%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM427+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 01:40:30 PM UTC 2026
% Result : Theorem 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 42 ( 11 unt; 4 def)
% Number of atoms : 130 ( 31 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 143 ( 55 ~; 53 |; 27 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 38 ( 32 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [W0] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) ),
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(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(f21,hypothesis,
( xq != sz00
& aInteger0(xq)
& aInteger0(xb)
& aInteger0(xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,hypothesis,
( sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb))
& aInteger0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,hypothesis,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,conjecture,
( sdteqdtlpzmzozddtrp0(xb,xa,xq)
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xa))
& aInteger0(W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
~ ( sdteqdtlpzmzozddtrp0(xb,xa,xq)
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xa))
& 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(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(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(f74,plain,
! [X0,X1,X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2)
| X1 = sz00
| ~ aInteger0(X1)
| aDivisorOf0(X1,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f83,plain,
aInteger0(xq),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f84,plain,
xq != sz00,
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f90,plain,
aInteger0(xn),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f92,plain,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f93,plain,
( ~ sdteqdtlpzmzozddtrp0(xb,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
& ! [W0] :
( sdtasdt0(xq,W0) != sdtpldt0(xb,smndt0(xa))
| ~ aInteger0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f95,plain,
~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa))),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f98,plain,
! [X1,X2] :
( ~ aInteger0(X2)
| X1 = sz00
| ~ aInteger0(X1)
| aDivisorOf0(X1,sdtasdt0(X1,X2))
| ~ aInteger0(sdtasdt0(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f74]) ).
fof(f99,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| X0 = sz00
| ~ aInteger0(X0)
| aDivisorOf0(X0,sdtasdt0(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f98,f37]) ).
fof(f105,plain,
~ aDivisorOf0(xq,sdtasdt0(xq,smndt0(xn))),
inference(forward_demodulation,[status(thm)],[f92,f95]) ).
fof(f122,definition,
( sQ2_spl
<=> aInteger0(xq) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f124,plain,
( sQ2_spl
| ~ aInteger0(xq) ),
inference(component_clause,[status(thm)],[f122]) ).
fof(f125,definition,
( sQ3_spl
<=> xq = sz00 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ3_spl
| xq = sz00 ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f157,plain,
( ~ aInteger0(smndt0(xn))
| xq = sz00
| ~ aInteger0(xq) ),
inference(resolution,[status(thm)],[f105,f99]) ).
fof(f158,definition,
( sQ9_spl
<=> aInteger0(smndt0(xn)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f160,plain,
( sQ9_spl
| ~ aInteger0(smndt0(xn)) ),
inference(component_clause,[status(thm)],[f158]) ).
fof(f161,plain,
( ~ sQ9_spl
| sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f157,f122,f125,f158]) ).
fof(f162,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f126,f84]) ).
fof(f163,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f162]) ).
fof(f164,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f124,f83]) ).
fof(f165,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f164]) ).
fof(f166,plain,
( sQ9_spl
| ~ aInteger0(xn) ),
inference(resolution,[status(thm)],[f160,f33]) ).
fof(f167,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f166,f90]) ).
fof(f168,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f167]) ).
fof(f169,plain,
$false,
inference(sat_refutation,[status(thm)],[f161,f163,f165,f168]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM427+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 02:23:41 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.14/0.40 % Refutation found
% 0.14/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.47 % Elapsed time: 0.107407 seconds
% 0.14/0.47 % CPU time: 0.211684 seconds
% 0.14/0.47 % Total memory used: 103.094 MB
% 0.14/0.47 % Net memory used: 102.962 MB
%------------------------------------------------------------------------------