TSTP Solution File: RNG121+4 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : RNG121+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n001.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 12:32:58 EDT 2023
% Result : Theorem 0.06s 0.28s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 39 ( 8 unt; 0 def)
% Number of atoms : 221 ( 51 equ)
% Maximal formula atoms : 28 ( 5 avg)
% Number of connectives : 251 ( 69 ~; 69 |; 99 &)
% ( 10 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 8 con; 0-2 aty)
% Number of variables : 88 (; 60 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [W0] :
( aElement0(W0)
=> ( sdtpldt0(W0,sz00) = W0
& W0 = sdtpldt0(sz00,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,
( 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)
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xa))
<=> ? [W1] :
( aElement0(W1)
& sdtasdt0(xa,W1) = W0 ) )
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xb))
<=> ? [W1] :
( aElement0(W1)
& sdtasdt0(xb,W1) = W0 ) )
& ! [W0] :
( aElementOf0(W0,xI)
<=> ? [W1,W2] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& sdtpldt0(W1,W2) = W0 ) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
( ? [W0] :
( aElement0(W0)
& sdtasdt0(xa,W0) = sz00 )
& aElementOf0(sz00,slsdtgt0(xa))
& ? [W0] :
( aElement0(W0)
& sdtasdt0(xa,W0) = xa )
& aElementOf0(xa,slsdtgt0(xa))
& ? [W0] :
( aElement0(W0)
& sdtasdt0(xb,W0) = sz00 )
& aElementOf0(sz00,slsdtgt0(xb))
& ? [W0] :
( aElement0(W0)
& sdtasdt0(xb,W0) = xb )
& aElementOf0(xb,slsdtgt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,conjecture,
( ? [W0,W1] :
( aElementOf0(W0,slsdtgt0(xa))
& aElementOf0(W1,slsdtgt0(xb))
& sdtpldt0(W0,W1) = xb )
| ? [W0,W1] :
( aElementOf0(W0,slsdtgt0(xa))
& aElementOf0(W1,slsdtgt0(xb))
& sdtpldt0(W0,W1) = xb )
| aElementOf0(xb,xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
~ ( ? [W0,W1] :
( aElementOf0(W0,slsdtgt0(xa))
& aElementOf0(W1,slsdtgt0(xb))
& sdtpldt0(W0,W1) = xb )
| ? [W0,W1] :
( aElementOf0(W0,slsdtgt0(xa))
& aElementOf0(W1,slsdtgt0(xb))
& sdtpldt0(W0,W1) = xb )
| aElementOf0(xb,xI) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f70,plain,
! [W0] :
( ~ aElement0(W0)
| ( sdtpldt0(W0,sz00) = W0
& W0 = sdtpldt0(sz00,W0) ) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f72,plain,
! [X0] :
( ~ aElement0(X0)
| X0 = sdtpldt0(sz00,X0) ),
inference(cnf_transformation,[status(esa)],[f70]) ).
fof(f208,plain,
aElement0(xb),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f228,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)
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xa))
<=> ? [W1] :
( aElement0(W1)
& sdtasdt0(xa,W1) = W0 ) )
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xb))
<=> ? [W1] :
( aElement0(W1)
& sdtasdt0(xb,W1) = W0 ) )
& ! [W0] :
( aElementOf0(W0,xI)
<=> ? [W1,W2] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& sdtpldt0(W1,W2) = W0 ) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
inference(pre_NNF_transformation,[status(esa)],[f42]) ).
fof(f229,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)
& ! [W0] :
( ( ~ aElementOf0(W0,slsdtgt0(xa))
| ? [W1] :
( aElement0(W1)
& sdtasdt0(xa,W1) = W0 ) )
& ( aElementOf0(W0,slsdtgt0(xa))
| ! [W1] :
( ~ aElement0(W1)
| sdtasdt0(xa,W1) != W0 ) ) )
& ! [W0] :
( ( ~ aElementOf0(W0,slsdtgt0(xb))
| ? [W1] :
( aElement0(W1)
& sdtasdt0(xb,W1) = W0 ) )
& ( aElementOf0(W0,slsdtgt0(xb))
| ! [W1] :
( ~ aElement0(W1)
| sdtasdt0(xb,W1) != W0 ) ) )
& ! [W0] :
( ( ~ aElementOf0(W0,xI)
| ? [W1,W2] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& sdtpldt0(W1,W2) = W0 ) )
& ( aElementOf0(W0,xI)
| ! [W1,W2] :
( ~ aElementOf0(W1,slsdtgt0(xa))
| ~ aElementOf0(W2,slsdtgt0(xb))
| sdtpldt0(W1,W2) != W0 ) ) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
inference(NNF_transformation,[status(esa)],[f228]) ).
fof(f230,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)
& ! [W0] :
( ~ aElementOf0(W0,slsdtgt0(xa))
| ? [W1] :
( aElement0(W1)
& sdtasdt0(xa,W1) = W0 ) )
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xa))
| ! [W1] :
( ~ aElement0(W1)
| sdtasdt0(xa,W1) != W0 ) )
& ! [W0] :
( ~ aElementOf0(W0,slsdtgt0(xb))
| ? [W1] :
( aElement0(W1)
& sdtasdt0(xb,W1) = W0 ) )
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xb))
| ! [W1] :
( ~ aElement0(W1)
| sdtasdt0(xb,W1) != W0 ) )
& ! [W0] :
( ~ aElementOf0(W0,xI)
| ? [W1,W2] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& sdtpldt0(W1,W2) = W0 ) )
& ! [W0] :
( aElementOf0(W0,xI)
| ! [W1,W2] :
( ~ aElementOf0(W1,slsdtgt0(xa))
| ~ aElementOf0(W2,slsdtgt0(xb))
| sdtpldt0(W1,W2) != W0 ) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
inference(miniscoping,[status(esa)],[f229]) ).
fof(f231,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)
& ! [W0] :
( ~ aElementOf0(W0,slsdtgt0(xa))
| ( aElement0(sk0_23(W0))
& sdtasdt0(xa,sk0_23(W0)) = W0 ) )
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xa))
| ! [W1] :
( ~ aElement0(W1)
| sdtasdt0(xa,W1) != W0 ) )
& ! [W0] :
( ~ aElementOf0(W0,slsdtgt0(xb))
| ( aElement0(sk0_24(W0))
& sdtasdt0(xb,sk0_24(W0)) = W0 ) )
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xb))
| ! [W1] :
( ~ aElement0(W1)
| sdtasdt0(xb,W1) != W0 ) )
& ! [W0] :
( ~ aElementOf0(W0,xI)
| ( aElementOf0(sk0_25(W0),slsdtgt0(xa))
& aElementOf0(sk0_26(W0),slsdtgt0(xb))
& sdtpldt0(sk0_25(W0),sk0_26(W0)) = W0 ) )
& ! [W0] :
( aElementOf0(W0,xI)
| ! [W1,W2] :
( ~ aElementOf0(W1,slsdtgt0(xa))
| ~ aElementOf0(W2,slsdtgt0(xb))
| sdtpldt0(W1,W2) != W0 ) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
inference(skolemization,[status(esa)],[f230]) ).
fof(f238,plain,
! [X0,X1] :
( aElementOf0(X0,slsdtgt0(xa))
| ~ aElement0(X1)
| sdtasdt0(xa,X1) != X0 ),
inference(cnf_transformation,[status(esa)],[f231]) ).
fof(f247,plain,
( aElement0(sk0_27)
& sdtasdt0(xa,sk0_27) = sz00
& aElementOf0(sz00,slsdtgt0(xa))
& aElement0(sk0_28)
& sdtasdt0(xa,sk0_28) = xa
& aElementOf0(xa,slsdtgt0(xa))
& aElement0(sk0_29)
& sdtasdt0(xb,sk0_29) = sz00
& aElementOf0(sz00,slsdtgt0(xb))
& aElement0(sk0_30)
& sdtasdt0(xb,sk0_30) = xb
& aElementOf0(xb,slsdtgt0(xb)) ),
inference(skolemization,[status(esa)],[f43]) ).
fof(f248,plain,
aElement0(sk0_27),
inference(cnf_transformation,[status(esa)],[f247]) ).
fof(f249,plain,
sdtasdt0(xa,sk0_27) = sz00,
inference(cnf_transformation,[status(esa)],[f247]) ).
fof(f259,plain,
aElementOf0(xb,slsdtgt0(xb)),
inference(cnf_transformation,[status(esa)],[f247]) ).
fof(f310,plain,
( ! [W0,W1] :
( ~ aElementOf0(W0,slsdtgt0(xa))
| ~ aElementOf0(W1,slsdtgt0(xb))
| sdtpldt0(W0,W1) != xb )
& ! [W0,W1] :
( ~ aElementOf0(W0,slsdtgt0(xa))
| ~ aElementOf0(W1,slsdtgt0(xb))
| sdtpldt0(W0,W1) != xb )
& ~ aElementOf0(xb,xI) ),
inference(pre_NNF_transformation,[status(esa)],[f54]) ).
fof(f311,plain,
! [X0,X1] :
( ~ aElementOf0(X0,slsdtgt0(xa))
| ~ aElementOf0(X1,slsdtgt0(xb))
| sdtpldt0(X0,X1) != xb ),
inference(cnf_transformation,[status(esa)],[f310]) ).
fof(f394,plain,
! [X0] :
( aElementOf0(sdtasdt0(xa,X0),slsdtgt0(xa))
| ~ aElement0(X0) ),
inference(destructive_equality_resolution,[status(esa)],[f238]) ).
fof(f401,plain,
( spl0_11
<=> aElement0(xb) ),
introduced(split_symbol_definition) ).
fof(f403,plain,
( ~ aElement0(xb)
| spl0_11 ),
inference(component_clause,[status(thm)],[f401]) ).
fof(f412,plain,
( spl0_14
<=> aElementOf0(sz00,slsdtgt0(xa)) ),
introduced(split_symbol_definition) ).
fof(f415,plain,
( spl0_15
<=> aElementOf0(xb,slsdtgt0(xb)) ),
introduced(split_symbol_definition) ).
fof(f417,plain,
( ~ aElementOf0(xb,slsdtgt0(xb))
| spl0_15 ),
inference(component_clause,[status(thm)],[f415]) ).
fof(f418,plain,
( ~ aElement0(xb)
| ~ aElementOf0(sz00,slsdtgt0(xa))
| ~ aElementOf0(xb,slsdtgt0(xb)) ),
inference(resolution,[status(thm)],[f72,f311]) ).
fof(f419,plain,
( ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(split_clause,[status(thm)],[f418,f401,f412,f415]) ).
fof(f420,plain,
( $false
| spl0_15 ),
inference(forward_subsumption_resolution,[status(thm)],[f417,f259]) ).
fof(f421,plain,
spl0_15,
inference(contradiction_clause,[status(thm)],[f420]) ).
fof(f474,plain,
( $false
| spl0_11 ),
inference(forward_subsumption_resolution,[status(thm)],[f403,f208]) ).
fof(f475,plain,
spl0_11,
inference(contradiction_clause,[status(thm)],[f474]) ).
fof(f530,plain,
( spl0_36
<=> aElement0(sk0_27) ),
introduced(split_symbol_definition) ).
fof(f532,plain,
( ~ aElement0(sk0_27)
| spl0_36 ),
inference(component_clause,[status(thm)],[f530]) ).
fof(f533,plain,
( aElementOf0(sz00,slsdtgt0(xa))
| ~ aElement0(sk0_27) ),
inference(paramodulation,[status(thm)],[f249,f394]) ).
fof(f534,plain,
( spl0_14
| ~ spl0_36 ),
inference(split_clause,[status(thm)],[f533,f412,f530]) ).
fof(f575,plain,
( $false
| spl0_36 ),
inference(forward_subsumption_resolution,[status(thm)],[f532,f248]) ).
fof(f576,plain,
spl0_36,
inference(contradiction_clause,[status(thm)],[f575]) ).
fof(f577,plain,
$false,
inference(sat_refutation,[status(thm)],[f419,f421,f475,f534,f576]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.06 % Problem : RNG121+4 : TPTP v8.1.2. Released v4.0.0.
% 0.05/0.07 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.06/0.25 % Computer : n001.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 300
% 0.06/0.25 % DateTime : Tue May 30 11:07:15 EDT 2023
% 0.06/0.25 % CPUTime :
% 0.06/0.27 % Drodi V3.5.1
% 0.06/0.28 % Refutation found
% 0.06/0.28 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.06/0.28 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.49 % Elapsed time: 0.023297 seconds
% 0.10/0.49 % CPU time: 0.026516 seconds
% 0.10/0.49 % Memory used: 4.133 MB
%------------------------------------------------------------------------------