%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM494+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 : n020.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 01:40:44 PM UTC 2026
% Result : Theorem 0.15s 0.41s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 8 unt; 0 def)
% Number of atoms : 145 ( 45 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 189 ( 80 ~; 76 |; 27 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 28 ( 25 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0)
| sdtpldt0(W0,W1) = sdtpldt0(W0,W2) )
=> W1 = W2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W0,W1)
& W0 != W1 )
=> ! [W2] :
( aNaturalNumber0(W2)
=> ( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2))
& sdtpldt0(W0,W2) != sdtpldt0(W1,W2)
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& sdtpldt0(W2,W0) != sdtpldt0(W2,W1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
( xr = sdtmndt0(xn,xp)
& sdtpldt0(xp,xr) = xn
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,hypothesis,
( sdtlseqdt0(xr,xn)
& ? [W0] :
( sdtpldt0(xr,W0) = xn
& aNaturalNumber0(W0) )
& xr != xn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,conjecture,
( ( sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ? [W0] :
( sdtpldt0(sdtpldt0(sdtpldt0(xr,xm),xp),W0) = sdtpldt0(sdtpldt0(xn,xm),xp)
& aNaturalNumber0(W0) ) )
& sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
~ ( ( sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ? [W0] :
( sdtpldt0(sdtpldt0(sdtpldt0(xr,xm),xp),W0) = sdtpldt0(sdtpldt0(xn,xm),xp)
& aNaturalNumber0(W0) ) )
& sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f54,plain,
! [W0,W1] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f55,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f78,plain,
! [W0,W1,W2] :
( W1 = W2
| ( sdtpldt0(W1,W0) != sdtpldt0(W2,W0)
& sdtpldt0(W0,W1) != sdtpldt0(W0,W2) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f80,plain,
! [X0,X1,X2] :
( X1 = X2
| sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f110,plain,
! [W0,W1] :
( ! [W2] :
( ( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2))
& sdtpldt0(W0,W2) != sdtpldt0(W1,W2)
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
| ~ aNaturalNumber0(W2) )
| ~ sdtlseqdt0(W0,W1)
| W0 = W1
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f114,plain,
! [X0,X1,X2] :
( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f166,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f167,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f168,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f194,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f197,plain,
( sdtlseqdt0(xr,xn)
& sdtpldt0(xr,sK7_skl) = xn
& aNaturalNumber0(sK7_skl)
& xr != xn ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(W0,sK7_skl)],[f44]) ).
fof(f198,plain,
xr != xn,
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f201,plain,
sdtlseqdt0(xr,xn),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f206,plain,
( ( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& ! [W0] :
( sdtpldt0(sdtpldt0(sdtpldt0(xr,xm),xp),W0) != sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ aNaturalNumber0(W0) ) )
| sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f208,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(cnf_transformation,[status(thm)],[f206]) ).
fof(f480,plain,
( sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(sdtpldt0(xr,xm),sdtpldt0(xn,xm))
| sdtpldt0(xr,xm) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xr,xm)) ),
inference(resolution,[status(thm)],[f114,f208]) ).
fof(f488,plain,
( ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(sdtpldt0(xr,xm),sdtpldt0(xn,xm))
| sdtpldt0(xr,xm) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xr,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[f480,f80]) ).
fof(f553,plain,
( ~ sdtlseqdt0(sdtpldt0(xr,xm),sdtpldt0(xn,xm))
| sdtpldt0(xr,xm) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xr,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[f488,f168]) ).
fof(f554,plain,
( ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(xr,xn)
| xr = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| sdtpldt0(xr,xm) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xr,xm)) ),
inference(resolution,[status(thm)],[f553,f114]) ).
fof(f557,plain,
( ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(xr,xn)
| xr = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| sdtpldt0(xr,xm) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[f554,f55]) ).
fof(f560,plain,
( ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(xr,xn)
| xr = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| sdtpldt0(xr,xm) = sdtpldt0(xn,xm) ),
inference(forward_subsumption_resolution,[status(thm)],[f557,f55]) ).
fof(f561,plain,
( xr = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(xr,xn)
| xr = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f560,f80]) ).
fof(f563,plain,
( ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(xr,xn)
| xr = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr) ),
inference(duplicate_literals_removal,[status(thm)],[f561]) ).
fof(f564,plain,
( ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(xr,xn)
| xr = xn
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[status(thm)],[f563,f194]) ).
fof(f567,plain,
( ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(xr,xn)
| xr = xn ),
inference(forward_subsumption_resolution,[status(thm)],[f564,f166]) ).
fof(f568,plain,
( ~ aNaturalNumber0(xm)
| xr = xn ),
inference(resolution,[status(thm)],[f567,f201]) ).
fof(f571,plain,
~ aNaturalNumber0(xm),
inference(forward_subsumption_resolution,[status(thm)],[f568,f198]) ).
fof(f574,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f571,f167]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM494+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 02:35:47 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.15/0.41 % Refutation found
% 0.15/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.45 % Elapsed time: 0.074978 seconds
% 0.15/0.45 % CPU time: 0.304085 seconds
% 0.15/0.45 % Total memory used: 109.241 MB
% 0.15/0.45 % Net memory used: 108.774 MB
%------------------------------------------------------------------------------