%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM547+3 : 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 : n007.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 02:25:58 PM UTC 2026
% Result : Theorem 0.27s 1.05s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 18 ( 6 unt; 0 def)
% Number of atoms : 294 ( 46 equ)
% Maximal formula atoms : 43 ( 16 avg)
% Number of connectives : 378 ( 102 ~; 84 |; 162 &)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 9 avg)
% Maximal term depth : 2 ( 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 : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 76 ( 0 sgn 59 !; 17 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
fof(f63,axiom,
( ~ ( ! [X0] :
( ( ( sbrdtbr0(X0) = xk
& ( aSubsetOf0(X0,xS)
| ( ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
=> aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
=> ( sbrdtbr0(X0) = xk
& aSubsetOf0(X0,xS)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
=> ( slbdtsldtrb0(xS,xk) = slcrc0
| ~ ? [X0] : aElementOf0(X0,slbdtsldtrb0(xS,xk)) ) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [X0] :
( aElementOf0(X0,slbdtsldtrb0(xS,xk))
=> aElementOf0(X0,slbdtsldtrb0(xT,xk)) )
& ! [X0] :
( ( ( sbrdtbr0(X0) = xk
& ( aSubsetOf0(X0,xT)
| ( ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xT) )
& aSet0(X0) ) ) )
=> aElementOf0(X0,slbdtsldtrb0(xT,xk)) )
& ( aElementOf0(X0,slbdtsldtrb0(xT,xk))
=> ( sbrdtbr0(X0) = xk
& aSubsetOf0(X0,xT)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xT) )
& aSet0(X0) ) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X0] :
( ( ( sbrdtbr0(X0) = xk
& ( aSubsetOf0(X0,xS)
| ( ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
=> aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
=> ( sbrdtbr0(X0) = xk
& aSubsetOf0(X0,xS)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2227) ).
fof(f65,conjecture,
? [X0] :
( aElementOf0(X0,slbdtsldtrb0(xS,xk))
| ( sbrdtbr0(X0) = xk
& ( aSubsetOf0(X0,xS)
| ( ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSet0(X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f66,negated_conjecture,
~ ? [X0] :
( aElementOf0(X0,slbdtsldtrb0(xS,xk))
| ( sbrdtbr0(X0) = xk
& ( aSubsetOf0(X0,xS)
| ( ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSet0(X0) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f65]) ).
fof(f73,plain,
( ~ ( ! [X7] :
( ( ( xk = sbrdtbr0(X7)
& ( aSubsetOf0(X7,xS)
| ( ! [X9] :
( aElementOf0(X9,X7)
=> aElementOf0(X9,xS) )
& aSet0(X7) ) ) )
=> aElementOf0(X7,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X7,slbdtsldtrb0(xS,xk))
=> ( xk = sbrdtbr0(X7)
& aSubsetOf0(X7,xS)
& ! [X8] :
( aElementOf0(X8,X7)
=> aElementOf0(X8,xS) )
& aSet0(X7) ) ) )
=> ( slbdtsldtrb0(xS,xk) = slcrc0
| ~ ? [X10] : aElementOf0(X10,slbdtsldtrb0(xS,xk)) ) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [X6] :
( aElementOf0(X6,slbdtsldtrb0(xS,xk))
=> aElementOf0(X6,slbdtsldtrb0(xT,xk)) )
& ! [X3] :
( ( ( sbrdtbr0(X3) = xk
& ( aSubsetOf0(X3,xT)
| ( ! [X5] :
( aElementOf0(X5,X3)
=> aElementOf0(X5,xT) )
& aSet0(X3) ) ) )
=> aElementOf0(X3,slbdtsldtrb0(xT,xk)) )
& ( aElementOf0(X3,slbdtsldtrb0(xT,xk))
=> ( sbrdtbr0(X3) = xk
& aSubsetOf0(X3,xT)
& ! [X4] :
( aElementOf0(X4,X3)
=> aElementOf0(X4,xT) )
& aSet0(X3) ) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X0] :
( ( ( sbrdtbr0(X0) = xk
& ( aSubsetOf0(X0,xS)
| ( ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(X2,xS) )
& aSet0(X0) ) ) )
=> aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
=> ( sbrdtbr0(X0) = xk
& aSubsetOf0(X0,xS)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
inference(rectify,[],[f63]) ).
fof(f156,plain,
( ! [X7] :
( ( xk != sbrdtbr0(X7)
| ( ~ aSubsetOf0(X7,xS)
& ( ? [X9] :
( aElementOf0(X9,X7)
& ~ aElementOf0(X9,xS) )
| ~ aSet0(X7) ) )
| aElementOf0(X7,slbdtsldtrb0(xS,xk)) )
& ( ~ aElementOf0(X7,slbdtsldtrb0(xS,xk))
| ( xk = sbrdtbr0(X7)
& aSubsetOf0(X7,xS)
& ! [X8] :
( ~ aElementOf0(X8,X7)
| aElementOf0(X8,xS) )
& aSet0(X7) ) ) )
& slcrc0 != slbdtsldtrb0(xS,xk)
& ? [X10] : aElementOf0(X10,slbdtsldtrb0(xS,xk))
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [X6] :
( ~ aElementOf0(X6,slbdtsldtrb0(xS,xk))
| aElementOf0(X6,slbdtsldtrb0(xT,xk)) )
& ! [X3] :
( ( sbrdtbr0(X3) != xk
| ( ~ aSubsetOf0(X3,xT)
& ( ? [X5] :
( aElementOf0(X5,X3)
& ~ aElementOf0(X5,xT) )
| ~ aSet0(X3) ) )
| aElementOf0(X3,slbdtsldtrb0(xT,xk)) )
& ( ~ aElementOf0(X3,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(X3) = xk
& aSubsetOf0(X3,xT)
& ! [X4] :
( ~ aElementOf0(X4,X3)
| aElementOf0(X4,xT) )
& aSet0(X3) ) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X0] :
( ( sbrdtbr0(X0) != xk
| ( ~ aSubsetOf0(X0,xS)
& ( ? [X2] :
( aElementOf0(X2,X0)
& ~ aElementOf0(X2,xS) )
| ~ aSet0(X0) ) )
| aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
& ( ~ aElementOf0(X0,slbdtsldtrb0(xS,xk))
| ( sbrdtbr0(X0) = xk
& aSubsetOf0(X0,xS)
& ! [X1] :
( ~ aElementOf0(X1,X0)
| aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
inference(ennf_transformation,[],[f73]) ).
fof(f157,plain,
( ! [X7] :
( ( xk != sbrdtbr0(X7)
| ( ~ aSubsetOf0(X7,xS)
& ( ? [X9] :
( aElementOf0(X9,X7)
& ~ aElementOf0(X9,xS) )
| ~ aSet0(X7) ) )
| aElementOf0(X7,slbdtsldtrb0(xS,xk)) )
& ( ~ aElementOf0(X7,slbdtsldtrb0(xS,xk))
| ( xk = sbrdtbr0(X7)
& aSubsetOf0(X7,xS)
& ! [X8] :
( ~ aElementOf0(X8,X7)
| aElementOf0(X8,xS) )
& aSet0(X7) ) ) )
& slcrc0 != slbdtsldtrb0(xS,xk)
& ? [X10] : aElementOf0(X10,slbdtsldtrb0(xS,xk))
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [X6] :
( ~ aElementOf0(X6,slbdtsldtrb0(xS,xk))
| aElementOf0(X6,slbdtsldtrb0(xT,xk)) )
& ! [X3] :
( ( sbrdtbr0(X3) != xk
| ( ~ aSubsetOf0(X3,xT)
& ( ? [X5] :
( aElementOf0(X5,X3)
& ~ aElementOf0(X5,xT) )
| ~ aSet0(X3) ) )
| aElementOf0(X3,slbdtsldtrb0(xT,xk)) )
& ( ~ aElementOf0(X3,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(X3) = xk
& aSubsetOf0(X3,xT)
& ! [X4] :
( ~ aElementOf0(X4,X3)
| aElementOf0(X4,xT) )
& aSet0(X3) ) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X0] :
( ( sbrdtbr0(X0) != xk
| ( ~ aSubsetOf0(X0,xS)
& ( ? [X2] :
( aElementOf0(X2,X0)
& ~ aElementOf0(X2,xS) )
| ~ aSet0(X0) ) )
| aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
& ( ~ aElementOf0(X0,slbdtsldtrb0(xS,xk))
| ( sbrdtbr0(X0) = xk
& aSubsetOf0(X0,xS)
& ! [X1] :
( ~ aElementOf0(X1,X0)
| aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
inference(flattening,[],[f156]) ).
fof(f158,plain,
! [X0] :
( ~ aElementOf0(X0,slbdtsldtrb0(xS,xk))
& ( sbrdtbr0(X0) != xk
| ( ~ aSubsetOf0(X0,xS)
& ( ? [X1] :
( aElementOf0(X1,X0)
& ~ aElementOf0(X1,xS) )
| ~ aSet0(X0) ) ) ) ),
inference(ennf_transformation,[],[f66]) ).
fof(f210,plain,
( ! [X8] :
( ( xk != sbrdtbr0(X8)
| ( ~ aSubsetOf0(X8,xS)
& ( ? [X10] :
( aElementOf0(X10,X8)
& ~ aElementOf0(X10,xS) )
| ~ aSet0(X8) ) )
| aElementOf0(X8,slbdtsldtrb0(xS,xk)) )
& ( ~ aElementOf0(X8,slbdtsldtrb0(xS,xk))
| ( xk = sbrdtbr0(X8)
& aSubsetOf0(X8,xS)
& ! [X9] :
( ~ aElementOf0(X9,X8)
| aElementOf0(X9,xS) )
& aSet0(X8) ) ) )
& slcrc0 != slbdtsldtrb0(xS,xk)
& ? [X7] : aElementOf0(X7,slbdtsldtrb0(xS,xk))
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [X6] :
( ~ aElementOf0(X6,slbdtsldtrb0(xS,xk))
| aElementOf0(X6,slbdtsldtrb0(xT,xk)) )
& ! [X3] :
( ( sbrdtbr0(X3) != xk
| ( ~ aSubsetOf0(X3,xT)
& ( ? [X5] :
( aElementOf0(X5,X3)
& ~ aElementOf0(X5,xT) )
| ~ aSet0(X3) ) )
| aElementOf0(X3,slbdtsldtrb0(xT,xk)) )
& ( ~ aElementOf0(X3,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(X3) = xk
& aSubsetOf0(X3,xT)
& ! [X4] :
( ~ aElementOf0(X4,X3)
| aElementOf0(X4,xT) )
& aSet0(X3) ) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X0] :
( ( sbrdtbr0(X0) != xk
| ( ~ aSubsetOf0(X0,xS)
& ( ? [X2] :
( aElementOf0(X2,X0)
& ~ aElementOf0(X2,xS) )
| ~ aSet0(X0) ) )
| aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
& ( ~ aElementOf0(X0,slbdtsldtrb0(xS,xk))
| ( sbrdtbr0(X0) = xk
& aSubsetOf0(X0,xS)
& ! [X1] :
( ~ aElementOf0(X1,X0)
| aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
inference(rectify,[],[f157]) ).
fof(f211,plain,
( ! [X8] :
( ( xk != sbrdtbr0(X8)
| ( ~ aSubsetOf0(X8,xS)
& ( ( aElementOf0(sK18(X8),X8)
& ~ aElementOf0(sK18(X8),xS) )
| ~ aSet0(X8) ) )
| aElementOf0(X8,slbdtsldtrb0(xS,xk)) )
& ( ~ aElementOf0(X8,slbdtsldtrb0(xS,xk))
| ( xk = sbrdtbr0(X8)
& aSubsetOf0(X8,xS)
& ! [X9] :
( ~ aElementOf0(X9,X8)
| aElementOf0(X9,xS) )
& aSet0(X8) ) ) )
& slcrc0 != slbdtsldtrb0(xS,xk)
& aElementOf0(sK17,slbdtsldtrb0(xS,xk))
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [X6] :
( ~ aElementOf0(X6,slbdtsldtrb0(xS,xk))
| aElementOf0(X6,slbdtsldtrb0(xT,xk)) )
& ! [X3] :
( ( sbrdtbr0(X3) != xk
| ( ~ aSubsetOf0(X3,xT)
& ( ( aElementOf0(sK16(X3),X3)
& ~ aElementOf0(sK16(X3),xT) )
| ~ aSet0(X3) ) )
| aElementOf0(X3,slbdtsldtrb0(xT,xk)) )
& ( ~ aElementOf0(X3,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(X3) = xk
& aSubsetOf0(X3,xT)
& ! [X4] :
( ~ aElementOf0(X4,X3)
| aElementOf0(X4,xT) )
& aSet0(X3) ) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X0] :
( ( sbrdtbr0(X0) != xk
| ( ~ aSubsetOf0(X0,xS)
& ( ( aElementOf0(sK15(X0),X0)
& ~ aElementOf0(sK15(X0),xS) )
| ~ aSet0(X0) ) )
| aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
& ( ~ aElementOf0(X0,slbdtsldtrb0(xS,xk))
| ( sbrdtbr0(X0) = xk
& aSubsetOf0(X0,xS)
& ! [X1] :
( ~ aElementOf0(X1,X0)
| aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16,sK17,sK18]),skolemize(X2,sK15(X0)),skolemize(X5,sK16(X3)),skolemize(X7,sK17),skolemize(X10,sK18(X8))],[f210]) ).
fof(f212,plain,
! [X0] :
( ~ aElementOf0(X0,slbdtsldtrb0(xS,xk))
& ( sbrdtbr0(X0) != xk
| ( ~ aSubsetOf0(X0,xS)
& ( ( aElementOf0(sK19(X0),X0)
& ~ aElementOf0(sK19(X0),xS) )
| ~ aSet0(X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(X1,sK19(X0))],[f158]) ).
fof(f334,plain,
aElementOf0(sK17,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[],[f211]) ).
fof(f350,plain,
! [X0,X1] :
( ~ aElementOf0(X0,slbdtsldtrb0(xS,xk))
| ~ aElementOf0(X1,X0)
| aElementOf0(X1,xS) ),
inference(cnf_transformation,[],[f211]) ).
fof(f354,plain,
! [X0] : ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[],[f212]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,X0)
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) ),
inference(cnf_transformation,[],[f350]) ).
tcf(c_180,plain,
aElementOf0(sK17,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[],[f334]) ).
tcf(c_193,negated_conjecture,
! [X0: $i] : ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[],[f354]) ).
tcf(c_306,plain,
! [X0: $i] : ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)),
inference(global_subsumption_just,[status(thm)],[c_164,c_193]) ).
tcf(c_361,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_180,c_306]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM547+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.35 % Computer : n007.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Thu Sep 24 04:31:52 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.38 Running first-order theorem proving
% 0.13/0.38 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
% 0.13/0.39
% 0.13/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.39
% 0.13/0.39 % Detected problem language: tptp
% 0.13/0.40 % Proving...
% 0.27/1.05 % SZS status Started for theBenchmark.p
% 0.27/1.05 % SZS status Theorem for theBenchmark.p
% 0.27/1.05
% 0.27/1.05 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.27/1.05
% 0.27/1.05 % ------ iProver source info
% 0.27/1.05
% 0.27/1.05 % git: date: 2026-07-19 20:42:38 +0200
% 0.27/1.05 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.27/1.05 % git: non_committed_changes: false
% 0.27/1.05
% 0.27/1.05 % ------ Parsing...
% 0.27/1.05 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.27/1.05
% 0.27/1.05 % ------ Preprocessing...%
% 0.27/1.05
% 0.27/1.05 % SZS status Theorem for theBenchmark.p
% 0.27/1.05
% 0.27/1.05 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.27/1.05
% 0.27/1.05
%------------------------------------------------------------------------------