TSTP Solution File: NUM429+3 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : NUM429+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n009.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 : Tue Apr 30 20:34:39 EDT 2024
% Result : Theorem 0.09s 0.31s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 47 ( 7 unt; 1 def)
% Number of atoms : 148 ( 26 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 158 ( 57 ~; 52 |; 39 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 38 ( 30 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [W0] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [W0,W1] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> aInteger0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,definition,
! [W0] :
( aInteger0(W0)
=> ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( aInteger0(W1)
& W1 != sz00
& ? [W2] :
( aInteger0(W2)
& sdtasdt0(W1,W2) = W0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xq)
& xq != sz00
& aInteger0(xc) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,hypothesis,
( ? [W0] :
( aInteger0(W0)
& sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb)) )
& aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xa,xb,xq)
& ? [W0] :
( aInteger0(W0)
& sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xc)) )
& aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
& sdteqdtlpzmzozddtrp0(xb,xc,xq) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,conjecture,
? [W0] :
( aInteger0(W0)
& sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
~ ? [W0] :
( aInteger0(W0)
& sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb)) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f31,plain,
! [W0] :
( ~ aInteger0(W0)
| aInteger0(smndt0(W0)) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f32,plain,
! [X0] :
( ~ aInteger0(X0)
| aInteger0(smndt0(X0)) ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f33,plain,
! [W0,W1] :
( ~ aInteger0(W0)
| ~ aInteger0(W1)
| aInteger0(sdtpldt0(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f34,plain,
! [X0,X1] :
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| aInteger0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f33]) ).
fof(f65,plain,
! [W0] :
( ~ aInteger0(W0)
| ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( aInteger0(W1)
& W1 != sz00
& ? [W2] :
( aInteger0(W2)
& sdtasdt0(W1,W2) = W0 ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f66,plain,
! [W0] :
( ~ aInteger0(W0)
| ! [W1] :
( ( ~ aDivisorOf0(W1,W0)
| ( aInteger0(W1)
& W1 != sz00
& ? [W2] :
( aInteger0(W2)
& sdtasdt0(W1,W2) = W0 ) ) )
& ( aDivisorOf0(W1,W0)
| ~ aInteger0(W1)
| W1 = sz00
| ! [W2] :
( ~ aInteger0(W2)
| sdtasdt0(W1,W2) != W0 ) ) ) ),
inference(NNF_transformation,[status(esa)],[f65]) ).
fof(f67,plain,
! [W0] :
( ~ aInteger0(W0)
| ( ! [W1] :
( ~ aDivisorOf0(W1,W0)
| ( aInteger0(W1)
& W1 != sz00
& ? [W2] :
( aInteger0(W2)
& sdtasdt0(W1,W2) = W0 ) ) )
& ! [W1] :
( aDivisorOf0(W1,W0)
| ~ aInteger0(W1)
| W1 = sz00
| ! [W2] :
( ~ aInteger0(W2)
| sdtasdt0(W1,W2) != W0 ) ) ) ),
inference(miniscoping,[status(esa)],[f66]) ).
fof(f68,plain,
! [W0] :
( ~ aInteger0(W0)
| ( ! [W1] :
( ~ aDivisorOf0(W1,W0)
| ( aInteger0(W1)
& W1 != sz00
& aInteger0(sk0_0(W1,W0))
& sdtasdt0(W1,sk0_0(W1,W0)) = W0 ) )
& ! [W1] :
( aDivisorOf0(W1,W0)
| ~ aInteger0(W1)
| W1 = sz00
| ! [W2] :
( ~ aInteger0(W2)
| sdtasdt0(W1,W2) != W0 ) ) ) ),
inference(skolemization,[status(esa)],[f67]) ).
fof(f71,plain,
! [X0,X1] :
( ~ aInteger0(X0)
| ~ aDivisorOf0(X1,X0)
| aInteger0(sk0_0(X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f68]) ).
fof(f72,plain,
! [X0,X1] :
( ~ aInteger0(X0)
| ~ aDivisorOf0(X1,X0)
| sdtasdt0(X1,sk0_0(X1,X0)) = X0 ),
inference(cnf_transformation,[status(esa)],[f68]) ).
fof(f82,plain,
aInteger0(xa),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f83,plain,
aInteger0(xb),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f87,plain,
( aInteger0(sk0_1)
& sdtasdt0(xq,sk0_1) = sdtpldt0(xa,smndt0(xb))
& aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xa,xb,xq)
& aInteger0(sk0_2)
& sdtasdt0(xq,sk0_2) = sdtpldt0(xb,smndt0(xc))
& aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
& sdteqdtlpzmzozddtrp0(xb,xc,xq) ),
inference(skolemization,[status(esa)],[f23]) ).
fof(f90,plain,
aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb))),
inference(cnf_transformation,[status(esa)],[f87]) ).
fof(f96,plain,
! [W0] :
( ~ aInteger0(W0)
| sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xb)) ),
inference(pre_NNF_transformation,[status(esa)],[f25]) ).
fof(f97,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtasdt0(xq,X0) != sdtpldt0(xa,smndt0(xb)) ),
inference(cnf_transformation,[status(esa)],[f96]) ).
fof(f100,plain,
( spl0_0
<=> aInteger0(sdtpldt0(xa,smndt0(xb))) ),
introduced(split_symbol_definition) ).
fof(f102,plain,
( ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| spl0_0 ),
inference(component_clause,[status(thm)],[f100]) ).
fof(f140,plain,
( spl0_8
<=> aInteger0(xa) ),
introduced(split_symbol_definition) ).
fof(f142,plain,
( ~ aInteger0(xa)
| spl0_8 ),
inference(component_clause,[status(thm)],[f140]) ).
fof(f143,plain,
( spl0_9
<=> aInteger0(smndt0(xb)) ),
introduced(split_symbol_definition) ).
fof(f145,plain,
( ~ aInteger0(smndt0(xb))
| spl0_9 ),
inference(component_clause,[status(thm)],[f143]) ).
fof(f146,plain,
( ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb))
| spl0_0 ),
inference(resolution,[status(thm)],[f102,f34]) ).
fof(f147,plain,
( ~ spl0_8
| ~ spl0_9
| spl0_0 ),
inference(split_clause,[status(thm)],[f146,f140,f143,f100]) ).
fof(f148,plain,
( ~ aInteger0(xb)
| spl0_9 ),
inference(resolution,[status(thm)],[f145,f32]) ).
fof(f149,plain,
( $false
| spl0_9 ),
inference(forward_subsumption_resolution,[status(thm)],[f148,f83]) ).
fof(f150,plain,
spl0_9,
inference(contradiction_clause,[status(thm)],[f149]) ).
fof(f151,plain,
( $false
| spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f142,f82]) ).
fof(f152,plain,
spl0_8,
inference(contradiction_clause,[status(thm)],[f151]) ).
fof(f153,plain,
( spl0_10
<=> aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb))) ),
introduced(split_symbol_definition) ).
fof(f155,plain,
( ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| spl0_10 ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,plain,
( spl0_11
<=> aInteger0(sk0_0(xq,sdtpldt0(xa,smndt0(xb)))) ),
introduced(split_symbol_definition) ).
fof(f158,plain,
( ~ aInteger0(sk0_0(xq,sdtpldt0(xa,smndt0(xb))))
| spl0_11 ),
inference(component_clause,[status(thm)],[f156]) ).
fof(f159,plain,
( ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(sk0_0(xq,sdtpldt0(xa,smndt0(xb)))) ),
inference(resolution,[status(thm)],[f72,f97]) ).
fof(f160,plain,
( ~ spl0_0
| ~ spl0_10
| ~ spl0_11 ),
inference(split_clause,[status(thm)],[f159,f100,f153,f156]) ).
fof(f166,plain,
( $false
| spl0_10 ),
inference(forward_subsumption_resolution,[status(thm)],[f155,f90]) ).
fof(f167,plain,
spl0_10,
inference(contradiction_clause,[status(thm)],[f166]) ).
fof(f168,plain,
( ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| spl0_11 ),
inference(resolution,[status(thm)],[f158,f71]) ).
fof(f169,plain,
( ~ spl0_0
| ~ spl0_10
| spl0_11 ),
inference(split_clause,[status(thm)],[f168,f100,f153,f156]) ).
fof(f170,plain,
$false,
inference(sat_refutation,[status(thm)],[f147,f150,f152,f160,f167,f169]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : NUM429+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n009.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Mon Apr 29 20:31:26 EDT 2024
% 0.09/0.30 % CPUTime :
% 0.09/0.31 % Drodi V3.6.0
% 0.09/0.31 % Refutation found
% 0.09/0.31 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.32 % Elapsed time: 0.017086 seconds
% 0.14/0.32 % CPU time: 0.025278 seconds
% 0.14/0.32 % Total memory used: 13.173 MB
% 0.14/0.32 % Net memory used: 13.086 MB
%------------------------------------------------------------------------------