TSTP Solution File: NUM490+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUM490+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n023.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 12:29:22 EDT 2023
% Result : Theorem 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 26
% Syntax : Number of formulae : 101 ( 27 unt; 2 def)
% Number of atoms : 257 ( 42 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 271 ( 115 ~; 113 |; 20 &)
% ( 18 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 15 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 57 (; 54 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,definition,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2] :
( aNaturalNumber0(W2)
& sdtpldt0(W0,W2) = W1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,definition,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2] :
( W2 = sdtmndt0(W1,W0)
<=> ( aNaturalNumber0(W2)
& sdtpldt0(W0,W2) = W1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,hypothesis,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
xr = sdtmndt0(xn,xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,hypothesis,
( xr != xn
& sdtlseqdt0(xr,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,hypothesis,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,conjecture,
sdtasdt0(xr,xm) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
sdtasdt0(xr,xm) != sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f52,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f53,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f54,plain,
sz10 != sz00,
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f55,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| aNaturalNumber0(sdtpldt0(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f56,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f55]) ).
fof(f57,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| aNaturalNumber0(sdtasdt0(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f58,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f57]) ).
fof(f90,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| ( sdtlseqdt0(W0,W1)
<=> ? [W2] :
( aNaturalNumber0(W2)
& sdtpldt0(W0,W2) = W1 ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f91,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| ( ( ~ sdtlseqdt0(W0,W1)
| ? [W2] :
( aNaturalNumber0(W2)
& sdtpldt0(W0,W2) = W1 ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2] :
( ~ aNaturalNumber0(W2)
| sdtpldt0(W0,W2) != W1 ) ) ) ),
inference(NNF_transformation,[status(esa)],[f90]) ).
fof(f92,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| ( ( ~ sdtlseqdt0(W0,W1)
| ( aNaturalNumber0(sk0_0(W1,W0))
& sdtpldt0(W0,sk0_0(W1,W0)) = W1 ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2] :
( ~ aNaturalNumber0(W2)
| sdtpldt0(W0,W2) != W1 ) ) ) ),
inference(skolemization,[status(esa)],[f91]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 ),
inference(cnf_transformation,[status(esa)],[f92]) ).
fof(f96,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ! [W2] :
( W2 = sdtmndt0(W1,W0)
<=> ( aNaturalNumber0(W2)
& sdtpldt0(W0,W2) = W1 ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f19]) ).
fof(f97,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ! [W2] :
( ( W2 != sdtmndt0(W1,W0)
| ( aNaturalNumber0(W2)
& sdtpldt0(W0,W2) = W1 ) )
& ( W2 = sdtmndt0(W1,W0)
| ~ aNaturalNumber0(W2)
| sdtpldt0(W0,W2) != W1 ) ) ),
inference(NNF_transformation,[status(esa)],[f96]) ).
fof(f98,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ( ! [W2] :
( W2 != sdtmndt0(W1,W0)
| ( aNaturalNumber0(W2)
& sdtpldt0(W0,W2) = W1 ) )
& ! [W2] :
( W2 = sdtmndt0(W1,W0)
| ~ aNaturalNumber0(W2)
| sdtpldt0(W0,W2) != W1 ) ) ),
inference(miniscoping,[status(esa)],[f97]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,X1)
| X2 != sdtmndt0(X1,X0)
| aNaturalNumber0(X2) ),
inference(cnf_transformation,[status(esa)],[f98]) ).
fof(f101,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,X1)
| X2 = sdtmndt0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 ),
inference(cnf_transformation,[status(esa)],[f98]) ).
fof(f167,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f168,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f169,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f174,plain,
sdtlseqdt0(xp,xn),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f175,plain,
xr = sdtmndt0(xn,xp),
inference(cnf_transformation,[status(esa)],[f43]) ).
fof(f176,plain,
xr != xn,
inference(cnf_transformation,[status(esa)],[f44]) ).
fof(f179,plain,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f180,plain,
sdtasdt0(xr,xm) != sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(cnf_transformation,[status(esa)],[f48]) ).
fof(f181,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1) ),
inference(destructive_equality_resolution,[status(esa)],[f95]) ).
fof(f182,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,X1)
| aNaturalNumber0(sdtmndt0(X1,X0)) ),
inference(destructive_equality_resolution,[status(esa)],[f99]) ).
fof(f184,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ sdtlseqdt0(X0,sdtpldt0(X0,X1))
| X1 = sdtmndt0(sdtpldt0(X0,X1),X0)
| ~ aNaturalNumber0(X1) ),
inference(destructive_equality_resolution,[status(esa)],[f101]) ).
fof(f193,plain,
( spl0_0
<=> aNaturalNumber0(xp) ),
introduced(split_symbol_definition) ).
fof(f195,plain,
( ~ aNaturalNumber0(xp)
| spl0_0 ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,plain,
( spl0_1
<=> aNaturalNumber0(xn) ),
introduced(split_symbol_definition) ).
fof(f198,plain,
( ~ aNaturalNumber0(xn)
| spl0_1 ),
inference(component_clause,[status(thm)],[f196]) ).
fof(f199,plain,
( spl0_2
<=> sdtlseqdt0(xp,xn) ),
introduced(split_symbol_definition) ).
fof(f201,plain,
( ~ sdtlseqdt0(xp,xn)
| spl0_2 ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f202,plain,
( spl0_3
<=> aNaturalNumber0(xr) ),
introduced(split_symbol_definition) ).
fof(f205,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn)
| aNaturalNumber0(xr) ),
inference(paramodulation,[status(thm)],[f175,f182]) ).
fof(f206,plain,
( ~ spl0_0
| ~ spl0_1
| ~ spl0_2
| spl0_3 ),
inference(split_clause,[status(thm)],[f205,f193,f196,f199,f202]) ).
fof(f207,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f201,f174]) ).
fof(f208,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f207]) ).
fof(f209,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f198,f167]) ).
fof(f210,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f209]) ).
fof(f211,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f195,f169]) ).
fof(f212,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f211]) ).
fof(f218,plain,
( spl0_5
<=> aNaturalNumber0(sdtasdt0(xp,xm)) ),
introduced(split_symbol_definition) ).
fof(f220,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| spl0_5 ),
inference(component_clause,[status(thm)],[f218]) ).
fof(f224,plain,
( spl0_7
<=> sdtlseqdt0(sdtasdt0(xp,xm),sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm))) ),
introduced(split_symbol_definition) ).
fof(f226,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)))
| spl0_7 ),
inference(component_clause,[status(thm)],[f224]) ).
fof(f227,plain,
( spl0_8
<=> sdtasdt0(xr,xm) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) ),
introduced(split_symbol_definition) ).
fof(f228,plain,
( sdtasdt0(xr,xm) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| ~ spl0_8 ),
inference(component_clause,[status(thm)],[f227]) ).
fof(f230,plain,
( spl0_9
<=> aNaturalNumber0(sdtasdt0(xr,xm)) ),
introduced(split_symbol_definition) ).
fof(f232,plain,
( ~ aNaturalNumber0(sdtasdt0(xr,xm))
| spl0_9 ),
inference(component_clause,[status(thm)],[f230]) ).
fof(f256,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sdtpldt0(X0,X1))
| X1 = sdtmndt0(sdtpldt0(X0,X1),X0)
| ~ aNaturalNumber0(X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f184,f56]) ).
fof(f264,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| spl0_7 ),
inference(forward_demodulation,[status(thm)],[f179,f226]) ).
fof(f276,plain,
( spl0_16
<=> aNaturalNumber0(xm) ),
introduced(split_symbol_definition) ).
fof(f278,plain,
( ~ aNaturalNumber0(xm)
| spl0_16 ),
inference(component_clause,[status(thm)],[f276]) ).
fof(f284,plain,
( $false
| spl0_16 ),
inference(forward_subsumption_resolution,[status(thm)],[f278,f168]) ).
fof(f285,plain,
spl0_16,
inference(contradiction_clause,[status(thm)],[f284]) ).
fof(f286,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm)
| spl0_9 ),
inference(resolution,[status(thm)],[f232,f58]) ).
fof(f287,plain,
( ~ spl0_3
| ~ spl0_16
| spl0_9 ),
inference(split_clause,[status(thm)],[f286,f202,f276,f230]) ).
fof(f288,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| spl0_5 ),
inference(resolution,[status(thm)],[f220,f58]) ).
fof(f289,plain,
( ~ spl0_0
| ~ spl0_16
| spl0_5 ),
inference(split_clause,[status(thm)],[f288,f193,f276,f218]) ).
fof(f290,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)))
| sdtasdt0(xr,xm) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xr,xm)) ),
inference(paramodulation,[status(thm)],[f179,f256]) ).
fof(f291,plain,
( ~ spl0_5
| ~ spl0_7
| spl0_8
| ~ spl0_9 ),
inference(split_clause,[status(thm)],[f290,f218,f224,f227,f230]) ).
fof(f299,plain,
( $false
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f228,f180]) ).
fof(f300,plain,
~ spl0_8,
inference(contradiction_clause,[status(thm)],[f299]) ).
fof(f305,plain,
( spl0_19
<=> aNaturalNumber0(sz00) ),
introduced(split_symbol_definition) ).
fof(f307,plain,
( ~ aNaturalNumber0(sz00)
| spl0_19 ),
inference(component_clause,[status(thm)],[f305]) ).
fof(f339,plain,
( $false
| spl0_19 ),
inference(forward_subsumption_resolution,[status(thm)],[f307,f52]) ).
fof(f340,plain,
spl0_19,
inference(contradiction_clause,[status(thm)],[f339]) ).
fof(f381,plain,
( spl0_30
<=> sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)) ),
introduced(split_symbol_definition) ).
fof(f382,plain,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| ~ spl0_30 ),
inference(component_clause,[status(thm)],[f381]) ).
fof(f421,plain,
( spl0_35
<=> aNaturalNumber0(sz10) ),
introduced(split_symbol_definition) ).
fof(f423,plain,
( ~ aNaturalNumber0(sz10)
| spl0_35 ),
inference(component_clause,[status(thm)],[f421]) ).
fof(f424,plain,
( spl0_36
<=> sz10 = sz00 ),
introduced(split_symbol_definition) ).
fof(f425,plain,
( sz10 = sz00
| ~ spl0_36 ),
inference(component_clause,[status(thm)],[f424]) ).
fof(f439,plain,
( $false
| spl0_35 ),
inference(forward_subsumption_resolution,[status(thm)],[f423,f53]) ).
fof(f440,plain,
spl0_35,
inference(contradiction_clause,[status(thm)],[f439]) ).
fof(f441,plain,
( $false
| ~ spl0_36 ),
inference(forward_subsumption_resolution,[status(thm)],[f425,f54]) ).
fof(f442,plain,
~ spl0_36,
inference(contradiction_clause,[status(thm)],[f441]) ).
fof(f516,plain,
( spl0_52
<=> xn = xr ),
introduced(split_symbol_definition) ).
fof(f517,plain,
( xn = xr
| ~ spl0_52 ),
inference(component_clause,[status(thm)],[f516]) ).
fof(f558,plain,
( $false
| ~ spl0_52 ),
inference(forward_subsumption_resolution,[status(thm)],[f517,f176]) ).
fof(f559,plain,
~ spl0_52,
inference(contradiction_clause,[status(thm)],[f558]) ).
fof(f614,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f181,f56]) ).
fof(f622,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xr,xm)) ),
inference(paramodulation,[status(thm)],[f179,f614]) ).
fof(f623,plain,
( ~ spl0_5
| spl0_30
| ~ spl0_9 ),
inference(split_clause,[status(thm)],[f622,f218,f381,f230]) ).
fof(f626,plain,
( $false
| spl0_7
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[status(thm)],[f382,f264]) ).
fof(f627,plain,
( spl0_7
| ~ spl0_30 ),
inference(contradiction_clause,[status(thm)],[f626]) ).
fof(f628,plain,
$false,
inference(sat_refutation,[status(thm)],[f206,f208,f210,f212,f285,f287,f289,f291,f300,f340,f440,f442,f559,f623,f627]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM490+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue May 30 10:08:08 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % Drodi V3.5.1
% 0.12/0.36 % Refutation found
% 0.12/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.38 % Elapsed time: 0.033179 seconds
% 0.12/0.38 % CPU time: 0.096469 seconds
% 0.12/0.38 % Memory used: 15.684 MB
%------------------------------------------------------------------------------