%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU425+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 02:20:32 PM UTC 2026
% Result : Theorem 0.02s 0.39s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 21
% Syntax : Number of formulae : 104 ( 12 unt; 9 def)
% Number of atoms : 317 ( 76 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 351 ( 138 ~; 141 |; 39 &)
% ( 18 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 9 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 166 ( 158 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
=> ( m2_relset_1(k5_relset_2(A,C),k1_zfmisc_1(A),k1_zfmisc_1(k2_relat_1(C)))
& v1_funct_2(k5_relset_2(A,C),k1_zfmisc_1(A),k1_zfmisc_1(k2_relat_1(C)))
& v1_funct_1(k5_relset_2(A,C)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
=> ( m2_relset_1(k5_relset_2(A,C),k1_zfmisc_1(A),k1_zfmisc_1(k2_relat_1(C)))
& v1_funct_2(k5_relset_2(A,C),k1_zfmisc_1(A),k1_zfmisc_1(k2_relat_1(C)))
& v1_funct_1(k5_relset_2(A,C)) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f5,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
=> v1_relat_1(C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
=> ( ( B = k1_xboole_0
=> ( ( v1_funct_2(C,A,B)
<=> C = k1_xboole_0 )
| A = k1_xboole_0 ) )
& ( ( B = k1_xboole_0
=> A = k1_xboole_0 )
=> ( v1_funct_2(C,A,B)
<=> A = k4_relset_1(A,B,C) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( v1_relat_1(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_relat_1(C) )
=> ( C = k5_relset_2(A,B)
<=> ( ! [D] :
( r1_tarski(D,A)
=> k1_funct_1(C,D) = k9_relat_1(B,D) )
& k1_relat_1(C) = k1_zfmisc_1(A) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B] :
( v1_relat_1(B)
=> ( v1_funct_1(k5_relset_2(A,B))
& v1_relat_1(k5_relset_2(A,B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
( v3_relat_1(k1_xboole_0)
& v1_relat_1(k1_xboole_0)
& v1_xboole_0(k1_xboole_0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [A,B,C] :
( m1_relset_1(C,A,B)
=> k4_relset_1(A,B,C) = k1_relat_1(C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
<=> m1_relset_1(C,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [A,B] : r1_tarski(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> ( ( r1_tarski(k2_relat_1(C),B)
& r1_tarski(k1_relat_1(C),A) )
=> m2_relset_1(C,A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
=> r1_tarski(k2_relat_1(k5_relset_2(A,C)),k1_zfmisc_1(k2_relat_1(C))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,plain,
? [A,B,C] :
( ( ~ m2_relset_1(k5_relset_2(A,C),k1_zfmisc_1(A),k1_zfmisc_1(k2_relat_1(C)))
| ~ v1_funct_2(k5_relset_2(A,C),k1_zfmisc_1(A),k1_zfmisc_1(k2_relat_1(C)))
| ~ v1_funct_1(k5_relset_2(A,C)) )
& m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f52,plain,
? [A,C] :
( ( ~ m2_relset_1(k5_relset_2(A,C),k1_zfmisc_1(A),k1_zfmisc_1(k2_relat_1(C)))
| ~ v1_funct_2(k5_relset_2(A,C),k1_zfmisc_1(A),k1_zfmisc_1(k2_relat_1(C)))
| ~ v1_funct_1(k5_relset_2(A,C)) )
& ? [B] : m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ),
inference(miniscoping,[status(thm)],[f51]) ).
fof(f53,plain,
( ( ~ m2_relset_1(k5_relset_2(sK0_skl,sK1_skl),k1_zfmisc_1(sK0_skl),k1_zfmisc_1(k2_relat_1(sK1_skl)))
| ~ v1_funct_2(k5_relset_2(sK0_skl,sK1_skl),k1_zfmisc_1(sK0_skl),k1_zfmisc_1(k2_relat_1(sK1_skl)))
| ~ v1_funct_1(k5_relset_2(sK0_skl,sK1_skl)) )
& m1_subset_1(sK1_skl,k1_zfmisc_1(k2_zfmisc_1(sK0_skl,sK2_skl))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(A,sK0_skl),skolemize(C,sK1_skl),skolemize(B,sK2_skl)],[f52]) ).
fof(f54,plain,
m1_subset_1(sK1_skl,k1_zfmisc_1(k2_zfmisc_1(sK0_skl,sK2_skl))),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f55,plain,
( ~ m2_relset_1(k5_relset_2(sK0_skl,sK1_skl),k1_zfmisc_1(sK0_skl),k1_zfmisc_1(k2_relat_1(sK1_skl)))
| ~ v1_funct_2(k5_relset_2(sK0_skl,sK1_skl),k1_zfmisc_1(sK0_skl),k1_zfmisc_1(k2_relat_1(sK1_skl)))
| ~ v1_funct_1(k5_relset_2(sK0_skl,sK1_skl)) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f60,plain,
! [A,B,C] :
( v1_relat_1(C)
| ~ m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f61,plain,
! [C] :
( v1_relat_1(C)
| ! [A,B] : ~ m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ),
inference(miniscoping,[status(thm)],[f60]) ).
fof(f62,plain,
! [X0,X1,X2] :
( v1_relat_1(X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
! [A,B,C] :
( ( ( ( v1_funct_2(C,A,B)
<=> C = k1_xboole_0 )
| A = k1_xboole_0
| B != k1_xboole_0 )
& ( ( v1_funct_2(C,A,B)
<=> A = k4_relset_1(A,B,C) )
| ( A != k1_xboole_0
& B = k1_xboole_0 ) ) )
| ~ m2_relset_1(C,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f64,definition,
! [A,B] :
( sP0_prd(B,A)
<=> ( A != k1_xboole_0
& B = k1_xboole_0 ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f65,plain,
! [A,B,C] :
( ( ( ( v1_funct_2(C,A,B)
<=> C = k1_xboole_0 )
| A = k1_xboole_0
| B != k1_xboole_0 )
& ( ( v1_funct_2(C,A,B)
<=> A = k4_relset_1(A,B,C) )
| sP0_prd(B,A) ) )
| ~ m2_relset_1(C,A,B) ),
inference(formula_renaming,[status(thm)],[f63,f64]) ).
fof(f66,plain,
! [A,B,C] :
( ( ( ( ( C != k1_xboole_0
| v1_funct_2(C,A,B) )
& ( C = k1_xboole_0
| ~ v1_funct_2(C,A,B) ) )
| A = k1_xboole_0
| B != k1_xboole_0 )
& ( ( ( A != k4_relset_1(A,B,C)
| v1_funct_2(C,A,B) )
& ( A = k4_relset_1(A,B,C)
| ~ v1_funct_2(C,A,B) ) )
| sP0_prd(B,A) ) )
| ~ m2_relset_1(C,A,B) ),
inference(NNF_transformation,[status(thm)],[f65]) ).
fof(f68,plain,
! [X0,X1,X2] :
( X1 != k4_relset_1(X1,X2,X0)
| v1_funct_2(X0,X1,X2)
| sP0_prd(X2,X1)
| ~ m2_relset_1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f71,plain,
! [A,B] :
( ! [C] :
( ( C = k5_relset_2(A,B)
<=> ( ! [D] :
( k1_funct_1(C,D) = k9_relat_1(B,D)
| ~ r1_tarski(D,A) )
& k1_relat_1(C) = k1_zfmisc_1(A) ) )
| ~ v1_funct_1(C)
| ~ v1_relat_1(C) )
| ~ v1_relat_1(B) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f72,plain,
! [A,B] :
( ! [C] :
( ( ( ? [D] :
( k1_funct_1(C,D) != k9_relat_1(B,D)
& r1_tarski(D,A) )
| k1_relat_1(C) != k1_zfmisc_1(A)
| C = k5_relset_2(A,B) )
& ( ( ! [D] :
( k1_funct_1(C,D) = k9_relat_1(B,D)
| ~ r1_tarski(D,A) )
& k1_relat_1(C) = k1_zfmisc_1(A) )
| C != k5_relset_2(A,B) ) )
| ~ v1_funct_1(C)
| ~ v1_relat_1(C) )
| ~ v1_relat_1(B) ),
inference(NNF_transformation,[status(thm)],[f71]) ).
fof(f73,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ? [D] :
( k1_funct_1(C,D) != k9_relat_1(B,D)
& r1_tarski(D,A) )
| k1_relat_1(C) != k1_zfmisc_1(A)
| C = k5_relset_2(A,B) )
& ! [A] :
( ( ! [D] :
( k1_funct_1(C,D) = k9_relat_1(B,D)
| ~ r1_tarski(D,A) )
& k1_relat_1(C) = k1_zfmisc_1(A) )
| C != k5_relset_2(A,B) ) )
| ~ v1_funct_1(C)
| ~ v1_relat_1(C) )
| ~ v1_relat_1(B) ),
inference(miniscoping,[status(thm)],[f72]) ).
fof(f74,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ( k1_funct_1(C,sK3_skl(A,C,B)) != k9_relat_1(B,sK3_skl(A,C,B))
& r1_tarski(sK3_skl(A,C,B),A) )
| k1_relat_1(C) != k1_zfmisc_1(A)
| C = k5_relset_2(A,B) )
& ! [A] :
( ( ! [D] :
( k1_funct_1(C,D) = k9_relat_1(B,D)
| ~ r1_tarski(D,A) )
& k1_relat_1(C) = k1_zfmisc_1(A) )
| C != k5_relset_2(A,B) ) )
| ~ v1_funct_1(C)
| ~ v1_relat_1(C) )
| ~ v1_relat_1(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(D,sK3_skl(A,C,B))],[f73]) ).
fof(f75,plain,
! [X0,X1,X2] :
( k1_relat_1(X1) = k1_zfmisc_1(X2)
| X1 != k5_relset_2(X2,X0)
| ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f81,plain,
! [A,B] :
( ( v1_funct_1(k5_relset_2(A,B))
& v1_relat_1(k5_relset_2(A,B)) )
| ~ v1_relat_1(B) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f82,plain,
! [B] :
( ( ! [A] : v1_funct_1(k5_relset_2(A,B))
& ! [A] : v1_relat_1(k5_relset_2(A,B)) )
| ~ v1_relat_1(B) ),
inference(miniscoping,[status(thm)],[f81]) ).
fof(f83,plain,
! [X0,X1] :
( v1_relat_1(k5_relset_2(X1,X0))
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f84,plain,
! [X0,X1] :
( v1_funct_1(k5_relset_2(X1,X0))
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f93,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f96,plain,
! [X0] : ~ v1_xboole_0(k1_zfmisc_1(X0)),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f132,plain,
! [A,B,C] :
( k4_relset_1(A,B,C) = k1_relat_1(C)
| ~ m1_relset_1(C,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f133,plain,
! [X0,X1,X2] :
( k4_relset_1(X1,X2,X0) = k1_relat_1(X0)
| ~ m1_relset_1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f134,plain,
! [A,B,C] :
( ( ~ m1_relset_1(C,A,B)
| m2_relset_1(C,A,B) )
& ( m1_relset_1(C,A,B)
| ~ m2_relset_1(C,A,B) ) ),
inference(NNF_transformation,[status(thm)],[f39]) ).
fof(f135,plain,
( ! [A,B,C] :
( ~ m1_relset_1(C,A,B)
| m2_relset_1(C,A,B) )
& ! [A,B,C] :
( m1_relset_1(C,A,B)
| ~ m2_relset_1(C,A,B) ) ),
inference(miniscoping,[status(thm)],[f134]) ).
fof(f136,plain,
! [X0,X1,X2] :
( m1_relset_1(X0,X1,X2)
| ~ m2_relset_1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f138,plain,
! [A] : r1_tarski(A,A),
inference(miniscoping,[status(thm)],[f40]) ).
fof(f139,plain,
! [X0] : r1_tarski(X0,X0),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f140,plain,
! [A,B,C] :
( m2_relset_1(C,A,B)
| ~ r1_tarski(k2_relat_1(C),B)
| ~ r1_tarski(k1_relat_1(C),A)
| ~ v1_relat_1(C) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f141,plain,
! [C] :
( ! [A,B] :
( m2_relset_1(C,A,B)
| ~ r1_tarski(k2_relat_1(C),B)
| ~ r1_tarski(k1_relat_1(C),A) )
| ~ v1_relat_1(C) ),
inference(miniscoping,[status(thm)],[f140]) ).
fof(f142,plain,
! [X0,X1,X2] :
( m2_relset_1(X0,X1,X2)
| ~ r1_tarski(k2_relat_1(X0),X2)
| ~ r1_tarski(k1_relat_1(X0),X1)
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f145,plain,
! [A,B,C] :
( r1_tarski(k2_relat_1(k5_relset_2(A,C)),k1_zfmisc_1(k2_relat_1(C)))
| ~ m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f146,plain,
! [A,C] :
( r1_tarski(k2_relat_1(k5_relset_2(A,C)),k1_zfmisc_1(k2_relat_1(C)))
| ! [B] : ~ m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ),
inference(miniscoping,[status(thm)],[f145]) ).
fof(f147,plain,
! [X0,X1,X2] :
( r1_tarski(k2_relat_1(k5_relset_2(X1,X0)),k1_zfmisc_1(k2_relat_1(X0)))
| ~ m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f168,plain,
! [A,B] :
( ( A = k1_xboole_0
| B != k1_xboole_0
| sP0_prd(B,A) )
& ( ( A != k1_xboole_0
& B = k1_xboole_0 )
| ~ sP0_prd(B,A) ) ),
inference(NNF_transformation,[status(thm)],[f64]) ).
fof(f169,plain,
( ! [A,B] :
( A = k1_xboole_0
| B != k1_xboole_0
| sP0_prd(B,A) )
& ! [A,B] :
( ( A != k1_xboole_0
& B = k1_xboole_0 )
| ~ sP0_prd(B,A) ) ),
inference(miniscoping,[status(thm)],[f168]) ).
fof(f170,plain,
! [X0,X1] :
( X0 = k1_xboole_0
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f169]) ).
fof(f173,definition,
( sQ0_spl
<=> v1_funct_1(k5_relset_2(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f175,plain,
( sQ0_spl
| ~ v1_funct_1(k5_relset_2(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f176,definition,
( sQ1_spl
<=> v1_funct_2(k5_relset_2(sK0_skl,sK1_skl),k1_zfmisc_1(sK0_skl),k1_zfmisc_1(k2_relat_1(sK1_skl))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f179,definition,
( sQ2_spl
<=> m2_relset_1(k5_relset_2(sK0_skl,sK1_skl),k1_zfmisc_1(sK0_skl),k1_zfmisc_1(k2_relat_1(sK1_skl))) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f180,plain,
( ~ sQ2_spl
| m2_relset_1(k5_relset_2(sK0_skl,sK1_skl),k1_zfmisc_1(sK0_skl),k1_zfmisc_1(k2_relat_1(sK1_skl))) ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f181,plain,
( sQ2_spl
| ~ m2_relset_1(k5_relset_2(sK0_skl,sK1_skl),k1_zfmisc_1(sK0_skl),k1_zfmisc_1(k2_relat_1(sK1_skl))) ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f182,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f55,f173,f176,f179]) ).
fof(f185,plain,
! [X0,X1] :
( k1_relat_1(k5_relset_2(X1,X0)) = k1_zfmisc_1(X1)
| ~ v1_funct_1(k5_relset_2(X1,X0))
| ~ v1_relat_1(k5_relset_2(X1,X0))
| ~ v1_relat_1(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f75]) ).
fof(f190,plain,
! [X0,X1] :
( k1_relat_1(k5_relset_2(X1,X0)) = k1_zfmisc_1(X1)
| ~ v1_funct_1(k5_relset_2(X1,X0))
| ~ v1_relat_1(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f185,f83]) ).
fof(f191,plain,
! [X0,X1] :
( ~ v1_relat_1(X0)
| k1_relat_1(k5_relset_2(X1,X0)) = k1_zfmisc_1(X1)
| ~ v1_relat_1(X0) ),
inference(resolution,[status(thm)],[f190,f84]) ).
fof(f192,plain,
! [X0,X1] :
( k1_relat_1(k5_relset_2(X1,X0)) = k1_zfmisc_1(X1)
| ~ v1_relat_1(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f191]) ).
fof(f196,plain,
! [X0,X1,X2,X3] :
( ~ m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))
| k1_relat_1(k5_relset_2(X0,X1)) = k1_zfmisc_1(X0) ),
inference(resolution,[status(thm)],[f192,f62]) ).
fof(f201,plain,
! [X0,X1] :
( m2_relset_1(X0,k1_relat_1(X0),X1)
| ~ r1_tarski(k2_relat_1(X0),X1)
| ~ v1_relat_1(X0) ),
inference(resolution,[status(thm)],[f139,f142]) ).
fof(f208,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X0,X2)))
| m2_relset_1(k5_relset_2(X0,X1),k1_relat_1(k5_relset_2(X0,X1)),k1_zfmisc_1(k2_relat_1(X1)))
| ~ v1_relat_1(k5_relset_2(X0,X1)) ),
inference(resolution,[status(thm)],[f201,f147]) ).
fof(f237,plain,
! [X0] : k1_relat_1(k5_relset_2(X0,sK1_skl)) = k1_zfmisc_1(X0),
inference(resolution,[status(thm)],[f196,f54]) ).
fof(f239,plain,
( m2_relset_1(k5_relset_2(sK0_skl,sK1_skl),k1_relat_1(k5_relset_2(sK0_skl,sK1_skl)),k1_zfmisc_1(k2_relat_1(sK1_skl)))
| ~ v1_relat_1(k5_relset_2(sK0_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f208,f54]) ).
fof(f241,definition,
( sQ3_spl
<=> v1_relat_1(k5_relset_2(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f243,plain,
( sQ3_spl
| ~ v1_relat_1(k5_relset_2(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f241]) ).
fof(f244,definition,
( sQ4_spl
<=> m2_relset_1(k5_relset_2(sK0_skl,sK1_skl),k1_relat_1(k5_relset_2(sK0_skl,sK1_skl)),k1_zfmisc_1(k2_relat_1(sK1_skl))) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f245,plain,
( ~ sQ4_spl
| m2_relset_1(k5_relset_2(sK0_skl,sK1_skl),k1_relat_1(k5_relset_2(sK0_skl,sK1_skl)),k1_zfmisc_1(k2_relat_1(sK1_skl))) ),
inference(component_clause,[status(thm)],[f244]) ).
fof(f247,plain,
( sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f239,f241,f244]) ).
fof(f296,plain,
( sQ3_spl
| ~ v1_relat_1(sK1_skl) ),
inference(resolution,[status(thm)],[f243,f83]) ).
fof(f300,plain,
! [X0,X1] :
( sQ3_spl
| ~ m1_subset_1(sK1_skl,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(resolution,[status(thm)],[f296,f62]) ).
fof(f303,plain,
( ~ sQ4_spl
| m2_relset_1(k5_relset_2(sK0_skl,sK1_skl),k1_zfmisc_1(sK0_skl),k1_zfmisc_1(k2_relat_1(sK1_skl))) ),
inference(forward_demodulation,[status(thm)],[f237,f245]) ).
fof(f304,plain,
( ~ sQ4_spl
| sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f303,f181]) ).
fof(f305,plain,
( ~ sQ4_spl
| sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f304]) ).
fof(f323,definition,
( sQ10_spl
<=> v1_xboole_0(k1_xboole_0) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f325,plain,
( sQ10_spl
| ~ v1_xboole_0(k1_xboole_0) ),
inference(component_clause,[status(thm)],[f323]) ).
fof(f331,plain,
( sQ0_spl
| ~ v1_relat_1(sK1_skl) ),
inference(resolution,[status(thm)],[f175,f84]) ).
fof(f365,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f325,f93]) ).
fof(f366,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f365]) ).
fof(f368,plain,
( sQ3_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f54,f300]) ).
fof(f370,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f368]) ).
fof(f372,plain,
! [X0,X1] :
( sQ0_spl
| ~ m1_subset_1(sK1_skl,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(resolution,[status(thm)],[f331,f62]) ).
fof(f373,plain,
( ~ sQ2_spl
| k1_zfmisc_1(sK0_skl) != k4_relset_1(k1_zfmisc_1(sK0_skl),k1_zfmisc_1(k2_relat_1(sK1_skl)),k5_relset_2(sK0_skl,sK1_skl))
| v1_funct_2(k5_relset_2(sK0_skl,sK1_skl),k1_zfmisc_1(sK0_skl),k1_zfmisc_1(k2_relat_1(sK1_skl)))
| sP0_prd(k1_zfmisc_1(k2_relat_1(sK1_skl)),k1_zfmisc_1(sK0_skl)) ),
inference(resolution,[status(thm)],[f180,f68]) ).
fof(f375,definition,
( sQ16_spl
<=> sP0_prd(k1_zfmisc_1(k2_relat_1(sK1_skl)),k1_zfmisc_1(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f376,plain,
( ~ sQ16_spl
| sP0_prd(k1_zfmisc_1(k2_relat_1(sK1_skl)),k1_zfmisc_1(sK0_skl)) ),
inference(component_clause,[status(thm)],[f375]) ).
fof(f378,definition,
( sQ17_spl
<=> k1_zfmisc_1(sK0_skl) = k4_relset_1(k1_zfmisc_1(sK0_skl),k1_zfmisc_1(k2_relat_1(sK1_skl)),k5_relset_2(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f380,plain,
( sQ17_spl
| k1_zfmisc_1(sK0_skl) != k4_relset_1(k1_zfmisc_1(sK0_skl),k1_zfmisc_1(k2_relat_1(sK1_skl)),k5_relset_2(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f378]) ).
fof(f381,plain,
( ~ sQ2_spl
| ~ sQ17_spl
| sQ1_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f373,f375,f176,f378,f179]) ).
fof(f429,plain,
( sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f54,f372]) ).
fof(f432,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f429]) ).
fof(f439,plain,
( ~ sQ16_spl
| k1_zfmisc_1(k2_relat_1(sK1_skl)) = k1_xboole_0 ),
inference(resolution,[status(thm)],[f376,f170]) ).
fof(f447,plain,
( ~ sQ16_spl
| ~ v1_xboole_0(k1_xboole_0) ),
inference(paramodulation,[status(thm)],[f439,f96]) ).
fof(f455,plain,
( ~ sQ16_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f447,f323,f375]) ).
fof(f508,plain,
! [X0,X1,X2] :
( ~ m2_relset_1(X2,X0,X1)
| k4_relset_1(X0,X1,X2) = k1_relat_1(X2) ),
inference(resolution,[status(thm)],[f133,f136]) ).
fof(f510,plain,
( ~ sQ2_spl
| k4_relset_1(k1_zfmisc_1(sK0_skl),k1_zfmisc_1(k2_relat_1(sK1_skl)),k5_relset_2(sK0_skl,sK1_skl)) = k1_relat_1(k5_relset_2(sK0_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f508,f180]) ).
fof(f516,plain,
( ~ sQ2_spl
| k4_relset_1(k1_zfmisc_1(sK0_skl),k1_zfmisc_1(k2_relat_1(sK1_skl)),k5_relset_2(sK0_skl,sK1_skl)) = k1_zfmisc_1(sK0_skl) ),
inference(forward_demodulation,[status(thm)],[f237,f510]) ).
fof(f557,plain,
( ~ sQ2_spl
| sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f516,f380]) ).
fof(f558,plain,
( ~ sQ2_spl
| sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f557]) ).
fof(f559,plain,
$false,
inference(sat_refutation,[status(thm)],[f182,f247,f305,f366,f370,f381,f432,f455,f558]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU425+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n016.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 06:31:38 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 % Drodi V4.1.1
% 0.02/0.39 % Refutation found
% 0.02/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.02/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.02/0.43 % Elapsed time: 0.058746 seconds
% 0.02/0.43 % CPU time: 0.229649 seconds
% 0.02/0.43 % Total memory used: 85.271 MB
% 0.02/0.43 % Net memory used: 85.016 MB
%------------------------------------------------------------------------------