TSTP Solution File: RNG099+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : RNG099+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n003.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 12:32:53 EDT 2023
% Result : Theorem 0.19s 0.34s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 25
% Syntax : Number of formulae : 91 ( 21 unt; 2 def)
% Number of atoms : 251 ( 3 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 259 ( 99 ~; 100 |; 35 &)
% ( 17 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 14 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 63 (; 55 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> aElement0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> aElement0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f27,definition,
! [W0,W1,W2] :
( ( aElement0(W0)
& aElement0(W1)
& aIdeal0(W2) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
( aIdeal0(xI)
& aIdeal0(xJ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,hypothesis,
( aElement0(xx)
& aElement0(xy) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,hypothesis,
( aElementOf0(xa,xI)
& aElementOf0(xb,xJ)
& sdtpldt0(xa,xb) = sz10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,hypothesis,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,hypothesis,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,hypothesis,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,conjecture,
? [W0] :
( aElement0(W0)
& sdteqdtlpzmzozddtrp0(W0,xx,xI)
& sdteqdtlpzmzozddtrp0(W0,xy,xJ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
~ ? [W0] :
( aElement0(W0)
& sdteqdtlpzmzozddtrp0(W0,xx,xI)
& sdteqdtlpzmzozddtrp0(W0,xy,xJ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f44,plain,
! [W0,W1] :
( ~ aElement0(W0)
| ~ aElement0(W1)
| aElement0(sdtpldt0(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f45,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ aElement0(X1)
| aElement0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f44]) ).
fof(f46,plain,
! [W0,W1] :
( ~ aElement0(W0)
| ~ aElement0(W1)
| aElement0(sdtasdt0(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f47,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ aElement0(X1)
| aElement0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f80,plain,
! [W0] :
( ~ aSet0(W0)
| ! [W1] :
( ~ aElementOf0(W1,W0)
| aElement0(W1) ) ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f81,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[status(esa)],[f80]) ).
fof(f110,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(f111,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)],[f110]) ).
fof(f112,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)],[f111]) ).
fof(f113,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)],[f112]) ).
fof(f114,plain,
! [X0] :
( ~ aIdeal0(X0)
| aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f113]) ).
fof(f126,plain,
! [W0,W1,W2] :
( ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aIdeal0(W2)
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) ) ),
inference(pre_NNF_transformation,[status(esa)],[f27]) ).
fof(f127,plain,
! [W0,W1,W2] :
( ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aIdeal0(W2)
| ( ( ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) )
& ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) ) ) ),
inference(NNF_transformation,[status(esa)],[f126]) ).
fof(f129,plain,
! [X0,X1,X2] :
( ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aIdeal0(X2)
| sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aElementOf0(sdtpldt0(X0,smndt0(X1)),X2) ),
inference(cnf_transformation,[status(esa)],[f127]) ).
fof(f130,plain,
aIdeal0(xI),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f131,plain,
aIdeal0(xJ),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f134,plain,
aElement0(xx),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f135,plain,
aElement0(xy),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f136,plain,
aElementOf0(xa,xI),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f137,plain,
aElementOf0(xb,xJ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f139,plain,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f140,plain,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(cnf_transformation,[status(esa)],[f33]) ).
fof(f141,plain,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f142,plain,
! [W0] :
( ~ aElement0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xx,xI)
| ~ sdteqdtlpzmzozddtrp0(W0,xy,xJ) ),
inference(pre_NNF_transformation,[status(esa)],[f36]) ).
fof(f143,plain,
! [X0] :
( ~ aElement0(X0)
| ~ sdteqdtlpzmzozddtrp0(X0,xx,xI)
| ~ sdteqdtlpzmzozddtrp0(X0,xy,xJ) ),
inference(cnf_transformation,[status(esa)],[f142]) ).
fof(f169,plain,
aSet0(xJ),
inference(resolution,[status(thm)],[f114,f131]) ).
fof(f170,plain,
aSet0(xI),
inference(resolution,[status(thm)],[f114,f130]) ).
fof(f171,plain,
( spl0_2
<=> aElement0(xa) ),
introduced(split_symbol_definition) ).
fof(f174,plain,
( spl0_3
<=> aElement0(xb) ),
introduced(split_symbol_definition) ).
fof(f182,plain,
( spl0_5
<=> aSet0(xJ) ),
introduced(split_symbol_definition) ).
fof(f184,plain,
( ~ aSet0(xJ)
| spl0_5 ),
inference(component_clause,[status(thm)],[f182]) ).
fof(f185,plain,
( ~ aSet0(xJ)
| aElement0(xb) ),
inference(resolution,[status(thm)],[f81,f137]) ).
fof(f186,plain,
( ~ spl0_5
| spl0_3 ),
inference(split_clause,[status(thm)],[f185,f182,f174]) ).
fof(f187,plain,
( spl0_6
<=> aSet0(xI) ),
introduced(split_symbol_definition) ).
fof(f189,plain,
( ~ aSet0(xI)
| spl0_6 ),
inference(component_clause,[status(thm)],[f187]) ).
fof(f190,plain,
( ~ aSet0(xI)
| aElement0(xa) ),
inference(resolution,[status(thm)],[f81,f136]) ).
fof(f191,plain,
( ~ spl0_6
| spl0_2 ),
inference(split_clause,[status(thm)],[f190,f187,f171]) ).
fof(f202,plain,
( $false
| spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f189,f170]) ).
fof(f203,plain,
spl0_6,
inference(contradiction_clause,[status(thm)],[f202]) ).
fof(f204,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f184,f169]) ).
fof(f205,plain,
spl0_5,
inference(contradiction_clause,[status(thm)],[f204]) ).
fof(f215,plain,
( spl0_10
<=> aIdeal0(xI) ),
introduced(split_symbol_definition) ).
fof(f217,plain,
( ~ aIdeal0(xI)
| spl0_10 ),
inference(component_clause,[status(thm)],[f215]) ).
fof(f218,plain,
( spl0_11
<=> aIdeal0(xJ) ),
introduced(split_symbol_definition) ).
fof(f220,plain,
( ~ aIdeal0(xJ)
| spl0_11 ),
inference(component_clause,[status(thm)],[f218]) ).
fof(f224,plain,
( $false
| spl0_11 ),
inference(forward_subsumption_resolution,[status(thm)],[f220,f131]) ).
fof(f225,plain,
spl0_11,
inference(contradiction_clause,[status(thm)],[f224]) ).
fof(f226,plain,
( $false
| spl0_10 ),
inference(forward_subsumption_resolution,[status(thm)],[f217,f130]) ).
fof(f227,plain,
spl0_10,
inference(contradiction_clause,[status(thm)],[f226]) ).
fof(f229,plain,
( spl0_12
<=> aElement0(xw) ),
introduced(split_symbol_definition) ).
fof(f232,plain,
( spl0_13
<=> aElement0(xx) ),
introduced(split_symbol_definition) ).
fof(f234,plain,
( ~ aElement0(xx)
| spl0_13 ),
inference(component_clause,[status(thm)],[f232]) ).
fof(f235,plain,
( spl0_14
<=> sdteqdtlpzmzozddtrp0(xw,xx,xI) ),
introduced(split_symbol_definition) ).
fof(f238,plain,
( ~ aElement0(xw)
| ~ aElement0(xx)
| ~ aIdeal0(xI)
| sdteqdtlpzmzozddtrp0(xw,xx,xI) ),
inference(resolution,[status(thm)],[f140,f129]) ).
fof(f239,plain,
( ~ spl0_12
| ~ spl0_13
| ~ spl0_10
| spl0_14 ),
inference(split_clause,[status(thm)],[f238,f229,f232,f215,f235]) ).
fof(f245,plain,
( $false
| spl0_13 ),
inference(forward_subsumption_resolution,[status(thm)],[f234,f134]) ).
fof(f246,plain,
spl0_13,
inference(contradiction_clause,[status(thm)],[f245]) ).
fof(f247,plain,
( spl0_16
<=> aElement0(xy) ),
introduced(split_symbol_definition) ).
fof(f249,plain,
( ~ aElement0(xy)
| spl0_16 ),
inference(component_clause,[status(thm)],[f247]) ).
fof(f250,plain,
( spl0_17
<=> sdteqdtlpzmzozddtrp0(xw,xy,xJ) ),
introduced(split_symbol_definition) ).
fof(f251,plain,
( sdteqdtlpzmzozddtrp0(xw,xy,xJ)
| ~ spl0_17 ),
inference(component_clause,[status(thm)],[f250]) ).
fof(f253,plain,
( ~ aElement0(xw)
| ~ aElement0(xy)
| ~ aIdeal0(xJ)
| sdteqdtlpzmzozddtrp0(xw,xy,xJ) ),
inference(resolution,[status(thm)],[f141,f129]) ).
fof(f254,plain,
( ~ spl0_12
| ~ spl0_16
| ~ spl0_11
| spl0_17 ),
inference(split_clause,[status(thm)],[f253,f229,f247,f218,f250]) ).
fof(f260,plain,
( spl0_19
<=> aElement0(sdtasdt0(xy,xa)) ),
introduced(split_symbol_definition) ).
fof(f262,plain,
( ~ aElement0(sdtasdt0(xy,xa))
| spl0_19 ),
inference(component_clause,[status(thm)],[f260]) ).
fof(f263,plain,
( spl0_20
<=> aElement0(sdtasdt0(xx,xb)) ),
introduced(split_symbol_definition) ).
fof(f265,plain,
( ~ aElement0(sdtasdt0(xx,xb))
| spl0_20 ),
inference(component_clause,[status(thm)],[f263]) ).
fof(f278,plain,
( ~ aElement0(sdtasdt0(xy,xa))
| ~ aElement0(sdtasdt0(xx,xb))
| aElement0(xw) ),
inference(paramodulation,[status(thm)],[f139,f45]) ).
fof(f279,plain,
( ~ spl0_19
| ~ spl0_20
| spl0_12 ),
inference(split_clause,[status(thm)],[f278,f260,f263,f229]) ).
fof(f280,plain,
( ~ aElement0(xy)
| ~ aElement0(xa)
| spl0_19 ),
inference(resolution,[status(thm)],[f262,f47]) ).
fof(f281,plain,
( ~ spl0_16
| ~ spl0_2
| spl0_19 ),
inference(split_clause,[status(thm)],[f280,f247,f171,f260]) ).
fof(f282,plain,
( $false
| spl0_16 ),
inference(forward_subsumption_resolution,[status(thm)],[f249,f135]) ).
fof(f283,plain,
spl0_16,
inference(contradiction_clause,[status(thm)],[f282]) ).
fof(f284,plain,
( ~ aElement0(xx)
| ~ aElement0(xb)
| spl0_20 ),
inference(resolution,[status(thm)],[f265,f47]) ).
fof(f285,plain,
( ~ spl0_13
| ~ spl0_3
| spl0_20 ),
inference(split_clause,[status(thm)],[f284,f232,f174,f263]) ).
fof(f286,plain,
( ~ aElement0(xw)
| ~ sdteqdtlpzmzozddtrp0(xw,xx,xI)
| ~ spl0_17 ),
inference(resolution,[status(thm)],[f251,f143]) ).
fof(f287,plain,
( ~ spl0_12
| ~ spl0_14
| ~ spl0_17 ),
inference(split_clause,[status(thm)],[f286,f229,f235,f250]) ).
fof(f288,plain,
$false,
inference(sat_refutation,[status(thm)],[f186,f191,f203,f205,f225,f227,f239,f246,f254,f279,f281,f283,f285,f287]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : RNG099+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32 % Computer : n003.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 : Tue May 30 10:38:23 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % Drodi V3.5.1
% 0.19/0.34 % Refutation found
% 0.19/0.34 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.35 % Elapsed time: 0.025215 seconds
% 0.19/0.36 % CPU time: 0.046250 seconds
% 0.19/0.36 % Memory used: 15.006 MB
%------------------------------------------------------------------------------