%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM620+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n009.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 : Fri Sep 25 02:26:16 PM UTC 2026
% Result : Theorem 10.45s 2.72s
% Output : CNFRefutation 10.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 14
% Syntax : Number of formulae : 116 ( 25 unt; 0 def)
% Number of atoms : 379 ( 57 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 456 ( 193 ~; 190 |; 53 &)
% ( 7 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 11 con; 0-2 aty)
% Number of variables : 133 ( 0 sgn 123 !; 10 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( X0 = slcrc0
<=> ( ~ ? [X1] : aElementOf0(X1,X0)
& aSet0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
fof(f9,axiom,
! [X0] :
( ( isCountable0(X0)
& aSet0(X0) )
=> X0 != slcrc0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin_01) ).
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aSet0(X2)
& aSet0(X1)
& aSet0(X0) )
=> ( ( aSubsetOf0(X1,X2)
& aSubsetOf0(X0,X1) )
=> aSubsetOf0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubTrans) ).
fof(f17,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> sdtpldt0(sdtmndt0(X0,X1),X1) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mConsDiff) ).
fof(f23,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
fof(f25,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( szszuzczcdt0(X0) != sz00
& aElementOf0(szszuzczcdt0(X0),szNzAzT0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNum) ).
fof(f47,axiom,
! [X0] :
( ( X0 != slcrc0
& aSubsetOf0(X0,szNzAzT0) )
=> ! [X1] :
( X1 = szmzizndt0(X0)
<=> ( ! [X2] :
( aElementOf0(X2,X0)
=> sdtlseqdt0(X1,X2) )
& aElementOf0(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefMin) ).
fof(f82,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( isCountable0(sdtlpdtrp0(xN,X0))
& aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3671) ).
fof(f101,axiom,
aSubsetOf0(xQ,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5106) ).
fof(f111,axiom,
( sdtlpdtrp0(xe,xn) = xp
& aElementOf0(xn,szNzAzT0)
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5309) ).
fof(f115,axiom,
( xx = sdtlpdtrp0(xe,xm)
& aElementOf0(xm,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5389) ).
fof(f116,axiom,
xx = szmzizndt0(sdtlpdtrp0(xN,xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5401) ).
fof(f117,conjecture,
( aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
=> aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f118,negated_conjecture,
~ ( aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
=> aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(negated_conjecture,[status(cth)],[f117]) ).
fof(f130,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ( isCountable0(sdtlpdtrp0(xN,X0))
& aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) ) ),
inference(ennf_transformation,[],[f82]) ).
fof(f150,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
& ~ aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(ennf_transformation,[],[f118]) ).
fof(f151,plain,
! [X0,X1,X2] :
( ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1)
| aSubsetOf0(X0,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f152,plain,
! [X0,X1,X2] :
( ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1)
| aSubsetOf0(X0,X2) ),
inference(flattening,[],[f151]) ).
fof(f156,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f187,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ( szszuzczcdt0(X0) != sz00
& aElementOf0(szszuzczcdt0(X0),szNzAzT0) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f202,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| sdtpldt0(sdtmndt0(X0,X1),X1) = X0 ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f207,plain,
! [X0] :
( slcrc0 = X0
| ~ aSubsetOf0(X0,szNzAzT0)
| ! [X1] :
( X1 = szmzizndt0(X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X0)
| sdtlseqdt0(X1,X2) )
& aElementOf0(X1,X0) ) ) ),
inference(ennf_transformation,[],[f47]) ).
fof(f208,plain,
! [X0] :
( slcrc0 = X0
| ~ aSubsetOf0(X0,szNzAzT0)
| ! [X1] :
( X1 = szmzizndt0(X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X0)
| sdtlseqdt0(X1,X2) )
& aElementOf0(X1,X0) ) ) ),
inference(flattening,[],[f207]) ).
fof(f226,plain,
! [X0] :
( ~ isCountable0(X0)
| ~ aSet0(X0)
| X0 != slcrc0 ),
inference(ennf_transformation,[],[f9]) ).
fof(f227,plain,
! [X0] :
( ~ isCountable0(X0)
| ~ aSet0(X0)
| X0 != slcrc0 ),
inference(flattening,[],[f226]) ).
fof(f228,plain,
! [X0] :
( X0 = slcrc0
<=> ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f257,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) )
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(nnf_transformation,[],[f156]) ).
fof(f258,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) )
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(flattening,[],[f257]) ).
fof(f259,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X3] :
( ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aSet0(X1) ) )
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(rectify,[],[f258]) ).
fof(f260,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X3] :
( ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aSet0(X1) ) )
& ( ( aElementOf0(sK10(X0,X1),X1)
& ~ aElementOf0(sK10(X0,X1),X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10(X0,X1))],[f259]) ).
fof(f276,plain,
! [X0] :
( slcrc0 = X0
| ~ aSubsetOf0(X0,szNzAzT0)
| ! [X1] :
( ( szmzizndt0(X0) != X1
| ( ! [X2] :
( ~ aElementOf0(X2,X0)
| sdtlseqdt0(X1,X2) )
& aElementOf0(X1,X0) ) )
& ( ? [X2] :
( aElementOf0(X2,X0)
& ~ sdtlseqdt0(X1,X2) )
| ~ aElementOf0(X1,X0)
| X1 = szmzizndt0(X0) ) ) ),
inference(nnf_transformation,[],[f208]) ).
fof(f277,plain,
! [X0] :
( slcrc0 = X0
| ~ aSubsetOf0(X0,szNzAzT0)
| ! [X1] :
( ( szmzizndt0(X0) != X1
| ( ! [X2] :
( ~ aElementOf0(X2,X0)
| sdtlseqdt0(X1,X2) )
& aElementOf0(X1,X0) ) )
& ( ? [X2] :
( aElementOf0(X2,X0)
& ~ sdtlseqdt0(X1,X2) )
| ~ aElementOf0(X1,X0)
| X1 = szmzizndt0(X0) ) ) ),
inference(flattening,[],[f276]) ).
fof(f278,plain,
! [X0] :
( slcrc0 = X0
| ~ aSubsetOf0(X0,szNzAzT0)
| ! [X1] :
( ( szmzizndt0(X0) != X1
| ( ! [X3] :
( ~ aElementOf0(X3,X0)
| sdtlseqdt0(X1,X3) )
& aElementOf0(X1,X0) ) )
& ( ? [X2] :
( aElementOf0(X2,X0)
& ~ sdtlseqdt0(X1,X2) )
| ~ aElementOf0(X1,X0)
| X1 = szmzizndt0(X0) ) ) ),
inference(rectify,[],[f277]) ).
fof(f279,plain,
! [X0] :
( slcrc0 = X0
| ~ aSubsetOf0(X0,szNzAzT0)
| ! [X1] :
( ( szmzizndt0(X0) != X1
| ( ! [X3] :
( ~ aElementOf0(X3,X0)
| sdtlseqdt0(X1,X3) )
& aElementOf0(X1,X0) ) )
& ( ( aElementOf0(sK19(X0,X1),X0)
& ~ sdtlseqdt0(X1,sK19(X0,X1)) )
| ~ aElementOf0(X1,X0)
| X1 = szmzizndt0(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(X2,sK19(X0,X1))],[f278]) ).
fof(f290,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(nnf_transformation,[],[f228]) ).
fof(f291,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(flattening,[],[f290]) ).
fof(f292,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(rectify,[],[f291]) ).
fof(f293,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) ) )
& ( aElementOf0(sK22(X0),X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(X1,sK22(X0))],[f292]) ).
fof(f329,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,X0)) ),
inference(cnf_transformation,[],[f130]) ).
fof(f330,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f367,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(cnf_transformation,[],[f101]) ).
fof(f379,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[],[f111]) ).
fof(f386,plain,
aElementOf0(xm,szNzAzT0),
inference(cnf_transformation,[],[f115]) ).
fof(f387,plain,
xx = szmzizndt0(sdtlpdtrp0(xN,xm)),
inference(cnf_transformation,[],[f116]) ).
fof(f388,plain,
aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(cnf_transformation,[],[f150]) ).
fof(f389,plain,
~ aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(cnf_transformation,[],[f150]) ).
fof(f390,plain,
! [X2,X0,X1] :
( ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1)
| aSubsetOf0(X0,X2) ),
inference(cnf_transformation,[],[f152]) ).
fof(f393,plain,
! [X3,X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) ),
inference(cnf_transformation,[],[f260]) ).
fof(f394,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| aSet0(X1) ),
inference(cnf_transformation,[],[f260]) ).
fof(f405,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f433,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(szszuzczcdt0(X0),szNzAzT0) ),
inference(cnf_transformation,[],[f187]) ).
fof(f444,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| sdtpldt0(sdtmndt0(X0,X1),X1) = X0 ),
inference(cnf_transformation,[],[f202]) ).
fof(f459,plain,
! [X0,X1] :
( slcrc0 = X0
| ~ aSubsetOf0(X0,szNzAzT0)
| szmzizndt0(X0) != X1
| aElementOf0(X1,X0) ),
inference(cnf_transformation,[],[f279]) ).
fof(f488,plain,
! [X0] :
( ~ isCountable0(X0)
| ~ aSet0(X0)
| slcrc0 != X0 ),
inference(cnf_transformation,[],[f227]) ).
fof(f491,plain,
! [X0] :
( slcrc0 != X0
| aSet0(X0) ),
inference(cnf_transformation,[],[f293]) ).
fof(f532,plain,
! [X0] :
( slcrc0 = X0
| ~ aSubsetOf0(X0,szNzAzT0)
| aElementOf0(szmzizndt0(X0),X0) ),
inference(equality_resolution,[],[f459]) ).
fof(f541,plain,
( ~ isCountable0(slcrc0)
| ~ aSet0(slcrc0) ),
inference(equality_resolution,[],[f488]) ).
fof(f542,plain,
aSet0(slcrc0),
inference(equality_resolution,[],[f491]) ).
tcf(c_70,plain,
! [X0: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f330]) ).
tcf(c_71,plain,
! [X0: $i] :
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f329]) ).
tcf(c_108,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(cnf_transformation,[],[f367]) ).
tcf(c_120,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[],[f379]) ).
tcf(c_126,plain,
aElementOf0(xm,szNzAzT0),
inference(cnf_transformation,[],[f386]) ).
tcf(c_128,plain,
szmzizndt0(sdtlpdtrp0(xN,xm)) = xx,
inference(cnf_transformation,[],[f387]) ).
tcf(c_129,negated_conjecture,
~ aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(cnf_transformation,[],[f389]) ).
tcf(c_130,negated_conjecture,
aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(cnf_transformation,[],[f388]) ).
tcf(c_131,plain,
! [X0: $i,X1: $i,X2: $i] :
( aSubsetOf0(X0,X2)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f390]) ).
tcf(c_136,plain,
! [X0: $i,X1: $i] :
( aSet0(X0)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f394]) ).
tcf(c_137,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,X2)
| ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f393]) ).
tcf(c_145,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f405]) ).
tcf(c_173,plain,
! [X0: $i] :
( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f433]) ).
tcf(c_185,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtmndt0(X1,X0),X0) = X1 )
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f444]) ).
tcf(c_201,plain,
! [X0: $i] :
( aElementOf0(szmzizndt0(X0),X0)
| ( X0 = slcrc0 )
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f532]) ).
tcf(c_229,plain,
( ~ isCountable0(slcrc0)
| ~ aSet0(slcrc0) ),
inference(cnf_transformation,[],[f541]) ).
tcf(c_232,plain,
aSet0(slcrc0),
inference(cnf_transformation,[],[f542]) ).
tcf(c_394,plain,
~ isCountable0(slcrc0),
inference(global_subsumption_just,[status(thm)],[c_229,c_232,c_229]) ).
tcf(c_405,plain,
! [X0: $i,X1: $i,X2: $i] :
( aSubsetOf0(X0,X2)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X1,X2) ),
inference(global_subsumption_just,[status(thm)],[c_131,c_136,c_131]) ).
tcf(c_406,plain,
! [X0: $i,X1: $i,X2: $i] :
( aSubsetOf0(X0,X2)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1) ),
inference(renaming,[status(thm)],[c_405]) ).
tcf(c_683,plain,
! [X0: $i,X1: $i,X2: $i] :
( aSubsetOf0(X0,X2)
| ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_406,c_136]) ).
tcf(c_24349,plain,
! [X0: $i] :
( aSet0(sdtlpdtrp0(xN,X0))
| ~ aSet0(szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(superposition,[status(thm)],[c_70,c_136]) ).
tcf(c_24369,plain,
! [X0: $i] :
( aSet0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24349,c_145]) ).
tcf(c_24692,plain,
! [X0: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,xm),X0)
| ~ aSet0(X0)
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),X0) ),
inference(superposition,[status(thm)],[c_130,c_683]) ).
tcf(c_24848,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aSet0(szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
inference(superposition,[status(thm)],[c_70,c_24692]) ).
tcf(c_24850,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24848,c_145]) ).
tcf(c_24860,plain,
! [X0: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,xm),X0)
| ~ aSet0(X0)
| ~ aSubsetOf0(szNzAzT0,X0)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
inference(superposition,[status(thm)],[c_24850,c_683]) ).
tcf(c_24862,plain,
( aSet0(sdtlpdtrp0(xN,xm))
| ~ aSet0(szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
inference(superposition,[status(thm)],[c_24850,c_136]) ).
tcf(c_24863,plain,
( aSet0(sdtlpdtrp0(xN,xm))
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24862,c_145]) ).
tcf(c_24903,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,xm),X1)
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(szNzAzT0,X0)
| ~ aSubsetOf0(X0,X1)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
inference(superposition,[status(thm)],[c_24860,c_683]) ).
tcf(c_24946,plain,
( aSet0(sdtlpdtrp0(xN,xm))
| ~ aElementOf0(xn,szNzAzT0) ),
inference(superposition,[status(thm)],[c_173,c_24863]) ).
tcf(c_24947,plain,
aSet0(sdtlpdtrp0(xN,xm)),
inference(forward_subsumption_resolution,[status(thm)],[c_24946,c_120]) ).
tcf(c_25031,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,xm),X1)
| ~ aSet0(X1)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(szNzAzT0,X0) ),
inference(global_subsumption_just,[status(thm)],[c_24903,c_136,c_24903]) ).
tcf(c_25032,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,xm),X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(szNzAzT0,X0)
| ~ aSubsetOf0(X0,X1)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
inference(renaming,[status(thm)],[c_25031]) ).
tcf(c_25049,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aSet0(szNzAzT0)
| ~ aSubsetOf0(szNzAzT0,xQ)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
inference(superposition,[status(thm)],[c_108,c_25032]) ).
tcf(c_25069,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aSubsetOf0(szNzAzT0,xQ)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25049,c_145]) ).
tcf(c_25274,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_25446,plain,
aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0),
inference(global_subsumption_just,[status(thm)],[c_25069,c_126,c_25274]) ).
tcf(c_25815,plain,
( aElementOf0(xx,sdtlpdtrp0(xN,xm))
| ( sdtlpdtrp0(xN,xm) = slcrc0 )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0) ),
inference(superposition,[status(thm)],[c_128,c_201]) ).
tcf(c_25863,plain,
( aElementOf0(xx,sdtlpdtrp0(xN,xm))
| ( sdtlpdtrp0(xN,xm) = slcrc0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25815,c_25446]) ).
tcf(c_25880,plain,
( aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_173]) ).
tcf(c_27053,plain,
! [X0: $i] :
( aElementOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xm)) ),
inference(superposition,[status(thm)],[c_130,c_137]) ).
tcf(c_27479,plain,
( ~ aElementOf0(xx,sdtlpdtrp0(xN,xm))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(superposition,[status(thm)],[c_27053,c_129]) ).
tcf(c_30796,plain,
( aSet0(sdtlpdtrp0(xN,xm))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(superposition,[status(thm)],[c_130,c_136]) ).
tcf(c_31091,plain,
aSet0(sdtlpdtrp0(xN,xm)),
inference(global_subsumption_just,[status(thm)],[c_30796,c_24947]) ).
tcf(c_33253,plain,
! [X0: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,xm),X0)
| ~ aSet0(X0)
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),X0) ),
inference(superposition,[status(thm)],[c_130,c_683]) ).
tcf(c_34557,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aSet0(szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
inference(superposition,[status(thm)],[c_70,c_33253]) ).
tcf(c_34559,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34557,c_145]) ).
tcf(c_34666,plain,
aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0),
inference(global_subsumption_just,[status(thm)],[c_34559,c_126,c_25274]) ).
tcf(c_40469,plain,
( aElementOf0(xx,sdtlpdtrp0(xN,xm))
| ( sdtlpdtrp0(xN,xm) = slcrc0 )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0) ),
inference(superposition,[status(thm)],[c_128,c_201]) ).
tcf(c_40521,plain,
( aElementOf0(xx,sdtlpdtrp0(xN,xm))
| ( sdtlpdtrp0(xN,xm) = slcrc0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40469,c_34666]) ).
tcf(c_50377,plain,
( ( sdtlpdtrp0(xN,xm) = slcrc0 )
| ( sdtpldt0(sdtmndt0(sdtlpdtrp0(xN,xm),xx),xx) = sdtlpdtrp0(xN,xm) )
| ~ aSet0(sdtlpdtrp0(xN,xm)) ),
inference(superposition,[status(thm)],[c_40521,c_185]) ).
tcf(c_50438,plain,
( ( sdtlpdtrp0(xN,xm) = slcrc0 )
| ( sdtpldt0(sdtmndt0(sdtlpdtrp0(xN,xm),xx),xx) = sdtlpdtrp0(xN,xm) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_50377,c_31091]) ).
tcf(c_52680,plain,
( ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ~ aElementOf0(xx,sdtlpdtrp0(xN,xm)) ),
inference(superposition,[status(thm)],[c_24369,c_27479]) ).
tcf(c_53206,plain,
sdtlpdtrp0(xN,xm) = slcrc0,
inference(global_subsumption_just,[status(thm)],[c_50438,c_120,c_25863,c_25880,c_52680]) ).
tcf(c_53378,plain,
( isCountable0(slcrc0)
| ~ aElementOf0(xm,szNzAzT0) ),
inference(superposition,[status(thm)],[c_53206,c_71]) ).
tcf(c_53380,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_53378,c_394,c_126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM620+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n009.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 : Thu Sep 24 04:56:59 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.42 % Proving...
% 10.45/2.72 % SZS status Started for theBenchmark.p
% 10.45/2.72 % SZS status Theorem for theBenchmark.p
% 10.45/2.72
% 10.45/2.72 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.45/2.72
% 10.45/2.72 % ------ iProver source info
% 10.45/2.72
% 10.45/2.72 % git: date: 2026-07-19 20:42:38 +0200
% 10.45/2.72 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.45/2.72 % git: non_committed_changes: false
% 10.45/2.72
% 10.45/2.72 % ------ Parsing...
% 10.45/2.72 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.45/2.72
% 10.45/2.72 % ------ Preprocessing... sup_sim: 3 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 10.45/2.72
% 10.45/2.72 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.45/2.72
% 10.45/2.72 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.45/2.72 % ------ Proving...
% 10.45/2.72 % ------ Problem Properties
% 10.45/2.72
% 10.45/2.72 %
% 10.45/2.72 % clauses 211
% 10.45/2.72 % conjectures 2
% 10.45/2.72 % EPR 57
% 10.45/2.72 % Horn 177
% 10.45/2.72 % unary 62
% 10.45/2.72 % binary 32
% 10.45/2.72 % lits 633
% 10.45/2.72 % lits eq 100
% 10.45/2.72 % fd_pure 0
% 10.45/2.72 % fd_pseudo 0
% 10.45/2.72 % fd_cond 8
% 10.45/2.72 % fd_pseudo_cond 23
% 10.45/2.72 % AC symbols 0
% 10.45/2.72
% 10.45/2.72 % ------ Schedule dynamic 5 is on
% 10.45/2.72
% 10.45/2.72 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.45/2.72
% 10.45/2.72
% 10.45/2.72 % ------
% 10.45/2.72 % Current options:
% 10.45/2.72 % ------
% 10.45/2.72
% 10.45/2.72
% 10.45/2.72 %
% 10.45/2.72
% 10.45/2.72 % ------ Proving...
% 10.45/2.72 %
% 10.45/2.72
% 10.45/2.72 % SZS status Theorem for theBenchmark.p
% 10.45/2.72
% 10.45/2.72 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.45/2.72
% 10.45/2.72
%------------------------------------------------------------------------------