%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM436+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 0.14s 5.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 20
% Syntax : Number of formulae : 83 ( 17 unt; 15 def)
% Number of atoms : 246 ( 41 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 268 ( 105 ~; 111 |; 32 &)
% ( 17 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 14 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 44 ( 40 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> aInteger0(sdtasdt0(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(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/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)
& sdteqdtlpzmzozddtrp0(xa,xb,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
~ ( sdteqdtlpzmzozddtrp0(xa,xb,xq)
& sdteqdtlpzmzozddtrp0(xa,xb,xp) ),
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(f68,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(f69,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)],[f68]) ).
fof(f70,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)],[f69]) ).
fof(f71,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))],[f70]) ).
fof(f76,plain,
! [X0,X1,X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2)
| X1 = sz00
| ~ aInteger0(X1)
| aDivisorOf0(X1,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f77,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(f78,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)],[f77]) ).
fof(f80,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)],[f78]) ).
fof(f87,plain,
aInteger0(xa),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f88,plain,
aInteger0(xb),
inference(cnf_transformation,[status(thm)],[f23]) ).
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(f92,plain,
xq != sz00,
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f94,plain,
aInteger0(xm),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f96,plain,
sdtasdt0(xp,sdtasdt0(xq,xm)) = sdtpldt0(xa,smndt0(xb)),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f97,plain,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f98,plain,
( ~ sdteqdtlpzmzozddtrp0(xa,xb,xq)
| ~ sdteqdtlpzmzozddtrp0(xa,xb,xp) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f99,plain,
( ~ sdteqdtlpzmzozddtrp0(xa,xb,xq)
| ~ sdteqdtlpzmzozddtrp0(xa,xb,xp) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f100,definition,
( sQ0_spl
<=> sdteqdtlpzmzozddtrp0(xa,xb,xp) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f103,definition,
( sQ1_spl
<=> sdteqdtlpzmzozddtrp0(xa,xb,xq) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f99,f100,f103]) ).
fof(f108,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| X0 = sz00
| ~ aInteger0(X0)
| aDivisorOf0(X0,sdtasdt0(X0,X1))
| ~ aInteger0(sdtasdt0(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f76]) ).
fof(f111,definition,
( sQ2_spl
<=> aInteger0(xa) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f113,plain,
( sQ2_spl
| ~ aInteger0(xa) ),
inference(component_clause,[status(thm)],[f111]) ).
fof(f114,definition,
( sQ3_spl
<=> aInteger0(xb) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f116,plain,
( sQ3_spl
| ~ aInteger0(xb) ),
inference(component_clause,[status(thm)],[f114]) ).
fof(f145,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f116,f88]) ).
fof(f146,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f145]) ).
fof(f147,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f113,f87]) ).
fof(f148,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f147]) ).
fof(f163,definition,
( sQ13_spl
<=> aInteger0(xp) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f165,plain,
( sQ13_spl
| ~ aInteger0(xp) ),
inference(component_clause,[status(thm)],[f163]) ).
fof(f166,definition,
( sQ14_spl
<=> aInteger0(xq) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f168,plain,
( sQ14_spl
| ~ aInteger0(xq) ),
inference(component_clause,[status(thm)],[f166]) ).
fof(f172,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f168,f91]) ).
fof(f173,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f172]) ).
fof(f178,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f165,f89]) ).
fof(f179,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f178]) ).
fof(f209,definition,
( sQ17_spl
<=> xp = sz00 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f210,plain,
( ~ sQ17_spl
| xp = sz00 ),
inference(component_clause,[status(thm)],[f209]) ).
fof(f212,definition,
( sQ18_spl
<=> xq = sz00 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f213,plain,
( ~ sQ18_spl
| xq = sz00 ),
inference(component_clause,[status(thm)],[f212]) ).
fof(f236,plain,
( ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f213,f92]) ).
fof(f237,plain,
~ sQ18_spl,
inference(contradiction_clause,[status(thm)],[f236]) ).
fof(f238,plain,
( ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f210,f90]) ).
fof(f239,plain,
~ sQ17_spl,
inference(contradiction_clause,[status(thm)],[f238]) ).
fof(f269,definition,
( sQ26_spl
<=> aInteger0(xm) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f271,plain,
( sQ26_spl
| ~ aInteger0(xm) ),
inference(component_clause,[status(thm)],[f269]) ).
fof(f288,plain,
( sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f271,f94]) ).
fof(f289,plain,
sQ26_spl,
inference(contradiction_clause,[status(thm)],[f288]) ).
fof(f292,definition,
( sQ31_spl
<=> aInteger0(sdtasdt0(xq,xm)) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f294,plain,
( sQ31_spl
| ~ aInteger0(sdtasdt0(xq,xm)) ),
inference(component_clause,[status(thm)],[f292]) ).
fof(f302,definition,
( sQ33_spl
<=> aInteger0(sdtasdt0(xp,xm)) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f304,plain,
( sQ33_spl
| ~ aInteger0(sdtasdt0(xp,xm)) ),
inference(component_clause,[status(thm)],[f302]) ).
fof(f314,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| X0 = sz00
| ~ aInteger0(X0)
| aDivisorOf0(X0,sdtasdt0(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f108,f39]) ).
fof(f318,plain,
( ~ aInteger0(sdtasdt0(xp,xm))
| xq = sz00
| ~ aInteger0(xq)
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb))) ),
inference(paramodulation,[status(thm)],[f97,f314]) ).
fof(f319,plain,
( ~ aInteger0(sdtasdt0(xq,xm))
| xp = sz00
| ~ aInteger0(xp)
| aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb))) ),
inference(paramodulation,[status(thm)],[f96,f314]) ).
fof(f329,definition,
( sQ37_spl
<=> aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb))) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f330,plain,
( ~ sQ37_spl
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb))) ),
inference(component_clause,[status(thm)],[f329]) ).
fof(f332,plain,
( ~ sQ33_spl
| sQ18_spl
| ~ sQ14_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f318,f329,f166,f212,f302]) ).
fof(f333,definition,
( sQ38_spl
<=> aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb))) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f334,plain,
( ~ sQ38_spl
| aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb))) ),
inference(component_clause,[status(thm)],[f333]) ).
fof(f336,plain,
( ~ sQ31_spl
| sQ17_spl
| ~ sQ13_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f319,f333,f163,f209,f292]) ).
fof(f363,plain,
( sQ33_spl
| ~ aInteger0(xm)
| ~ aInteger0(xp) ),
inference(resolution,[status(thm)],[f304,f39]) ).
fof(f364,plain,
( sQ33_spl
| ~ sQ26_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f363,f163,f269,f302]) ).
fof(f510,plain,
( sQ31_spl
| ~ aInteger0(xm)
| ~ aInteger0(xq) ),
inference(resolution,[status(thm)],[f294,f39]) ).
fof(f511,plain,
( sQ31_spl
| ~ sQ26_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f510,f166,f269,f292]) ).
fof(f519,plain,
( ~ sQ37_spl
| sdteqdtlpzmzozddtrp0(xa,xb,xq)
| xq = sz00
| ~ aInteger0(xq)
| ~ aInteger0(xb)
| ~ aInteger0(xa) ),
inference(resolution,[status(thm)],[f330,f80]) ).
fof(f521,plain,
( ~ sQ37_spl
| sQ1_spl
| sQ18_spl
| ~ sQ14_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f519,f111,f114,f166,f212,f103,f329]) ).
fof(f820,plain,
( ~ sQ38_spl
| sdteqdtlpzmzozddtrp0(xa,xb,xp)
| xp = sz00
| ~ aInteger0(xp)
| ~ aInteger0(xb)
| ~ aInteger0(xa) ),
inference(resolution,[status(thm)],[f80,f334]) ).
fof(f822,plain,
( ~ sQ38_spl
| sQ0_spl
| sQ17_spl
| ~ sQ13_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f820,f111,f114,f163,f209,f100,f333]) ).
fof(f824,plain,
$false,
inference(sat_refutation,[status(thm)],[f106,f146,f148,f173,f179,f237,f239,f289,f332,f336,f364,f511,f521,f822]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM436+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n011.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Mon Sep 21 02:29:17 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.38 % Drodi V4.1.1
% 0.14/5.40 % Refutation found
% 0.14/5.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.50 % Elapsed time: 0.120896 seconds
% 0.14/5.50 % CPU time: 0.133781 seconds
% 0.14/5.50 % Total memory used: 13.514 MB
% 0.14/5.50 % Net memory used: 13.468 MB
%------------------------------------------------------------------------------