%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM542+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 01:40:56 PM UTC 2026
% Result : Theorem 0.14s 5.64s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of formulae : 95 ( 11 unt; 2 def)
% Number of atoms : 553 ( 21 equ)
% Maximal formula atoms : 38 ( 5 avg)
% Number of connectives : 710 ( 252 ~; 259 |; 157 &)
% ( 21 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 151 ( 141 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f25,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( szszuzczcdt0(W0) != sz00
& aElementOf0(szszuzczcdt0(W0),szNzAzT0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> W0 != szszuzczcdt0(W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> sdtlseqdt0(W0,szszuzczcdt0(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(f37,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( sdtlseqdt0(szszuzczcdt0(W1),W0)
| sdtlseqdt0(W0,W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,definition,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1] :
( W1 = slbdtrb0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ( sdtlseqdt0(szszuzczcdt0(W2),W0)
& aElementOf0(W2,szNzAzT0) ) )
& aSet0(W1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,hypothesis,
( aElementOf0(xn,szNzAzT0)
& aElementOf0(xm,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,conjecture,
( ( ( aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn))
& ! [W0] :
( aElementOf0(W0,slbdtrb0(xm))
=> aElementOf0(W0,slbdtrb0(xn)) )
& ! [W0] :
( aElementOf0(W0,slbdtrb0(xn))
<=> ( sdtlseqdt0(szszuzczcdt0(W0),xn)
& aElementOf0(W0,szNzAzT0) ) )
& aSet0(slbdtrb0(xn))
& ! [W0] :
( aElementOf0(W0,slbdtrb0(xm))
<=> ( sdtlseqdt0(szszuzczcdt0(W0),xm)
& aElementOf0(W0,szNzAzT0) ) )
& aSet0(slbdtrb0(xm)) )
=> sdtlseqdt0(xm,xn) )
& ( sdtlseqdt0(xm,xn)
=> ( ( ! [W0] :
( aElementOf0(W0,slbdtrb0(xm))
<=> ( sdtlseqdt0(szszuzczcdt0(W0),xm)
& aElementOf0(W0,szNzAzT0) ) )
& aSet0(slbdtrb0(xm)) )
=> ( ( ! [W0] :
( aElementOf0(W0,slbdtrb0(xn))
<=> ( sdtlseqdt0(szszuzczcdt0(W0),xn)
& aElementOf0(W0,szNzAzT0) ) )
& aSet0(slbdtrb0(xn)) )
=> ( aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn))
| ! [W0] :
( aElementOf0(W0,slbdtrb0(xm))
=> aElementOf0(W0,slbdtrb0(xn)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,negated_conjecture,
~ ( ( ( aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn))
& ! [W0] :
( aElementOf0(W0,slbdtrb0(xm))
=> aElementOf0(W0,slbdtrb0(xn)) )
& ! [W0] :
( aElementOf0(W0,slbdtrb0(xn))
<=> ( sdtlseqdt0(szszuzczcdt0(W0),xn)
& aElementOf0(W0,szNzAzT0) ) )
& aSet0(slbdtrb0(xn))
& ! [W0] :
( aElementOf0(W0,slbdtrb0(xm))
<=> ( sdtlseqdt0(szszuzczcdt0(W0),xm)
& aElementOf0(W0,szNzAzT0) ) )
& aSet0(slbdtrb0(xm)) )
=> sdtlseqdt0(xm,xn) )
& ( sdtlseqdt0(xm,xn)
=> ( ( ! [W0] :
( aElementOf0(W0,slbdtrb0(xm))
<=> ( sdtlseqdt0(szszuzczcdt0(W0),xm)
& aElementOf0(W0,szNzAzT0) ) )
& aSet0(slbdtrb0(xm)) )
=> ( ( ! [W0] :
( aElementOf0(W0,slbdtrb0(xn))
<=> ( sdtlseqdt0(szszuzczcdt0(W0),xn)
& aElementOf0(W0,szNzAzT0) ) )
& aSet0(slbdtrb0(xn)) )
=> ( aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn))
| ! [W0] :
( aElementOf0(W0,slbdtrb0(xm))
=> aElementOf0(W0,slbdtrb0(xn)) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f55]) ).
fof(f136,plain,
! [W0] :
( ( szszuzczcdt0(W0) != sz00
& aElementOf0(szszuzczcdt0(W0),szNzAzT0) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f137,plain,
! [X0] :
( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f145,plain,
! [W0] :
( W0 != szszuzczcdt0(W0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f146,plain,
! [X0] :
( X0 != szszuzczcdt0(X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f157,plain,
! [W0] :
( sdtlseqdt0(W0,szszuzczcdt0(W0))
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f158,plain,
! [X0] :
( sdtlseqdt0(X0,szszuzczcdt0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f157]) ).
fof(f161,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(f162,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f161]) ).
fof(f163,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(f164,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)],[f163]) ).
fof(f165,plain,
! [W0,W1] :
( sdtlseqdt0(szszuzczcdt0(W1),W0)
| sdtlseqdt0(W0,W1)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f166,plain,
! [X0,X1] :
( sdtlseqdt0(szszuzczcdt0(X1),X0)
| sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f165]) ).
fof(f209,plain,
! [W0] :
( ! [W1] :
( W1 = slbdtrb0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ( sdtlseqdt0(szszuzczcdt0(W2),W0)
& aElementOf0(W2,szNzAzT0) ) )
& aSet0(W1) ) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f210,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ( ( sdtlseqdt0(szszuzczcdt0(W2),W0)
& aElementOf0(W2,szNzAzT0) )
| aElementOf0(W2,W1) )
& ( ~ sdtlseqdt0(szszuzczcdt0(W2),W0)
| ~ aElementOf0(W2,szNzAzT0)
| ~ aElementOf0(W2,W1) ) )
| ~ aSet0(W1)
| W1 = slbdtrb0(W0) )
& ( ( ! [W2] :
( ( ~ sdtlseqdt0(szszuzczcdt0(W2),W0)
| ~ aElementOf0(W2,szNzAzT0)
| aElementOf0(W2,W1) )
& ( ( sdtlseqdt0(szszuzczcdt0(W2),W0)
& aElementOf0(W2,szNzAzT0) )
| ~ aElementOf0(W2,W1) ) )
& aSet0(W1) )
| W1 != slbdtrb0(W0) ) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(NNF_transformation,[status(thm)],[f209]) ).
fof(f211,plain,
! [W0] :
( ( ! [W1] :
( ? [W2] :
( ( ( sdtlseqdt0(szszuzczcdt0(W2),W0)
& aElementOf0(W2,szNzAzT0) )
| aElementOf0(W2,W1) )
& ( ~ sdtlseqdt0(szszuzczcdt0(W2),W0)
| ~ aElementOf0(W2,szNzAzT0)
| ~ aElementOf0(W2,W1) ) )
| ~ aSet0(W1)
| W1 = slbdtrb0(W0) )
& ! [W1] :
( ( ! [W2] :
( ~ sdtlseqdt0(szszuzczcdt0(W2),W0)
| ~ aElementOf0(W2,szNzAzT0)
| aElementOf0(W2,W1) )
& ! [W2] :
( ( sdtlseqdt0(szszuzczcdt0(W2),W0)
& aElementOf0(W2,szNzAzT0) )
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| W1 != slbdtrb0(W0) ) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(miniscoping,[status(thm)],[f210]) ).
fof(f212,plain,
! [W0] :
( ( ! [W1] :
( ( ( ( sdtlseqdt0(szszuzczcdt0(sK8_skl(W1,W0)),W0)
& aElementOf0(sK8_skl(W1,W0),szNzAzT0) )
| aElementOf0(sK8_skl(W1,W0),W1) )
& ( ~ sdtlseqdt0(szszuzczcdt0(sK8_skl(W1,W0)),W0)
| ~ aElementOf0(sK8_skl(W1,W0),szNzAzT0)
| ~ aElementOf0(sK8_skl(W1,W0),W1) ) )
| ~ aSet0(W1)
| W1 = slbdtrb0(W0) )
& ! [W1] :
( ( ! [W2] :
( ~ sdtlseqdt0(szszuzczcdt0(W2),W0)
| ~ aElementOf0(W2,szNzAzT0)
| aElementOf0(W2,W1) )
& ! [W2] :
( ( sdtlseqdt0(szszuzczcdt0(W2),W0)
& aElementOf0(W2,szNzAzT0) )
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| W1 != slbdtrb0(W0) ) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(W2,sK8_skl(W1,W0))],[f211]) ).
fof(f214,plain,
! [X0,X1,X2] :
( aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X2,X1)
| X1 != slbdtrb0(X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f212]) ).
fof(f215,plain,
! [X0,X1,X2] :
( sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,X1)
| X1 != slbdtrb0(X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f212]) ).
fof(f228,plain,
aElementOf0(xm,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f229,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f230,plain,
( ( ~ sdtlseqdt0(xm,xn)
& aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn))
& ! [W0] :
( aElementOf0(W0,slbdtrb0(xn))
| ~ aElementOf0(W0,slbdtrb0(xm)) )
& ! [W0] :
( aElementOf0(W0,slbdtrb0(xn))
<=> ( sdtlseqdt0(szszuzczcdt0(W0),xn)
& aElementOf0(W0,szNzAzT0) ) )
& aSet0(slbdtrb0(xn))
& ! [W0] :
( aElementOf0(W0,slbdtrb0(xm))
<=> ( sdtlseqdt0(szszuzczcdt0(W0),xm)
& aElementOf0(W0,szNzAzT0) ) )
& aSet0(slbdtrb0(xm)) )
| ( ~ aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn))
& ? [W0] :
( ~ aElementOf0(W0,slbdtrb0(xn))
& aElementOf0(W0,slbdtrb0(xm)) )
& ! [W0] :
( aElementOf0(W0,slbdtrb0(xn))
<=> ( sdtlseqdt0(szszuzczcdt0(W0),xn)
& aElementOf0(W0,szNzAzT0) ) )
& aSet0(slbdtrb0(xn))
& ! [W0] :
( aElementOf0(W0,slbdtrb0(xm))
<=> ( sdtlseqdt0(szszuzczcdt0(W0),xm)
& aElementOf0(W0,szNzAzT0) ) )
& aSet0(slbdtrb0(xm))
& sdtlseqdt0(xm,xn) ) ),
inference(pre_NNF_transformation,[status(thm)],[f56]) ).
fof(f231,definition,
( sP1_prd
<=> ( ~ aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn))
& ? [W0] :
( ~ aElementOf0(W0,slbdtrb0(xn))
& aElementOf0(W0,slbdtrb0(xm)) )
& ! [W0] :
( aElementOf0(W0,slbdtrb0(xn))
<=> ( sdtlseqdt0(szszuzczcdt0(W0),xn)
& aElementOf0(W0,szNzAzT0) ) )
& aSet0(slbdtrb0(xn))
& ! [W0] :
( aElementOf0(W0,slbdtrb0(xm))
<=> ( sdtlseqdt0(szszuzczcdt0(W0),xm)
& aElementOf0(W0,szNzAzT0) ) )
& aSet0(slbdtrb0(xm))
& sdtlseqdt0(xm,xn) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f232,plain,
( ( ~ sdtlseqdt0(xm,xn)
& aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn))
& ! [W0] :
( aElementOf0(W0,slbdtrb0(xn))
| ~ aElementOf0(W0,slbdtrb0(xm)) )
& ! [W0] :
( aElementOf0(W0,slbdtrb0(xn))
<=> ( sdtlseqdt0(szszuzczcdt0(W0),xn)
& aElementOf0(W0,szNzAzT0) ) )
& aSet0(slbdtrb0(xn))
& ! [W0] :
( aElementOf0(W0,slbdtrb0(xm))
<=> ( sdtlseqdt0(szszuzczcdt0(W0),xm)
& aElementOf0(W0,szNzAzT0) ) )
& aSet0(slbdtrb0(xm)) )
| sP1_prd ),
inference(formula_renaming,[status(thm)],[f230,f231]) ).
fof(f233,plain,
( ( ~ sdtlseqdt0(xm,xn)
& aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn))
& ! [W0] :
( aElementOf0(W0,slbdtrb0(xn))
| ~ aElementOf0(W0,slbdtrb0(xm)) )
& ! [W0] :
( ( ~ sdtlseqdt0(szszuzczcdt0(W0),xn)
| ~ aElementOf0(W0,szNzAzT0)
| aElementOf0(W0,slbdtrb0(xn)) )
& ( ( sdtlseqdt0(szszuzczcdt0(W0),xn)
& aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(W0,slbdtrb0(xn)) ) )
& aSet0(slbdtrb0(xn))
& ! [W0] :
( ( ~ sdtlseqdt0(szszuzczcdt0(W0),xm)
| ~ aElementOf0(W0,szNzAzT0)
| aElementOf0(W0,slbdtrb0(xm)) )
& ( ( sdtlseqdt0(szszuzczcdt0(W0),xm)
& aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(W0,slbdtrb0(xm)) ) )
& aSet0(slbdtrb0(xm)) )
| sP1_prd ),
inference(NNF_transformation,[status(thm)],[f232]) ).
fof(f234,plain,
( ( ~ sdtlseqdt0(xm,xn)
& aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn))
& ! [W0] :
( aElementOf0(W0,slbdtrb0(xn))
| ~ aElementOf0(W0,slbdtrb0(xm)) )
& ! [W0] :
( ~ sdtlseqdt0(szszuzczcdt0(W0),xn)
| ~ aElementOf0(W0,szNzAzT0)
| aElementOf0(W0,slbdtrb0(xn)) )
& ! [W0] :
( ( sdtlseqdt0(szszuzczcdt0(W0),xn)
& aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(W0,slbdtrb0(xn)) )
& aSet0(slbdtrb0(xn))
& ! [W0] :
( ~ sdtlseqdt0(szszuzczcdt0(W0),xm)
| ~ aElementOf0(W0,szNzAzT0)
| aElementOf0(W0,slbdtrb0(xm)) )
& ! [W0] :
( ( sdtlseqdt0(szszuzczcdt0(W0),xm)
& aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(W0,slbdtrb0(xm)) )
& aSet0(slbdtrb0(xm)) )
| sP1_prd ),
inference(miniscoping,[status(thm)],[f233]) ).
fof(f236,plain,
! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,slbdtrb0(xm))
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(f238,plain,
! [X0] :
( ~ sdtlseqdt0(szszuzczcdt0(X0),xm)
| ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(X0,slbdtrb0(xm))
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(f240,plain,
! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,slbdtrb0(xn))
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(f241,plain,
! [X0] :
( sdtlseqdt0(szszuzczcdt0(X0),xn)
| ~ aElementOf0(X0,slbdtrb0(xn))
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(f243,plain,
! [X0] :
( aElementOf0(X0,slbdtrb0(xn))
| ~ aElementOf0(X0,slbdtrb0(xm))
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(f245,plain,
( ~ sdtlseqdt0(xm,xn)
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(f252,plain,
( ( aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn))
| ! [W0] :
( aElementOf0(W0,slbdtrb0(xn))
| ~ aElementOf0(W0,slbdtrb0(xm)) )
| ? [W0] :
( ( ( sdtlseqdt0(szszuzczcdt0(W0),xn)
& aElementOf0(W0,szNzAzT0) )
| aElementOf0(W0,slbdtrb0(xn)) )
& ( ~ sdtlseqdt0(szszuzczcdt0(W0),xn)
| ~ aElementOf0(W0,szNzAzT0)
| ~ aElementOf0(W0,slbdtrb0(xn)) ) )
| ~ aSet0(slbdtrb0(xn))
| ? [W0] :
( ( ( sdtlseqdt0(szszuzczcdt0(W0),xm)
& aElementOf0(W0,szNzAzT0) )
| aElementOf0(W0,slbdtrb0(xm)) )
& ( ~ sdtlseqdt0(szszuzczcdt0(W0),xm)
| ~ aElementOf0(W0,szNzAzT0)
| ~ aElementOf0(W0,slbdtrb0(xm)) ) )
| ~ aSet0(slbdtrb0(xm))
| ~ sdtlseqdt0(xm,xn)
| sP1_prd )
& ( ( ~ aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn))
& ? [W0] :
( ~ aElementOf0(W0,slbdtrb0(xn))
& aElementOf0(W0,slbdtrb0(xm)) )
& ! [W0] :
( ( ~ sdtlseqdt0(szszuzczcdt0(W0),xn)
| ~ aElementOf0(W0,szNzAzT0)
| aElementOf0(W0,slbdtrb0(xn)) )
& ( ( sdtlseqdt0(szszuzczcdt0(W0),xn)
& aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(W0,slbdtrb0(xn)) ) )
& aSet0(slbdtrb0(xn))
& ! [W0] :
( ( ~ sdtlseqdt0(szszuzczcdt0(W0),xm)
| ~ aElementOf0(W0,szNzAzT0)
| aElementOf0(W0,slbdtrb0(xm)) )
& ( ( sdtlseqdt0(szszuzczcdt0(W0),xm)
& aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(W0,slbdtrb0(xm)) ) )
& aSet0(slbdtrb0(xm))
& sdtlseqdt0(xm,xn) )
| ~ sP1_prd ) ),
inference(NNF_transformation,[status(thm)],[f231]) ).
fof(f253,plain,
( ( aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn))
| ! [W0] :
( aElementOf0(W0,slbdtrb0(xn))
| ~ aElementOf0(W0,slbdtrb0(xm)) )
| ? [W0] :
( ( ( sdtlseqdt0(szszuzczcdt0(W0),xn)
& aElementOf0(W0,szNzAzT0) )
| aElementOf0(W0,slbdtrb0(xn)) )
& ( ~ sdtlseqdt0(szszuzczcdt0(W0),xn)
| ~ aElementOf0(W0,szNzAzT0)
| ~ aElementOf0(W0,slbdtrb0(xn)) ) )
| ~ aSet0(slbdtrb0(xn))
| ? [W0] :
( ( ( sdtlseqdt0(szszuzczcdt0(W0),xm)
& aElementOf0(W0,szNzAzT0) )
| aElementOf0(W0,slbdtrb0(xm)) )
& ( ~ sdtlseqdt0(szszuzczcdt0(W0),xm)
| ~ aElementOf0(W0,szNzAzT0)
| ~ aElementOf0(W0,slbdtrb0(xm)) ) )
| ~ aSet0(slbdtrb0(xm))
| ~ sdtlseqdt0(xm,xn)
| sP1_prd )
& ( ( ~ aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn))
& ? [W0] :
( ~ aElementOf0(W0,slbdtrb0(xn))
& aElementOf0(W0,slbdtrb0(xm)) )
& ! [W0] :
( ~ sdtlseqdt0(szszuzczcdt0(W0),xn)
| ~ aElementOf0(W0,szNzAzT0)
| aElementOf0(W0,slbdtrb0(xn)) )
& ! [W0] :
( ( sdtlseqdt0(szszuzczcdt0(W0),xn)
& aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(W0,slbdtrb0(xn)) )
& aSet0(slbdtrb0(xn))
& ! [W0] :
( ~ sdtlseqdt0(szszuzczcdt0(W0),xm)
| ~ aElementOf0(W0,szNzAzT0)
| aElementOf0(W0,slbdtrb0(xm)) )
& ! [W0] :
( ( sdtlseqdt0(szszuzczcdt0(W0),xm)
& aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(W0,slbdtrb0(xm)) )
& aSet0(slbdtrb0(xm))
& sdtlseqdt0(xm,xn) )
| ~ sP1_prd ) ),
inference(miniscoping,[status(thm)],[f252]) ).
fof(f254,plain,
( ( aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn))
| ! [W0] :
( aElementOf0(W0,slbdtrb0(xn))
| ~ aElementOf0(W0,slbdtrb0(xm)) )
| ( ( ( sdtlseqdt0(szszuzczcdt0(sK11_skl),xn)
& aElementOf0(sK11_skl,szNzAzT0) )
| aElementOf0(sK11_skl,slbdtrb0(xn)) )
& ( ~ sdtlseqdt0(szszuzczcdt0(sK11_skl),xn)
| ~ aElementOf0(sK11_skl,szNzAzT0)
| ~ aElementOf0(sK11_skl,slbdtrb0(xn)) ) )
| ~ aSet0(slbdtrb0(xn))
| ( ( ( sdtlseqdt0(szszuzczcdt0(sK10_skl),xm)
& aElementOf0(sK10_skl,szNzAzT0) )
| aElementOf0(sK10_skl,slbdtrb0(xm)) )
& ( ~ sdtlseqdt0(szszuzczcdt0(sK10_skl),xm)
| ~ aElementOf0(sK10_skl,szNzAzT0)
| ~ aElementOf0(sK10_skl,slbdtrb0(xm)) ) )
| ~ aSet0(slbdtrb0(xm))
| ~ sdtlseqdt0(xm,xn)
| sP1_prd )
& ( ( ~ aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn))
& ~ aElementOf0(sK9_skl,slbdtrb0(xn))
& aElementOf0(sK9_skl,slbdtrb0(xm))
& ! [W0] :
( ~ sdtlseqdt0(szszuzczcdt0(W0),xn)
| ~ aElementOf0(W0,szNzAzT0)
| aElementOf0(W0,slbdtrb0(xn)) )
& ! [W0] :
( ( sdtlseqdt0(szszuzczcdt0(W0),xn)
& aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(W0,slbdtrb0(xn)) )
& aSet0(slbdtrb0(xn))
& ! [W0] :
( ~ sdtlseqdt0(szszuzczcdt0(W0),xm)
| ~ aElementOf0(W0,szNzAzT0)
| aElementOf0(W0,slbdtrb0(xm)) )
& ! [W0] :
( ( sdtlseqdt0(szszuzczcdt0(W0),xm)
& aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(W0,slbdtrb0(xm)) )
& aSet0(slbdtrb0(xm))
& sdtlseqdt0(xm,xn) )
| ~ sP1_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl,sK11_skl]),skolemize(W0,sK9_skl),skolemize(W0,sK10_skl),skolemize(W0,sK11_skl)],[f253]) ).
fof(f255,plain,
( sdtlseqdt0(xm,xn)
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f254]) ).
fof(f257,plain,
! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,slbdtrb0(xm))
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f254]) ).
fof(f259,plain,
! [X0] :
( ~ sdtlseqdt0(szszuzczcdt0(X0),xm)
| ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(X0,slbdtrb0(xm))
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f254]) ).
fof(f261,plain,
! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,slbdtrb0(xn))
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f254]) ).
fof(f263,plain,
! [X0] :
( ~ sdtlseqdt0(szszuzczcdt0(X0),xn)
| ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(X0,slbdtrb0(xn))
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f254]) ).
fof(f264,plain,
( aElementOf0(sK9_skl,slbdtrb0(xm))
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f254]) ).
fof(f265,plain,
( ~ aElementOf0(sK9_skl,slbdtrb0(xn))
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f254]) ).
fof(f294,plain,
! [X0,X1] :
( aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(destructive_equality_resolution,[status(thm)],[f214]) ).
fof(f295,plain,
! [X0,X1] :
( sdtlseqdt0(szszuzczcdt0(X1),X0)
| ~ aElementOf0(X1,slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(destructive_equality_resolution,[status(thm)],[f215]) ).
fof(f415,plain,
! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,slbdtrb0(xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[f257,f236]) ).
fof(f417,plain,
( ~ sP1_prd
| aElementOf0(sK9_skl,szNzAzT0) ),
inference(resolution,[status(thm)],[f415,f264]) ).
fof(f425,plain,
! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,slbdtrb0(xn)) ),
inference(forward_subsumption_resolution,[status(thm)],[f261,f240]) ).
fof(f449,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| X0 = szszuzczcdt0(X0)
| ~ sdtlseqdt0(szszuzczcdt0(X0),X0)
| ~ aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[status(thm)],[f162,f158]) ).
fof(f469,plain,
! [X0] :
( X0 = szszuzczcdt0(X0)
| ~ sdtlseqdt0(szszuzczcdt0(X0),X0)
| ~ aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(duplicate_literals_removal,[status(thm)],[f449]) ).
fof(f470,plain,
! [X0] :
( X0 = szszuzczcdt0(X0)
| ~ sdtlseqdt0(szszuzczcdt0(X0),X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[f469,f137]) ).
fof(f517,plain,
! [X0] :
( ~ sdtlseqdt0(szszuzczcdt0(X0),X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[f470,f146]) ).
fof(f518,plain,
( ~ aElementOf0(xn,slbdtrb0(xn))
| sP1_prd
| ~ aElementOf0(xn,szNzAzT0) ),
inference(resolution,[status(thm)],[f517,f241]) ).
fof(f521,plain,
( ~ aElementOf0(xn,slbdtrb0(xn))
| sP1_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f518,f425]) ).
fof(f537,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(xn,X1)
| ~ sdtlseqdt0(X0,xn)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[status(thm)],[f164,f229]) ).
fof(f572,plain,
! [X0,X1] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(szszuzczcdt0(X0),X1)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(X0),szNzAzT0) ),
inference(resolution,[status(thm)],[f164,f517]) ).
fof(f614,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(szszuzczcdt0(X0),X1)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(X0),szNzAzT0) ),
inference(duplicate_literals_removal,[status(thm)],[f572]) ).
fof(f615,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(szszuzczcdt0(X1),X0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[f614,f137]) ).
fof(f736,plain,
( sP1_prd
| ~ aElementOf0(xn,slbdtrb0(xm))
| sP1_prd ),
inference(resolution,[status(thm)],[f243,f521]) ).
fof(f743,plain,
( ~ aElementOf0(xn,slbdtrb0(xm))
| sP1_prd ),
inference(duplicate_literals_removal,[status(thm)],[f736]) ).
fof(f855,plain,
! [X0] :
( ~ sdtlseqdt0(szszuzczcdt0(X0),xm)
| ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(X0,slbdtrb0(xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[f259,f238]) ).
fof(f858,plain,
! [X0] :
( sdtlseqdt0(xm,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(X0,slbdtrb0(xm)) ),
inference(resolution,[status(thm)],[f855,f166]) ).
fof(f860,plain,
! [X0] :
( sdtlseqdt0(xm,X0)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(X0,slbdtrb0(xm)) ),
inference(duplicate_literals_removal,[status(thm)],[f858]) ).
fof(f861,plain,
! [X0] :
( sdtlseqdt0(xm,X0)
| ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(X0,slbdtrb0(xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[f860,f228]) ).
fof(f953,plain,
( sP1_prd
| sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(resolution,[status(thm)],[f861,f743]) ).
fof(f963,plain,
( sP1_prd
| sdtlseqdt0(xm,xn) ),
inference(forward_subsumption_resolution,[status(thm)],[f953,f229]) ).
fof(f970,plain,
aElementOf0(sK9_skl,szNzAzT0),
inference(backward_subsumption_resolution,[status(thm)],[f417,f976]) ).
fof(f972,plain,
~ aElementOf0(sK9_skl,slbdtrb0(xn)),
inference(backward_subsumption_resolution,[status(thm)],[f265,f976]) ).
fof(f974,plain,
aElementOf0(sK9_skl,slbdtrb0(xm)),
inference(backward_subsumption_resolution,[status(thm)],[f264,f976]) ).
fof(f975,plain,
sdtlseqdt0(xm,xn),
inference(backward_subsumption_resolution,[status(thm)],[f255,f976]) ).
fof(f976,plain,
sP1_prd,
inference(forward_subsumption_resolution,[status(thm)],[f963,f245]) ).
fof(f977,plain,
! [X0] :
( ~ sdtlseqdt0(szszuzczcdt0(X0),xn)
| ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(X0,slbdtrb0(xn)) ),
inference(forward_subsumption_resolution,[status(thm)],[f263,f976]) ).
fof(f980,plain,
! [X0] :
( sdtlseqdt0(xn,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(X0,slbdtrb0(xn)) ),
inference(resolution,[status(thm)],[f977,f166]) ).
fof(f982,plain,
! [X0] :
( sdtlseqdt0(xn,X0)
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(X0,slbdtrb0(xn)) ),
inference(duplicate_literals_removal,[status(thm)],[f980]) ).
fof(f983,plain,
! [X0] :
( sdtlseqdt0(xn,X0)
| ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(X0,slbdtrb0(xn)) ),
inference(forward_subsumption_resolution,[status(thm)],[f982,f229]) ).
fof(f1085,plain,
( sdtlseqdt0(xn,sK9_skl)
| ~ aElementOf0(sK9_skl,szNzAzT0) ),
inference(resolution,[status(thm)],[f983,f972]) ).
fof(f1095,plain,
sdtlseqdt0(xn,sK9_skl),
inference(forward_subsumption_resolution,[status(thm)],[f1085,f970]) ).
fof(f3032,plain,
! [X0,X1] :
( ~ aElementOf0(X1,slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[status(thm)],[f615,f295]) ).
fof(f3054,plain,
! [X0,X1] :
( ~ aElementOf0(X1,slbdtrb0(X0))
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(duplicate_literals_removal,[status(thm)],[f3032]) ).
fof(f3055,plain,
! [X0,X1] :
( ~ aElementOf0(X1,slbdtrb0(X0))
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3054,f294]) ).
fof(f3069,plain,
( ~ sdtlseqdt0(xm,sK9_skl)
| ~ aElementOf0(xm,szNzAzT0) ),
inference(resolution,[status(thm)],[f3055,f974]) ).
fof(f3083,plain,
~ sdtlseqdt0(xm,sK9_skl),
inference(forward_subsumption_resolution,[status(thm)],[f3069,f228]) ).
fof(f3265,plain,
! [X0] :
( sdtlseqdt0(X0,sK9_skl)
| ~ sdtlseqdt0(xn,sK9_skl)
| ~ sdtlseqdt0(X0,xn)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[status(thm)],[f537,f970]) ).
fof(f3410,plain,
! [X0] :
( sdtlseqdt0(X0,sK9_skl)
| ~ sdtlseqdt0(X0,xn)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3265,f1095]) ).
fof(f3569,plain,
( sdtlseqdt0(xm,sK9_skl)
| ~ aElementOf0(xm,szNzAzT0) ),
inference(resolution,[status(thm)],[f3410,f975]) ).
fof(f3624,plain,
sdtlseqdt0(xm,sK9_skl),
inference(forward_subsumption_resolution,[status(thm)],[f3569,f228]) ).
fof(f3671,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3624,f3083]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM542+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n008.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Mon Sep 21 02:39:29 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.14/5.40 % Drodi V4.1.1
% 0.14/5.64 % Refutation found
% 0.14/5.64 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/5.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.66 % Elapsed time: 0.267553 seconds
% 0.14/5.66 % CPU time: 1.838685 seconds
% 0.14/5.66 % Total memory used: 134.674 MB
% 0.14/5.66 % Net memory used: 132.204 MB
%------------------------------------------------------------------------------