%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM543+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 : 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 : Fri Sep 25 02:25:57 PM UTC 2026
% Result : Theorem 85.21s 12.51s
% Output : CNFRefutation 85.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 111 ( 16 unt; 0 def)
% Number of atoms : 475 ( 65 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 617 ( 253 ~; 265 |; 77 &)
% ( 14 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 167 ( 0 sgn 152 !; 15 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( X0 = slcrc0
<=> ( ~ ? [X1] : aElementOf0(X1,X0)
& aSet0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
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(f12,axiom,
! [X0] :
( aSet0(X0)
=> aSubsetOf0(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubRefl) ).
fof(f23,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
fof(f24,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNum) ).
fof(f25,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( szszuzczcdt0(X0) != sz00
& aElementOf0(szszuzczcdt0(X0),szNzAzT0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNum) ).
fof(f32,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( sdtlseqdt0(X0,X1)
<=> sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccLess) ).
fof(f48,axiom,
! [X0] :
( ( X0 != slcrc0
& isFinite0(X0)
& aSubsetOf0(X0,szNzAzT0) )
=> ! [X1] :
( X1 = szmzazxdt0(X0)
<=> ( ! [X2] :
( aElementOf0(X2,X0)
=> sdtlseqdt0(X2,X1) )
& aElementOf0(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefMax) ).
fof(f50,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( X1 = slbdtrb0(X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
<=> ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSeg) ).
fof(f52,axiom,
slbdtrb0(sz00) = slcrc0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSegZero) ).
fof(f55,axiom,
( isFinite0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1986) ).
fof(f56,conjecture,
? [X0] :
( aSubsetOf0(xS,slbdtrb0(X0))
& aElementOf0(X0,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f57,negated_conjecture,
~ ? [X0] :
( aSubsetOf0(xS,slbdtrb0(X0))
& aElementOf0(X0,szNzAzT0) ),
inference(negated_conjecture,[status(cth)],[f56]) ).
fof(f66,plain,
! [X0] :
( X0 = slcrc0
<=> ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f71,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f74,plain,
! [X0] :
( ~ aSet0(X0)
| aSubsetOf0(X0,X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f94,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ( szszuzczcdt0(X0) != sz00
& aElementOf0(szszuzczcdt0(X0),szNzAzT0) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f102,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ( sdtlseqdt0(X0,X1)
<=> sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1)) ) ),
inference(ennf_transformation,[],[f32]) ).
fof(f103,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ( sdtlseqdt0(X0,X1)
<=> sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1)) ) ),
inference(flattening,[],[f102]) ).
fof(f125,plain,
! [X0] :
( slcrc0 = X0
| ~ isFinite0(X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| ! [X1] :
( X1 = szmzazxdt0(X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X0)
| sdtlseqdt0(X2,X1) )
& aElementOf0(X1,X0) ) ) ),
inference(ennf_transformation,[],[f48]) ).
fof(f126,plain,
! [X0] :
( slcrc0 = X0
| ~ isFinite0(X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| ! [X1] :
( X1 = szmzazxdt0(X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X0)
| sdtlseqdt0(X2,X1) )
& aElementOf0(X1,X0) ) ) ),
inference(flattening,[],[f125]) ).
fof(f129,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ! [X1] :
( X1 = slbdtrb0(X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
<=> ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f50]) ).
fof(f135,plain,
! [X0] :
( ~ aSubsetOf0(xS,slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f142,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(nnf_transformation,[],[f66]) ).
fof(f143,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(flattening,[],[f142]) ).
fof(f144,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(rectify,[],[f143]) ).
fof(f145,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) ) )
& ( aElementOf0(sK4(X0),X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f144]) ).
fof(f146,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,[],[f71]) ).
fof(f147,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,[],[f146]) ).
fof(f148,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,[],[f147]) ).
fof(f149,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X3] :
( ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aSet0(X1) ) )
& ( ( aElementOf0(sK5(X0,X1),X1)
& ~ aElementOf0(sK5(X0,X1),X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f148]) ).
fof(f163,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ( ( ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1)) )
& ( ~ sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1))
| sdtlseqdt0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f103]) ).
fof(f171,plain,
! [X0] :
( slcrc0 = X0
| ~ isFinite0(X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| ! [X1] :
( ( szmzazxdt0(X0) != X1
| ( ! [X2] :
( ~ aElementOf0(X2,X0)
| sdtlseqdt0(X2,X1) )
& aElementOf0(X1,X0) ) )
& ( ? [X2] :
( aElementOf0(X2,X0)
& ~ sdtlseqdt0(X2,X1) )
| ~ aElementOf0(X1,X0)
| X1 = szmzazxdt0(X0) ) ) ),
inference(nnf_transformation,[],[f126]) ).
fof(f172,plain,
! [X0] :
( slcrc0 = X0
| ~ isFinite0(X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| ! [X1] :
( ( szmzazxdt0(X0) != X1
| ( ! [X2] :
( ~ aElementOf0(X2,X0)
| sdtlseqdt0(X2,X1) )
& aElementOf0(X1,X0) ) )
& ( ? [X2] :
( aElementOf0(X2,X0)
& ~ sdtlseqdt0(X2,X1) )
| ~ aElementOf0(X1,X0)
| X1 = szmzazxdt0(X0) ) ) ),
inference(flattening,[],[f171]) ).
fof(f173,plain,
! [X0] :
( slcrc0 = X0
| ~ isFinite0(X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| ! [X1] :
( ( szmzazxdt0(X0) != X1
| ( ! [X3] :
( ~ aElementOf0(X3,X0)
| sdtlseqdt0(X3,X1) )
& aElementOf0(X1,X0) ) )
& ( ? [X2] :
( aElementOf0(X2,X0)
& ~ sdtlseqdt0(X2,X1) )
| ~ aElementOf0(X1,X0)
| X1 = szmzazxdt0(X0) ) ) ),
inference(rectify,[],[f172]) ).
fof(f174,plain,
! [X0] :
( slcrc0 = X0
| ~ isFinite0(X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| ! [X1] :
( ( szmzazxdt0(X0) != X1
| ( ! [X3] :
( ~ aElementOf0(X3,X0)
| sdtlseqdt0(X3,X1) )
& aElementOf0(X1,X0) ) )
& ( ( aElementOf0(sK11(X0,X1),X0)
& ~ sdtlseqdt0(sK11(X0,X1),X1) )
| ~ aElementOf0(X1,X0)
| X1 = szmzazxdt0(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X2,sK11(X0,X1))],[f173]) ).
fof(f175,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ! [X1] :
( ( slbdtrb0(X0) != X1
| ( ! [X2] :
( ( ~ aElementOf0(X2,X1)
| ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& ( ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,szNzAzT0)
| aElementOf0(X2,X1) ) )
& aSet0(X1) ) )
& ( ? [X2] :
( ( aElementOf0(X2,X1)
| ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& ( ~ aElementOf0(X2,X1)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,szNzAzT0) ) )
| ~ aSet0(X1)
| X1 = slbdtrb0(X0) ) ) ),
inference(nnf_transformation,[],[f129]) ).
fof(f176,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ! [X1] :
( ( slbdtrb0(X0) != X1
| ( ! [X2] :
( ( ~ aElementOf0(X2,X1)
| ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& ( ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,szNzAzT0)
| aElementOf0(X2,X1) ) )
& aSet0(X1) ) )
& ( ? [X2] :
( ( aElementOf0(X2,X1)
| ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& ( ~ aElementOf0(X2,X1)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,szNzAzT0) ) )
| ~ aSet0(X1)
| X1 = slbdtrb0(X0) ) ) ),
inference(flattening,[],[f175]) ).
fof(f177,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ! [X1] :
( ( slbdtrb0(X0) != X1
| ( ! [X3] :
( ( ~ aElementOf0(X3,X1)
| ( sdtlseqdt0(szszuzczcdt0(X3),X0)
& aElementOf0(X3,szNzAzT0) ) )
& ( ~ sdtlseqdt0(szszuzczcdt0(X3),X0)
| ~ aElementOf0(X3,szNzAzT0)
| aElementOf0(X3,X1) ) )
& aSet0(X1) ) )
& ( ? [X2] :
( ( aElementOf0(X2,X1)
| ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& ( ~ aElementOf0(X2,X1)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,szNzAzT0) ) )
| ~ aSet0(X1)
| X1 = slbdtrb0(X0) ) ) ),
inference(rectify,[],[f176]) ).
fof(f178,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ! [X1] :
( ( slbdtrb0(X0) != X1
| ( ! [X3] :
( ( ~ aElementOf0(X3,X1)
| ( sdtlseqdt0(szszuzczcdt0(X3),X0)
& aElementOf0(X3,szNzAzT0) ) )
& ( ~ sdtlseqdt0(szszuzczcdt0(X3),X0)
| ~ aElementOf0(X3,szNzAzT0)
| aElementOf0(X3,X1) ) )
& aSet0(X1) ) )
& ( ( ( aElementOf0(sK12(X0,X1),X1)
| ( sdtlseqdt0(szszuzczcdt0(sK12(X0,X1)),X0)
& aElementOf0(sK12(X0,X1),szNzAzT0) ) )
& ( ~ aElementOf0(sK12(X0,X1),X1)
| ~ sdtlseqdt0(szszuzczcdt0(sK12(X0,X1)),X0)
| ~ aElementOf0(sK12(X0,X1),szNzAzT0) ) )
| ~ aSet0(X1)
| X1 = slbdtrb0(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X2,sK12(X0,X1))],[f177]) ).
fof(f184,plain,
! [X0] :
( slcrc0 != X0
| aSet0(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f189,plain,
! [X3,X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f190,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| aSet0(X1) ),
inference(cnf_transformation,[],[f149]) ).
fof(f191,plain,
! [X0,X1] :
( ~ aSet0(X0)
| aElementOf0(sK5(X0,X1),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f192,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(sK5(X0,X1),X0)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f194,plain,
! [X0] :
( ~ aSet0(X0)
| aSubsetOf0(X0,X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f228,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f229,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[],[f24]) ).
fof(f231,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(szszuzczcdt0(X0),szNzAzT0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f238,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1)) ),
inference(cnf_transformation,[],[f163]) ).
fof(f259,plain,
! [X3,X0,X1] :
( slcrc0 = X0
| ~ isFinite0(X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| szmzazxdt0(X0) != X1
| ~ aElementOf0(X3,X0)
| sdtlseqdt0(X3,X1) ),
inference(cnf_transformation,[],[f174]) ).
fof(f260,plain,
! [X0,X1] :
( slcrc0 = X0
| ~ isFinite0(X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| szmzazxdt0(X0) != X1
| aElementOf0(X1,X0) ),
inference(cnf_transformation,[],[f174]) ).
fof(f266,plain,
! [X3,X0,X1] :
( ~ aElementOf0(X0,szNzAzT0)
| slbdtrb0(X0) != X1
| ~ sdtlseqdt0(szszuzczcdt0(X3),X0)
| ~ aElementOf0(X3,szNzAzT0)
| aElementOf0(X3,X1) ),
inference(cnf_transformation,[],[f178]) ).
fof(f267,plain,
! [X0,X1] :
( ~ aElementOf0(X0,szNzAzT0)
| slbdtrb0(X0) != X1
| aSet0(X1) ),
inference(cnf_transformation,[],[f178]) ).
fof(f272,plain,
slcrc0 = slbdtrb0(sz00),
inference(cnf_transformation,[],[f52]) ).
fof(f278,plain,
isFinite0(xS),
inference(cnf_transformation,[],[f55]) ).
fof(f279,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[],[f55]) ).
fof(f280,plain,
! [X0] :
( ~ aSubsetOf0(xS,slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f281,plain,
aSet0(slcrc0),
inference(equality_resolution,[],[f184]) ).
fof(f291,plain,
! [X0] :
( slcrc0 = X0
| ~ isFinite0(X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| aElementOf0(szmzazxdt0(X0),X0) ),
inference(equality_resolution,[],[f260]) ).
fof(f292,plain,
! [X3,X0] :
( slcrc0 = X0
| ~ isFinite0(X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ aElementOf0(X3,X0)
| sdtlseqdt0(X3,szmzazxdt0(X0)) ),
inference(equality_resolution,[],[f259]) ).
fof(f293,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aSet0(slbdtrb0(X0)) ),
inference(equality_resolution,[],[f267]) ).
fof(f294,plain,
! [X3,X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X3),X0)
| ~ aElementOf0(X3,szNzAzT0)
| aElementOf0(X3,slbdtrb0(X0)) ),
inference(equality_resolution,[],[f266]) ).
tcf(c_51,plain,
aSet0(slcrc0),
inference(cnf_transformation,[],[f281]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aElementOf0(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f192]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(X0,X1)
| aElementOf0(sK5(X1,X0),X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f191]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( aSet0(X0)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f190]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,X2)
| ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_61,plain,
! [X0: $i] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f194]) ).
tcf(c_94,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f228]) ).
tcf(c_96,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[],[f229]) ).
tcf(c_97,plain,
! [X0: $i] :
( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f231]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f238]) ).
tcf(c_128,plain,
! [X0: $i] :
( aElementOf0(szmzazxdt0(X0),X0)
| ( X0 = slcrc0 )
| ~ isFinite0(X0)
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f291]) ).
tcf(c_129,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,szmzazxdt0(X1))
| ( X1 = slcrc0 )
| ~ isFinite0(X1)
| ~ aSubsetOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f292]) ).
tcf(c_134,plain,
! [X0: $i] :
( aSet0(slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f293]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,slbdtrb0(X1))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X0),X1) ),
inference(cnf_transformation,[],[f294]) ).
tcf(c_139,plain,
slbdtrb0(sz00) = slcrc0,
inference(cnf_transformation,[],[f272]) ).
tcf(c_145,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[],[f279]) ).
tcf(c_146,plain,
isFinite0(xS),
inference(cnf_transformation,[],[f278]) ).
tcf(c_147,negated_conjecture,
! [X0: $i] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ aSubsetOf0(xS,slbdtrb0(X0)) ),
inference(cnf_transformation,[],[f280]) ).
tcf(c_8268,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_9766,plain,
( ~ aElementOf0(sz00,szNzAzT0)
| ~ aSubsetOf0(xS,slbdtrb0(sz00)) ),
inference(instantiation,[status(thm)],[c_147]) ).
tcf(c_9935,plain,
( aSet0(xS)
| ~ aSet0(szNzAzT0) ),
inference(superposition,[status(thm)],[c_145,c_58]) ).
tcf(c_9936,plain,
aSet0(xS),
inference(forward_subsumption_resolution,[status(thm)],[c_9935,c_94]) ).
tcf(c_9945,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(xS,slbdtrb0(sz00))
| ~ aSubsetOf0(X1,X0)
| ( xS != X1 )
| ( slbdtrb0(sz00) != X0 ) ),
inference(instantiation,[status(thm)],[c_8268]) ).
tcf(c_11094,plain,
( aSubsetOf0(slcrc0,slcrc0)
| ~ aSet0(slcrc0) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_12305,plain,
! [X0: $i] :
( aSubsetOf0(xS,slbdtrb0(sz00))
| ~ aSubsetOf0(slcrc0,X0)
| ( xS != slcrc0 )
| ( slbdtrb0(sz00) != X0 ) ),
inference(instantiation,[status(thm)],[c_9945]) ).
tcf(c_13995,plain,
! [X0: $i] :
( aElementOf0(X0,szNzAzT0)
| ~ aSet0(szNzAzT0)
| ~ aElementOf0(X0,xS) ),
inference(resolution,[status(thm)],[c_59,c_145]) ).
tcf(c_14136,plain,
! [X0: $i] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xS) ),
inference(global_subsumption_just,[status(thm)],[c_13995,c_94,c_13995]) ).
tcf(c_15009,plain,
( aElementOf0(szmzazxdt0(xS),szNzAzT0)
| ( xS = slcrc0 )
| ~ isFinite0(xS)
| ~ aSubsetOf0(xS,szNzAzT0) ),
inference(resolution,[status(thm)],[c_128,c_14136]) ).
tcf(c_21182,plain,
( aSubsetOf0(xS,slbdtrb0(sz00))
| ~ aSubsetOf0(slcrc0,slcrc0)
| ( xS != slcrc0 )
| ( slbdtrb0(sz00) != slcrc0 ) ),
inference(instantiation,[status(thm)],[c_12305]) ).
tcf(c_72024,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,slbdtrb0(szszuzczcdt0(X1)))
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(X1),szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1)) ),
inference(instantiation,[status(thm)],[c_135]) ).
tcf(c_72031,plain,
! [X0: $i] :
( aSubsetOf0(xS,slbdtrb0(X0))
| ~ aSet0(xS)
| ~ aSet0(slbdtrb0(X0))
| ~ aElementOf0(sK5(slbdtrb0(X0),xS),slbdtrb0(X0)) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_72032,plain,
! [X0: $i] :
( aSubsetOf0(xS,slbdtrb0(X0))
| aElementOf0(sK5(slbdtrb0(X0),xS),xS)
| ~ aSet0(xS)
| ~ aSet0(slbdtrb0(X0)) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_72169,plain,
! [X0: $i] :
( sdtlseqdt0(X0,szmzazxdt0(xS))
| ( xS = slcrc0 )
| ~ isFinite0(xS)
| ~ aSubsetOf0(xS,szNzAzT0)
| ~ aElementOf0(X0,xS) ),
inference(instantiation,[status(thm)],[c_129]) ).
tcf(c_72276,plain,
! [X0: $i] :
( aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(X0)))
| ~ aSet0(xS)
| ~ aSet0(slbdtrb0(szszuzczcdt0(X0)))
| ~ aElementOf0(sK5(slbdtrb0(szszuzczcdt0(X0)),xS),slbdtrb0(szszuzczcdt0(X0))) ),
inference(instantiation,[status(thm)],[c_72031]) ).
tcf(c_73458,plain,
! [X0: $i] :
( aElementOf0(sK5(slbdtrb0(szszuzczcdt0(X0)),xS),slbdtrb0(szszuzczcdt0(X0)))
| ~ aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(sK5(slbdtrb0(szszuzczcdt0(X0)),xS),szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(sK5(slbdtrb0(szszuzczcdt0(X0)),xS)),szszuzczcdt0(X0)) ),
inference(instantiation,[status(thm)],[c_72024]) ).
tcf(c_77472,plain,
! [X0: $i] :
( sdtlseqdt0(szszuzczcdt0(sK5(slbdtrb0(szszuzczcdt0(X0)),xS)),szszuzczcdt0(X0))
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(sK5(slbdtrb0(szszuzczcdt0(X0)),xS),szNzAzT0)
| ~ sdtlseqdt0(sK5(slbdtrb0(szszuzczcdt0(X0)),xS),X0) ),
inference(instantiation,[status(thm)],[c_106]) ).
tcf(c_81475,plain,
( aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| aElementOf0(sK5(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))),xS),xS)
| ~ aSet0(xS)
| ~ aSet0(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) ),
inference(instantiation,[status(thm)],[c_72032]) ).
tcf(c_81486,plain,
( aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0)
| ~ aElementOf0(szmzazxdt0(xS),szNzAzT0) ),
inference(instantiation,[status(thm)],[c_97]) ).
tcf(c_81645,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sK5(slbdtrb0(X0),xS),X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X1)
| ~ aElementOf0(sK5(slbdtrb0(X0),xS),xS) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_83326,plain,
( sdtlseqdt0(szszuzczcdt0(sK5(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))),xS)),szszuzczcdt0(szmzazxdt0(xS)))
| ~ aElementOf0(szmzazxdt0(xS),szNzAzT0)
| ~ aElementOf0(sK5(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))),xS),szNzAzT0)
| ~ sdtlseqdt0(sK5(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))),xS),szmzazxdt0(xS)) ),
inference(instantiation,[status(thm)],[c_77472]) ).
tcf(c_83327,plain,
( sdtlseqdt0(sK5(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))),xS),szmzazxdt0(xS))
| ( xS = slcrc0 )
| ~ isFinite0(xS)
| ~ aSubsetOf0(xS,szNzAzT0)
| ~ aElementOf0(sK5(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))),xS),xS) ),
inference(instantiation,[status(thm)],[c_72169]) ).
tcf(c_84830,plain,
( aSet0(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| ~ aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0) ),
inference(instantiation,[status(thm)],[c_134]) ).
tcf(c_84905,plain,
! [X0: $i] :
( aElementOf0(sK5(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))),xS),X0)
| ~ aSet0(X0)
| ~ aSubsetOf0(xS,X0)
| ~ aElementOf0(sK5(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))),xS),xS) ),
inference(instantiation,[status(thm)],[c_81645]) ).
tcf(c_84906,plain,
( aElementOf0(sK5(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))),xS),szNzAzT0)
| ~ aSet0(szNzAzT0)
| ~ aSubsetOf0(xS,szNzAzT0)
| ~ aElementOf0(sK5(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))),xS),xS) ),
inference(instantiation,[status(thm)],[c_84905]) ).
tcf(c_89211,plain,
( ~ aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0)
| ~ aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) ),
inference(instantiation,[status(thm)],[c_147]) ).
tcf(c_95190,plain,
( aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| ~ aSet0(xS)
| ~ aSet0(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| ~ aElementOf0(sK5(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))),xS),slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) ),
inference(instantiation,[status(thm)],[c_72276]) ).
tcf(c_104933,plain,
( aElementOf0(sK5(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))),xS),slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| ~ aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0)
| ~ aElementOf0(sK5(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))),xS),szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(sK5(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))),xS)),szszuzczcdt0(szmzazxdt0(xS))) ),
inference(instantiation,[status(thm)],[c_73458]) ).
tcf(c_104934,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_104933,c_95190,c_89211,c_84906,c_84830,c_83327,c_83326,c_81486,c_81475,c_21182,c_15009,c_11094,c_9936,c_9766,c_139,c_96,c_145,c_51,c_94,c_146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM543+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n019.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Sep 24 04:32:35 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 85.21/12.51 % SZS status Started for theBenchmark.p
% 85.21/12.51 % SZS status Theorem for theBenchmark.p
% 85.21/12.51
% 85.21/12.51 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 85.21/12.51
% 85.21/12.51 % ------ iProver source info
% 85.21/12.51
% 85.21/12.51 % git: date: 2026-07-19 20:42:38 +0200
% 85.21/12.51 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 85.21/12.51 % git: non_committed_changes: false
% 85.21/12.51
% 85.21/12.51 % ------ Parsing...
% 85.21/12.51 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 85.21/12.51
% 85.21/12.51 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 85.21/12.51
% 85.21/12.51 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 85.21/12.51
% 85.21/12.51 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 85.21/12.51 % ------ Proving...
% 85.21/12.51 % ------ Problem Properties
% 85.21/12.51
% 85.21/12.51 %
% 85.21/12.51 % clauses 97
% 85.21/12.51 % conjectures 1
% 85.21/12.51 % EPR 31
% 85.21/12.51 % Horn 70
% 85.21/12.51 % unary 11
% 85.21/12.51 % binary 16
% 85.21/12.51 % lits 326
% 85.21/12.51 % lits eq 46
% 85.21/12.51 % fd_pure 0
% 85.21/12.51 % fd_pseudo 0
% 85.21/12.51 % fd_cond 8
% 85.21/12.51 % fd_pseudo_cond 15
% 85.21/12.51 % AC symbols 0
% 85.21/12.51
% 85.21/12.51 % ------ Input Options Time Limit: Unbounded
% 85.21/12.51
% 85.21/12.51
% 85.21/12.51 % ------
% 85.21/12.51 % Current options:
% 85.21/12.51 % ------
% 85.21/12.51
% 85.21/12.51
% 85.21/12.51 %
% 85.21/12.51
% 85.21/12.51 % ------ Proving...
% 85.21/12.51 %
% 85.21/12.51
% 85.21/12.51 % SZS status Theorem for theBenchmark.p
% 85.21/12.51
% 85.21/12.51 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 85.21/12.51
% 85.21/12.51
%------------------------------------------------------------------------------