%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM432+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 44 ( 14 unt; 2 def)
% Number of atoms : 158 ( 37 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 189 ( 75 ~; 76 |; 30 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 50 ( 46 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> aInteger0(sdtpldt0(W0,W1)) ),
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(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/sandbox/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
( aInteger0(xc)
& xq != sz00
& aInteger0(xq)
& aInteger0(xb)
& aInteger0(xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,hypothesis,
( sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb))
& aInteger0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,hypothesis,
( sdtasdt0(xq,xm) = sdtpldt0(xb,smndt0(xc))
& aInteger0(xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,hypothesis,
sdtasdt0(xq,sdtpldt0(xn,xm)) = sdtpldt0(xa,smndt0(xc)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,conjecture,
sdteqdtlpzmzozddtrp0(xa,xc,xq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xa,xc,xq),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f36,plain,
! [W0,W1] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f37,plain,
! [X0,X1] :
( aInteger0(sdtpldt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
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(f85,plain,
aInteger0(xa),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f87,plain,
aInteger0(xq),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f88,plain,
xq != sz00,
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f89,plain,
aInteger0(xc),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f92,plain,
aInteger0(xn),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f94,plain,
aInteger0(xm),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f96,plain,
sdtasdt0(xq,sdtpldt0(xn,xm)) = sdtpldt0(xa,smndt0(xc)),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f97,plain,
~ sdteqdtlpzmzozddtrp0(xa,xc,xq),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f99,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(f129,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| X0 = sz00
| ~ aInteger0(X0)
| aDivisorOf0(X0,sdtasdt0(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f99,f39]) ).
fof(f132,plain,
( ~ aInteger0(sdtpldt0(xn,xm))
| xq = sz00
| ~ aInteger0(xq)
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xc))) ),
inference(paramodulation,[status(thm)],[f96,f129]) ).
fof(f133,plain,
( ~ aInteger0(sdtpldt0(xn,xm))
| xq = sz00
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xc))) ),
inference(forward_subsumption_resolution,[status(thm)],[f132,f87]) ).
fof(f149,plain,
( ~ aInteger0(sdtpldt0(xn,xm))
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xc))) ),
inference(forward_subsumption_resolution,[status(thm)],[f133,f88]) ).
fof(f150,plain,
( sdteqdtlpzmzozddtrp0(xa,xc,xq)
| xq = sz00
| ~ aInteger0(xq)
| ~ aInteger0(xc)
| ~ aInteger0(xa)
| ~ aInteger0(sdtpldt0(xn,xm)) ),
inference(resolution,[status(thm)],[f149,f80]) ).
fof(f152,plain,
( sdteqdtlpzmzozddtrp0(xa,xc,xq)
| xq = sz00
| ~ aInteger0(xq)
| ~ aInteger0(xc)
| ~ aInteger0(sdtpldt0(xn,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[f150,f85]) ).
fof(f160,plain,
( sdteqdtlpzmzozddtrp0(xa,xc,xq)
| xq = sz00
| ~ aInteger0(xq)
| ~ aInteger0(sdtpldt0(xn,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[f152,f89]) ).
fof(f161,plain,
( xq = sz00
| ~ aInteger0(xq)
| ~ aInteger0(sdtpldt0(xn,xm)) ),
inference(resolution,[status(thm)],[f160,f97]) ).
fof(f162,plain,
( xq = sz00
| ~ aInteger0(sdtpldt0(xn,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[f161,f87]) ).
fof(f163,plain,
~ aInteger0(sdtpldt0(xn,xm)),
inference(forward_subsumption_resolution,[status(thm)],[f162,f88]) ).
fof(f164,plain,
( ~ aInteger0(xm)
| ~ aInteger0(xn) ),
inference(resolution,[status(thm)],[f163,f37]) ).
fof(f165,plain,
~ aInteger0(xm),
inference(forward_subsumption_resolution,[status(thm)],[f164,f92]) ).
fof(f166,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f165,f94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM432+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n006.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 02:28:42 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.049937 seconds
% 0.13/0.40 % CPU time: 0.147645 seconds
% 0.13/0.40 % Total memory used: 71.420 MB
% 0.13/0.40 % Net memory used: 71.271 MB
%------------------------------------------------------------------------------