%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM434+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 : n015.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 01:40:31 PM UTC 2026
% Result : Theorem 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 22
% Syntax : Number of formulae : 91 ( 16 unt; 15 def)
% Number of atoms : 262 ( 47 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 285 ( 114 ~; 115 |; 32 &)
% ( 17 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 14 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 60 ( 54 !; 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(f6,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> aInteger0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> ( sdtasdt0(W0,W1) = sz00
=> ( W1 = sz00
| W0 = sz00 ) ) ),
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(f23,hypothesis,
( xq != sz00
& aInteger0(xq)
& xp != sz00
& aInteger0(xp)
& aInteger0(xb)
& aInteger0(xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,hypothesis,
sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,conjecture,
? [W0] :
( sdtasdt0(sdtasdt0(xp,xq),W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
~ ? [W0] :
( sdtasdt0(sdtasdt0(xp,xq),W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f32,plain,
! [W0] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f33,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
! [W0,W1] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f35,plain,
! [X0,X1] :
( aInteger0(sdtpldt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
! [W0,W1] :
( aInteger0(sdtasdt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f37,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f64,plain,
! [W0,W1] :
( W1 = sz00
| W0 = sz00
| sdtasdt0(W0,W1) != sz00
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f65,plain,
! [X0,X1] :
( X1 = sz00
| X0 = sz00
| sdtasdt0(X0,X1) != sz00
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f66,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(f67,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)],[f66]) ).
fof(f68,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)],[f67]) ).
fof(f69,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))],[f68]) ).
fof(f72,plain,
! [X0,X1] :
( aInteger0(sK0_skl(X1,X0))
| ~ aDivisorOf0(X1,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f73,plain,
! [X0,X1] :
( sdtasdt0(X1,sK0_skl(X1,X0)) = X0
| ~ aDivisorOf0(X1,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f75,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(f76,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)],[f75]) ).
fof(f77,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)],[f76]) ).
fof(f85,plain,
aInteger0(xa),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f86,plain,
aInteger0(xb),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f87,plain,
aInteger0(xp),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f88,plain,
xp != sz00,
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f89,plain,
aInteger0(xq),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f90,plain,
xq != sz00,
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f91,plain,
sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f92,plain,
! [W0] :
( sdtasdt0(sdtasdt0(xp,xq),W0) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f93,plain,
! [X0] :
( sdtasdt0(sdtasdt0(xp,xq),X0) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f96,plain,
( ~ aInteger0(sK0_skl(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb))))
| ~ aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(sdtpldt0(xa,smndt0(xb))) ),
inference(resolution,[status(thm)],[f73,f93]) ).
fof(f97,definition,
( sQ0_spl
<=> aInteger0(sdtpldt0(xa,smndt0(xb))) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f99,plain,
( sQ0_spl
| ~ aInteger0(sdtpldt0(xa,smndt0(xb))) ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,definition,
( sQ1_spl
<=> aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( sQ1_spl
| ~ aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb))) ),
inference(component_clause,[status(thm)],[f100]) ).
fof(f103,definition,
( sQ2_spl
<=> aInteger0(sK0_skl(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f105,plain,
( sQ2_spl
| ~ aInteger0(sK0_skl(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))) ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f96,f97,f100,f103]) ).
fof(f170,plain,
( sQ2_spl
| ~ aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(sdtpldt0(xa,smndt0(xb))) ),
inference(resolution,[status(thm)],[f105,f72]) ).
fof(f171,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f170,f97,f100,f103]) ).
fof(f172,plain,
( sQ1_spl
| ~ sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq))
| sdtasdt0(xp,xq) = sz00
| ~ aInteger0(sdtasdt0(xp,xq))
| ~ aInteger0(xb)
| ~ aInteger0(xa) ),
inference(resolution,[status(thm)],[f102,f77]) ).
fof(f173,definition,
( sQ11_spl
<=> aInteger0(xa) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f175,plain,
( sQ11_spl
| ~ aInteger0(xa) ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f176,definition,
( sQ12_spl
<=> aInteger0(xb) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f178,plain,
( sQ12_spl
| ~ aInteger0(xb) ),
inference(component_clause,[status(thm)],[f176]) ).
fof(f179,definition,
( sQ13_spl
<=> aInteger0(sdtasdt0(xp,xq)) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f181,plain,
( sQ13_spl
| ~ aInteger0(sdtasdt0(xp,xq)) ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f182,definition,
( sQ14_spl
<=> sdtasdt0(xp,xq) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f183,plain,
( ~ sQ14_spl
| sdtasdt0(xp,xq) = sz00 ),
inference(component_clause,[status(thm)],[f182]) ).
fof(f185,definition,
( sQ15_spl
<=> sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f187,plain,
( sQ15_spl
| ~ sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)) ),
inference(component_clause,[status(thm)],[f185]) ).
fof(f188,plain,
( sQ1_spl
| ~ sQ15_spl
| sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f172,f173,f176,f179,f182,f185,f100]) ).
fof(f189,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f187,f91]) ).
fof(f190,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f189]) ).
fof(f203,definition,
( sQ17_spl
<=> aInteger0(xp) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f205,plain,
( sQ17_spl
| ~ aInteger0(xp) ),
inference(component_clause,[status(thm)],[f203]) ).
fof(f206,definition,
( sQ18_spl
<=> xp = sz00 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f207,plain,
( ~ sQ18_spl
| xp = sz00 ),
inference(component_clause,[status(thm)],[f206]) ).
fof(f209,definition,
( sQ19_spl
<=> aInteger0(xq) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f211,plain,
( sQ19_spl
| ~ aInteger0(xq) ),
inference(component_clause,[status(thm)],[f209]) ).
fof(f234,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f211,f89]) ).
fof(f235,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f234]) ).
fof(f236,plain,
( sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f205,f87]) ).
fof(f237,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f236]) ).
fof(f238,plain,
( ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f207,f88]) ).
fof(f239,plain,
~ sQ18_spl,
inference(contradiction_clause,[status(thm)],[f238]) ).
fof(f242,plain,
( sQ13_spl
| ~ aInteger0(xq)
| ~ aInteger0(xp) ),
inference(resolution,[status(thm)],[f181,f37]) ).
fof(f243,plain,
( sQ13_spl
| ~ sQ19_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f242,f203,f209,f179]) ).
fof(f244,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f178,f86]) ).
fof(f245,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f244]) ).
fof(f246,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f175,f85]) ).
fof(f247,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f246]) ).
fof(f268,plain,
( sQ0_spl
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(xa) ),
inference(resolution,[status(thm)],[f99,f35]) ).
fof(f269,definition,
( sQ25_spl
<=> aInteger0(smndt0(xb)) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f271,plain,
( sQ25_spl
| ~ aInteger0(smndt0(xb)) ),
inference(component_clause,[status(thm)],[f269]) ).
fof(f272,plain,
( sQ0_spl
| ~ sQ25_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f268,f173,f269,f97]) ).
fof(f273,plain,
( sQ25_spl
| ~ aInteger0(xb) ),
inference(resolution,[status(thm)],[f271,f33]) ).
fof(f274,plain,
( sQ25_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f273,f176,f269]) ).
fof(f449,plain,
( ~ sQ14_spl
| xq = sz00
| xp = sz00
| ~ aInteger0(xq)
| ~ aInteger0(xp) ),
inference(resolution,[status(thm)],[f65,f183]) ).
fof(f456,definition,
( sQ56_spl
<=> xq = sz00 ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f457,plain,
( ~ sQ56_spl
| xq = sz00 ),
inference(component_clause,[status(thm)],[f456]) ).
fof(f459,plain,
( ~ sQ14_spl
| sQ56_spl
| sQ18_spl
| ~ sQ19_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f449,f203,f209,f206,f456,f182]) ).
fof(f466,plain,
( ~ sQ56_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f457,f90]) ).
fof(f467,plain,
~ sQ56_spl,
inference(contradiction_clause,[status(thm)],[f466]) ).
fof(f468,plain,
$false,
inference(sat_refutation,[status(thm)],[f106,f171,f188,f190,f235,f237,f239,f243,f245,f247,f272,f274,f459,f467]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM434+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 02:32:22 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.42 % Elapsed time: 0.045425 seconds
% 0.10/0.42 % CPU time: 0.152763 seconds
% 0.10/0.42 % Total memory used: 59.204 MB
% 0.10/0.42 % Net memory used: 59.077 MB
%------------------------------------------------------------------------------