TSTP Solution File: RNG099+2 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : RNG099+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n012.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 0.17s 0.33s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 23
% Syntax : Number of formulae : 80 ( 22 unt; 0 def)
% Number of atoms : 192 ( 3 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 177 ( 65 ~; 62 |; 28 &)
% ( 11 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 12 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 38 (; 36 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aElement0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> aElement0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> aElement0(sdtasdt0(W0,W1)) ),
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(f28,hypothesis,
( aSet0(xI)
& ! [W0] :
( aElementOf0(W0,xI)
=> ( ! [W1] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
& aIdeal0(xI)
& aSet0(xJ)
& ! [W0] :
( aElementOf0(W0,xJ)
=> ( ! [W1] :
( aElementOf0(W1,xJ)
=> aElementOf0(sdtpldt0(W0,W1),xJ) )
& ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xJ) ) ) )
& aIdeal0(xJ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,hypothesis,
( aElement0(xx)
& aElement0(xy) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,hypothesis,
( aElementOf0(xa,xI)
& aElementOf0(xb,xJ)
& sdtpldt0(xa,xb) = sz10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,hypothesis,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,hypothesis,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,hypothesis,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,conjecture,
? [W0] :
( aElement0(W0)
& ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
& ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
~ ? [W0] :
( aElement0(W0)
& ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
& ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f40,plain,
aElement0(sz00),
inference(cnf_transformation,[status(esa)],[f2]) ).
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(f130,plain,
( aSet0(xI)
& ! [W0] :
( ~ aElementOf0(W0,xI)
| ( ! [W1] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
& aIdeal0(xI)
& aSet0(xJ)
& ! [W0] :
( ~ aElementOf0(W0,xJ)
| ( ! [W1] :
( ~ aElementOf0(W1,xJ)
| aElementOf0(sdtpldt0(W0,W1),xJ) )
& ! [W1] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xJ) ) ) )
& aIdeal0(xJ) ),
inference(pre_NNF_transformation,[status(esa)],[f28]) ).
fof(f131,plain,
aSet0(xI),
inference(cnf_transformation,[status(esa)],[f130]) ).
fof(f135,plain,
aSet0(xJ),
inference(cnf_transformation,[status(esa)],[f130]) ).
fof(f145,plain,
aElement0(xx),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f146,plain,
aElement0(xy),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f147,plain,
aElementOf0(xa,xI),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f148,plain,
aElementOf0(xb,xJ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f150,plain,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f151,plain,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(cnf_transformation,[status(esa)],[f33]) ).
fof(f152,plain,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f153,plain,
! [W0] :
( ~ aElement0(W0)
| ( ~ aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
& ~ sdteqdtlpzmzozddtrp0(W0,xx,xI) )
| ( ~ aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
& ~ sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f36]) ).
fof(f154,plain,
! [W0] :
( pd0_2(W0)
=> ( ~ aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
& ~ sdteqdtlpzmzozddtrp0(W0,xx,xI) ) ),
introduced(predicate_definition,[f153]) ).
fof(f155,plain,
! [W0] :
( ~ aElement0(W0)
| pd0_2(W0)
| ( ~ aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
& ~ sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ),
inference(formula_renaming,[status(thm)],[f153,f154]) ).
fof(f156,plain,
! [X0] :
( ~ aElement0(X0)
| pd0_2(X0)
| ~ aElementOf0(sdtpldt0(X0,smndt0(xy)),xJ) ),
inference(cnf_transformation,[status(esa)],[f155]) ).
fof(f167,plain,
! [W0] :
( ~ pd0_2(W0)
| ( ~ aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
& ~ sdteqdtlpzmzozddtrp0(W0,xx,xI) ) ),
inference(pre_NNF_transformation,[status(esa)],[f154]) ).
fof(f168,plain,
! [X0] :
( ~ pd0_2(X0)
| ~ aElementOf0(sdtpldt0(X0,smndt0(xx)),xI) ),
inference(cnf_transformation,[status(esa)],[f167]) ).
fof(f181,plain,
( spl0_1
<=> aElement0(xy) ),
introduced(split_symbol_definition) ).
fof(f183,plain,
( ~ aElement0(xy)
| spl0_1 ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f192,plain,
( spl0_4
<=> aElement0(xx) ),
introduced(split_symbol_definition) ).
fof(f194,plain,
( ~ aElement0(xx)
| spl0_4 ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f202,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f194,f145]) ).
fof(f203,plain,
spl0_4,
inference(contradiction_clause,[status(thm)],[f202]) ).
fof(f206,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f183,f146]) ).
fof(f207,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f206]) ).
fof(f211,plain,
( spl0_6
<=> aElement0(xa) ),
introduced(split_symbol_definition) ).
fof(f214,plain,
( spl0_7
<=> aElement0(xb) ),
introduced(split_symbol_definition) ).
fof(f279,plain,
( spl0_22
<=> aSet0(xJ) ),
introduced(split_symbol_definition) ).
fof(f281,plain,
( ~ aSet0(xJ)
| spl0_22 ),
inference(component_clause,[status(thm)],[f279]) ).
fof(f282,plain,
( ~ aSet0(xJ)
| aElement0(xb) ),
inference(resolution,[status(thm)],[f81,f148]) ).
fof(f283,plain,
( ~ spl0_22
| spl0_7 ),
inference(split_clause,[status(thm)],[f282,f279,f214]) ).
fof(f284,plain,
( spl0_23
<=> aSet0(xI) ),
introduced(split_symbol_definition) ).
fof(f286,plain,
( ~ aSet0(xI)
| spl0_23 ),
inference(component_clause,[status(thm)],[f284]) ).
fof(f287,plain,
( ~ aSet0(xI)
| aElement0(xa) ),
inference(resolution,[status(thm)],[f81,f147]) ).
fof(f288,plain,
( ~ spl0_23
| spl0_6 ),
inference(split_clause,[status(thm)],[f287,f284,f211]) ).
fof(f311,plain,
( $false
| spl0_23 ),
inference(forward_subsumption_resolution,[status(thm)],[f286,f131]) ).
fof(f312,plain,
spl0_23,
inference(contradiction_clause,[status(thm)],[f311]) ).
fof(f313,plain,
( $false
| spl0_22 ),
inference(forward_subsumption_resolution,[status(thm)],[f281,f135]) ).
fof(f314,plain,
spl0_22,
inference(contradiction_clause,[status(thm)],[f313]) ).
fof(f349,plain,
~ pd0_2(xw),
inference(resolution,[status(thm)],[f151,f168]) ).
fof(f350,plain,
( spl0_34
<=> aElement0(xw) ),
introduced(split_symbol_definition) ).
fof(f363,plain,
( spl0_37
<=> pd0_2(xw) ),
introduced(split_symbol_definition) ).
fof(f364,plain,
( pd0_2(xw)
| ~ spl0_37 ),
inference(component_clause,[status(thm)],[f363]) ).
fof(f366,plain,
( ~ aElement0(xw)
| pd0_2(xw) ),
inference(resolution,[status(thm)],[f152,f156]) ).
fof(f367,plain,
( ~ spl0_34
| spl0_37 ),
inference(split_clause,[status(thm)],[f366,f350,f363]) ).
fof(f404,plain,
( spl0_46
<=> aElement0(sdtasdt0(xy,xa)) ),
introduced(split_symbol_definition) ).
fof(f406,plain,
( ~ aElement0(sdtasdt0(xy,xa))
| spl0_46 ),
inference(component_clause,[status(thm)],[f404]) ).
fof(f407,plain,
( spl0_47
<=> aElement0(sdtasdt0(xx,xb)) ),
introduced(split_symbol_definition) ).
fof(f409,plain,
( ~ aElement0(sdtasdt0(xx,xb))
| spl0_47 ),
inference(component_clause,[status(thm)],[f407]) ).
fof(f422,plain,
( ~ aElement0(sdtasdt0(xy,xa))
| ~ aElement0(sdtasdt0(xx,xb))
| aElement0(xw) ),
inference(paramodulation,[status(thm)],[f150,f45]) ).
fof(f423,plain,
( ~ spl0_46
| ~ spl0_47
| spl0_34 ),
inference(split_clause,[status(thm)],[f422,f404,f407,f350]) ).
fof(f424,plain,
( $false
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[status(thm)],[f364,f349]) ).
fof(f425,plain,
~ spl0_37,
inference(contradiction_clause,[status(thm)],[f424]) ).
fof(f445,plain,
( spl0_51
<=> aElement0(sz00) ),
introduced(split_symbol_definition) ).
fof(f447,plain,
( ~ aElement0(sz00)
| spl0_51 ),
inference(component_clause,[status(thm)],[f445]) ).
fof(f462,plain,
( $false
| spl0_51 ),
inference(forward_subsumption_resolution,[status(thm)],[f447,f40]) ).
fof(f463,plain,
spl0_51,
inference(contradiction_clause,[status(thm)],[f462]) ).
fof(f617,plain,
( ~ aElement0(xy)
| ~ aElement0(xa)
| spl0_46 ),
inference(resolution,[status(thm)],[f406,f47]) ).
fof(f618,plain,
( ~ spl0_1
| ~ spl0_6
| spl0_46 ),
inference(split_clause,[status(thm)],[f617,f181,f211,f404]) ).
fof(f629,plain,
( ~ aElement0(xx)
| ~ aElement0(xb)
| spl0_47 ),
inference(resolution,[status(thm)],[f409,f47]) ).
fof(f630,plain,
( ~ spl0_4
| ~ spl0_7
| spl0_47 ),
inference(split_clause,[status(thm)],[f629,f192,f214,f407]) ).
fof(f631,plain,
$false,
inference(sat_refutation,[status(thm)],[f203,f207,f283,f288,f312,f314,f367,f423,f425,f463,f618,f630]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : RNG099+2 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.31 % Computer : n012.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue May 30 10:32:25 EDT 2023
% 0.12/0.31 % CPUTime :
% 0.17/0.32 % Drodi V3.5.1
% 0.17/0.33 % Refutation found
% 0.17/0.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.55 % Elapsed time: 0.024040 seconds
% 0.17/0.55 % CPU time: 0.067929 seconds
% 0.17/0.55 % Memory used: 19.101 MB
%------------------------------------------------------------------------------