%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG093+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 : n008.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 02:04:56 PM UTC 2026
% Result : Theorem 0.09s 0.47s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 107
% Syntax : Number of formulae : 403 ( 19 unt; 99 def)
% Number of atoms : 1321 ( 209 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 1653 ( 735 ~; 757 |; 50 &)
% ( 103 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 103 ( 101 usr; 98 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 174 ( 166 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aElement0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
aElement0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> aElement0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [W0] :
( aElement0(W0)
=> ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> ( sdtasdt0(W0,W1) = sz00
=> ( W1 = sz00
| W0 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
sz10 != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,definition,
! [W0,W1] :
( ( aSet0(W1)
& aSet0(W0) )
=> ! [W2] :
( W2 = sdtasasdt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( aElementOf0(W3,W1)
& aElementOf0(W3,W0) ) )
& aSet0(W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,definition,
! [W0] :
( aIdeal0(W0)
<=> ( ! [W1] :
( aElementOf0(W1,W0)
=> ( ! [W2] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) )
& ! [W2] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) ) ) )
& aSet0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,hypothesis,
( aIdeal0(xJ)
& aIdeal0(xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,conjecture,
aIdeal0(sdtasasdt0(xI,xJ)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
~ aIdeal0(sdtasasdt0(xI,xJ)),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f32,plain,
aElement0(sz00),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f33,plain,
aElement0(sz10),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f38,plain,
! [W0,W1] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f39,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f63,plain,
! [W0] :
( ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 )
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f64,plain,
! [X0] :
( sdtasdt0(X0,sz00) = sz00
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f66,plain,
! [W0,W1] :
( W1 = sz00
| W0 = sz00
| sdtasdt0(W0,W1) != sz00
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f67,plain,
! [X0,X1] :
( X1 = sz00
| X0 = sz00
| sdtasdt0(X0,X1) != sz00
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f68,plain,
sz10 != sz00,
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f91,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtasasdt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( aElementOf0(W3,W1)
& aElementOf0(W3,W0) ) )
& aSet0(W2) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f92,plain,
! [W0,W1] :
( ! [W2] :
( ( ? [W3] :
( ( ( aElementOf0(W3,W1)
& aElementOf0(W3,W0) )
| aElementOf0(W3,W2) )
& ( ~ aElementOf0(W3,W1)
| ~ aElementOf0(W3,W0)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtasasdt0(W0,W1) )
& ( ( ! [W3] :
( ( ~ aElementOf0(W3,W1)
| ~ aElementOf0(W3,W0)
| aElementOf0(W3,W2) )
& ( ( aElementOf0(W3,W1)
& aElementOf0(W3,W0) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != sdtasasdt0(W0,W1) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f91]) ).
fof(f93,plain,
! [W0,W1] :
( ( ! [W2] :
( ? [W3] :
( ( ( aElementOf0(W3,W1)
& aElementOf0(W3,W0) )
| aElementOf0(W3,W2) )
& ( ~ aElementOf0(W3,W1)
| ~ aElementOf0(W3,W0)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtasasdt0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ~ aElementOf0(W3,W1)
| ~ aElementOf0(W3,W0)
| aElementOf0(W3,W2) )
& ! [W3] :
( ( aElementOf0(W3,W1)
& aElementOf0(W3,W0) )
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtasasdt0(W0,W1) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(miniscoping,[status(thm)],[f92]) ).
fof(f94,plain,
! [W0,W1] :
( ( ! [W2] :
( ( ( ( aElementOf0(sK7_skl(W2,W1,W0),W1)
& aElementOf0(sK7_skl(W2,W1,W0),W0) )
| aElementOf0(sK7_skl(W2,W1,W0),W2) )
& ( ~ aElementOf0(sK7_skl(W2,W1,W0),W1)
| ~ aElementOf0(sK7_skl(W2,W1,W0),W0)
| ~ aElementOf0(sK7_skl(W2,W1,W0),W2) ) )
| ~ aSet0(W2)
| W2 = sdtasasdt0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ~ aElementOf0(W3,W1)
| ~ aElementOf0(W3,W0)
| aElementOf0(W3,W2) )
& ! [W3] :
( ( aElementOf0(W3,W1)
& aElementOf0(W3,W0) )
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtasasdt0(W0,W1) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(W3,sK7_skl(W2,W1,W0))],[f93]) ).
fof(f95,plain,
! [X0,X1,X2] :
( aSet0(X2)
| X2 != sdtasasdt0(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f96,plain,
! [X0,X1,X2,X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X2)
| X2 != sdtasasdt0(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f97,plain,
! [X0,X1,X2,X3] :
( aElementOf0(X3,X1)
| ~ aElementOf0(X3,X2)
| X2 != sdtasasdt0(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f98,plain,
! [X0,X1,X2,X3] :
( ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0)
| aElementOf0(X3,X2)
| X2 != sdtasasdt0(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f102,plain,
! [W0] :
( aIdeal0(W0)
<=> ( ! [W1] :
( ( ! [W2] :
( aElementOf0(sdtasdt0(W2,W1),W0)
| ~ aElement0(W2) )
& ! [W2] :
( aElementOf0(sdtpldt0(W1,W2),W0)
| ~ aElementOf0(W2,W0) ) )
| ~ aElementOf0(W1,W0) )
& aSet0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f103,plain,
! [W0] :
( ( ? [W1] :
( ( ? [W2] :
( ~ aElementOf0(sdtasdt0(W2,W1),W0)
& aElement0(W2) )
| ? [W2] :
( ~ aElementOf0(sdtpldt0(W1,W2),W0)
& aElementOf0(W2,W0) ) )
& aElementOf0(W1,W0) )
| ~ aSet0(W0)
| aIdeal0(W0) )
& ( ( ! [W1] :
( ( ! [W2] :
( aElementOf0(sdtasdt0(W2,W1),W0)
| ~ aElement0(W2) )
& ! [W2] :
( aElementOf0(sdtpldt0(W1,W2),W0)
| ~ aElementOf0(W2,W0) ) )
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aIdeal0(W0) ) ),
inference(NNF_transformation,[status(thm)],[f102]) ).
fof(f104,plain,
( ! [W0] :
( ? [W1] :
( ( ? [W2] :
( ~ aElementOf0(sdtasdt0(W2,W1),W0)
& aElement0(W2) )
| ? [W2] :
( ~ aElementOf0(sdtpldt0(W1,W2),W0)
& aElementOf0(W2,W0) ) )
& aElementOf0(W1,W0) )
| ~ aSet0(W0)
| aIdeal0(W0) )
& ! [W0] :
( ( ! [W1] :
( ( ! [W2] :
( aElementOf0(sdtasdt0(W2,W1),W0)
| ~ aElement0(W2) )
& ! [W2] :
( aElementOf0(sdtpldt0(W1,W2),W0)
| ~ aElementOf0(W2,W0) ) )
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aIdeal0(W0) ) ),
inference(miniscoping,[status(thm)],[f103]) ).
fof(f105,plain,
( ! [W0] :
( ( ( ( ~ aElementOf0(sdtasdt0(sK10_skl(W0),sK8_skl(W0)),W0)
& aElement0(sK10_skl(W0)) )
| ( ~ aElementOf0(sdtpldt0(sK8_skl(W0),sK9_skl(W0)),W0)
& aElementOf0(sK9_skl(W0),W0) ) )
& aElementOf0(sK8_skl(W0),W0) )
| ~ aSet0(W0)
| aIdeal0(W0) )
& ! [W0] :
( ( ! [W1] :
( ( ! [W2] :
( aElementOf0(sdtasdt0(W2,W1),W0)
| ~ aElement0(W2) )
& ! [W2] :
( aElementOf0(sdtpldt0(W1,W2),W0)
| ~ aElementOf0(W2,W0) ) )
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aIdeal0(W0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl,sK10_skl]),skolemize(W1,sK8_skl(W0)),skolemize(W2,sK9_skl(W0)),skolemize(W2,sK10_skl(W0))],[f104]) ).
fof(f106,plain,
! [X0] :
( aSet0(X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f107,plain,
! [X0,X1,X2] :
( aElementOf0(sdtpldt0(X1,X2),X0)
| ~ aElementOf0(X2,X0)
| ~ aElementOf0(X1,X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f108,plain,
! [X0,X1,X2] :
( aElementOf0(sdtasdt0(X2,X1),X0)
| ~ aElement0(X2)
| ~ aElementOf0(X1,X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f109,plain,
! [X0] :
( aElementOf0(sK8_skl(X0),X0)
| ~ aSet0(X0)
| aIdeal0(X0) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f110,plain,
! [X0] :
( aElement0(sK10_skl(X0))
| aElementOf0(sK9_skl(X0),X0)
| ~ aSet0(X0)
| aIdeal0(X0) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f111,plain,
! [X0] :
( ~ aElementOf0(sdtasdt0(sK10_skl(X0),sK8_skl(X0)),X0)
| aElementOf0(sK9_skl(X0),X0)
| ~ aSet0(X0)
| aIdeal0(X0) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f112,plain,
! [X0] :
( aElement0(sK10_skl(X0))
| ~ aElementOf0(sdtpldt0(sK8_skl(X0),sK9_skl(X0)),X0)
| ~ aSet0(X0)
| aIdeal0(X0) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f113,plain,
! [X0] :
( ~ aElementOf0(sdtasdt0(sK10_skl(X0),sK8_skl(X0)),X0)
| ~ aElementOf0(sdtpldt0(sK8_skl(X0),sK9_skl(X0)),X0)
| ~ aSet0(X0)
| aIdeal0(X0) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f116,plain,
aIdeal0(xI),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f117,plain,
aIdeal0(xJ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f118,plain,
~ aIdeal0(sdtasasdt0(xI,xJ)),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f133,plain,
! [X0,X1] :
( aSet0(sdtasasdt0(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f95]) ).
fof(f134,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,sdtasasdt0(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f96]) ).
fof(f135,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X1)
| ~ aElementOf0(X2,sdtasasdt0(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f97]) ).
fof(f136,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X2,X1)
| ~ aElementOf0(X2,X0)
| aElementOf0(X2,sdtasasdt0(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f98]) ).
fof(f139,plain,
( sdtasdt0(sz10,sz10) != sz00
| ~ aElement0(sz10)
| ~ aElement0(sz10) ),
inference(resolution,[status(thm)],[f67,f68]) ).
fof(f140,plain,
! [X0] :
( X0 = sz00
| sdtasdt0(sz10,X0) != sz00
| ~ aElement0(X0)
| ~ aElement0(sz10) ),
inference(resolution,[status(thm)],[f67,f68]) ).
fof(f141,plain,
! [X0] :
( X0 = sz00
| sdtasdt0(X0,sz10) != sz00
| ~ aElement0(sz10)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f67,f68]) ).
fof(f142,plain,
! [X0] :
( X0 = sz00
| sz00 != sz00
| sdtasdt0(X0,X0) != sz00
| ~ aElement0(X0)
| ~ aElement0(X0) ),
inference(equality_factoring,[status(thm)],[f67]) ).
fof(f143,plain,
! [X0] :
( sz00 = sz00
| X0 != sz00
| sdtasdt0(X0,sz00) != sz00
| ~ aElement0(sz00)
| ~ aElement0(X0) ),
inference(equality_factoring,[status(thm)],[f67]) ).
fof(f146,definition,
( sQ0_spl
<=> aElement0(sz10) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f148,plain,
( sQ0_spl
| ~ aElement0(sz10) ),
inference(component_clause,[status(thm)],[f146]) ).
fof(f149,definition,
( sQ1_spl
<=> sdtasdt0(sz10,sz10) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f151,plain,
( sQ1_spl
| sdtasdt0(sz10,sz10) != sz00 ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f152,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f139,f146,f149]) ).
fof(f153,definition,
! [X0] :
( sQ2_spl
<=> ( X0 = sz00
| sdtasdt0(sz10,X0) != sz00
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f154,plain,
! [X0] :
( ~ sQ2_spl
| X0 = sz00
| sdtasdt0(sz10,X0) != sz00
| ~ aElement0(X0) ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,plain,
( sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f140,f146,f153]) ).
fof(f157,definition,
! [X0] :
( sQ3_spl
<=> ( X0 = sz00
| sdtasdt0(X0,sz10) != sz00
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f158,plain,
! [X0] :
( ~ sQ3_spl
| X0 = sz00
| sdtasdt0(X0,sz10) != sz00
| ~ aElement0(X0) ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,plain,
( ~ sQ0_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f141,f157,f146]) ).
fof(f161,definition,
! [X0] :
( sQ4_spl
<=> ( X0 = sz00
| sdtasdt0(X0,X0) != sz00
| ~ aElement0(X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f164,definition,
( sQ5_spl
<=> sz00 = sz00 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f167,plain,
( ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f142,f161,f164]) ).
fof(f168,definition,
! [X0] :
( sQ6_spl
<=> ( X0 != sz00
| sdtasdt0(X0,sz00) != sz00
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f169,plain,
! [X0] :
( ~ sQ6_spl
| X0 != sz00
| sdtasdt0(X0,sz00) != sz00
| ~ aElement0(X0) ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f171,definition,
( sQ7_spl
<=> aElement0(sz00) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f173,plain,
( sQ7_spl
| ~ aElement0(sz00) ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f174,plain,
( sQ5_spl
| ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f143,f168,f171,f164]) ).
fof(f178,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f148,f33]) ).
fof(f179,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f178]) ).
fof(f181,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f173,f32]) ).
fof(f182,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f181]) ).
fof(f183,plain,
( ~ sQ6_spl
| sdtasdt0(sz00,sz00) != sz00
| ~ aElement0(sz00) ),
inference(destructive_equality_resolution,[status(thm)],[f169]) ).
fof(f184,plain,
( ~ sQ6_spl
| sdtasdt0(sz00,sz00) != sz00 ),
inference(forward_subsumption_resolution,[status(thm)],[f183,f32]) ).
fof(f185,plain,
( sQ1_spl
| sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sz10)) != sz00
| ~ aElement0(sdtasdt0(sz10,sz10))
| ~ aElement0(sdtasdt0(sz10,sz10)) ),
inference(resolution,[status(thm)],[f151,f67]) ).
fof(f186,plain,
! [X0] :
( sQ1_spl
| X0 = sz00
| sdtasdt0(X0,sdtasdt0(sz10,sz10)) != sz00
| ~ aElement0(sdtasdt0(sz10,sz10))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f151,f67]) ).
fof(f188,plain,
! [X0] :
( sQ1_spl
| X0 = sz00
| sdtasdt0(sdtasdt0(sz10,sz10),X0) != sz00
| ~ aElement0(X0)
| ~ aElement0(sdtasdt0(sz10,sz10)) ),
inference(resolution,[status(thm)],[f151,f67]) ).
fof(f189,definition,
( sQ8_spl
<=> aElement0(sdtasdt0(sz10,sz10)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f191,plain,
( sQ8_spl
| ~ aElement0(sdtasdt0(sz10,sz10)) ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f192,definition,
( sQ9_spl
<=> sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sz10)) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f194,plain,
( sQ9_spl
| sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sz10)) != sz00 ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f195,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f185,f189,f192,f149]) ).
fof(f196,definition,
! [X0] :
( sQ10_spl
<=> ( X0 = sz00
| sdtasdt0(X0,sdtasdt0(sz10,sz10)) != sz00
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f197,plain,
! [X0] :
( ~ sQ10_spl
| X0 = sz00
| sdtasdt0(X0,sdtasdt0(sz10,sz10)) != sz00
| ~ aElement0(X0) ),
inference(component_clause,[status(thm)],[f196]) ).
fof(f199,plain,
( sQ1_spl
| ~ sQ8_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f186,f196,f189,f149]) ).
fof(f201,definition,
! [X0] :
( sQ11_spl
<=> ( X0 = sz00
| sdtasdt0(sdtasdt0(sz10,sz10),X0) != sz00
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f202,plain,
! [X0] :
( ~ sQ11_spl
| X0 = sz00
| sdtasdt0(sdtasdt0(sz10,sz10),X0) != sz00
| ~ aElement0(X0) ),
inference(component_clause,[status(thm)],[f201]) ).
fof(f204,plain,
( sQ1_spl
| sQ11_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f188,f189,f201,f149]) ).
fof(f205,plain,
( ~ sQ6_spl
| ~ aElement0(sz00) ),
inference(resolution,[status(thm)],[f184,f64]) ).
fof(f211,plain,
( ~ sQ6_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f205,f171,f168]) ).
fof(f212,definition,
( sQ12_spl
<=> aElement0(sdtasdt0(sz00,sz00)) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f214,plain,
( sQ12_spl
| ~ aElement0(sdtasdt0(sz00,sz00)) ),
inference(component_clause,[status(thm)],[f212]) ).
fof(f229,plain,
( sQ8_spl
| ~ aElement0(sz10)
| ~ aElement0(sz10) ),
inference(resolution,[status(thm)],[f191,f39]) ).
fof(f231,plain,
( sQ8_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f229,f146,f189]) ).
fof(f240,definition,
( sQ16_spl
<=> sdtasdt0(sz10,sdtasdt0(sz10,sz10)) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f242,plain,
( sQ16_spl
| sdtasdt0(sz10,sdtasdt0(sz10,sz10)) != sz00 ),
inference(component_clause,[status(thm)],[f240]) ).
fof(f245,plain,
( ~ sQ2_spl
| sQ16_spl
| sdtasdt0(sz10,sdtasdt0(sz10,sdtasdt0(sz10,sz10))) != sz00
| ~ aElement0(sdtasdt0(sz10,sdtasdt0(sz10,sz10))) ),
inference(resolution,[status(thm)],[f242,f154]) ).
fof(f246,plain,
( sQ16_spl
| sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),sdtasdt0(sz10,sdtasdt0(sz10,sz10))) != sz00
| ~ aElement0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)))
| ~ aElement0(sdtasdt0(sz10,sdtasdt0(sz10,sz10))) ),
inference(resolution,[status(thm)],[f242,f67]) ).
fof(f247,plain,
! [X0] :
( sQ16_spl
| X0 = sz00
| sdtasdt0(X0,sdtasdt0(sz10,sdtasdt0(sz10,sz10))) != sz00
| ~ aElement0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f242,f67]) ).
fof(f249,plain,
! [X0] :
( sQ16_spl
| X0 = sz00
| sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),X0) != sz00
| ~ aElement0(X0)
| ~ aElement0(sdtasdt0(sz10,sdtasdt0(sz10,sz10))) ),
inference(resolution,[status(thm)],[f242,f67]) ).
fof(f251,definition,
( sQ17_spl
<=> aElement0(sdtasdt0(sz10,sdtasdt0(sz10,sz10))) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f253,plain,
( sQ17_spl
| ~ aElement0(sdtasdt0(sz10,sdtasdt0(sz10,sz10))) ),
inference(component_clause,[status(thm)],[f251]) ).
fof(f254,definition,
( sQ18_spl
<=> sdtasdt0(sz10,sdtasdt0(sz10,sdtasdt0(sz10,sz10))) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f256,plain,
( sQ18_spl
| sdtasdt0(sz10,sdtasdt0(sz10,sdtasdt0(sz10,sz10))) != sz00 ),
inference(component_clause,[status(thm)],[f254]) ).
fof(f257,plain,
( ~ sQ2_spl
| sQ16_spl
| ~ sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f245,f251,f254,f240,f153]) ).
fof(f258,definition,
( sQ19_spl
<=> sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),sdtasdt0(sz10,sdtasdt0(sz10,sz10))) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f261,plain,
( sQ16_spl
| ~ sQ19_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f246,f251,f258,f240]) ).
fof(f262,definition,
! [X0] :
( sQ20_spl
<=> ( X0 = sz00
| sdtasdt0(X0,sdtasdt0(sz10,sdtasdt0(sz10,sz10))) != sz00
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f265,plain,
( sQ16_spl
| ~ sQ17_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f247,f262,f251,f240]) ).
fof(f267,definition,
! [X0] :
( sQ21_spl
<=> ( X0 = sz00
| sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),X0) != sz00
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f270,plain,
( sQ16_spl
| sQ21_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f249,f251,f267,f240]) ).
fof(f272,plain,
( sQ17_spl
| ~ aElement0(sdtasdt0(sz10,sz10))
| ~ aElement0(sz10) ),
inference(resolution,[status(thm)],[f253,f39]) ).
fof(f274,plain,
( sQ17_spl
| ~ sQ8_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f272,f146,f189,f251]) ).
fof(f275,plain,
( sQ16_spl
| ~ sQ3_spl
| sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),sz10) != sz00
| ~ aElement0(sdtasdt0(sz10,sdtasdt0(sz10,sz10))) ),
inference(resolution,[status(thm)],[f158,f242]) ).
fof(f278,definition,
( sQ22_spl
<=> sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),sz10) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f280,plain,
( sQ22_spl
| sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),sz10) != sz00 ),
inference(component_clause,[status(thm)],[f278]) ).
fof(f281,plain,
( sQ16_spl
| ~ sQ3_spl
| ~ sQ22_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f275,f251,f278,f157,f240]) ).
fof(f282,definition,
( sQ23_spl
<=> sdtasdt0(sdtasdt0(sz10,sz10),sz10) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f284,plain,
( sQ23_spl
| sdtasdt0(sdtasdt0(sz10,sz10),sz10) != sz00 ),
inference(component_clause,[status(thm)],[f282]) ).
fof(f287,plain,
( ~ sQ3_spl
| sQ23_spl
| sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),sz10) != sz00
| ~ aElement0(sdtasdt0(sdtasdt0(sz10,sz10),sz10)) ),
inference(resolution,[status(thm)],[f284,f158]) ).
fof(f288,plain,
( ~ sQ2_spl
| sQ23_spl
| sdtasdt0(sz10,sdtasdt0(sdtasdt0(sz10,sz10),sz10)) != sz00
| ~ aElement0(sdtasdt0(sdtasdt0(sz10,sz10),sz10)) ),
inference(resolution,[status(thm)],[f284,f154]) ).
fof(f289,plain,
( sQ23_spl
| sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),sdtasdt0(sdtasdt0(sz10,sz10),sz10)) != sz00
| ~ aElement0(sdtasdt0(sdtasdt0(sz10,sz10),sz10))
| ~ aElement0(sdtasdt0(sdtasdt0(sz10,sz10),sz10)) ),
inference(resolution,[status(thm)],[f284,f67]) ).
fof(f290,plain,
! [X0] :
( sQ23_spl
| X0 = sz00
| sdtasdt0(X0,sdtasdt0(sdtasdt0(sz10,sz10),sz10)) != sz00
| ~ aElement0(sdtasdt0(sdtasdt0(sz10,sz10),sz10))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f284,f67]) ).
fof(f292,plain,
! [X0] :
( sQ23_spl
| X0 = sz00
| sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),X0) != sz00
| ~ aElement0(X0)
| ~ aElement0(sdtasdt0(sdtasdt0(sz10,sz10),sz10)) ),
inference(resolution,[status(thm)],[f284,f67]) ).
fof(f294,definition,
( sQ24_spl
<=> aElement0(sdtasdt0(sdtasdt0(sz10,sz10),sz10)) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f296,plain,
( sQ24_spl
| ~ aElement0(sdtasdt0(sdtasdt0(sz10,sz10),sz10)) ),
inference(component_clause,[status(thm)],[f294]) ).
fof(f297,definition,
( sQ25_spl
<=> sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),sz10) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f299,plain,
( sQ25_spl
| sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),sz10) != sz00 ),
inference(component_clause,[status(thm)],[f297]) ).
fof(f300,plain,
( ~ sQ3_spl
| sQ23_spl
| ~ sQ25_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f287,f294,f297,f282,f157]) ).
fof(f301,definition,
( sQ26_spl
<=> sdtasdt0(sz10,sdtasdt0(sdtasdt0(sz10,sz10),sz10)) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f303,plain,
( sQ26_spl
| sdtasdt0(sz10,sdtasdt0(sdtasdt0(sz10,sz10),sz10)) != sz00 ),
inference(component_clause,[status(thm)],[f301]) ).
fof(f304,plain,
( ~ sQ2_spl
| sQ23_spl
| ~ sQ26_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f288,f294,f301,f282,f153]) ).
fof(f305,definition,
( sQ27_spl
<=> sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),sdtasdt0(sdtasdt0(sz10,sz10),sz10)) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f308,plain,
( sQ23_spl
| ~ sQ27_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f289,f294,f305,f282]) ).
fof(f309,definition,
! [X0] :
( sQ28_spl
<=> ( X0 = sz00
| sdtasdt0(X0,sdtasdt0(sdtasdt0(sz10,sz10),sz10)) != sz00
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f312,plain,
( sQ23_spl
| ~ sQ24_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f290,f309,f294,f282]) ).
fof(f314,definition,
! [X0] :
( sQ29_spl
<=> ( X0 = sz00
| sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),X0) != sz00
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f317,plain,
( sQ23_spl
| sQ29_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f292,f294,f314,f282]) ).
fof(f319,plain,
( sQ24_spl
| ~ aElement0(sz10)
| ~ aElement0(sdtasdt0(sz10,sz10)) ),
inference(resolution,[status(thm)],[f296,f39]) ).
fof(f321,plain,
( sQ24_spl
| ~ sQ0_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f319,f189,f146,f294]) ).
fof(f322,plain,
( ~ sQ3_spl
| sQ9_spl
| sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sz10)),sz10) != sz00
| ~ aElement0(sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sz10))) ),
inference(resolution,[status(thm)],[f194,f158]) ).
fof(f323,plain,
( ~ sQ2_spl
| sQ9_spl
| sdtasdt0(sz10,sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sz10))) != sz00
| ~ aElement0(sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sz10))) ),
inference(resolution,[status(thm)],[f194,f154]) ).
fof(f324,plain,
( sQ9_spl
| sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sz10)),sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sz10))) != sz00
| ~ aElement0(sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sz10)))
| ~ aElement0(sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sz10))) ),
inference(resolution,[status(thm)],[f194,f67]) ).
fof(f325,plain,
! [X0] :
( sQ9_spl
| X0 = sz00
| sdtasdt0(X0,sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sz10))) != sz00
| ~ aElement0(sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sz10)))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f194,f67]) ).
fof(f327,plain,
! [X0] :
( sQ9_spl
| X0 = sz00
| sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sz10)),X0) != sz00
| ~ aElement0(X0)
| ~ aElement0(sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sz10))) ),
inference(resolution,[status(thm)],[f194,f67]) ).
fof(f329,definition,
( sQ30_spl
<=> aElement0(sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sz10))) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f331,plain,
( sQ30_spl
| ~ aElement0(sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sz10))) ),
inference(component_clause,[status(thm)],[f329]) ).
fof(f332,definition,
( sQ31_spl
<=> sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sz10)),sz10) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f335,plain,
( ~ sQ3_spl
| sQ9_spl
| ~ sQ31_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f322,f329,f332,f192,f157]) ).
fof(f336,definition,
( sQ32_spl
<=> sdtasdt0(sz10,sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sz10))) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f339,plain,
( ~ sQ2_spl
| sQ9_spl
| ~ sQ32_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f323,f329,f336,f192,f153]) ).
fof(f340,definition,
( sQ33_spl
<=> sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sz10)),sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sz10))) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f343,plain,
( sQ9_spl
| ~ sQ33_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f324,f329,f340,f192]) ).
fof(f344,definition,
! [X0] :
( sQ34_spl
<=> ( X0 = sz00
| sdtasdt0(X0,sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sz10))) != sz00
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f347,plain,
( sQ9_spl
| ~ sQ30_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f325,f344,f329,f192]) ).
fof(f349,definition,
! [X0] :
( sQ35_spl
<=> ( X0 = sz00
| sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sz10)),X0) != sz00
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f352,plain,
( sQ9_spl
| sQ35_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f327,f329,f349,f192]) ).
fof(f354,plain,
( ~ sQ3_spl
| sQ18_spl
| sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sdtasdt0(sz10,sz10))),sz10) != sz00
| ~ aElement0(sdtasdt0(sz10,sdtasdt0(sz10,sdtasdt0(sz10,sz10)))) ),
inference(resolution,[status(thm)],[f256,f158]) ).
fof(f355,plain,
( ~ sQ2_spl
| sQ18_spl
| sdtasdt0(sz10,sdtasdt0(sz10,sdtasdt0(sz10,sdtasdt0(sz10,sz10)))) != sz00
| ~ aElement0(sdtasdt0(sz10,sdtasdt0(sz10,sdtasdt0(sz10,sz10)))) ),
inference(resolution,[status(thm)],[f256,f154]) ).
fof(f356,plain,
( sQ18_spl
| sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sdtasdt0(sz10,sz10))),sdtasdt0(sz10,sdtasdt0(sz10,sdtasdt0(sz10,sz10)))) != sz00
| ~ aElement0(sdtasdt0(sz10,sdtasdt0(sz10,sdtasdt0(sz10,sz10))))
| ~ aElement0(sdtasdt0(sz10,sdtasdt0(sz10,sdtasdt0(sz10,sz10)))) ),
inference(resolution,[status(thm)],[f256,f67]) ).
fof(f357,plain,
! [X0] :
( sQ18_spl
| X0 = sz00
| sdtasdt0(X0,sdtasdt0(sz10,sdtasdt0(sz10,sdtasdt0(sz10,sz10)))) != sz00
| ~ aElement0(sdtasdt0(sz10,sdtasdt0(sz10,sdtasdt0(sz10,sz10))))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f256,f67]) ).
fof(f359,plain,
! [X0] :
( sQ18_spl
| X0 = sz00
| sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sdtasdt0(sz10,sz10))),X0) != sz00
| ~ aElement0(X0)
| ~ aElement0(sdtasdt0(sz10,sdtasdt0(sz10,sdtasdt0(sz10,sz10)))) ),
inference(resolution,[status(thm)],[f256,f67]) ).
fof(f361,definition,
( sQ36_spl
<=> aElement0(sdtasdt0(sz10,sdtasdt0(sz10,sdtasdt0(sz10,sz10)))) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f363,plain,
( sQ36_spl
| ~ aElement0(sdtasdt0(sz10,sdtasdt0(sz10,sdtasdt0(sz10,sz10)))) ),
inference(component_clause,[status(thm)],[f361]) ).
fof(f364,definition,
( sQ37_spl
<=> sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sdtasdt0(sz10,sz10))),sz10) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f367,plain,
( ~ sQ3_spl
| sQ18_spl
| ~ sQ37_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f354,f361,f364,f254,f157]) ).
fof(f368,definition,
( sQ38_spl
<=> sdtasdt0(sz10,sdtasdt0(sz10,sdtasdt0(sz10,sdtasdt0(sz10,sz10)))) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f371,plain,
( ~ sQ2_spl
| sQ18_spl
| ~ sQ38_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f355,f361,f368,f254,f153]) ).
fof(f372,definition,
( sQ39_spl
<=> sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sdtasdt0(sz10,sz10))),sdtasdt0(sz10,sdtasdt0(sz10,sdtasdt0(sz10,sz10)))) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f375,plain,
( sQ18_spl
| ~ sQ39_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f356,f361,f372,f254]) ).
fof(f376,definition,
! [X0] :
( sQ40_spl
<=> ( X0 = sz00
| sdtasdt0(X0,sdtasdt0(sz10,sdtasdt0(sz10,sdtasdt0(sz10,sz10)))) != sz00
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f379,plain,
( sQ18_spl
| ~ sQ36_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f357,f376,f361,f254]) ).
fof(f381,definition,
! [X0] :
( sQ41_spl
<=> ( X0 = sz00
| sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sdtasdt0(sz10,sz10))),X0) != sz00
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f384,plain,
( sQ18_spl
| sQ41_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f359,f361,f381,f254]) ).
fof(f386,plain,
( ~ sQ3_spl
| sQ22_spl
| sdtasdt0(sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),sz10),sz10) != sz00
| ~ aElement0(sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),sz10)) ),
inference(resolution,[status(thm)],[f280,f158]) ).
fof(f387,plain,
( ~ sQ2_spl
| sQ22_spl
| sdtasdt0(sz10,sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),sz10)) != sz00
| ~ aElement0(sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),sz10)) ),
inference(resolution,[status(thm)],[f280,f154]) ).
fof(f388,plain,
( sQ22_spl
| sdtasdt0(sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),sz10),sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),sz10)) != sz00
| ~ aElement0(sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),sz10))
| ~ aElement0(sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),sz10)) ),
inference(resolution,[status(thm)],[f280,f67]) ).
fof(f389,plain,
! [X0] :
( sQ22_spl
| X0 = sz00
| sdtasdt0(X0,sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),sz10)) != sz00
| ~ aElement0(sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),sz10))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f280,f67]) ).
fof(f391,plain,
! [X0] :
( sQ22_spl
| X0 = sz00
| sdtasdt0(sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),sz10),X0) != sz00
| ~ aElement0(X0)
| ~ aElement0(sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),sz10)) ),
inference(resolution,[status(thm)],[f280,f67]) ).
fof(f393,definition,
( sQ42_spl
<=> aElement0(sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),sz10)) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f395,plain,
( sQ42_spl
| ~ aElement0(sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),sz10)) ),
inference(component_clause,[status(thm)],[f393]) ).
fof(f396,definition,
( sQ43_spl
<=> sdtasdt0(sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),sz10),sz10) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f399,plain,
( ~ sQ3_spl
| sQ22_spl
| ~ sQ43_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f386,f393,f396,f278,f157]) ).
fof(f400,definition,
( sQ44_spl
<=> sdtasdt0(sz10,sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),sz10)) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f403,plain,
( ~ sQ2_spl
| sQ22_spl
| ~ sQ44_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f387,f393,f400,f278,f153]) ).
fof(f404,definition,
( sQ45_spl
<=> sdtasdt0(sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),sz10),sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),sz10)) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f407,plain,
( sQ22_spl
| ~ sQ45_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f388,f393,f404,f278]) ).
fof(f408,definition,
! [X0] :
( sQ46_spl
<=> ( X0 = sz00
| sdtasdt0(X0,sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),sz10)) != sz00
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f411,plain,
( sQ22_spl
| ~ sQ42_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f389,f408,f393,f278]) ).
fof(f413,definition,
! [X0] :
( sQ47_spl
<=> ( X0 = sz00
| sdtasdt0(sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),sz10),X0) != sz00
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f416,plain,
( sQ22_spl
| sQ47_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f391,f393,f413,f278]) ).
fof(f418,plain,
( ~ sQ3_spl
| sQ25_spl
| sdtasdt0(sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),sz10),sz10) != sz00
| ~ aElement0(sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),sz10)) ),
inference(resolution,[status(thm)],[f299,f158]) ).
fof(f419,plain,
( ~ sQ2_spl
| sQ25_spl
| sdtasdt0(sz10,sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),sz10)) != sz00
| ~ aElement0(sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),sz10)) ),
inference(resolution,[status(thm)],[f299,f154]) ).
fof(f420,plain,
( sQ25_spl
| sdtasdt0(sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),sz10),sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),sz10)) != sz00
| ~ aElement0(sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),sz10))
| ~ aElement0(sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),sz10)) ),
inference(resolution,[status(thm)],[f299,f67]) ).
fof(f421,plain,
! [X0] :
( sQ25_spl
| X0 = sz00
| sdtasdt0(X0,sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),sz10)) != sz00
| ~ aElement0(sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),sz10))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f299,f67]) ).
fof(f423,plain,
! [X0] :
( sQ25_spl
| X0 = sz00
| sdtasdt0(sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),sz10),X0) != sz00
| ~ aElement0(X0)
| ~ aElement0(sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),sz10)) ),
inference(resolution,[status(thm)],[f299,f67]) ).
fof(f425,definition,
( sQ48_spl
<=> aElement0(sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),sz10)) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f427,plain,
( sQ48_spl
| ~ aElement0(sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),sz10)) ),
inference(component_clause,[status(thm)],[f425]) ).
fof(f428,definition,
( sQ49_spl
<=> sdtasdt0(sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),sz10),sz10) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f431,plain,
( ~ sQ3_spl
| sQ25_spl
| ~ sQ49_spl
| ~ sQ48_spl ),
inference(split_clause,[status(thm)],[f418,f425,f428,f297,f157]) ).
fof(f432,definition,
( sQ50_spl
<=> sdtasdt0(sz10,sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),sz10)) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f435,plain,
( ~ sQ2_spl
| sQ25_spl
| ~ sQ50_spl
| ~ sQ48_spl ),
inference(split_clause,[status(thm)],[f419,f425,f432,f297,f153]) ).
fof(f436,definition,
( sQ51_spl
<=> sdtasdt0(sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),sz10),sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),sz10)) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f439,plain,
( sQ25_spl
| ~ sQ51_spl
| ~ sQ48_spl ),
inference(split_clause,[status(thm)],[f420,f425,f436,f297]) ).
fof(f440,definition,
! [X0] :
( sQ52_spl
<=> ( X0 = sz00
| sdtasdt0(X0,sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),sz10)) != sz00
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f443,plain,
( sQ25_spl
| ~ sQ48_spl
| sQ52_spl ),
inference(split_clause,[status(thm)],[f421,f440,f425,f297]) ).
fof(f445,definition,
! [X0] :
( sQ53_spl
<=> ( X0 = sz00
| sdtasdt0(sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),sz10),X0) != sz00
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f448,plain,
( sQ25_spl
| sQ53_spl
| ~ sQ48_spl ),
inference(split_clause,[status(thm)],[f423,f425,f445,f297]) ).
fof(f450,plain,
( ~ sQ3_spl
| sQ26_spl
| sdtasdt0(sdtasdt0(sz10,sdtasdt0(sdtasdt0(sz10,sz10),sz10)),sz10) != sz00
| ~ aElement0(sdtasdt0(sz10,sdtasdt0(sdtasdt0(sz10,sz10),sz10))) ),
inference(resolution,[status(thm)],[f303,f158]) ).
fof(f451,plain,
( ~ sQ2_spl
| sQ26_spl
| sdtasdt0(sz10,sdtasdt0(sz10,sdtasdt0(sdtasdt0(sz10,sz10),sz10))) != sz00
| ~ aElement0(sdtasdt0(sz10,sdtasdt0(sdtasdt0(sz10,sz10),sz10))) ),
inference(resolution,[status(thm)],[f303,f154]) ).
fof(f452,plain,
( sQ26_spl
| sdtasdt0(sdtasdt0(sz10,sdtasdt0(sdtasdt0(sz10,sz10),sz10)),sdtasdt0(sz10,sdtasdt0(sdtasdt0(sz10,sz10),sz10))) != sz00
| ~ aElement0(sdtasdt0(sz10,sdtasdt0(sdtasdt0(sz10,sz10),sz10)))
| ~ aElement0(sdtasdt0(sz10,sdtasdt0(sdtasdt0(sz10,sz10),sz10))) ),
inference(resolution,[status(thm)],[f303,f67]) ).
fof(f453,plain,
! [X0] :
( sQ26_spl
| X0 = sz00
| sdtasdt0(X0,sdtasdt0(sz10,sdtasdt0(sdtasdt0(sz10,sz10),sz10))) != sz00
| ~ aElement0(sdtasdt0(sz10,sdtasdt0(sdtasdt0(sz10,sz10),sz10)))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f303,f67]) ).
fof(f455,plain,
! [X0] :
( sQ26_spl
| X0 = sz00
| sdtasdt0(sdtasdt0(sz10,sdtasdt0(sdtasdt0(sz10,sz10),sz10)),X0) != sz00
| ~ aElement0(X0)
| ~ aElement0(sdtasdt0(sz10,sdtasdt0(sdtasdt0(sz10,sz10),sz10))) ),
inference(resolution,[status(thm)],[f303,f67]) ).
fof(f457,definition,
( sQ54_spl
<=> aElement0(sdtasdt0(sz10,sdtasdt0(sdtasdt0(sz10,sz10),sz10))) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f459,plain,
( sQ54_spl
| ~ aElement0(sdtasdt0(sz10,sdtasdt0(sdtasdt0(sz10,sz10),sz10))) ),
inference(component_clause,[status(thm)],[f457]) ).
fof(f460,definition,
( sQ55_spl
<=> sdtasdt0(sdtasdt0(sz10,sdtasdt0(sdtasdt0(sz10,sz10),sz10)),sz10) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f463,plain,
( ~ sQ3_spl
| sQ26_spl
| ~ sQ55_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f450,f457,f460,f301,f157]) ).
fof(f464,definition,
( sQ56_spl
<=> sdtasdt0(sz10,sdtasdt0(sz10,sdtasdt0(sdtasdt0(sz10,sz10),sz10))) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f467,plain,
( ~ sQ2_spl
| sQ26_spl
| ~ sQ56_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f451,f457,f464,f301,f153]) ).
fof(f468,definition,
( sQ57_spl
<=> sdtasdt0(sdtasdt0(sz10,sdtasdt0(sdtasdt0(sz10,sz10),sz10)),sdtasdt0(sz10,sdtasdt0(sdtasdt0(sz10,sz10),sz10))) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f471,plain,
( sQ26_spl
| ~ sQ57_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f452,f457,f468,f301]) ).
fof(f472,definition,
! [X0] :
( sQ58_spl
<=> ( X0 = sz00
| sdtasdt0(X0,sdtasdt0(sz10,sdtasdt0(sdtasdt0(sz10,sz10),sz10))) != sz00
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f475,plain,
( sQ26_spl
| ~ sQ54_spl
| sQ58_spl ),
inference(split_clause,[status(thm)],[f453,f472,f457,f301]) ).
fof(f477,definition,
! [X0] :
( sQ59_spl
<=> ( X0 = sz00
| sdtasdt0(sdtasdt0(sz10,sdtasdt0(sdtasdt0(sz10,sz10),sz10)),X0) != sz00
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f480,plain,
( sQ26_spl
| sQ59_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f455,f457,f477,f301]) ).
fof(f482,plain,
( sQ30_spl
| ~ aElement0(sdtasdt0(sz10,sz10))
| ~ aElement0(sdtasdt0(sz10,sz10)) ),
inference(resolution,[status(thm)],[f331,f39]) ).
fof(f484,plain,
( sQ30_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f482,f189,f329]) ).
fof(f485,plain,
( sQ36_spl
| ~ aElement0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)))
| ~ aElement0(sz10) ),
inference(resolution,[status(thm)],[f363,f39]) ).
fof(f487,plain,
( sQ36_spl
| ~ sQ17_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f485,f146,f251,f361]) ).
fof(f488,plain,
( sQ42_spl
| ~ aElement0(sz10)
| ~ aElement0(sdtasdt0(sz10,sdtasdt0(sz10,sz10))) ),
inference(resolution,[status(thm)],[f395,f39]) ).
fof(f490,plain,
( sQ42_spl
| ~ sQ0_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f488,f251,f146,f393]) ).
fof(f491,plain,
( sQ48_spl
| ~ aElement0(sz10)
| ~ aElement0(sdtasdt0(sdtasdt0(sz10,sz10),sz10)) ),
inference(resolution,[status(thm)],[f427,f39]) ).
fof(f493,plain,
( sQ48_spl
| ~ sQ0_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f491,f294,f146,f425]) ).
fof(f496,plain,
( sQ54_spl
| ~ aElement0(sdtasdt0(sdtasdt0(sz10,sz10),sz10))
| ~ aElement0(sz10) ),
inference(resolution,[status(thm)],[f459,f39]) ).
fof(f498,plain,
( sQ54_spl
| ~ sQ24_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f496,f146,f294,f457]) ).
fof(f501,plain,
( sQ25_spl
| ~ sQ10_spl
| sdtasdt0(sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),sz10),sdtasdt0(sz10,sz10)) != sz00
| ~ aElement0(sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),sz10)) ),
inference(resolution,[status(thm)],[f197,f299]) ).
fof(f502,plain,
( sQ22_spl
| ~ sQ10_spl
| sdtasdt0(sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),sz10),sdtasdt0(sz10,sz10)) != sz00
| ~ aElement0(sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),sz10)) ),
inference(resolution,[status(thm)],[f197,f280]) ).
fof(f503,plain,
( sQ9_spl
| ~ sQ10_spl
| sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sz10)),sdtasdt0(sz10,sz10)) != sz00
| ~ aElement0(sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sz10))) ),
inference(resolution,[status(thm)],[f197,f194]) ).
fof(f504,plain,
( sQ23_spl
| ~ sQ10_spl
| sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),sdtasdt0(sz10,sz10)) != sz00
| ~ aElement0(sdtasdt0(sdtasdt0(sz10,sz10),sz10)) ),
inference(resolution,[status(thm)],[f197,f284]) ).
fof(f505,plain,
( sQ26_spl
| ~ sQ10_spl
| sdtasdt0(sdtasdt0(sz10,sdtasdt0(sdtasdt0(sz10,sz10),sz10)),sdtasdt0(sz10,sz10)) != sz00
| ~ aElement0(sdtasdt0(sz10,sdtasdt0(sdtasdt0(sz10,sz10),sz10))) ),
inference(resolution,[status(thm)],[f197,f303]) ).
fof(f506,plain,
( sQ18_spl
| ~ sQ10_spl
| sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sdtasdt0(sz10,sz10))),sdtasdt0(sz10,sz10)) != sz00
| ~ aElement0(sdtasdt0(sz10,sdtasdt0(sz10,sdtasdt0(sz10,sz10)))) ),
inference(resolution,[status(thm)],[f197,f256]) ).
fof(f507,plain,
( sQ16_spl
| ~ sQ10_spl
| sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),sdtasdt0(sz10,sz10)) != sz00
| ~ aElement0(sdtasdt0(sz10,sdtasdt0(sz10,sz10))) ),
inference(resolution,[status(thm)],[f197,f242]) ).
fof(f509,plain,
( ~ sQ10_spl
| sdtasdt0(sz10,sdtasdt0(sz10,sz10)) != sz00
| ~ aElement0(sz10) ),
inference(resolution,[status(thm)],[f197,f68]) ).
fof(f510,definition,
( sQ60_spl
<=> sdtasdt0(sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),sz10),sdtasdt0(sz10,sz10)) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f513,plain,
( sQ25_spl
| ~ sQ10_spl
| ~ sQ60_spl
| ~ sQ48_spl ),
inference(split_clause,[status(thm)],[f501,f425,f510,f196,f297]) ).
fof(f514,definition,
( sQ61_spl
<=> sdtasdt0(sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),sz10),sdtasdt0(sz10,sz10)) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f517,plain,
( sQ22_spl
| ~ sQ10_spl
| ~ sQ61_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f502,f393,f514,f196,f278]) ).
fof(f518,definition,
( sQ62_spl
<=> sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sz10)),sdtasdt0(sz10,sz10)) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f521,plain,
( sQ9_spl
| ~ sQ10_spl
| ~ sQ62_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f503,f329,f518,f196,f192]) ).
fof(f522,definition,
( sQ63_spl
<=> sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),sdtasdt0(sz10,sz10)) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f525,plain,
( sQ23_spl
| ~ sQ10_spl
| ~ sQ63_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f504,f294,f522,f196,f282]) ).
fof(f526,definition,
( sQ64_spl
<=> sdtasdt0(sdtasdt0(sz10,sdtasdt0(sdtasdt0(sz10,sz10),sz10)),sdtasdt0(sz10,sz10)) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f529,plain,
( sQ26_spl
| ~ sQ10_spl
| ~ sQ64_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f505,f457,f526,f196,f301]) ).
fof(f530,definition,
( sQ65_spl
<=> sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sdtasdt0(sz10,sz10))),sdtasdt0(sz10,sz10)) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f533,plain,
( sQ18_spl
| ~ sQ10_spl
| ~ sQ65_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f506,f361,f530,f196,f254]) ).
fof(f534,definition,
( sQ66_spl
<=> sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),sdtasdt0(sz10,sz10)) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f537,plain,
( sQ16_spl
| ~ sQ10_spl
| ~ sQ66_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f507,f251,f534,f196,f240]) ).
fof(f539,plain,
( ~ sQ10_spl
| ~ sQ16_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f509,f146,f240,f196]) ).
fof(f540,plain,
( sQ25_spl
| ~ sQ11_spl
| sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),sz10)) != sz00
| ~ aElement0(sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),sz10)) ),
inference(resolution,[status(thm)],[f202,f299]) ).
fof(f541,plain,
( sQ22_spl
| ~ sQ11_spl
| sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),sz10)) != sz00
| ~ aElement0(sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),sz10)) ),
inference(resolution,[status(thm)],[f202,f280]) ).
fof(f542,plain,
( sQ9_spl
| ~ sQ11_spl
| sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sz10))) != sz00
| ~ aElement0(sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sz10))) ),
inference(resolution,[status(thm)],[f202,f194]) ).
fof(f543,plain,
( sQ23_spl
| ~ sQ11_spl
| sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sdtasdt0(sz10,sz10),sz10)) != sz00
| ~ aElement0(sdtasdt0(sdtasdt0(sz10,sz10),sz10)) ),
inference(resolution,[status(thm)],[f202,f284]) ).
fof(f544,plain,
( sQ26_spl
| ~ sQ11_spl
| sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sdtasdt0(sdtasdt0(sz10,sz10),sz10))) != sz00
| ~ aElement0(sdtasdt0(sz10,sdtasdt0(sdtasdt0(sz10,sz10),sz10))) ),
inference(resolution,[status(thm)],[f202,f303]) ).
fof(f545,plain,
( sQ18_spl
| ~ sQ11_spl
| sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sdtasdt0(sz10,sdtasdt0(sz10,sz10)))) != sz00
| ~ aElement0(sdtasdt0(sz10,sdtasdt0(sz10,sdtasdt0(sz10,sz10)))) ),
inference(resolution,[status(thm)],[f202,f256]) ).
fof(f546,plain,
( sQ16_spl
| ~ sQ11_spl
| sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sdtasdt0(sz10,sz10))) != sz00
| ~ aElement0(sdtasdt0(sz10,sdtasdt0(sz10,sz10))) ),
inference(resolution,[status(thm)],[f202,f242]) ).
fof(f548,plain,
( ~ sQ11_spl
| sdtasdt0(sdtasdt0(sz10,sz10),sz10) != sz00
| ~ aElement0(sz10) ),
inference(resolution,[status(thm)],[f202,f68]) ).
fof(f549,definition,
( sQ67_spl
<=> sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sdtasdt0(sdtasdt0(sz10,sz10),sz10),sz10)) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f552,plain,
( sQ25_spl
| ~ sQ11_spl
| ~ sQ67_spl
| ~ sQ48_spl ),
inference(split_clause,[status(thm)],[f540,f425,f549,f201,f297]) ).
fof(f553,definition,
( sQ68_spl
<=> sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sdtasdt0(sz10,sdtasdt0(sz10,sz10)),sz10)) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f556,plain,
( sQ22_spl
| ~ sQ11_spl
| ~ sQ68_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f541,f393,f553,f201,f278]) ).
fof(f557,definition,
( sQ69_spl
<=> sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sz10))) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f560,plain,
( sQ9_spl
| ~ sQ11_spl
| ~ sQ69_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f542,f329,f557,f201,f192]) ).
fof(f561,definition,
( sQ70_spl
<=> sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sdtasdt0(sz10,sz10),sz10)) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f564,plain,
( sQ23_spl
| ~ sQ11_spl
| ~ sQ70_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f543,f294,f561,f201,f282]) ).
fof(f565,definition,
( sQ71_spl
<=> sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sdtasdt0(sdtasdt0(sz10,sz10),sz10))) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f568,plain,
( sQ26_spl
| ~ sQ11_spl
| ~ sQ71_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f544,f457,f565,f201,f301]) ).
fof(f569,definition,
( sQ72_spl
<=> sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sdtasdt0(sz10,sdtasdt0(sz10,sz10)))) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f572,plain,
( sQ18_spl
| ~ sQ11_spl
| ~ sQ72_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f545,f361,f569,f201,f254]) ).
fof(f573,definition,
( sQ73_spl
<=> sdtasdt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sdtasdt0(sz10,sz10))) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f576,plain,
( sQ16_spl
| ~ sQ11_spl
| ~ sQ73_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f546,f251,f573,f201,f240]) ).
fof(f578,plain,
( ~ sQ11_spl
| ~ sQ23_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f548,f146,f282,f201]) ).
fof(f747,plain,
( ~ aElementOf0(sdtasdt0(sK10_skl(sdtasasdt0(xI,xJ)),sK8_skl(sdtasasdt0(xI,xJ))),sdtasasdt0(xI,xJ))
| ~ aElementOf0(sdtpldt0(sK8_skl(sdtasasdt0(xI,xJ)),sK9_skl(sdtasasdt0(xI,xJ))),sdtasasdt0(xI,xJ))
| ~ aSet0(sdtasasdt0(xI,xJ)) ),
inference(resolution,[status(thm)],[f113,f118]) ).
fof(f748,definition,
( sQ106_spl
<=> aSet0(sdtasasdt0(xI,xJ)) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f750,plain,
( sQ106_spl
| ~ aSet0(sdtasasdt0(xI,xJ)) ),
inference(component_clause,[status(thm)],[f748]) ).
fof(f751,definition,
( sQ107_spl
<=> aElementOf0(sdtpldt0(sK8_skl(sdtasasdt0(xI,xJ)),sK9_skl(sdtasasdt0(xI,xJ))),sdtasasdt0(xI,xJ)) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f753,plain,
( sQ107_spl
| ~ aElementOf0(sdtpldt0(sK8_skl(sdtasasdt0(xI,xJ)),sK9_skl(sdtasasdt0(xI,xJ))),sdtasasdt0(xI,xJ)) ),
inference(component_clause,[status(thm)],[f751]) ).
fof(f754,definition,
( sQ108_spl
<=> aElementOf0(sdtasdt0(sK10_skl(sdtasasdt0(xI,xJ)),sK8_skl(sdtasasdt0(xI,xJ))),sdtasasdt0(xI,xJ)) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f756,plain,
( sQ108_spl
| ~ aElementOf0(sdtasdt0(sK10_skl(sdtasasdt0(xI,xJ)),sK8_skl(sdtasasdt0(xI,xJ))),sdtasasdt0(xI,xJ)) ),
inference(component_clause,[status(thm)],[f754]) ).
fof(f757,plain,
( ~ sQ108_spl
| ~ sQ107_spl
| ~ sQ106_spl ),
inference(split_clause,[status(thm)],[f747,f748,f751,f754]) ).
fof(f759,plain,
( sQ108_spl
| ~ aElementOf0(sdtasdt0(sK10_skl(sdtasasdt0(xI,xJ)),sK8_skl(sdtasasdt0(xI,xJ))),xJ)
| ~ aElementOf0(sdtasdt0(sK10_skl(sdtasasdt0(xI,xJ)),sK8_skl(sdtasasdt0(xI,xJ))),xI)
| ~ aSet0(xJ)
| ~ aSet0(xI) ),
inference(resolution,[status(thm)],[f756,f136]) ).
fof(f765,definition,
( sQ109_spl
<=> aIdeal0(sdtasasdt0(xI,xJ)) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f766,plain,
( ~ sQ109_spl
| aIdeal0(sdtasasdt0(xI,xJ)) ),
inference(component_clause,[status(thm)],[f765]) ).
fof(f768,definition,
( sQ110_spl
<=> aElementOf0(sK8_skl(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,xJ)) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f769,plain,
( ~ sQ110_spl
| aElementOf0(sK8_skl(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,xJ)) ),
inference(component_clause,[status(thm)],[f768]) ).
fof(f770,plain,
( sQ110_spl
| ~ aElementOf0(sK8_skl(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,xJ)) ),
inference(component_clause,[status(thm)],[f768]) ).
fof(f771,definition,
( sQ111_spl
<=> aElement0(sK10_skl(sdtasasdt0(xI,xJ))) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f773,plain,
( sQ111_spl
| ~ aElement0(sK10_skl(sdtasasdt0(xI,xJ))) ),
inference(component_clause,[status(thm)],[f771]) ).
fof(f775,definition,
( sQ112_spl
<=> aSet0(xI) ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f777,plain,
( sQ112_spl
| ~ aSet0(xI) ),
inference(component_clause,[status(thm)],[f775]) ).
fof(f778,definition,
( sQ113_spl
<=> aSet0(xJ) ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f780,plain,
( sQ113_spl
| ~ aSet0(xJ) ),
inference(component_clause,[status(thm)],[f778]) ).
fof(f781,definition,
( sQ114_spl
<=> aElementOf0(sdtasdt0(sK10_skl(sdtasasdt0(xI,xJ)),sK8_skl(sdtasasdt0(xI,xJ))),xI) ),
introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition]) ).
fof(f783,plain,
( sQ114_spl
| ~ aElementOf0(sdtasdt0(sK10_skl(sdtasasdt0(xI,xJ)),sK8_skl(sdtasasdt0(xI,xJ))),xI) ),
inference(component_clause,[status(thm)],[f781]) ).
fof(f784,definition,
( sQ115_spl
<=> aElementOf0(sdtasdt0(sK10_skl(sdtasasdt0(xI,xJ)),sK8_skl(sdtasasdt0(xI,xJ))),xJ) ),
introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition]) ).
fof(f786,plain,
( sQ115_spl
| ~ aElementOf0(sdtasdt0(sK10_skl(sdtasasdt0(xI,xJ)),sK8_skl(sdtasasdt0(xI,xJ))),xJ) ),
inference(component_clause,[status(thm)],[f784]) ).
fof(f787,plain,
( sQ108_spl
| ~ sQ115_spl
| ~ sQ114_spl
| ~ sQ113_spl
| ~ sQ112_spl ),
inference(split_clause,[status(thm)],[f759,f775,f778,f781,f784,f754]) ).
fof(f796,plain,
( sQ113_spl
| ~ aIdeal0(xJ) ),
inference(resolution,[status(thm)],[f780,f106]) ).
fof(f797,plain,
( sQ113_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f796,f117]) ).
fof(f798,plain,
sQ113_spl,
inference(contradiction_clause,[status(thm)],[f797]) ).
fof(f799,plain,
( sQ112_spl
| ~ aIdeal0(xI) ),
inference(resolution,[status(thm)],[f777,f106]) ).
fof(f800,plain,
( sQ112_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f799,f116]) ).
fof(f801,plain,
sQ112_spl,
inference(contradiction_clause,[status(thm)],[f800]) ).
fof(f802,plain,
( sQ106_spl
| ~ aSet0(xJ)
| ~ aSet0(xI) ),
inference(resolution,[status(thm)],[f750,f133]) ).
fof(f804,plain,
( sQ106_spl
| ~ sQ113_spl
| ~ sQ112_spl ),
inference(split_clause,[status(thm)],[f802,f775,f778,f748]) ).
fof(f805,plain,
( sQ111_spl
| ~ aElementOf0(sdtpldt0(sK8_skl(sdtasasdt0(xI,xJ)),sK9_skl(sdtasasdt0(xI,xJ))),sdtasasdt0(xI,xJ))
| ~ aSet0(sdtasasdt0(xI,xJ))
| aIdeal0(sdtasasdt0(xI,xJ)) ),
inference(resolution,[status(thm)],[f773,f112]) ).
fof(f807,plain,
( sQ111_spl
| ~ sQ107_spl
| ~ sQ106_spl
| sQ109_spl ),
inference(split_clause,[status(thm)],[f805,f765,f748,f751,f771]) ).
fof(f808,plain,
( sQ110_spl
| ~ aSet0(sdtasasdt0(xI,xJ))
| aIdeal0(sdtasasdt0(xI,xJ)) ),
inference(resolution,[status(thm)],[f770,f109]) ).
fof(f815,plain,
( sQ110_spl
| ~ sQ106_spl
| sQ109_spl ),
inference(split_clause,[status(thm)],[f808,f765,f748,f768]) ).
fof(f816,definition,
( sQ118_spl
<=> aElementOf0(sK8_skl(sdtasasdt0(xI,xJ)),xI) ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f817,plain,
( ~ sQ118_spl
| aElementOf0(sK8_skl(sdtasasdt0(xI,xJ)),xI) ),
inference(component_clause,[status(thm)],[f816]) ).
fof(f818,plain,
( sQ118_spl
| ~ aElementOf0(sK8_skl(sdtasasdt0(xI,xJ)),xI) ),
inference(component_clause,[status(thm)],[f816]) ).
fof(f819,definition,
( sQ119_spl
<=> aElementOf0(sK8_skl(sdtasasdt0(xI,xJ)),xJ) ),
introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition]) ).
fof(f821,plain,
( sQ119_spl
| ~ aElementOf0(sK8_skl(sdtasasdt0(xI,xJ)),xJ) ),
inference(component_clause,[status(thm)],[f819]) ).
fof(f843,plain,
( sQ107_spl
| ~ aElementOf0(sdtpldt0(sK8_skl(sdtasasdt0(xI,xJ)),sK9_skl(sdtasasdt0(xI,xJ))),xJ)
| ~ aElementOf0(sdtpldt0(sK8_skl(sdtasasdt0(xI,xJ)),sK9_skl(sdtasasdt0(xI,xJ))),xI)
| ~ aSet0(xJ)
| ~ aSet0(xI) ),
inference(resolution,[status(thm)],[f753,f136]) ).
fof(f849,definition,
( sQ122_spl
<=> aElementOf0(sK9_skl(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,xJ)) ),
introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition]) ).
fof(f850,plain,
( ~ sQ122_spl
| aElementOf0(sK9_skl(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,xJ)) ),
inference(component_clause,[status(thm)],[f849]) ).
fof(f851,plain,
( sQ122_spl
| ~ aElementOf0(sK9_skl(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,xJ)) ),
inference(component_clause,[status(thm)],[f849]) ).
fof(f853,definition,
( sQ123_spl
<=> aElementOf0(sdtpldt0(sK8_skl(sdtasasdt0(xI,xJ)),sK9_skl(sdtasasdt0(xI,xJ))),xI) ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f855,plain,
( sQ123_spl
| ~ aElementOf0(sdtpldt0(sK8_skl(sdtasasdt0(xI,xJ)),sK9_skl(sdtasasdt0(xI,xJ))),xI) ),
inference(component_clause,[status(thm)],[f853]) ).
fof(f856,definition,
( sQ124_spl
<=> aElementOf0(sdtpldt0(sK8_skl(sdtasasdt0(xI,xJ)),sK9_skl(sdtasasdt0(xI,xJ))),xJ) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f858,plain,
( sQ124_spl
| ~ aElementOf0(sdtpldt0(sK8_skl(sdtasasdt0(xI,xJ)),sK9_skl(sdtasasdt0(xI,xJ))),xJ) ),
inference(component_clause,[status(thm)],[f856]) ).
fof(f859,plain,
( sQ107_spl
| ~ sQ124_spl
| ~ sQ123_spl
| ~ sQ113_spl
| ~ sQ112_spl ),
inference(split_clause,[status(thm)],[f843,f775,f778,f853,f856,f751]) ).
fof(f1683,plain,
( sQ122_spl
| ~ aElementOf0(sdtasdt0(sK10_skl(sdtasasdt0(xI,xJ)),sK8_skl(sdtasasdt0(xI,xJ))),sdtasasdt0(xI,xJ))
| ~ aSet0(sdtasasdt0(xI,xJ))
| aIdeal0(sdtasasdt0(xI,xJ)) ),
inference(resolution,[status(thm)],[f851,f111]) ).
fof(f1684,plain,
( sQ122_spl
| aElement0(sK10_skl(sdtasasdt0(xI,xJ)))
| ~ aSet0(sdtasasdt0(xI,xJ))
| aIdeal0(sdtasasdt0(xI,xJ)) ),
inference(resolution,[status(thm)],[f851,f110]) ).
fof(f1691,plain,
( sQ122_spl
| ~ sQ108_spl
| ~ sQ106_spl
| sQ109_spl ),
inference(split_clause,[status(thm)],[f1683,f765,f748,f754,f849]) ).
fof(f1692,plain,
( sQ122_spl
| sQ111_spl
| ~ sQ106_spl
| sQ109_spl ),
inference(split_clause,[status(thm)],[f1684,f765,f748,f771,f849]) ).
fof(f1693,definition,
( sQ312_spl
<=> aElementOf0(sK9_skl(sdtasasdt0(xI,xJ)),xI) ),
introduced(definition,[new_symbols(definition,[sQ312_spl])],[split_symbol_definition]) ).
fof(f1695,plain,
( sQ312_spl
| ~ aElementOf0(sK9_skl(sdtasasdt0(xI,xJ)),xI) ),
inference(component_clause,[status(thm)],[f1693]) ).
fof(f1696,definition,
( sQ313_spl
<=> aElementOf0(sK9_skl(sdtasasdt0(xI,xJ)),xJ) ),
introduced(definition,[new_symbols(definition,[sQ313_spl])],[split_symbol_definition]) ).
fof(f1698,plain,
( sQ313_spl
| ~ aElementOf0(sK9_skl(sdtasasdt0(xI,xJ)),xJ) ),
inference(component_clause,[status(thm)],[f1696]) ).
fof(f1708,plain,
( ~ sQ109_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f766,f118]) ).
fof(f1709,plain,
~ sQ109_spl,
inference(contradiction_clause,[status(thm)],[f1708]) ).
fof(f1714,plain,
! [X0] :
( sQ312_spl
| ~ aElementOf0(sK9_skl(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,X0))
| ~ aSet0(X0)
| ~ aSet0(xI) ),
inference(resolution,[status(thm)],[f1695,f134]) ).
fof(f1719,definition,
! [X0] :
( sQ317_spl
<=> ( ~ aElementOf0(sK9_skl(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,X0))
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ317_spl])],[split_symbol_definition]) ).
fof(f1720,plain,
! [X0] :
( ~ sQ317_spl
| ~ aElementOf0(sK9_skl(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,X0))
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f1719]) ).
fof(f1722,plain,
( sQ312_spl
| sQ317_spl
| ~ sQ112_spl ),
inference(split_clause,[status(thm)],[f1714,f775,f1719,f1693]) ).
fof(f1726,plain,
! [X0] :
( sQ313_spl
| ~ aElementOf0(sK9_skl(sdtasasdt0(xI,xJ)),sdtasasdt0(X0,xJ))
| ~ aSet0(xJ)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f1698,f135]) ).
fof(f1728,definition,
! [X0] :
( sQ318_spl
<=> ( ~ aElementOf0(sK9_skl(sdtasasdt0(xI,xJ)),sdtasasdt0(X0,xJ))
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ318_spl])],[split_symbol_definition]) ).
fof(f1729,plain,
! [X0] :
( ~ sQ318_spl
| ~ aElementOf0(sK9_skl(sdtasasdt0(xI,xJ)),sdtasasdt0(X0,xJ))
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f1728]) ).
fof(f1731,plain,
( sQ313_spl
| ~ sQ113_spl
| sQ318_spl ),
inference(split_clause,[status(thm)],[f1726,f1728,f778,f1696]) ).
fof(f1737,definition,
! [X0,X1] :
( sQ320_spl
<=> ~ aElementOf0(X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ320_spl])],[split_symbol_definition]) ).
fof(f1738,plain,
! [X0,X1] :
( ~ sQ320_spl
| ~ aElementOf0(X0,X1) ),
inference(component_clause,[status(thm)],[f1737]) ).
fof(f1805,plain,
( sQ12_spl
| ~ aElement0(sz00)
| ~ aElement0(sz00) ),
inference(resolution,[status(thm)],[f214,f39]) ).
fof(f1807,plain,
( sQ12_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1805,f171,f212]) ).
fof(f1838,plain,
( sQ123_spl
| ~ aElementOf0(sK9_skl(sdtasasdt0(xI,xJ)),xI)
| ~ aElementOf0(sK8_skl(sdtasasdt0(xI,xJ)),xI)
| ~ aIdeal0(xI) ),
inference(resolution,[status(thm)],[f855,f107]) ).
fof(f1844,definition,
( sQ331_spl
<=> aIdeal0(xI) ),
introduced(definition,[new_symbols(definition,[sQ331_spl])],[split_symbol_definition]) ).
fof(f1846,plain,
( sQ331_spl
| ~ aIdeal0(xI) ),
inference(component_clause,[status(thm)],[f1844]) ).
fof(f1847,plain,
( sQ123_spl
| ~ sQ312_spl
| ~ sQ118_spl
| ~ sQ331_spl ),
inference(split_clause,[status(thm)],[f1838,f1844,f816,f1693,f853]) ).
fof(f1856,plain,
( sQ331_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1846,f116]) ).
fof(f1857,plain,
sQ331_spl,
inference(contradiction_clause,[status(thm)],[f1856]) ).
fof(f1862,plain,
! [X0] :
( sQ118_spl
| ~ aElementOf0(sK8_skl(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,X0))
| ~ aSet0(X0)
| ~ aSet0(xI) ),
inference(resolution,[status(thm)],[f818,f134]) ).
fof(f1863,definition,
! [X0] :
( sQ334_spl
<=> ( ~ aElementOf0(sK8_skl(sdtasasdt0(xI,xJ)),sdtasasdt0(X0,xI))
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ334_spl])],[split_symbol_definition]) ).
fof(f1864,plain,
! [X0] :
( ~ sQ334_spl
| ~ aElementOf0(sK8_skl(sdtasasdt0(xI,xJ)),sdtasasdt0(X0,xI))
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f1863]) ).
fof(f1867,definition,
! [X0] :
( sQ335_spl
<=> ( ~ aElementOf0(sK8_skl(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,X0))
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ335_spl])],[split_symbol_definition]) ).
fof(f1868,plain,
! [X0] :
( ~ sQ335_spl
| ~ aElementOf0(sK8_skl(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,X0))
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f1867]) ).
fof(f1870,plain,
( sQ118_spl
| sQ335_spl
| ~ sQ112_spl ),
inference(split_clause,[status(thm)],[f1862,f775,f1867,f816]) ).
fof(f1887,plain,
( ~ sQ122_spl
| ~ sQ317_spl
| ~ aSet0(xJ) ),
inference(resolution,[status(thm)],[f1720,f850]) ).
fof(f1896,plain,
( ~ sQ122_spl
| ~ sQ317_spl
| ~ sQ113_spl ),
inference(split_clause,[status(thm)],[f1887,f778,f1719,f849]) ).
fof(f1901,plain,
( ~ sQ318_spl
| ~ aElementOf0(sdtasdt0(sK10_skl(sdtasasdt0(xI,xJ)),sK8_skl(sdtasasdt0(xI,xJ))),sdtasasdt0(xI,xJ))
| ~ aSet0(sdtasasdt0(xI,xJ))
| aIdeal0(sdtasasdt0(xI,xJ))
| ~ aSet0(xI) ),
inference(resolution,[status(thm)],[f1729,f111]) ).
fof(f1902,plain,
( ~ sQ318_spl
| aElement0(sK10_skl(sdtasasdt0(xI,xJ)))
| ~ aSet0(sdtasasdt0(xI,xJ))
| aIdeal0(sdtasasdt0(xI,xJ))
| ~ aSet0(xI) ),
inference(resolution,[status(thm)],[f1729,f110]) ).
fof(f1910,plain,
( ~ sQ318_spl
| ~ sQ108_spl
| ~ sQ106_spl
| sQ109_spl
| ~ sQ112_spl ),
inference(split_clause,[status(thm)],[f1901,f775,f765,f748,f754,f1728]) ).
fof(f1911,plain,
( ~ sQ318_spl
| sQ111_spl
| ~ sQ106_spl
| sQ109_spl
| ~ sQ112_spl ),
inference(split_clause,[status(thm)],[f1902,f775,f765,f748,f771,f1728]) ).
fof(f1960,plain,
! [X0] :
( ~ sQ334_spl
| ~ aElementOf0(sK8_skl(sdtasasdt0(xI,xJ)),xI)
| ~ aElementOf0(sK8_skl(sdtasasdt0(xI,xJ)),X0)
| ~ aSet0(xI)
| ~ aSet0(X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f1864,f136]) ).
fof(f1966,definition,
! [X0] :
( sQ339_spl
<=> ( ~ aElementOf0(sK8_skl(sdtasasdt0(xI,xJ)),X0)
| ~ aSet0(X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ339_spl])],[split_symbol_definition]) ).
fof(f1967,plain,
! [X0] :
( ~ sQ339_spl
| ~ aElementOf0(sK8_skl(sdtasasdt0(xI,xJ)),X0)
| ~ aSet0(X0)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f1966]) ).
fof(f1969,plain,
( ~ sQ334_spl
| ~ sQ118_spl
| ~ sQ112_spl
| sQ339_spl ),
inference(split_clause,[status(thm)],[f1960,f1966,f775,f816,f1863]) ).
fof(f1970,plain,
! [X0] :
( ~ sQ339_spl
| ~ aElementOf0(sK8_skl(sdtasasdt0(xI,xJ)),X0)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1967]) ).
fof(f1980,plain,
( sQ114_spl
| ~ aElement0(sK10_skl(sdtasasdt0(xI,xJ)))
| ~ aElementOf0(sK8_skl(sdtasasdt0(xI,xJ)),xI)
| ~ aIdeal0(xI) ),
inference(resolution,[status(thm)],[f783,f108]) ).
fof(f1986,plain,
( sQ114_spl
| ~ sQ111_spl
| ~ sQ118_spl
| ~ sQ331_spl ),
inference(split_clause,[status(thm)],[f1980,f1844,f816,f771,f781]) ).
fof(f2015,plain,
( ~ sQ110_spl
| ~ sQ335_spl
| ~ aSet0(xJ) ),
inference(resolution,[status(thm)],[f1868,f769]) ).
fof(f2023,plain,
( ~ sQ110_spl
| ~ sQ335_spl
| ~ sQ113_spl ),
inference(split_clause,[status(thm)],[f2015,f778,f1867,f768]) ).
fof(f2040,plain,
( ~ sQ118_spl
| ~ sQ339_spl
| ~ aSet0(xI) ),
inference(resolution,[status(thm)],[f1970,f817]) ).
fof(f2050,plain,
( ~ sQ118_spl
| ~ sQ339_spl
| ~ sQ112_spl ),
inference(split_clause,[status(thm)],[f2040,f775,f1966,f816]) ).
fof(f2098,plain,
( sQ115_spl
| ~ aElement0(sK10_skl(sdtasasdt0(xI,xJ)))
| ~ aElementOf0(sK8_skl(sdtasasdt0(xI,xJ)),xJ)
| ~ aIdeal0(xJ) ),
inference(resolution,[status(thm)],[f786,f108]) ).
fof(f2104,definition,
( sQ345_spl
<=> aIdeal0(xJ) ),
introduced(definition,[new_symbols(definition,[sQ345_spl])],[split_symbol_definition]) ).
fof(f2106,plain,
( sQ345_spl
| ~ aIdeal0(xJ) ),
inference(component_clause,[status(thm)],[f2104]) ).
fof(f2107,plain,
( sQ115_spl
| ~ sQ111_spl
| ~ sQ119_spl
| ~ sQ345_spl ),
inference(split_clause,[status(thm)],[f2098,f2104,f819,f771,f784]) ).
fof(f2119,plain,
! [X0] :
( sQ119_spl
| ~ aElementOf0(sK8_skl(sdtasasdt0(xI,xJ)),sdtasasdt0(X0,xJ))
| ~ aSet0(xJ)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f821,f135]) ).
fof(f2121,definition,
! [X0] :
( sQ348_spl
<=> ( ~ aElementOf0(sK8_skl(sdtasasdt0(xI,xJ)),sdtasasdt0(X0,xJ))
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ348_spl])],[split_symbol_definition]) ).
fof(f2122,plain,
! [X0] :
( ~ sQ348_spl
| ~ aElementOf0(sK8_skl(sdtasasdt0(xI,xJ)),sdtasasdt0(X0,xJ))
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f2121]) ).
fof(f2124,plain,
( sQ119_spl
| ~ sQ113_spl
| sQ348_spl ),
inference(split_clause,[status(thm)],[f2119,f2121,f778,f819]) ).
fof(f2129,plain,
( sQ345_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2106,f117]) ).
fof(f2130,plain,
sQ345_spl,
inference(contradiction_clause,[status(thm)],[f2129]) ).
fof(f2144,plain,
( sQ124_spl
| ~ aElementOf0(sK9_skl(sdtasasdt0(xI,xJ)),xJ)
| ~ aElementOf0(sK8_skl(sdtasasdt0(xI,xJ)),xJ)
| ~ aIdeal0(xJ) ),
inference(resolution,[status(thm)],[f858,f107]) ).
fof(f2150,plain,
( sQ124_spl
| ~ sQ313_spl
| ~ sQ119_spl
| ~ sQ345_spl ),
inference(split_clause,[status(thm)],[f2144,f2104,f819,f1696,f856]) ).
fof(f2205,plain,
( ~ sQ118_spl
| ~ sQ320_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f817,f1738]) ).
fof(f2216,plain,
( ~ sQ118_spl
| ~ sQ320_spl ),
inference(contradiction_clause,[status(thm)],[f2205]) ).
fof(f2231,plain,
( ~ sQ110_spl
| ~ sQ348_spl
| ~ aSet0(xI) ),
inference(resolution,[status(thm)],[f2122,f769]) ).
fof(f2238,plain,
( ~ sQ110_spl
| ~ sQ348_spl
| ~ sQ112_spl ),
inference(split_clause,[status(thm)],[f2231,f775,f2121,f768]) ).
fof(f2240,plain,
$false,
inference(sat_refutation,[status(thm)],[f152,f156,f160,f167,f174,f179,f182,f195,f199,f204,f211,f231,f257,f261,f265,f270,f274,f281,f300,f304,f308,f312,f317,f321,f335,f339,f343,f347,f352,f367,f371,f375,f379,f384,f399,f403,f407,f411,f416,f431,f435,f439,f443,f448,f463,f467,f471,f475,f480,f484,f487,f490,f493,f498,f513,f517,f521,f525,f529,f533,f537,f539,f552,f556,f560,f564,f568,f572,f576,f578,f757,f787,f798,f801,f804,f807,f815,f859,f1691,f1692,f1709,f1722,f1731,f1807,f1847,f1857,f1870,f1896,f1910,f1911,f1969,f1986,f2023,f2050,f2107,f2124,f2130,f2150,f2216,f2238]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG093+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n008.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 04:19:40 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.40 % Drodi V4.1.1
% 0.09/0.47 % Refutation found
% 0.09/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.50 % Elapsed time: 0.126454 seconds
% 0.09/0.50 % CPU time: 0.575219 seconds
% 0.09/0.50 % Total memory used: 94.063 MB
% 0.09/0.50 % Net memory used: 93.132 MB
%------------------------------------------------------------------------------