%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU134+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 02:19:19 PM UTC 2026
% Result : Theorem 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 51 ( 6 unt; 7 def)
% Number of atoms : 121 ( 40 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 119 ( 49 ~; 49 |; 9 &)
% ( 11 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 36 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,lemma,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,conjecture,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
~ ! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f42,axiom,
! [A] : set_difference(empty_set,A) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f54,plain,
( ! [A,B] :
( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(miniscoping,[status(thm)],[f53]) ).
fof(f55,plain,
! [X0,X1] :
( subset(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f57,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f112,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)],[f20]) ).
fof(f113,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)],[f112]) ).
fof(f114,plain,
! [X0,X1] :
( subset(X0,X1)
| set_difference(X0,X1) != empty_set ),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f115,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_difference(X0,X1) = empty_set ),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f149,plain,
? [A,B] :
( set_difference(A,B) = empty_set
<~> subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f150,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)],[f149]) ).
fof(f151,plain,
( ( ~ subset(sK8_skl,sK9_skl)
| set_difference(sK8_skl,sK9_skl) != empty_set )
& ( subset(sK8_skl,sK9_skl)
| set_difference(sK8_skl,sK9_skl) = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(A,sK8_skl),skolemize(B,sK9_skl)],[f150]) ).
fof(f152,plain,
( subset(sK8_skl,sK9_skl)
| set_difference(sK8_skl,sK9_skl) = empty_set ),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f153,plain,
( ~ subset(sK8_skl,sK9_skl)
| set_difference(sK8_skl,sK9_skl) != empty_set ),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f163,plain,
! [X0] : set_difference(empty_set,X0) = empty_set,
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f180,definition,
( sQ0_spl
<=> set_difference(sK8_skl,sK9_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f181,plain,
( ~ sQ0_spl
| set_difference(sK8_skl,sK9_skl) = empty_set ),
inference(component_clause,[status(thm)],[f180]) ).
fof(f182,plain,
( sQ0_spl
| set_difference(sK8_skl,sK9_skl) != empty_set ),
inference(component_clause,[status(thm)],[f180]) ).
fof(f183,definition,
( sQ1_spl
<=> subset(sK8_skl,sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f184,plain,
( ~ sQ1_spl
| subset(sK8_skl,sK9_skl) ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f186,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f152,f180,f183]) ).
fof(f187,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f153,f180,f183]) ).
fof(f188,plain,
! [X0] : subset(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f55]) ).
fof(f201,plain,
( ~ sQ1_spl
| ~ subset(sK9_skl,sK8_skl)
| sK9_skl = sK8_skl ),
inference(resolution,[status(thm)],[f57,f184]) ).
fof(f203,definition,
( sQ2_spl
<=> sK9_skl = sK8_skl ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f204,plain,
( ~ sQ2_spl
| sK9_skl = sK8_skl ),
inference(component_clause,[status(thm)],[f203]) ).
fof(f206,definition,
( sQ3_spl
<=> subset(sK9_skl,sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f209,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f201,f203,f206,f183]) ).
fof(f213,plain,
( sQ0_spl
| ~ sQ2_spl
| set_difference(sK8_skl,sK8_skl) != empty_set ),
inference(backward_demodulation,[status(thm)],[f204,f182]) ).
fof(f288,plain,
! [X0] :
( subset(empty_set,X0)
| empty_set != empty_set ),
inference(paramodulation,[status(thm)],[f163,f114]) ).
fof(f290,definition,
( sQ4_spl
<=> empty_set = empty_set ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f292,plain,
( sQ4_spl
| empty_set != empty_set ),
inference(component_clause,[status(thm)],[f290]) ).
fof(f293,definition,
! [X0] :
( sQ5_spl
<=> subset(empty_set,X0) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f296,plain,
( sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f288,f290,f293]) ).
fof(f298,plain,
( sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f292]) ).
fof(f299,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f298]) ).
fof(f305,plain,
! [X0] : set_difference(X0,X0) = empty_set,
inference(resolution,[status(thm)],[f115,f188]) ).
fof(f315,plain,
( sQ0_spl
| ~ sQ2_spl
| empty_set != empty_set ),
inference(backward_demodulation,[status(thm)],[f305,f213]) ).
fof(f321,plain,
! [X0] :
( subset(X0,X0)
| empty_set != empty_set ),
inference(paramodulation,[status(thm)],[f305,f114]) ).
fof(f326,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f315,f290,f203,f180]) ).
fof(f327,definition,
! [X0] :
( sQ6_spl
<=> subset(X0,X0) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f330,plain,
( sQ6_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f321,f290,f327]) ).
fof(f366,plain,
( ~ sQ0_spl
| subset(sK8_skl,sK9_skl)
| empty_set != empty_set ),
inference(paramodulation,[status(thm)],[f181,f114]) ).
fof(f372,plain,
( ~ sQ0_spl
| sQ1_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f366,f290,f183,f180]) ).
fof(f376,plain,
( ~ sQ1_spl
| set_difference(sK8_skl,sK9_skl) = empty_set ),
inference(resolution,[status(thm)],[f184,f115]) ).
fof(f379,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f376,f180,f183]) ).
fof(f381,plain,
$false,
inference(sat_refutation,[status(thm)],[f186,f187,f209,f296,f299,f326,f330,f372,f379]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU134+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n020.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 05:53:02 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 % Drodi V4.1.1
% 0.10/0.39 % Refutation found
% 0.10/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.44 % Elapsed time: 0.071735 seconds
% 0.13/0.44 % CPU time: 0.198461 seconds
% 0.13/0.44 % Total memory used: 103.753 MB
% 0.13/0.44 % Net memory used: 103.659 MB
%------------------------------------------------------------------------------