%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET019+4 : TPTP v9.3.1. Released v2.2.0.
% 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 02:08:54 PM UTC 2026
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 6 unt; 2 def)
% Number of atoms : 52 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 48 ( 18 ~; 14 |; 11 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 16 ( 14 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,B] :
( ( subset(B,A)
& subset(A,B) )
=> equal_set(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
=> equal_set(A,B) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f21,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| equal_set(A,B) )
& ( ( subset(B,A)
& subset(A,B) )
| ~ equal_set(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f22,plain,
( ! [A,B] :
( ~ subset(B,A)
| ~ subset(A,B)
| equal_set(A,B) )
& ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
| ~ equal_set(A,B) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f25,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f68,plain,
? [A,B] :
( ~ equal_set(A,B)
& subset(B,A)
& subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f69,plain,
( ~ equal_set(sK3_skl,sK4_skl)
& subset(sK4_skl,sK3_skl)
& subset(sK3_skl,sK4_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl)],[f68]) ).
fof(f70,plain,
subset(sK3_skl,sK4_skl),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f71,plain,
subset(sK4_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f72,plain,
~ equal_set(sK3_skl,sK4_skl),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f76,plain,
( ~ subset(sK3_skl,sK4_skl)
| equal_set(sK3_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f25,f71]) ).
fof(f78,definition,
( sQ0_spl
<=> equal_set(sK3_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f79,plain,
( ~ sQ0_spl
| equal_set(sK3_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f78]) ).
fof(f81,definition,
( sQ1_spl
<=> subset(sK3_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f83,plain,
( sQ1_spl
| ~ subset(sK3_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f76,f78,f81]) ).
fof(f92,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f79,f72]) ).
fof(f93,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f92]) ).
fof(f94,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f83,f70]) ).
fof(f95,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f94]) ).
fof(f96,plain,
$false,
inference(sat_refutation,[status(thm)],[f84,f93,f95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET019+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n003.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 04:44:45 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.36 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.40 % Elapsed time: 0.044137 seconds
% 0.12/0.40 % CPU time: 0.125994 seconds
% 0.12/0.40 % Total memory used: 57.872 MB
% 0.12/0.40 % Net memory used: 57.697 MB
%------------------------------------------------------------------------------