%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM539+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 01:40:55 PM UTC 2026
% Result : Theorem 1.11s 0.71s
% Output : CNFRefutation 1.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 24
% Syntax : Number of formulae : 106 ( 19 unt; 17 def)
% Number of atoms : 361 ( 45 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 437 ( 182 ~; 194 |; 33 &)
% ( 19 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 16 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 88 ( 84 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& aSet0(W1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> sdtlseqdt0(W0,W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( ( sdtlseqdt0(W1,W0)
& sdtlseqdt0(W0,W1) )
=> W0 = W1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [W0,W1,W2] :
( ( aElementOf0(W2,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( ( sdtlseqdt0(W1,W2)
& sdtlseqdt0(W0,W1) )
=> sdtlseqdt0(W0,W2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,definition,
! [W0] :
( ( W0 != slcrc0
& aSubsetOf0(W0,szNzAzT0) )
=> ! [W1] :
( W1 = szmzizndt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W0)
=> sdtlseqdt0(W1,W2) )
& aElementOf0(W1,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,hypothesis,
( xT != slcrc0
& xS != slcrc0
& aSubsetOf0(xT,szNzAzT0)
& aSubsetOf0(xS,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,hypothesis,
( aElementOf0(szmzizndt0(xT),xS)
& aElementOf0(szmzizndt0(xS),xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,conjecture,
szmzizndt0(xS) = szmzizndt0(xT),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
szmzizndt0(xS) != szmzizndt0(xT),
inference(negated_conjecture,[status(cth)],[f51]) ).
fof(f77,plain,
! [W0] :
( ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) ) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f78,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f77]) ).
fof(f79,plain,
! [W0] :
( ( ! [W1] :
( ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ! [W1] :
( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(miniscoping,[status(thm)],[f78]) ).
fof(f80,plain,
! [W0] :
( ( ! [W1] :
( ( ~ aElementOf0(sK1_skl(W1,W0),W0)
& aElementOf0(sK1_skl(W1,W0),W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ! [W1] :
( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W2,sK1_skl(W1,W0))],[f79]) ).
fof(f82,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f129,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f155,plain,
! [W0] :
( sdtlseqdt0(W0,W0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f156,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f157,plain,
! [W0,W1] :
( W0 = W1
| ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f158,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f157]) ).
fof(f159,plain,
! [W0,W1,W2] :
( sdtlseqdt0(W0,W2)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1)
| ~ aElementOf0(W2,szNzAzT0)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f160,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f187,plain,
! [W0] :
( ! [W1] :
( W1 = szmzizndt0(W0)
<=> ( ! [W2] :
( sdtlseqdt0(W1,W2)
| ~ aElementOf0(W2,W0) )
& aElementOf0(W1,W0) ) )
| W0 = slcrc0
| ~ aSubsetOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f188,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ~ sdtlseqdt0(W1,W2)
& aElementOf0(W2,W0) )
| ~ aElementOf0(W1,W0)
| W1 = szmzizndt0(W0) )
& ( ( ! [W2] :
( sdtlseqdt0(W1,W2)
| ~ aElementOf0(W2,W0) )
& aElementOf0(W1,W0) )
| W1 != szmzizndt0(W0) ) )
| W0 = slcrc0
| ~ aSubsetOf0(W0,szNzAzT0) ),
inference(NNF_transformation,[status(thm)],[f187]) ).
fof(f189,plain,
! [W0] :
( ( ! [W1] :
( ? [W2] :
( ~ sdtlseqdt0(W1,W2)
& aElementOf0(W2,W0) )
| ~ aElementOf0(W1,W0)
| W1 = szmzizndt0(W0) )
& ! [W1] :
( ( ! [W2] :
( sdtlseqdt0(W1,W2)
| ~ aElementOf0(W2,W0) )
& aElementOf0(W1,W0) )
| W1 != szmzizndt0(W0) ) )
| W0 = slcrc0
| ~ aSubsetOf0(W0,szNzAzT0) ),
inference(miniscoping,[status(thm)],[f188]) ).
fof(f190,plain,
! [W0] :
( ( ! [W1] :
( ( ~ sdtlseqdt0(W1,sK6_skl(W1,W0))
& aElementOf0(sK6_skl(W1,W0),W0) )
| ~ aElementOf0(W1,W0)
| W1 = szmzizndt0(W0) )
& ! [W1] :
( ( ! [W2] :
( sdtlseqdt0(W1,W2)
| ~ aElementOf0(W2,W0) )
& aElementOf0(W1,W0) )
| W1 != szmzizndt0(W0) ) )
| W0 = slcrc0
| ~ aSubsetOf0(W0,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(W2,sK6_skl(W1,W0))],[f189]) ).
fof(f191,plain,
! [X0,X1] :
( aElementOf0(X1,X0)
| X1 != szmzizndt0(X0)
| X0 = slcrc0
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f192,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,X0)
| X1 != szmzizndt0(X0)
| X0 = slcrc0
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f203,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f204,plain,
aSubsetOf0(xT,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f205,plain,
xS != slcrc0,
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f206,plain,
xT != slcrc0,
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f207,plain,
aElementOf0(szmzizndt0(xS),xT),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f208,plain,
aElementOf0(szmzizndt0(xT),xS),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f209,plain,
szmzizndt0(xS) != szmzizndt0(xT),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f229,plain,
! [X0] :
( aElementOf0(szmzizndt0(X0),X0)
| X0 = slcrc0
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(destructive_equality_resolution,[status(thm)],[f191]) ).
fof(f230,plain,
! [X0,X1] :
( sdtlseqdt0(szmzizndt0(X0),X1)
| ~ aElementOf0(X1,X0)
| X0 = slcrc0
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(destructive_equality_resolution,[status(thm)],[f192]) ).
fof(f247,definition,
( sQ2_spl
<=> aSet0(szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f249,plain,
( sQ2_spl
| ~ aSet0(szNzAzT0) ),
inference(component_clause,[status(thm)],[f247]) ).
fof(f268,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f249,f129]) ).
fof(f269,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f268]) ).
fof(f273,definition,
( sQ8_spl
<=> xT = slcrc0 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f274,plain,
( ~ sQ8_spl
| xT = slcrc0 ),
inference(component_clause,[status(thm)],[f273]) ).
fof(f277,definition,
( sQ9_spl
<=> xS = slcrc0 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f278,plain,
( ~ sQ9_spl
| xS = slcrc0 ),
inference(component_clause,[status(thm)],[f277]) ).
fof(f340,plain,
! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xT)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[status(thm)],[f82,f204]) ).
fof(f341,plain,
! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xS)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[status(thm)],[f82,f203]) ).
fof(f343,definition,
! [X0] :
( sQ18_spl
<=> ( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xT) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f344,plain,
! [X0] :
( ~ sQ18_spl
| aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xT) ),
inference(component_clause,[status(thm)],[f343]) ).
fof(f346,plain,
( sQ18_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f340,f247,f343]) ).
fof(f347,definition,
! [X0] :
( sQ19_spl
<=> ( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f348,plain,
! [X0] :
( ~ sQ19_spl
| aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xS) ),
inference(component_clause,[status(thm)],[f347]) ).
fof(f350,plain,
( sQ19_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f341,f247,f347]) ).
fof(f352,plain,
( ~ sQ18_spl
| aElementOf0(szmzizndt0(xS),szNzAzT0) ),
inference(resolution,[status(thm)],[f344,f207]) ).
fof(f357,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f274,f206]) ).
fof(f358,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f357]) ).
fof(f359,plain,
( ~ sQ18_spl
| sdtlseqdt0(szmzizndt0(xS),szmzizndt0(xS)) ),
inference(resolution,[status(thm)],[f352,f156]) ).
fof(f369,plain,
( ~ sQ19_spl
| aElementOf0(szmzizndt0(xT),szNzAzT0) ),
inference(resolution,[status(thm)],[f348,f208]) ).
fof(f374,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f278,f205]) ).
fof(f375,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f374]) ).
fof(f376,plain,
( ~ sQ19_spl
| sdtlseqdt0(szmzizndt0(xT),szmzizndt0(xT)) ),
inference(resolution,[status(thm)],[f369,f156]) ).
fof(f385,plain,
( ~ sQ19_spl
| aElementOf0(szmzizndt0(xS),szNzAzT0)
| xS = slcrc0
| ~ aSubsetOf0(xS,szNzAzT0) ),
inference(resolution,[status(thm)],[f229,f348]) ).
fof(f386,plain,
( ~ sQ18_spl
| aElementOf0(szmzizndt0(xT),szNzAzT0)
| xT = slcrc0
| ~ aSubsetOf0(xT,szNzAzT0) ),
inference(resolution,[status(thm)],[f229,f344]) ).
fof(f390,definition,
( sQ24_spl
<=> aSubsetOf0(xS,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f392,plain,
( sQ24_spl
| ~ aSubsetOf0(xS,szNzAzT0) ),
inference(component_clause,[status(thm)],[f390]) ).
fof(f393,definition,
( sQ25_spl
<=> aElementOf0(szmzizndt0(xS),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f396,plain,
( ~ sQ19_spl
| sQ25_spl
| sQ9_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f385,f390,f277,f393,f347]) ).
fof(f397,definition,
( sQ26_spl
<=> aSubsetOf0(xT,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f399,plain,
( sQ26_spl
| ~ aSubsetOf0(xT,szNzAzT0) ),
inference(component_clause,[status(thm)],[f397]) ).
fof(f400,definition,
( sQ27_spl
<=> aElementOf0(szmzizndt0(xT),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f403,plain,
( ~ sQ18_spl
| sQ27_spl
| sQ8_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f386,f397,f273,f400,f343]) ).
fof(f406,plain,
( sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f392,f203]) ).
fof(f407,plain,
sQ24_spl,
inference(contradiction_clause,[status(thm)],[f406]) ).
fof(f408,plain,
( sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f399,f204]) ).
fof(f409,plain,
sQ26_spl,
inference(contradiction_clause,[status(thm)],[f408]) ).
fof(f1911,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X2,X1)
| X1 = slcrc0
| ~ aSubsetOf0(X1,szNzAzT0)
| sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,szmzizndt0(X1))
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(szmzizndt0(X1),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[status(thm)],[f160,f230]) ).
fof(f2924,plain,
! [X0] :
( ~ sQ18_spl
| ~ aElementOf0(X0,xS)
| xS = slcrc0
| ~ aSubsetOf0(xS,szNzAzT0)
| sdtlseqdt0(szmzizndt0(xS),X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(szmzizndt0(xS),szNzAzT0)
| ~ aElementOf0(szmzizndt0(xS),szNzAzT0) ),
inference(resolution,[status(thm)],[f1911,f359]) ).
fof(f2925,plain,
! [X0] :
( ~ sQ19_spl
| ~ aElementOf0(X0,xT)
| xT = slcrc0
| ~ aSubsetOf0(xT,szNzAzT0)
| sdtlseqdt0(szmzizndt0(xT),X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(szmzizndt0(xT),szNzAzT0)
| ~ aElementOf0(szmzizndt0(xT),szNzAzT0) ),
inference(resolution,[status(thm)],[f1911,f376]) ).
fof(f2951,definition,
! [X0] :
( sQ293_spl
<=> ( ~ aElementOf0(X0,xS)
| sdtlseqdt0(szmzizndt0(xS),X0)
| ~ aElementOf0(X0,szNzAzT0) ) ),
introduced(definition,[new_symbols(definition,[sQ293_spl])],[split_symbol_definition]) ).
fof(f2952,plain,
! [X0] :
( ~ sQ293_spl
| ~ aElementOf0(X0,xS)
| sdtlseqdt0(szmzizndt0(xS),X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(component_clause,[status(thm)],[f2951]) ).
fof(f2954,plain,
( ~ sQ18_spl
| sQ9_spl
| ~ sQ24_spl
| sQ293_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f2924,f393,f2951,f390,f277,f343]) ).
fof(f2955,definition,
! [X0] :
( sQ294_spl
<=> ( ~ aElementOf0(X0,xT)
| sdtlseqdt0(szmzizndt0(xT),X0)
| ~ aElementOf0(X0,szNzAzT0) ) ),
introduced(definition,[new_symbols(definition,[sQ294_spl])],[split_symbol_definition]) ).
fof(f2956,plain,
! [X0] :
( ~ sQ294_spl
| ~ aElementOf0(X0,xT)
| sdtlseqdt0(szmzizndt0(xT),X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(component_clause,[status(thm)],[f2955]) ).
fof(f2958,plain,
( ~ sQ19_spl
| sQ8_spl
| ~ sQ26_spl
| sQ294_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f2925,f400,f2955,f397,f273,f347]) ).
fof(f2974,plain,
! [X0] :
( ~ sQ293_spl
| ~ sQ19_spl
| ~ aElementOf0(X0,xS)
| sdtlseqdt0(szmzizndt0(xS),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2952,f348]) ).
fof(f2975,plain,
! [X0] :
( ~ sQ294_spl
| ~ sQ18_spl
| ~ aElementOf0(X0,xT)
| sdtlseqdt0(szmzizndt0(xT),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2956,f344]) ).
fof(f3276,plain,
! [X0] :
( ~ sQ293_spl
| ~ sQ19_spl
| X0 = szmzizndt0(xS)
| ~ sdtlseqdt0(X0,szmzizndt0(xS))
| ~ aElementOf0(szmzizndt0(xS),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xS) ),
inference(resolution,[status(thm)],[f2974,f158]) ).
fof(f3302,definition,
! [X0] :
( sQ335_spl
<=> ( X0 = szmzizndt0(xS)
| ~ sdtlseqdt0(X0,szmzizndt0(xS))
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ335_spl])],[split_symbol_definition]) ).
fof(f3303,plain,
! [X0] :
( ~ sQ335_spl
| X0 = szmzizndt0(xS)
| ~ sdtlseqdt0(X0,szmzizndt0(xS))
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xS) ),
inference(component_clause,[status(thm)],[f3302]) ).
fof(f3305,plain,
( ~ sQ293_spl
| ~ sQ19_spl
| ~ sQ25_spl
| sQ335_spl ),
inference(split_clause,[status(thm)],[f3276,f3302,f393,f347,f2951]) ).
fof(f3311,plain,
! [X0] :
( ~ sQ335_spl
| ~ sQ19_spl
| X0 = szmzizndt0(xS)
| ~ sdtlseqdt0(X0,szmzizndt0(xS))
| ~ aElementOf0(X0,xS) ),
inference(forward_subsumption_resolution,[status(thm)],[f3303,f348]) ).
fof(f3338,definition,
( sQ337_spl
<=> aElementOf0(szmzizndt0(xT),xS) ),
introduced(definition,[new_symbols(definition,[sQ337_spl])],[split_symbol_definition]) ).
fof(f3340,plain,
( sQ337_spl
| ~ aElementOf0(szmzizndt0(xT),xS) ),
inference(component_clause,[status(thm)],[f3338]) ).
fof(f3385,definition,
( sQ344_spl
<=> aElementOf0(szmzizndt0(xS),xT) ),
introduced(definition,[new_symbols(definition,[sQ344_spl])],[split_symbol_definition]) ).
fof(f3387,plain,
( sQ344_spl
| ~ aElementOf0(szmzizndt0(xS),xT) ),
inference(component_clause,[status(thm)],[f3385]) ).
fof(f3949,plain,
( ~ sQ294_spl
| ~ sQ18_spl
| ~ sQ335_spl
| ~ sQ19_spl
| ~ aElementOf0(szmzizndt0(xS),xT)
| szmzizndt0(xT) = szmzizndt0(xS)
| ~ aElementOf0(szmzizndt0(xT),xS) ),
inference(resolution,[status(thm)],[f3311,f2975]) ).
fof(f3959,definition,
( sQ406_spl
<=> szmzizndt0(xT) = szmzizndt0(xS) ),
introduced(definition,[new_symbols(definition,[sQ406_spl])],[split_symbol_definition]) ).
fof(f3960,plain,
( ~ sQ406_spl
| szmzizndt0(xT) = szmzizndt0(xS) ),
inference(component_clause,[status(thm)],[f3959]) ).
fof(f3962,plain,
( ~ sQ294_spl
| ~ sQ18_spl
| ~ sQ335_spl
| ~ sQ19_spl
| ~ sQ344_spl
| sQ406_spl
| ~ sQ337_spl ),
inference(split_clause,[status(thm)],[f3949,f3338,f3959,f3385,f347,f3302,f343,f2955]) ).
fof(f3963,plain,
( sQ344_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3387,f207]) ).
fof(f3964,plain,
sQ344_spl,
inference(contradiction_clause,[status(thm)],[f3963]) ).
fof(f3965,plain,
( sQ337_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3340,f208]) ).
fof(f3966,plain,
sQ337_spl,
inference(contradiction_clause,[status(thm)],[f3965]) ).
fof(f3967,plain,
( ~ sQ406_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3960,f209]) ).
fof(f3968,plain,
~ sQ406_spl,
inference(contradiction_clause,[status(thm)],[f3967]) ).
fof(f3969,plain,
$false,
inference(sat_refutation,[status(thm)],[f269,f346,f350,f358,f375,f396,f403,f407,f409,f2954,f2958,f3305,f3962,f3964,f3966,f3968]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM539+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 02:38:51 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 1.11/0.71 % Refutation found
% 1.11/0.71 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.11/0.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.25/0.74 % Elapsed time: 0.368422 seconds
% 0.25/0.74 % CPU time: 2.640175 seconds
% 0.25/0.74 % Total memory used: 126.935 MB
% 0.25/0.74 % Net memory used: 122.769 MB
%------------------------------------------------------------------------------