%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM482+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 : n019.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 01:40:41 PM UTC 2026
% Result : Theorem 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 7 unt; 4 def)
% Number of atoms : 171 ( 57 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 203 ( 65 ~; 64 |; 63 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 30 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,hypothesis,
aNaturalNumber0(xk),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,conjecture,
( ( isPrime0(xk)
& ! [W0] :
( ( ( doDivides0(W0,xk)
| ? [W1] :
( xk = sdtasdt0(W0,W1)
& aNaturalNumber0(W1) ) )
& aNaturalNumber0(W0) )
=> ( W0 = xk
| W0 = sz10 ) ) )
=> ? [W0] :
( ( isPrime0(W0)
| ( ! [W1] :
( ( doDivides0(W1,W0)
& ? [W2] :
( W0 = sdtasdt0(W1,W2)
& aNaturalNumber0(W2) )
& aNaturalNumber0(W1) )
=> ( W1 = W0
| W1 = sz10 ) )
& W0 != sz10
& W0 != sz00 ) )
& ( doDivides0(W0,xk)
| ? [W1] :
( xk = sdtasdt0(W0,W1)
& aNaturalNumber0(W1) ) )
& aNaturalNumber0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
~ ( ( isPrime0(xk)
& ! [W0] :
( ( ( doDivides0(W0,xk)
| ? [W1] :
( xk = sdtasdt0(W0,W1)
& aNaturalNumber0(W1) ) )
& aNaturalNumber0(W0) )
=> ( W0 = xk
| W0 = sz10 ) ) )
=> ? [W0] :
( ( isPrime0(W0)
| ( ! [W1] :
( ( doDivides0(W1,W0)
& ? [W2] :
( W0 = sdtasdt0(W1,W2)
& aNaturalNumber0(W2) )
& aNaturalNumber0(W1) )
=> ( W1 = W0
| W1 = sz10 ) )
& W0 != sz10
& W0 != sz00 ) )
& ( doDivides0(W0,xk)
| ? [W1] :
( xk = sdtasdt0(W0,W1)
& aNaturalNumber0(W1) ) )
& aNaturalNumber0(W0) ) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
fof(f47,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f64,plain,
! [W0] :
( ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 )
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f65,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f156,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f170,plain,
( ! [W0] :
( ( ~ isPrime0(W0)
& ( ? [W1] :
( W1 != W0
& W1 != sz10
& doDivides0(W1,W0)
& ? [W2] :
( W0 = sdtasdt0(W1,W2)
& aNaturalNumber0(W2) )
& aNaturalNumber0(W1) )
| W0 = sz10
| W0 = sz00 ) )
| ( ~ doDivides0(W0,xk)
& ! [W1] :
( xk != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(W0) )
& isPrime0(xk)
& ! [W0] :
( W0 = xk
| W0 = sz10
| ( ~ doDivides0(W0,xk)
& ! [W1] :
( xk != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f171,definition,
! [W0] :
( sP0_prd(W0)
<=> ( ~ doDivides0(W0,xk)
& ! [W1] :
( xk != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f172,plain,
( ! [W0] :
( ( ~ isPrime0(W0)
& ( ? [W1] :
( W1 != W0
& W1 != sz10
& doDivides0(W1,W0)
& ? [W2] :
( W0 = sdtasdt0(W1,W2)
& aNaturalNumber0(W2) )
& aNaturalNumber0(W1) )
| W0 = sz10
| W0 = sz00 ) )
| sP0_prd(W0)
| ~ aNaturalNumber0(W0) )
& isPrime0(xk)
& ! [W0] :
( W0 = xk
| W0 = sz10
| ( ~ doDivides0(W0,xk)
& ! [W1] :
( xk != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(W0) ) ),
inference(formula_renaming,[status(thm)],[f170,f171]) ).
fof(f173,plain,
( ! [W0] :
( ( ~ isPrime0(W0)
& ( ( sK5_skl(W0) != W0
& sK5_skl(W0) != sz10
& doDivides0(sK5_skl(W0),W0)
& W0 = sdtasdt0(sK5_skl(W0),sK6_skl(W0))
& aNaturalNumber0(sK6_skl(W0))
& aNaturalNumber0(sK5_skl(W0)) )
| W0 = sz10
| W0 = sz00 ) )
| sP0_prd(W0)
| ~ aNaturalNumber0(W0) )
& isPrime0(xk)
& ! [W0] :
( W0 = xk
| W0 = sz10
| ( ~ doDivides0(W0,xk)
& ! [W1] :
( xk != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(W0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl]),skolemize(W1,sK5_skl(W0)),skolemize(W2,sK6_skl(W0))],[f172]) ).
fof(f176,plain,
isPrime0(xk),
inference(cnf_transformation,[status(thm)],[f173]) ).
fof(f183,plain,
! [X0] :
( ~ isPrime0(X0)
| sP0_prd(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f173]) ).
fof(f184,plain,
! [W0] :
( ( doDivides0(W0,xk)
| ? [W1] :
( xk = sdtasdt0(W0,W1)
& aNaturalNumber0(W1) )
| sP0_prd(W0) )
& ( ( ~ doDivides0(W0,xk)
& ! [W1] :
( xk != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ sP0_prd(W0) ) ),
inference(NNF_transformation,[status(thm)],[f171]) ).
fof(f185,plain,
( ! [W0] :
( doDivides0(W0,xk)
| ? [W1] :
( xk = sdtasdt0(W0,W1)
& aNaturalNumber0(W1) )
| sP0_prd(W0) )
& ! [W0] :
( ( ~ doDivides0(W0,xk)
& ! [W1] :
( xk != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ sP0_prd(W0) ) ),
inference(miniscoping,[status(thm)],[f184]) ).
fof(f186,plain,
( ! [W0] :
( doDivides0(W0,xk)
| ( xk = sdtasdt0(W0,sK7_skl(W0))
& aNaturalNumber0(sK7_skl(W0)) )
| sP0_prd(W0) )
& ! [W0] :
( ( ~ doDivides0(W0,xk)
& ! [W1] :
( xk != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ sP0_prd(W0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(W1,sK7_skl(W0))],[f185]) ).
fof(f187,plain,
! [X0,X1] :
( xk != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f203,plain,
( sP0_prd(xk)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[f183,f176]) ).
fof(f204,definition,
( sQ0_spl
<=> aNaturalNumber0(xk) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f206,plain,
( sQ0_spl
| ~ aNaturalNumber0(xk) ),
inference(component_clause,[status(thm)],[f204]) ).
fof(f207,definition,
( sQ1_spl
<=> sP0_prd(xk) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f210,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f203,f204,f207]) ).
fof(f212,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f156,f206]) ).
fof(f213,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f212]) ).
fof(f217,plain,
( ~ aNaturalNumber0(sz10)
| ~ sP0_prd(xk)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[f65,f187]) ).
fof(f218,definition,
( sQ2_spl
<=> aNaturalNumber0(sz10) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f220,plain,
( sQ2_spl
| ~ aNaturalNumber0(sz10) ),
inference(component_clause,[status(thm)],[f218]) ).
fof(f228,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f217,f204,f207,f218]) ).
fof(f229,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f220,f47]) ).
fof(f230,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f229]) ).
fof(f231,plain,
$false,
inference(sat_refutation,[status(thm)],[f210,f213,f228,f230]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM482+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n019.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 02:33:51 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.38 % Drodi V4.1.1
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.062801 seconds
% 0.13/0.43 % CPU time: 0.160037 seconds
% 0.13/0.43 % Total memory used: 83.647 MB
% 0.13/0.43 % Net memory used: 83.551 MB
%------------------------------------------------------------------------------