%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM543+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 134.20s 37.42s
% Output : CNFRefutation 134.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 10
% Syntax : Number of formulae : 91 ( 13 unt; 0 def)
% Number of atoms : 384 ( 53 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 495 ( 202 ~; 188 |; 80 &)
% ( 13 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 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 : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 139 ( 0 sgn 124 !; 15 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( X0 = slcrc0
<=> ( ~ ? [X1] : aElementOf0(X1,X0)
& aSet0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
fof(f12,axiom,
! [X0] :
( aSet0(X0)
=> aSubsetOf0(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).
fof(f24,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
fof(f25,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( szszuzczcdt0(X0) != sz00
& aElementOf0(szszuzczcdt0(X0),szNzAzT0) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mDefMax) ).
fof(f52,axiom,
slbdtrb0(sz00) = slcrc0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSegZero) ).
fof(f55,axiom,
( isFinite0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,szNzAzT0) )
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1986) ).
fof(f56,conjecture,
? [X0] :
( ( ( ! [X1] :
( aElementOf0(X1,slbdtrb0(X0))
<=> ( sdtlseqdt0(szszuzczcdt0(X1),X0)
& aElementOf0(X1,szNzAzT0) ) )
& aSet0(slbdtrb0(X0)) )
=> ( aSubsetOf0(xS,slbdtrb0(X0))
| ! [X1] :
( aElementOf0(X1,xS)
=> aElementOf0(X1,slbdtrb0(X0)) ) ) )
& aElementOf0(X0,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f57,negated_conjecture,
~ ? [X0] :
( ( ( ! [X1] :
( aElementOf0(X1,slbdtrb0(X0))
<=> ( sdtlseqdt0(szszuzczcdt0(X1),X0)
& aElementOf0(X1,szNzAzT0) ) )
& aSet0(slbdtrb0(X0)) )
=> ( aSubsetOf0(xS,slbdtrb0(X0))
| ! [X1] :
( aElementOf0(X1,xS)
=> aElementOf0(X1,slbdtrb0(X0)) ) ) )
& aElementOf0(X0,szNzAzT0) ),
inference(negated_conjecture,[status(cth)],[f56]) ).
fof(f64,plain,
~ ? [X0] :
( ( ( ! [X1] :
( aElementOf0(X1,slbdtrb0(X0))
<=> ( sdtlseqdt0(szszuzczcdt0(X1),X0)
& aElementOf0(X1,szNzAzT0) ) )
& aSet0(slbdtrb0(X0)) )
=> ( aSubsetOf0(xS,slbdtrb0(X0))
| ! [X2] :
( aElementOf0(X2,xS)
=> aElementOf0(X2,slbdtrb0(X0)) ) ) )
& aElementOf0(X0,szNzAzT0) ),
inference(rectify,[],[f57]) ).
fof(f67,plain,
! [X0] :
( X0 = slcrc0
<=> ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f75,plain,
! [X0] :
( ~ aSet0(X0)
| aSubsetOf0(X0,X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f95,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ( szszuzczcdt0(X0) != sz00
& aElementOf0(szszuzczcdt0(X0),szNzAzT0) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f103,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ( sdtlseqdt0(X0,X1)
<=> sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1)) ) ),
inference(ennf_transformation,[],[f32]) ).
fof(f104,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ( sdtlseqdt0(X0,X1)
<=> sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1)) ) ),
inference(flattening,[],[f103]) ).
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(ennf_transformation,[],[f48]) ).
fof(f127,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,[],[f126]) ).
fof(f136,plain,
( isFinite0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [X0] :
( ~ aElementOf0(X0,xS)
| aElementOf0(X0,szNzAzT0) )
& aSet0(xS) ),
inference(ennf_transformation,[],[f55]) ).
fof(f137,plain,
! [X0] :
( ( ! [X1] :
( aElementOf0(X1,slbdtrb0(X0))
<=> ( sdtlseqdt0(szszuzczcdt0(X1),X0)
& aElementOf0(X1,szNzAzT0) ) )
& aSet0(slbdtrb0(X0))
& ~ aSubsetOf0(xS,slbdtrb0(X0))
& ? [X2] :
( aElementOf0(X2,xS)
& ~ aElementOf0(X2,slbdtrb0(X0)) ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f64]) ).
fof(f138,plain,
! [X0] :
( ( ! [X1] :
( aElementOf0(X1,slbdtrb0(X0))
<=> ( sdtlseqdt0(szszuzczcdt0(X1),X0)
& aElementOf0(X1,szNzAzT0) ) )
& aSet0(slbdtrb0(X0))
& ~ aSubsetOf0(xS,slbdtrb0(X0))
& ? [X2] :
( aElementOf0(X2,xS)
& ~ aElementOf0(X2,slbdtrb0(X0)) ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(flattening,[],[f137]) ).
fof(f145,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(nnf_transformation,[],[f67]) ).
fof(f146,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(flattening,[],[f145]) ).
fof(f147,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(rectify,[],[f146]) ).
fof(f148,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))],[f147]) ).
fof(f166,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,[],[f104]) ).
fof(f174,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,[],[f127]) ).
fof(f175,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,[],[f174]) ).
fof(f176,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,[],[f175]) ).
fof(f177,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))],[f176]) ).
fof(f185,plain,
! [X0] :
( ( ! [X1] :
( ( ~ aElementOf0(X1,slbdtrb0(X0))
| ( sdtlseqdt0(szszuzczcdt0(X1),X0)
& aElementOf0(X1,szNzAzT0) ) )
& ( ~ sdtlseqdt0(szszuzczcdt0(X1),X0)
| ~ aElementOf0(X1,szNzAzT0)
| aElementOf0(X1,slbdtrb0(X0)) ) )
& aSet0(slbdtrb0(X0))
& ~ aSubsetOf0(xS,slbdtrb0(X0))
& ? [X2] :
( aElementOf0(X2,xS)
& ~ aElementOf0(X2,slbdtrb0(X0)) ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(nnf_transformation,[],[f138]) ).
fof(f186,plain,
! [X0] :
( ( ! [X1] :
( ( ~ aElementOf0(X1,slbdtrb0(X0))
| ( sdtlseqdt0(szszuzczcdt0(X1),X0)
& aElementOf0(X1,szNzAzT0) ) )
& ( ~ sdtlseqdt0(szszuzczcdt0(X1),X0)
| ~ aElementOf0(X1,szNzAzT0)
| aElementOf0(X1,slbdtrb0(X0)) ) )
& aSet0(slbdtrb0(X0))
& ~ aSubsetOf0(xS,slbdtrb0(X0))
& ? [X2] :
( aElementOf0(X2,xS)
& ~ aElementOf0(X2,slbdtrb0(X0)) ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(flattening,[],[f185]) ).
fof(f187,plain,
! [X0] :
( ( ! [X2] :
( ( ~ aElementOf0(X2,slbdtrb0(X0))
| ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& ( ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,szNzAzT0)
| aElementOf0(X2,slbdtrb0(X0)) ) )
& aSet0(slbdtrb0(X0))
& ~ aSubsetOf0(xS,slbdtrb0(X0))
& ? [X1] :
( aElementOf0(X1,xS)
& ~ aElementOf0(X1,slbdtrb0(X0)) ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(rectify,[],[f186]) ).
fof(f188,plain,
! [X0] :
( ( ! [X2] :
( ( ~ aElementOf0(X2,slbdtrb0(X0))
| ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& ( ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,szNzAzT0)
| aElementOf0(X2,slbdtrb0(X0)) ) )
& aSet0(slbdtrb0(X0))
& ~ aSubsetOf0(xS,slbdtrb0(X0))
& aElementOf0(sK13(X0),xS)
& ~ aElementOf0(sK13(X0),slbdtrb0(X0)) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X1,sK13(X0))],[f187]) ).
fof(f191,plain,
! [X0] :
( slcrc0 != X0
| aSet0(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f201,plain,
! [X0] :
( ~ aSet0(X0)
| aSubsetOf0(X0,X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f236,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[],[f24]) ).
fof(f238,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(szszuzczcdt0(X0),szNzAzT0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f245,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1)) ),
inference(cnf_transformation,[],[f166]) ).
fof(f266,plain,
! [X3,X0,X1] :
( slcrc0 = X0
| ~ isFinite0(X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| szmzazxdt0(X0) != X1
| ~ aElementOf0(X3,X0)
| sdtlseqdt0(X3,X1) ),
inference(cnf_transformation,[],[f177]) ).
fof(f267,plain,
! [X0,X1] :
( slcrc0 = X0
| ~ isFinite0(X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| szmzazxdt0(X0) != X1
| aElementOf0(X1,X0) ),
inference(cnf_transformation,[],[f177]) ).
fof(f279,plain,
slcrc0 = slbdtrb0(sz00),
inference(cnf_transformation,[],[f52]) ).
fof(f285,plain,
isFinite0(xS),
inference(cnf_transformation,[],[f136]) ).
fof(f286,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[],[f136]) ).
fof(f287,plain,
! [X0] :
( ~ aElementOf0(X0,xS)
| aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f291,plain,
! [X2,X0] :
( ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,szNzAzT0)
| aElementOf0(X2,slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f188]) ).
fof(f293,plain,
! [X0] :
( ~ aSubsetOf0(xS,slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f188]) ).
fof(f294,plain,
! [X0] :
( aElementOf0(sK13(X0),xS)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f188]) ).
fof(f295,plain,
! [X0] :
( ~ aElementOf0(sK13(X0),slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f188]) ).
fof(f296,plain,
aSet0(slcrc0),
inference(equality_resolution,[],[f191]) ).
fof(f306,plain,
! [X0] :
( slcrc0 = X0
| ~ isFinite0(X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| aElementOf0(szmzazxdt0(X0),X0) ),
inference(equality_resolution,[],[f267]) ).
fof(f307,plain,
! [X3,X0] :
( slcrc0 = X0
| ~ isFinite0(X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ aElementOf0(X3,X0)
| sdtlseqdt0(X3,szmzazxdt0(X0)) ),
inference(equality_resolution,[],[f266]) ).
tcf(c_51,plain,
aSet0(slcrc0),
inference(cnf_transformation,[],[f296]) ).
tcf(c_61,plain,
! [X0: $i] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f201]) ).
tcf(c_96,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[],[f236]) ).
tcf(c_97,plain,
! [X0: $i] :
( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f238]) ).
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,[],[f245]) ).
tcf(c_128,plain,
! [X0: $i] :
( aElementOf0(szmzazxdt0(X0),X0)
| ( X0 = slcrc0 )
| ~ isFinite0(X0)
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f306]) ).
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,[],[f307]) ).
tcf(c_139,plain,
slbdtrb0(sz00) = slcrc0,
inference(cnf_transformation,[],[f279]) ).
tcf(c_146,plain,
! [X0: $i] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f287]) ).
tcf(c_147,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[],[f286]) ).
tcf(c_148,plain,
isFinite0(xS),
inference(cnf_transformation,[],[f285]) ).
tcf(c_149,negated_conjecture,
! [X0: $i] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(sK13(X0),slbdtrb0(X0)) ),
inference(cnf_transformation,[],[f295]) ).
tcf(c_150,negated_conjecture,
! [X0: $i] :
( aElementOf0(sK13(X0),xS)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f294]) ).
tcf(c_151,negated_conjecture,
! [X0: $i] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ aSubsetOf0(xS,slbdtrb0(X0)) ),
inference(cnf_transformation,[],[f293]) ).
tcf(c_153,negated_conjecture,
! [X0: $i,X1: $i] :
( aElementOf0(X0,slbdtrb0(X1))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X0),X1) ),
inference(cnf_transformation,[],[f291]) ).
tcf(c_8331,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_9864,plain,
( ~ aElementOf0(sz00,szNzAzT0)
| ~ aSubsetOf0(xS,slbdtrb0(sz00)) ),
inference(instantiation,[status(thm)],[c_151]) ).
tcf(c_11579,plain,
( aSubsetOf0(slcrc0,slcrc0)
| ~ aSet0(slcrc0) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_13236,plain,
! [X0: $i] :
( aElementOf0(sK13(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(superposition,[status(thm)],[c_150,c_146]) ).
tcf(c_14125,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X1,slbdtrb0(szszuzczcdt0(X0)))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(szszuzczcdt0(X0),szNzAzT0) ),
inference(superposition,[status(thm)],[c_106,c_153]) ).
tcf(c_14139,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X1,slbdtrb0(szszuzczcdt0(X0)))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_14125,c_97,c_14125]) ).
tcf(c_14140,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,slbdtrb0(szszuzczcdt0(X1)))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X0,X1) ),
inference(renaming,[status(thm)],[c_14139]) ).
tcf(c_14152,plain,
! [X0: $i] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(sK13(szszuzczcdt0(X0)),szNzAzT0)
| ~ sdtlseqdt0(sK13(szszuzczcdt0(X0)),X0) ),
inference(superposition,[status(thm)],[c_14140,c_149]) ).
tcf(c_14160,plain,
! [X0: $i] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(sK13(szszuzczcdt0(X0)),X0)
| ~ aElementOf0(sK13(szszuzczcdt0(X0)),szNzAzT0) ),
inference(global_subsumption_just,[status(thm)],[c_14152,c_97,c_14152]) ).
tcf(c_14161,plain,
! [X0: $i] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(sK13(szszuzczcdt0(X0)),szNzAzT0)
| ~ sdtlseqdt0(sK13(szszuzczcdt0(X0)),X0) ),
inference(renaming,[status(thm)],[c_14160]) ).
tcf(c_14167,plain,
! [X0: $i] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ sdtlseqdt0(sK13(szszuzczcdt0(X0)),X0) ),
inference(superposition,[status(thm)],[c_13236,c_14161]) ).
tcf(c_16029,plain,
( aElementOf0(szmzazxdt0(xS),szNzAzT0)
| ( xS = slcrc0 )
| ~ isFinite0(xS)
| ~ aSubsetOf0(xS,szNzAzT0) ),
inference(resolution,[status(thm)],[c_128,c_146]) ).
tcf(c_16681,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X1,slbdtrb0(szszuzczcdt0(X0)))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(szszuzczcdt0(X0),szNzAzT0) ),
inference(resolution,[status(thm)],[c_106,c_153]) ).
tcf(c_17034,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X1,slbdtrb0(szszuzczcdt0(X0)))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_16681,c_97,c_14125]) ).
tcf(c_17035,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,slbdtrb0(szszuzczcdt0(X1)))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X0,X1) ),
inference(renaming,[status(thm)],[c_17034]) ).
tcf(c_17055,plain,
! [X0: $i] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(sK13(szszuzczcdt0(X0)),szNzAzT0)
| ~ sdtlseqdt0(sK13(szszuzczcdt0(X0)),X0) ),
inference(resolution,[status(thm)],[c_17035,c_149]) ).
tcf(c_17175,plain,
! [X0: $i] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(sK13(szszuzczcdt0(X0)),X0) ),
inference(global_subsumption_just,[status(thm)],[c_17055,c_97,c_14167]) ).
tcf(c_21141,plain,
! [X0: $i] :
( ( X0 = slcrc0 )
| ~ isFinite0(X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ aElementOf0(szmzazxdt0(X0),szNzAzT0)
| ~ aElementOf0(sK13(szszuzczcdt0(szmzazxdt0(X0))),X0) ),
inference(resolution,[status(thm)],[c_129,c_17175]) ).
tcf(c_30902,plain,
! [X0: $i,X1: $i,X2: $i] :
( aSubsetOf0(xS,slbdtrb0(X0))
| ~ aSubsetOf0(X2,X1)
| ( xS != X2 )
| ( slbdtrb0(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_8331]) ).
tcf(c_37826,plain,
! [X0: $i] :
( aSubsetOf0(xS,slbdtrb0(sz00))
| ~ aSubsetOf0(X0,slcrc0)
| ( xS != X0 )
| ( slbdtrb0(sz00) != slcrc0 ) ),
inference(instantiation,[status(thm)],[c_30902]) ).
tcf(c_55823,plain,
( aSubsetOf0(xS,slbdtrb0(sz00))
| ~ aSubsetOf0(slcrc0,slcrc0)
| ( xS != slcrc0 )
| ( slbdtrb0(sz00) != slcrc0 ) ),
inference(instantiation,[status(thm)],[c_37826]) ).
tcf(c_78236,plain,
( aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0)
| ~ aElementOf0(szmzazxdt0(xS),szNzAzT0) ),
inference(instantiation,[status(thm)],[c_97]) ).
tcf(c_512655,plain,
( ( xS = slcrc0 )
| ~ isFinite0(xS)
| ~ aSubsetOf0(xS,szNzAzT0)
| ~ aElementOf0(szmzazxdt0(xS),szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0) ),
inference(resolution,[status(thm)],[c_21141,c_150]) ).
tcf(c_512656,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_512655,c_78236,c_55823,c_16029,c_11579,c_9864,c_139,c_96,c_147,c_51,c_148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM543+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n019.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 04:32:51 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.39 Running first-order theorem proving
% 0.08/0.39 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.40
% 0.08/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.40
% 0.08/0.40 % Detected problem language: tptp
% 0.08/0.41 % Proving...
% 134.20/37.42 % SZS status Started for theBenchmark.p
% 134.20/37.42 % SZS status Theorem for theBenchmark.p
% 134.20/37.42
% 134.20/37.42 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 134.20/37.42
% 134.20/37.42 % ------ iProver source info
% 134.20/37.42
% 134.20/37.42 % git: date: 2026-07-19 20:42:38 +0200
% 134.20/37.42 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 134.20/37.42 % git: non_committed_changes: false
% 134.20/37.42
% 134.20/37.42 % ------ Parsing...
% 134.20/37.42 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 134.20/37.42
% 134.20/37.42 % ------ 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 %
% 134.20/37.42
% 134.20/37.42 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 134.20/37.42
% 134.20/37.42 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 134.20/37.42 % ------ Proving...
% 134.20/37.42 % ------ Problem Properties
% 134.20/37.42
% 134.20/37.42 %
% 134.20/37.42 % clauses 101
% 134.20/37.42 % conjectures 7
% 134.20/37.42 % EPR 33
% 134.20/37.42 % Horn 74
% 134.20/37.42 % unary 12
% 134.20/37.42 % binary 19
% 134.20/37.42 % lits 333
% 134.20/37.42 % lits eq 46
% 134.20/37.42 % fd_pure 0
% 134.20/37.42 % fd_pseudo 0
% 134.20/37.42 % fd_cond 8
% 134.20/37.42 % fd_pseudo_cond 15
% 134.20/37.42 % AC symbols 0
% 134.20/37.42
% 134.20/37.42 % ------ Input Options Time Limit: Unbounded
% 134.20/37.42
% 134.20/37.42
% 134.20/37.42 % ------
% 134.20/37.42 % Current options:
% 134.20/37.42 % ------
% 134.20/37.42
% 134.20/37.42
% 134.20/37.42 %
% 134.20/37.42
% 134.20/37.42 % ------ Proving...
% 134.20/37.42 %
% 134.20/37.42
% 134.20/37.42 % SZS status Theorem for theBenchmark.p
% 134.20/37.42
% 134.20/37.42 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 134.20/37.43
% 134.20/37.43
%------------------------------------------------------------------------------