TSTP Solution File: NUM430+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : NUM430+1 : 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 : Tue Apr 30 20:34:40 EDT 2024
% Result : Theorem 0.14s 0.37s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 18
% Syntax : Number of formulae : 73 ( 10 unt; 2 def)
% Number of atoms : 237 ( 35 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 273 ( 109 ~; 111 |; 33 &)
% ( 14 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 11 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 57 ( 51 !; 6 ?)
% 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(f19,definition,
! [W0,W1,W2] :
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& W2 != sz00 )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [W0,W1,W2] :
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& W2 != sz00 )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
=> sdteqdtlpzmzozddtrp0(W1,W0,W2) ) ),
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,
( sdteqdtlpzmzozddtrp0(xa,xb,xq)
& sdteqdtlpzmzozddtrp0(xb,xc,xq) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,conjecture,
? [W0] :
( aInteger0(W0)
& sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xc)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
~ ? [W0] :
( aInteger0(W0)
& sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xc)) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f32,plain,
! [W0] :
( ~ aInteger0(W0)
| aInteger0(smndt0(W0)) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f33,plain,
! [X0] :
( ~ aInteger0(X0)
| aInteger0(smndt0(X0)) ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f34,plain,
! [W0,W1] :
( ~ aInteger0(W0)
| ~ aInteger0(W1)
| aInteger0(sdtpldt0(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f35,plain,
! [X0,X1] :
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| aInteger0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f66,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(f67,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)],[f66]) ).
fof(f68,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)],[f67]) ).
fof(f69,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)],[f68]) ).
fof(f72,plain,
! [X0,X1] :
( ~ aInteger0(X0)
| ~ aDivisorOf0(X1,X0)
| aInteger0(sk0_0(X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f69]) ).
fof(f73,plain,
! [X0,X1] :
( ~ aInteger0(X0)
| ~ aDivisorOf0(X1,X0)
| sdtasdt0(X1,sk0_0(X1,X0)) = X0 ),
inference(cnf_transformation,[status(esa)],[f69]) ).
fof(f75,plain,
! [W0,W1,W2] :
( ~ aInteger0(W0)
| ~ aInteger0(W1)
| ~ aInteger0(W2)
| W2 = sz00
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ),
inference(pre_NNF_transformation,[status(esa)],[f19]) ).
fof(f76,plain,
! [W0,W1,W2] :
( ~ aInteger0(W0)
| ~ aInteger0(W1)
| ~ aInteger0(W2)
| W2 = sz00
| ( ( ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) )
& ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ) ),
inference(NNF_transformation,[status(esa)],[f75]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| X2 = sz00
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) ),
inference(cnf_transformation,[status(esa)],[f76]) ).
fof(f81,plain,
! [W0,W1,W2] :
( ~ aInteger0(W0)
| ~ aInteger0(W1)
| ~ aInteger0(W2)
| W2 = sz00
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| sdteqdtlpzmzozddtrp0(W1,W0,W2) ),
inference(pre_NNF_transformation,[status(esa)],[f21]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| X2 = sz00
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| sdteqdtlpzmzozddtrp0(X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f81]) ).
fof(f84,plain,
aInteger0(xb),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f85,plain,
aInteger0(xq),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f86,plain,
xq != sz00,
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f87,plain,
aInteger0(xc),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f89,plain,
sdteqdtlpzmzozddtrp0(xb,xc,xq),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f92,plain,
! [W0] :
( ~ aInteger0(W0)
| sdtasdt0(xq,W0) != sdtpldt0(xb,smndt0(xc)) ),
inference(pre_NNF_transformation,[status(esa)],[f26]) ).
fof(f93,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtasdt0(xq,X0) != sdtpldt0(xb,smndt0(xc)) ),
inference(cnf_transformation,[status(esa)],[f92]) ).
fof(f123,plain,
( spl0_5
<=> aInteger0(sdtpldt0(xb,smndt0(xc))) ),
introduced(split_symbol_definition) ).
fof(f125,plain,
( ~ aInteger0(sdtpldt0(xb,smndt0(xc)))
| spl0_5 ),
inference(component_clause,[status(thm)],[f123]) ).
fof(f126,plain,
( spl0_6
<=> aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc))) ),
introduced(split_symbol_definition) ).
fof(f128,plain,
( ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
| spl0_6 ),
inference(component_clause,[status(thm)],[f126]) ).
fof(f129,plain,
( spl0_7
<=> aInteger0(sk0_0(xq,sdtpldt0(xb,smndt0(xc)))) ),
introduced(split_symbol_definition) ).
fof(f131,plain,
( ~ aInteger0(sk0_0(xq,sdtpldt0(xb,smndt0(xc))))
| spl0_7 ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f132,plain,
( ~ aInteger0(sdtpldt0(xb,smndt0(xc)))
| ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
| ~ aInteger0(sk0_0(xq,sdtpldt0(xb,smndt0(xc)))) ),
inference(resolution,[status(thm)],[f73,f93]) ).
fof(f133,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(split_clause,[status(thm)],[f132,f123,f126,f129]) ).
fof(f139,plain,
( ~ aInteger0(sdtpldt0(xb,smndt0(xc)))
| ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
| spl0_7 ),
inference(resolution,[status(thm)],[f131,f72]) ).
fof(f140,plain,
( ~ spl0_5
| ~ spl0_6
| spl0_7 ),
inference(split_clause,[status(thm)],[f139,f123,f126,f129]) ).
fof(f174,plain,
( spl0_15
<=> aInteger0(xb) ),
introduced(split_symbol_definition) ).
fof(f176,plain,
( ~ aInteger0(xb)
| spl0_15 ),
inference(component_clause,[status(thm)],[f174]) ).
fof(f177,plain,
( spl0_16
<=> aInteger0(xq) ),
introduced(split_symbol_definition) ).
fof(f179,plain,
( ~ aInteger0(xq)
| spl0_16 ),
inference(component_clause,[status(thm)],[f177]) ).
fof(f180,plain,
( spl0_17
<=> xq = sz00 ),
introduced(split_symbol_definition) ).
fof(f181,plain,
( xq = sz00
| ~ spl0_17 ),
inference(component_clause,[status(thm)],[f180]) ).
fof(f188,plain,
( spl0_19
<=> aInteger0(xc) ),
introduced(split_symbol_definition) ).
fof(f190,plain,
( ~ aInteger0(xc)
| spl0_19 ),
inference(component_clause,[status(thm)],[f188]) ).
fof(f191,plain,
( spl0_20
<=> sdteqdtlpzmzozddtrp0(xc,xb,xq) ),
introduced(split_symbol_definition) ).
fof(f192,plain,
( sdteqdtlpzmzozddtrp0(xc,xb,xq)
| ~ spl0_20 ),
inference(component_clause,[status(thm)],[f191]) ).
fof(f194,plain,
( ~ aInteger0(xb)
| ~ aInteger0(xc)
| ~ aInteger0(xq)
| xq = sz00
| sdteqdtlpzmzozddtrp0(xc,xb,xq) ),
inference(resolution,[status(thm)],[f82,f89]) ).
fof(f195,plain,
( ~ spl0_15
| ~ spl0_19
| ~ spl0_16
| spl0_17
| spl0_20 ),
inference(split_clause,[status(thm)],[f194,f174,f188,f177,f180,f191]) ).
fof(f198,plain,
( $false
| spl0_19 ),
inference(forward_subsumption_resolution,[status(thm)],[f190,f87]) ).
fof(f199,plain,
spl0_19,
inference(contradiction_clause,[status(thm)],[f198]) ).
fof(f200,plain,
( $false
| spl0_16 ),
inference(forward_subsumption_resolution,[status(thm)],[f179,f85]) ).
fof(f201,plain,
spl0_16,
inference(contradiction_clause,[status(thm)],[f200]) ).
fof(f202,plain,
( $false
| spl0_15 ),
inference(forward_subsumption_resolution,[status(thm)],[f176,f84]) ).
fof(f203,plain,
spl0_15,
inference(contradiction_clause,[status(thm)],[f202]) ).
fof(f204,plain,
( $false
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[status(thm)],[f181,f86]) ).
fof(f205,plain,
~ spl0_17,
inference(contradiction_clause,[status(thm)],[f204]) ).
fof(f206,plain,
( spl0_21
<=> sdteqdtlpzmzozddtrp0(xb,xc,xq) ),
introduced(split_symbol_definition) ).
fof(f209,plain,
( ~ aInteger0(xc)
| ~ aInteger0(xb)
| ~ aInteger0(xq)
| xq = sz00
| sdteqdtlpzmzozddtrp0(xb,xc,xq)
| ~ spl0_20 ),
inference(resolution,[status(thm)],[f192,f82]) ).
fof(f210,plain,
( ~ spl0_19
| ~ spl0_15
| ~ spl0_16
| spl0_17
| spl0_21
| ~ spl0_20 ),
inference(split_clause,[status(thm)],[f209,f188,f174,f177,f180,f206,f191]) ).
fof(f216,plain,
( ~ aInteger0(xb)
| ~ aInteger0(xc)
| ~ aInteger0(xq)
| xq = sz00
| ~ sdteqdtlpzmzozddtrp0(xb,xc,xq)
| spl0_6 ),
inference(resolution,[status(thm)],[f77,f128]) ).
fof(f217,plain,
( ~ spl0_15
| ~ spl0_19
| ~ spl0_16
| spl0_17
| ~ spl0_21
| spl0_6 ),
inference(split_clause,[status(thm)],[f216,f174,f188,f177,f180,f206,f126]) ).
fof(f228,plain,
( spl0_25
<=> aInteger0(smndt0(xc)) ),
introduced(split_symbol_definition) ).
fof(f230,plain,
( ~ aInteger0(smndt0(xc))
| spl0_25 ),
inference(component_clause,[status(thm)],[f228]) ).
fof(f231,plain,
( ~ aInteger0(xb)
| ~ aInteger0(smndt0(xc))
| spl0_5 ),
inference(resolution,[status(thm)],[f125,f35]) ).
fof(f232,plain,
( ~ spl0_15
| ~ spl0_25
| spl0_5 ),
inference(split_clause,[status(thm)],[f231,f174,f228,f123]) ).
fof(f233,plain,
( ~ aInteger0(xc)
| spl0_25 ),
inference(resolution,[status(thm)],[f230,f33]) ).
fof(f234,plain,
( ~ spl0_19
| spl0_25 ),
inference(split_clause,[status(thm)],[f233,f188,f228]) ).
fof(f235,plain,
$false,
inference(sat_refutation,[status(thm)],[f133,f140,f195,f199,f201,f203,f205,f210,f217,f232,f234]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM430+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Apr 29 21:17:02 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % Drodi V3.6.0
% 0.14/0.37 % Refutation found
% 0.14/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.38 % Elapsed time: 0.022167 seconds
% 0.21/0.38 % CPU time: 0.042502 seconds
% 0.21/0.38 % Total memory used: 13.250 MB
% 0.21/0.38 % Net memory used: 13.212 MB
%------------------------------------------------------------------------------