%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET923+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 02:10:58 PM UTC 2026
% Result : Theorem 0.08s 0.39s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 6 unt; 2 def)
% Number of atoms : 68 ( 38 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 73 ( 33 ~; 22 |; 14 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 24 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
! [A,B] :
~ ( A != singleton(B)
& A != empty_set
& set_difference(A,singleton(B)) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [A,B] :
~ ( A != singleton(B)
& A != empty_set
& set_difference(A,singleton(B)) = empty_set ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f10,plain,
! [A,B] :
( ( ( A != singleton(B)
& A != empty_set )
| subset(A,singleton(B)) )
& ( A = singleton(B)
| A = empty_set
| ~ subset(A,singleton(B)) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f11,plain,
( ! [A,B] :
( ( A != singleton(B)
& A != empty_set )
| subset(A,singleton(B)) )
& ! [A,B] :
( A = singleton(B)
| A = empty_set
| ~ subset(A,singleton(B)) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f12,plain,
! [X0,X1] :
( X0 = singleton(X1)
| X0 = empty_set
| ~ subset(X0,singleton(X1)) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f21,plain,
! [A,B] :
( ( ~ subset(A,B)
| set_difference(A,B) = empty_set )
& ( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f22,plain,
( ! [A,B] :
( ~ subset(A,B)
| set_difference(A,B) = empty_set )
& ! [A,B] :
( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( subset(X0,X1)
| set_difference(X0,X1) != empty_set ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f25,plain,
? [A,B] :
( A != singleton(B)
& A != empty_set
& set_difference(A,singleton(B)) = empty_set ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f26,plain,
( sK2_skl != singleton(sK3_skl)
& sK2_skl != empty_set
& set_difference(sK2_skl,singleton(sK3_skl)) = empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl)],[f25]) ).
fof(f27,plain,
set_difference(sK2_skl,singleton(sK3_skl)) = empty_set,
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
sK2_skl != empty_set,
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f29,plain,
sK2_skl != singleton(sK3_skl),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f36,definition,
( sQ1_spl
<=> subset(sK2_skl,singleton(sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f38,plain,
( sQ1_spl
| ~ subset(sK2_skl,singleton(sK3_skl)) ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f40,plain,
( sK2_skl = empty_set
| ~ subset(sK2_skl,singleton(sK3_skl)) ),
inference(resolution,[status(thm)],[f12,f29]) ).
fof(f42,definition,
( sQ2_spl
<=> sK2_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f43,plain,
( ~ sQ2_spl
| sK2_skl = empty_set ),
inference(component_clause,[status(thm)],[f42]) ).
fof(f45,plain,
( sQ2_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f40,f36,f42]) ).
fof(f47,plain,
( sQ1_spl
| set_difference(sK2_skl,singleton(sK3_skl)) != empty_set ),
inference(resolution,[status(thm)],[f38,f23]) ).
fof(f48,plain,
( sQ1_spl
| empty_set != empty_set ),
inference(forward_demodulation,[status(thm)],[f27,f47]) ).
fof(f49,plain,
( sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f48]) ).
fof(f50,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f49]) ).
fof(f51,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f43,f28]) ).
fof(f52,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f51]) ).
fof(f53,plain,
$false,
inference(sat_refutation,[status(thm)],[f45,f50,f52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET923+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n006.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 05:44:12 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.39 % Refutation found
% 0.08/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.42 % Elapsed time: 0.051001 seconds
% 0.08/0.42 % CPU time: 0.153244 seconds
% 0.08/0.42 % Total memory used: 98.068 MB
% 0.08/0.42 % Net memory used: 97.631 MB
%------------------------------------------------------------------------------