%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM578+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 : n019.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 01:41:04 PM UTC 2026
% Result : Theorem 0.14s 10.67s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 8 unt; 5 def)
% Number of atoms : 81 ( 17 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 84 ( 35 ~; 27 |; 8 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 8 ( 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f84,hypothesis,
( aElementOf0(xj,szNzAzT0)
& aElementOf0(xi,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f85,hypothesis,
( xi != xj
=> ( sdtlseqdt0(szszuzczcdt0(xi),xj)
| sdtlseqdt0(szszuzczcdt0(xj),xi) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f86,conjecture,
( ! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( sdtlseqdt0(szszuzczcdt0(W0),W1)
=> ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0))
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
=> ( xi != xj
=> szmzizndt0(sdtlpdtrp0(xN,xi)) != szmzizndt0(sdtlpdtrp0(xN,xj)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f87,negated_conjecture,
~ ( ! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( sdtlseqdt0(szszuzczcdt0(W0),W1)
=> ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0))
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
=> ( xi != xj
=> szmzizndt0(sdtlpdtrp0(xN,xi)) != szmzizndt0(sdtlpdtrp0(xN,xj)) ) ),
inference(negated_conjecture,[status(cth)],[f86]) ).
fof(f373,plain,
aElementOf0(xi,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f374,plain,
aElementOf0(xj,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f375,plain,
( sdtlseqdt0(szszuzczcdt0(xi),xj)
| sdtlseqdt0(szszuzczcdt0(xj),xi)
| xi = xj ),
inference(pre_NNF_transformation,[status(thm)],[f85]) ).
fof(f376,plain,
( sdtlseqdt0(szszuzczcdt0(xi),xj)
| sdtlseqdt0(szszuzczcdt0(xj),xi)
| xi = xj ),
inference(cnf_transformation,[status(thm)],[f375]) ).
fof(f377,plain,
( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj))
& xi != xj
& ! [W0,W1] :
( ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0))
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ sdtlseqdt0(szszuzczcdt0(W0),W1)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f87]) ).
fof(f379,plain,
! [X0,X1] :
( szmzizndt0(sdtlpdtrp0(xN,X1)) != szmzizndt0(sdtlpdtrp0(xN,X0))
| ~ sdtlseqdt0(szszuzczcdt0(X0),X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f377]) ).
fof(f380,plain,
xi != xj,
inference(cnf_transformation,[status(thm)],[f377]) ).
fof(f381,plain,
szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)),
inference(cnf_transformation,[status(thm)],[f377]) ).
fof(f388,definition,
( sQ0_spl
<=> xi = xj ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f389,plain,
( ~ sQ0_spl
| xi = xj ),
inference(component_clause,[status(thm)],[f388]) ).
fof(f391,definition,
( sQ1_spl
<=> sdtlseqdt0(szszuzczcdt0(xj),xi) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f394,definition,
( sQ2_spl
<=> sdtlseqdt0(szszuzczcdt0(xi),xj) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f397,plain,
( sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f376,f388,f391,f394]) ).
fof(f439,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xj),xi)
| ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(xj,szNzAzT0) ),
inference(resolution,[status(thm)],[f379,f381]) ).
fof(f440,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xi),xj)
| ~ aElementOf0(xj,szNzAzT0)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(resolution,[status(thm)],[f379,f381]) ).
fof(f444,definition,
( sQ3_spl
<=> aElementOf0(xj,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f446,plain,
( sQ3_spl
| ~ aElementOf0(xj,szNzAzT0) ),
inference(component_clause,[status(thm)],[f444]) ).
fof(f447,definition,
( sQ4_spl
<=> aElementOf0(xi,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f449,plain,
( sQ4_spl
| ~ aElementOf0(xi,szNzAzT0) ),
inference(component_clause,[status(thm)],[f447]) ).
fof(f450,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f439,f444,f447,f391]) ).
fof(f451,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f440,f447,f444,f394]) ).
fof(f461,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f389,f380]) ).
fof(f462,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f461]) ).
fof(f468,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f373,f449]) ).
fof(f469,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f468]) ).
fof(f470,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f446,f374]) ).
fof(f471,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f470]) ).
fof(f472,plain,
$false,
inference(sat_refutation,[status(thm)],[f397,f450,f451,f462,f469,f471]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM578+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/10.62 % Computer : n019.cluster.edu
% 0.14/10.62 % Model : x86_64 x86_64
% 0.14/10.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/10.62 % Memory : 8046.5625MB
% 0.14/10.62 % OS : Linux 6.8.0-71-generic
% 0.14/10.62 % CPULimit : 300
% 0.14/10.62 % WCLimit : 300
% 0.14/10.62 % DateTime : Mon Sep 21 02:42:01 UTC 2026
% 0.14/10.63 % CPUTime :
% 0.14/10.65 % Drodi V4.1.1
% 0.14/10.67 % Refutation found
% 0.14/10.67 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/10.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/10.78 % Elapsed time: 0.144699 seconds
% 0.18/10.78 % CPU time: 0.126120 seconds
% 0.18/10.78 % Total memory used: 10.415 MB
% 0.18/10.78 % Net memory used: 10.407 MB
%------------------------------------------------------------------------------