%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM465+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 : n005.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 7.39s 1.40s
% Output : CNFRefutation 7.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 17
% Syntax : Number of formulae : 70 ( 14 unt; 9 def)
% Number of atoms : 171 ( 44 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 172 ( 71 ~; 67 |; 17 &)
% ( 9 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 10 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 24 ( 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> sdtlseqdt0(W0,W0) ),
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(f27,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
( xm != sz00
=> sdtlseqdt0(sz10,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
( xm != sz00
=> sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ( xm != sz00
=> sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f35,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f52,plain,
! [W0] :
( ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 )
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f53,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f55,plain,
! [W0] :
( ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 )
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f57,plain,
! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f84,plain,
! [W0] :
( sdtlseqdt0(W0,W0)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f85,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f98,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(f100,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)],[f98]) ).
fof(f106,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f107,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f108,plain,
( sdtlseqdt0(sz10,xm)
| xm = sz00 ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f109,plain,
( sdtlseqdt0(sz10,xm)
| xm = sz00 ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f110,plain,
( ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
& xm != sz00 ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f111,plain,
xm != sz00,
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f112,plain,
~ sdtlseqdt0(xn,sdtasdt0(xn,xm)),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f113,definition,
( sQ0_spl
<=> xm = sz00 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f114,plain,
( ~ sQ0_spl
| xm = sz00 ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f116,definition,
( sQ1_spl
<=> sdtlseqdt0(sz10,xm) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f117,plain,
( ~ sQ1_spl
| sdtlseqdt0(sz10,xm) ),
inference(component_clause,[status(thm)],[f116]) ).
fof(f119,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f109,f113,f116]) ).
fof(f128,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f114,f111]) ).
fof(f129,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f128]) ).
fof(f147,plain,
sdtlseqdt0(xn,xn),
inference(resolution,[status(thm)],[f85,f107]) ).
fof(f186,plain,
sdtasdt0(xn,sz10) = xn,
inference(resolution,[status(thm)],[f53,f107]) ).
fof(f197,plain,
sz00 = sdtasdt0(sz00,xm),
inference(resolution,[status(thm)],[f57,f106]) ).
fof(f263,definition,
( sQ6_spl
<=> aNaturalNumber0(xm) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f265,plain,
( sQ6_spl
| ~ aNaturalNumber0(xm) ),
inference(component_clause,[status(thm)],[f263]) ).
fof(f286,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f265,f106]) ).
fof(f287,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f286]) ).
fof(f389,definition,
( sQ29_spl
<=> sdtlseqdt0(xn,xn) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f391,plain,
( sQ29_spl
| ~ sdtlseqdt0(xn,xn) ),
inference(component_clause,[status(thm)],[f389]) ).
fof(f400,plain,
( sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f391,f147]) ).
fof(f401,plain,
sQ29_spl,
inference(contradiction_clause,[status(thm)],[f400]) ).
fof(f472,definition,
( sQ42_spl
<=> aNaturalNumber0(sz10) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f474,plain,
( sQ42_spl
| ~ aNaturalNumber0(sz10) ),
inference(component_clause,[status(thm)],[f472]) ).
fof(f475,definition,
( sQ43_spl
<=> sz10 = xm ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f476,plain,
( ~ sQ43_spl
| sz10 = xm ),
inference(component_clause,[status(thm)],[f475]) ).
fof(f506,plain,
( sQ42_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f474,f35]) ).
fof(f507,plain,
sQ42_spl,
inference(contradiction_clause,[status(thm)],[f506]) ).
fof(f509,plain,
( ~ sQ43_spl
| sdtasdt0(xn,xm) = xn ),
inference(backward_demodulation,[status(thm)],[f476,f186]) ).
fof(f547,plain,
( ~ sQ43_spl
| ~ sdtlseqdt0(xn,xn) ),
inference(backward_demodulation,[status(thm)],[f509,f112]) ).
fof(f577,plain,
( ~ sQ43_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f547,f389,f475]) ).
fof(f671,definition,
( sQ62_spl
<=> xn = sz00 ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f672,plain,
( ~ sQ62_spl
| xn = sz00 ),
inference(component_clause,[status(thm)],[f671]) ).
fof(f734,plain,
( ~ sQ62_spl
| sz00 = sdtasdt0(xn,xm) ),
inference(backward_demodulation,[status(thm)],[f672,f197]) ).
fof(f785,plain,
( ~ sQ62_spl
| ~ sdtlseqdt0(xn,xn) ),
inference(backward_demodulation,[status(thm)],[f786,f112]) ).
fof(f786,plain,
( ~ sQ62_spl
| xn = sdtasdt0(xn,xm) ),
inference(forward_demodulation,[status(thm)],[f672,f734]) ).
fof(f800,plain,
( ~ sQ62_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f785,f389,f671]) ).
fof(f1011,plain,
! [X0,X1] :
( sdtlseqdt0(sdtasdt0(xn,X0),sdtasdt0(xn,X1))
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| xn = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f100,f107]) ).
fof(f1017,definition,
! [X0,X1] :
( sQ73_spl
<=> ( sdtlseqdt0(sdtasdt0(xn,X0),sdtasdt0(xn,X1))
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f1018,plain,
! [X0,X1] :
( ~ sQ73_spl
| sdtlseqdt0(sdtasdt0(xn,X0),sdtasdt0(xn,X1))
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f1017]) ).
fof(f1020,plain,
( sQ62_spl
| sQ73_spl ),
inference(split_clause,[status(thm)],[f1011,f1017,f671]) ).
fof(f3889,plain,
( ~ sQ1_spl
| ~ sQ73_spl
| sdtlseqdt0(sdtasdt0(xn,sz10),sdtasdt0(xn,xm))
| sz10 = xm
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[f1018,f117]) ).
fof(f3910,definition,
( sQ194_spl
<=> sdtlseqdt0(sdtasdt0(xn,sz10),sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ194_spl])],[split_symbol_definition]) ).
fof(f3911,plain,
( ~ sQ194_spl
| sdtlseqdt0(sdtasdt0(xn,sz10),sdtasdt0(xn,xm)) ),
inference(component_clause,[status(thm)],[f3910]) ).
fof(f3913,plain,
( ~ sQ1_spl
| ~ sQ73_spl
| sQ194_spl
| sQ43_spl
| ~ sQ6_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f3889,f472,f263,f475,f3910,f1017,f116]) ).
fof(f3931,plain,
( ~ sQ194_spl
| sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
inference(forward_demodulation,[status(thm)],[f186,f3911]) ).
fof(f3932,plain,
( ~ sQ194_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3931,f112]) ).
fof(f3933,plain,
~ sQ194_spl,
inference(contradiction_clause,[status(thm)],[f3932]) ).
fof(f3934,plain,
$false,
inference(sat_refutation,[status(thm)],[f119,f129,f287,f401,f507,f577,f800,f1020,f3913,f3933]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM465+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 02:32:18 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 7.39/1.40 % Refutation found
% 7.39/1.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 7.39/1.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.39/1.41 % Elapsed time: 1.037710 seconds
% 7.39/1.41 % CPU time: 7.926847 seconds
% 7.39/1.41 % Total memory used: 170.599 MB
% 7.39/1.41 % Net memory used: 160.813 MB
%------------------------------------------------------------------------------