%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM552+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 : n005.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 02:25:59 PM UTC 2026
% Result : Theorem 3.91s 1.22s
% Output : CNFRefutation 3.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 52 ( 16 unt; 0 def)
% Number of atoms : 225 ( 34 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 286 ( 113 ~; 111 |; 49 &)
% ( 8 <=>; 5 =>; 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 : 12 ( 12 usr; 8 con; 0-3 aty)
% Number of variables : 78 ( 0 sgn 72 !; 6 ?; 11 :)
% 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(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/sandbox/benchmark/theBenchmark.p',mDefSel) ).
fof(f61,axiom,
aElementOf0(xk,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202) ).
fof(f62,axiom,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202_02) ).
fof(f63,axiom,
( slbdtsldtrb0(xS,xk) != slcrc0
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2227) ).
fof(f65,axiom,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2270) ).
fof(f68,conjecture,
( aElementOf0(xx,xQ)
=> aElementOf0(xx,xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f69,negated_conjecture,
~ ( aElementOf0(xx,xQ)
=> aElementOf0(xx,xT) ),
inference(negated_conjecture,[status(cth)],[f68]) ).
fof(f83,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f150,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(f151,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,[],[f150]) ).
fof(f158,plain,
( aElementOf0(xx,xQ)
& ~ aElementOf0(xx,xT) ),
inference(ennf_transformation,[],[f69]) ).
fof(f169,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,[],[f83]) ).
fof(f170,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,[],[f169]) ).
fof(f171,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,[],[f170]) ).
fof(f172,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))],[f171]) ).
fof(f206,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,[],[f151]) ).
fof(f207,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,[],[f206]) ).
fof(f208,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,[],[f207]) ).
fof(f209,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))],[f208]) ).
fof(f217,plain,
! [X3,X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) ),
inference(cnf_transformation,[],[f172]) ).
fof(f310,plain,
! [X2,X0,X1,X4] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| slbdtsldtrb0(X0,X1) != X2
| ~ aElementOf0(X4,X2)
| aSubsetOf0(X4,X0) ),
inference(cnf_transformation,[],[f209]) ).
fof(f312,plain,
! [X2,X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| slbdtsldtrb0(X0,X1) != X2
| aSet0(X2) ),
inference(cnf_transformation,[],[f209]) ).
fof(f319,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f61]) ).
fof(f321,plain,
aSet0(xT),
inference(cnf_transformation,[],[f62]) ).
fof(f324,plain,
aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)),
inference(cnf_transformation,[],[f63]) ).
fof(f326,plain,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[],[f65]) ).
fof(f332,plain,
aElementOf0(xx,xQ),
inference(cnf_transformation,[],[f158]) ).
fof(f333,plain,
~ aElementOf0(xx,xT),
inference(cnf_transformation,[],[f158]) ).
fof(f351,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| aSet0(slbdtsldtrb0(X0,X1)) ),
inference(equality_resolution,[],[f312]) ).
fof(f354,plain,
! [X0,X1,X4] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ~ aElementOf0(X4,slbdtsldtrb0(X0,X1))
| aSubsetOf0(X4,X0) ),
inference(equality_resolution,[],[f310]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,X2)
| ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f217]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i] :
( aSet0(slbdtsldtrb0(X1,X0))
| ~ aSet0(X1)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f351]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i,X2: $i] :
( aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X0,slbdtsldtrb0(X1,X2)) ),
inference(cnf_transformation,[],[f354]) ).
tcf(c_158,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f319]) ).
tcf(c_160,plain,
aSet0(xT),
inference(cnf_transformation,[],[f321]) ).
tcf(c_162,plain,
aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)),
inference(cnf_transformation,[],[f324]) ).
tcf(c_165,plain,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[],[f326]) ).
tcf(c_171,negated_conjecture,
~ aElementOf0(xx,xT),
inference(cnf_transformation,[],[f333]) ).
tcf(c_172,negated_conjecture,
aElementOf0(xx,xQ),
inference(cnf_transformation,[],[f332]) ).
tcf(c_790,plain,
! [X0: $i] :
( aElementOf0(xQ,X0)
| ~ aSet0(X0)
| ~ aSubsetOf0(slbdtsldtrb0(xS,xk),X0) ),
inference(superposition,[status(thm)],[c_165,c_59]) ).
tcf(c_1127,plain,
( aElementOf0(xQ,slbdtsldtrb0(xT,xk))
| ~ aSet0(slbdtsldtrb0(xT,xk)) ),
inference(superposition,[status(thm)],[c_162,c_790]) ).
tcf(c_1242,plain,
! [X0: $i] :
( aElementOf0(xQ,X0)
| ~ aSet0(X0)
| ~ aSubsetOf0(slbdtsldtrb0(xS,xk),X0) ),
inference(superposition,[status(thm)],[c_165,c_59]) ).
tcf(c_1243,plain,
! [X0: $i] :
( aElementOf0(xx,X0)
| ~ aSet0(X0)
| ~ aSubsetOf0(xQ,X0) ),
inference(superposition,[status(thm)],[c_172,c_59]) ).
tcf(c_1987,plain,
( aSubsetOf0(xQ,xT)
| ~ aSet0(xT)
| ~ aElementOf0(xk,szNzAzT0)
| ~ aSet0(slbdtsldtrb0(xT,xk)) ),
inference(superposition,[status(thm)],[c_1127,c_153]) ).
tcf(c_2074,plain,
( aElementOf0(xQ,slbdtsldtrb0(xT,xk))
| ~ aSet0(slbdtsldtrb0(xT,xk)) ),
inference(superposition,[status(thm)],[c_162,c_1242]) ).
tcf(c_3863,plain,
( aSubsetOf0(xQ,xT)
| ~ aSet0(slbdtsldtrb0(xT,xk)) ),
inference(global_subsumption_just,[status(thm)],[c_1987,c_160,c_158,c_1987]) ).
tcf(c_3869,plain,
( aSubsetOf0(xQ,xT)
| ~ aSet0(xT)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(superposition,[status(thm)],[c_151,c_3863]) ).
tcf(c_4046,plain,
( aSubsetOf0(xQ,xT)
| ~ aSet0(xT)
| ~ aElementOf0(xk,szNzAzT0)
| ~ aSet0(slbdtsldtrb0(xT,xk)) ),
inference(superposition,[status(thm)],[c_2074,c_153]) ).
tcf(c_6552,plain,
aSubsetOf0(xQ,xT),
inference(global_subsumption_just,[status(thm)],[c_4046,c_160,c_158,c_3869]) ).
tcf(c_6562,plain,
( aElementOf0(xx,xT)
| ~ aSet0(xT) ),
inference(superposition,[status(thm)],[c_6552,c_1243]) ).
tcf(c_6563,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_6562,c_171,c_160]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM552+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.38 % Computer : n005.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Thu Sep 24 04:34:48 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 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...
% 3.91/1.22 % SZS status Started for theBenchmark.p
% 3.91/1.22 % SZS status Theorem for theBenchmark.p
% 3.91/1.22
% 3.91/1.22 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.91/1.22
% 3.91/1.22 % ------ iProver source info
% 3.91/1.22
% 3.91/1.22 % git: date: 2026-07-19 20:42:38 +0200
% 3.91/1.22 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.91/1.22 % git: non_committed_changes: false
% 3.91/1.22
% 3.91/1.22 % ------ Parsing...
% 3.91/1.22 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.91/1.22 % ------ Proving...
% 3.91/1.22 % ------ Problem Properties
% 3.91/1.22
% 3.91/1.22 %
% 3.91/1.22 % clauses 124
% 3.91/1.22 % conjectures 2
% 3.91/1.22 % EPR 42
% 3.91/1.22 % Horn 94
% 3.91/1.22 % unary 22
% 3.91/1.22 % binary 20
% 3.91/1.22 % lits 404
% 3.91/1.22 % lits eq 58
% 3.91/1.22 % fd_pure 0
% 3.91/1.22 % fd_pseudo 0
% 3.91/1.22 % fd_cond 9
% 3.91/1.22 % fd_pseudo_cond 18
% 3.91/1.22 % AC symbols 0
% 3.91/1.22
% 3.91/1.22 % ------ Input Options Time Limit: Unbounded
% 3.91/1.22
% 3.91/1.22
% 3.91/1.22 % ------
% 3.91/1.22 % Current options:
% 3.91/1.22 % ------
% 3.91/1.22
% 3.91/1.22
% 3.91/1.22 %
% 3.91/1.22
% 3.91/1.22 % ------ Proving...
% 3.91/1.22 %
% 3.91/1.22
% 3.91/1.22 % ------ Proving...
% 3.91/1.22 %
% 3.91/1.22
% 3.91/1.22 % ------ Proving...
% 3.91/1.22 %
% 3.91/1.22
% 3.91/1.22 % SZS status Theorem for theBenchmark.p
% 3.91/1.22
% 3.91/1.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.91/1.22
% 3.91/1.22
%------------------------------------------------------------------------------