%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM464+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 : 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 0.19s 5.48s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 45 ( 10 unt; 6 def)
% Number of atoms : 102 ( 24 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 100 ( 43 ~; 39 |; 8 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 9 ( 9 !; 0 ?)
% 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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ ( xm != sz00
=> sdtlseqdt0(sz10,xm) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f34,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f35,plain,
sz10 != sz00,
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)
& xm != sz00 ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f108,plain,
xm != sz00,
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f109,plain,
~ sdtlseqdt0(sz10,xm),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f116,plain,
( sdtlseqdt0(xm,sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f91,f109]) ).
fof(f117,definition,
( sQ0_spl
<=> aNaturalNumber0(xm) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f119,plain,
( sQ0_spl
| ~ aNaturalNumber0(xm) ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,definition,
( sQ1_spl
<=> aNaturalNumber0(sz10) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( sQ1_spl
| ~ aNaturalNumber0(sz10) ),
inference(component_clause,[status(thm)],[f120]) ).
fof(f123,definition,
( sQ2_spl
<=> sdtlseqdt0(xm,sz10) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f124,plain,
( ~ sQ2_spl
| sdtlseqdt0(xm,sz10) ),
inference(component_clause,[status(thm)],[f123]) ).
fof(f126,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f116,f117,f120,f123]) ).
fof(f127,plain,
( xm = sz10
| xm = sz00
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f104,f109]) ).
fof(f128,definition,
( sQ3_spl
<=> xm = sz00 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f129,plain,
( ~ sQ3_spl
| xm = sz00 ),
inference(component_clause,[status(thm)],[f128]) ).
fof(f131,definition,
( sQ4_spl
<=> xm = sz10 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f132,plain,
( ~ sQ4_spl
| xm = sz10 ),
inference(component_clause,[status(thm)],[f131]) ).
fof(f134,plain,
( sQ4_spl
| sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f127,f117,f128,f131]) ).
fof(f135,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f119,f105]) ).
fof(f136,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f135]) ).
fof(f137,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f122,f34]) ).
fof(f138,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f137]) ).
fof(f139,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f129,f108]) ).
fof(f140,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f139]) ).
fof(f142,plain,
( ~ sQ4_spl
| ~ sdtlseqdt0(sz10,sz10) ),
inference(backward_demodulation,[status(thm)],[f132,f109]) ).
fof(f144,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| sdtlseqdt0(sz10,sz10) ),
inference(forward_demodulation,[status(thm)],[f132,f124]) ).
fof(f148,definition,
( sQ5_spl
<=> sz10 = sz00 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f149,plain,
( ~ sQ5_spl
| sz10 = sz00 ),
inference(component_clause,[status(thm)],[f148]) ).
fof(f163,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f149,f35]) ).
fof(f164,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f163]) ).
fof(f176,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f142,f144]) ).
fof(f177,plain,
( ~ sQ4_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f176]) ).
fof(f178,plain,
$false,
inference(sat_refutation,[status(thm)],[f126,f134,f136,f138,f140,f164,f177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM464+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/5.44 % Computer : n009.cluster.edu
% 0.19/5.44 % Model : x86_64 x86_64
% 0.19/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.44 % Memory : 8046.5625MB
% 0.19/5.44 % OS : Linux 6.8.0-71-generic
% 0.19/5.44 % CPULimit : 300
% 0.19/5.44 % WCLimit : 300
% 0.19/5.44 % DateTime : Mon Sep 21 02:32:03 UTC 2026
% 0.19/5.44 % CPUTime :
% 0.19/5.46 % Drodi V4.1.1
% 0.19/5.48 % Refutation found
% 0.19/5.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/5.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/5.55 % Elapsed time: 0.100661 seconds
% 0.23/5.55 % CPU time: 0.127169 seconds
% 0.23/5.55 % Total memory used: 15.544 MB
% 0.23/5.55 % Net memory used: 15.514 MB
%------------------------------------------------------------------------------