TSTP Solution File: NUM427+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : NUM427+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n011.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 0.07s 0.28s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 62 ( 17 unt; 2 def)
% Number of atoms : 186 ( 33 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 201 ( 77 ~; 82 |; 27 &)
% ( 11 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 8 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 47 ( 43 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [W0] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [W0,W1] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> aInteger0(sdtasdt0(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(f23,hypothesis,
( aInteger0(xn)
& sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,hypothesis,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,conjecture,
sdteqdtlpzmzozddtrp0(xb,xa,xq),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
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(f36,plain,
! [W0,W1] :
( ~ aInteger0(W0)
| ~ aInteger0(W1)
| aInteger0(sdtasdt0(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f37,plain,
! [X0,X1] :
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| aInteger0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
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(f74,plain,
! [X0,X1,X2] :
( ~ aInteger0(X0)
| aDivisorOf0(X1,X0)
| ~ aInteger0(X1)
| X1 = sz00
| ~ aInteger0(X2)
| sdtasdt0(X1,X2) != 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(f78,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,
aInteger0(xa),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f82,plain,
aInteger0(xb),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f83,plain,
aInteger0(xq),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f84,plain,
xq != sz00,
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f86,plain,
aInteger0(xn),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f88,plain,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f89,plain,
~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f91,plain,
! [X0,X1] :
( ~ aInteger0(sdtasdt0(X0,X1))
| aDivisorOf0(X0,sdtasdt0(X0,X1))
| ~ aInteger0(X0)
| X0 = sz00
| ~ aInteger0(X1) ),
inference(destructive_equality_resolution,[status(esa)],[f74]) ).
fof(f105,plain,
( spl0_3
<=> aInteger0(xa) ),
introduced(split_symbol_definition) ).
fof(f107,plain,
( ~ aInteger0(xa)
| spl0_3 ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f108,plain,
( spl0_4
<=> aInteger0(xb) ),
introduced(split_symbol_definition) ).
fof(f110,plain,
( ~ aInteger0(xb)
| spl0_4 ),
inference(component_clause,[status(thm)],[f108]) ).
fof(f129,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f110,f82]) ).
fof(f130,plain,
spl0_4,
inference(contradiction_clause,[status(thm)],[f129]) ).
fof(f131,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f107,f81]) ).
fof(f132,plain,
spl0_3,
inference(contradiction_clause,[status(thm)],[f131]) ).
fof(f133,plain,
( spl0_9
<=> aInteger0(xq) ),
introduced(split_symbol_definition) ).
fof(f135,plain,
( ~ aInteger0(xq)
| spl0_9 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,plain,
( spl0_10
<=> aInteger0(smndt0(xn)) ),
introduced(split_symbol_definition) ).
fof(f138,plain,
( ~ aInteger0(smndt0(xn))
| spl0_10 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f181,plain,
( ~ aInteger0(xn)
| spl0_10 ),
inference(resolution,[status(thm)],[f138,f33]) ).
fof(f182,plain,
( $false
| spl0_10 ),
inference(forward_subsumption_resolution,[status(thm)],[f181,f86]) ).
fof(f183,plain,
spl0_10,
inference(contradiction_clause,[status(thm)],[f182]) ).
fof(f184,plain,
( $false
| spl0_9 ),
inference(forward_subsumption_resolution,[status(thm)],[f135,f83]) ).
fof(f185,plain,
spl0_9,
inference(contradiction_clause,[status(thm)],[f184]) ).
fof(f363,plain,
( spl0_50
<=> xq = sz00 ),
introduced(split_symbol_definition) ).
fof(f364,plain,
( xq = sz00
| ~ spl0_50 ),
inference(component_clause,[status(thm)],[f363]) ).
fof(f379,plain,
! [X0,X1] :
( aDivisorOf0(X0,sdtasdt0(X0,X1))
| ~ aInteger0(X0)
| X0 = sz00
| ~ aInteger0(X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f91,f37]) ).
fof(f398,plain,
( spl0_58
<=> aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa))) ),
introduced(split_symbol_definition) ).
fof(f399,plain,
( aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ spl0_58 ),
inference(component_clause,[status(thm)],[f398]) ).
fof(f401,plain,
( aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(xq)
| xq = sz00
| ~ aInteger0(smndt0(xn)) ),
inference(paramodulation,[status(thm)],[f88,f379]) ).
fof(f402,plain,
( spl0_58
| ~ spl0_9
| spl0_50
| ~ spl0_10 ),
inference(split_clause,[status(thm)],[f401,f398,f133,f363,f136]) ).
fof(f403,plain,
( $false
| ~ spl0_50 ),
inference(forward_subsumption_resolution,[status(thm)],[f364,f84]) ).
fof(f404,plain,
~ spl0_50,
inference(contradiction_clause,[status(thm)],[f403]) ).
fof(f427,plain,
( spl0_63
<=> sdteqdtlpzmzozddtrp0(xb,xa,xq) ),
introduced(split_symbol_definition) ).
fof(f428,plain,
( sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ spl0_63 ),
inference(component_clause,[status(thm)],[f427]) ).
fof(f430,plain,
( ~ aInteger0(xb)
| ~ aInteger0(xa)
| ~ aInteger0(xq)
| xq = sz00
| sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ spl0_58 ),
inference(resolution,[status(thm)],[f399,f78]) ).
fof(f431,plain,
( ~ spl0_4
| ~ spl0_3
| ~ spl0_9
| spl0_50
| spl0_63
| ~ spl0_58 ),
inference(split_clause,[status(thm)],[f430,f108,f105,f133,f363,f427,f398]) ).
fof(f434,plain,
( $false
| ~ spl0_63 ),
inference(forward_subsumption_resolution,[status(thm)],[f428,f89]) ).
fof(f435,plain,
~ spl0_63,
inference(contradiction_clause,[status(thm)],[f434]) ).
fof(f436,plain,
$false,
inference(sat_refutation,[status(thm)],[f130,f132,f183,f185,f402,f404,f431,f435]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : NUM427+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.07 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.26 % Computer : n011.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Mon Apr 29 20:51:46 EDT 2024
% 0.07/0.26 % CPUTime :
% 0.07/0.27 % Drodi V3.6.0
% 0.07/0.28 % Refutation found
% 0.07/0.28 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/0.28 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.31 % Elapsed time: 0.032410 seconds
% 0.11/0.31 % CPU time: 0.098342 seconds
% 0.11/0.31 % Total memory used: 21.227 MB
% 0.11/0.31 % Net memory used: 21.102 MB
%------------------------------------------------------------------------------