%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM505+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 01:40:46 PM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 7 unt; 4 def)
% Number of atoms : 90 ( 16 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 91 ( 36 ~; 31 |; 16 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 15 ( 11 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f20,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> sdtlseqdt0(W0,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W0)
& W1 != W0 )
| sdtlseqdt0(W0,W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,hypothesis,
( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& aNaturalNumber0(xk) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,conjecture,
( ~ ( sdtlseqdt0(xp,xk)
| ? [W0] :
( sdtpldt0(xp,W0) = xk
& aNaturalNumber0(W0) ) )
=> ( ( sdtlseqdt0(xk,xp)
| ? [W0] :
( sdtpldt0(xk,W0) = xp
& aNaturalNumber0(W0) ) )
& xk != xp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,negated_conjecture,
~ ( ~ ( sdtlseqdt0(xp,xk)
| ? [W0] :
( sdtpldt0(xp,W0) = xk
& aNaturalNumber0(W0) ) )
=> ( ( sdtlseqdt0(xk,xp)
| ? [W0] :
( sdtpldt0(xk,W0) = xp
& aNaturalNumber0(W0) ) )
& xk != xp ) ),
inference(negated_conjecture,[status(cth)],[f50]) ).
fof(f105,plain,
! [W0] :
( sdtlseqdt0(W0,W0)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f106,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f111,plain,
! [W0,W1] :
( ( sdtlseqdt0(W1,W0)
& W1 != W0 )
| sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f113,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f172,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f209,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f234,plain,
( ( ( ~ sdtlseqdt0(xk,xp)
& ! [W0] :
( sdtpldt0(xk,W0) != xp
| ~ aNaturalNumber0(W0) ) )
| xk = xp )
& ~ sdtlseqdt0(xp,xk)
& ! [W0] :
( sdtpldt0(xp,W0) != xk
| ~ aNaturalNumber0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f51]) ).
fof(f236,plain,
~ sdtlseqdt0(xp,xk),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(f238,plain,
( ~ sdtlseqdt0(xk,xp)
| xk = xp ),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(f259,definition,
( sQ0_spl
<=> xk = xp ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f260,plain,
( ~ sQ0_spl
| xk = xp ),
inference(component_clause,[status(thm)],[f259]) ).
fof(f266,definition,
( sQ2_spl
<=> sdtlseqdt0(xk,xp) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f269,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f238,f259,f266]) ).
fof(f286,plain,
( ~ sQ0_spl
| ~ sdtlseqdt0(xk,xk) ),
inference(forward_demodulation,[status(thm)],[f260,f236]) ).
fof(f288,plain,
( ~ sQ0_spl
| aNaturalNumber0(xk) ),
inference(forward_demodulation,[status(thm)],[f260,f172]) ).
fof(f291,plain,
( ~ sQ0_spl
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[f106,f286]) ).
fof(f292,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f291,f288]) ).
fof(f293,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f292]) ).
fof(f319,plain,
( sdtlseqdt0(xk,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[f113,f236]) ).
fof(f321,definition,
( sQ8_spl
<=> aNaturalNumber0(xk) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f323,plain,
( sQ8_spl
| ~ aNaturalNumber0(xk) ),
inference(component_clause,[status(thm)],[f321]) ).
fof(f324,definition,
( sQ9_spl
<=> aNaturalNumber0(xp) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f326,plain,
( sQ9_spl
| ~ aNaturalNumber0(xp) ),
inference(component_clause,[status(thm)],[f324]) ).
fof(f327,plain,
( sQ2_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f319,f321,f324,f266]) ).
fof(f332,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f323,f209]) ).
fof(f333,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f332]) ).
fof(f334,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f326,f172]) ).
fof(f335,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f334]) ).
fof(f336,plain,
$false,
inference(sat_refutation,[status(thm)],[f269,f293,f327,f333,f335]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM505+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n001.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 02:41:13 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 0.17/0.47 % Refutation found
% 0.17/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.50 % Elapsed time: 0.066196 seconds
% 0.17/0.50 % CPU time: 0.162061 seconds
% 0.17/0.50 % Total memory used: 53.456 MB
% 0.17/0.50 % Net memory used: 53.378 MB
%------------------------------------------------------------------------------