TSTP Solution File: RNG123+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : RNG123+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n002.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 : Thu Aug 31 13:55:26 EDT 2023
% Result : Theorem 7.85s 1.68s
% Output : CNFRefutation 7.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 55 ( 19 unt; 0 def)
% Number of atoms : 198 ( 47 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 242 ( 99 ~; 79 |; 51 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-2 aty)
% Number of variables : 79 ( 0 sgn; 38 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p',mDefIdeal) ).
fof(f42,axiom,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& aIdeal0(xI) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',m__2273) ).
fof(f50,axiom,
( ( iLess0(sbrdtbr0(xr),sbrdtbr0(xu))
| sz00 = xr )
& xb = sdtpldt0(sdtasdt0(xq,xu),xr)
& aElement0(xr)
& aElement0(xq) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2666) ).
fof(f51,axiom,
sz00 != xr,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2673) ).
fof(f52,axiom,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2690) ).
fof(f53,axiom,
aElementOf0(xb,xI),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2699) ).
fof(f54,axiom,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2718) ).
fof(f60,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(f95,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,[],[f60]) ).
fof(f115,plain,
( ! [X0] :
( ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu))
| sz00 = X0
| ~ aElementOf0(X0,xI) )
& sz00 != xu
& aElementOf0(xu,xI) ),
inference(ennf_transformation,[],[f45]) ).
fof(f116,plain,
( ! [X0] :
( ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu))
| sz00 = X0
| ~ aElementOf0(X0,xI) )
& sz00 != xu
& aElementOf0(xu,xI) ),
inference(flattening,[],[f115]) ).
fof(f137,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,[],[f95]) ).
fof(f138,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,[],[f137]) ).
fof(f139,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,[],[f138]) ).
fof(f140,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(f141,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(f142,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(f143,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])],[f139,f142,f141,f140]) ).
fof(f222,plain,
! [X0,X6,X4] :
( aElementOf0(sdtpldt0(X4,X6),X0)
| ~ aElementOf0(X6,X0)
| ~ aElementOf0(X4,X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f269,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f42]) ).
fof(f279,plain,
! [X0] :
( ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu))
| sz00 = X0
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f116]) ).
fof(f289,plain,
( iLess0(sbrdtbr0(xr),sbrdtbr0(xu))
| sz00 = xr ),
inference(cnf_transformation,[],[f50]) ).
fof(f290,plain,
sz00 != xr,
inference(cnf_transformation,[],[f51]) ).
fof(f291,plain,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(cnf_transformation,[],[f52]) ).
fof(f292,plain,
aElementOf0(xb,xI),
inference(cnf_transformation,[],[f53]) ).
fof(f293,plain,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
inference(cnf_transformation,[],[f54]) ).
cnf(c_102,plain,
( ~ aElementOf0(X0,X1)
| ~ aElementOf0(X2,X1)
| ~ aIdeal0(X1)
| aElementOf0(sdtpldt0(X0,X2),X1) ),
inference(cnf_transformation,[],[f222]) ).
cnf(c_145,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f269]) ).
cnf(c_152,plain,
( ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu))
| ~ aElementOf0(X0,xI)
| X0 = sz00 ),
inference(cnf_transformation,[],[f279]) ).
cnf(c_161,plain,
( sz00 = xr
| iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ),
inference(cnf_transformation,[],[f289]) ).
cnf(c_165,plain,
sz00 != xr,
inference(cnf_transformation,[],[f290]) ).
cnf(c_166,plain,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(cnf_transformation,[],[f291]) ).
cnf(c_167,plain,
aElementOf0(xb,xI),
inference(cnf_transformation,[],[f292]) ).
cnf(c_168,plain,
sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) = xr,
inference(cnf_transformation,[],[f293]) ).
cnf(c_248,plain,
iLess0(sbrdtbr0(xr),sbrdtbr0(xu)),
inference(global_subsumption_just,[status(thm)],[c_161,c_165,c_161]) ).
cnf(c_1092,plain,
( sbrdtbr0(X0) != sbrdtbr0(xr)
| sbrdtbr0(xu) != sbrdtbr0(xu)
| ~ aElementOf0(X0,xI)
| X0 = sz00 ),
inference(resolution_lifted,[status(thm)],[c_152,c_248]) ).
cnf(c_4356,plain,
X0 = X0,
theory(equality) ).
cnf(c_4358,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_4368,plain,
( X0 != X1
| sbrdtbr0(X0) = sbrdtbr0(X1) ),
theory(equality) ).
cnf(c_6179,plain,
( sz00 != X0
| xr != X0 ),
inference(resolution,[status(thm)],[c_4358,c_165]) ).
cnf(c_6206,plain,
( X0 != X1
| sz00 != X0
| xr != X1 ),
inference(resolution,[status(thm)],[c_6179,c_4358]) ).
cnf(c_6386,plain,
( ~ aElementOf0(X0,xI)
| ~ aElementOf0(X1,xI)
| ~ aIdeal0(xI)
| aElementOf0(sdtpldt0(X0,X1),xI) ),
inference(instantiation,[status(thm)],[c_102]) ).
cnf(c_6762,plain,
( X0 != xr
| sz00 != X0 ),
inference(resolution,[status(thm)],[c_6206,c_4356]) ).
cnf(c_6879,plain,
( X0 != X1
| X0 != xr
| sz00 != X1 ),
inference(resolution,[status(thm)],[c_6762,c_4358]) ).
cnf(c_7178,plain,
( ~ aElementOf0(X0,xI)
| ~ aElementOf0(xb,xI)
| ~ aIdeal0(xI)
| aElementOf0(sdtpldt0(X0,xb),xI) ),
inference(instantiation,[status(thm)],[c_6386]) ).
cnf(c_7523,plain,
sbrdtbr0(xu) = sbrdtbr0(xu),
inference(instantiation,[status(thm)],[c_4356]) ).
cnf(c_9480,plain,
( ~ aElementOf0(smndt0(sdtasdt0(xq,xu)),xI)
| ~ aElementOf0(xb,xI)
| ~ aIdeal0(xI)
| aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),xI) ),
inference(instantiation,[status(thm)],[c_7178]) ).
cnf(c_9948,plain,
( X0 != xr
| sbrdtbr0(X0) = sbrdtbr0(xr) ),
inference(instantiation,[status(thm)],[c_4368]) ).
cnf(c_12279,plain,
( X0 != sz00
| X0 != xr ),
inference(resolution,[status(thm)],[c_6879,c_4356]) ).
cnf(c_12318,plain,
( X0 != xr
| sz00 != sz00
| ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu))
| ~ aElementOf0(X0,xI) ),
inference(resolution,[status(thm)],[c_6879,c_152]) ).
cnf(c_12319,plain,
( X0 != xr
| ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu))
| ~ aElementOf0(X0,xI) ),
inference(equality_resolution_simp,[status(thm)],[c_12318]) ).
cnf(c_12320,plain,
( X0 != xr
| ~ aElementOf0(X0,xI) ),
inference(global_subsumption_just,[status(thm)],[c_12319,c_1092,c_7523,c_9948,c_12279]) ).
cnf(c_12560,plain,
~ aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),xI),
inference(resolution,[status(thm)],[c_12320,c_168]) ).
cnf(c_12561,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_12560,c_9480,c_166,c_167,c_145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : RNG123+1 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.14 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 02:35:18 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.85/1.68 % SZS status Started for theBenchmark.p
% 7.85/1.68 % SZS status Theorem for theBenchmark.p
% 7.85/1.68
% 7.85/1.68 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 7.85/1.68
% 7.85/1.68 ------ iProver source info
% 7.85/1.68
% 7.85/1.68 git: date: 2023-05-31 18:12:56 +0000
% 7.85/1.68 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 7.85/1.68 git: non_committed_changes: false
% 7.85/1.68 git: last_make_outside_of_git: false
% 7.85/1.68
% 7.85/1.68 ------ Parsing...
% 7.85/1.68 ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.85/1.68
% 7.85/1.68 ------ 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: 2 0s sf_e pe_s pe_e
% 7.85/1.68
% 7.85/1.68 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 7.85/1.68
% 7.85/1.68 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.85/1.68 ------ Proving...
% 7.85/1.68 ------ Problem Properties
% 7.85/1.68
% 7.85/1.68
% 7.85/1.68 clauses 116
% 7.85/1.68 conjectures 1
% 7.85/1.68 EPR 30
% 7.85/1.68 Horn 92
% 7.85/1.68 unary 31
% 7.85/1.68 binary 16
% 7.85/1.68 lits 359
% 7.85/1.68 lits eq 54
% 7.85/1.68 fd_pure 0
% 7.85/1.68 fd_pseudo 0
% 7.85/1.68 fd_cond 5
% 7.85/1.68 fd_pseudo_cond 11
% 7.85/1.68 AC symbols 0
% 7.85/1.68
% 7.85/1.68 ------ Input Options Time Limit: Unbounded
% 7.85/1.68
% 7.85/1.68
% 7.85/1.68 ------
% 7.85/1.68 Current options:
% 7.85/1.68 ------
% 7.85/1.68
% 7.85/1.68
% 7.85/1.68
% 7.85/1.68
% 7.85/1.68 ------ Proving...
% 7.85/1.68
% 7.85/1.68
% 7.85/1.68 % SZS status Theorem for theBenchmark.p
% 7.85/1.68
% 7.85/1.68 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.85/1.68
% 7.85/1.69
%------------------------------------------------------------------------------