%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM540+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 : 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 02:25:56 PM UTC 2026
% Result : Theorem 3.95s 1.28s
% Output : CNFRefutation 3.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 48 ( 16 unt; 1 def)
% Number of atoms : 192 ( 35 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 223 ( 92 ~; 85 |; 38 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 58 !; 7 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( X0 = slcrc0
<=> ( ~ ? [X1] : aElementOf0(X1,X0)
& aSet0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
fof(f24,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
fof(f31,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ~ sdtlseqdt0(szszuzczcdt0(X0),sz00) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNoScLessZr) ).
fof(f50,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( X1 = slbdtrb0(X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
<=> ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSeg) ).
fof(f52,conjecture,
slbdtrb0(sz00) = slcrc0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f53,negated_conjecture,
slbdtrb0(sz00) != slcrc0,
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f60,plain,
slcrc0 != slbdtrb0(sz00),
inference(flattening,[],[f53]) ).
fof(f63,plain,
! [X0] :
( X0 = slcrc0
<=> ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f98,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X0),sz00) ),
inference(ennf_transformation,[],[f31]) ).
fof(f126,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ! [X1] :
( X1 = slbdtrb0(X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
<=> ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f50]) ).
fof(f134,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(nnf_transformation,[],[f63]) ).
fof(f135,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(flattening,[],[f134]) ).
fof(f136,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(rectify,[],[f135]) ).
fof(f137,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))],[f136]) ).
fof(f167,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ! [X1] :
( ( slbdtrb0(X0) != X1
| ( ! [X2] :
( ( ~ aElementOf0(X2,X1)
| ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& ( ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,szNzAzT0)
| aElementOf0(X2,X1) ) )
& aSet0(X1) ) )
& ( ? [X2] :
( ( aElementOf0(X2,X1)
| ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& ( ~ aElementOf0(X2,X1)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,szNzAzT0) ) )
| ~ aSet0(X1)
| X1 = slbdtrb0(X0) ) ) ),
inference(nnf_transformation,[],[f126]) ).
fof(f168,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ! [X1] :
( ( slbdtrb0(X0) != X1
| ( ! [X2] :
( ( ~ aElementOf0(X2,X1)
| ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& ( ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,szNzAzT0)
| aElementOf0(X2,X1) ) )
& aSet0(X1) ) )
& ( ? [X2] :
( ( aElementOf0(X2,X1)
| ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& ( ~ aElementOf0(X2,X1)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,szNzAzT0) ) )
| ~ aSet0(X1)
| X1 = slbdtrb0(X0) ) ) ),
inference(flattening,[],[f167]) ).
fof(f169,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ! [X1] :
( ( slbdtrb0(X0) != X1
| ( ! [X3] :
( ( ~ aElementOf0(X3,X1)
| ( sdtlseqdt0(szszuzczcdt0(X3),X0)
& aElementOf0(X3,szNzAzT0) ) )
& ( ~ sdtlseqdt0(szszuzczcdt0(X3),X0)
| ~ aElementOf0(X3,szNzAzT0)
| aElementOf0(X3,X1) ) )
& aSet0(X1) ) )
& ( ? [X2] :
( ( aElementOf0(X2,X1)
| ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& ( ~ aElementOf0(X2,X1)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,szNzAzT0) ) )
| ~ aSet0(X1)
| X1 = slbdtrb0(X0) ) ) ),
inference(rectify,[],[f168]) ).
fof(f170,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ! [X1] :
( ( slbdtrb0(X0) != X1
| ( ! [X3] :
( ( ~ aElementOf0(X3,X1)
| ( sdtlseqdt0(szszuzczcdt0(X3),X0)
& aElementOf0(X3,szNzAzT0) ) )
& ( ~ sdtlseqdt0(szszuzczcdt0(X3),X0)
| ~ aElementOf0(X3,szNzAzT0)
| aElementOf0(X3,X1) ) )
& aSet0(X1) ) )
& ( ( ( aElementOf0(sK12(X0,X1),X1)
| ( sdtlseqdt0(szszuzczcdt0(sK12(X0,X1)),X0)
& aElementOf0(sK12(X0,X1),szNzAzT0) ) )
& ( ~ aElementOf0(sK12(X0,X1),X1)
| ~ sdtlseqdt0(szszuzczcdt0(sK12(X0,X1)),X0)
| ~ aElementOf0(sK12(X0,X1),szNzAzT0) ) )
| ~ aSet0(X1)
| X1 = slbdtrb0(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X2,sK12(X0,X1))],[f169]) ).
fof(f174,plain,
! [X0] :
( aElementOf0(sK4(X0),X0)
| ~ aSet0(X0)
| slcrc0 = X0 ),
inference(cnf_transformation,[],[f137]) ).
fof(f218,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[],[f24]) ).
fof(f226,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X0),sz00) ),
inference(cnf_transformation,[],[f98]) ).
fof(f253,plain,
! [X3,X0,X1] :
( ~ aElementOf0(X0,szNzAzT0)
| slbdtrb0(X0) != X1
| ~ aElementOf0(X3,X1)
| sdtlseqdt0(szszuzczcdt0(X3),X0) ),
inference(cnf_transformation,[],[f170]) ).
fof(f254,plain,
! [X3,X0,X1] :
( ~ aElementOf0(X0,szNzAzT0)
| slbdtrb0(X0) != X1
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,szNzAzT0) ),
inference(cnf_transformation,[],[f170]) ).
fof(f256,plain,
! [X0,X1] :
( ~ aElementOf0(X0,szNzAzT0)
| slbdtrb0(X0) != X1
| aSet0(X1) ),
inference(cnf_transformation,[],[f170]) ).
fof(f261,plain,
slcrc0 != slbdtrb0(sz00),
inference(cnf_transformation,[],[f60]) ).
fof(f274,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aSet0(slbdtrb0(X0)) ),
inference(equality_resolution,[],[f256]) ).
fof(f276,plain,
! [X3,X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X3,slbdtrb0(X0))
| aElementOf0(X3,szNzAzT0) ),
inference(equality_resolution,[],[f254]) ).
fof(f277,plain,
! [X3,X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X3,slbdtrb0(X0))
| sdtlseqdt0(szszuzczcdt0(X3),X0) ),
inference(equality_resolution,[],[f253]) ).
tcf(c_50,plain,
! [X0: $i] :
( aElementOf0(sK4(X0),X0)
| ( X0 = slcrc0 )
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_96,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[],[f218]) ).
tcf(c_104,plain,
! [X0: $i] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X0),sz00) ),
inference(cnf_transformation,[],[f226]) ).
tcf(c_134,plain,
! [X0: $i] :
( aSet0(slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f274]) ).
tcf(c_136,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,slbdtrb0(X1)) ),
inference(cnf_transformation,[],[f276]) ).
tcf(c_137,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(szszuzczcdt0(X0),X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,slbdtrb0(X1)) ),
inference(cnf_transformation,[],[f277]) ).
tcf(c_139,negated_conjecture,
slbdtrb0(sz00) != slcrc0,
inference(cnf_transformation,[],[f261]) ).
tcf(c_8078,definition,
iPr_def_10 = slbdtrb0(sz00),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_8079,negated_conjecture,
iPr_def_10 != slcrc0,
inference(demodulation,[status(thm)],[c_139,c_8078]) ).
tcf(c_9532,plain,
aSet0(slbdtrb0(sz00)),
inference(superposition,[status(thm)],[c_96,c_134]) ).
tcf(c_9533,plain,
aSet0(iPr_def_10),
inference(light_normalisation,[status(thm)],[c_9532,c_8078]) ).
tcf(c_9935,plain,
! [X0: $i] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(sz00,szNzAzT0)
| ~ aElementOf0(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_8078,c_136]) ).
tcf(c_9936,plain,
! [X0: $i] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9935,c_96]) ).
tcf(c_10311,plain,
! [X0: $i] :
( sdtlseqdt0(szszuzczcdt0(X0),sz00)
| ~ aElementOf0(sz00,szNzAzT0)
| ~ aElementOf0(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_8078,c_137]) ).
tcf(c_10312,plain,
! [X0: $i] :
( sdtlseqdt0(szszuzczcdt0(X0),sz00)
| ~ aElementOf0(X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10311,c_96]) ).
tcf(c_10485,plain,
! [X0: $i] : ~ aElementOf0(X0,iPr_def_10),
inference(global_subsumption_just,[status(thm)],[c_10312,c_104,c_9936,c_10312]) ).
tcf(c_10488,plain,
( ( slcrc0 = iPr_def_10 )
| ~ aSet0(iPr_def_10) ),
inference(superposition,[status(thm)],[c_50,c_10485]) ).
tcf(c_10491,plain,
slcrc0 = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_10488,c_9533]) ).
tcf(c_10515,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_8079,c_10491]) ).
tcf(c_10516,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_10515]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM540+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.35 % Computer : n019.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Thu Sep 24 04:31:34 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.41 % Proving...
% 3.95/1.28 % SZS status Started for theBenchmark.p
% 3.95/1.28 % SZS status Theorem for theBenchmark.p
% 3.95/1.28
% 3.95/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.95/1.28
% 3.95/1.28 % ------ iProver source info
% 3.95/1.28
% 3.95/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.95/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.95/1.28 % git: non_committed_changes: false
% 3.95/1.28
% 3.95/1.28 % ------ Parsing...
% 3.95/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.95/1.28
% 3.95/1.28 % ------ 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 %
% 3.95/1.28
% 3.95/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.95/1.28
% 3.95/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.95/1.28 % ------ Proving...
% 3.95/1.28 % ------ Problem Properties
% 3.95/1.28
% 3.95/1.28 %
% 3.95/1.28 % clauses 90
% 3.95/1.28 % conjectures 1
% 3.95/1.28 % EPR 30
% 3.95/1.28 % Horn 64
% 3.95/1.28 % unary 10
% 3.95/1.28 % binary 14
% 3.95/1.28 % lits 305
% 3.95/1.28 % lits eq 46
% 3.95/1.28 % fd_pure 0
% 3.95/1.28 % fd_pseudo 0
% 3.95/1.28 % fd_cond 8
% 3.95/1.28 % fd_pseudo_cond 14
% 3.95/1.28 % AC symbols 0
% 3.95/1.28
% 3.95/1.28 % ------ Schedule dynamic 5 is on
% 3.95/1.28
% 3.95/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.95/1.28
% 3.95/1.28
% 3.95/1.28 % ------
% 3.95/1.28 % Current options:
% 3.95/1.28 % ------
% 3.95/1.28
% 3.95/1.28
% 3.95/1.28 %
% 3.95/1.28
% 3.95/1.28 % ------ Proving...
% 3.95/1.28 %
% 3.95/1.28
% 3.95/1.28 % SZS status Theorem for theBenchmark.p
% 3.95/1.28
% 3.95/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.95/1.28
% 3.95/1.28
%------------------------------------------------------------------------------