%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM429+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:40:30 PM UTC 2026
% Result : Theorem 0.09s 0.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 47 ( 7 unt; 6 def)
% Number of atoms : 148 ( 26 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 158 ( 57 ~; 52 |; 39 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 38 ( 30 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [W0] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> aInteger0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,definition,
! [W0] :
( aInteger0(W0)
=> ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( ? [W2] :
( sdtasdt0(W1,W2) = W0
& aInteger0(W2) )
& W1 != sz00
& aInteger0(W1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
( aInteger0(xc)
& xq != sz00
& aInteger0(xq)
& aInteger0(xb)
& aInteger0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,hypothesis,
( sdteqdtlpzmzozddtrp0(xb,xc,xq)
& aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
& ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xc))
& aInteger0(W0) )
& sdteqdtlpzmzozddtrp0(xa,xb,xq)
& aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,conjecture,
? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
~ ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f31,plain,
! [W0] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f32,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [W0,W1] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f34,plain,
! [X0,X1] :
( aInteger0(sdtpldt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f65,plain,
! [W0] :
( ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( ? [W2] :
( sdtasdt0(W1,W2) = W0
& aInteger0(W2) )
& W1 != sz00
& aInteger0(W1) ) )
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f66,plain,
! [W0] :
( ! [W1] :
( ( ! [W2] :
( sdtasdt0(W1,W2) != W0
| ~ aInteger0(W2) )
| W1 = sz00
| ~ aInteger0(W1)
| aDivisorOf0(W1,W0) )
& ( ( ? [W2] :
( sdtasdt0(W1,W2) = W0
& aInteger0(W2) )
& W1 != sz00
& aInteger0(W1) )
| ~ aDivisorOf0(W1,W0) ) )
| ~ aInteger0(W0) ),
inference(NNF_transformation,[status(thm)],[f65]) ).
fof(f67,plain,
! [W0] :
( ( ! [W1] :
( ! [W2] :
( sdtasdt0(W1,W2) != W0
| ~ aInteger0(W2) )
| W1 = sz00
| ~ aInteger0(W1)
| aDivisorOf0(W1,W0) )
& ! [W1] :
( ( ? [W2] :
( sdtasdt0(W1,W2) = W0
& aInteger0(W2) )
& W1 != sz00
& aInteger0(W1) )
| ~ aDivisorOf0(W1,W0) ) )
| ~ aInteger0(W0) ),
inference(miniscoping,[status(thm)],[f66]) ).
fof(f68,plain,
! [W0] :
( ( ! [W1] :
( ! [W2] :
( sdtasdt0(W1,W2) != W0
| ~ aInteger0(W2) )
| W1 = sz00
| ~ aInteger0(W1)
| aDivisorOf0(W1,W0) )
& ! [W1] :
( ( sdtasdt0(W1,sK0_skl(W1,W0)) = W0
& aInteger0(sK0_skl(W1,W0))
& W1 != sz00
& aInteger0(W1) )
| ~ aDivisorOf0(W1,W0) ) )
| ~ aInteger0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(W2,sK0_skl(W1,W0))],[f67]) ).
fof(f71,plain,
! [X0,X1] :
( aInteger0(sK0_skl(X1,X0))
| ~ aDivisorOf0(X1,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f72,plain,
! [X0,X1] :
( sdtasdt0(X1,sK0_skl(X1,X0)) = X0
| ~ aDivisorOf0(X1,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f82,plain,
aInteger0(xa),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f83,plain,
aInteger0(xb),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f87,plain,
( sdteqdtlpzmzozddtrp0(xb,xc,xq)
& aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
& sdtasdt0(xq,sK2_skl) = sdtpldt0(xb,smndt0(xc))
& aInteger0(sK2_skl)
& sdteqdtlpzmzozddtrp0(xa,xb,xq)
& aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& sdtasdt0(xq,sK1_skl) = sdtpldt0(xa,smndt0(xb))
& aInteger0(sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(W0,sK1_skl),skolemize(W0,sK2_skl)],[f23]) ).
fof(f90,plain,
aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb))),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f96,plain,
! [W0] :
( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f97,plain,
! [X0] :
( sdtasdt0(xq,X0) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f101,definition,
( sQ0_spl
<=> aInteger0(sdtpldt0(xa,smndt0(xb))) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f103,plain,
( sQ0_spl
| ~ aInteger0(sdtpldt0(xa,smndt0(xb))) ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f108,plain,
( sQ0_spl
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(xa) ),
inference(resolution,[status(thm)],[f103,f34]) ).
fof(f109,definition,
( sQ2_spl
<=> aInteger0(xa) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f111,plain,
( sQ2_spl
| ~ aInteger0(xa) ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,definition,
( sQ3_spl
<=> aInteger0(smndt0(xb)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f114,plain,
( sQ3_spl
| ~ aInteger0(smndt0(xb)) ),
inference(component_clause,[status(thm)],[f112]) ).
fof(f115,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f108,f109,f112,f101]) ).
fof(f144,plain,
( sQ3_spl
| ~ aInteger0(xb) ),
inference(resolution,[status(thm)],[f114,f32]) ).
fof(f145,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f144,f83]) ).
fof(f146,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f145]) ).
fof(f147,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f111,f82]) ).
fof(f148,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f147]) ).
fof(f154,plain,
( ~ aInteger0(sK0_skl(xq,sdtpldt0(xa,smndt0(xb))))
| ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(sdtpldt0(xa,smndt0(xb))) ),
inference(resolution,[status(thm)],[f72,f97]) ).
fof(f156,definition,
( sQ10_spl
<=> aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb))) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f158,plain,
( sQ10_spl
| ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb))) ),
inference(component_clause,[status(thm)],[f156]) ).
fof(f159,definition,
( sQ11_spl
<=> aInteger0(sK0_skl(xq,sdtpldt0(xa,smndt0(xb)))) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f161,plain,
( sQ11_spl
| ~ aInteger0(sK0_skl(xq,sdtpldt0(xa,smndt0(xb)))) ),
inference(component_clause,[status(thm)],[f159]) ).
fof(f162,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f154,f101,f156,f159]) ).
fof(f167,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f158,f90]) ).
fof(f168,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f167]) ).
fof(f169,plain,
( sQ11_spl
| ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(sdtpldt0(xa,smndt0(xb))) ),
inference(resolution,[status(thm)],[f161,f71]) ).
fof(f170,plain,
( sQ11_spl
| ~ sQ10_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f169,f101,f156,f159]) ).
fof(f171,plain,
$false,
inference(sat_refutation,[status(thm)],[f115,f146,f148,f162,f168,f170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM429+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 02:23:56 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.39 % Drodi V4.1.1
% 0.09/0.41 % Refutation found
% 0.09/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.50 % Elapsed time: 0.120863 seconds
% 0.14/0.50 % CPU time: 0.119161 seconds
% 0.14/0.50 % Total memory used: 9.868 MB
% 0.14/0.50 % Net memory used: 9.842 MB
%------------------------------------------------------------------------------