%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM574+1 : 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 : n009.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 02:26:04 PM UTC 2026
% Result : Theorem 8.84s 1.81s
% Output : CNFRefutation 8.84s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f427ERROR: Could not build tree for root c_13530ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(f12,axiom,
! [X0] :
( aSet0(X0)
=> aSubsetOf0(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).
fof(f23,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
fof(f24,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
fof(f27,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ? [X1] :
( X0 = szszuzczcdt0(X1)
& aElementOf0(X1,szNzAzT0) )
| X0 = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatExtra) ).
fof(f30,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> sdtlseqdt0(sz00,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroLess) ).
fof(f35,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessASymm) ).
fof(f75,axiom,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
fof(f81,axiom,
( ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ( isCountable0(sdtlpdtrp0(xN,X0))
& aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
=> ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3623) ).
fof(f83,axiom,
( aElementOf0(xi,szNzAzT0)
& aElementOf0(xj,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3786) ).
fof(f86,conjecture,
( sdtlseqdt0(xj,xi)
=> aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f87,negated_conjecture,
~ ( sdtlseqdt0(xj,xi)
=> aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ),
inference(negated_conjecture,[status(cth)],[f86]) ).
fof(f97,plain,
( ! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(ennf_transformation,[],[f81]) ).
fof(f98,plain,
( ! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(flattening,[],[f97]) ).
fof(f104,plain,
( sdtlseqdt0(xj,xi)
& ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ),
inference(ennf_transformation,[],[f87]) ).
fof(f109,plain,
! [X0] :
( ~ aSet0(X0)
| aSubsetOf0(X0,X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f110,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f138,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(sz00,X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f139,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ? [X1] :
( X0 = szszuzczcdt0(X1)
& aElementOf0(X1,szNzAzT0) )
| X0 = sz00 ),
inference(ennf_transformation,[],[f27]) ).
fof(f140,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ? [X1] :
( X0 = szszuzczcdt0(X1)
& aElementOf0(X1,szNzAzT0) )
| X0 = sz00 ),
inference(flattening,[],[f139]) ).
fof(f167,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f35]) ).
fof(f168,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f167]) ).
fof(f202,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,[],[f110]) ).
fof(f203,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,[],[f202]) ).
fof(f204,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,[],[f203]) ).
fof(f205,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X3] :
( ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aSet0(X1) ) )
& ( ( aElementOf0(sK6(X0,X1),X1)
& ~ aElementOf0(sK6(X0,X1),X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f204]) ).
fof(f217,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ( szszuzczcdt0(sK14(X0)) = X0
& aElementOf0(sK14(X0),szNzAzT0) )
| X0 = sz00 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X1,sK14(X0))],[f140]) ).
fof(f253,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[],[f75]) ).
fof(f267,plain,
xS = sdtlpdtrp0(xN,sz00),
inference(cnf_transformation,[],[f98]) ).
fof(f272,plain,
aElementOf0(xi,szNzAzT0),
inference(cnf_transformation,[],[f83]) ).
fof(f273,plain,
aElementOf0(xj,szNzAzT0),
inference(cnf_transformation,[],[f83]) ).
fof(f276,plain,
sdtlseqdt0(xj,xi),
inference(cnf_transformation,[],[f104]) ).
fof(f277,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)),
inference(cnf_transformation,[],[f104]) ).
fof(f280,plain,
! [X0] :
( ~ aSet0(X0)
| aSubsetOf0(X0,X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f282,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| aSet0(X1) ),
inference(cnf_transformation,[],[f205]) ).
fof(f288,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f322,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(sz00,X0) ),
inference(cnf_transformation,[],[f138]) ).
fof(f323,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| szszuzczcdt0(sK14(X0)) = X0
| sz00 = X0 ),
inference(cnf_transformation,[],[f217]) ).
fof(f324,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(sK14(X0),szNzAzT0)
| sz00 = X0 ),
inference(cnf_transformation,[],[f217]) ).
fof(f327,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[],[f24]) ).
fof(f357,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f168]) ).
tcf(c_52,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[],[f253]) ).
tcf(c_67,plain,
sdtlpdtrp0(xN,sz00) = xS,
inference(cnf_transformation,[],[f267]) ).
tcf(c_72,plain,
aElementOf0(xj,szNzAzT0),
inference(cnf_transformation,[],[f273]) ).
tcf(c_73,plain,
aElementOf0(xi,szNzAzT0),
inference(cnf_transformation,[],[f272]) ).
tcf(c_75,plain,
! [X0: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
| ~ sdtlseqdt0(xj,xi)
| ~ aElementOf0(X0,szNzAzT0)
| ( szszuzczcdt0(X0) != xi ) ),
inference(cnf_transformation,[],[f427]) ).
tcf(c_76,negated_conjecture,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)),
inference(cnf_transformation,[],[f277]) ).
tcf(c_77,negated_conjecture,
sdtlseqdt0(xj,xi),
inference(cnf_transformation,[],[f276]) ).
tcf(c_80,plain,
! [X0: $i] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f280]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( aSet0(X0)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f282]) ).
tcf(c_87,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f288]) ).
tcf(c_122,plain,
! [X0: $i] :
( sdtlseqdt0(sz00,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f322]) ).
tcf(c_123,plain,
! [X0: $i] :
( aElementOf0(sK14(X0),szNzAzT0)
| ( X0 = sz00 )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f324]) ).
tcf(c_124,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ( szszuzczcdt0(sK14(X0)) = X0 )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f323]) ).
tcf(c_127,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[],[f327]) ).
tcf(c_157,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f357]) ).
tcf(c_317,plain,
! [X0: $i] :
( ~ aElementOf0(X0,szNzAzT0)
| ( szszuzczcdt0(X0) != xi ) ),
inference(global_subsumption_just,[status(thm)],[c_75,c_77,c_76,c_75]) ).
tcf(c_9030,plain,
sdtlseqdt0(sz00,xj),
inference(superposition,[status(thm)],[c_72,c_122]) ).
tcf(c_9160,plain,
( aSet0(xS)
| ~ aSet0(szNzAzT0) ),
inference(superposition,[status(thm)],[c_52,c_83]) ).
tcf(c_9164,plain,
aSet0(xS),
inference(forward_subsumption_resolution,[status(thm)],[c_9160,c_87]) ).
tcf(c_10728,plain,
( ( sz00 = xi )
| ( szszuzczcdt0(sK14(xi)) = xi ) ),
inference(superposition,[status(thm)],[c_73,c_124]) ).
tcf(c_12042,plain,
( ( sz00 = xi )
| ~ aElementOf0(sK14(xi),szNzAzT0) ),
inference(superposition,[status(thm)],[c_10728,c_317]) ).
tcf(c_12095,plain,
( ( sz00 = xi )
| ~ aElementOf0(xi,szNzAzT0) ),
inference(superposition,[status(thm)],[c_123,c_12042]) ).
tcf(c_12097,plain,
sz00 = xi,
inference(forward_subsumption_resolution,[status(thm)],[c_12095,c_73]) ).
tcf(c_12115,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,sz00),sdtlpdtrp0(xN,xj)),
inference(demodulation,[status(thm)],[c_76,c_12097]) ).
tcf(c_12116,plain,
sdtlseqdt0(xj,sz00),
inference(demodulation,[status(thm)],[c_77,c_12097]) ).
tcf(c_12117,plain,
~ aSubsetOf0(xS,sdtlpdtrp0(xN,xj)),
inference(light_normalisation,[status(thm)],[c_12115,c_67]) ).
tcf(c_13364,plain,
( ( sz00 = xj )
| ~ sdtlseqdt0(sz00,xj)
| ~ aElementOf0(xj,szNzAzT0)
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(superposition,[status(thm)],[c_12116,c_157]) ).
tcf(c_13382,plain,
sz00 = xj,
inference(forward_subsumption_resolution,[status(thm)],[c_13364,c_9030,c_72,c_127]) ).
tcf(c_13498,plain,
~ aSubsetOf0(xS,sdtlpdtrp0(xN,sz00)),
inference(demodulation,[status(thm)],[c_12117,c_13382]) ).
tcf(c_13513,plain,
~ aSubsetOf0(xS,xS),
inference(light_normalisation,[status(thm)],[c_13498,c_67]) ).
tcf(c_13529,plain,
~ aSet0(xS),
inference(superposition,[status(thm)],[c_80,c_13513]) ).
tcf(c_13530,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_13529,c_9164]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM574+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n009.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 04:42:29 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 8.84/1.81 % SZS status Started for theBenchmark.p
% 8.84/1.81 % SZS status Theorem for theBenchmark.p
% 8.84/1.81
% 8.84/1.81 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.84/1.81
% 8.84/1.81 % ------ iProver source info
% 8.84/1.81
% 8.84/1.81 % git: date: 2026-07-19 20:42:38 +0200
% 8.84/1.81 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.84/1.81 % git: non_committed_changes: false
% 8.84/1.81
% 8.84/1.81 % ------ Parsing...
% 8.84/1.81 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.84/1.81
% 8.84/1.81 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e %
% 8.84/1.81
% 8.84/1.81 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.84/1.81
% 8.84/1.81 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 8.84/1.81 % ------ Proving...
% 8.84/1.81 % ------ Problem Properties
% 8.84/1.81
% 8.84/1.81 %
% 8.84/1.81 % clauses 164
% 8.84/1.81 % conjectures 2
% 8.84/1.81 % EPR 39
% 8.84/1.81 % Horn 127
% 8.84/1.81 % unary 27
% 8.84/1.81 % binary 27
% 8.84/1.81 % lits 553
% 8.84/1.81 % lits eq 91
% 8.84/1.81 % fd_pure 0
% 8.84/1.81 % fd_pseudo 0
% 8.84/1.81 % fd_cond 8
% 8.84/1.81 % fd_pseudo_cond 22
% 8.84/1.81 % AC symbols 0
% 8.84/1.81
% 8.84/1.81 % ------ Schedule dynamic 5 is on
% 8.84/1.81
% 8.84/1.81 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 8.84/1.81
% 8.84/1.81
% 8.84/1.81 % ------
% 8.84/1.81 % Current options:
% 8.84/1.81 % ------
% 8.84/1.81
% 8.84/1.81
% 8.84/1.81 %
% 8.84/1.81
% 8.84/1.81 % ------ Proving...
% 8.84/1.81 %
% 8.84/1.81
% 8.84/1.81 % SZS status Theorem for theBenchmark.p
% 8.84/1.81
% 8.84/1.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.84/1.81
% 8.84/1.81
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