TSTP Solution File: NUM504+3 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : NUM504+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n008.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 20:34:57 EDT 2024
% Result : Theorem 0.14s 0.35s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 18
% Syntax : Number of formulae : 68 ( 19 unt; 0 def)
% Number of atoms : 172 ( 31 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 159 ( 55 ~; 50 |; 40 &)
% ( 10 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 11 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 23 ( 18 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> W0 = W1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,hypothesis,
( xn != xp
& ? [W0] :
( aNaturalNumber0(W0)
& sdtpldt0(xn,W0) = xp )
& sdtlseqdt0(xn,xp)
& xm != xp
& ? [W0] :
( aNaturalNumber0(W0)
& sdtpldt0(xm,W0) = xp )
& sdtlseqdt0(xm,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,hypothesis,
( aNaturalNumber0(xk)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,hypothesis,
( ? [W0] :
( aNaturalNumber0(W0)
& sdtpldt0(xp,W0) = xk )
& sdtlseqdt0(xp,xk) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,hypothesis,
( sdtasdt0(xn,xm) != sdtasdt0(xp,xm)
& ? [W0] :
( aNaturalNumber0(W0)
& sdtpldt0(sdtasdt0(xn,xm),W0) = sdtasdt0(xp,xm) )
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& ? [W0] :
( aNaturalNumber0(W0)
& sdtpldt0(sdtasdt0(xp,xm),W0) = sdtasdt0(xp,xk) )
& sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f60,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| aNaturalNumber0(sdtpldt0(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f61,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f60]) ).
fof(f62,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| aNaturalNumber0(sdtasdt0(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f63,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f62]) ).
fof(f109,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| W0 = W1 ),
inference(pre_NNF_transformation,[status(esa)],[f21]) ).
fof(f110,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f109]) ).
fof(f172,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f202,plain,
( xn != xp
& aNaturalNumber0(sk0_6)
& sdtpldt0(xn,sk0_6) = xp
& sdtlseqdt0(xn,xp)
& xm != xp
& aNaturalNumber0(sk0_7)
& sdtpldt0(xm,sk0_7) = xp
& sdtlseqdt0(xm,xp) ),
inference(skolemization,[status(esa)],[f44]) ).
fof(f204,plain,
aNaturalNumber0(sk0_6),
inference(cnf_transformation,[status(esa)],[f202]) ).
fof(f205,plain,
sdtpldt0(xn,sk0_6) = xp,
inference(cnf_transformation,[status(esa)],[f202]) ).
fof(f212,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(cnf_transformation,[status(esa)],[f45]) ).
fof(f236,plain,
( aNaturalNumber0(sk0_11)
& sdtpldt0(xp,sk0_11) = xk
& sdtlseqdt0(xp,xk) ),
inference(skolemization,[status(esa)],[f50]) ).
fof(f237,plain,
aNaturalNumber0(sk0_11),
inference(cnf_transformation,[status(esa)],[f236]) ).
fof(f238,plain,
sdtpldt0(xp,sk0_11) = xk,
inference(cnf_transformation,[status(esa)],[f236]) ).
fof(f240,plain,
( sdtasdt0(xn,xm) != sdtasdt0(xp,xm)
& aNaturalNumber0(sk0_12)
& sdtpldt0(sdtasdt0(xn,xm),sk0_12) = sdtasdt0(xp,xm)
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& aNaturalNumber0(sk0_13)
& sdtpldt0(sdtasdt0(xp,xm),sk0_13) = sdtasdt0(xp,xk)
& sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(skolemization,[status(esa)],[f51]) ).
fof(f241,plain,
sdtasdt0(xn,xm) != sdtasdt0(xp,xm),
inference(cnf_transformation,[status(esa)],[f240]) ).
fof(f242,plain,
aNaturalNumber0(sk0_12),
inference(cnf_transformation,[status(esa)],[f240]) ).
fof(f243,plain,
sdtpldt0(sdtasdt0(xn,xm),sk0_12) = sdtasdt0(xp,xm),
inference(cnf_transformation,[status(esa)],[f240]) ).
fof(f244,plain,
sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(cnf_transformation,[status(esa)],[f240]) ).
fof(f248,plain,
sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)),
inference(cnf_transformation,[status(esa)],[f240]) ).
fof(f277,plain,
( spl0_0
<=> aNaturalNumber0(xn) ),
introduced(split_symbol_definition) ).
fof(f279,plain,
( ~ aNaturalNumber0(xn)
| spl0_0 ),
inference(component_clause,[status(thm)],[f277]) ).
fof(f280,plain,
( spl0_1
<=> aNaturalNumber0(sk0_6) ),
introduced(split_symbol_definition) ).
fof(f282,plain,
( ~ aNaturalNumber0(sk0_6)
| spl0_1 ),
inference(component_clause,[status(thm)],[f280]) ).
fof(f288,plain,
( spl0_3
<=> aNaturalNumber0(xp) ),
introduced(split_symbol_definition) ).
fof(f291,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sk0_6)
| aNaturalNumber0(xp) ),
inference(paramodulation,[status(thm)],[f205,f61]) ).
fof(f292,plain,
( ~ spl0_0
| ~ spl0_1
| spl0_3 ),
inference(split_clause,[status(thm)],[f291,f277,f280,f288]) ).
fof(f293,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f282,f204]) ).
fof(f294,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f293]) ).
fof(f295,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f279,f172]) ).
fof(f296,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f295]) ).
fof(f320,plain,
( spl0_9
<=> aNaturalNumber0(xk) ),
introduced(split_symbol_definition) ).
fof(f346,plain,
( spl0_13
<=> aNaturalNumber0(sk0_11) ),
introduced(split_symbol_definition) ).
fof(f348,plain,
( ~ aNaturalNumber0(sk0_11)
| spl0_13 ),
inference(component_clause,[status(thm)],[f346]) ).
fof(f354,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sk0_11)
| aNaturalNumber0(xk) ),
inference(paramodulation,[status(thm)],[f238,f61]) ).
fof(f355,plain,
( ~ spl0_3
| ~ spl0_13
| spl0_9 ),
inference(split_clause,[status(thm)],[f354,f288,f346,f320]) ).
fof(f356,plain,
( $false
| spl0_13 ),
inference(forward_subsumption_resolution,[status(thm)],[f348,f237]) ).
fof(f357,plain,
spl0_13,
inference(contradiction_clause,[status(thm)],[f356]) ).
fof(f396,plain,
( spl0_23
<=> aNaturalNumber0(sdtasdt0(xn,xm)) ),
introduced(split_symbol_definition) ).
fof(f418,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(paramodulation,[status(thm)],[f212,f63]) ).
fof(f419,plain,
( ~ spl0_3
| ~ spl0_9
| spl0_23 ),
inference(split_clause,[status(thm)],[f418,f288,f320,f396]) ).
fof(f580,plain,
sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)),
inference(forward_demodulation,[status(thm)],[f212,f248]) ).
fof(f693,plain,
( spl0_80
<=> aNaturalNumber0(sdtasdt0(xp,xm)) ),
introduced(split_symbol_definition) ).
fof(f696,plain,
( spl0_81
<=> sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) ),
introduced(split_symbol_definition) ).
fof(f698,plain,
( ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| spl0_81 ),
inference(component_clause,[status(thm)],[f696]) ).
fof(f699,plain,
( spl0_82
<=> sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
introduced(split_symbol_definition) ).
fof(f700,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xm)
| ~ spl0_82 ),
inference(component_clause,[status(thm)],[f699]) ).
fof(f702,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
inference(resolution,[status(thm)],[f110,f580]) ).
fof(f703,plain,
( ~ spl0_23
| ~ spl0_80
| ~ spl0_81
| spl0_82 ),
inference(split_clause,[status(thm)],[f702,f396,f693,f696,f699]) ).
fof(f745,plain,
( $false
| spl0_81 ),
inference(forward_subsumption_resolution,[status(thm)],[f698,f244]) ).
fof(f746,plain,
spl0_81,
inference(contradiction_clause,[status(thm)],[f745]) ).
fof(f1471,plain,
( spl0_168
<=> aNaturalNumber0(sk0_12) ),
introduced(split_symbol_definition) ).
fof(f1473,plain,
( ~ aNaturalNumber0(sk0_12)
| spl0_168 ),
inference(component_clause,[status(thm)],[f1471]) ).
fof(f1512,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sk0_12)
| aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(paramodulation,[status(thm)],[f243,f61]) ).
fof(f1513,plain,
( ~ spl0_23
| ~ spl0_168
| spl0_80 ),
inference(split_clause,[status(thm)],[f1512,f396,f1471,f693]) ).
fof(f1514,plain,
( $false
| spl0_168 ),
inference(forward_subsumption_resolution,[status(thm)],[f1473,f242]) ).
fof(f1515,plain,
spl0_168,
inference(contradiction_clause,[status(thm)],[f1514]) ).
fof(f1516,plain,
( $false
| ~ spl0_82 ),
inference(forward_subsumption_resolution,[status(thm)],[f700,f241]) ).
fof(f1517,plain,
~ spl0_82,
inference(contradiction_clause,[status(thm)],[f1516]) ).
fof(f1518,plain,
$false,
inference(sat_refutation,[status(thm)],[f292,f294,f296,f355,f357,f419,f703,f746,f1513,f1515,f1517]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.10 % Problem : NUM504+3 : TPTP v8.1.2. Released v4.0.0.
% 0.04/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n008.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 20:38:42 EDT 2024
% 0.09/0.30 % CPUTime :
% 0.14/0.31 % Drodi V3.6.0
% 0.14/0.35 % Refutation found
% 0.14/0.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.37 % Elapsed time: 0.053184 seconds
% 0.14/0.37 % CPU time: 0.321000 seconds
% 0.14/0.37 % Total memory used: 66.617 MB
% 0.14/0.37 % Net memory used: 66.479 MB
%------------------------------------------------------------------------------