%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM538+2 : 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 : n019.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 02:25:55 PM UTC 2026
% Result : Theorem 3.88s 1.27s
% Output : CNFRefutation 3.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 56 ( 24 unt; 4 def)
% Number of atoms : 181 ( 36 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 177 ( 74 ~; 61 |; 27 &)
% ( 4 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 43 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f17,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> sdtpldt0(sdtmndt0(X0,X1),X1) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mConsDiff) ).
fof(f22,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( ( isFinite0(X1)
& aSet0(X1) )
=> isFinite0(sdtmndt0(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFDiffSet) ).
fof(f43,axiom,
! [X0] :
( ( isFinite0(X0)
& aSet0(X0) )
=> ! [X1] :
( aElement0(X1)
=> ( ~ aElementOf0(X1,X0)
=> sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardCons) ).
fof(f44,axiom,
aSet0(xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1522) ).
fof(f45,axiom,
( aElementOf0(xx,xS)
& isFinite0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1522_02) ).
fof(f46,conjecture,
( ( ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( X0 != xx
& aElementOf0(X0,xS)
& aElement0(X0) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f47,negated_conjecture,
~ ( ( ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( X0 != xx
& aElementOf0(X0,xS)
& aElement0(X0) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(xS) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f55,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f73,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| sdtpldt0(sdtmndt0(X0,X1),X1) = X0 ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f82,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ~ isFinite0(X1)
| ~ aSet0(X1)
| isFinite0(sdtmndt0(X1,X0)) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f83,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ~ isFinite0(X1)
| ~ aSet0(X1)
| isFinite0(sdtmndt0(X1,X0)) ) ),
inference(flattening,[],[f82]) ).
fof(f105,plain,
! [X0] :
( ~ isFinite0(X0)
| ~ aSet0(X0)
| ! [X1] :
( ~ aElement0(X1)
| aElementOf0(X1,X0)
| sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0)) ) ),
inference(ennf_transformation,[],[f43]) ).
fof(f106,plain,
! [X0] :
( ~ isFinite0(X0)
| ~ aSet0(X0)
| ! [X1] :
( ~ aElement0(X1)
| aElementOf0(X1,X0)
| sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0)) ) ),
inference(flattening,[],[f105]) ).
fof(f107,plain,
( ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( X0 != xx
& aElementOf0(X0,xS)
& aElement0(X0) ) )
& aSet0(sdtmndt0(xS,xx))
& szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS) ),
inference(ennf_transformation,[],[f47]) ).
fof(f108,plain,
( ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( X0 != xx
& aElementOf0(X0,xS)
& aElement0(X0) ) )
& aSet0(sdtmndt0(xS,xx))
& szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS) ),
inference(flattening,[],[f107]) ).
fof(f139,plain,
( ! [X0] :
( ( ~ aElementOf0(X0,sdtmndt0(xS,xx))
| ( X0 != xx
& aElementOf0(X0,xS)
& aElement0(X0) ) )
& ( xx = X0
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0)
| aElementOf0(X0,sdtmndt0(xS,xx)) ) )
& aSet0(sdtmndt0(xS,xx))
& szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS) ),
inference(nnf_transformation,[],[f108]) ).
fof(f140,plain,
( ! [X0] :
( ( ~ aElementOf0(X0,sdtmndt0(xS,xx))
| ( X0 != xx
& aElementOf0(X0,xS)
& aElement0(X0) ) )
& ( xx = X0
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0)
| aElementOf0(X0,sdtmndt0(xS,xx)) ) )
& aSet0(sdtmndt0(xS,xx))
& szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS) ),
inference(flattening,[],[f139]) ).
fof(f141,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f180,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| sdtpldt0(sdtmndt0(X0,X1),X1) = X0 ),
inference(cnf_transformation,[],[f73]) ).
fof(f185,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ isFinite0(X1)
| ~ aSet0(X1)
| isFinite0(sdtmndt0(X1,X0)) ),
inference(cnf_transformation,[],[f83]) ).
fof(f209,plain,
! [X0,X1] :
( ~ isFinite0(X0)
| ~ aSet0(X0)
| ~ aElement0(X1)
| aElementOf0(X1,X0)
| sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0)) ),
inference(cnf_transformation,[],[f106]) ).
fof(f210,plain,
aSet0(xS),
inference(cnf_transformation,[],[f44]) ).
fof(f211,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[],[f45]) ).
fof(f212,plain,
isFinite0(xS),
inference(cnf_transformation,[],[f45]) ).
fof(f213,plain,
! [X0] :
( ~ aElementOf0(X0,sdtmndt0(xS,xx))
| xx != X0 ),
inference(cnf_transformation,[],[f140]) ).
fof(f217,plain,
aSet0(sdtmndt0(xS,xx)),
inference(cnf_transformation,[],[f140]) ).
fof(f218,plain,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS),
inference(cnf_transformation,[],[f140]) ).
fof(f227,plain,
~ aElementOf0(xx,sdtmndt0(xS,xx)),
inference(equality_resolution,[],[f213]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtmndt0(X1,X0),X0) = X1 )
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] :
( isFinite0(sdtmndt0(X1,X0))
| ~ isFinite0(X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,X1)
| ( sbrdtbr0(sdtpldt0(X1,X0)) = szszuzczcdt0(sbrdtbr0(X1)) )
| ~ isFinite0(X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f209]) ).
tcf(c_118,plain,
aSet0(xS),
inference(cnf_transformation,[],[f210]) ).
tcf(c_119,plain,
isFinite0(xS),
inference(cnf_transformation,[],[f212]) ).
tcf(c_120,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[],[f211]) ).
tcf(c_121,negated_conjecture,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS),
inference(cnf_transformation,[],[f218]) ).
tcf(c_122,negated_conjecture,
aSet0(sdtmndt0(xS,xx)),
inference(cnf_transformation,[],[f217]) ).
tcf(c_126,negated_conjecture,
~ aElementOf0(xx,sdtmndt0(xS,xx)),
inference(cnf_transformation,[],[f227]) ).
tcf(c_8121,definition,
iPr_def_10 = sdtmndt0(xS,xx),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_8122,definition,
iPr_def_11 = sbrdtbr0(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_8123,definition,
iPr_def_12 = szszuzczcdt0(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_8124,definition,
iPr_def_13 = sbrdtbr0(xS),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_8125,negated_conjecture,
~ aElementOf0(xx,iPr_def_10),
inference(demodulation,[status(thm)],[c_126,c_8121]) ).
tcf(c_8129,negated_conjecture,
aSet0(iPr_def_10),
inference(demodulation,[status(thm)],[c_122]) ).
tcf(c_8130,negated_conjecture,
iPr_def_12 != iPr_def_13,
inference(demodulation,[status(thm)],[c_121,c_8124,c_8122,c_8123]) ).
tcf(c_9321,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_120,c_49]) ).
tcf(c_9322,plain,
aElement0(xx),
inference(forward_subsumption_resolution,[status(thm)],[c_9321,c_118]) ).
tcf(c_9945,plain,
( isFinite0(iPr_def_10)
| ~ isFinite0(xS)
| ~ aSet0(xS)
| ~ aElement0(xx) ),
inference(superposition,[status(thm)],[c_8121,c_93]) ).
tcf(c_9946,plain,
isFinite0(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_9945,c_119,c_118,c_9322]) ).
tcf(c_10611,plain,
( ( sdtpldt0(sdtmndt0(xS,xx),xx) = xS )
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_120,c_88]) ).
tcf(c_10629,plain,
( ( sdtpldt0(iPr_def_10,xx) = xS )
| ~ aSet0(xS) ),
inference(light_normalisation,[status(thm)],[c_10611,c_8121]) ).
tcf(c_10630,plain,
sdtpldt0(iPr_def_10,xx) = xS,
inference(forward_subsumption_resolution,[status(thm)],[c_10629,c_118]) ).
tcf(c_12266,plain,
( ( sbrdtbr0(sdtpldt0(iPr_def_10,xx)) = szszuzczcdt0(sbrdtbr0(iPr_def_10)) )
| ~ isFinite0(iPr_def_10)
| ~ aSet0(iPr_def_10)
| ~ aElement0(xx) ),
inference(superposition,[status(thm)],[c_117,c_8125]) ).
tcf(c_12269,plain,
( ( iPr_def_12 = iPr_def_13 )
| ~ isFinite0(iPr_def_10)
| ~ aSet0(iPr_def_10)
| ~ aElement0(xx) ),
inference(light_normalisation,[status(thm)],[c_12266,c_8122,c_8123,c_8124,c_10630]) ).
tcf(c_12270,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_12269,c_8130,c_9946,c_8129,c_9322]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM538+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % 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 04:31:22 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.42 % Proving...
% 3.88/1.27 % SZS status Started for theBenchmark.p
% 3.88/1.27 % SZS status Theorem for theBenchmark.p
% 3.88/1.27
% 3.88/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.88/1.27
% 3.88/1.27 % ------ iProver source info
% 3.88/1.27
% 3.88/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 3.88/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.88/1.27 % git: non_committed_changes: false
% 3.88/1.27
% 3.88/1.27 % ------ Parsing...
% 3.88/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.88/1.27
% 3.88/1.27 % ------ 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 %
% 3.88/1.27
% 3.88/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.88/1.27
% 3.88/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.88/1.27 % ------ Proving...
% 3.88/1.27 % ------ Problem Properties
% 3.88/1.27
% 3.88/1.27 %
% 3.88/1.27 % clauses 80
% 3.88/1.27 % conjectures 6
% 3.88/1.27 % EPR 38
% 3.88/1.27 % Horn 64
% 3.88/1.27 % unary 18
% 3.88/1.27 % binary 14
% 3.88/1.27 % lits 228
% 3.88/1.27 % lits eq 30
% 3.88/1.27 % fd_pure 0
% 3.88/1.27 % fd_pseudo 0
% 3.88/1.27 % fd_cond 4
% 3.88/1.27 % fd_pseudo_cond 7
% 3.88/1.27 % AC symbols 0
% 3.88/1.27
% 3.88/1.27 % ------ Schedule dynamic 5 is on
% 3.88/1.27
% 3.88/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.88/1.27
% 3.88/1.27
% 3.88/1.27 % ------
% 3.88/1.27 % Current options:
% 3.88/1.27 % ------
% 3.88/1.27
% 3.88/1.27
% 3.88/1.27 %
% 3.88/1.27
% 3.88/1.27 % ------ Proving...
% 3.88/1.27 %
% 3.88/1.27
% 3.88/1.27 % SZS status Theorem for theBenchmark.p
% 3.88/1.27
% 3.88/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.88/1.27
% 3.88/1.27
%------------------------------------------------------------------------------