TSTP Solution File: RNG125+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : RNG125+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n029.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 : Wed May 31 12:32:59 EDT 2023
% Result : Theorem 0.14s 0.31s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 22
% Syntax : Number of formulae : 84 ( 17 unt; 3 def)
% Number of atoms : 282 ( 28 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 312 ( 114 ~; 110 |; 61 &)
% ( 18 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 11 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-3 aty)
% Number of variables : 87 (; 73 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f20,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,definition,
! [W0] :
( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> ( ! [W2] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,definition,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( aElement0(W1)
& doDivides0(W1,W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,definition,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( W1 = slsdtgt0(W0)
<=> ( aSet0(W1)
& ! [W2] :
( aElementOf0(W2,W1)
<=> ? [W3] :
( aElement0(W3)
& sdtasdt0(W0,W3) = W2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [W0] :
( aElement0(W0)
=> aIdeal0(slsdtgt0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,hypothesis,
( aIdeal0(xI)
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
( aElementOf0(sz00,slsdtgt0(xa))
& aElementOf0(xa,slsdtgt0(xa))
& aElementOf0(sz00,slsdtgt0(xb))
& aElementOf0(xb,slsdtgt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,hypothesis,
( aElementOf0(xu,xI)
& xu != sz00
& ! [W0] :
( ( aElementOf0(W0,xI)
& W0 != sz00 )
=> ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,hypothesis,
~ ( aDivisorOf0(xu,xa)
& aDivisorOf0(xu,xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,hypothesis,
~ ~ doDivides0(xu,xa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,hypothesis,
~ ~ doDivides0(xu,xb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f95,plain,
! [W0] :
( ~ aSet0(W0)
| ! [W1] :
( ~ aElementOf0(W1,W0)
| aElement0(W1) ) ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f96,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[status(esa)],[f95]) ).
fof(f125,plain,
! [W0] :
( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1] :
( ~ aElementOf0(W1,W0)
| ( ! [W2] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f24]) ).
fof(f126,plain,
! [W0] :
( ( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1] :
( ~ aElementOf0(W1,W0)
| ( ! [W2] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ? [W1] :
( aElementOf0(W1,W0)
& ( ? [W2] :
( aElementOf0(W2,W0)
& ~ aElementOf0(sdtpldt0(W1,W2),W0) )
| ? [W2] :
( aElement0(W2)
& ~ aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f125]) ).
fof(f127,plain,
( ! [W0] :
( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1] :
( ~ aElementOf0(W1,W0)
| ( ! [W2] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ! [W0] :
( aIdeal0(W0)
| ~ aSet0(W0)
| ? [W1] :
( aElementOf0(W1,W0)
& ( ? [W2] :
( aElementOf0(W2,W0)
& ~ aElementOf0(sdtpldt0(W1,W2),W0) )
| ? [W2] :
( aElement0(W2)
& ~ aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f126]) ).
fof(f128,plain,
( ! [W0] :
( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1] :
( ~ aElementOf0(W1,W0)
| ( ! [W2] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ! [W0] :
( aIdeal0(W0)
| ~ aSet0(W0)
| ( aElementOf0(sk0_8(W0),W0)
& ( ( aElementOf0(sk0_9(W0),W0)
& ~ aElementOf0(sdtpldt0(sk0_8(W0),sk0_9(W0)),W0) )
| ( aElement0(sk0_10(W0))
& ~ aElementOf0(sdtasdt0(sk0_10(W0),sk0_8(W0)),W0) ) ) ) ) ),
inference(skolemization,[status(esa)],[f127]) ).
fof(f129,plain,
! [X0] :
( ~ aIdeal0(X0)
| aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f128]) ).
fof(f171,plain,
! [W0] :
( ~ aElement0(W0)
| ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( aElement0(W1)
& doDivides0(W1,W0) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f34]) ).
fof(f172,plain,
! [W0] :
( ~ aElement0(W0)
| ! [W1] :
( ( ~ aDivisorOf0(W1,W0)
| ( aElement0(W1)
& doDivides0(W1,W0) ) )
& ( aDivisorOf0(W1,W0)
| ~ aElement0(W1)
| ~ doDivides0(W1,W0) ) ) ),
inference(NNF_transformation,[status(esa)],[f171]) ).
fof(f173,plain,
! [W0] :
( ~ aElement0(W0)
| ( ! [W1] :
( ~ aDivisorOf0(W1,W0)
| ( aElement0(W1)
& doDivides0(W1,W0) ) )
& ! [W1] :
( aDivisorOf0(W1,W0)
| ~ aElement0(W1)
| ~ doDivides0(W1,W0) ) ) ),
inference(miniscoping,[status(esa)],[f172]) ).
fof(f176,plain,
! [X0,X1] :
( ~ aElement0(X0)
| aDivisorOf0(X1,X0)
| ~ aElement0(X1)
| ~ doDivides0(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f173]) ).
fof(f191,plain,
! [W0] :
( ~ aElement0(W0)
| ! [W1] :
( W1 = slsdtgt0(W0)
<=> ( aSet0(W1)
& ! [W2] :
( aElementOf0(W2,W1)
<=> ? [W3] :
( aElement0(W3)
& sdtasdt0(W0,W3) = W2 ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f37]) ).
fof(f192,plain,
! [W0] :
( ~ aElement0(W0)
| ! [W1] :
( ( W1 != slsdtgt0(W0)
| ( aSet0(W1)
& ! [W2] :
( ( ~ aElementOf0(W2,W1)
| ? [W3] :
( aElement0(W3)
& sdtasdt0(W0,W3) = W2 ) )
& ( aElementOf0(W2,W1)
| ! [W3] :
( ~ aElement0(W3)
| sdtasdt0(W0,W3) != W2 ) ) ) ) )
& ( W1 = slsdtgt0(W0)
| ~ aSet0(W1)
| ? [W2] :
( ( ~ aElementOf0(W2,W1)
| ! [W3] :
( ~ aElement0(W3)
| sdtasdt0(W0,W3) != W2 ) )
& ( aElementOf0(W2,W1)
| ? [W3] :
( aElement0(W3)
& sdtasdt0(W0,W3) = W2 ) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f191]) ).
fof(f193,plain,
! [W0] :
( ~ aElement0(W0)
| ( ! [W1] :
( W1 != slsdtgt0(W0)
| ( aSet0(W1)
& ! [W2] :
( ~ aElementOf0(W2,W1)
| ? [W3] :
( aElement0(W3)
& sdtasdt0(W0,W3) = W2 ) )
& ! [W2] :
( aElementOf0(W2,W1)
| ! [W3] :
( ~ aElement0(W3)
| sdtasdt0(W0,W3) != W2 ) ) ) )
& ! [W1] :
( W1 = slsdtgt0(W0)
| ~ aSet0(W1)
| ? [W2] :
( ( ~ aElementOf0(W2,W1)
| ! [W3] :
( ~ aElement0(W3)
| sdtasdt0(W0,W3) != W2 ) )
& ( aElementOf0(W2,W1)
| ? [W3] :
( aElement0(W3)
& sdtasdt0(W0,W3) = W2 ) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f192]) ).
fof(f194,plain,
! [W0] :
( ~ aElement0(W0)
| ( ! [W1] :
( W1 != slsdtgt0(W0)
| ( aSet0(W1)
& ! [W2] :
( ~ aElementOf0(W2,W1)
| ( aElement0(sk0_17(W2,W1,W0))
& sdtasdt0(W0,sk0_17(W2,W1,W0)) = W2 ) )
& ! [W2] :
( aElementOf0(W2,W1)
| ! [W3] :
( ~ aElement0(W3)
| sdtasdt0(W0,W3) != W2 ) ) ) )
& ! [W1] :
( W1 = slsdtgt0(W0)
| ~ aSet0(W1)
| ( ( ~ aElementOf0(sk0_18(W1,W0),W1)
| ! [W3] :
( ~ aElement0(W3)
| sdtasdt0(W0,W3) != sk0_18(W1,W0) ) )
& ( aElementOf0(sk0_18(W1,W0),W1)
| ( aElement0(sk0_19(W1,W0))
& sdtasdt0(W0,sk0_19(W1,W0)) = sk0_18(W1,W0) ) ) ) ) ) ),
inference(skolemization,[status(esa)],[f193]) ).
fof(f195,plain,
! [X0,X1] :
( ~ aElement0(X0)
| X1 != slsdtgt0(X0)
| aSet0(X1) ),
inference(cnf_transformation,[status(esa)],[f194]) ).
fof(f202,plain,
! [W0] :
( ~ aElement0(W0)
| aIdeal0(slsdtgt0(W0)) ),
inference(pre_NNF_transformation,[status(esa)],[f38]) ).
fof(f203,plain,
! [X0] :
( ~ aElement0(X0)
| aIdeal0(slsdtgt0(X0)) ),
inference(cnf_transformation,[status(esa)],[f202]) ).
fof(f204,plain,
aElement0(xa),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f205,plain,
aElement0(xb),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f208,plain,
aIdeal0(xI),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f211,plain,
aElementOf0(xa,slsdtgt0(xa)),
inference(cnf_transformation,[status(esa)],[f43]) ).
fof(f213,plain,
aElementOf0(xb,slsdtgt0(xb)),
inference(cnf_transformation,[status(esa)],[f43]) ).
fof(f217,plain,
( aElementOf0(xu,xI)
& xu != sz00
& ! [W0] :
( ~ aElementOf0(W0,xI)
| W0 = sz00
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f45]) ).
fof(f218,plain,
aElementOf0(xu,xI),
inference(cnf_transformation,[status(esa)],[f217]) ).
fof(f221,plain,
( ~ aDivisorOf0(xu,xa)
| ~ aDivisorOf0(xu,xb) ),
inference(pre_NNF_transformation,[status(esa)],[f46]) ).
fof(f222,plain,
( ~ aDivisorOf0(xu,xa)
| ~ aDivisorOf0(xu,xb) ),
inference(cnf_transformation,[status(esa)],[f221]) ).
fof(f227,plain,
doDivides0(xu,xa),
inference(cnf_transformation,[status(esa)],[f48]) ).
fof(f228,plain,
doDivides0(xu,xb),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f249,plain,
( spl0_2
<=> aDivisorOf0(xu,xa) ),
introduced(split_symbol_definition) ).
fof(f252,plain,
( spl0_3
<=> aDivisorOf0(xu,xb) ),
introduced(split_symbol_definition) ).
fof(f255,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f222,f249,f252]) ).
fof(f264,plain,
! [X0] :
( ~ aElement0(X0)
| aSet0(slsdtgt0(X0)) ),
inference(destructive_equality_resolution,[status(esa)],[f195]) ).
fof(f269,plain,
aSet0(xI),
inference(resolution,[status(thm)],[f129,f208]) ).
fof(f271,plain,
( spl0_4
<=> aSet0(slsdtgt0(xb)) ),
introduced(split_symbol_definition) ).
fof(f273,plain,
( ~ aSet0(slsdtgt0(xb))
| spl0_4 ),
inference(component_clause,[status(thm)],[f271]) ).
fof(f274,plain,
( spl0_5
<=> aElement0(xb) ),
introduced(split_symbol_definition) ).
fof(f277,plain,
( ~ aSet0(slsdtgt0(xb))
| aElement0(xb) ),
inference(resolution,[status(thm)],[f96,f213]) ).
fof(f278,plain,
( ~ spl0_4
| spl0_5 ),
inference(split_clause,[status(thm)],[f277,f271,f274]) ).
fof(f279,plain,
( spl0_6
<=> aSet0(slsdtgt0(xa)) ),
introduced(split_symbol_definition) ).
fof(f281,plain,
( ~ aSet0(slsdtgt0(xa))
| spl0_6 ),
inference(component_clause,[status(thm)],[f279]) ).
fof(f282,plain,
( spl0_7
<=> aElement0(xa) ),
introduced(split_symbol_definition) ).
fof(f285,plain,
( ~ aSet0(slsdtgt0(xa))
| aElement0(xa) ),
inference(resolution,[status(thm)],[f96,f211]) ).
fof(f286,plain,
( ~ spl0_6
| spl0_7 ),
inference(split_clause,[status(thm)],[f285,f279,f282]) ).
fof(f294,plain,
( spl0_9
<=> aSet0(xI) ),
introduced(split_symbol_definition) ).
fof(f296,plain,
( ~ aSet0(xI)
| spl0_9 ),
inference(component_clause,[status(thm)],[f294]) ).
fof(f297,plain,
( spl0_10
<=> aElement0(xu) ),
introduced(split_symbol_definition) ).
fof(f300,plain,
( ~ aSet0(xI)
| aElement0(xu) ),
inference(resolution,[status(thm)],[f96,f218]) ).
fof(f301,plain,
( ~ spl0_9
| spl0_10 ),
inference(split_clause,[status(thm)],[f300,f294,f297]) ).
fof(f302,plain,
( $false
| spl0_9 ),
inference(forward_subsumption_resolution,[status(thm)],[f296,f269]) ).
fof(f303,plain,
spl0_9,
inference(contradiction_clause,[status(thm)],[f302]) ).
fof(f304,plain,
( ~ aElement0(xa)
| spl0_6 ),
inference(resolution,[status(thm)],[f281,f264]) ).
fof(f305,plain,
( $false
| spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f304,f204]) ).
fof(f306,plain,
spl0_6,
inference(contradiction_clause,[status(thm)],[f305]) ).
fof(f307,plain,
( ~ aElement0(xb)
| spl0_4 ),
inference(resolution,[status(thm)],[f273,f264]) ).
fof(f308,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f307,f205]) ).
fof(f309,plain,
spl0_4,
inference(contradiction_clause,[status(thm)],[f308]) ).
fof(f314,plain,
( spl0_11
<=> aIdeal0(slsdtgt0(xa)) ),
introduced(split_symbol_definition) ).
fof(f316,plain,
( ~ aIdeal0(slsdtgt0(xa))
| spl0_11 ),
inference(component_clause,[status(thm)],[f314]) ).
fof(f317,plain,
( spl0_12
<=> aIdeal0(slsdtgt0(xb)) ),
introduced(split_symbol_definition) ).
fof(f319,plain,
( ~ aIdeal0(slsdtgt0(xb))
| spl0_12 ),
inference(component_clause,[status(thm)],[f317]) ).
fof(f327,plain,
( ~ aElement0(xb)
| spl0_12 ),
inference(resolution,[status(thm)],[f319,f203]) ).
fof(f328,plain,
( $false
| spl0_12 ),
inference(forward_subsumption_resolution,[status(thm)],[f327,f205]) ).
fof(f329,plain,
spl0_12,
inference(contradiction_clause,[status(thm)],[f328]) ).
fof(f330,plain,
( ~ aElement0(xa)
| spl0_11 ),
inference(resolution,[status(thm)],[f316,f203]) ).
fof(f331,plain,
( $false
| spl0_11 ),
inference(forward_subsumption_resolution,[status(thm)],[f330,f204]) ).
fof(f332,plain,
spl0_11,
inference(contradiction_clause,[status(thm)],[f331]) ).
fof(f335,plain,
( ~ aElement0(xb)
| aDivisorOf0(xu,xb)
| ~ aElement0(xu) ),
inference(resolution,[status(thm)],[f176,f228]) ).
fof(f336,plain,
( ~ spl0_5
| spl0_3
| ~ spl0_10 ),
inference(split_clause,[status(thm)],[f335,f274,f252,f297]) ).
fof(f337,plain,
( ~ aElement0(xa)
| aDivisorOf0(xu,xa)
| ~ aElement0(xu) ),
inference(resolution,[status(thm)],[f176,f227]) ).
fof(f338,plain,
( ~ spl0_7
| spl0_2
| ~ spl0_10 ),
inference(split_clause,[status(thm)],[f337,f282,f249,f297]) ).
fof(f339,plain,
$false,
inference(sat_refutation,[status(thm)],[f255,f278,f286,f301,f303,f306,f309,f329,f332,f336,f338]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.09 % Problem : RNG125+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n029.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue May 30 10:49:36 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.09/0.31 % Drodi V3.5.1
% 0.14/0.31 % Refutation found
% 0.14/0.31 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.53 % Elapsed time: 0.014000 seconds
% 0.14/0.53 % CPU time: 0.016515 seconds
% 0.14/0.53 % Memory used: 3.930 MB
%------------------------------------------------------------------------------