%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM612+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 : n016.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 02:26:14 PM UTC 2026
% Result : Theorem 16.98s 4.75s
% Output : CNFRefutation 16.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 67 ( 26 unt; 2 def)
% Number of atoms : 204 ( 40 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 203 ( 76 ~; 66 |; 46 &)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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 : 10 ( 8 usr; 3 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 43 !; 0 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [X0] :
( ( isFinite0(X0)
& aSet0(X0) )
=> ! [X1] :
( aSubsetOf0(X1,X0)
=> isFinite0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubFSet) ).
fof(f41,axiom,
! [X0] :
( aSet0(X0)
=> ( aElementOf0(sbrdtbr0(X0),szNzAzT0)
<=> isFinite0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardNum) ).
fof(f44,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( ( aElementOf0(X1,X0)
& isFinite0(X0) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) = sbrdtbr0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardDiff) ).
fof(f74,axiom,
aElementOf0(xK,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3418) ).
fof(f99,axiom,
( aElementOf0(xQ,slbdtsldtrb0(xO,xK))
& sbrdtbr0(xQ) = xK
& aSubsetOf0(xQ,xO)
& ! [X0] :
( aElementOf0(X0,xQ)
=> aElementOf0(X0,xO) )
& aSet0(xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5078) ).
fof(f103,axiom,
( xp = szmzizndt0(xQ)
& ! [X0] :
( aElementOf0(X0,xQ)
=> sdtlseqdt0(xp,X0) )
& aElementOf0(xp,xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5147) ).
fof(f104,axiom,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [X0] :
( aElementOf0(X0,xP)
<=> ( X0 != szmzizndt0(xQ)
& aElementOf0(X0,xQ)
& aElement0(X0) ) )
& ! [X0] :
( aElementOf0(X0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),X0) )
& aSet0(xP) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5164) ).
fof(f105,axiom,
aElementOf0(xp,xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5173) ).
fof(f107,axiom,
( aSubsetOf0(xP,xQ)
& ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,xQ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5195) ).
fof(f109,conjecture,
( aElementOf0(sbrdtbr0(xP),szNzAzT0)
& szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f110,negated_conjecture,
~ ( aElementOf0(sbrdtbr0(xP),szNzAzT0)
& szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ) ),
inference(negated_conjecture,[status(cth)],[f109]) ).
fof(f132,plain,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [X1] :
( aElementOf0(X1,xP)
<=> ( szmzizndt0(xQ) != X1
& aElementOf0(X1,xQ)
& aElement0(X1) ) )
& ! [X0] :
( aElementOf0(X0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),X0) )
& aSet0(xP) ),
inference(rectify,[],[f104]) ).
fof(f140,plain,
! [X0] :
( ~ isFinite0(X0)
| ~ aSet0(X0)
| ! [X1] :
( ~ aSubsetOf0(X1,X0)
| isFinite0(X1) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f141,plain,
! [X0] :
( ~ isFinite0(X0)
| ~ aSet0(X0)
| ! [X1] :
( ~ aSubsetOf0(X1,X0)
| isFinite0(X1) ) ),
inference(flattening,[],[f140]) ).
fof(f182,plain,
! [X0] :
( ~ aSet0(X0)
| ( aElementOf0(sbrdtbr0(X0),szNzAzT0)
<=> isFinite0(X0) ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f186,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| ~ isFinite0(X0)
| szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) = sbrdtbr0(X0) ) ),
inference(ennf_transformation,[],[f44]) ).
fof(f187,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| ~ isFinite0(X0)
| szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) = sbrdtbr0(X0) ) ),
inference(flattening,[],[f186]) ).
fof(f261,plain,
( aElementOf0(xQ,slbdtsldtrb0(xO,xK))
& sbrdtbr0(xQ) = xK
& aSubsetOf0(xQ,xO)
& ! [X0] :
( ~ aElementOf0(X0,xQ)
| aElementOf0(X0,xO) )
& aSet0(xQ) ),
inference(ennf_transformation,[],[f99]) ).
fof(f266,plain,
( xp = szmzizndt0(xQ)
& ! [X0] :
( ~ aElementOf0(X0,xQ)
| sdtlseqdt0(xp,X0) )
& aElementOf0(xp,xQ) ),
inference(ennf_transformation,[],[f103]) ).
fof(f267,plain,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [X1] :
( aElementOf0(X1,xP)
<=> ( szmzizndt0(xQ) != X1
& aElementOf0(X1,xQ)
& aElement0(X1) ) )
& ! [X0] :
( ~ aElementOf0(X0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),X0) )
& aSet0(xP) ),
inference(ennf_transformation,[],[f132]) ).
fof(f268,plain,
( aSubsetOf0(xP,xQ)
& ! [X0] :
( ~ aElementOf0(X0,xP)
| aElementOf0(X0,xQ) ) ),
inference(ennf_transformation,[],[f107]) ).
fof(f270,plain,
( ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| sbrdtbr0(xQ) != szszuzczcdt0(sbrdtbr0(xP)) ),
inference(ennf_transformation,[],[f110]) ).
fof(f326,plain,
! [X0] :
( ~ aSet0(X0)
| ( ( ~ aElementOf0(sbrdtbr0(X0),szNzAzT0)
| isFinite0(X0) )
& ( ~ isFinite0(X0)
| aElementOf0(sbrdtbr0(X0),szNzAzT0) ) ) ),
inference(nnf_transformation,[],[f182]) ).
fof(f452,plain,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [X1] :
( ( ~ aElementOf0(X1,xP)
| ( szmzizndt0(xQ) != X1
& aElementOf0(X1,xQ)
& aElement0(X1) ) )
& ( szmzizndt0(xQ) = X1
| ~ aElementOf0(X1,xQ)
| ~ aElement0(X1)
| aElementOf0(X1,xP) ) )
& ! [X0] :
( ~ aElementOf0(X0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),X0) )
& aSet0(xP) ),
inference(nnf_transformation,[],[f267]) ).
fof(f453,plain,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [X1] :
( ( ~ aElementOf0(X1,xP)
| ( szmzizndt0(xQ) != X1
& aElementOf0(X1,xQ)
& aElement0(X1) ) )
& ( szmzizndt0(xQ) = X1
| ~ aElementOf0(X1,xQ)
| ~ aElement0(X1)
| aElementOf0(X1,xP) ) )
& ! [X0] :
( ~ aElementOf0(X0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),X0) )
& aSet0(xP) ),
inference(flattening,[],[f452]) ).
fof(f466,plain,
! [X0,X1] :
( ~ isFinite0(X0)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| isFinite0(X1) ),
inference(cnf_transformation,[],[f141]) ).
fof(f520,plain,
! [X0] :
( ~ aSet0(X0)
| ~ aElementOf0(sbrdtbr0(X0),szNzAzT0)
| isFinite0(X0) ),
inference(cnf_transformation,[],[f326]) ).
fof(f521,plain,
! [X0] :
( ~ aSet0(X0)
| ~ isFinite0(X0)
| aElementOf0(sbrdtbr0(X0),szNzAzT0) ),
inference(cnf_transformation,[],[f326]) ).
fof(f525,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| ~ isFinite0(X0)
| sbrdtbr0(X0) = szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) ),
inference(cnf_transformation,[],[f187]) ).
fof(f600,plain,
aElementOf0(xK,szNzAzT0),
inference(cnf_transformation,[],[f74]) ).
fof(f848,plain,
xK = sbrdtbr0(xQ),
inference(cnf_transformation,[],[f261]) ).
fof(f851,plain,
aSet0(xQ),
inference(cnf_transformation,[],[f261]) ).
fof(f862,plain,
xp = szmzizndt0(xQ),
inference(cnf_transformation,[],[f266]) ).
fof(f865,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(cnf_transformation,[],[f453]) ).
fof(f871,plain,
aSet0(xP),
inference(cnf_transformation,[],[f453]) ).
fof(f872,plain,
aElementOf0(xp,xQ),
inference(cnf_transformation,[],[f105]) ).
fof(f875,plain,
aSubsetOf0(xP,xQ),
inference(cnf_transformation,[],[f268]) ).
fof(f879,plain,
( ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| sbrdtbr0(xQ) != szszuzczcdt0(sbrdtbr0(xP)) ),
inference(cnf_transformation,[],[f270]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( isFinite0(X0)
| ~ isFinite0(X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f466]) ).
tcf(c_114,plain,
! [X0: $i] :
( aElementOf0(sbrdtbr0(X0),szNzAzT0)
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f521]) ).
tcf(c_115,plain,
! [X0: $i] :
( isFinite0(X0)
| ~ aSet0(X0)
| ~ aElementOf0(sbrdtbr0(X0),szNzAzT0) ),
inference(cnf_transformation,[],[f520]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i] :
( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X0))) = sbrdtbr0(X1) )
| ~ isFinite0(X1)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f525]) ).
tcf(c_194,plain,
aElementOf0(xK,szNzAzT0),
inference(cnf_transformation,[],[f600]) ).
tcf(c_441,plain,
aSet0(xQ),
inference(cnf_transformation,[],[f851]) ).
tcf(c_444,plain,
sbrdtbr0(xQ) = xK,
inference(cnf_transformation,[],[f848]) ).
tcf(c_458,plain,
szmzizndt0(xQ) = xp,
inference(cnf_transformation,[],[f862]) ).
tcf(c_459,plain,
aSet0(xP),
inference(cnf_transformation,[],[f871]) ).
tcf(c_465,plain,
sdtmndt0(xQ,szmzizndt0(xQ)) = xP,
inference(cnf_transformation,[],[f865]) ).
tcf(c_466,plain,
aElementOf0(xp,xQ),
inference(cnf_transformation,[],[f872]) ).
tcf(c_470,plain,
aSubsetOf0(xP,xQ),
inference(cnf_transformation,[],[f875]) ).
tcf(c_473,negated_conjecture,
( ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| ( szszuzczcdt0(sbrdtbr0(xP)) != sbrdtbr0(xQ) ) ),
inference(cnf_transformation,[],[f879]) ).
tcf(c_3417,plain,
sdtmndt0(xQ,xp) = xP,
inference(light_normalisation,[status(thm)],[c_465,c_458]) ).
tcf(c_3884,plain,
( ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| ( szszuzczcdt0(sbrdtbr0(xP)) != xK ) ),
inference(light_normalisation,[status(thm)],[c_473,c_444]) ).
tcf(c_26305,definition,
iPr_def_10 = sbrdtbr0(xP),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_26306,definition,
iPr_def_11 = szszuzczcdt0(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_26307,plain,
( ~ aElementOf0(iPr_def_10,szNzAzT0)
| ( iPr_def_11 != xK ) ),
inference(demodulation,[status(thm)],[c_3884,c_26305,c_26306]) ).
tcf(c_32061,plain,
( aElementOf0(iPr_def_10,szNzAzT0)
| ~ isFinite0(xP)
| ~ aSet0(xP) ),
inference(superposition,[status(thm)],[c_26305,c_114]) ).
tcf(c_32067,plain,
( aElementOf0(iPr_def_10,szNzAzT0)
| ~ isFinite0(xP) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32061,c_459]) ).
tcf(c_32201,plain,
( isFinite0(xQ)
| ~ aSet0(xQ)
| ~ aElementOf0(xK,szNzAzT0) ),
inference(superposition,[status(thm)],[c_444,c_115]) ).
tcf(c_32206,plain,
isFinite0(xQ),
inference(forward_subsumption_resolution,[status(thm)],[c_32201,c_441,c_194]) ).
tcf(c_32782,plain,
( isFinite0(xP)
| ~ isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(superposition,[status(thm)],[c_470,c_60]) ).
tcf(c_32785,plain,
isFinite0(xP),
inference(forward_subsumption_resolution,[status(thm)],[c_32782,c_32206,c_441]) ).
tcf(c_32803,plain,
aElementOf0(iPr_def_10,szNzAzT0),
inference(backward_subsumption_resolution,[status(thm)],[c_32067,c_32785]) ).
tcf(c_32805,plain,
xK != iPr_def_11,
inference(backward_subsumption_resolution,[status(thm)],[c_26307,c_32803]) ).
tcf(c_47211,plain,
( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xp))) = sbrdtbr0(xQ) )
| ~ isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(superposition,[status(thm)],[c_466,c_119]) ).
tcf(c_47275,plain,
( ( xK = iPr_def_11 )
| ~ isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(light_normalisation,[status(thm)],[c_47211,c_444,c_3417,c_26305,c_26306]) ).
tcf(c_47276,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_47275,c_32805,c_32206,c_441]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM612+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.07/0.34 % Computer : n016.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Thu Sep 24 04:59:26 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.38 Running first-order theorem proving
% 0.12/0.38 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
% 0.12/0.38
% 0.12/0.38 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.38
% 0.12/0.39 % Detected problem language: tptp
% 0.12/0.39 % Proving...
% 16.98/4.75 % SZS status Started for theBenchmark.p
% 16.98/4.75 % SZS status Theorem for theBenchmark.p
% 16.98/4.75
% 16.98/4.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 16.98/4.75
% 16.98/4.75 % ------ iProver source info
% 16.98/4.75
% 16.98/4.75 % git: date: 2026-07-19 20:42:38 +0200
% 16.98/4.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 16.98/4.75 % git: non_committed_changes: false
% 16.98/4.75
% 16.98/4.75 % ------ Parsing...
% 16.98/4.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 16.98/4.75
% 16.98/4.75 % ------ Preprocessing... sup_sim: 14 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 16.98/4.75
% 16.98/4.75 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 16.98/4.75
% 16.98/4.75 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 16.98/4.75 % ------ Proving...
% 16.98/4.75 % ------ Problem Properties
% 16.98/4.75
% 16.98/4.75 %
% 16.98/4.75 % clauses 382
% 16.98/4.75 % conjectures 0
% 16.98/4.75 % EPR 75
% 16.98/4.75 % Horn 307
% 16.98/4.75 % unary 59
% 16.98/4.75 % binary 104
% 16.98/4.75 % lits 1185
% 16.98/4.75 % lits eq 173
% 16.98/4.75 % fd_pure 0
% 16.98/4.75 % fd_pseudo 0
% 16.98/4.75 % fd_cond 11
% 16.98/4.75 % fd_pseudo_cond 39
% 16.98/4.75 % AC symbols 0
% 16.98/4.75
% 16.98/4.75 % ------ Schedule dynamic 5 is on
% 16.98/4.75
% 16.98/4.75 % ------ no conjectures: strip conj schedule
% 16.98/4.75
% 16.98/4.75 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 16.98/4.75
% 16.98/4.75
% 16.98/4.75 % ------
% 16.98/4.75 % Current options:
% 16.98/4.75 % ------
% 16.98/4.75
% 16.98/4.75
% 16.98/4.75 %
% 16.98/4.75
% 16.98/4.75 % ------ Proving...
% 16.98/4.75 %
% 16.98/4.75
% 16.98/4.75 % SZS status Theorem for theBenchmark.p
% 16.98/4.75
% 16.98/4.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 16.98/4.76
% 16.98/4.76
%------------------------------------------------------------------------------