%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM521+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 : n003.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 01:40:50 PM UTC 2026
% Result : Theorem 0.17s 0.55s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 14
% Syntax : Number of formulae : 54 ( 14 unt; 8 def)
% Number of atoms : 119 ( 12 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 116 ( 51 ~; 48 |; 8 &)
% ( 8 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 9 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 6 ( 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
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(f39,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,hypothesis,
~ sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
~ sdtlseqdt0(xp,xm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,hypothesis,
~ ( sdtlseqdt0(xm,xp)
& xm != xp
& sdtlseqdt0(xn,xp)
& xn != xp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f106,plain,
! [W0,W1] :
( ( sdtlseqdt0(W1,W0)
& W1 != W0 )
| sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f108,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f165,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f166,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f167,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f172,plain,
~ sdtlseqdt0(xp,xn),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f173,plain,
~ sdtlseqdt0(xp,xm),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f174,plain,
( ~ sdtlseqdt0(xm,xp)
| xm = xp
| ~ sdtlseqdt0(xn,xp)
| xn = xp ),
inference(pre_NNF_transformation,[status(thm)],[f44]) ).
fof(f175,plain,
( ~ sdtlseqdt0(xm,xp)
| xm = xp
| ~ sdtlseqdt0(xn,xp)
| xn = xp ),
inference(cnf_transformation,[status(thm)],[f174]) ).
fof(f179,definition,
( sQ0_spl
<=> xn = xp ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f180,plain,
( ~ sQ0_spl
| xn = xp ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f182,definition,
( sQ1_spl
<=> sdtlseqdt0(xn,xp) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f183,plain,
( ~ sQ1_spl
| sdtlseqdt0(xn,xp) ),
inference(component_clause,[status(thm)],[f182]) ).
fof(f185,definition,
( sQ2_spl
<=> xm = xp ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f186,plain,
( ~ sQ2_spl
| xm = xp ),
inference(component_clause,[status(thm)],[f185]) ).
fof(f188,definition,
( sQ3_spl
<=> sdtlseqdt0(xm,xp) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f189,plain,
( ~ sQ3_spl
| sdtlseqdt0(xm,xp) ),
inference(component_clause,[status(thm)],[f188]) ).
fof(f191,plain,
( ~ sQ3_spl
| sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f175,f179,f182,f185,f188]) ).
fof(f206,definition,
( sQ4_spl
<=> aNaturalNumber0(xp) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f208,plain,
( sQ4_spl
| ~ aNaturalNumber0(xp) ),
inference(component_clause,[status(thm)],[f206]) ).
fof(f220,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f208,f167]) ).
fof(f221,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f220]) ).
fof(f224,definition,
( sQ8_spl
<=> aNaturalNumber0(xn) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f226,plain,
( sQ8_spl
| ~ aNaturalNumber0(xn) ),
inference(component_clause,[status(thm)],[f224]) ).
fof(f230,definition,
( sQ10_spl
<=> aNaturalNumber0(xm) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f232,plain,
( sQ10_spl
| ~ aNaturalNumber0(xm) ),
inference(component_clause,[status(thm)],[f230]) ).
fof(f234,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f232,f166]) ).
fof(f235,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f234]) ).
fof(f236,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f226,f165]) ).
fof(f237,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f236]) ).
fof(f239,definition,
( sQ11_spl
<=> aNaturalNumber0(sz00) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f241,plain,
( sQ11_spl
| ~ aNaturalNumber0(sz00) ),
inference(component_clause,[status(thm)],[f239]) ).
fof(f263,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f50,f241]) ).
fof(f264,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f263]) ).
fof(f353,plain,
( sdtlseqdt0(xm,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f108,f173]) ).
fof(f354,plain,
( sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f108,f172]) ).
fof(f359,plain,
( sQ3_spl
| ~ sQ4_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f353,f230,f206,f188]) ).
fof(f360,plain,
( sQ1_spl
| ~ sQ4_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f354,f224,f206,f182]) ).
fof(f365,plain,
( ~ sQ0_spl
| ~ sdtlseqdt0(xp,xp) ),
inference(backward_demodulation,[status(thm)],[f180,f172]) ).
fof(f368,plain,
( ~ sQ1_spl
| ~ sQ0_spl
| sdtlseqdt0(xp,xp) ),
inference(forward_demodulation,[status(thm)],[f180,f183]) ).
fof(f369,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f365,f368]) ).
fof(f370,plain,
( ~ sQ0_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sdtlseqdt0(xp,xp) ),
inference(backward_demodulation,[status(thm)],[f186,f189]) ).
fof(f372,plain,
( ~ sQ2_spl
| ~ sdtlseqdt0(xp,xp) ),
inference(backward_demodulation,[status(thm)],[f186,f173]) ).
fof(f381,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f372,f371]) ).
fof(f382,plain,
( ~ sQ2_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f381]) ).
fof(f383,plain,
$false,
inference(sat_refutation,[status(thm)],[f191,f221,f235,f237,f264,f359,f360,f370,f382]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM521+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n003.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 02:38:01 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.46 % Drodi V4.1.1
% 0.17/0.55 % Refutation found
% 0.17/0.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.58 % Elapsed time: 0.121927 seconds
% 0.17/0.58 % CPU time: 0.500776 seconds
% 0.17/0.58 % Total memory used: 72.056 MB
% 0.17/0.58 % Net memory used: 71.582 MB
%------------------------------------------------------------------------------