%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM463+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 : n008.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 01:40:37 PM UTC 2026
% Result : Theorem 6.80s 1.30s
% Output : CNFRefutation 6.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 12 unt; 0 def)
% Number of atoms : 128 ( 58 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 130 ( 46 ~; 57 |; 19 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 23 ( 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> sdtlseqdt0(W0,W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W2)
& W1 != W2
& W0 != sz00 )
=> ( sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W1,W0) != sdtasdt0(W2,W0)
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& sdtasdt0(W0,W1) != sdtasdt0(W0,W2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtlseqdt0(sz10,W0)
& sz10 != W0 )
| W0 = sz10
| W0 = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,conjecture,
( xm != sz00
=> sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ ( xm != sz00
=> sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f34,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f51,plain,
! [W0] :
( ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 )
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f52,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f54,plain,
! [W0] :
( ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 )
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f56,plain,
! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f83,plain,
! [W0] :
( sdtlseqdt0(W0,W0)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f84,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f97,plain,
! [W0,W1,W2] :
( ( sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W1,W0) != sdtasdt0(W2,W0)
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
| ~ sdtlseqdt0(W1,W2)
| W1 = W2
| W0 = sz00
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f99,plain,
! [X0,X1,X2] :
( sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| X0 = sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f102,plain,
! [W0] :
( ( sdtlseqdt0(sz10,W0)
& sz10 != W0 )
| W0 = sz10
| W0 = sz00
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f104,plain,
! [X0] :
( sdtlseqdt0(sz10,X0)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f105,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f106,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f107,plain,
( ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
& xm != sz00 ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f108,plain,
xm != sz00,
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f109,plain,
~ sdtlseqdt0(xn,sdtasdt0(xn,xm)),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f133,plain,
sdtlseqdt0(xn,xn),
inference(resolution,[status(thm)],[f84,f106]) ).
fof(f171,plain,
sdtasdt0(xn,sz10) = xn,
inference(resolution,[status(thm)],[f52,f106]) ).
fof(f184,plain,
sz00 = sdtasdt0(sz00,xm),
inference(resolution,[status(thm)],[f56,f105]) ).
fof(f385,plain,
! [X0,X1] :
( sdtlseqdt0(sdtasdt0(xn,X0),sdtasdt0(xn,X1))
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| xn = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f99,f106]) ).
fof(f445,plain,
( sdtlseqdt0(sz10,xm)
| xm = sz10
| xm = sz00 ),
inference(resolution,[status(thm)],[f104,f105]) ).
fof(f447,plain,
( sdtlseqdt0(sz10,xm)
| xm = sz10 ),
inference(forward_subsumption_resolution,[status(thm)],[f445,f108]) ).
fof(f3122,plain,
( xm = sz10
| sdtlseqdt0(sdtasdt0(xn,sz10),sdtasdt0(xn,xm))
| sz10 = xm
| xn = sz00
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f385,f447]) ).
fof(f3131,plain,
( xm = sz10
| sdtlseqdt0(xn,sdtasdt0(xn,xm))
| sz10 = xm
| xn = sz00
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10) ),
inference(forward_demodulation,[status(thm)],[f171,f3122]) ).
fof(f3132,plain,
( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| sz10 = xm
| xn = sz00
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10) ),
inference(duplicate_literals_removal,[status(thm)],[f3131]) ).
fof(f3133,plain,
( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| sz10 = xm
| xn = sz00
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[status(thm)],[f3132,f34]) ).
fof(f3491,plain,
( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| sz10 = xm
| xn = sz00 ),
inference(forward_subsumption_resolution,[status(thm)],[f3133,f105]) ).
fof(f3492,plain,
( sz10 = xm
| xn = sz00 ),
inference(resolution,[status(thm)],[f3491,f109]) ).
fof(f4156,plain,
( sz10 = xm
| sdtlseqdt0(xn,sz00) ),
inference(paramodulation,[status(thm)],[f3492,f133]) ).
fof(f4159,plain,
( sz10 = xm
| ~ sdtlseqdt0(xn,sdtasdt0(sz00,xm)) ),
inference(paramodulation,[status(thm)],[f3492,f109]) ).
fof(f4179,plain,
( sz10 = xm
| ~ sdtlseqdt0(xn,sz00) ),
inference(forward_demodulation,[status(thm)],[f184,f4159]) ).
fof(f4897,plain,
~ sdtlseqdt0(xn,sdtasdt0(xn,sz10)),
inference(backward_demodulation,[status(thm)],[f4899,f109]) ).
fof(f4899,plain,
sz10 = xm,
inference(forward_subsumption_resolution,[status(thm)],[f4179,f4156]) ).
fof(f4950,plain,
~ sdtlseqdt0(xn,xn),
inference(forward_demodulation,[status(thm)],[f171,f4897]) ).
fof(f4951,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f4950,f133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM463+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n008.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 02:32:41 UTC 2026
% 0.14/0.35 % CPUTime :
% 0.14/0.37 % Drodi V4.1.1
% 6.80/1.30 % Refutation found
% 6.80/1.30 % SZS status Theorem for theBenchmark: Theorem is valid
% 6.80/1.30 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 6.80/1.33 % Elapsed time: 0.962952 seconds
% 6.80/1.33 % CPU time: 7.257343 seconds
% 6.80/1.33 % Total memory used: 166.035 MB
% 6.80/1.33 % Net memory used: 157.470 MB
%------------------------------------------------------------------------------