%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM527+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 01:40:51 PM UTC 2026
% Result : Theorem 0.14s 0.45s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 20
% Syntax : Number of formulae : 81 ( 11 unt; 12 def)
% Number of atoms : 264 ( 36 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 325 ( 142 ~; 135 |; 25 &)
% ( 12 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 13 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 48 ( 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> sdtlseqdt0(W0,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W0)
& sdtlseqdt0(W0,W1) )
=> W0 = W1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W2)
& sdtlseqdt0(W0,W1) )
=> sdtlseqdt0(W0,W2) ) ),
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(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/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,conjecture,
( sdtlseqdt0(xn,xm)
=> sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
~ ( sdtlseqdt0(xn,xm)
=> sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f57,plain,
! [W0,W1] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f58,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f102,plain,
! [W0] :
( sdtlseqdt0(W0,W0)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f103,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f104,plain,
! [W0,W1] :
( W0 = W1
| ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f105,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f106,plain,
! [W0,W1,W2] :
( sdtlseqdt0(W0,W2)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f107,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f108,plain,
! [W0,W1] :
( ( sdtlseqdt0(W1,W0)
& W1 != W0 )
| sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f110,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f116,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(f118,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)],[f116]) ).
fof(f120,plain,
! [X0,X1,X2] :
( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| X0 = sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f169,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f170,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f172,plain,
xn != sz00,
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f173,plain,
xm != sz00,
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f183,plain,
( ~ sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
& sdtlseqdt0(xn,xm) ),
inference(pre_NNF_transformation,[status(thm)],[f48]) ).
fof(f184,plain,
sdtlseqdt0(xn,xm),
inference(cnf_transformation,[status(thm)],[f183]) ).
fof(f185,plain,
~ sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)),
inference(cnf_transformation,[status(thm)],[f183]) ).
fof(f202,plain,
( xm = xn
| ~ sdtlseqdt0(xm,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f105,f184]) ).
fof(f204,definition,
( sQ0_spl
<=> aNaturalNumber0(xm) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f206,plain,
( sQ0_spl
| ~ aNaturalNumber0(xm) ),
inference(component_clause,[status(thm)],[f204]) ).
fof(f207,definition,
( sQ1_spl
<=> aNaturalNumber0(xn) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f209,plain,
( sQ1_spl
| ~ aNaturalNumber0(xn) ),
inference(component_clause,[status(thm)],[f207]) ).
fof(f210,definition,
( sQ2_spl
<=> sdtlseqdt0(xm,xn) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f212,plain,
( sQ2_spl
| ~ sdtlseqdt0(xm,xn) ),
inference(component_clause,[status(thm)],[f210]) ).
fof(f213,definition,
( sQ3_spl
<=> xm = xn ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f214,plain,
( ~ sQ3_spl
| xm = xn ),
inference(component_clause,[status(thm)],[f213]) ).
fof(f216,plain,
( sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f202,f204,f207,f210,f213]) ).
fof(f242,plain,
( ~ sQ3_spl
| ~ sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xn)) ),
inference(backward_demodulation,[status(thm)],[f214,f185]) ).
fof(f244,plain,
( ~ sQ3_spl
| ~ sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xn,xn)) ),
inference(forward_demodulation,[status(thm)],[f214,f242]) ).
fof(f245,plain,
( ~ sQ3_spl
| ~ aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(resolution,[status(thm)],[f244,f103]) ).
fof(f254,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f209,f169]) ).
fof(f255,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f254]) ).
fof(f270,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f206,f170]) ).
fof(f271,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f270]) ).
fof(f279,plain,
! [X0] :
( ~ sdtlseqdt0(X0,sdtasdt0(xm,xm))
| ~ sdtlseqdt0(sdtasdt0(xn,xn),X0)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(resolution,[status(thm)],[f185,f107]) ).
fof(f280,definition,
( sQ11_spl
<=> aNaturalNumber0(sdtasdt0(xn,xn)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f282,plain,
( sQ11_spl
| ~ aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(component_clause,[status(thm)],[f280]) ).
fof(f283,definition,
! [X0] :
( sQ12_spl
<=> ( ~ sdtlseqdt0(X0,sdtasdt0(xm,xm))
| ~ sdtlseqdt0(sdtasdt0(xn,xn),X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f284,plain,
! [X0] :
( ~ sQ12_spl
| ~ sdtlseqdt0(X0,sdtasdt0(xm,xm))
| ~ sdtlseqdt0(sdtasdt0(xn,xn),X0)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f283]) ).
fof(f286,definition,
( sQ13_spl
<=> aNaturalNumber0(sdtasdt0(xm,xm)) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f288,plain,
( sQ13_spl
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(component_clause,[status(thm)],[f286]) ).
fof(f289,plain,
( ~ sQ13_spl
| sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f279,f280,f283,f286]) ).
fof(f302,plain,
( sQ13_spl
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f288,f58]) ).
fof(f303,plain,
( sQ13_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f302,f204,f286]) ).
fof(f305,plain,
( sQ2_spl
| sdtlseqdt0(xn,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f110,f212]) ).
fof(f312,definition,
( sQ17_spl
<=> sdtlseqdt0(xn,xm) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f315,plain,
( sQ2_spl
| sQ17_spl
| ~ sQ0_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f305,f207,f204,f312,f210]) ).
fof(f404,plain,
( sQ11_spl
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f58,f282]) ).
fof(f405,plain,
( sQ11_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f404,f207,f280]) ).
fof(f445,plain,
! [X0] :
( ~ sQ12_spl
| ~ sdtlseqdt0(xn,X0)
| xn = X0
| xn = sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(sdtasdt0(xn,X0),sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,X0)) ),
inference(resolution,[status(thm)],[f284,f118]) ).
fof(f448,definition,
! [X0] :
( sQ35_spl
<=> ( ~ sdtlseqdt0(xn,X0)
| xn = X0
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sdtasdt0(xn,X0),sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f449,plain,
! [X0] :
( ~ sQ35_spl
| ~ sdtlseqdt0(xn,X0)
| xn = X0
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sdtasdt0(xn,X0),sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,X0)) ),
inference(component_clause,[status(thm)],[f448]) ).
fof(f451,definition,
( sQ36_spl
<=> xn = sz00 ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f452,plain,
( ~ sQ36_spl
| xn = sz00 ),
inference(component_clause,[status(thm)],[f451]) ).
fof(f454,plain,
( ~ sQ12_spl
| sQ36_spl
| ~ sQ1_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f445,f448,f207,f451,f283]) ).
fof(f457,plain,
( ~ sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f452,f172]) ).
fof(f458,plain,
~ sQ36_spl,
inference(contradiction_clause,[status(thm)],[f457]) ).
fof(f481,definition,
( sQ41_spl
<=> xm = sz00 ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f482,plain,
( ~ sQ41_spl
| xm = sz00 ),
inference(component_clause,[status(thm)],[f481]) ).
fof(f489,plain,
( ~ sQ41_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f482,f173]) ).
fof(f490,plain,
~ sQ41_spl,
inference(contradiction_clause,[status(thm)],[f489]) ).
fof(f549,plain,
( ~ sQ3_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f245,f280,f213]) ).
fof(f591,plain,
( ~ sQ35_spl
| ~ sdtlseqdt0(xn,xm)
| xn = xm
| xm = sz00
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(xn,xm)
| xn = xm
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolution,[status(thm)],[f449,f120]) ).
fof(f593,definition,
( sQ54_spl
<=> aNaturalNumber0(sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f595,plain,
( sQ54_spl
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(component_clause,[status(thm)],[f593]) ).
fof(f596,plain,
( ~ sQ35_spl
| sQ41_spl
| ~ sQ1_spl
| ~ sQ17_spl
| sQ3_spl
| ~ sQ0_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f591,f593,f204,f213,f312,f207,f481,f448]) ).
fof(f602,plain,
( sQ54_spl
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f595,f58]) ).
fof(f603,plain,
( sQ54_spl
| ~ sQ0_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f602,f207,f204,f593]) ).
fof(f604,plain,
$false,
inference(sat_refutation,[status(thm)],[f216,f255,f271,f289,f303,f315,f405,f454,f458,f490,f549,f596,f603]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM527+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 02:40:46 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.14/0.45 % Refutation found
% 0.14/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.50 % Elapsed time: 0.133606 seconds
% 0.14/0.50 % CPU time: 0.432246 seconds
% 0.14/0.50 % Total memory used: 72.184 MB
% 0.14/0.50 % Net memory used: 71.698 MB
%------------------------------------------------------------------------------