%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM590+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 : n014.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 02:26:08 PM UTC 2026
% Result : Theorem 4.44s 1.28s
% Output : CNFRefutation 4.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 10 unt; 0 def)
% Number of atoms : 172 ( 17 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 199 ( 66 ~; 58 |; 62 &)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 49 !; 4 ?; 10 :)
% 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(f23,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
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(f90,axiom,
aElementOf0(xi,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4448) ).
fof(f91,axiom,
( xd = sdtlpdtrp0(xC,xi)
& xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
& ! [X0] :
( aElementOf0(X0,xY)
<=> ( X0 != szmzizndt0(sdtlpdtrp0(xN,xi))
& aElementOf0(X0,sdtlpdtrp0(xN,xi))
& aElement0(X0) ) )
& aSet0(xY)
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4448_02) ).
fof(f92,conjecture,
( aSubsetOf0(xY,szNzAzT0)
| ! [X0] :
( aElementOf0(X0,xY)
=> aElementOf0(X0,szNzAzT0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f93,negated_conjecture,
~ ( aSubsetOf0(xY,szNzAzT0)
| ! [X0] :
( aElementOf0(X0,xY)
=> aElementOf0(X0,szNzAzT0) ) ),
inference(negated_conjecture,[status(cth)],[f92]) ).
fof(f109,plain,
( xd = sdtlpdtrp0(xC,xi)
& xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
& ! [X1] :
( aElementOf0(X1,xY)
<=> ( szmzizndt0(sdtlpdtrp0(xN,xi)) != X1
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& aElement0(X1) ) )
& aSet0(xY)
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
inference(rectify,[],[f91]) ).
fof(f116,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f216,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(f228,plain,
( xd = sdtlpdtrp0(xC,xi)
& xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
& ! [X1] :
( aElementOf0(X1,xY)
<=> ( szmzizndt0(sdtlpdtrp0(xN,xi)) != X1
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& aElement0(X1) ) )
& aSet0(xY)
& ! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
inference(ennf_transformation,[],[f109]) ).
fof(f229,plain,
( ~ aSubsetOf0(xY,szNzAzT0)
& ? [X0] :
( aElementOf0(X0,xY)
& ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f93]) ).
fof(f263,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,[],[f116]) ).
fof(f264,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,[],[f263]) ).
fof(f265,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,[],[f264]) ).
fof(f266,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X3] :
( ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aSet0(X1) ) )
& ( ( aElementOf0(sK23(X0,X1),X1)
& ~ aElementOf0(sK23(X0,X1),X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(X2,sK23(X0,X1))],[f265]) ).
fof(f383,plain,
( xd = sdtlpdtrp0(xC,xi)
& xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
& ! [X1] :
( ( ~ aElementOf0(X1,xY)
| ( szmzizndt0(sdtlpdtrp0(xN,xi)) != X1
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& aElement0(X1) ) )
& ( szmzizndt0(sdtlpdtrp0(xN,xi)) = X1
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xi))
| ~ aElement0(X1)
| aElementOf0(X1,xY) ) )
& aSet0(xY)
& ! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
inference(nnf_transformation,[],[f228]) ).
fof(f384,plain,
( xd = sdtlpdtrp0(xC,xi)
& xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
& ! [X1] :
( ( ~ aElementOf0(X1,xY)
| ( szmzizndt0(sdtlpdtrp0(xN,xi)) != X1
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& aElement0(X1) ) )
& ( szmzizndt0(sdtlpdtrp0(xN,xi)) = X1
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xi))
| ~ aElement0(X1)
| aElementOf0(X1,xY) ) )
& aSet0(xY)
& ! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
inference(flattening,[],[f383]) ).
fof(f385,plain,
( ~ aSubsetOf0(xY,szNzAzT0)
& aElementOf0(sK59,xY)
& ~ aElementOf0(sK59,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(X0,sK59)],[f229]) ).
fof(f393,plain,
! [X3,X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) ),
inference(cnf_transformation,[],[f266]) ).
fof(f432,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f605,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) ),
inference(cnf_transformation,[],[f216]) ).
fof(f712,plain,
aElementOf0(xi,szNzAzT0),
inference(cnf_transformation,[],[f90]) ).
fof(f716,plain,
! [X1] :
( ~ aElementOf0(X1,xY)
| aElementOf0(X1,sdtlpdtrp0(xN,xi)) ),
inference(cnf_transformation,[],[f384]) ).
fof(f723,plain,
aElementOf0(sK59,xY),
inference(cnf_transformation,[],[f385]) ).
fof(f724,plain,
~ aElementOf0(sK59,szNzAzT0),
inference(cnf_transformation,[],[f385]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,X2)
| ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f393]) ).
tcf(c_94,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f432]) ).
tcf(c_269,plain,
! [X0: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f605]) ).
tcf(c_375,plain,
aElementOf0(xi,szNzAzT0),
inference(cnf_transformation,[],[f712]) ).
tcf(c_381,plain,
! [X0: $i] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X0,xY) ),
inference(cnf_transformation,[],[f716]) ).
tcf(c_385,negated_conjecture,
~ aElementOf0(sK59,szNzAzT0),
inference(cnf_transformation,[],[f724]) ).
tcf(c_386,negated_conjecture,
aElementOf0(sK59,xY),
inference(cnf_transformation,[],[f723]) ).
tcf(c_459,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X1,X0)
| ~ aSet0(X0)
| ~ aElementOf0(X1,xY)
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),X0) ),
inference(superposition,[status(thm)],[c_381,c_59]) ).
tcf(c_523,plain,
! [X0: $i] :
( aElementOf0(X0,szNzAzT0)
| ~ aSet0(szNzAzT0)
| ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(X0,xY) ),
inference(superposition,[status(thm)],[c_269,c_459]) ).
tcf(c_546,plain,
! [X0: $i] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xY)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(global_subsumption_just,[status(thm)],[c_523,c_94,c_523]) ).
tcf(c_547,plain,
! [X0: $i] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(X0,xY) ),
inference(renaming,[status(thm)],[c_546]) ).
tcf(c_555,plain,
( aElementOf0(sK59,szNzAzT0)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(superposition,[status(thm)],[c_386,c_547]) ).
tcf(c_1190,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_375,c_555,c_385]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM590+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 04:48:04 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 4.44/1.28 % SZS status Started for theBenchmark.p
% 4.44/1.28 % SZS status Theorem for theBenchmark.p
% 4.44/1.28
% 4.44/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.44/1.28
% 4.44/1.28 % ------ iProver source info
% 4.44/1.28
% 4.44/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 4.44/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.44/1.28 % git: non_committed_changes: false
% 4.44/1.28
% 4.44/1.28 % ------ Parsing...
% 4.44/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.44/1.28 % ------ Proving...
% 4.44/1.28 % ------ Problem Properties
% 4.44/1.28
% 4.44/1.28 %
% 4.44/1.28 % clauses 339
% 4.44/1.28 % conjectures 3
% 4.44/1.28 % EPR 63
% 4.44/1.28 % Horn 258
% 4.44/1.28 % unary 36
% 4.44/1.28 % binary 86
% 4.44/1.28 % lits 1125
% 4.44/1.28 % lits eq 132
% 4.44/1.28 % fd_pure 0
% 4.44/1.28 % fd_pseudo 0
% 4.44/1.28 % fd_cond 11
% 4.44/1.28 % fd_pseudo_cond 42
% 4.44/1.28 % AC symbols 0
% 4.44/1.28
% 4.44/1.28 % ------ Input Options Time Limit: Unbounded
% 4.44/1.28
% 4.44/1.28
% 4.44/1.28 % ------
% 4.44/1.28 % Current options:
% 4.44/1.28 % ------
% 4.44/1.28
% 4.44/1.28
% 4.44/1.28 %
% 4.44/1.28
% 4.44/1.28 % ------ Proving...
% 4.44/1.28 %
% 4.44/1.28
% 4.44/1.28 % ------ Proving...
% 4.44/1.28 %
% 4.44/1.28
% 4.44/1.28 % ------ Proving...
% 4.44/1.28 %
% 4.44/1.28
% 4.44/1.28 % ------ Proving...
% 4.44/1.28 %
% 4.44/1.28
% 4.44/1.28 % SZS status Theorem for theBenchmark.p
% 4.44/1.28
% 4.44/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.44/1.29
% 4.44/1.29
%------------------------------------------------------------------------------