%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM436+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 : n007.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 0.42s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 13
% Syntax : Number of formulae : 51 ( 11 unt; 8 def)
% Number of atoms : 148 ( 28 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 169 ( 72 ~; 58 |; 30 &)
% ( 8 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 23 ( 18 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> aInteger0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,hypothesis,
( xq != sz00
& aInteger0(xq)
& xp != sz00
& aInteger0(xp)
& aInteger0(xb)
& aInteger0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,hypothesis,
( sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb))
& aInteger0(xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,hypothesis,
( sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm))
& sdtasdt0(xp,sdtasdt0(xq,xm)) = sdtpldt0(xa,smndt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,conjecture,
( ( sdteqdtlpzmzozddtrp0(xa,xb,xq)
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) ) )
& ( sdteqdtlpzmzozddtrp0(xa,xb,xp)
| aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
| ? [W0] :
( sdtasdt0(xp,W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
~ ( ( sdteqdtlpzmzozddtrp0(xa,xb,xq)
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) ) )
& ( sdteqdtlpzmzozddtrp0(xa,xb,xp)
| aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
| ? [W0] :
( sdtasdt0(xp,W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) ) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f38,plain,
! [W0,W1] :
( aInteger0(sdtasdt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f39,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f89,plain,
aInteger0(xp),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f90,plain,
xp != sz00,
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f91,plain,
aInteger0(xq),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f99,plain,
aInteger0(xm),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f101,plain,
sdtasdt0(xp,sdtasdt0(xq,xm)) = sdtpldt0(xa,smndt0(xb)),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f102,plain,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f103,plain,
( ( ~ sdteqdtlpzmzozddtrp0(xa,xb,xq)
& ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& ! [W0] :
( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(W0) ) )
| ( ~ sdteqdtlpzmzozddtrp0(xa,xb,xp)
& ~ aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
& ! [W0] :
( sdtasdt0(xp,W0) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(W0) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f104,definition,
( sP0_prd
<=> ( ~ sdteqdtlpzmzozddtrp0(xa,xb,xp)
& ~ aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
& ! [W0] :
( sdtasdt0(xp,W0) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(W0) ) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f105,plain,
( ( ~ sdteqdtlpzmzozddtrp0(xa,xb,xq)
& ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& ! [W0] :
( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(W0) ) )
| sP0_prd ),
inference(formula_renaming,[status(thm)],[f103,f104]) ).
fof(f106,plain,
! [X0] :
( sdtasdt0(xq,X0) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(X0)
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f109,plain,
( ( sdteqdtlpzmzozddtrp0(xa,xb,xp)
| aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
| ? [W0] :
( sdtasdt0(xp,W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) )
| sP0_prd )
& ( ( ~ sdteqdtlpzmzozddtrp0(xa,xb,xp)
& ~ aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
& ! [W0] :
( sdtasdt0(xp,W0) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(W0) ) )
| ~ sP0_prd ) ),
inference(NNF_transformation,[status(thm)],[f104]) ).
fof(f110,plain,
( ( sdteqdtlpzmzozddtrp0(xa,xb,xp)
| aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
| ( sdtasdt0(xp,sK2_skl) = sdtpldt0(xa,smndt0(xb))
& aInteger0(sK2_skl) )
| sP0_prd )
& ( ( ~ sdteqdtlpzmzozddtrp0(xa,xb,xp)
& ~ aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
& ! [W0] :
( sdtasdt0(xp,W0) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(W0) ) )
| ~ sP0_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(W0,sK2_skl)],[f109]) ).
fof(f111,plain,
! [X0] :
( sdtasdt0(xp,X0) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(X0)
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f116,definition,
( sQ0_spl
<=> sP0_prd ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f119,definition,
! [X0] :
( sQ1_spl
<=> ( sdtasdt0(xq,X0) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f120,plain,
! [X0] :
( ~ sQ1_spl
| sdtasdt0(xq,X0) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(X0) ),
inference(component_clause,[status(thm)],[f119]) ).
fof(f122,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f106,f116,f119]) ).
fof(f131,definition,
! [X0] :
( sQ4_spl
<=> ( sdtasdt0(xp,X0) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f132,plain,
! [X0] :
( ~ sQ4_spl
| sdtasdt0(xp,X0) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(X0) ),
inference(component_clause,[status(thm)],[f131]) ).
fof(f134,plain,
( sQ4_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f111,f116,f131]) ).
fof(f219,definition,
( sQ19_spl
<=> aInteger0(xp) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f221,plain,
( sQ19_spl
| ~ aInteger0(xp) ),
inference(component_clause,[status(thm)],[f219]) ).
fof(f222,definition,
( sQ20_spl
<=> xp = sz00 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f223,plain,
( ~ sQ20_spl
| xp = sz00 ),
inference(component_clause,[status(thm)],[f222]) ).
fof(f308,definition,
( sQ32_spl
<=> aInteger0(xq) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f310,plain,
( sQ32_spl
| ~ aInteger0(xq) ),
inference(component_clause,[status(thm)],[f308]) ).
fof(f357,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f221,f89]) ).
fof(f358,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f357]) ).
fof(f359,plain,
( sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f310,f91]) ).
fof(f360,plain,
sQ32_spl,
inference(contradiction_clause,[status(thm)],[f359]) ).
fof(f372,definition,
( sQ44_spl
<=> aInteger0(xm) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f374,plain,
( sQ44_spl
| ~ aInteger0(xm) ),
inference(component_clause,[status(thm)],[f372]) ).
fof(f410,plain,
( sQ44_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f374,f99]) ).
fof(f411,plain,
sQ44_spl,
inference(contradiction_clause,[status(thm)],[f410]) ).
fof(f412,plain,
( ~ sQ4_spl
| ~ aInteger0(sdtasdt0(xq,xm)) ),
inference(resolution,[status(thm)],[f101,f132]) ).
fof(f455,plain,
( ~ sQ4_spl
| ~ aInteger0(xm)
| ~ aInteger0(xq) ),
inference(resolution,[status(thm)],[f412,f39]) ).
fof(f456,plain,
( ~ sQ4_spl
| ~ sQ44_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f455,f308,f372,f131]) ).
fof(f457,plain,
( ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f223,f90]) ).
fof(f458,plain,
~ sQ20_spl,
inference(contradiction_clause,[status(thm)],[f457]) ).
fof(f502,plain,
( ~ sQ1_spl
| ~ aInteger0(sdtasdt0(xp,xm)) ),
inference(resolution,[status(thm)],[f120,f102]) ).
fof(f511,plain,
( ~ sQ1_spl
| ~ aInteger0(xm)
| ~ aInteger0(xp) ),
inference(resolution,[status(thm)],[f502,f39]) ).
fof(f512,plain,
( ~ sQ1_spl
| ~ sQ44_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f511,f219,f372,f119]) ).
fof(f513,plain,
$false,
inference(sat_refutation,[status(thm)],[f122,f134,f358,f360,f411,f456,f458,f512]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM436+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n007.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 02:27:07 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.42 % Refutation found
% 0.10/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.45 % Elapsed time: 0.061725 seconds
% 0.10/0.45 % CPU time: 0.201571 seconds
% 0.10/0.45 % Total memory used: 104.604 MB
% 0.10/0.45 % Net memory used: 104.435 MB
%------------------------------------------------------------------------------