%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM549+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 : 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 02:25:58 PM UTC 2026
% Result : Theorem 3.22s 1.19s
% Output : CNFRefutation 3.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 52 ( 15 unt; 0 def)
% Number of atoms : 132 ( 43 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 131 ( 51 ~; 47 |; 25 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 34 !; 6 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(f5,axiom,
! [X0] :
( X0 = slcrc0
<=> ( ~ ? [X1] : aElementOf0(X1,X0)
& aSet0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
fof(f42,axiom,
! [X0] :
( aSet0(X0)
=> ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardEmpty) ).
fof(f62,axiom,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202_02) ).
fof(f65,axiom,
( aElementOf0(xQ,slbdtsldtrb0(xS,xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,xS)
& ! [X0] :
( aElementOf0(X0,xQ)
=> aElementOf0(X0,xS) )
& aSet0(xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2270) ).
fof(f66,axiom,
( sbrdtbr0(xQ) = xk
& isFinite0(xQ)
& aSet0(xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2291) ).
fof(f67,conjecture,
? [X0] :
( aElementOf0(X0,xQ)
& aElement0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f68,negated_conjecture,
~ ? [X0] :
( aElementOf0(X0,xQ)
& aElement0(X0) ),
inference(negated_conjecture,[status(cth)],[f67]) ).
fof(f77,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f78,plain,
! [X0] :
( X0 = slcrc0
<=> ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f126,plain,
! [X0] :
( ~ aSet0(X0)
| ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 ) ),
inference(ennf_transformation,[],[f42]) ).
fof(f160,plain,
( aElementOf0(xQ,slbdtsldtrb0(xS,xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,xS)
& ! [X0] :
( ~ aElementOf0(X0,xQ)
| aElementOf0(X0,xS) )
& aSet0(xQ) ),
inference(ennf_transformation,[],[f65]) ).
fof(f161,plain,
! [X0] :
( ~ aElementOf0(X0,xQ)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f68]) ).
fof(f168,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(nnf_transformation,[],[f78]) ).
fof(f169,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(flattening,[],[f168]) ).
fof(f170,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(rectify,[],[f169]) ).
fof(f171,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))],[f170]) ).
fof(f191,plain,
! [X0] :
( ~ aSet0(X0)
| ( ( sz00 != sbrdtbr0(X0)
| X0 = slcrc0 )
& ( slcrc0 != X0
| sbrdtbr0(X0) = sz00 ) ) ),
inference(nnf_transformation,[],[f126]) ).
fof(f215,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f217,plain,
! [X0] :
( slcrc0 != X0
| aSet0(X0) ),
inference(cnf_transformation,[],[f171]) ).
fof(f218,plain,
! [X0] :
( aElementOf0(sK4(X0),X0)
| ~ aSet0(X0)
| slcrc0 = X0 ),
inference(cnf_transformation,[],[f171]) ).
fof(f282,plain,
! [X0] :
( ~ aSet0(X0)
| slcrc0 != X0
| sz00 = sbrdtbr0(X0) ),
inference(cnf_transformation,[],[f191]) ).
fof(f325,plain,
sz00 != xk,
inference(cnf_transformation,[],[f62]) ).
fof(f327,plain,
aSet0(xS),
inference(cnf_transformation,[],[f62]) ).
fof(f359,plain,
! [X0] :
( ~ aElementOf0(X0,xQ)
| aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f160]) ).
fof(f361,plain,
xk = sbrdtbr0(xQ),
inference(cnf_transformation,[],[f66]) ).
fof(f363,plain,
aSet0(xQ),
inference(cnf_transformation,[],[f66]) ).
fof(f364,plain,
! [X0] :
( ~ aElementOf0(X0,xQ)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f161]) ).
fof(f365,plain,
aSet0(slcrc0),
inference(equality_resolution,[],[f217]) ).
fof(f372,plain,
( ~ aSet0(slcrc0)
| sz00 = sbrdtbr0(slcrc0) ),
inference(equality_resolution,[],[f282]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f215]) ).
tcf(c_50,plain,
! [X0: $i] :
( aElementOf0(sK4(X0),X0)
| ( X0 = slcrc0 )
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f218]) ).
tcf(c_51,plain,
aSet0(slcrc0),
inference(cnf_transformation,[],[f365]) ).
tcf(c_115,plain,
( ( sbrdtbr0(slcrc0) = sz00 )
| ~ aSet0(slcrc0) ),
inference(cnf_transformation,[],[f372]) ).
tcf(c_159,plain,
aSet0(xS),
inference(cnf_transformation,[],[f327]) ).
tcf(c_161,plain,
sz00 != xk,
inference(cnf_transformation,[],[f325]) ).
tcf(c_191,plain,
! [X0: $i] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xQ) ),
inference(cnf_transformation,[],[f359]) ).
tcf(c_195,plain,
aSet0(xQ),
inference(cnf_transformation,[],[f363]) ).
tcf(c_197,plain,
sbrdtbr0(xQ) = xk,
inference(cnf_transformation,[],[f361]) ).
tcf(c_198,negated_conjecture,
! [X0: $i] :
( ~ aElement0(X0)
| ~ aElementOf0(X0,xQ) ),
inference(cnf_transformation,[],[f364]) ).
tcf(c_296,plain,
sbrdtbr0(slcrc0) = sz00,
inference(global_subsumption_just,[status(thm)],[c_115,c_51,c_115]) ).
tcf(c_9414,negated_conjecture,
! [X0: $i] :
( ~ aElement0(X0)
| ~ aElementOf0(X0,xQ) ),
inference(demodulation,[status(thm)],[c_198]) ).
tcf(c_11741,plain,
( aElementOf0(sK4(xQ),xS)
| ( slcrc0 = xQ )
| ~ aSet0(xQ) ),
inference(superposition,[status(thm)],[c_50,c_191]) ).
tcf(c_11742,plain,
( ( slcrc0 = xQ )
| ~ aSet0(xQ)
| ~ aElement0(sK4(xQ)) ),
inference(superposition,[status(thm)],[c_50,c_9414]) ).
tcf(c_11746,plain,
( ( slcrc0 = xQ )
| ~ aElement0(sK4(xQ)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11742,c_195]) ).
tcf(c_11749,plain,
( aElementOf0(sK4(xQ),xS)
| ( slcrc0 = xQ ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11741,c_195]) ).
tcf(c_11794,plain,
( aElement0(sK4(xQ))
| ( slcrc0 = xQ )
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_11749,c_49]) ).
tcf(c_11795,plain,
( aElement0(sK4(xQ))
| ( slcrc0 = xQ ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11794,c_159]) ).
tcf(c_11798,plain,
slcrc0 = xQ,
inference(global_subsumption_just,[status(thm)],[c_11795,c_11746,c_11795]) ).
tcf(c_11804,plain,
sbrdtbr0(slcrc0) = xk,
inference(demodulation,[status(thm)],[c_197,c_11798]) ).
tcf(c_11810,plain,
sz00 = xk,
inference(demodulation,[status(thm)],[c_296,c_11804]) ).
tcf(c_11811,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_11810,c_161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM549+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n005.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 04:34:18 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 3.22/1.19 % SZS status Started for theBenchmark.p
% 3.22/1.19 % SZS status Theorem for theBenchmark.p
% 3.22/1.19
% 3.22/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.22/1.19
% 3.22/1.19 % ------ iProver source info
% 3.22/1.19
% 3.22/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 3.22/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.22/1.19 % git: non_committed_changes: false
% 3.22/1.19
% 3.22/1.19 % ------ Parsing...
% 3.22/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.22/1.19
% 3.22/1.19 % ------ 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 %
% 3.22/1.19
% 3.22/1.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.22/1.19
% 3.22/1.19 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.22/1.19 % ------ Proving...
% 3.22/1.19 % ------ Problem Properties
% 3.22/1.19
% 3.22/1.19 %
% 3.22/1.19 % clauses 141
% 3.22/1.19 % conjectures 1
% 3.22/1.19 % EPR 39
% 3.22/1.19 % Horn 108
% 3.22/1.19 % unary 24
% 3.22/1.19 % binary 25
% 3.22/1.19 % lits 446
% 3.22/1.19 % lits eq 68
% 3.22/1.19 % fd_pure 0
% 3.22/1.19 % fd_pseudo 0
% 3.22/1.19 % fd_cond 9
% 3.22/1.19 % fd_pseudo_cond 18
% 3.22/1.19 % AC symbols 0
% 3.22/1.19
% 3.22/1.19 % ------ Schedule dynamic 5 is on
% 3.22/1.19
% 3.22/1.19 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.22/1.19
% 3.22/1.19
% 3.22/1.19 % ------
% 3.22/1.19 % Current options:
% 3.22/1.19 % ------
% 3.22/1.19
% 3.22/1.19
% 3.22/1.19 %
% 3.22/1.19
% 3.22/1.19 % ------ Proving...
% 3.22/1.19 %
% 3.22/1.19
% 3.22/1.19 % SZS status Theorem for theBenchmark.p
% 3.22/1.19
% 3.22/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.22/1.19
%------------------------------------------------------------------------------