%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU430+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 02:20:34 PM UTC 2026
% Result : Theorem 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 35
% Syntax : Number of formulae : 164 ( 29 unt; 19 def)
% Number of atoms : 403 ( 77 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 401 ( 162 ~; 169 |; 33 &)
% ( 25 <=>; 11 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 20 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 185 ( 170 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ( k5_setfam_1(A,B) = k1_xboole_0
<=> ! [C] :
( r2_hidden(C,B)
=> C = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ( k5_setfam_1(A,B) = k1_xboole_0
<=> ! [C] :
( r2_hidden(C,B)
=> C = k1_xboole_0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
! [A,B] :
( r2_hidden(A,B)
=> ~ r2_hidden(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] :
( A = k1_xboole_0
<=> ! [B] : ~ r2_hidden(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B] :
( B = k3_tarski(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> ? [D] :
( r2_hidden(D,A)
& r2_hidden(C,D) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> m1_subset_1(k5_setfam_1(A,B),k1_zfmisc_1(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A] :
? [B] : m1_subset_1(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
( v3_relat_1(k1_xboole_0)
& v1_relat_1(k1_xboole_0)
& v1_xboole_0(k1_xboole_0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> k5_setfam_1(A,B) = k3_tarski(B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [A,B] : r1_tarski(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [A,B] :
( r2_hidden(A,B)
=> m1_subset_1(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [A,B] :
( m1_subset_1(A,B)
=> ( r2_hidden(A,B)
| v1_xboole_0(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [A,B] :
( m1_subset_1(A,k1_zfmisc_1(B))
<=> r1_tarski(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [A,B,C] :
( ( m1_subset_1(B,k1_zfmisc_1(C))
& r2_hidden(A,B) )
=> m1_subset_1(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [A,B,C] :
~ ( v1_xboole_0(C)
& m1_subset_1(B,k1_zfmisc_1(C))
& r2_hidden(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A] :
( v1_xboole_0(A)
=> A = k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,plain,
? [A,B] :
( ( k5_setfam_1(A,B) = k1_xboole_0
<~> ! [C] :
( C = k1_xboole_0
| ~ r2_hidden(C,B) ) )
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f32,plain,
? [A,B] :
( ( ? [C] :
( C != k1_xboole_0
& r2_hidden(C,B) )
| k5_setfam_1(A,B) != k1_xboole_0 )
& ( ! [C] :
( C = k1_xboole_0
| ~ r2_hidden(C,B) )
| k5_setfam_1(A,B) = k1_xboole_0 )
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ),
inference(NNF_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
( ( ( sK2_skl != k1_xboole_0
& r2_hidden(sK2_skl,sK1_skl) )
| k5_setfam_1(sK0_skl,sK1_skl) != k1_xboole_0 )
& ( ! [C] :
( C = k1_xboole_0
| ~ r2_hidden(C,sK1_skl) )
| k5_setfam_1(sK0_skl,sK1_skl) = k1_xboole_0 )
& m1_subset_1(sK1_skl,k1_zfmisc_1(k1_zfmisc_1(sK0_skl))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl),skolemize(C,sK2_skl)],[f32]) ).
fof(f34,plain,
m1_subset_1(sK1_skl,k1_zfmisc_1(k1_zfmisc_1(sK0_skl))),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [X0] :
( X0 = k1_xboole_0
| ~ r2_hidden(X0,sK1_skl)
| k5_setfam_1(sK0_skl,sK1_skl) = k1_xboole_0 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f36,plain,
( r2_hidden(sK2_skl,sK1_skl)
| k5_setfam_1(sK0_skl,sK1_skl) != k1_xboole_0 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f37,plain,
( sK2_skl != k1_xboole_0
| k5_setfam_1(sK0_skl,sK1_skl) != k1_xboole_0 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f38,plain,
! [A,B] :
( ~ r2_hidden(B,A)
| ~ r2_hidden(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f39,plain,
! [X0,X1] :
( ~ r2_hidden(X1,X0)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f42,plain,
! [A] :
( ( ? [B] : r2_hidden(B,A)
| A = k1_xboole_0 )
& ( ! [B] : ~ r2_hidden(B,A)
| A != k1_xboole_0 ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f43,plain,
( ! [A] :
( ? [B] : r2_hidden(B,A)
| A = k1_xboole_0 )
& ! [A] :
( ! [B] : ~ r2_hidden(B,A)
| A != k1_xboole_0 ) ),
inference(miniscoping,[status(thm)],[f42]) ).
fof(f44,plain,
( ! [A] :
( r2_hidden(sK3_skl(A),A)
| A = k1_xboole_0 )
& ! [A] :
( ! [B] : ~ r2_hidden(B,A)
| A != k1_xboole_0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(B,sK3_skl(A))],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( ~ r2_hidden(X1,X0)
| X0 != k1_xboole_0 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
! [X0] :
( r2_hidden(sK3_skl(X0),X0)
| X0 = k1_xboole_0 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f47,plain,
! [A,B] :
( ( ? [C] :
( ( ? [D] :
( r2_hidden(D,A)
& r2_hidden(C,D) )
| r2_hidden(C,B) )
& ( ! [D] :
( ~ r2_hidden(D,A)
| ~ r2_hidden(C,D) )
| ~ r2_hidden(C,B) ) )
| B = k3_tarski(A) )
& ( ! [C] :
( ( ! [D] :
( ~ r2_hidden(D,A)
| ~ r2_hidden(C,D) )
| r2_hidden(C,B) )
& ( ? [D] :
( r2_hidden(D,A)
& r2_hidden(C,D) )
| ~ r2_hidden(C,B) ) )
| B != k3_tarski(A) ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f48,plain,
( ! [A,B] :
( ? [C] :
( ( ? [D] :
( r2_hidden(D,A)
& r2_hidden(C,D) )
| r2_hidden(C,B) )
& ( ! [D] :
( ~ r2_hidden(D,A)
| ~ r2_hidden(C,D) )
| ~ r2_hidden(C,B) ) )
| B = k3_tarski(A) )
& ! [A,B] :
( ( ! [C] :
( ! [D] :
( ~ r2_hidden(D,A)
| ~ r2_hidden(C,D) )
| r2_hidden(C,B) )
& ! [C] :
( ? [D] :
( r2_hidden(D,A)
& r2_hidden(C,D) )
| ~ r2_hidden(C,B) ) )
| B != k3_tarski(A) ) ),
inference(miniscoping,[status(thm)],[f47]) ).
fof(f49,plain,
( ! [A,B] :
( ( ( ( r2_hidden(sK6_skl(B,A),A)
& r2_hidden(sK5_skl(B,A),sK6_skl(B,A)) )
| r2_hidden(sK5_skl(B,A),B) )
& ( ! [D] :
( ~ r2_hidden(D,A)
| ~ r2_hidden(sK5_skl(B,A),D) )
| ~ r2_hidden(sK5_skl(B,A),B) ) )
| B = k3_tarski(A) )
& ! [A,B] :
( ( ! [C] :
( ! [D] :
( ~ r2_hidden(D,A)
| ~ r2_hidden(C,D) )
| r2_hidden(C,B) )
& ! [C] :
( ( r2_hidden(sK4_skl(C,B,A),A)
& r2_hidden(C,sK4_skl(C,B,A)) )
| ~ r2_hidden(C,B) ) )
| B != k3_tarski(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl]),skolemize(D,sK4_skl(C,B,A)),skolemize(C,sK5_skl(B,A)),skolemize(D,sK6_skl(B,A))],[f48]) ).
fof(f52,plain,
! [X0,X1,X2,X3] :
( ~ r2_hidden(X3,X1)
| ~ r2_hidden(X2,X3)
| r2_hidden(X2,X0)
| X0 != k3_tarski(X1) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f54,plain,
! [X0,X1] :
( r2_hidden(sK5_skl(X0,X1),sK6_skl(X0,X1))
| r2_hidden(sK5_skl(X0,X1),X0)
| X0 = k3_tarski(X1) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f55,plain,
! [X0,X1] :
( r2_hidden(sK6_skl(X0,X1),X1)
| r2_hidden(sK5_skl(X0,X1),X0)
| X0 = k3_tarski(X1) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f56,plain,
! [A,B] :
( m1_subset_1(k5_setfam_1(A,B),k1_zfmisc_1(A))
| ~ m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f57,plain,
! [X0,X1] :
( m1_subset_1(k5_setfam_1(X1,X0),k1_zfmisc_1(X1))
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_zfmisc_1(X1))) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f58,plain,
! [A] : m1_subset_1(sK7_skl(A),A),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(B,sK7_skl(A))],[f12]) ).
fof(f59,plain,
! [X0] : m1_subset_1(sK7_skl(X0),X0),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f60,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f63,plain,
! [X0] : ~ v1_xboole_0(k1_zfmisc_1(X0)),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f82,plain,
! [A,B] :
( k5_setfam_1(A,B) = k3_tarski(B)
| ~ m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f83,plain,
! [X0,X1] :
( k5_setfam_1(X1,X0) = k3_tarski(X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_zfmisc_1(X1))) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f84,plain,
! [A] : r1_tarski(A,A),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f85,plain,
! [X0] : r1_tarski(X0,X0),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f86,plain,
! [A,B] :
( m1_subset_1(A,B)
| ~ r2_hidden(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f87,plain,
! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f88,plain,
! [A,B] :
( r2_hidden(A,B)
| v1_xboole_0(B)
| ~ m1_subset_1(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f89,plain,
! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f88]) ).
fof(f90,plain,
! [A,B] :
( ( ~ r1_tarski(A,B)
| m1_subset_1(A,k1_zfmisc_1(B)) )
& ( r1_tarski(A,B)
| ~ m1_subset_1(A,k1_zfmisc_1(B)) ) ),
inference(NNF_transformation,[status(thm)],[f25]) ).
fof(f91,plain,
( ! [A,B] :
( ~ r1_tarski(A,B)
| m1_subset_1(A,k1_zfmisc_1(B)) )
& ! [A,B] :
( r1_tarski(A,B)
| ~ m1_subset_1(A,k1_zfmisc_1(B)) ) ),
inference(miniscoping,[status(thm)],[f90]) ).
fof(f93,plain,
! [X0,X1] :
( ~ r1_tarski(X0,X1)
| m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f94,plain,
! [A,B,C] :
( m1_subset_1(A,C)
| ~ m1_subset_1(B,k1_zfmisc_1(C))
| ~ r2_hidden(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f95,plain,
! [A,C] :
( m1_subset_1(A,C)
| ! [B] :
( ~ m1_subset_1(B,k1_zfmisc_1(C))
| ~ r2_hidden(A,B) ) ),
inference(miniscoping,[status(thm)],[f94]) ).
fof(f96,plain,
! [X0,X1,X2] :
( m1_subset_1(X0,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f97,plain,
! [A,B,C] :
( ~ v1_xboole_0(C)
| ~ m1_subset_1(B,k1_zfmisc_1(C))
| ~ r2_hidden(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f98,plain,
! [C] :
( ~ v1_xboole_0(C)
| ! [B] :
( ~ m1_subset_1(B,k1_zfmisc_1(C))
| ! [A] : ~ r2_hidden(A,B) ) ),
inference(miniscoping,[status(thm)],[f97]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ~ v1_xboole_0(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f100,plain,
! [A] :
( A = k1_xboole_0
| ~ v1_xboole_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f101,plain,
! [X0] :
( X0 = k1_xboole_0
| ~ v1_xboole_0(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f108,definition,
( sQ0_spl
<=> k5_setfam_1(sK0_skl,sK1_skl) = k1_xboole_0 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f109,plain,
( ~ sQ0_spl
| k5_setfam_1(sK0_skl,sK1_skl) = k1_xboole_0 ),
inference(component_clause,[status(thm)],[f108]) ).
fof(f110,plain,
( sQ0_spl
| k5_setfam_1(sK0_skl,sK1_skl) != k1_xboole_0 ),
inference(component_clause,[status(thm)],[f108]) ).
fof(f111,definition,
! [X0] :
( sQ1_spl
<=> ( X0 = k1_xboole_0
| ~ r2_hidden(X0,sK1_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f112,plain,
! [X0] :
( ~ sQ1_spl
| X0 = k1_xboole_0
| ~ r2_hidden(X0,sK1_skl) ),
inference(component_clause,[status(thm)],[f111]) ).
fof(f114,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f35,f108,f111]) ).
fof(f115,definition,
( sQ2_spl
<=> r2_hidden(sK2_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f116,plain,
( ~ sQ2_spl
| r2_hidden(sK2_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f118,plain,
( sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f36,f108,f115]) ).
fof(f119,definition,
( sQ3_spl
<=> sK2_skl = k1_xboole_0 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f121,plain,
( sQ3_spl
| sK2_skl != k1_xboole_0 ),
inference(component_clause,[status(thm)],[f119]) ).
fof(f122,plain,
( ~ sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f37,f108,f119]) ).
fof(f123,plain,
! [X0] : ~ r2_hidden(X0,k1_xboole_0),
inference(destructive_equality_resolution,[status(thm)],[f45]) ).
fof(f126,plain,
! [X0,X1,X2] :
( ~ r2_hidden(X2,X1)
| ~ r2_hidden(X0,X2)
| r2_hidden(X0,k3_tarski(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f52]) ).
fof(f128,plain,
( r2_hidden(sK1_skl,k1_zfmisc_1(k1_zfmisc_1(sK0_skl)))
| v1_xboole_0(k1_zfmisc_1(k1_zfmisc_1(sK0_skl))) ),
inference(resolution,[status(thm)],[f89,f34]) ).
fof(f129,definition,
( sQ4_spl
<=> v1_xboole_0(k1_zfmisc_1(k1_zfmisc_1(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f130,plain,
( ~ sQ4_spl
| v1_xboole_0(k1_zfmisc_1(k1_zfmisc_1(sK0_skl))) ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f132,definition,
( sQ5_spl
<=> r2_hidden(sK1_skl,k1_zfmisc_1(k1_zfmisc_1(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f135,plain,
( sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f128,f129,f132]) ).
fof(f136,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f130,f63]) ).
fof(f137,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f136]) ).
fof(f145,plain,
m1_subset_1(k5_setfam_1(sK0_skl,sK1_skl),k1_zfmisc_1(sK0_skl)),
inference(resolution,[status(thm)],[f57,f34]) ).
fof(f147,plain,
k5_setfam_1(sK0_skl,sK1_skl) = k3_tarski(sK1_skl),
inference(resolution,[status(thm)],[f83,f34]) ).
fof(f148,plain,
( ~ sQ0_spl
| k1_xboole_0 = k3_tarski(sK1_skl) ),
inference(forward_demodulation,[status(thm)],[f109,f147]) ).
fof(f156,plain,
! [X0] :
( r2_hidden(sK7_skl(X0),X0)
| v1_xboole_0(X0) ),
inference(resolution,[status(thm)],[f59,f89]) ).
fof(f158,plain,
! [X0] :
( m1_subset_1(sK3_skl(X0),X0)
| X0 = k1_xboole_0 ),
inference(resolution,[status(thm)],[f46,f87]) ).
fof(f167,definition,
( sQ7_spl
<=> v1_xboole_0(k1_zfmisc_1(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f168,plain,
( ~ sQ7_spl
| v1_xboole_0(k1_zfmisc_1(sK0_skl)) ),
inference(component_clause,[status(thm)],[f167]) ).
fof(f174,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f168,f63]) ).
fof(f175,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f174]) ).
fof(f193,plain,
! [X0] : r2_hidden(sK7_skl(k1_zfmisc_1(X0)),k1_zfmisc_1(X0)),
inference(resolution,[status(thm)],[f156,f63]) ).
fof(f194,plain,
! [X0] :
( X0 = k1_xboole_0
| r2_hidden(sK7_skl(X0),X0) ),
inference(resolution,[status(thm)],[f156,f101]) ).
fof(f204,plain,
! [X0] :
( ~ r2_hidden(X0,sK7_skl(X0))
| X0 = k1_xboole_0 ),
inference(resolution,[status(thm)],[f194,f39]) ).
fof(f213,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(k1_xboole_0))
| ~ r2_hidden(X0,X1) ),
inference(resolution,[status(thm)],[f99,f60]) ).
fof(f230,plain,
! [X0] : m1_subset_1(X0,k1_zfmisc_1(X0)),
inference(resolution,[status(thm)],[f93,f85]) ).
fof(f231,plain,
! [X0] : k5_setfam_1(X0,k1_zfmisc_1(X0)) = k3_tarski(k1_zfmisc_1(X0)),
inference(resolution,[status(thm)],[f230,f83]) ).
fof(f232,plain,
! [X0] : m1_subset_1(k5_setfam_1(X0,k1_zfmisc_1(X0)),k1_zfmisc_1(X0)),
inference(resolution,[status(thm)],[f230,f57]) ).
fof(f337,plain,
! [X0] :
( k1_zfmisc_1(k1_xboole_0) = k1_xboole_0
| ~ r2_hidden(X0,sK3_skl(k1_zfmisc_1(k1_xboole_0))) ),
inference(resolution,[status(thm)],[f213,f158]) ).
fof(f338,plain,
! [X0] : ~ r2_hidden(X0,sK7_skl(k1_zfmisc_1(k1_xboole_0))),
inference(resolution,[status(thm)],[f213,f59]) ).
fof(f347,definition,
! [X0] :
( sQ22_spl
<=> ~ r2_hidden(X0,sK3_skl(k1_zfmisc_1(k1_xboole_0))) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f348,plain,
! [X0] :
( ~ sQ22_spl
| ~ r2_hidden(X0,sK3_skl(k1_zfmisc_1(k1_xboole_0))) ),
inference(component_clause,[status(thm)],[f347]) ).
fof(f350,definition,
( sQ23_spl
<=> k1_zfmisc_1(k1_xboole_0) = k1_xboole_0 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f351,plain,
( ~ sQ23_spl
| k1_zfmisc_1(k1_xboole_0) = k1_xboole_0 ),
inference(component_clause,[status(thm)],[f350]) ).
fof(f353,plain,
( sQ23_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f337,f347,f350]) ).
fof(f370,plain,
! [X0] :
( m1_subset_1(X0,k1_zfmisc_1(sK0_skl))
| ~ r2_hidden(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f34,f96]) ).
fof(f394,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ r2_hidden(X1,sK1_skl)
| ~ r2_hidden(X0,X1)
| r2_hidden(X0,k1_xboole_0) ),
inference(paramodulation,[status(thm)],[f148,f126]) ).
fof(f397,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ r2_hidden(X1,sK1_skl)
| ~ r2_hidden(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f394,f123]) ).
fof(f407,definition,
( sQ24_spl
<=> m1_subset_1(k1_xboole_0,k1_zfmisc_1(k1_xboole_0)) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f425,plain,
sK7_skl(k1_zfmisc_1(k1_xboole_0)) = k1_xboole_0,
inference(resolution,[status(thm)],[f338,f194]) ).
fof(f433,plain,
( ~ r2_hidden(k1_zfmisc_1(k1_xboole_0),k1_xboole_0)
| k1_zfmisc_1(k1_xboole_0) = k1_xboole_0 ),
inference(paramodulation,[status(thm)],[f425,f204]) ).
fof(f434,plain,
( k1_zfmisc_1(k1_xboole_0) = k1_xboole_0
| r2_hidden(k1_xboole_0,k1_zfmisc_1(k1_xboole_0)) ),
inference(paramodulation,[status(thm)],[f425,f194]) ).
fof(f436,definition,
! [X0] :
( sQ25_spl
<=> ~ r2_hidden(X0,k1_zfmisc_1(k1_xboole_0)) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f437,plain,
! [X0] :
( ~ sQ25_spl
| ~ r2_hidden(X0,k1_zfmisc_1(k1_xboole_0)) ),
inference(component_clause,[status(thm)],[f436]) ).
fof(f439,definition,
( sQ26_spl
<=> r2_hidden(k1_zfmisc_1(k1_xboole_0),k1_xboole_0) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f443,definition,
( sQ27_spl
<=> r2_hidden(k1_xboole_0,k1_zfmisc_1(k1_xboole_0)) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f447,plain,
( ~ sQ26_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f433,f350,f439]) ).
fof(f448,plain,
( sQ23_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f434,f443,f350]) ).
fof(f458,plain,
( ~ sQ23_spl
| r2_hidden(sK7_skl(k1_zfmisc_1(k1_xboole_0)),k1_xboole_0) ),
inference(paramodulation,[status(thm)],[f351,f193]) ).
fof(f482,plain,
( ~ sQ23_spl
| r2_hidden(sK7_skl(k1_xboole_0),k1_xboole_0) ),
inference(forward_demodulation,[status(thm)],[f351,f458]) ).
fof(f483,plain,
( ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f482,f123]) ).
fof(f484,plain,
~ sQ23_spl,
inference(contradiction_clause,[status(thm)],[f483]) ).
fof(f497,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ0_spl
| ~ r2_hidden(X0,sK2_skl) ),
inference(resolution,[status(thm)],[f397,f116]) ).
fof(f516,plain,
! [X0] :
( ~ sQ1_spl
| r2_hidden(sK5_skl(X0,sK1_skl),X0)
| X0 = k3_tarski(sK1_skl)
| sK6_skl(X0,sK1_skl) = k1_xboole_0 ),
inference(resolution,[status(thm)],[f112,f55]) ).
fof(f538,plain,
( ~ sQ22_spl
| sK3_skl(k1_zfmisc_1(k1_xboole_0)) = k1_xboole_0 ),
inference(resolution,[status(thm)],[f348,f194]) ).
fof(f542,plain,
( ~ sQ22_spl
| m1_subset_1(k1_xboole_0,k1_zfmisc_1(k1_xboole_0))
| k1_zfmisc_1(k1_xboole_0) = k1_xboole_0 ),
inference(paramodulation,[status(thm)],[f538,f158]) ).
fof(f545,plain,
( ~ sQ22_spl
| sQ24_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f542,f350,f407,f347]) ).
fof(f549,plain,
( sQ0_spl
| k3_tarski(sK1_skl) != k1_xboole_0 ),
inference(backward_demodulation,[status(thm)],[f147,f110]) ).
fof(f579,definition,
( sQ37_spl
<=> k3_tarski(sK1_skl) = k1_xboole_0 ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f580,plain,
( ~ sQ37_spl
| k3_tarski(sK1_skl) = k1_xboole_0 ),
inference(component_clause,[status(thm)],[f579]) ).
fof(f594,plain,
( ~ sQ37_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f580,f549]) ).
fof(f595,plain,
( ~ sQ37_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f594]) ).
fof(f596,plain,
m1_subset_1(k3_tarski(sK1_skl),k1_zfmisc_1(sK0_skl)),
inference(forward_demodulation,[status(thm)],[f147,f145]) ).
fof(f598,plain,
( r2_hidden(k3_tarski(sK1_skl),k1_zfmisc_1(sK0_skl))
| v1_xboole_0(k1_zfmisc_1(sK0_skl)) ),
inference(resolution,[status(thm)],[f596,f89]) ).
fof(f599,definition,
( sQ41_spl
<=> r2_hidden(k3_tarski(sK1_skl),k1_zfmisc_1(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f602,plain,
( sQ41_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f598,f167,f599]) ).
fof(f609,plain,
! [X0] : m1_subset_1(k3_tarski(k1_zfmisc_1(X0)),k1_zfmisc_1(X0)),
inference(forward_demodulation,[status(thm)],[f231,f232]) ).
fof(f613,plain,
! [X0] :
( r2_hidden(k3_tarski(k1_zfmisc_1(X0)),k1_zfmisc_1(X0))
| v1_xboole_0(k1_zfmisc_1(X0)) ),
inference(resolution,[status(thm)],[f609,f89]) ).
fof(f614,plain,
! [X0] : r2_hidden(k3_tarski(k1_zfmisc_1(X0)),k1_zfmisc_1(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f613,f63]) ).
fof(f621,plain,
! [X0] : ~ r2_hidden(X0,k3_tarski(k1_zfmisc_1(k1_xboole_0))),
inference(resolution,[status(thm)],[f213,f609]) ).
fof(f636,plain,
! [X0,X1] :
( ~ r2_hidden(X1,k1_zfmisc_1(k1_xboole_0))
| ~ r2_hidden(X0,X1) ),
inference(resolution,[status(thm)],[f621,f126]) ).
fof(f692,plain,
! [X0] :
( k1_zfmisc_1(k1_xboole_0) = k1_xboole_0
| ~ r2_hidden(X0,sK7_skl(k1_zfmisc_1(k1_xboole_0))) ),
inference(resolution,[status(thm)],[f636,f194]) ).
fof(f703,definition,
! [X0] :
( sQ49_spl
<=> ~ r2_hidden(X0,sK7_skl(k1_zfmisc_1(k1_xboole_0))) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f707,plain,
( sQ23_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f692,f703,f350]) ).
fof(f720,plain,
! [X0] :
( r2_hidden(X0,k1_zfmisc_1(sK0_skl))
| v1_xboole_0(k1_zfmisc_1(sK0_skl))
| ~ r2_hidden(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f370,f89]) ).
fof(f721,definition,
! [X0] :
( sQ50_spl
<=> ( r2_hidden(X0,k1_zfmisc_1(sK0_skl))
| ~ r2_hidden(X0,sK1_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f724,plain,
( sQ7_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f720,f721,f167]) ).
fof(f803,plain,
( ~ sQ1_spl
| k1_xboole_0 = k3_tarski(sK1_skl)
| sK6_skl(k1_xboole_0,sK1_skl) = k1_xboole_0 ),
inference(resolution,[status(thm)],[f516,f123]) ).
fof(f827,definition,
( sQ60_spl
<=> sK6_skl(k1_xboole_0,sK1_skl) = k1_xboole_0 ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f828,plain,
( ~ sQ60_spl
| sK6_skl(k1_xboole_0,sK1_skl) = k1_xboole_0 ),
inference(component_clause,[status(thm)],[f827]) ).
fof(f830,plain,
( ~ sQ1_spl
| sQ37_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f803,f827,f579,f111]) ).
fof(f873,plain,
( ~ sQ25_spl
| $false ),
inference(resolution,[status(thm)],[f437,f614]) ).
fof(f883,plain,
~ sQ25_spl,
inference(contradiction_clause,[status(thm)],[f873]) ).
fof(f885,plain,
( ~ sQ60_spl
| r2_hidden(sK5_skl(k1_xboole_0,sK1_skl),k1_xboole_0)
| r2_hidden(sK5_skl(k1_xboole_0,sK1_skl),k1_xboole_0)
| k1_xboole_0 = k3_tarski(sK1_skl) ),
inference(paramodulation,[status(thm)],[f828,f54]) ).
fof(f886,definition,
( sQ66_spl
<=> r2_hidden(sK5_skl(k1_xboole_0,sK1_skl),k1_xboole_0) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f887,plain,
( ~ sQ66_spl
| r2_hidden(sK5_skl(k1_xboole_0,sK1_skl),k1_xboole_0) ),
inference(component_clause,[status(thm)],[f886]) ).
fof(f890,plain,
( ~ sQ60_spl
| sQ66_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f885,f579,f886,f827]) ).
fof(f891,plain,
( ~ sQ66_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f887,f123]) ).
fof(f892,plain,
~ sQ66_spl,
inference(contradiction_clause,[status(thm)],[f891]) ).
fof(f901,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| sK2_skl = k1_xboole_0 ),
inference(resolution,[status(thm)],[f497,f194]) ).
fof(f903,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f901,f121]) ).
fof(f904,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f903]) ).
fof(f905,plain,
$false,
inference(sat_refutation,[status(thm)],[f114,f118,f122,f135,f137,f175,f353,f447,f448,f484,f545,f595,f602,f707,f724,f830,f883,f890,f892,f904]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU430+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.34 % Computer : n003.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Mon Sep 21 06:29:45 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.44 % Elapsed time: 0.084256 seconds
% 0.13/0.44 % CPU time: 0.432577 seconds
% 0.13/0.44 % Total memory used: 88.955 MB
% 0.13/0.44 % Net memory used: 87.938 MB
%------------------------------------------------------------------------------