%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET924+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 02:10:59 PM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 1 unt; 2 def)
% Number of atoms : 58 ( 20 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 59 ( 26 ~; 23 |; 4 &)
% ( 5 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 20 ( 16 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,conjecture,
! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
<=> ~ in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
~ ! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
<=> ~ in(A,B) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,axiom,
! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
<=> ~ in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,plain,
? [A,B] :
( set_difference(singleton(A),B) = singleton(A)
<~> ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f14,plain,
? [A,B] :
( ( in(A,B)
| set_difference(singleton(A),B) != singleton(A) )
& ( ~ in(A,B)
| set_difference(singleton(A),B) = singleton(A) ) ),
inference(NNF_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
( ( in(sK2_skl,sK3_skl)
| set_difference(singleton(sK2_skl),sK3_skl) != singleton(sK2_skl) )
& ( ~ in(sK2_skl,sK3_skl)
| set_difference(singleton(sK2_skl),sK3_skl) = singleton(sK2_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl)],[f14]) ).
fof(f16,plain,
( ~ in(sK2_skl,sK3_skl)
| set_difference(singleton(sK2_skl),sK3_skl) = singleton(sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
( in(sK2_skl,sK3_skl)
| set_difference(singleton(sK2_skl),sK3_skl) != singleton(sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f18,plain,
! [A,B] :
( ( in(A,B)
| set_difference(singleton(A),B) = singleton(A) )
& ( ~ in(A,B)
| set_difference(singleton(A),B) != singleton(A) ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f19,plain,
( ! [A,B] :
( in(A,B)
| set_difference(singleton(A),B) = singleton(A) )
& ! [A,B] :
( ~ in(A,B)
| set_difference(singleton(A),B) != singleton(A) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_difference(singleton(X0),X1) != singleton(X0) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( in(X0,X1)
| set_difference(singleton(X0),X1) = singleton(X0) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f22,definition,
( sQ0_spl
<=> set_difference(singleton(sK2_skl),sK3_skl) = singleton(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f24,plain,
( sQ0_spl
| set_difference(singleton(sK2_skl),sK3_skl) != singleton(sK2_skl) ),
inference(component_clause,[status(thm)],[f22]) ).
fof(f25,definition,
( sQ1_spl
<=> in(sK2_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f26,plain,
( ~ sQ1_spl
| in(sK2_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f25]) ).
fof(f27,plain,
( sQ1_spl
| ~ in(sK2_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f25]) ).
fof(f28,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f16,f22,f25]) ).
fof(f29,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f17,f22,f25]) ).
fof(f30,plain,
( sQ1_spl
| set_difference(singleton(sK2_skl),sK3_skl) = singleton(sK2_skl) ),
inference(resolution,[status(thm)],[f21,f27]) ).
fof(f33,plain,
( sQ1_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f30,f24]) ).
fof(f34,plain,
( sQ1_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f33]) ).
fof(f35,plain,
( ~ sQ1_spl
| set_difference(singleton(sK2_skl),sK3_skl) != singleton(sK2_skl) ),
inference(resolution,[status(thm)],[f26,f20]) ).
fof(f37,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f35,f22,f25]) ).
fof(f38,plain,
$false,
inference(sat_refutation,[status(thm)],[f28,f29,f34,f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET924+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:39:41 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.42 % Elapsed time: 0.048495 seconds
% 0.14/0.42 % CPU time: 0.146594 seconds
% 0.14/0.42 % Total memory used: 69.792 MB
% 0.14/0.42 % Net memory used: 69.293 MB
%------------------------------------------------------------------------------