TSTP Solution File: RNG109+4 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : RNG109+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n015.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 12:32:56 EDT 2023
% Result : Theorem 0.20s 0.36s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 46 ( 9 unt; 0 def)
% Number of atoms : 185 ( 61 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 208 ( 69 ~; 63 |; 61 &)
% ( 10 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 67 (; 47 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [W0] :
( aElement0(W0)
=> ( sdtpldt0(W0,sz00) = W0
& W0 = sdtpldt0(sz00,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,hypothesis,
( xa != sz00
| xb != sz00 ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f44,conjecture,
? [W0] :
( ( ! [W1] :
( aElementOf0(W1,slsdtgt0(xa))
<=> ? [W2] :
( aElement0(W2)
& sdtasdt0(xa,W2) = W1 ) )
=> ( ! [W1] :
( aElementOf0(W1,slsdtgt0(xb))
<=> ? [W2] :
( aElement0(W2)
& sdtasdt0(xb,W2) = W1 ) )
=> ( ? [W1,W2] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& sdtpldt0(W1,W2) = W0 )
| aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) )
& W0 != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ ? [W0] :
( ( ! [W1] :
( aElementOf0(W1,slsdtgt0(xa))
<=> ? [W2] :
( aElement0(W2)
& sdtasdt0(xa,W2) = W1 ) )
=> ( ! [W1] :
( aElementOf0(W1,slsdtgt0(xb))
<=> ? [W2] :
( aElement0(W2)
& sdtasdt0(xb,W2) = W1 ) )
=> ( ? [W1,W2] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& sdtpldt0(W1,W2) = W0 )
| aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) )
& W0 != sz00 ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f61,plain,
! [W0] :
( ~ aElement0(W0)
| ( sdtpldt0(W0,sz00) = W0
& W0 = sdtpldt0(sz00,W0) ) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f62,plain,
! [X0] :
( ~ aElement0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[status(esa)],[f61]) ).
fof(f63,plain,
! [X0] :
( ~ aElement0(X0)
| X0 = sdtpldt0(sz00,X0) ),
inference(cnf_transformation,[status(esa)],[f61]) ).
fof(f198,plain,
aElement0(xa),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f199,plain,
aElement0(xb),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f200,plain,
( xa != sz00
| xb != sz00 ),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f238,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(f244,plain,
aElementOf0(xa,slsdtgt0(xa)),
inference(cnf_transformation,[status(esa)],[f238]) ).
fof(f247,plain,
aElementOf0(sz00,slsdtgt0(xb)),
inference(cnf_transformation,[status(esa)],[f238]) ).
fof(f250,plain,
aElementOf0(xb,slsdtgt0(xb)),
inference(cnf_transformation,[status(esa)],[f238]) ).
fof(f251,plain,
! [W0] :
( ( ! [W1] :
( aElementOf0(W1,slsdtgt0(xa))
<=> ? [W2] :
( aElement0(W2)
& sdtasdt0(xa,W2) = W1 ) )
& ! [W1] :
( aElementOf0(W1,slsdtgt0(xb))
<=> ? [W2] :
( aElement0(W2)
& sdtasdt0(xb,W2) = W1 ) )
& ! [W1,W2] :
( ~ aElementOf0(W1,slsdtgt0(xa))
| ~ aElementOf0(W2,slsdtgt0(xb))
| sdtpldt0(W1,W2) != W0 )
& ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| W0 = sz00 ),
inference(pre_NNF_transformation,[status(esa)],[f45]) ).
fof(f252,plain,
! [W0] :
( ( ! [W1] :
( ( ~ aElementOf0(W1,slsdtgt0(xa))
| ? [W2] :
( aElement0(W2)
& sdtasdt0(xa,W2) = W1 ) )
& ( aElementOf0(W1,slsdtgt0(xa))
| ! [W2] :
( ~ aElement0(W2)
| sdtasdt0(xa,W2) != W1 ) ) )
& ! [W1] :
( ( ~ aElementOf0(W1,slsdtgt0(xb))
| ? [W2] :
( aElement0(W2)
& sdtasdt0(xb,W2) = W1 ) )
& ( aElementOf0(W1,slsdtgt0(xb))
| ! [W2] :
( ~ aElement0(W2)
| sdtasdt0(xb,W2) != W1 ) ) )
& ! [W1,W2] :
( ~ aElementOf0(W1,slsdtgt0(xa))
| ~ aElementOf0(W2,slsdtgt0(xb))
| sdtpldt0(W1,W2) != W0 )
& ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| W0 = sz00 ),
inference(NNF_transformation,[status(esa)],[f251]) ).
fof(f253,plain,
! [W0] :
( ( ! [W1] :
( ~ aElementOf0(W1,slsdtgt0(xa))
| ? [W2] :
( aElement0(W2)
& sdtasdt0(xa,W2) = W1 ) )
& ! [W1] :
( aElementOf0(W1,slsdtgt0(xa))
| ! [W2] :
( ~ aElement0(W2)
| sdtasdt0(xa,W2) != W1 ) )
& ! [W1] :
( ~ aElementOf0(W1,slsdtgt0(xb))
| ? [W2] :
( aElement0(W2)
& sdtasdt0(xb,W2) = W1 ) )
& ! [W1] :
( aElementOf0(W1,slsdtgt0(xb))
| ! [W2] :
( ~ aElement0(W2)
| sdtasdt0(xb,W2) != W1 ) )
& ! [W1,W2] :
( ~ aElementOf0(W1,slsdtgt0(xa))
| ~ aElementOf0(W2,slsdtgt0(xb))
| sdtpldt0(W1,W2) != W0 )
& ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| W0 = sz00 ),
inference(miniscoping,[status(esa)],[f252]) ).
fof(f254,plain,
! [W0] :
( ( ! [W1] :
( ~ aElementOf0(W1,slsdtgt0(xa))
| ( aElement0(sk0_31(W1,W0))
& sdtasdt0(xa,sk0_31(W1,W0)) = W1 ) )
& ! [W1] :
( aElementOf0(W1,slsdtgt0(xa))
| ! [W2] :
( ~ aElement0(W2)
| sdtasdt0(xa,W2) != W1 ) )
& ! [W1] :
( ~ aElementOf0(W1,slsdtgt0(xb))
| ( aElement0(sk0_32(W1,W0))
& sdtasdt0(xb,sk0_32(W1,W0)) = W1 ) )
& ! [W1] :
( aElementOf0(W1,slsdtgt0(xb))
| ! [W2] :
( ~ aElement0(W2)
| sdtasdt0(xb,W2) != W1 ) )
& ! [W1,W2] :
( ~ aElementOf0(W1,slsdtgt0(xa))
| ~ aElementOf0(W2,slsdtgt0(xb))
| sdtpldt0(W1,W2) != W0 )
& ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| W0 = sz00 ),
inference(skolemization,[status(esa)],[f253]) ).
fof(f261,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X0,slsdtgt0(xa))
| ~ aElementOf0(X1,slsdtgt0(xb))
| sdtpldt0(X0,X1) != X2
| X2 = sz00 ),
inference(cnf_transformation,[status(esa)],[f254]) ).
fof(f286,plain,
( spl0_0
<=> xa = sz00 ),
introduced(split_symbol_definition) ).
fof(f287,plain,
( xa = sz00
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f286]) ).
fof(f289,plain,
( spl0_1
<=> xb = sz00 ),
introduced(split_symbol_definition) ).
fof(f292,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f200,f286,f289]) ).
fof(f319,plain,
! [X0,X1] :
( ~ aElementOf0(X0,slsdtgt0(xa))
| ~ aElementOf0(X1,slsdtgt0(xb))
| sdtpldt0(X0,X1) = sz00 ),
inference(destructive_equality_resolution,[status(esa)],[f261]) ).
fof(f323,plain,
! [X0] :
( ~ aElementOf0(X0,slsdtgt0(xa))
| sdtpldt0(X0,sz00) = sz00 ),
inference(resolution,[status(thm)],[f247,f319]) ).
fof(f336,plain,
sdtpldt0(xa,sz00) = sz00,
inference(resolution,[status(thm)],[f323,f244]) ).
fof(f338,plain,
( spl0_5
<=> aElement0(xa) ),
introduced(split_symbol_definition) ).
fof(f340,plain,
( ~ aElement0(xa)
| spl0_5 ),
inference(component_clause,[status(thm)],[f338]) ).
fof(f341,plain,
( ~ aElement0(xa)
| sz00 = xa ),
inference(paramodulation,[status(thm)],[f336,f62]) ).
fof(f342,plain,
( ~ spl0_5
| spl0_0 ),
inference(split_clause,[status(thm)],[f341,f338,f286]) ).
fof(f360,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f340,f198]) ).
fof(f361,plain,
spl0_5,
inference(contradiction_clause,[status(thm)],[f360]) ).
fof(f369,plain,
! [X0,X1] :
( ~ aElementOf0(X0,slsdtgt0(sz00))
| ~ aElementOf0(X1,slsdtgt0(xb))
| sdtpldt0(X0,X1) = sz00
| ~ spl0_0 ),
inference(backward_demodulation,[status(thm)],[f287,f319]) ).
fof(f374,plain,
( aElementOf0(xa,slsdtgt0(sz00))
| ~ spl0_0 ),
inference(backward_demodulation,[status(thm)],[f287,f244]) ).
fof(f375,plain,
( aElementOf0(sz00,slsdtgt0(sz00))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f287,f374]) ).
fof(f379,plain,
! [X0] :
( ~ aElementOf0(X0,slsdtgt0(sz00))
| sdtpldt0(X0,xb) = sz00
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f369,f250]) ).
fof(f399,plain,
( sdtpldt0(sz00,xb) = sz00
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f379,f375]) ).
fof(f400,plain,
( spl0_11
<=> aElement0(xb) ),
introduced(split_symbol_definition) ).
fof(f402,plain,
( ~ aElement0(xb)
| spl0_11 ),
inference(component_clause,[status(thm)],[f400]) ).
fof(f403,plain,
( ~ aElement0(xb)
| xb = sz00
| ~ spl0_0 ),
inference(paramodulation,[status(thm)],[f399,f63]) ).
fof(f404,plain,
( ~ spl0_11
| spl0_1
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f403,f400,f289,f286]) ).
fof(f412,plain,
( $false
| spl0_11 ),
inference(forward_subsumption_resolution,[status(thm)],[f402,f199]) ).
fof(f413,plain,
spl0_11,
inference(contradiction_clause,[status(thm)],[f412]) ).
fof(f414,plain,
$false,
inference(sat_refutation,[status(thm)],[f292,f342,f361,f404,f413]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG109+4 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 10:52:04 EDT 2023
% 0.20/0.34 % CPUTime :
% 0.20/0.36 % Drodi V3.5.1
% 0.20/0.36 % Refutation found
% 0.20/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.38 % Elapsed time: 0.028980 seconds
% 0.20/0.38 % CPU time: 0.050657 seconds
% 0.20/0.38 % Memory used: 15.758 MB
%------------------------------------------------------------------------------