%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM425+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 01:40:29 PM UTC 2026
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 16
% Syntax : Number of formulae : 67 ( 12 unt; 11 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/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> aInteger0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f19,definition,
! [W0,W1,W2] :
( ( W2 != sz00
& aInteger0(W2)
& aInteger0(W1)
& aInteger0(W0) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
( xq != sz00
& aInteger0(xq)
& aInteger0(xb)
& aInteger0(xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
sdteqdtlpzmzozddtrp0(xa,xb,xq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,conjecture,
? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
~ ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f30,plain,
! [W0] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f31,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
! [W0,W1] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f33,plain,
! [X0,X1] :
( aInteger0(sdtpldt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f64,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(f65,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)],[f64]) ).
fof(f66,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)],[f65]) ).
fof(f67,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))],[f66]) ).
fof(f70,plain,
! [X0,X1] :
( aInteger0(sK0_skl(X1,X0))
| ~ aDivisorOf0(X1,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f71,plain,
! [X0,X1] :
( sdtasdt0(X1,sK0_skl(X1,X0)) = X0
| ~ aDivisorOf0(X1,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f73,plain,
! [W0,W1,W2] :
( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) )
| W2 = sz00
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f74,plain,
! [W0,W1,W2] :
( ( ( ~ aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1)))
| sdteqdtlpzmzozddtrp0(W0,W1,W2) )
& ( aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1)))
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2) ) )
| W2 = sz00
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(NNF_transformation,[status(thm)],[f73]) ).
fof(f75,plain,
! [X0,X1,X2] :
( aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| X2 = sz00
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f79,plain,
aInteger0(xa),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f80,plain,
aInteger0(xb),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f81,plain,
aInteger0(xq),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f82,plain,
xq != sz00,
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f83,plain,
sdteqdtlpzmzozddtrp0(xa,xb,xq),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f84,plain,
! [W0] :
( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f85,plain,
! [X0] :
( sdtasdt0(xq,X0) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f88,plain,
( ~ aInteger0(sK0_skl(xq,sdtpldt0(xa,smndt0(xb))))
| ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(sdtpldt0(xa,smndt0(xb))) ),
inference(resolution,[status(thm)],[f71,f85]) ).
fof(f89,definition,
( sQ0_spl
<=> aInteger0(sdtpldt0(xa,smndt0(xb))) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f91,plain,
( sQ0_spl
| ~ aInteger0(sdtpldt0(xa,smndt0(xb))) ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f92,definition,
( sQ1_spl
<=> aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( sQ1_spl
| ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb))) ),
inference(component_clause,[status(thm)],[f92]) ).
fof(f95,definition,
( sQ2_spl
<=> aInteger0(sK0_skl(xq,sdtpldt0(xa,smndt0(xb)))) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f97,plain,
( sQ2_spl
| ~ aInteger0(sK0_skl(xq,sdtpldt0(xa,smndt0(xb)))) ),
inference(component_clause,[status(thm)],[f95]) ).
fof(f98,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f88,f89,f92,f95]) ).
fof(f99,plain,
( sQ2_spl
| ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(sdtpldt0(xa,smndt0(xb))) ),
inference(resolution,[status(thm)],[f97,f70]) ).
fof(f100,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f99,f89,f92,f95]) ).
fof(f144,plain,
( sQ1_spl
| ~ sdteqdtlpzmzozddtrp0(xa,xb,xq)
| xq = sz00
| ~ aInteger0(xq)
| ~ aInteger0(xb)
| ~ aInteger0(xa) ),
inference(resolution,[status(thm)],[f75,f94]) ).
fof(f147,definition,
( sQ11_spl
<=> aInteger0(xa) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f149,plain,
( sQ11_spl
| ~ aInteger0(xa) ),
inference(component_clause,[status(thm)],[f147]) ).
fof(f150,definition,
( sQ12_spl
<=> aInteger0(xb) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f152,plain,
( sQ12_spl
| ~ aInteger0(xb) ),
inference(component_clause,[status(thm)],[f150]) ).
fof(f153,definition,
( sQ13_spl
<=> aInteger0(xq) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f155,plain,
( sQ13_spl
| ~ aInteger0(xq) ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,definition,
( sQ14_spl
<=> xq = sz00 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f157,plain,
( ~ sQ14_spl
| xq = sz00 ),
inference(component_clause,[status(thm)],[f156]) ).
fof(f159,definition,
( sQ15_spl
<=> sdteqdtlpzmzozddtrp0(xa,xb,xq) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f161,plain,
( sQ15_spl
| ~ sdteqdtlpzmzozddtrp0(xa,xb,xq) ),
inference(component_clause,[status(thm)],[f159]) ).
fof(f162,plain,
( sQ1_spl
| ~ sQ15_spl
| sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f144,f147,f150,f153,f156,f159,f92]) ).
fof(f167,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f161,f83]) ).
fof(f168,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f167]) ).
fof(f169,plain,
( ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f157,f82]) ).
fof(f170,plain,
~ sQ14_spl,
inference(contradiction_clause,[status(thm)],[f169]) ).
fof(f171,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f155,f81]) ).
fof(f172,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f171]) ).
fof(f173,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f152,f80]) ).
fof(f174,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f173]) ).
fof(f175,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f149,f79]) ).
fof(f176,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f175]) ).
fof(f178,plain,
( sQ0_spl
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(xa) ),
inference(resolution,[status(thm)],[f91,f33]) ).
fof(f179,definition,
( sQ17_spl
<=> aInteger0(smndt0(xb)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f181,plain,
( sQ17_spl
| ~ aInteger0(smndt0(xb)) ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f182,plain,
( sQ0_spl
| ~ sQ17_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f178,f147,f179,f89]) ).
fof(f187,plain,
( sQ17_spl
| ~ aInteger0(xb) ),
inference(resolution,[status(thm)],[f181,f31]) ).
fof(f188,plain,
( sQ17_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f187,f150,f179]) ).
fof(f189,plain,
$false,
inference(sat_refutation,[status(thm)],[f98,f100,f162,f168,f170,f172,f174,f176,f182,f188]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM425+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n018.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 02:30:28 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.41 % Elapsed time: 0.045688 seconds
% 0.12/0.41 % CPU time: 0.142559 seconds
% 0.12/0.41 % Total memory used: 61.369 MB
% 0.12/0.41 % Net memory used: 61.220 MB
%------------------------------------------------------------------------------