%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM557+1 : 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 : 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 02:26:00 PM UTC 2026
% Result : Theorem 3.45s 1.12s
% Output : CNFRefutation 3.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 15 unt; 0 def)
% Number of atoms : 145 ( 37 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 187 ( 74 ~; 72 |; 34 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 45 ( 0 sgn 42 !; 3 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
fof(f57,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aSet0(X0) )
=> ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSel) ).
fof(f61,axiom,
aElementOf0(xk,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202) ).
fof(f62,axiom,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202_02) ).
fof(f72,axiom,
( sbrdtbr0(xP) = xk
& aSubsetOf0(xP,xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2431) ).
fof(f73,conjecture,
aElementOf0(xP,slbdtsldtrb0(xS,xk)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f74,negated_conjecture,
~ aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(negated_conjecture,[status(cth)],[f73]) ).
fof(f81,plain,
~ aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(flattening,[],[f74]) ).
fof(f156,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& aSet0(X2) ) ) ),
inference(ennf_transformation,[],[f57]) ).
fof(f157,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& aSet0(X2) ) ) ),
inference(flattening,[],[f156]) ).
fof(f211,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ! [X2] :
( ( slbdtsldtrb0(X0,X1) != X2
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& ( sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& ( ~ aElementOf0(X3,X2)
| sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0) ) )
| ~ aSet0(X2)
| X2 = slbdtsldtrb0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f157]) ).
fof(f212,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ! [X2] :
( ( slbdtsldtrb0(X0,X1) != X2
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& ( sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& ( ~ aElementOf0(X3,X2)
| sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0) ) )
| ~ aSet0(X2)
| X2 = slbdtsldtrb0(X0,X1) ) ) ),
inference(flattening,[],[f211]) ).
fof(f213,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ! [X2] :
( ( slbdtsldtrb0(X0,X1) != X2
| ( ! [X4] :
( ( ~ aElementOf0(X4,X2)
| ( sbrdtbr0(X4) = X1
& aSubsetOf0(X4,X0) ) )
& ( sbrdtbr0(X4) != X1
| ~ aSubsetOf0(X4,X0)
| aElementOf0(X4,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& ( ~ aElementOf0(X3,X2)
| sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0) ) )
| ~ aSet0(X2)
| X2 = slbdtsldtrb0(X0,X1) ) ) ),
inference(rectify,[],[f212]) ).
fof(f214,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ! [X2] :
( ( slbdtsldtrb0(X0,X1) != X2
| ( ! [X4] :
( ( ~ aElementOf0(X4,X2)
| ( sbrdtbr0(X4) = X1
& aSubsetOf0(X4,X0) ) )
& ( sbrdtbr0(X4) != X1
| ~ aSubsetOf0(X4,X0)
| aElementOf0(X4,X2) ) )
& aSet0(X2) ) )
& ( ( ( aElementOf0(sK14(X0,X1,X2),X2)
| ( sbrdtbr0(sK14(X0,X1,X2)) = X1
& aSubsetOf0(sK14(X0,X1,X2),X0) ) )
& ( ~ aElementOf0(sK14(X0,X1,X2),X2)
| sbrdtbr0(sK14(X0,X1,X2)) != X1
| ~ aSubsetOf0(sK14(X0,X1,X2),X0) ) )
| ~ aSet0(X2)
| X2 = slbdtsldtrb0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X3,sK14(X0,X1,X2))],[f213]) ).
fof(f316,plain,
! [X2,X0,X1,X4] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| slbdtsldtrb0(X0,X1) != X2
| sbrdtbr0(X4) != X1
| ~ aSubsetOf0(X4,X0)
| aElementOf0(X4,X2) ),
inference(cnf_transformation,[],[f214]) ).
fof(f324,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f61]) ).
fof(f327,plain,
aSet0(xS),
inference(cnf_transformation,[],[f62]) ).
fof(f342,plain,
xk = sbrdtbr0(xP),
inference(cnf_transformation,[],[f72]) ).
fof(f343,plain,
aSubsetOf0(xP,xS),
inference(cnf_transformation,[],[f72]) ).
fof(f344,plain,
~ aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[],[f81]) ).
fof(f363,plain,
! [X2,X0,X4] :
( ~ aElementOf0(sbrdtbr0(X4),szNzAzT0)
| ~ aSet0(X0)
| slbdtsldtrb0(X0,sbrdtbr0(X4)) != X2
| ~ aSubsetOf0(X4,X0)
| aElementOf0(X4,X2) ),
inference(equality_resolution,[],[f316]) ).
fof(f364,plain,
! [X0,X4] :
( ~ aElementOf0(sbrdtbr0(X4),szNzAzT0)
| ~ aSet0(X0)
| ~ aSubsetOf0(X4,X0)
| aElementOf0(X4,slbdtsldtrb0(X0,sbrdtbr0(X4))) ),
inference(equality_resolution,[],[f363]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,slbdtsldtrb0(X1,sbrdtbr0(X0)))
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1)
| ~ aElementOf0(sbrdtbr0(X0),szNzAzT0) ),
inference(cnf_transformation,[],[f364]) ).
tcf(c_158,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f324]) ).
tcf(c_159,plain,
aSet0(xS),
inference(cnf_transformation,[],[f327]) ).
tcf(c_176,plain,
aSubsetOf0(xP,xS),
inference(cnf_transformation,[],[f343]) ).
tcf(c_177,plain,
sbrdtbr0(xP) = xk,
inference(cnf_transformation,[],[f342]) ).
tcf(c_178,negated_conjecture,
~ aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[],[f344]) ).
tcf(c_251,plain,
! [X0: $i] :
( aElementOf0(xP,slbdtsldtrb0(X0,xk))
| ~ aSet0(X0)
| ~ aSubsetOf0(xP,X0)
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(superposition,[status(thm)],[c_177,c_152]) ).
tcf(c_262,plain,
! [X0: $i] :
( aElementOf0(xP,slbdtsldtrb0(X0,xk))
| ~ aSet0(X0)
| ~ aElementOf0(xk,szNzAzT0)
| ~ aSubsetOf0(xP,X0) ),
inference(light_normalisation,[status(thm)],[c_251,c_177]) ).
tcf(c_267,plain,
! [X0: $i] :
( aElementOf0(xP,slbdtsldtrb0(X0,xk))
| ~ aSet0(X0)
| ~ aSubsetOf0(xP,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_262,c_158]) ).
tcf(c_276,plain,
( ~ aSet0(xS)
| ~ aSubsetOf0(xP,xS) ),
inference(superposition,[status(thm)],[c_267,c_178]) ).
tcf(c_277,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_276,c_176,c_159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM557+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.39 % Computer : n009.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Thu Sep 24 04:37:00 UTC 2026
% 0.10/0.40 % CPUTime :
% 0.10/0.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.43 Running first-order theorem proving
% 0.10/0.43 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
% 0.10/0.45
% 0.10/0.45 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.45
% 0.10/0.45 % Detected problem language: tptp
% 0.10/0.46 % Proving...
% 3.45/1.12 % SZS status Started for theBenchmark.p
% 3.45/1.12 % SZS status Theorem for theBenchmark.p
% 3.45/1.12
% 3.45/1.12 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.45/1.12
% 3.45/1.12 % ------ iProver source info
% 3.45/1.12
% 3.45/1.12 % git: date: 2026-07-19 20:42:38 +0200
% 3.45/1.12 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.45/1.12 % git: non_committed_changes: false
% 3.45/1.12
% 3.45/1.12 % ------ Parsing...
% 3.45/1.12 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.45/1.12 % ------ Proving...
% 3.45/1.12 % ------ Problem Properties
% 3.45/1.12
% 3.45/1.12 %
% 3.45/1.12 % clauses 130
% 3.45/1.12 % conjectures 1
% 3.45/1.12 % EPR 43
% 3.45/1.12 % Horn 100
% 3.45/1.12 % unary 28
% 3.45/1.12 % binary 20
% 3.45/1.12 % lits 410
% 3.45/1.12 % lits eq 61
% 3.45/1.12 % fd_pure 0
% 3.45/1.12 % fd_pseudo 0
% 3.45/1.12 % fd_cond 9
% 3.45/1.12 % fd_pseudo_cond 18
% 3.45/1.12 % AC symbols 0
% 3.45/1.12
% 3.45/1.12 % ------ Input Options Time Limit: Unbounded
% 3.45/1.12
% 3.45/1.12
% 3.45/1.12 % ------
% 3.45/1.12 % Current options:
% 3.45/1.12 % ------
% 3.45/1.12
% 3.45/1.12
% 3.45/1.12 %
% 3.45/1.12
% 3.45/1.12 % ------ Proving...
% 3.45/1.12 %
% 3.45/1.12
% 3.45/1.12 % SZS status Theorem for theBenchmark.p
% 3.45/1.12
% 3.45/1.12 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.45/1.12
% 3.45/1.12
%------------------------------------------------------------------------------