%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM601+3 : 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 : 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 : Fri Sep 25 02:26:11 PM UTC 2026
% Result : Theorem 19.19s 9.48s
% Output : CNFRefutation 19.19s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f260ERROR: Could not build tree for root c_48196ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
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(f24,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNum) ).
fof(f30,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> sdtlseqdt0(sz00,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroLess) ).
fof(f82,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( isCountable0(sdtlpdtrp0(xN,X0))
& aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3671) ).
fof(f83,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( sdtlseqdt0(X1,X0)
=> ( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> aElementOf0(X2,sdtlpdtrp0(xN,X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3754) ).
fof(f91,axiom,
( ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( sdtlpdtrp0(xe,X0) = szmzizndt0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(sdtlpdtrp0(xe,X0),X1) )
& aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0)) ) )
& szDzozmdt0(xe) = szNzAzT0
& aFunction0(xe) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4660) ).
fof(f95,axiom,
( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [X0] :
( aElementOf0(X0,xO)
<=> ? [X1] :
( sdtlpdtrp0(xe,X1) = X0
& aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
& ! [X0] :
( aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
<=> ( sdtlpdtrp0(xd,X0) = szDzizrdt0(xd)
& aElementOf0(X0,szDzozmdt0(xd)) ) )
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aSet0(xO) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4891) ).
fof(f97,axiom,
! [X0] :
( ( aElementOf0(X0,xO)
| ? [X1] :
( sdtlpdtrp0(xe,X1) = X0
& aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
=> ? [X1] :
( sdtlpdtrp0(xe,X1) = X0
& aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xd,X1) = szDzizrdt0(xd)
& aElementOf0(X1,szNzAzT0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4982) ).
fof(f98,conjecture,
( aSubsetOf0(xO,xS)
| ! [X0] :
( aElementOf0(X0,xO)
=> aElementOf0(X0,xS) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f99,negated_conjecture,
~ ( aSubsetOf0(xO,xS)
| ! [X0] :
( aElementOf0(X0,xO)
=> aElementOf0(X0,xS) ) ),
inference(negated_conjecture,[status(cth)],[f98]) ).
fof(f117,plain,
( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [X1] :
( aElementOf0(X1,xO)
<=> ? [X2] :
( sdtlpdtrp0(xe,X2) = X1
& aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
& ! [X0] :
( aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
<=> ( sdtlpdtrp0(xd,X0) = szDzizrdt0(xd)
& aElementOf0(X0,szDzozmdt0(xd)) ) )
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aSet0(xO) ),
inference(rectify,[],[f95]) ).
fof(f118,plain,
! [X0] :
( ( aElementOf0(X0,xO)
| ? [X1] :
( sdtlpdtrp0(xe,X1) = X0
& aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
=> ? [X2] :
( sdtlpdtrp0(xe,X2) = X0
& aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& szDzizrdt0(xd) = sdtlpdtrp0(xd,X2)
& aElementOf0(X2,szNzAzT0) ) ),
inference(rectify,[],[f97]) ).
fof(f125,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f154,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(sz00,X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f225,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ( isCountable0(sdtlpdtrp0(xN,X0))
& aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ! [X1] :
( ~ aElementOf0(X1,sdtlpdtrp0(xN,X0))
| aElementOf0(X1,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X0)) ) ),
inference(ennf_transformation,[],[f82]) ).
fof(f226,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
& ! [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
| aElementOf0(X2,sdtlpdtrp0(xN,X1)) ) ) ),
inference(ennf_transformation,[],[f83]) ).
fof(f227,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
& ! [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
| aElementOf0(X2,sdtlpdtrp0(xN,X1)) ) ) ),
inference(flattening,[],[f226]) ).
fof(f241,plain,
( ! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ( sdtlpdtrp0(xe,X0) = szmzizndt0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( ~ aElementOf0(X1,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(sdtlpdtrp0(xe,X0),X1) )
& aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0)) ) )
& szDzozmdt0(xe) = szNzAzT0
& aFunction0(xe) ),
inference(ennf_transformation,[],[f91]) ).
fof(f245,plain,
! [X0] :
( ( ~ aElementOf0(X0,xO)
& ! [X1] :
( sdtlpdtrp0(xe,X1) != X0
| ~ aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
| ? [X2] :
( sdtlpdtrp0(xe,X2) = X0
& aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& szDzizrdt0(xd) = sdtlpdtrp0(xd,X2)
& aElementOf0(X2,szNzAzT0) ) ),
inference(ennf_transformation,[],[f118]) ).
fof(f246,plain,
( ~ aSubsetOf0(xO,xS)
& ? [X0] :
( aElementOf0(X0,xO)
& ~ aElementOf0(X0,xS) ) ),
inference(ennf_transformation,[],[f99]) ).
fof(f284,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,[],[f125]) ).
fof(f285,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,[],[f284]) ).
fof(f286,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,[],[f285]) ).
fof(f287,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X3] :
( ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aSet0(X1) ) )
& ( ( aElementOf0(sK26(X0,X1),X1)
& ~ aElementOf0(sK26(X0,X1),X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(X2,sK26(X0,X1))],[f286]) ).
fof(f360,plain,
( ! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ( ( aElementOf0(sK54(X0),sdtlpdtrp0(xN,X0))
& ~ aElementOf0(sK54(X0),szNzAzT0) )
| ~ aSet0(sdtlpdtrp0(xN,X0)) ) )
| sP9(X0) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(X1,sK54(X0))],[f260]) ).
fof(f421,plain,
( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [X1] :
( ( ~ aElementOf0(X1,xO)
| ? [X2] :
( sdtlpdtrp0(xe,X2) = X1
& aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
& ( ! [X2] :
( sdtlpdtrp0(xe,X2) != X1
| ~ aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| aElementOf0(X1,xO) ) )
& ! [X0] :
( ( ~ aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xd,X0) = szDzizrdt0(xd)
& aElementOf0(X0,szDzozmdt0(xd)) ) )
& ( sdtlpdtrp0(xd,X0) != szDzizrdt0(xd)
| ~ aElementOf0(X0,szDzozmdt0(xd))
| aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aSet0(xO) ),
inference(nnf_transformation,[],[f117]) ).
fof(f422,plain,
( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [X1] :
( ( ~ aElementOf0(X1,xO)
| ? [X2] :
( sdtlpdtrp0(xe,X2) = X1
& aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
& ( ! [X2] :
( sdtlpdtrp0(xe,X2) != X1
| ~ aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| aElementOf0(X1,xO) ) )
& ! [X0] :
( ( ~ aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xd,X0) = szDzizrdt0(xd)
& aElementOf0(X0,szDzozmdt0(xd)) ) )
& ( sdtlpdtrp0(xd,X0) != szDzizrdt0(xd)
| ~ aElementOf0(X0,szDzozmdt0(xd))
| aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aSet0(xO) ),
inference(flattening,[],[f421]) ).
fof(f423,plain,
( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [X1] :
( ( ~ aElementOf0(X1,xO)
| ? [X3] :
( sdtlpdtrp0(xe,X3) = X1
& aElementOf0(X3,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
& ( ! [X2] :
( sdtlpdtrp0(xe,X2) != X1
| ~ aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| aElementOf0(X1,xO) ) )
& ! [X0] :
( ( ~ aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xd,X0) = szDzizrdt0(xd)
& aElementOf0(X0,szDzozmdt0(xd)) ) )
& ( sdtlpdtrp0(xd,X0) != szDzizrdt0(xd)
| ~ aElementOf0(X0,szDzozmdt0(xd))
| aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aSet0(xO) ),
inference(rectify,[],[f422]) ).
fof(f424,plain,
( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [X1] :
( ( ~ aElementOf0(X1,xO)
| ( sdtlpdtrp0(xe,sK69(X1)) = X1
& aElementOf0(sK69(X1),sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
& ( ! [X2] :
( sdtlpdtrp0(xe,X2) != X1
| ~ aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| aElementOf0(X1,xO) ) )
& ! [X0] :
( ( ~ aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xd,X0) = szDzizrdt0(xd)
& aElementOf0(X0,szDzozmdt0(xd)) ) )
& ( sdtlpdtrp0(xd,X0) != szDzizrdt0(xd)
| ~ aElementOf0(X0,szDzozmdt0(xd))
| aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aSet0(xO) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(X3,sK69(X1))],[f423]) ).
fof(f425,plain,
! [X0] :
( ( ~ aElementOf0(X0,xO)
& ! [X2] :
( sdtlpdtrp0(xe,X2) != X0
| ~ aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
| ? [X1] :
( sdtlpdtrp0(xe,X1) = X0
& aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xd,X1) = szDzizrdt0(xd)
& aElementOf0(X1,szNzAzT0) ) ),
inference(rectify,[],[f245]) ).
fof(f426,plain,
! [X0] :
( ( ~ aElementOf0(X0,xO)
& ! [X2] :
( sdtlpdtrp0(xe,X2) != X0
| ~ aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
| ( sdtlpdtrp0(xe,sK70(X0)) = X0
& aElementOf0(sK70(X0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
& szDzizrdt0(xd) = sdtlpdtrp0(xd,sK70(X0))
& aElementOf0(sK70(X0),szNzAzT0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(X1,sK70(X0))],[f425]) ).
fof(f427,plain,
( ~ aSubsetOf0(xO,xS)
& aElementOf0(sK71,xO)
& ~ aElementOf0(sK71,xS) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(X0,sK71)],[f246]) ).
fof(f435,plain,
! [X3,X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) ),
inference(cnf_transformation,[],[f287]) ).
fof(f475,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[],[f24]) ).
fof(f482,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(sz00,X0) ),
inference(cnf_transformation,[],[f154]) ).
fof(f643,plain,
xS = sdtlpdtrp0(xN,sz00),
inference(cnf_transformation,[],[f360]) ).
fof(f649,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aSet0(sdtlpdtrp0(xN,X0)) ),
inference(cnf_transformation,[],[f225]) ).
fof(f650,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1)) ),
inference(cnf_transformation,[],[f227]) ).
fof(f779,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0)) ),
inference(cnf_transformation,[],[f241]) ).
fof(f800,plain,
! [X1] :
( ~ aElementOf0(X1,xO)
| sdtlpdtrp0(xe,sK69(X1)) = X1 ),
inference(cnf_transformation,[],[f424]) ).
fof(f801,plain,
! [X1] :
( ~ aElementOf0(X1,xO)
| aElementOf0(sK69(X1),sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(cnf_transformation,[],[f424]) ).
fof(f810,plain,
! [X0] :
( ~ aElementOf0(X0,xO)
| sdtlpdtrp0(xe,sK70(X0)) = X0 ),
inference(cnf_transformation,[],[f426]) ).
fof(f817,plain,
! [X2,X0] :
( sdtlpdtrp0(xe,X2) != X0
| ~ aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(sK70(X0),szNzAzT0) ),
inference(cnf_transformation,[],[f426]) ).
fof(f819,plain,
aElementOf0(sK71,xO),
inference(cnf_transformation,[],[f427]) ).
fof(f820,plain,
~ aElementOf0(sK71,xS),
inference(cnf_transformation,[],[f427]) ).
fof(f875,plain,
! [X2] :
( ~ aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(sK70(sdtlpdtrp0(xe,X2)),szNzAzT0) ),
inference(equality_resolution,[],[f817]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,X2)
| ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f435]) ).
tcf(c_96,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[],[f475]) ).
tcf(c_103,plain,
! [X0: $i] :
( sdtlseqdt0(sz00,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f482]) ).
tcf(c_263,plain,
sdtlpdtrp0(xN,sz00) = xS,
inference(cnf_transformation,[],[f643]) ).
tcf(c_267,plain,
! [X0: $i] :
( aSet0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f649]) ).
tcf(c_272,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,X1),sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f650]) ).
tcf(c_400,plain,
! [X0: $i] :
( aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f779]) ).
tcf(c_426,plain,
! [X0: $i] :
( aElementOf0(sK69(X0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aElementOf0(X0,xO) ),
inference(cnf_transformation,[],[f801]) ).
tcf(c_427,plain,
! [X0: $i] :
( ( sdtlpdtrp0(xe,sK69(X0)) = X0 )
| ~ aElementOf0(X0,xO) ),
inference(cnf_transformation,[],[f800]) ).
tcf(c_431,plain,
! [X0: $i] :
( aElementOf0(sK70(sdtlpdtrp0(xe,X0)),szNzAzT0)
| ~ aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(cnf_transformation,[],[f875]) ).
tcf(c_438,plain,
! [X0: $i] :
( ( sdtlpdtrp0(xe,sK70(X0)) = X0 )
| ~ aElementOf0(X0,xO) ),
inference(cnf_transformation,[],[f810]) ).
tcf(c_439,negated_conjecture,
~ aElementOf0(sK71,xS),
inference(cnf_transformation,[],[f820]) ).
tcf(c_440,negated_conjecture,
aElementOf0(sK71,xO),
inference(cnf_transformation,[],[f819]) ).
tcf(c_26010,negated_conjecture,
aElementOf0(sK71,xO),
inference(demodulation,[status(thm)],[c_440]) ).
tcf(c_26011,negated_conjecture,
~ aElementOf0(sK71,xS),
inference(demodulation,[status(thm)],[c_439]) ).
tcf(c_32156,plain,
sdtlpdtrp0(xe,sK69(sK71)) = sK71,
inference(superposition,[status(thm)],[c_26010,c_427]) ).
tcf(c_32171,plain,
sdtlpdtrp0(xe,sK70(sK71)) = sK71,
inference(superposition,[status(thm)],[c_26010,c_438]) ).
tcf(c_32220,plain,
( aElementOf0(sK71,sdtlpdtrp0(xN,sK70(sK71)))
| ~ aElementOf0(sK70(sK71),szNzAzT0) ),
inference(superposition,[status(thm)],[c_32171,c_400]) ).
tcf(c_34350,plain,
! [X0: $i] :
( aElementOf0(sK70(sdtlpdtrp0(xe,sK69(X0))),szNzAzT0)
| ~ aElementOf0(X0,xO) ),
inference(superposition,[status(thm)],[c_426,c_431]) ).
tcf(c_34539,plain,
( aElementOf0(sK70(sK71),szNzAzT0)
| ~ aElementOf0(sK71,xO) ),
inference(superposition,[status(thm)],[c_32156,c_34350]) ).
tcf(c_34551,plain,
aElementOf0(sK70(sK71),szNzAzT0),
inference(forward_subsumption_resolution,[status(thm)],[c_34539,c_26010]) ).
tcf(c_34575,plain,
aElementOf0(sK71,sdtlpdtrp0(xN,sK70(sK71))),
inference(backward_subsumption_resolution,[status(thm)],[c_32220,c_34551]) ).
tcf(c_35434,plain,
sdtlseqdt0(sz00,sK70(sK71)),
inference(superposition,[status(thm)],[c_34551,c_103]) ).
tcf(c_35481,plain,
! [X0: $i] :
( aElementOf0(sK71,X0)
| ~ aSet0(X0)
| ~ aSubsetOf0(sdtlpdtrp0(xN,sK70(sK71)),X0) ),
inference(superposition,[status(thm)],[c_34575,c_59]) ).
tcf(c_47623,plain,
! [X0: $i] :
( aElementOf0(sK71,sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(sK70(sK71),szNzAzT0)
| ~ sdtlseqdt0(X0,sK70(sK71))
| ~ aSet0(sdtlpdtrp0(xN,X0)) ),
inference(superposition,[status(thm)],[c_272,c_35481]) ).
tcf(c_47637,plain,
! [X0: $i] :
( aElementOf0(sK71,sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X0,sK70(sK71))
| ~ aSet0(sdtlpdtrp0(xN,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_47623,c_34551]) ).
tcf(c_48173,plain,
! [X0: $i] :
( aElementOf0(sK71,sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X0,sK70(sK71)) ),
inference(global_subsumption_just,[status(thm)],[c_47637,c_267,c_47637]) ).
tcf(c_48182,plain,
( aElementOf0(sK71,xS)
| ~ aElementOf0(sz00,szNzAzT0)
| ~ sdtlseqdt0(sz00,sK70(sK71)) ),
inference(superposition,[status(thm)],[c_263,c_48173]) ).
tcf(c_48196,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_48182,c_26011,c_96,c_35434]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM601+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/5.39 % Computer : n008.cluster.edu
% 0.13/5.39 % Model : x86_64 x86_64
% 0.13/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.39 % Memory : 8046.5625MB
% 0.13/5.39 % OS : Linux 6.8.0-71-generic
% 0.13/5.39 % CPULimit : 300
% 0.13/5.39 % WCLimit : 300
% 0.13/5.39 % DateTime : Thu Sep 24 04:52:23 UTC 2026
% 0.17/5.40 % CPUTime :
% 0.17/5.40 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.17/5.46 Running first-order theorem proving
% 0.17/5.46 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
% 0.17/5.48
% 0.17/5.48 % ======== iProver multi-core TPTP/SMT =========
% 0.17/5.48
% 0.17/5.48 % Detected problem language: tptp
% 0.17/5.50 % Proving...
% 19.19/9.48 % SZS status Started for theBenchmark.p
% 19.19/9.48 % SZS status Theorem for theBenchmark.p
% 19.19/9.48
% 19.19/9.48 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 19.19/9.48
% 19.19/9.48 % ------ iProver source info
% 19.19/9.48
% 19.19/9.48 % git: date: 2026-07-19 20:42:38 +0200
% 19.19/9.48 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 19.19/9.48 % git: non_committed_changes: false
% 19.19/9.48
% 19.19/9.48 % ------ Parsing...
% 19.19/9.48 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 19.19/9.48
% 19.19/9.48 % ------ Preprocessing... sup_sim: 9 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 19.19/9.48
% 19.19/9.48 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 19.19/9.48
% 19.19/9.48 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 19.19/9.48 % ------ Proving...
% 19.19/9.48 % ------ Problem Properties
% 19.19/9.48
% 19.19/9.48 %
% 19.19/9.48 % clauses 354
% 19.19/9.48 % conjectures 3
% 19.19/9.48 % EPR 56
% 19.19/9.48 % Horn 280
% 19.19/9.48 % unary 41
% 19.19/9.48 % binary 95
% 19.19/9.48 % lits 1145
% 19.19/9.48 % lits eq 164
% 19.19/9.48 % fd_pure 0
% 19.19/9.48 % fd_pseudo 0
% 19.19/9.48 % fd_cond 10
% 19.19/9.48 % fd_pseudo_cond 39
% 19.19/9.48 % AC symbols 0
% 19.19/9.48
% 19.19/9.48 % ------ Schedule dynamic 5 is on
% 19.19/9.48
% 19.19/9.48 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 19.19/9.48
% 19.19/9.48
% 19.19/9.48 % ------
% 19.19/9.48 % Current options:
% 19.19/9.48 % ------
% 19.19/9.48
% 19.19/9.48
% 19.19/9.48 %
% 19.19/9.48
% 19.19/9.48 % ------ Proving...
% 19.19/9.48 %
% 19.19/9.48
% 19.19/9.48 % SZS status Theorem for theBenchmark.p
% 19.19/9.48
% 19.19/9.48 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 19.19/9.49
% 19.19/9.49
%------------------------------------------------------------------------------