%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU146+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 : n002.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 02:19:23 PM UTC 2026
% Result : Theorem 0.14s 0.58s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of formulae : 89 ( 8 unt; 9 def)
% Number of atoms : 260 ( 78 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 277 ( 106 ~; 119 |; 31 &)
% ( 19 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 10 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 115 ( 105 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,lemma,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,lemma,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,conjecture,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ ! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f47,lemma,
! [A] : subset(empty_set,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [A] : set_difference(empty_set,A) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f76,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f77,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)],[f76]) ).
fof(f78,plain,
! [X0,X1] :
( subset(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f80,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f81,plain,
! [A,B] :
( ( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ( ! [C] :
( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f82,plain,
( ! [A,B] :
( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(miniscoping,[status(thm)],[f81]) ).
fof(f83,plain,
( ! [A,B] :
( ( ( sK0_skl(B,A) = A
| in(sK0_skl(B,A),B) )
& ( sK0_skl(B,A) != A
| ~ in(sK0_skl(B,A),B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f82]) ).
fof(f84,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f88,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f89,plain,
( ! [A] :
( ? [B] : in(B,A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(miniscoping,[status(thm)],[f88]) ).
fof(f90,plain,
( ! [A] :
( in(sK1_skl(A),A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(B,sK1_skl(A))],[f89]) ).
fof(f92,plain,
! [X0] :
( in(sK1_skl(X0),X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f111,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f112,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f111]) ).
fof(f113,plain,
( ! [A,B] :
( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f112]) ).
fof(f114,plain,
( ! [A,B] :
( ( ~ in(sK4_skl(B,A),B)
& in(sK4_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(C,sK4_skl(B,A))],[f113]) ).
fof(f115,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f159,plain,
! [A,B] :
( ( ~ in(A,B)
| subset(singleton(A),B) )
& ( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(NNF_transformation,[status(thm)],[f29]) ).
fof(f160,plain,
( ! [A,B] :
( ~ in(A,B)
| subset(singleton(A),B) )
& ! [A,B] :
( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(miniscoping,[status(thm)],[f159]) ).
fof(f162,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f163,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)],[f30]) ).
fof(f164,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)],[f163]) ).
fof(f165,plain,
! [X0,X1] :
( subset(X0,X1)
| set_difference(X0,X1) != empty_set ),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f166,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_difference(X0,X1) = empty_set ),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f170,plain,
? [A,B] :
( subset(A,singleton(B))
<~> ( A = singleton(B)
| A = empty_set ) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f171,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)],[f170]) ).
fof(f172,plain,
( ( ( sK7_skl != singleton(sK8_skl)
& sK7_skl != empty_set )
| ~ subset(sK7_skl,singleton(sK8_skl)) )
& ( sK7_skl = singleton(sK8_skl)
| sK7_skl = empty_set
| subset(sK7_skl,singleton(sK8_skl)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(A,sK7_skl),skolemize(B,sK8_skl)],[f171]) ).
fof(f173,plain,
( sK7_skl = singleton(sK8_skl)
| sK7_skl = empty_set
| subset(sK7_skl,singleton(sK8_skl)) ),
inference(cnf_transformation,[status(thm)],[f172]) ).
fof(f174,plain,
( sK7_skl != empty_set
| ~ subset(sK7_skl,singleton(sK8_skl)) ),
inference(cnf_transformation,[status(thm)],[f172]) ).
fof(f175,plain,
( sK7_skl != singleton(sK8_skl)
| ~ subset(sK7_skl,singleton(sK8_skl)) ),
inference(cnf_transformation,[status(thm)],[f172]) ).
fof(f204,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f227,plain,
! [X0] : set_difference(empty_set,X0) = empty_set,
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f254,definition,
( sQ0_spl
<=> subset(sK7_skl,singleton(sK8_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f255,plain,
( ~ sQ0_spl
| subset(sK7_skl,singleton(sK8_skl)) ),
inference(component_clause,[status(thm)],[f254]) ).
fof(f256,plain,
( sQ0_spl
| ~ subset(sK7_skl,singleton(sK8_skl)) ),
inference(component_clause,[status(thm)],[f254]) ).
fof(f257,definition,
( sQ1_spl
<=> sK7_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f258,plain,
( ~ sQ1_spl
| sK7_skl = empty_set ),
inference(component_clause,[status(thm)],[f257]) ).
fof(f260,definition,
( sQ2_spl
<=> sK7_skl = singleton(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f261,plain,
( ~ sQ2_spl
| sK7_skl = singleton(sK8_skl) ),
inference(component_clause,[status(thm)],[f260]) ).
fof(f263,plain,
( sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f173,f254,f257,f260]) ).
fof(f264,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f174,f254,f257]) ).
fof(f265,plain,
( ~ sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f175,f254,f260]) ).
fof(f266,plain,
! [X0] : subset(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f78]) ).
fof(f268,plain,
! [X0,X1] :
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f84]) ).
fof(f284,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ subset(empty_set,singleton(sK8_skl)) ),
inference(forward_demodulation,[status(thm)],[f258,f256]) ).
fof(f290,plain,
( sQ0_spl
| ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f284,f204]) ).
fof(f292,plain,
( sQ0_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f290]) ).
fof(f293,plain,
( ~ sQ0_spl
| ~ subset(singleton(sK8_skl),sK7_skl)
| singleton(sK8_skl) = sK7_skl ),
inference(resolution,[status(thm)],[f255,f80]) ).
fof(f294,definition,
( sQ3_spl
<=> subset(singleton(sK8_skl),sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f296,plain,
( sQ3_spl
| ~ subset(singleton(sK8_skl),sK7_skl) ),
inference(component_clause,[status(thm)],[f294]) ).
fof(f297,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f293,f260,f294,f254]) ).
fof(f326,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ subset(sK7_skl,sK7_skl) ),
inference(forward_demodulation,[status(thm)],[f261,f256]) ).
fof(f327,plain,
( sQ0_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f326,f266]) ).
fof(f328,plain,
( sQ0_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f327]) ).
fof(f333,plain,
( sQ3_spl
| ~ in(sK8_skl,sK7_skl) ),
inference(resolution,[status(thm)],[f162,f296]) ).
fof(f340,plain,
! [X0] :
( subset(empty_set,X0)
| empty_set != empty_set ),
inference(paramodulation,[status(thm)],[f227,f165]) ).
fof(f342,definition,
( sQ4_spl
<=> empty_set = empty_set ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f344,plain,
( sQ4_spl
| empty_set != empty_set ),
inference(component_clause,[status(thm)],[f342]) ).
fof(f345,definition,
! [X0] :
( sQ5_spl
<=> subset(empty_set,X0) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f348,plain,
( sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f340,f342,f345]) ).
fof(f350,plain,
( sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f344]) ).
fof(f351,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f350]) ).
fof(f377,plain,
! [X0] :
( ~ sQ0_spl
| in(X0,singleton(sK8_skl))
| ~ in(X0,sK7_skl) ),
inference(resolution,[status(thm)],[f255,f115]) ).
fof(f380,plain,
( ~ sQ0_spl
| sK7_skl = empty_set
| in(sK1_skl(sK7_skl),singleton(sK8_skl)) ),
inference(resolution,[status(thm)],[f377,f92]) ).
fof(f382,definition,
( sQ6_spl
<=> in(sK1_skl(sK7_skl),singleton(sK8_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f383,plain,
( ~ sQ6_spl
| in(sK1_skl(sK7_skl),singleton(sK8_skl)) ),
inference(component_clause,[status(thm)],[f382]) ).
fof(f385,plain,
( ~ sQ0_spl
| sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f380,f382,f257,f254]) ).
fof(f396,plain,
! [X0] : set_difference(X0,X0) = empty_set,
inference(resolution,[status(thm)],[f166,f266]) ).
fof(f402,plain,
! [X0] :
( subset(X0,X0)
| empty_set != empty_set ),
inference(paramodulation,[status(thm)],[f396,f165]) ).
fof(f403,definition,
! [X0] :
( sQ7_spl
<=> subset(X0,X0) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f406,plain,
( sQ7_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f402,f342,f403]) ).
fof(f465,plain,
( ~ sQ6_spl
| sK1_skl(sK7_skl) = sK8_skl ),
inference(resolution,[status(thm)],[f383,f268]) ).
fof(f468,plain,
( ~ sQ6_spl
| in(sK8_skl,sK7_skl)
| sK7_skl = empty_set ),
inference(paramodulation,[status(thm)],[f465,f92]) ).
fof(f469,definition,
( sQ8_spl
<=> in(sK8_skl,sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f470,plain,
( ~ sQ8_spl
| in(sK8_skl,sK7_skl) ),
inference(component_clause,[status(thm)],[f469]) ).
fof(f472,plain,
( ~ sQ6_spl
| sQ8_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f468,f257,f469,f382]) ).
fof(f473,plain,
( ~ sQ8_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f470,f333]) ).
fof(f474,plain,
( ~ sQ8_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f473]) ).
fof(f475,plain,
$false,
inference(sat_refutation,[status(thm)],[f263,f264,f265,f292,f297,f328,f348,f351,f385,f406,f472,f474]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU146+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.54 % Computer : n002.cluster.edu
% 0.09/0.54 % Model : x86_64 x86_64
% 0.09/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.54 % Memory : 8046.5625MB
% 0.09/0.54 % OS : Linux 6.8.0-71-generic
% 0.09/0.54 % CPULimit : 300
% 0.09/0.54 % WCLimit : 300
% 0.09/0.54 % DateTime : Mon Sep 21 05:55:32 UTC 2026
% 0.09/0.55 % CPUTime :
% 0.09/0.55 % Drodi V4.1.1
% 0.14/0.58 % Refutation found
% 0.14/0.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.61 % Elapsed time: 0.048805 seconds
% 0.14/0.61 % CPU time: 0.156485 seconds
% 0.14/0.61 % Total memory used: 105.229 MB
% 0.14/0.61 % Net memory used: 105.137 MB
%------------------------------------------------------------------------------