%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG125+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 : n010.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 02:39:14 PM UTC 2026
% Result : Theorem 3.36s 1.28s
% Output : CNFRefutation 3.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 52 ( 18 unt; 0 def)
% Number of atoms : 188 ( 11 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 221 ( 85 ~; 75 |; 46 &)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 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 : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn 57 !; 9 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
fof(f20,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f24,axiom,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),X0) )
& ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
& aSet0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefIdeal) ).
fof(f34,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( doDivides0(X1,X0)
& aElement0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDvs) ).
fof(f39,axiom,
( aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2091) ).
fof(f42,axiom,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& aIdeal0(xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).
fof(f45,axiom,
( ! [X0] :
( ( X0 != sz00
& aElementOf0(X0,xI) )
=> ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2273) ).
fof(f46,axiom,
~ ( aDivisorOf0(xu,xb)
& aDivisorOf0(xu,xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2383) ).
fof(f48,axiom,
doDivides0(xu,xa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2479) ).
fof(f49,axiom,
doDivides0(xu,xb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2612) ).
fof(f55,plain,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X1),X0) )
& ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
& aSet0(X0) ) ),
inference(rectify,[],[f24]) ).
fof(f83,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f90,plain,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( ~ aElementOf0(X1,X0)
| ( ! [X3] :
( ~ aElement0(X3)
| aElementOf0(sdtasdt0(X3,X1),X0) )
& ! [X2] :
( ~ aElementOf0(X2,X0)
| aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
& aSet0(X0) ) ),
inference(ennf_transformation,[],[f55]) ).
fof(f103,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( doDivides0(X1,X0)
& aElement0(X1) ) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f110,plain,
( ! [X0] :
( sz00 = X0
| ~ aElementOf0(X0,xI)
| ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI) ),
inference(ennf_transformation,[],[f45]) ).
fof(f111,plain,
( ! [X0] :
( sz00 = X0
| ~ aElementOf0(X0,xI)
| ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI) ),
inference(flattening,[],[f110]) ).
fof(f112,plain,
( ~ aDivisorOf0(xu,xb)
| ~ aDivisorOf0(xu,xa) ),
inference(ennf_transformation,[],[f46]) ).
fof(f127,plain,
! [X0] :
( ( ~ aIdeal0(X0)
| ( ! [X1] :
( ~ aElementOf0(X1,X0)
| ( ! [X3] :
( ~ aElement0(X3)
| aElementOf0(sdtasdt0(X3,X1),X0) )
& ! [X2] :
( ~ aElementOf0(X2,X0)
| aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
& aSet0(X0) ) )
& ( ? [X1] :
( aElementOf0(X1,X0)
& ( ? [X3] :
( aElement0(X3)
& ~ aElementOf0(sdtasdt0(X3,X1),X0) )
| ? [X2] :
( aElementOf0(X2,X0)
& ~ aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
| ~ aSet0(X0)
| aIdeal0(X0) ) ),
inference(nnf_transformation,[],[f90]) ).
fof(f128,plain,
! [X0] :
( ( ~ aIdeal0(X0)
| ( ! [X1] :
( ~ aElementOf0(X1,X0)
| ( ! [X3] :
( ~ aElement0(X3)
| aElementOf0(sdtasdt0(X3,X1),X0) )
& ! [X2] :
( ~ aElementOf0(X2,X0)
| aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
& aSet0(X0) ) )
& ( ? [X1] :
( aElementOf0(X1,X0)
& ( ? [X3] :
( aElement0(X3)
& ~ aElementOf0(sdtasdt0(X3,X1),X0) )
| ? [X2] :
( aElementOf0(X2,X0)
& ~ aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
| ~ aSet0(X0)
| aIdeal0(X0) ) ),
inference(flattening,[],[f127]) ).
fof(f129,plain,
! [X0] :
( ( ~ aIdeal0(X0)
| ( ! [X4] :
( ~ aElementOf0(X4,X0)
| ( ! [X6] :
( ~ aElement0(X6)
| aElementOf0(sdtasdt0(X6,X4),X0) )
& ! [X5] :
( ~ aElementOf0(X5,X0)
| aElementOf0(sdtpldt0(X4,X5),X0) ) ) )
& aSet0(X0) ) )
& ( ? [X1] :
( aElementOf0(X1,X0)
& ( ? [X3] :
( aElement0(X3)
& ~ aElementOf0(sdtasdt0(X3,X1),X0) )
| ? [X2] :
( aElementOf0(X2,X0)
& ~ aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
| ~ aSet0(X0)
| aIdeal0(X0) ) ),
inference(rectify,[],[f128]) ).
fof(f130,plain,
! [X0] :
( ( ~ aIdeal0(X0)
| ( ! [X4] :
( ~ aElementOf0(X4,X0)
| ( ! [X6] :
( ~ aElement0(X6)
| aElementOf0(sdtasdt0(X6,X4),X0) )
& ! [X5] :
( ~ aElementOf0(X5,X0)
| aElementOf0(sdtpldt0(X4,X5),X0) ) ) )
& aSet0(X0) ) )
& ( ( aElementOf0(sK10(X0),X0)
& ( ( aElement0(sK12(X0))
& ~ aElementOf0(sdtasdt0(sK12(X0),sK10(X0)),X0) )
| ( aElementOf0(sK11(X0),X0)
& ~ aElementOf0(sdtpldt0(sK10(X0),sK11(X0)),X0) ) ) )
| ~ aSet0(X0)
| aIdeal0(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12]),skolemize(X1,sK10(X0)),skolemize(X2,sK11(X0)),skolemize(X3,sK12(X0))],[f129]) ).
fof(f138,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ( ~ aDivisorOf0(X1,X0)
| ( doDivides0(X1,X0)
& aElement0(X1) ) )
& ( ~ doDivides0(X1,X0)
| ~ aElement0(X1)
| aDivisorOf0(X1,X0) ) ) ),
inference(nnf_transformation,[],[f103]) ).
fof(f139,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ( ~ aDivisorOf0(X1,X0)
| ( doDivides0(X1,X0)
& aElement0(X1) ) )
& ( ~ doDivides0(X1,X0)
| ~ aElement0(X1)
| aDivisorOf0(X1,X0) ) ) ),
inference(flattening,[],[f138]) ).
fof(f174,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f200,plain,
! [X0] :
( ~ aIdeal0(X0)
| aSet0(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f225,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ doDivides0(X1,X0)
| ~ aElement0(X1)
| aDivisorOf0(X1,X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f242,plain,
aElement0(xb),
inference(cnf_transformation,[],[f39]) ).
fof(f243,plain,
aElement0(xa),
inference(cnf_transformation,[],[f39]) ).
fof(f247,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f42]) ).
fof(f256,plain,
aElementOf0(xu,xI),
inference(cnf_transformation,[],[f111]) ).
fof(f257,plain,
( ~ aDivisorOf0(xu,xb)
| ~ aDivisorOf0(xu,xa) ),
inference(cnf_transformation,[],[f112]) ).
fof(f261,plain,
doDivides0(xu,xa),
inference(cnf_transformation,[],[f48]) ).
fof(f262,plain,
doDivides0(xu,xb),
inference(cnf_transformation,[],[f49]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_101,plain,
! [X0: $i] :
( aSet0(X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f200]) ).
tcf(c_121,plain,
! [X0: $i,X1: $i] :
( aDivisorOf0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f225]) ).
tcf(c_140,plain,
aElement0(xa),
inference(cnf_transformation,[],[f243]) ).
tcf(c_141,plain,
aElement0(xb),
inference(cnf_transformation,[],[f242]) ).
tcf(c_144,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f247]) ).
tcf(c_152,plain,
aElementOf0(xu,xI),
inference(cnf_transformation,[],[f256]) ).
tcf(c_155,plain,
( ~ aDivisorOf0(xu,xb)
| ~ aDivisorOf0(xu,xa) ),
inference(cnf_transformation,[],[f257]) ).
tcf(c_159,plain,
doDivides0(xu,xa),
inference(cnf_transformation,[],[f261]) ).
tcf(c_160,plain,
doDivides0(xu,xb),
inference(cnf_transformation,[],[f262]) ).
tcf(c_2240,plain,
! [X0: $i,X1: $i] :
( aDivisorOf0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ( X1 != xa )
| ( X0 != xu ) ),
inference(resolution_lifted,[status(thm)],[c_121,c_159]) ).
tcf(c_2241,plain,
( aDivisorOf0(xu,xa)
| ~ aElement0(xu)
| ~ aElement0(xa) ),
inference(unflattening,[status(thm)],[c_2240]) ).
tcf(c_2242,plain,
( aDivisorOf0(xu,xa)
| ~ aElement0(xu) ),
inference(global_subsumption_just,[status(thm)],[c_2241,c_140,c_2241]) ).
tcf(c_2270,plain,
! [X0: $i,X1: $i] :
( aDivisorOf0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ( X1 != xb )
| ( X0 != xu ) ),
inference(resolution_lifted,[status(thm)],[c_121,c_160]) ).
tcf(c_2271,plain,
( aDivisorOf0(xu,xb)
| ~ aElement0(xu)
| ~ aElement0(xb) ),
inference(unflattening,[status(thm)],[c_2270]) ).
tcf(c_2272,plain,
~ aElement0(xu),
inference(global_subsumption_just,[status(thm)],[c_2271,c_141,c_155,c_2242,c_2271]) ).
tcf(c_7213,plain,
aSet0(xI),
inference(superposition,[status(thm)],[c_144,c_101]) ).
tcf(c_7333,plain,
( aElement0(xu)
| ~ aSet0(xI) ),
inference(superposition,[status(thm)],[c_152,c_72]) ).
tcf(c_7336,plain,
aElement0(xu),
inference(forward_subsumption_resolution,[status(thm)],[c_7333,c_7213]) ).
tcf(c_7337,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_7336,c_2272]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG125+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n010.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 08:22:13 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 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
% 0.08/0.41
% 0.08/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.41
% 0.08/0.41 % Detected problem language: tptp
% 0.08/0.42 % Proving...
% 3.36/1.28 % SZS status Started for theBenchmark.p
% 3.36/1.28 % SZS status Theorem for theBenchmark.p
% 3.36/1.28
% 3.36/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.36/1.28
% 3.36/1.28 % ------ iProver source info
% 3.36/1.28
% 3.36/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.36/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.36/1.28 % git: non_committed_changes: false
% 3.36/1.28
% 3.36/1.28 % ------ Parsing...
% 3.36/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.36/1.28
% 3.36/1.28 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 3.36/1.28
% 3.36/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.36/1.28
% 3.36/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.36/1.28 % ------ Proving...
% 3.36/1.28 % ------ Problem Properties
% 3.36/1.28
% 3.36/1.28 %
% 3.36/1.28 % clauses 107
% 3.36/1.28 % conjectures 0
% 3.36/1.28 % EPR 26
% 3.36/1.28 % Horn 83
% 3.36/1.28 % unary 21
% 3.36/1.28 % binary 17
% 3.36/1.28 % lits 351
% 3.36/1.28 % lits eq 51
% 3.36/1.28 % fd_pure 0
% 3.36/1.28 % fd_pseudo 0
% 3.36/1.28 % fd_cond 5
% 3.36/1.28 % fd_pseudo_cond 11
% 3.36/1.28 % AC symbols 0
% 3.36/1.28
% 3.36/1.28 % ------ Schedule dynamic 5 is on
% 3.36/1.28
% 3.36/1.28 % ------ no conjectures: strip conj schedule
% 3.36/1.28
% 3.36/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.36/1.28
% 3.36/1.28
% 3.36/1.28 % ------
% 3.36/1.28 % Current options:
% 3.36/1.28 % ------
% 3.36/1.28
% 3.36/1.28
% 3.36/1.28 %
% 3.36/1.28
% 3.36/1.28 % ------ Proving...
% 3.36/1.28 %
% 3.36/1.28
% 3.36/1.28 % SZS status Theorem for theBenchmark.p
% 3.36/1.28
% 3.36/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.36/1.28
% 3.36/1.28
%------------------------------------------------------------------------------