%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM430+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 : 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 01:40:30 PM UTC 2026
% Result : Theorem 0.18s 0.48s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 8 unt; 2 def)
% Number of atoms : 149 ( 32 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 191 ( 82 ~; 71 |; 30 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 48 ( 42 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [W0] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> aInteger0(sdtpldt0(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(f22,hypothesis,
( aInteger0(xc)
& xq != sz00
& aInteger0(xq)
& aInteger0(xb)
& aInteger0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,hypothesis,
( sdteqdtlpzmzozddtrp0(xb,xc,xq)
& sdteqdtlpzmzozddtrp0(xa,xb,xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,conjecture,
? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xc))
& aInteger0(W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
~ ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xc))
& 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(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(f84,plain,
aInteger0(xb),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f85,plain,
aInteger0(xq),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f86,plain,
xq != sz00,
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f87,plain,
aInteger0(xc),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f89,plain,
sdteqdtlpzmzozddtrp0(xb,xc,xq),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f92,plain,
! [W0] :
( sdtasdt0(xq,W0) != sdtpldt0(xb,smndt0(xc))
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f93,plain,
! [X0] :
( sdtasdt0(xq,X0) != sdtpldt0(xb,smndt0(xc))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f100,plain,
( ~ aInteger0(sK0_skl(xq,sdtpldt0(xb,smndt0(xc))))
| ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
| ~ aInteger0(sdtpldt0(xb,smndt0(xc))) ),
inference(resolution,[status(thm)],[f73,f93]) ).
fof(f102,plain,
( ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
| ~ aInteger0(sdtpldt0(xb,smndt0(xc))) ),
inference(forward_subsumption_resolution,[status(thm)],[f100,f72]) ).
fof(f111,plain,
( ~ aInteger0(sdtpldt0(xb,smndt0(xc)))
| ~ sdteqdtlpzmzozddtrp0(xb,xc,xq)
| xq = sz00
| ~ aInteger0(xq)
| ~ aInteger0(xc)
| ~ aInteger0(xb) ),
inference(resolution,[status(thm)],[f77,f102]) ).
fof(f115,plain,
( ~ aInteger0(sdtpldt0(xb,smndt0(xc)))
| ~ sdteqdtlpzmzozddtrp0(xb,xc,xq)
| xq = sz00
| ~ aInteger0(xq)
| ~ aInteger0(xc) ),
inference(forward_subsumption_resolution,[status(thm)],[f111,f84]) ).
fof(f131,plain,
( ~ aInteger0(sdtpldt0(xb,smndt0(xc)))
| ~ sdteqdtlpzmzozddtrp0(xb,xc,xq)
| xq = sz00
| ~ aInteger0(xq) ),
inference(forward_subsumption_resolution,[status(thm)],[f115,f87]) ).
fof(f132,plain,
( ~ aInteger0(smndt0(xc))
| ~ aInteger0(xb)
| ~ sdteqdtlpzmzozddtrp0(xb,xc,xq)
| xq = sz00
| ~ aInteger0(xq) ),
inference(resolution,[status(thm)],[f131,f35]) ).
fof(f133,plain,
( ~ aInteger0(smndt0(xc))
| ~ aInteger0(xb)
| ~ sdteqdtlpzmzozddtrp0(xb,xc,xq)
| xq = sz00 ),
inference(forward_subsumption_resolution,[status(thm)],[f132,f85]) ).
fof(f134,plain,
( ~ aInteger0(smndt0(xc))
| ~ aInteger0(xb)
| ~ sdteqdtlpzmzozddtrp0(xb,xc,xq) ),
inference(forward_subsumption_resolution,[status(thm)],[f133,f86]) ).
fof(f135,plain,
( ~ aInteger0(smndt0(xc))
| ~ aInteger0(xb) ),
inference(resolution,[status(thm)],[f134,f89]) ).
fof(f137,plain,
~ aInteger0(smndt0(xc)),
inference(forward_subsumption_resolution,[status(thm)],[f135,f84]) ).
fof(f140,plain,
~ aInteger0(xc),
inference(resolution,[status(thm)],[f137,f33]) ).
fof(f141,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f140,f87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM430+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n019.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 02:28:49 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.46 % Drodi V4.1.1
% 0.18/0.48 % Refutation found
% 0.18/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/0.53 % Elapsed time: 0.080536 seconds
% 0.24/0.53 % CPU time: 0.128933 seconds
% 0.24/0.53 % Total memory used: 26.028 MB
% 0.24/0.53 % Net memory used: 25.971 MB
%------------------------------------------------------------------------------