TSTP Solution File: RNG123+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : RNG123+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n016.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 0.20s 0.40s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 24
% Syntax : Number of formulae : 84 ( 19 unt; 1 def)
% Number of atoms : 229 ( 23 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 234 ( 89 ~; 89 |; 34 &)
% ( 13 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 12 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-2 aty)
% Number of variables : 57 (; 51 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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(f25,axiom,
! [W0,W1] :
( ( aIdeal0(W0)
& aIdeal0(W1) )
=> aIdeal0(sdtpldt1(W0,W1)) ),
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(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(f50,hypothesis,
( aElement0(xq)
& aElement0(xr)
& xb = sdtpldt0(sdtasdt0(xq,xu),xr)
& ( xr = sz00
| iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,hypothesis,
xr != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,hypothesis,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,hypothesis,
aElementOf0(xb,xI),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,hypothesis,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f68,plain,
! [W0,W1] :
( ~ aElement0(W0)
| ~ aElement0(W1)
| sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ),
inference(pre_NNF_transformation,[status(esa)],[f7]) ).
fof(f69,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ aElement0(X1)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f68]) ).
fof(f100,plain,
! [W0] :
( ~ aSet0(W0)
| ! [W1] :
( ~ aElementOf0(W1,W0)
| aElement0(W1) ) ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f101,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[status(esa)],[f100]) ).
fof(f130,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(f131,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)],[f130]) ).
fof(f132,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)],[f131]) ).
fof(f133,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)],[f132]) ).
fof(f134,plain,
! [X0] :
( ~ aIdeal0(X0)
| aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f133]) ).
fof(f135,plain,
! [X0,X1,X2] :
( ~ aIdeal0(X0)
| ~ aElementOf0(X1,X0)
| ~ aElementOf0(X2,X0)
| aElementOf0(sdtpldt0(X1,X2),X0) ),
inference(cnf_transformation,[status(esa)],[f133]) ).
fof(f142,plain,
! [W0,W1] :
( ~ aIdeal0(W0)
| ~ aIdeal0(W1)
| aIdeal0(sdtpldt1(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f25]) ).
fof(f143,plain,
! [X0,X1] :
( ~ aIdeal0(X0)
| ~ aIdeal0(X1)
| aIdeal0(sdtpldt1(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f142]) ).
fof(f207,plain,
! [W0] :
( ~ aElement0(W0)
| aIdeal0(slsdtgt0(W0)) ),
inference(pre_NNF_transformation,[status(esa)],[f38]) ).
fof(f208,plain,
! [X0] :
( ~ aElement0(X0)
| aIdeal0(slsdtgt0(X0)) ),
inference(cnf_transformation,[status(esa)],[f207]) ).
fof(f209,plain,
aElement0(xa),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f210,plain,
aElement0(xb),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f213,plain,
aIdeal0(xI),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f214,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f222,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(f225,plain,
! [X0] :
( ~ aElementOf0(X0,xI)
| X0 = sz00
| ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu)) ),
inference(cnf_transformation,[status(esa)],[f222]) ).
fof(f237,plain,
( xr = sz00
| iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f238,plain,
xr != sz00,
inference(cnf_transformation,[status(esa)],[f51]) ).
fof(f239,plain,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(cnf_transformation,[status(esa)],[f52]) ).
fof(f240,plain,
aElementOf0(xb,xI),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f241,plain,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
inference(cnf_transformation,[status(esa)],[f54]) ).
fof(f270,plain,
( spl0_4
<=> xr = sz00 ),
introduced(split_symbol_definition) ).
fof(f271,plain,
( xr = sz00
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f270]) ).
fof(f273,plain,
( spl0_5
<=> iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ),
introduced(split_symbol_definition) ).
fof(f274,plain,
( iLess0(sbrdtbr0(xr),sbrdtbr0(xu))
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f273]) ).
fof(f276,plain,
( spl0_4
| spl0_5 ),
inference(split_clause,[status(thm)],[f237,f270,f273]) ).
fof(f290,plain,
aSet0(xI),
inference(resolution,[status(thm)],[f134,f213]) ).
fof(f292,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f271,f238]) ).
fof(f293,plain,
~ spl0_4,
inference(contradiction_clause,[status(thm)],[f292]) ).
fof(f312,plain,
( spl0_10
<=> aElement0(xb) ),
introduced(split_symbol_definition) ).
fof(f317,plain,
( spl0_11
<=> aSet0(xI) ),
introduced(split_symbol_definition) ).
fof(f319,plain,
( ~ aSet0(xI)
| spl0_11 ),
inference(component_clause,[status(thm)],[f317]) ).
fof(f320,plain,
( ~ aSet0(xI)
| aElement0(xb) ),
inference(resolution,[status(thm)],[f101,f240]) ).
fof(f321,plain,
( ~ spl0_11
| spl0_10 ),
inference(split_clause,[status(thm)],[f320,f317,f312]) ).
fof(f327,plain,
( $false
| spl0_11 ),
inference(forward_subsumption_resolution,[status(thm)],[f319,f290]) ).
fof(f328,plain,
spl0_11,
inference(contradiction_clause,[status(thm)],[f327]) ).
fof(f340,plain,
( spl0_13
<=> aIdeal0(slsdtgt0(xa)) ),
introduced(split_symbol_definition) ).
fof(f342,plain,
( ~ aIdeal0(slsdtgt0(xa))
| spl0_13 ),
inference(component_clause,[status(thm)],[f340]) ).
fof(f343,plain,
( spl0_14
<=> aIdeal0(slsdtgt0(xb)) ),
introduced(split_symbol_definition) ).
fof(f345,plain,
( ~ aIdeal0(slsdtgt0(xb))
| spl0_14 ),
inference(component_clause,[status(thm)],[f343]) ).
fof(f346,plain,
( spl0_15
<=> aIdeal0(xI) ),
introduced(split_symbol_definition) ).
fof(f349,plain,
( ~ aIdeal0(slsdtgt0(xa))
| ~ aIdeal0(slsdtgt0(xb))
| aIdeal0(xI) ),
inference(paramodulation,[status(thm)],[f214,f143]) ).
fof(f350,plain,
( ~ spl0_13
| ~ spl0_14
| spl0_15 ),
inference(split_clause,[status(thm)],[f349,f340,f343,f346]) ).
fof(f351,plain,
( ~ aElement0(xb)
| spl0_14 ),
inference(resolution,[status(thm)],[f345,f208]) ).
fof(f352,plain,
( $false
| spl0_14 ),
inference(forward_subsumption_resolution,[status(thm)],[f351,f210]) ).
fof(f353,plain,
spl0_14,
inference(contradiction_clause,[status(thm)],[f352]) ).
fof(f354,plain,
( ~ aElement0(xa)
| spl0_13 ),
inference(resolution,[status(thm)],[f342,f208]) ).
fof(f355,plain,
( $false
| spl0_13 ),
inference(forward_subsumption_resolution,[status(thm)],[f354,f209]) ).
fof(f356,plain,
spl0_13,
inference(contradiction_clause,[status(thm)],[f355]) ).
fof(f380,plain,
( spl0_20
<=> aElement0(smndt0(sdtasdt0(xq,xu))) ),
introduced(split_symbol_definition) ).
fof(f383,plain,
( ~ aSet0(xI)
| aElement0(smndt0(sdtasdt0(xq,xu))) ),
inference(resolution,[status(thm)],[f239,f101]) ).
fof(f384,plain,
( ~ spl0_11
| spl0_20 ),
inference(split_clause,[status(thm)],[f383,f317,f380]) ).
fof(f400,plain,
( spl0_23
<=> sdtpldt0(xb,smndt0(sdtasdt0(xq,xu))) = xr ),
introduced(split_symbol_definition) ).
fof(f401,plain,
( sdtpldt0(xb,smndt0(sdtasdt0(xq,xu))) = xr
| ~ spl0_23 ),
inference(component_clause,[status(thm)],[f400]) ).
fof(f403,plain,
( ~ aElement0(xb)
| ~ aElement0(smndt0(sdtasdt0(xq,xu)))
| sdtpldt0(xb,smndt0(sdtasdt0(xq,xu))) = xr ),
inference(paramodulation,[status(thm)],[f241,f69]) ).
fof(f404,plain,
( ~ spl0_10
| ~ spl0_20
| spl0_23 ),
inference(split_clause,[status(thm)],[f403,f312,f380,f400]) ).
fof(f475,plain,
( spl0_33
<=> aElementOf0(xr,xI) ),
introduced(split_symbol_definition) ).
fof(f478,plain,
( ~ aElementOf0(xr,xI)
| xr = sz00
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f225,f274]) ).
fof(f479,plain,
( ~ spl0_33
| spl0_4
| ~ spl0_5 ),
inference(split_clause,[status(thm)],[f478,f475,f270,f273]) ).
fof(f675,plain,
! [X0] :
( ~ aIdeal0(X0)
| ~ aElementOf0(xb,X0)
| ~ aElementOf0(smndt0(sdtasdt0(xq,xu)),X0)
| aElementOf0(xr,X0)
| ~ spl0_23 ),
inference(paramodulation,[status(thm)],[f401,f135]) ).
fof(f1101,plain,
( spl0_118
<=> aElementOf0(xb,xI) ),
introduced(split_symbol_definition) ).
fof(f1103,plain,
( ~ aElementOf0(xb,xI)
| spl0_118 ),
inference(component_clause,[status(thm)],[f1101]) ).
fof(f1104,plain,
( ~ aIdeal0(xI)
| ~ aElementOf0(xb,xI)
| aElementOf0(xr,xI)
| ~ spl0_23 ),
inference(resolution,[status(thm)],[f239,f675]) ).
fof(f1105,plain,
( ~ spl0_15
| ~ spl0_118
| spl0_33
| ~ spl0_23 ),
inference(split_clause,[status(thm)],[f1104,f346,f1101,f475,f400]) ).
fof(f1108,plain,
( $false
| spl0_118 ),
inference(forward_subsumption_resolution,[status(thm)],[f1103,f240]) ).
fof(f1109,plain,
spl0_118,
inference(contradiction_clause,[status(thm)],[f1108]) ).
fof(f1110,plain,
$false,
inference(sat_refutation,[status(thm)],[f276,f293,f321,f328,f350,f353,f356,f384,f404,f479,f1105,f1109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : RNG123+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n016.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue May 30 11:03:44 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % Drodi V3.5.1
% 0.20/0.40 % Refutation found
% 0.20/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.59/0.63 % Elapsed time: 0.062743 seconds
% 0.59/0.63 % CPU time: 0.329107 seconds
% 0.59/0.63 % Memory used: 34.093 MB
%------------------------------------------------------------------------------