%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM464+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 0.18s 5.48s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 40 ( 8 unt; 5 def)
% Number of atoms : 100 ( 24 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 101 ( 41 ~; 40 |; 11 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 12 ( 10 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W0)
& W1 != W0 )
| sdtlseqdt0(W0,W1) ) ),
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(sz10,xm)
| ? [W0] :
( sdtpldt0(sz10,W0) = xm
& aNaturalNumber0(W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ ( xm != sz00
=> ( sdtlseqdt0(sz10,xm)
| ? [W0] :
( sdtpldt0(sz10,W0) = xm
& aNaturalNumber0(W0) ) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f34,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f89,plain,
! [W0,W1] :
( ( sdtlseqdt0(W1,W0)
& W1 != W0 )
| sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f91,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
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(f107,plain,
( ~ sdtlseqdt0(sz10,xm)
& ! [W0] :
( sdtpldt0(sz10,W0) != xm
| ~ aNaturalNumber0(W0) )
& xm != sz00 ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f108,plain,
xm != sz00,
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f110,plain,
~ sdtlseqdt0(sz10,xm),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f117,plain,
( sdtlseqdt0(xm,sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f91,f110]) ).
fof(f118,definition,
( sQ0_spl
<=> aNaturalNumber0(xm) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f120,plain,
( sQ0_spl
| ~ aNaturalNumber0(xm) ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,definition,
( sQ1_spl
<=> aNaturalNumber0(sz10) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f123,plain,
( sQ1_spl
| ~ aNaturalNumber0(sz10) ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,definition,
( sQ2_spl
<=> sdtlseqdt0(xm,sz10) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f125,plain,
( ~ sQ2_spl
| sdtlseqdt0(xm,sz10) ),
inference(component_clause,[status(thm)],[f124]) ).
fof(f127,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f117,f118,f121,f124]) ).
fof(f155,plain,
( xm = sz10
| xm = sz00
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f104,f110]) ).
fof(f156,definition,
( sQ7_spl
<=> xm = sz00 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f157,plain,
( ~ sQ7_spl
| xm = sz00 ),
inference(component_clause,[status(thm)],[f156]) ).
fof(f159,definition,
( sQ8_spl
<=> xm = sz10 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f160,plain,
( ~ sQ8_spl
| xm = sz10 ),
inference(component_clause,[status(thm)],[f159]) ).
fof(f162,plain,
( sQ8_spl
| sQ7_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f155,f118,f156,f159]) ).
fof(f163,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f120,f105]) ).
fof(f164,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f163]) ).
fof(f165,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f123,f34]) ).
fof(f166,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f165]) ).
fof(f167,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f157,f108]) ).
fof(f168,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f167]) ).
fof(f171,plain,
( ~ sQ8_spl
| ~ sdtlseqdt0(sz10,sz10) ),
inference(backward_demodulation,[status(thm)],[f160,f110]) ).
fof(f173,plain,
( ~ sQ2_spl
| ~ sQ8_spl
| sdtlseqdt0(sz10,sz10) ),
inference(forward_demodulation,[status(thm)],[f160,f125]) ).
fof(f174,plain,
( ~ sQ8_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f171,f173]) ).
fof(f175,plain,
( ~ sQ8_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f174]) ).
fof(f176,plain,
$false,
inference(sat_refutation,[status(thm)],[f127,f162,f164,f166,f168,f175]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM464+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/5.45 % Computer : n009.cluster.edu
% 0.18/5.45 % Model : x86_64 x86_64
% 0.18/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.45 % Memory : 8046.5625MB
% 0.18/5.45 % OS : Linux 6.8.0-71-generic
% 0.18/5.45 % CPULimit : 300
% 0.18/5.45 % WCLimit : 300
% 0.18/5.45 % DateTime : Mon Sep 21 02:32:18 UTC 2026
% 0.18/5.45 % CPUTime :
% 0.18/5.46 % Drodi V4.1.1
% 0.18/5.48 % Refutation found
% 0.18/5.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/5.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/5.53 % Elapsed time: 0.063967 seconds
% 0.23/5.53 % CPU time: 0.106647 seconds
% 0.23/5.53 % Total memory used: 10.588 MB
% 0.23/5.53 % Net memory used: 10.549 MB
%------------------------------------------------------------------------------