TSTP Solution File: RNG125+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : RNG125+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 3 02:57:46 EDT 2024
% Result : Theorem 3.50s 1.13s
% Output : CNFRefutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 55 ( 18 unt; 0 def)
% Number of atoms : 206 ( 11 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 244 ( 93 ~; 77 |; 56 &)
% ( 5 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% 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 : 76 ( 0 sgn 51 !; 16 ?)
% 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] :
( ( sz00 != X0
& aElementOf0(X0,xI) )
=> ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu)) )
& sz00 != xu
& 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)
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),X0) )
& ! [X3] :
( aElementOf0(X3,X0)
=> aElementOf0(sdtpldt0(X1,X3),X0) ) ) )
& aSet0(X0) ) ),
inference(rectify,[],[f24]) ).
fof(f83,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f90,plain,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( ( ! [X2] :
( aElementOf0(sdtasdt0(X2,X1),X0)
| ~ aElement0(X2) )
& ! [X3] :
( aElementOf0(sdtpldt0(X1,X3),X0)
| ~ aElementOf0(X3,X0) ) )
| ~ aElementOf0(X1,X0) )
& aSet0(X0) ) ),
inference(ennf_transformation,[],[f55]) ).
fof(f103,plain,
! [X0] :
( ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( doDivides0(X1,X0)
& aElement0(X1) ) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f110,plain,
( ! [X0] :
( ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu))
| sz00 = X0
| ~ aElementOf0(X0,xI) )
& sz00 != xu
& aElementOf0(xu,xI) ),
inference(ennf_transformation,[],[f45]) ).
fof(f111,plain,
( ! [X0] :
( ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu))
| sz00 = X0
| ~ aElementOf0(X0,xI) )
& sz00 != xu
& aElementOf0(xu,xI) ),
inference(flattening,[],[f110]) ).
fof(f112,plain,
( ~ aDivisorOf0(xu,xb)
| ~ aDivisorOf0(xu,xa) ),
inference(ennf_transformation,[],[f46]) ).
fof(f132,plain,
! [X0] :
( ( aIdeal0(X0)
| ? [X1] :
( ( ? [X2] :
( ~ aElementOf0(sdtasdt0(X2,X1),X0)
& aElement0(X2) )
| ? [X3] :
( ~ aElementOf0(sdtpldt0(X1,X3),X0)
& aElementOf0(X3,X0) ) )
& aElementOf0(X1,X0) )
| ~ aSet0(X0) )
& ( ( ! [X1] :
( ( ! [X2] :
( aElementOf0(sdtasdt0(X2,X1),X0)
| ~ aElement0(X2) )
& ! [X3] :
( aElementOf0(sdtpldt0(X1,X3),X0)
| ~ aElementOf0(X3,X0) ) )
| ~ aElementOf0(X1,X0) )
& aSet0(X0) )
| ~ aIdeal0(X0) ) ),
inference(nnf_transformation,[],[f90]) ).
fof(f133,plain,
! [X0] :
( ( aIdeal0(X0)
| ? [X1] :
( ( ? [X2] :
( ~ aElementOf0(sdtasdt0(X2,X1),X0)
& aElement0(X2) )
| ? [X3] :
( ~ aElementOf0(sdtpldt0(X1,X3),X0)
& aElementOf0(X3,X0) ) )
& aElementOf0(X1,X0) )
| ~ aSet0(X0) )
& ( ( ! [X1] :
( ( ! [X2] :
( aElementOf0(sdtasdt0(X2,X1),X0)
| ~ aElement0(X2) )
& ! [X3] :
( aElementOf0(sdtpldt0(X1,X3),X0)
| ~ aElementOf0(X3,X0) ) )
| ~ aElementOf0(X1,X0) )
& aSet0(X0) )
| ~ aIdeal0(X0) ) ),
inference(flattening,[],[f132]) ).
fof(f134,plain,
! [X0] :
( ( aIdeal0(X0)
| ? [X1] :
( ( ? [X2] :
( ~ aElementOf0(sdtasdt0(X2,X1),X0)
& aElement0(X2) )
| ? [X3] :
( ~ aElementOf0(sdtpldt0(X1,X3),X0)
& aElementOf0(X3,X0) ) )
& aElementOf0(X1,X0) )
| ~ aSet0(X0) )
& ( ( ! [X4] :
( ( ! [X5] :
( aElementOf0(sdtasdt0(X5,X4),X0)
| ~ aElement0(X5) )
& ! [X6] :
( aElementOf0(sdtpldt0(X4,X6),X0)
| ~ aElementOf0(X6,X0) ) )
| ~ aElementOf0(X4,X0) )
& aSet0(X0) )
| ~ aIdeal0(X0) ) ),
inference(rectify,[],[f133]) ).
fof(f135,plain,
! [X0] :
( ? [X1] :
( ( ? [X2] :
( ~ aElementOf0(sdtasdt0(X2,X1),X0)
& aElement0(X2) )
| ? [X3] :
( ~ aElementOf0(sdtpldt0(X1,X3),X0)
& aElementOf0(X3,X0) ) )
& aElementOf0(X1,X0) )
=> ( ( ? [X2] :
( ~ aElementOf0(sdtasdt0(X2,sK10(X0)),X0)
& aElement0(X2) )
| ? [X3] :
( ~ aElementOf0(sdtpldt0(sK10(X0),X3),X0)
& aElementOf0(X3,X0) ) )
& aElementOf0(sK10(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f136,plain,
! [X0] :
( ? [X2] :
( ~ aElementOf0(sdtasdt0(X2,sK10(X0)),X0)
& aElement0(X2) )
=> ( ~ aElementOf0(sdtasdt0(sK11(X0),sK10(X0)),X0)
& aElement0(sK11(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f137,plain,
! [X0] :
( ? [X3] :
( ~ aElementOf0(sdtpldt0(sK10(X0),X3),X0)
& aElementOf0(X3,X0) )
=> ( ~ aElementOf0(sdtpldt0(sK10(X0),sK12(X0)),X0)
& aElementOf0(sK12(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f138,plain,
! [X0] :
( ( aIdeal0(X0)
| ( ( ( ~ aElementOf0(sdtasdt0(sK11(X0),sK10(X0)),X0)
& aElement0(sK11(X0)) )
| ( ~ aElementOf0(sdtpldt0(sK10(X0),sK12(X0)),X0)
& aElementOf0(sK12(X0),X0) ) )
& aElementOf0(sK10(X0),X0) )
| ~ aSet0(X0) )
& ( ( ! [X4] :
( ( ! [X5] :
( aElementOf0(sdtasdt0(X5,X4),X0)
| ~ aElement0(X5) )
& ! [X6] :
( aElementOf0(sdtpldt0(X4,X6),X0)
| ~ aElementOf0(X6,X0) ) )
| ~ aElementOf0(X4,X0) )
& aSet0(X0) )
| ~ aIdeal0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f134,f137,f136,f135]) ).
fof(f150,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ doDivides0(X1,X0)
| ~ aElement0(X1) )
& ( ( doDivides0(X1,X0)
& aElement0(X1) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aElement0(X0) ),
inference(nnf_transformation,[],[f103]) ).
fof(f151,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ doDivides0(X1,X0)
| ~ aElement0(X1) )
& ( ( doDivides0(X1,X0)
& aElement0(X1) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aElement0(X0) ),
inference(flattening,[],[f150]) ).
fof(f192,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f216,plain,
! [X0] :
( aSet0(X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f138]) ).
fof(f243,plain,
! [X0,X1] :
( aDivisorOf0(X1,X0)
| ~ doDivides0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f151]) ).
fof(f260,plain,
aElement0(xa),
inference(cnf_transformation,[],[f39]) ).
fof(f261,plain,
aElement0(xb),
inference(cnf_transformation,[],[f39]) ).
fof(f264,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f42]) ).
fof(f272,plain,
aElementOf0(xu,xI),
inference(cnf_transformation,[],[f111]) ).
fof(f275,plain,
( ~ aDivisorOf0(xu,xb)
| ~ aDivisorOf0(xu,xa) ),
inference(cnf_transformation,[],[f112]) ).
fof(f279,plain,
doDivides0(xu,xa),
inference(cnf_transformation,[],[f48]) ).
fof(f280,plain,
doDivides0(xu,xb),
inference(cnf_transformation,[],[f49]) ).
cnf(c_72,plain,
( ~ aElementOf0(X0,X1)
| ~ aSet0(X1)
| aElement0(X0) ),
inference(cnf_transformation,[],[f192]) ).
cnf(c_103,plain,
( ~ aIdeal0(X0)
| aSet0(X0) ),
inference(cnf_transformation,[],[f216]) ).
cnf(c_121,plain,
( ~ doDivides0(X0,X1)
| ~ aElement0(X0)
| ~ aElement0(X1)
| aDivisorOf0(X0,X1) ),
inference(cnf_transformation,[],[f243]) ).
cnf(c_140,plain,
aElement0(xb),
inference(cnf_transformation,[],[f261]) ).
cnf(c_141,plain,
aElement0(xa),
inference(cnf_transformation,[],[f260]) ).
cnf(c_145,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f264]) ).
cnf(c_154,plain,
aElementOf0(xu,xI),
inference(cnf_transformation,[],[f272]) ).
cnf(c_155,plain,
( ~ aDivisorOf0(xu,xb)
| ~ aDivisorOf0(xu,xa) ),
inference(cnf_transformation,[],[f275]) ).
cnf(c_159,plain,
doDivides0(xu,xa),
inference(cnf_transformation,[],[f279]) ).
cnf(c_160,plain,
doDivides0(xu,xb),
inference(cnf_transformation,[],[f280]) ).
cnf(c_2240,plain,
( X0 != xu
| X1 != xa
| ~ aElement0(X0)
| ~ aElement0(X1)
| aDivisorOf0(X0,X1) ),
inference(resolution_lifted,[status(thm)],[c_121,c_159]) ).
cnf(c_2241,plain,
( ~ aElement0(xa)
| ~ aElement0(xu)
| aDivisorOf0(xu,xa) ),
inference(unflattening,[status(thm)],[c_2240]) ).
cnf(c_2242,plain,
( ~ aElement0(xu)
| aDivisorOf0(xu,xa) ),
inference(global_subsumption_just,[status(thm)],[c_2241,c_141,c_2241]) ).
cnf(c_2270,plain,
( X0 != xu
| X1 != xb
| ~ aElement0(X0)
| ~ aElement0(X1)
| aDivisorOf0(X0,X1) ),
inference(resolution_lifted,[status(thm)],[c_121,c_160]) ).
cnf(c_2271,plain,
( ~ aElement0(xb)
| ~ aElement0(xu)
| aDivisorOf0(xu,xb) ),
inference(unflattening,[status(thm)],[c_2270]) ).
cnf(c_2272,plain,
~ aElement0(xu),
inference(global_subsumption_just,[status(thm)],[c_2271,c_140,c_155,c_2242,c_2271]) ).
cnf(c_7213,plain,
aSet0(xI),
inference(superposition,[status(thm)],[c_145,c_103]) ).
cnf(c_7333,plain,
( ~ aSet0(xI)
| aElement0(xu) ),
inference(superposition,[status(thm)],[c_154,c_72]) ).
cnf(c_7336,plain,
aElement0(xu),
inference(forward_subsumption_resolution,[status(thm)],[c_7333,c_7213]) ).
cnf(c_7337,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_7336,c_2272]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : RNG125+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.11 % Command : run_iprover %s %d THM
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu May 2 21:10:32 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.17/0.43 Running first-order theorem proving
% 0.17/0.43 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.50/1.13 % SZS status Started for theBenchmark.p
% 3.50/1.13 % SZS status Theorem for theBenchmark.p
% 3.50/1.13
% 3.50/1.13 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.50/1.13
% 3.50/1.13 ------ iProver source info
% 3.50/1.13
% 3.50/1.13 git: date: 2024-05-02 19:28:25 +0000
% 3.50/1.13 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.50/1.13 git: non_committed_changes: false
% 3.50/1.13
% 3.50/1.13 ------ Parsing...
% 3.50/1.13 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.50/1.13
% 3.50/1.13 ------ 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
% 3.50/1.13
% 3.50/1.13 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.50/1.13
% 3.50/1.13 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.50/1.13 ------ Proving...
% 3.50/1.13 ------ Problem Properties
% 3.50/1.13
% 3.50/1.13
% 3.50/1.13 clauses 107
% 3.50/1.13 conjectures 0
% 3.50/1.13 EPR 26
% 3.50/1.13 Horn 83
% 3.50/1.13 unary 21
% 3.50/1.13 binary 17
% 3.50/1.13 lits 351
% 3.50/1.13 lits eq 51
% 3.50/1.13 fd_pure 0
% 3.50/1.13 fd_pseudo 0
% 3.50/1.13 fd_cond 5
% 3.50/1.13 fd_pseudo_cond 11
% 3.50/1.13 AC symbols 0
% 3.50/1.13
% 3.50/1.13 ------ Schedule dynamic 5 is on
% 3.50/1.13
% 3.50/1.13 ------ no conjectures: strip conj schedule
% 3.50/1.13
% 3.50/1.13 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.50/1.13
% 3.50/1.13
% 3.50/1.13 ------
% 3.50/1.13 Current options:
% 3.50/1.13 ------
% 3.50/1.13
% 3.50/1.13
% 3.50/1.13
% 3.50/1.13
% 3.50/1.13 ------ Proving...
% 3.50/1.13
% 3.50/1.13
% 3.50/1.13 % SZS status Theorem for theBenchmark.p
% 3.50/1.13
% 3.50/1.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.50/1.13
% 3.50/1.13
%------------------------------------------------------------------------------