TSTP Solution File: NUM425+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUM425+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n026.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 12:29:05 EDT 2023
% Result : Theorem 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 16
% Syntax : Number of formulae : 67 ( 12 unt; 2 def)
% Number of atoms : 196 ( 30 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 215 ( 86 ~; 84 |; 28 &)
% ( 13 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 10 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 48 (; 42 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [W0] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [W0,W1] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> aInteger0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xq)
& xq != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
sdteqdtlpzmzozddtrp0(xa,xb,xq),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,conjecture,
? [W0] :
( aInteger0(W0)
& sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
~ ? [W0] :
( aInteger0(W0)
& sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb)) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f30,plain,
! [W0] :
( ~ aInteger0(W0)
| aInteger0(smndt0(W0)) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f31,plain,
! [X0] :
( ~ aInteger0(X0)
| aInteger0(smndt0(X0)) ),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f32,plain,
! [W0,W1] :
( ~ aInteger0(W0)
| ~ aInteger0(W1)
| aInteger0(sdtpldt0(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f33,plain,
! [X0,X1] :
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| aInteger0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f64,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(f65,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)],[f64]) ).
fof(f66,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)],[f65]) ).
fof(f67,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)],[f66]) ).
fof(f70,plain,
! [X0,X1] :
( ~ aInteger0(X0)
| ~ aDivisorOf0(X1,X0)
| aInteger0(sk0_0(X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f67]) ).
fof(f71,plain,
! [X0,X1] :
( ~ aInteger0(X0)
| ~ aDivisorOf0(X1,X0)
| sdtasdt0(X1,sk0_0(X1,X0)) = X0 ),
inference(cnf_transformation,[status(esa)],[f67]) ).
fof(f73,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(f74,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)],[f73]) ).
fof(f75,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)],[f74]) ).
fof(f79,plain,
aInteger0(xa),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f80,plain,
aInteger0(xb),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f81,plain,
aInteger0(xq),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f82,plain,
xq != sz00,
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f83,plain,
sdteqdtlpzmzozddtrp0(xa,xb,xq),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f84,plain,
! [W0] :
( ~ aInteger0(W0)
| sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xb)) ),
inference(pre_NNF_transformation,[status(esa)],[f24]) ).
fof(f85,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtasdt0(xq,X0) != sdtpldt0(xa,smndt0(xb)) ),
inference(cnf_transformation,[status(esa)],[f84]) ).
fof(f124,plain,
( spl0_7
<=> aInteger0(sdtpldt0(xa,smndt0(xb))) ),
introduced(split_symbol_definition) ).
fof(f126,plain,
( ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| spl0_7 ),
inference(component_clause,[status(thm)],[f124]) ).
fof(f127,plain,
( spl0_8
<=> aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb))) ),
introduced(split_symbol_definition) ).
fof(f129,plain,
( ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| spl0_8 ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f130,plain,
( spl0_9
<=> aInteger0(sk0_0(xq,sdtpldt0(xa,smndt0(xb)))) ),
introduced(split_symbol_definition) ).
fof(f132,plain,
( ~ aInteger0(sk0_0(xq,sdtpldt0(xa,smndt0(xb))))
| spl0_9 ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f133,plain,
( ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(sk0_0(xq,sdtpldt0(xa,smndt0(xb)))) ),
inference(resolution,[status(thm)],[f71,f85]) ).
fof(f134,plain,
( ~ spl0_7
| ~ spl0_8
| ~ spl0_9 ),
inference(split_clause,[status(thm)],[f133,f124,f127,f130]) ).
fof(f140,plain,
( ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| spl0_9 ),
inference(resolution,[status(thm)],[f132,f70]) ).
fof(f141,plain,
( ~ spl0_7
| ~ spl0_8
| spl0_9 ),
inference(split_clause,[status(thm)],[f140,f124,f127,f130]) ).
fof(f144,plain,
( spl0_11
<=> aInteger0(xa) ),
introduced(split_symbol_definition) ).
fof(f146,plain,
( ~ aInteger0(xa)
| spl0_11 ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f147,plain,
( spl0_12
<=> aInteger0(xb) ),
introduced(split_symbol_definition) ).
fof(f149,plain,
( ~ aInteger0(xb)
| spl0_12 ),
inference(component_clause,[status(thm)],[f147]) ).
fof(f150,plain,
( spl0_13
<=> aInteger0(xq) ),
introduced(split_symbol_definition) ).
fof(f152,plain,
( ~ aInteger0(xq)
| spl0_13 ),
inference(component_clause,[status(thm)],[f150]) ).
fof(f153,plain,
( spl0_14
<=> xq = sz00 ),
introduced(split_symbol_definition) ).
fof(f154,plain,
( xq = sz00
| ~ spl0_14 ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,plain,
( spl0_15
<=> sdteqdtlpzmzozddtrp0(xa,xb,xq) ),
introduced(split_symbol_definition) ).
fof(f158,plain,
( ~ sdteqdtlpzmzozddtrp0(xa,xb,xq)
| spl0_15 ),
inference(component_clause,[status(thm)],[f156]) ).
fof(f159,plain,
( ~ aInteger0(xa)
| ~ aInteger0(xb)
| ~ aInteger0(xq)
| xq = sz00
| ~ sdteqdtlpzmzozddtrp0(xa,xb,xq)
| spl0_8 ),
inference(resolution,[status(thm)],[f129,f75]) ).
fof(f160,plain,
( ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_14
| ~ spl0_15
| spl0_8 ),
inference(split_clause,[status(thm)],[f159,f144,f147,f150,f153,f156,f127]) ).
fof(f161,plain,
( $false
| spl0_15 ),
inference(forward_subsumption_resolution,[status(thm)],[f158,f83]) ).
fof(f162,plain,
spl0_15,
inference(contradiction_clause,[status(thm)],[f161]) ).
fof(f163,plain,
( $false
| spl0_13 ),
inference(forward_subsumption_resolution,[status(thm)],[f152,f81]) ).
fof(f164,plain,
spl0_13,
inference(contradiction_clause,[status(thm)],[f163]) ).
fof(f165,plain,
( $false
| spl0_12 ),
inference(forward_subsumption_resolution,[status(thm)],[f149,f80]) ).
fof(f166,plain,
spl0_12,
inference(contradiction_clause,[status(thm)],[f165]) ).
fof(f167,plain,
( $false
| spl0_11 ),
inference(forward_subsumption_resolution,[status(thm)],[f146,f79]) ).
fof(f168,plain,
spl0_11,
inference(contradiction_clause,[status(thm)],[f167]) ).
fof(f169,plain,
( spl0_16
<=> aInteger0(smndt0(xb)) ),
introduced(split_symbol_definition) ).
fof(f171,plain,
( ~ aInteger0(smndt0(xb))
| spl0_16 ),
inference(component_clause,[status(thm)],[f169]) ).
fof(f172,plain,
( ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb))
| spl0_7 ),
inference(resolution,[status(thm)],[f126,f33]) ).
fof(f173,plain,
( ~ spl0_11
| ~ spl0_16
| spl0_7 ),
inference(split_clause,[status(thm)],[f172,f144,f169,f124]) ).
fof(f174,plain,
( ~ aInteger0(xb)
| spl0_16 ),
inference(resolution,[status(thm)],[f171,f31]) ).
fof(f175,plain,
( ~ spl0_12
| spl0_16 ),
inference(split_clause,[status(thm)],[f174,f147,f169]) ).
fof(f176,plain,
( $false
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[status(thm)],[f154,f82]) ).
fof(f177,plain,
~ spl0_14,
inference(contradiction_clause,[status(thm)],[f176]) ).
fof(f178,plain,
$false,
inference(sat_refutation,[status(thm)],[f134,f141,f160,f162,f164,f166,f168,f173,f175,f177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM425+1 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n026.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 10:13:13 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
% 0.19/0.59 % Elapsed time: 0.035105 seconds
% 0.19/0.59 % CPU time: 0.042831 seconds
% 0.19/0.59 % Memory used: 4.599 MB
%------------------------------------------------------------------------------