) ).
fof(f432,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f431]) ).
fof(f504,plain,
! [X0,X1,X2,X3] :
( aElementOf0(sdtpldt0(X0,X2),sdtpldt1(X1,X3))
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X3)
| ~ aElementOf0(X0,X1) ),
inference(resolution,[status(thm)],[f246,f236]) ).
fof(f508,definition,
! [X0,X1] :
( sQ34_spl
<=> ~ aElementOf0(X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f509,plain,
! [X0,X1] :
( ~ sQ34_spl
| ~ aElementOf0(X0,X1) ),
inference(component_clause,[status(thm)],[f508]) ).
fof(f525,plain,
( ~ sQ34_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f207,f509]) ).
fof(f533,plain,
~ sQ34_spl,
inference(contradiction_clause,[status(thm)],[f525]) ).
fof(f1172,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f266,f50]) ).
fof(f1173,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f1172]) ).
fof(f1187,plain,
! [X0,X1] :
( aElementOf0(sdtpldt0(X0,X1),xI)
| ~ aSet0(slsdtgt0(xb))
| ~ aSet0(slsdtgt0(xa))
| ~ aElementOf0(X1,slsdtgt0(xb))
| ~ aElementOf0(X0,slsdtgt0(xa)) ),
inference(paramodulation,[status(thm)],[f203,f504]) ).
fof(f1192,definition,
! [X0,X1] :
( sQ100_spl
<=> ( aElementOf0(sdtpldt0(X0,X1),xI)
| ~ aElementOf0(X1,slsdtgt0(xb))
| ~ aElementOf0(X0,slsdtgt0(xa)) ) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f1193,plain,
! [X0,X1] :
( ~ sQ100_spl
| aElementOf0(sdtpldt0(X0,X1),xI)
| ~ aElementOf0(X1,slsdtgt0(xb))
| ~ aElementOf0(X0,slsdtgt0(xa)) ),
inference(component_clause,[status(thm)],[f1192]) ).
fof(f1195,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| sQ100_spl ),
inference(split_clause,[status(thm)],[f1187,f1192,f286,f279]) ).
fof(f1199,plain,
! [X0,X1] :
( ~ sQ100_spl
| sdtpldt0(X0,X1) = sz00
| ~ aElementOf0(X1,slsdtgt0(xb))
| ~ aElementOf0(X0,slsdtgt0(xa)) ),
inference(resolution,[status(thm)],[f1193,f332]) ).
fof(f1276,plain,
! [X0] :
( ~ sQ100_spl
| sdtpldt0(sz00,X0) = sz00
| ~ aElementOf0(X0,slsdtgt0(xb)) ),
inference(resolution,[status(thm)],[f1199,f204]) ).
fof(f1277,plain,
! [X0] :
( ~ sQ100_spl
| sdtpldt0(xa,X0) = sz00
| ~ aElementOf0(X0,slsdtgt0(xb)) ),
inference(resolution,[status(thm)],[f1199,f205]) ).
fof(f1476,definition,
( sQ152_spl
<=> aElementOf0(sz00,slsdtgt0(xa)) ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f1478,plain,
( sQ152_spl
| ~ aElementOf0(sz00,slsdtgt0(xa)) ),
inference(component_clause,[status(thm)],[f1476]) ).
fof(f1519,plain,
( sQ152_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1478,f204]) ).
fof(f1520,plain,
sQ152_spl,
inference(contradiction_clause,[status(thm)],[f1519]) ).
fof(f1578,plain,
( ~ sQ100_spl
| sdtpldt0(sz00,xb) = sz00 ),
inference(resolution,[status(thm)],[f1276,f207]) ).
fof(f1751,plain,
( ~ sQ100_spl
| xb = sz00
| ~ aElement0(xb) ),
inference(paramodulation,[status(thm)],[f1578,f63]) ).
fof(f1762,plain,
( ~ sQ100_spl
| sQ1_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1751,f282,f230,f1192]) ).
fof(f1860,plain,
! [X0] :
( ~ sQ1_spl
| sdtpldt0(X0,xb) = X0
| ~ aElement0(X0) ),
inference(backward_demodulation,[status(thm)],[f231,f62]) ).
fof(f1883,plain,
( sQ0_spl
| ~ sQ1_spl
| xa != xb ),
inference(forward_demodulation,[status(thm)],[f231,f229]) ).
fof(f2057,definition,
( sQ223_spl
<=> sP0_prd(xb,slsdtgt0(xb),xI) ),
introduced(definition,[new_symbols(definition,[sQ223_spl])],[split_symbol_definition]) ).
fof(f2058,plain,
( ~ sQ223_spl
| sP0_prd(xb,slsdtgt0(xb),xI) ),
inference(component_clause,[status(thm)],[f2057]) ).
fof(f2160,plain,
( ~ sQ223_spl
| ~ aElementOf0(xb,slsdtgt0(xb)) ),
inference(resolution,[status(thm)],[f2058,f213]) ).
fof(f2162,plain,
( ~ sQ223_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2160,f207]) ).
fof(f2163,plain,
~ sQ223_spl,
inference(contradiction_clause,[status(thm)],[f2162]) ).
fof(f2178,plain,
! [X0] :
( ~ sQ100_spl
| ~ sQ1_spl
| sdtpldt0(xa,X0) = xb
| ~ aElementOf0(X0,slsdtgt0(xb)) ),
inference(forward_demodulation,[status(thm)],[f231,f1277]) ).
fof(f2192,plain,
( ~ sQ100_spl
| ~ sQ1_spl
| sdtpldt0(xa,xb) = xb ),
inference(resolution,[status(thm)],[f2178,f207]) ).
fof(f2245,plain,
( ~ sQ100_spl
| ~ sQ1_spl
| xb = xa
| ~ aElement0(xa) ),
inference(paramodulation,[status(thm)],[f2192,f1860]) ).
fof(f2255,definition,
( sQ249_spl
<=> xb = xa ),
introduced(definition,[new_symbols(definition,[sQ249_spl])],[split_symbol_definition]) ).
fof(f2256,plain,
( ~ sQ249_spl
| xb = xa ),
inference(component_clause,[status(thm)],[f2255]) ).
fof(f2258,plain,
( ~ sQ100_spl
| ~ sQ1_spl
| sQ249_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2245,f289,f2255,f230,f1192]) ).
fof(f2277,plain,
( ~ sQ249_spl
| sQ0_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2256,f1883]) ).
fof(f2278,plain,
( ~ sQ249_spl
| sQ0_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f2277]) ).
fof(f2279,plain,
$false,
inference(sat_refutation,[status(thm)],[f233,f285,f292,f297,f300,f347,f350,f432,f533,f1173,f1195,f1520,f1762,f2163,f2258,f2278]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG109+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.36 % Computer : n007.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Mon Sep 21 04:18:20 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.41 % Drodi V4.1.1
% 3.82/1.02 % Refutation found
% 3.82/1.02 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.82/1.02 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.82/1.04 % Elapsed time: 0.649424 seconds
% 3.82/1.04 % CPU time: 4.683939 seconds
% 3.82/1.04 % Total memory used: 146.501 MB
% 3.82/1.04 % Net memory used: 142.340 MB
%------------------------------------------------------------------------------