%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP620+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 : n018.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 12:34:49 PM UTC 2026
% Result : Theorem 0.09s 0.54s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 51
% Syntax : Number of formulae : 220 ( 23 unt; 33 def)
% Number of atoms : 1207 ( 18 equ)
% Maximal formula atoms : 30 ( 5 avg)
% Number of connectives : 1690 ( 703 ~; 780 |; 131 &)
% ( 46 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 57 ( 55 usr; 33 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 232 ( 228 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A))
=> m2_fraenkel(k2_funct_1(B),u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A))
=> m2_fraenkel(k2_funct_1(B),u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f9,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
=> v1_relat_1(C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_group_1(B)
& v4_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(C,A,B)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(C) )
=> ( v2_group_6(C,A,B)
<=> v2_funct_1(C) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_group_1(B)
& v4_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(C,A,B)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(C) )
=> ( v4_group_6(C,A,B)
<=> ( v2_group_6(C,A,B)
& v3_group_6(C,A,B) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_fraenkel(B,u1_struct_0(A),u1_struct_0(A))
=> ( B = k1_autgroup(A)
<=> ( ! [C] :
( ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
& v1_group_6(C,A,A)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v1_funct_1(C) )
=> ( r2_hidden(C,B)
<=> ( v3_group_6(C,A,A)
& v2_funct_1(C) ) ) )
& ! [C] :
( m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),B)
=> ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
& v1_group_6(C,A,A)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v1_funct_1(C) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> m1_fraenkel(k1_autgroup(A),u1_struct_0(A),u1_struct_0(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [A] :
( l1_group_1(A)
=> l1_struct_0(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [A,B,C] :
( m1_fraenkel(C,A,B)
=> ( v1_fraenkel(C)
& ~ v1_xboole_0(C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [A] :
( ( l1_struct_0(A)
& ~ v3_struct_0(A) )
=> ~ v1_xboole_0(u1_struct_0(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,axiom,
v1_xboole_0(k1_xboole_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [A,B,C] :
( ( m1_fraenkel(C,A,B)
& ~ v1_xboole_0(B) )
=> ! [D] :
( m2_fraenkel(D,A,B,C)
<=> m1_subset_1(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f59,axiom,
! [A,B] : r1_tarski(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f60,axiom,
! [A,B] :
( r2_hidden(A,B)
=> m1_subset_1(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f61,axiom,
! [A,B] :
( m1_subset_1(A,B)
=> ( r2_hidden(A,B)
| v1_xboole_0(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f62,axiom,
! [A,B] :
( m1_subset_1(A,k1_zfmisc_1(B))
<=> r1_tarski(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A))
=> ( m2_relset_1(k2_funct_1(B),u1_struct_0(A),u1_struct_0(A))
& v1_group_6(k2_funct_1(B),A,A)
& v1_funct_2(k2_funct_1(B),u1_struct_0(A),u1_struct_0(A))
& v1_funct_1(k2_funct_1(B)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f67,axiom,
! [A] :
( v1_xboole_0(A)
=> A = k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f68,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_group_1(B)
& v4_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( ( m2_relset_1(C,u1_struct_0(B),u1_struct_0(A))
& v1_group_6(C,B,A)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v1_funct_1(C) )
=> ! [D] :
( ( m2_relset_1(D,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(D,A,B)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(D) )
=> ( ( D = k2_funct_1(C)
& v4_group_6(C,B,A) )
=> v4_group_6(D,A,B) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f71,plain,
? [A] :
( ? [B] :
( ~ m2_fraenkel(k2_funct_1(B),u1_struct_0(A),u1_struct_0(A),k1_autgroup(A))
& m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) )
& l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f72,plain,
( ~ m2_fraenkel(k2_funct_1(sK1_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl))
& m2_fraenkel(sK1_skl,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl))
& l1_group_1(sK0_skl)
& v4_group_1(sK0_skl)
& v3_group_1(sK0_skl)
& v1_group_1(sK0_skl)
& ~ v3_struct_0(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl)],[f71]) ).
fof(f73,plain,
~ v3_struct_0(sK0_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f74,plain,
v1_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f75,plain,
v3_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f76,plain,
v4_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f77,plain,
l1_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f78,plain,
m2_fraenkel(sK1_skl,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl)),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f79,plain,
~ m2_fraenkel(k2_funct_1(sK1_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl)),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f95,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)],[f9]) ).
fof(f96,plain,
! [C] :
( v1_relat_1(C)
| ! [A,B] : ~ m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ),
inference(miniscoping,[status(thm)],[f95]) ).
fof(f97,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)],[f96]) ).
fof(f112,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( v2_group_6(C,A,B)
<=> v2_funct_1(C) )
| ~ m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
| ~ v1_group_6(C,A,B)
| ~ v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
| ~ v1_funct_1(C) )
| ~ l1_group_1(B)
| ~ v4_group_1(B)
| ~ v3_group_1(B)
| v3_struct_0(B) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f113,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ~ v2_funct_1(C)
| v2_group_6(C,A,B) )
& ( v2_funct_1(C)
| ~ v2_group_6(C,A,B) ) )
| ~ m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
| ~ v1_group_6(C,A,B)
| ~ v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
| ~ v1_funct_1(C) )
| ~ l1_group_1(B)
| ~ v4_group_1(B)
| ~ v3_group_1(B)
| v3_struct_0(B) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(NNF_transformation,[status(thm)],[f112]) ).
fof(f114,plain,
! [X0,X1,X2] :
( v2_funct_1(X2)
| ~ v2_group_6(X2,X0,X1)
| ~ m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_group_6(X2,X0,X1)
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_1(X2)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| v3_struct_0(X1)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f115,plain,
! [X0,X1,X2] :
( ~ v2_funct_1(X2)
| v2_group_6(X2,X0,X1)
| ~ m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_group_6(X2,X0,X1)
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_1(X2)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| v3_struct_0(X1)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f116,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( v4_group_6(C,A,B)
<=> ( v2_group_6(C,A,B)
& v3_group_6(C,A,B) ) )
| ~ m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
| ~ v1_group_6(C,A,B)
| ~ v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
| ~ v1_funct_1(C) )
| ~ l1_group_1(B)
| ~ v4_group_1(B)
| ~ v3_group_1(B)
| v3_struct_0(B) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f117,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ~ v2_group_6(C,A,B)
| ~ v3_group_6(C,A,B)
| v4_group_6(C,A,B) )
& ( ( v2_group_6(C,A,B)
& v3_group_6(C,A,B) )
| ~ v4_group_6(C,A,B) ) )
| ~ m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
| ~ v1_group_6(C,A,B)
| ~ v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
| ~ v1_funct_1(C) )
| ~ l1_group_1(B)
| ~ v4_group_1(B)
| ~ v3_group_1(B)
| v3_struct_0(B) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(NNF_transformation,[status(thm)],[f116]) ).
fof(f118,plain,
! [X0,X1,X2] :
( v3_group_6(X2,X0,X1)
| ~ v4_group_6(X2,X0,X1)
| ~ m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_group_6(X2,X0,X1)
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_1(X2)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| v3_struct_0(X1)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f119,plain,
! [X0,X1,X2] :
( v2_group_6(X2,X0,X1)
| ~ v4_group_6(X2,X0,X1)
| ~ m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_group_6(X2,X0,X1)
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_1(X2)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| v3_struct_0(X1)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f120,plain,
! [X0,X1,X2] :
( ~ v2_group_6(X2,X0,X1)
| ~ v3_group_6(X2,X0,X1)
| v4_group_6(X2,X0,X1)
| ~ m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_group_6(X2,X0,X1)
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_1(X2)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| v3_struct_0(X1)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f121,plain,
! [A] :
( ! [B] :
( ( B = k1_autgroup(A)
<=> ( ! [C] :
( ( r2_hidden(C,B)
<=> ( v3_group_6(C,A,A)
& v2_funct_1(C) ) )
| ~ m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
| ~ v1_group_6(C,A,A)
| ~ v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
| ~ v1_funct_1(C) )
& ! [C] :
( ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
& v1_group_6(C,A,A)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v1_funct_1(C) )
| ~ m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),B) ) ) )
| ~ m1_fraenkel(B,u1_struct_0(A),u1_struct_0(A)) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| ~ v1_group_1(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f122,definition,
! [A,B,C] :
( sP0_prd(C,B,A)
<=> ( ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
& v1_group_6(C,A,A)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v1_funct_1(C) )
| ~ m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),B) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f123,plain,
! [A] :
( ! [B] :
( ( B = k1_autgroup(A)
<=> ( ! [C] :
( ( r2_hidden(C,B)
<=> ( v3_group_6(C,A,A)
& v2_funct_1(C) ) )
| ~ m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
| ~ v1_group_6(C,A,A)
| ~ v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
| ~ v1_funct_1(C) )
& ! [C] : sP0_prd(C,B,A) ) )
| ~ m1_fraenkel(B,u1_struct_0(A),u1_struct_0(A)) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| ~ v1_group_1(A)
| v3_struct_0(A) ),
inference(formula_renaming,[status(thm)],[f121,f122]) ).
fof(f124,plain,
! [A] :
( ! [B] :
( ( ( ? [C] :
( ( ( v3_group_6(C,A,A)
& v2_funct_1(C) )
| r2_hidden(C,B) )
& ( ~ v3_group_6(C,A,A)
| ~ v2_funct_1(C)
| ~ r2_hidden(C,B) )
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
& v1_group_6(C,A,A)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v1_funct_1(C) )
| ? [C] : ~ sP0_prd(C,B,A)
| B = k1_autgroup(A) )
& ( ( ! [C] :
( ( ( ~ v3_group_6(C,A,A)
| ~ v2_funct_1(C)
| r2_hidden(C,B) )
& ( ( v3_group_6(C,A,A)
& v2_funct_1(C) )
| ~ r2_hidden(C,B) ) )
| ~ m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
| ~ v1_group_6(C,A,A)
| ~ v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
| ~ v1_funct_1(C) )
& ! [C] : sP0_prd(C,B,A) )
| B != k1_autgroup(A) ) )
| ~ m1_fraenkel(B,u1_struct_0(A),u1_struct_0(A)) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| ~ v1_group_1(A)
| v3_struct_0(A) ),
inference(NNF_transformation,[status(thm)],[f123]) ).
fof(f125,plain,
! [A] :
( ! [B] :
( ( ( ( ( ( v3_group_6(sK3_skl(B,A),A,A)
& v2_funct_1(sK3_skl(B,A)) )
| r2_hidden(sK3_skl(B,A),B) )
& ( ~ v3_group_6(sK3_skl(B,A),A,A)
| ~ v2_funct_1(sK3_skl(B,A))
| ~ r2_hidden(sK3_skl(B,A),B) )
& m2_relset_1(sK3_skl(B,A),u1_struct_0(A),u1_struct_0(A))
& v1_group_6(sK3_skl(B,A),A,A)
& v1_funct_2(sK3_skl(B,A),u1_struct_0(A),u1_struct_0(A))
& v1_funct_1(sK3_skl(B,A)) )
| ~ sP0_prd(sK2_skl(B,A),B,A)
| B = k1_autgroup(A) )
& ( ( ! [C] :
( ( ( ~ v3_group_6(C,A,A)
| ~ v2_funct_1(C)
| r2_hidden(C,B) )
& ( ( v3_group_6(C,A,A)
& v2_funct_1(C) )
| ~ r2_hidden(C,B) ) )
| ~ m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
| ~ v1_group_6(C,A,A)
| ~ v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
| ~ v1_funct_1(C) )
& ! [C] : sP0_prd(C,B,A) )
| B != k1_autgroup(A) ) )
| ~ m1_fraenkel(B,u1_struct_0(A),u1_struct_0(A)) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| ~ v1_group_1(A)
| v3_struct_0(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(C,sK2_skl(B,A)),skolemize(C,sK3_skl(B,A))],[f124]) ).
fof(f126,plain,
! [X0,X1,X2] :
( sP0_prd(X2,X1,X0)
| X1 != k1_autgroup(X0)
| ~ m1_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f127,plain,
! [X0,X1,X2] :
( v2_funct_1(X2)
| ~ r2_hidden(X2,X1)
| ~ m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_group_6(X2,X0,X0)
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_funct_1(X2)
| X1 != k1_autgroup(X0)
| ~ m1_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f128,plain,
! [X0,X1,X2] :
( v3_group_6(X2,X0,X0)
| ~ r2_hidden(X2,X1)
| ~ m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_group_6(X2,X0,X0)
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_funct_1(X2)
| X1 != k1_autgroup(X0)
| ~ m1_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f129,plain,
! [X0,X1,X2] :
( ~ v3_group_6(X2,X0,X0)
| ~ v2_funct_1(X2)
| r2_hidden(X2,X1)
| ~ m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_group_6(X2,X0,X0)
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_funct_1(X2)
| X1 != k1_autgroup(X0)
| ~ m1_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f140,plain,
! [A] :
( m1_fraenkel(k1_autgroup(A),u1_struct_0(A),u1_struct_0(A))
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| ~ v1_group_1(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f141,plain,
! [X0] :
( m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f145,plain,
! [A] :
( l1_struct_0(A)
| ~ l1_group_1(A) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f146,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f147,plain,
! [A,B,C] :
( ( v1_fraenkel(C)
& ~ v1_xboole_0(C) )
| ~ m1_fraenkel(C,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f148,plain,
! [C] :
( ( v1_fraenkel(C)
& ~ v1_xboole_0(C) )
| ! [A,B] : ~ m1_fraenkel(C,A,B) ),
inference(miniscoping,[status(thm)],[f147]) ).
fof(f149,plain,
! [X0,X1,X2] :
( ~ v1_xboole_0(X0)
| ~ m1_fraenkel(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f179,plain,
! [A] :
( ~ v1_xboole_0(u1_struct_0(A))
| ~ l1_struct_0(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f180,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f179]) ).
fof(f181,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f247,plain,
! [A,B,C] :
( ! [D] :
( m2_fraenkel(D,A,B,C)
<=> m1_subset_1(D,C) )
| ~ m1_fraenkel(C,A,B)
| v1_xboole_0(B) ),
inference(pre_NNF_transformation,[status(thm)],[f57]) ).
fof(f248,plain,
! [A,B,C] :
( ! [D] :
( ( ~ m1_subset_1(D,C)
| m2_fraenkel(D,A,B,C) )
& ( m1_subset_1(D,C)
| ~ m2_fraenkel(D,A,B,C) ) )
| ~ m1_fraenkel(C,A,B)
| v1_xboole_0(B) ),
inference(NNF_transformation,[status(thm)],[f247]) ).
fof(f249,plain,
! [A,B,C] :
( ( ! [D] :
( ~ m1_subset_1(D,C)
| m2_fraenkel(D,A,B,C) )
& ! [D] :
( m1_subset_1(D,C)
| ~ m2_fraenkel(D,A,B,C) ) )
| ~ m1_fraenkel(C,A,B)
| v1_xboole_0(B) ),
inference(miniscoping,[status(thm)],[f248]) ).
fof(f250,plain,
! [X0,X1,X2,X3] :
( m1_subset_1(X3,X1)
| ~ m2_fraenkel(X3,X2,X0,X1)
| ~ m1_fraenkel(X1,X2,X0)
| v1_xboole_0(X0) ),
inference(cnf_transformation,[status(thm)],[f249]) ).
fof(f251,plain,
! [X0,X1,X2,X3] :
( ~ m1_subset_1(X3,X1)
| m2_fraenkel(X3,X2,X0,X1)
| ~ m1_fraenkel(X1,X2,X0)
| v1_xboole_0(X0) ),
inference(cnf_transformation,[status(thm)],[f249]) ).
fof(f256,plain,
! [A] : r1_tarski(A,A),
inference(miniscoping,[status(thm)],[f59]) ).
fof(f257,plain,
! [X0] : r1_tarski(X0,X0),
inference(cnf_transformation,[status(thm)],[f256]) ).
fof(f258,plain,
! [A,B] :
( m1_subset_1(A,B)
| ~ r2_hidden(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f60]) ).
fof(f259,plain,
! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f258]) ).
fof(f260,plain,
! [A,B] :
( r2_hidden(A,B)
| v1_xboole_0(B)
| ~ m1_subset_1(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f61]) ).
fof(f261,plain,
! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f260]) ).
fof(f262,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)],[f62]) ).
fof(f263,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)],[f262]) ).
fof(f265,plain,
! [X0,X1] :
( ~ r1_tarski(X0,X1)
| m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[status(thm)],[f263]) ).
fof(f276,plain,
! [A] :
( ! [B] :
( ( m2_relset_1(k2_funct_1(B),u1_struct_0(A),u1_struct_0(A))
& v1_group_6(k2_funct_1(B),A,A)
& v1_funct_2(k2_funct_1(B),u1_struct_0(A),u1_struct_0(A))
& v1_funct_1(k2_funct_1(B)) )
| ~ m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| ~ v1_group_1(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f66]) ).
fof(f277,plain,
! [X0,X1] :
( v1_funct_1(k2_funct_1(X1))
| ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f276]) ).
fof(f278,plain,
! [X0,X1] :
( v1_funct_2(k2_funct_1(X1),u1_struct_0(X0),u1_struct_0(X0))
| ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f276]) ).
fof(f279,plain,
! [X0,X1] :
( v1_group_6(k2_funct_1(X1),X0,X0)
| ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f276]) ).
fof(f280,plain,
! [X0,X1] :
( m2_relset_1(k2_funct_1(X1),u1_struct_0(X0),u1_struct_0(X0))
| ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f276]) ).
fof(f281,plain,
! [A] :
( A = k1_xboole_0
| ~ v1_xboole_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f67]) ).
fof(f282,plain,
! [X0] :
( X0 = k1_xboole_0
| ~ v1_xboole_0(X0) ),
inference(cnf_transformation,[status(thm)],[f281]) ).
fof(f283,plain,
! [A] :
( ! [B] :
( ! [C] :
( ! [D] :
( v4_group_6(D,A,B)
| D != k2_funct_1(C)
| ~ v4_group_6(C,B,A)
| ~ m2_relset_1(D,u1_struct_0(A),u1_struct_0(B))
| ~ v1_group_6(D,A,B)
| ~ v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
| ~ v1_funct_1(D) )
| ~ m2_relset_1(C,u1_struct_0(B),u1_struct_0(A))
| ~ v1_group_6(C,B,A)
| ~ v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
| ~ v1_funct_1(C) )
| ~ l1_group_1(B)
| ~ v4_group_1(B)
| ~ v3_group_1(B)
| v3_struct_0(B) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f68]) ).
fof(f284,plain,
! [X0,X1,X2,X3] :
( v4_group_6(X3,X0,X1)
| X3 != k2_funct_1(X2)
| ~ v4_group_6(X2,X1,X0)
| ~ m2_relset_1(X3,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_group_6(X3,X0,X1)
| ~ v1_funct_2(X3,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_1(X3)
| ~ m2_relset_1(X2,u1_struct_0(X1),u1_struct_0(X0))
| ~ v1_group_6(X2,X1,X0)
| ~ v1_funct_2(X2,u1_struct_0(X1),u1_struct_0(X0))
| ~ v1_funct_1(X2)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| v3_struct_0(X1)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f283]) ).
fof(f291,plain,
! [A,B,C] :
( ( ( ( ~ m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
| ~ v1_group_6(C,A,A)
| ~ v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
| ~ v1_funct_1(C) )
& m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),B) )
| sP0_prd(C,B,A) )
& ( ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
& v1_group_6(C,A,A)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v1_funct_1(C) )
| ~ m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),B)
| ~ sP0_prd(C,B,A) ) ),
inference(NNF_transformation,[status(thm)],[f122]) ).
fof(f292,plain,
( ! [A,B,C] :
( ( ( ~ m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
| ~ v1_group_6(C,A,A)
| ~ v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
| ~ v1_funct_1(C) )
& m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),B) )
| sP0_prd(C,B,A) )
& ! [A,B,C] :
( ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
& v1_group_6(C,A,A)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v1_funct_1(C) )
| ~ m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),B)
| ~ sP0_prd(C,B,A) ) ),
inference(miniscoping,[status(thm)],[f291]) ).
fof(f293,plain,
! [X0,X1,X2] :
( v1_funct_1(X0)
| ~ m2_fraenkel(X0,u1_struct_0(X2),u1_struct_0(X2),X1)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f292]) ).
fof(f294,plain,
! [X0,X1,X2] :
( v1_funct_2(X0,u1_struct_0(X2),u1_struct_0(X2))
| ~ m2_fraenkel(X0,u1_struct_0(X2),u1_struct_0(X2),X1)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f292]) ).
fof(f295,plain,
! [X0,X1,X2] :
( v1_group_6(X0,X2,X2)
| ~ m2_fraenkel(X0,u1_struct_0(X2),u1_struct_0(X2),X1)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f292]) ).
fof(f296,plain,
! [X0,X1,X2] :
( m2_relset_1(X0,u1_struct_0(X2),u1_struct_0(X2))
| ~ m2_fraenkel(X0,u1_struct_0(X2),u1_struct_0(X2),X1)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f292]) ).
fof(f299,plain,
! [X0,X1] :
( sP0_prd(X1,k1_autgroup(X0),X0)
| ~ m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f126]) ).
fof(f300,plain,
! [X0,X1] :
( v2_funct_1(X1)
| ~ r2_hidden(X1,k1_autgroup(X0))
| ~ m2_relset_1(X1,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_group_6(X1,X0,X0)
| ~ v1_funct_2(X1,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_funct_1(X1)
| ~ m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f127]) ).
fof(f301,plain,
! [X0,X1] :
( v3_group_6(X1,X0,X0)
| ~ r2_hidden(X1,k1_autgroup(X0))
| ~ m2_relset_1(X1,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_group_6(X1,X0,X0)
| ~ v1_funct_2(X1,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_funct_1(X1)
| ~ m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f128]) ).
fof(f302,plain,
! [X0,X1] :
( ~ v3_group_6(X1,X0,X0)
| ~ v2_funct_1(X1)
| r2_hidden(X1,k1_autgroup(X0))
| ~ m2_relset_1(X1,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_group_6(X1,X0,X0)
| ~ v1_funct_2(X1,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_funct_1(X1)
| ~ m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f129]) ).
fof(f303,plain,
! [X0,X1,X2] :
( v4_group_6(k2_funct_1(X2),X0,X1)
| ~ v4_group_6(X2,X1,X0)
| ~ m2_relset_1(k2_funct_1(X2),u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_group_6(k2_funct_1(X2),X0,X1)
| ~ v1_funct_2(k2_funct_1(X2),u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_1(k2_funct_1(X2))
| ~ m2_relset_1(X2,u1_struct_0(X1),u1_struct_0(X0))
| ~ v1_group_6(X2,X1,X0)
| ~ v1_funct_2(X2,u1_struct_0(X1),u1_struct_0(X0))
| ~ v1_funct_1(X2)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| v3_struct_0(X1)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f284]) ).
fof(f305,definition,
( sQ0_spl
<=> v1_xboole_0(u1_struct_0(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f306,plain,
( ~ sQ0_spl
| v1_xboole_0(u1_struct_0(sK0_skl)) ),
inference(component_clause,[status(thm)],[f305]) ).
fof(f308,definition,
( sQ1_spl
<=> m1_fraenkel(k1_autgroup(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f309,plain,
( ~ sQ1_spl
| m1_fraenkel(k1_autgroup(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl)) ),
inference(component_clause,[status(thm)],[f308]) ).
fof(f310,plain,
( sQ1_spl
| ~ m1_fraenkel(k1_autgroup(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl)) ),
inference(component_clause,[status(thm)],[f308]) ).
fof(f311,definition,
( sQ2_spl
<=> v1_funct_1(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f316,definition,
( sQ3_spl
<=> v1_funct_2(sK1_skl,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f320,plain,
( sQ1_spl
| ~ l1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| ~ v1_group_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f310,f141]) ).
fof(f321,definition,
( sQ4_spl
<=> v3_struct_0(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f322,plain,
( ~ sQ4_spl
| v3_struct_0(sK0_skl) ),
inference(component_clause,[status(thm)],[f321]) ).
fof(f324,definition,
( sQ5_spl
<=> v1_group_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f326,plain,
( sQ5_spl
| ~ v1_group_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f324]) ).
fof(f327,definition,
( sQ6_spl
<=> v3_group_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f329,plain,
( sQ6_spl
| ~ v3_group_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f327]) ).
fof(f330,definition,
( sQ7_spl
<=> v4_group_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f332,plain,
( sQ7_spl
| ~ v4_group_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f330]) ).
fof(f333,definition,
( sQ8_spl
<=> l1_group_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f335,plain,
( sQ8_spl
| ~ l1_group_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f333]) ).
fof(f336,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f320,f321,f324,f327,f330,f333,f308]) ).
fof(f337,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f335,f77]) ).
fof(f338,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f337]) ).
fof(f339,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f332,f76]) ).
fof(f340,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f339]) ).
fof(f341,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f329,f75]) ).
fof(f342,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f341]) ).
fof(f343,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f326,f74]) ).
fof(f344,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f343]) ).
fof(f345,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f322,f73]) ).
fof(f346,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f345]) ).
fof(f348,definition,
( sQ9_spl
<=> m2_relset_1(sK1_skl,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f349,plain,
( ~ sQ9_spl
| m2_relset_1(sK1_skl,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl)) ),
inference(component_clause,[status(thm)],[f348]) ).
fof(f352,plain,
( v1_funct_1(k2_funct_1(sK1_skl))
| ~ l1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| ~ v1_group_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f277,f78]) ).
fof(f353,definition,
( sQ10_spl
<=> v1_funct_1(k2_funct_1(sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f356,plain,
( sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f352,f321,f324,f327,f330,f333,f353]) ).
fof(f359,plain,
( v1_funct_2(k2_funct_1(sK1_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl))
| ~ l1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| ~ v1_group_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f278,f78]) ).
fof(f360,definition,
( sQ11_spl
<=> v1_funct_2(k2_funct_1(sK1_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f363,plain,
( sQ11_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f359,f321,f324,f327,f330,f333,f360]) ).
fof(f364,plain,
( v1_group_6(k2_funct_1(sK1_skl),sK0_skl,sK0_skl)
| ~ l1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| ~ v1_group_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f279,f78]) ).
fof(f365,definition,
( sQ12_spl
<=> v1_group_6(k2_funct_1(sK1_skl),sK0_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f368,plain,
( sQ12_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f364,f321,f324,f327,f330,f333,f365]) ).
fof(f369,plain,
( m2_relset_1(k2_funct_1(sK1_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl))
| ~ l1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| ~ v1_group_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f280,f78]) ).
fof(f370,definition,
( sQ13_spl
<=> m2_relset_1(k2_funct_1(sK1_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f371,plain,
( ~ sQ13_spl
| m2_relset_1(k2_funct_1(sK1_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl)) ),
inference(component_clause,[status(thm)],[f370]) ).
fof(f373,plain,
( sQ13_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f369,f321,f324,f327,f330,f333,f370]) ).
fof(f487,plain,
( ~ sQ13_spl
| v2_funct_1(k2_funct_1(sK1_skl))
| ~ v2_group_6(k2_funct_1(sK1_skl),sK0_skl,sK0_skl)
| ~ v1_group_6(k2_funct_1(sK1_skl),sK0_skl,sK0_skl)
| ~ v1_funct_2(k2_funct_1(sK1_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl))
| ~ v1_funct_1(k2_funct_1(sK1_skl))
| ~ l1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ l1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f114,f371]) ).
fof(f488,definition,
( sQ40_spl
<=> v2_group_6(k2_funct_1(sK1_skl),sK0_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f491,definition,
( sQ41_spl
<=> v2_funct_1(k2_funct_1(sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f494,plain,
( ~ sQ13_spl
| sQ41_spl
| ~ sQ40_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f487,f321,f327,f330,f333,f353,f360,f365,f488,f491,f370]) ).
fof(f497,plain,
( ~ sQ13_spl
| v3_group_6(k2_funct_1(sK1_skl),sK0_skl,sK0_skl)
| ~ v4_group_6(k2_funct_1(sK1_skl),sK0_skl,sK0_skl)
| ~ v1_group_6(k2_funct_1(sK1_skl),sK0_skl,sK0_skl)
| ~ v1_funct_2(k2_funct_1(sK1_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl))
| ~ v1_funct_1(k2_funct_1(sK1_skl))
| ~ l1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ l1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f118,f371]) ).
fof(f498,definition,
( sQ42_spl
<=> v4_group_6(k2_funct_1(sK1_skl),sK0_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f501,definition,
( sQ43_spl
<=> v3_group_6(k2_funct_1(sK1_skl),sK0_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f504,plain,
( ~ sQ13_spl
| sQ43_spl
| ~ sQ42_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f497,f321,f327,f330,f333,f353,f360,f365,f498,f501,f370]) ).
fof(f505,plain,
( ~ sQ13_spl
| v2_group_6(k2_funct_1(sK1_skl),sK0_skl,sK0_skl)
| ~ v4_group_6(k2_funct_1(sK1_skl),sK0_skl,sK0_skl)
| ~ v1_group_6(k2_funct_1(sK1_skl),sK0_skl,sK0_skl)
| ~ v1_funct_2(k2_funct_1(sK1_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl))
| ~ v1_funct_1(k2_funct_1(sK1_skl))
| ~ l1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ l1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f119,f371]) ).
fof(f506,plain,
( ~ sQ13_spl
| sQ40_spl
| ~ sQ42_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f505,f321,f327,f330,f333,f353,f360,f365,f498,f488,f370]) ).
fof(f509,plain,
! [X0,X1] :
( sP0_prd(X1,k1_autgroup(X0),X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f299,f141]) ).
fof(f510,plain,
! [X0,X1] :
( v2_funct_1(X1)
| ~ r2_hidden(X1,k1_autgroup(X0))
| ~ m2_relset_1(X1,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_group_6(X1,X0,X0)
| ~ v1_funct_2(X1,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_funct_1(X1)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f300,f141]) ).
fof(f512,definition,
( sQ44_spl
<=> r2_hidden(k2_funct_1(sK1_skl),k1_autgroup(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f513,plain,
( ~ sQ44_spl
| r2_hidden(k2_funct_1(sK1_skl),k1_autgroup(sK0_skl)) ),
inference(component_clause,[status(thm)],[f512]) ).
fof(f516,plain,
! [X0,X1] :
( v3_group_6(X1,X0,X0)
| ~ r2_hidden(X1,k1_autgroup(X0))
| ~ m2_relset_1(X1,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_group_6(X1,X0,X0)
| ~ v1_funct_2(X1,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_funct_1(X1)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f301,f141]) ).
fof(f519,plain,
! [X0,X1] :
( ~ v3_group_6(X1,X0,X0)
| ~ v2_funct_1(X1)
| r2_hidden(X1,k1_autgroup(X0))
| ~ m2_relset_1(X1,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_group_6(X1,X0,X0)
| ~ v1_funct_2(X1,u1_struct_0(X0),u1_struct_0(X0))
| ~ v1_funct_1(X1)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f302,f141]) ).
fof(f520,plain,
( ~ sQ13_spl
| ~ v3_group_6(k2_funct_1(sK1_skl),sK0_skl,sK0_skl)
| ~ v2_funct_1(k2_funct_1(sK1_skl))
| r2_hidden(k2_funct_1(sK1_skl),k1_autgroup(sK0_skl))
| ~ v1_group_6(k2_funct_1(sK1_skl),sK0_skl,sK0_skl)
| ~ v1_funct_2(k2_funct_1(sK1_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl))
| ~ v1_funct_1(k2_funct_1(sK1_skl))
| ~ l1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| ~ v1_group_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f519,f371]) ).
fof(f521,plain,
( ~ sQ13_spl
| ~ sQ43_spl
| ~ sQ41_spl
| sQ44_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f520,f321,f324,f327,f330,f333,f353,f360,f365,f512,f491,f501,f370]) ).
fof(f571,plain,
l1_struct_0(sK0_skl),
inference(resolution,[status(thm)],[f146,f77]) ).
fof(f572,plain,
( ~ sQ1_spl
| ~ v1_xboole_0(k1_autgroup(sK0_skl)) ),
inference(resolution,[status(thm)],[f149,f309]) ).
fof(f585,plain,
( ~ sQ0_spl
| u1_struct_0(sK0_skl) = k1_xboole_0 ),
inference(resolution,[status(thm)],[f282,f306]) ).
fof(f819,definition,
( sQ76_spl
<=> v1_xboole_0(k1_xboole_0) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f821,plain,
( sQ76_spl
| ~ v1_xboole_0(k1_xboole_0) ),
inference(component_clause,[status(thm)],[f819]) ).
fof(f1057,plain,
( ~ sQ0_spl
| ~ v1_xboole_0(k1_xboole_0)
| ~ l1_struct_0(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(paramodulation,[status(thm)],[f585,f180]) ).
fof(f1058,definition,
( sQ106_spl
<=> l1_struct_0(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f1060,plain,
( sQ106_spl
| ~ l1_struct_0(sK0_skl) ),
inference(component_clause,[status(thm)],[f1058]) ).
fof(f1061,plain,
( ~ sQ0_spl
| ~ sQ76_spl
| ~ sQ106_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f1057,f321,f1058,f819,f305]) ).
fof(f1062,plain,
( sQ106_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1060,f571]) ).
fof(f1063,plain,
sQ106_spl,
inference(contradiction_clause,[status(thm)],[f1062]) ).
fof(f1064,plain,
( sQ76_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f821,f181]) ).
fof(f1065,plain,
sQ76_spl,
inference(contradiction_clause,[status(thm)],[f1064]) ).
fof(f1084,definition,
( sQ109_spl
<=> v1_relat_1(k2_zfmisc_1(k1_xboole_0,k1_xboole_0)) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f1086,plain,
( sQ109_spl
| ~ v1_relat_1(k2_zfmisc_1(k1_xboole_0,k1_xboole_0)) ),
inference(component_clause,[status(thm)],[f1084]) ).
fof(f1379,plain,
( ~ sQ9_spl
| v3_group_6(sK1_skl,sK0_skl,sK0_skl)
| ~ r2_hidden(sK1_skl,k1_autgroup(sK0_skl))
| ~ v1_group_6(sK1_skl,sK0_skl,sK0_skl)
| ~ v1_funct_2(sK1_skl,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl))
| ~ v1_funct_1(sK1_skl)
| ~ l1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| ~ v1_group_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f349,f516]) ).
fof(f1380,plain,
( ~ sQ9_spl
| v2_funct_1(sK1_skl)
| ~ r2_hidden(sK1_skl,k1_autgroup(sK0_skl))
| ~ v1_group_6(sK1_skl,sK0_skl,sK0_skl)
| ~ v1_funct_2(sK1_skl,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl))
| ~ v1_funct_1(sK1_skl)
| ~ l1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| ~ v1_group_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f349,f510]) ).
fof(f1381,plain,
( ~ sQ9_spl
| ~ v2_group_6(sK1_skl,sK0_skl,sK0_skl)
| ~ v3_group_6(sK1_skl,sK0_skl,sK0_skl)
| v4_group_6(sK1_skl,sK0_skl,sK0_skl)
| ~ v1_group_6(sK1_skl,sK0_skl,sK0_skl)
| ~ v1_funct_2(sK1_skl,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl))
| ~ v1_funct_1(sK1_skl)
| ~ l1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ l1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f349,f120]) ).
fof(f1384,plain,
( ~ sQ9_spl
| ~ v2_funct_1(sK1_skl)
| v2_group_6(sK1_skl,sK0_skl,sK0_skl)
| ~ v1_group_6(sK1_skl,sK0_skl,sK0_skl)
| ~ v1_funct_2(sK1_skl,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl))
| ~ v1_funct_1(sK1_skl)
| ~ l1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ l1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f349,f115]) ).
fof(f1388,definition,
( sQ122_spl
<=> v1_group_6(sK1_skl,sK0_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition]) ).
fof(f1391,definition,
( sQ123_spl
<=> r2_hidden(sK1_skl,k1_autgroup(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f1394,definition,
( sQ124_spl
<=> v2_funct_1(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f1397,definition,
( sQ125_spl
<=> v3_group_6(sK1_skl,sK0_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f1401,plain,
( ~ sQ9_spl
| sQ125_spl
| ~ sQ123_spl
| ~ sQ122_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f1379,f321,f324,f327,f330,f333,f311,f316,f1388,f1391,f1397,f348]) ).
fof(f1402,plain,
( ~ sQ9_spl
| sQ124_spl
| ~ sQ123_spl
| ~ sQ122_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f1380,f321,f324,f327,f330,f333,f311,f316,f1388,f1391,f1394,f348]) ).
fof(f1403,definition,
( sQ126_spl
<=> v4_group_6(sK1_skl,sK0_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f1406,definition,
( sQ127_spl
<=> v2_group_6(sK1_skl,sK0_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ127_spl])],[split_symbol_definition]) ).
fof(f1409,plain,
( ~ sQ9_spl
| ~ sQ127_spl
| ~ sQ125_spl
| sQ126_spl
| ~ sQ122_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f1381,f321,f327,f330,f333,f311,f316,f1388,f1403,f1397,f1406,f348]) ).
fof(f1412,plain,
( ~ sQ9_spl
| ~ sQ124_spl
| sQ127_spl
| ~ sQ122_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f1384,f321,f327,f330,f333,f311,f316,f1388,f1406,f1394,f348]) ).
fof(f1436,plain,
! [X0,X1,X2] :
( v1_relat_1(X0)
| ~ r1_tarski(X0,k2_zfmisc_1(X1,X2)) ),
inference(resolution,[status(thm)],[f265,f97]) ).
fof(f1441,plain,
! [X0,X1] : v1_relat_1(k2_zfmisc_1(X0,X1)),
inference(resolution,[status(thm)],[f1436,f257]) ).
fof(f1442,plain,
( sQ109_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1086,f1441]) ).
fof(f1443,plain,
sQ109_spl,
inference(contradiction_clause,[status(thm)],[f1442]) ).
fof(f1448,plain,
( m1_subset_1(sK1_skl,k1_autgroup(sK0_skl))
| ~ m1_fraenkel(k1_autgroup(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl))
| v1_xboole_0(u1_struct_0(sK0_skl)) ),
inference(resolution,[status(thm)],[f250,f78]) ).
fof(f1450,definition,
( sQ128_spl
<=> m1_subset_1(sK1_skl,k1_autgroup(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f1451,plain,
( ~ sQ128_spl
| m1_subset_1(sK1_skl,k1_autgroup(sK0_skl)) ),
inference(component_clause,[status(thm)],[f1450]) ).
fof(f1453,plain,
( sQ128_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f1448,f305,f308,f1450]) ).
fof(f1455,plain,
( ~ m1_subset_1(k2_funct_1(sK1_skl),k1_autgroup(sK0_skl))
| ~ m1_fraenkel(k1_autgroup(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl))
| v1_xboole_0(u1_struct_0(sK0_skl)) ),
inference(resolution,[status(thm)],[f251,f79]) ).
fof(f1464,definition,
( sQ129_spl
<=> m1_subset_1(k2_funct_1(sK1_skl),k1_autgroup(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition]) ).
fof(f1466,plain,
( sQ129_spl
| ~ m1_subset_1(k2_funct_1(sK1_skl),k1_autgroup(sK0_skl)) ),
inference(component_clause,[status(thm)],[f1464]) ).
fof(f1467,plain,
( ~ sQ129_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f1455,f305,f308,f1464]) ).
fof(f1479,plain,
( ~ sQ128_spl
| r2_hidden(sK1_skl,k1_autgroup(sK0_skl))
| v1_xboole_0(k1_autgroup(sK0_skl)) ),
inference(resolution,[status(thm)],[f1451,f261]) ).
fof(f1482,definition,
( sQ130_spl
<=> v1_xboole_0(k1_autgroup(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ130_spl])],[split_symbol_definition]) ).
fof(f1483,plain,
( ~ sQ130_spl
| v1_xboole_0(k1_autgroup(sK0_skl)) ),
inference(component_clause,[status(thm)],[f1482]) ).
fof(f1485,plain,
( ~ sQ128_spl
| sQ123_spl
| sQ130_spl ),
inference(split_clause,[status(thm)],[f1479,f1482,f1391,f1450]) ).
fof(f1496,plain,
( ~ sQ130_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1483,f572]) ).
fof(f1497,plain,
( ~ sQ130_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f1496]) ).
fof(f1593,plain,
( ~ sQ13_spl
| v4_group_6(k2_funct_1(sK1_skl),sK0_skl,sK0_skl)
| ~ v4_group_6(sK1_skl,sK0_skl,sK0_skl)
| ~ v1_group_6(k2_funct_1(sK1_skl),sK0_skl,sK0_skl)
| ~ v1_funct_2(k2_funct_1(sK1_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl))
| ~ v1_funct_1(k2_funct_1(sK1_skl))
| ~ m2_relset_1(sK1_skl,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl))
| ~ v1_group_6(sK1_skl,sK0_skl,sK0_skl)
| ~ v1_funct_2(sK1_skl,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl))
| ~ v1_funct_1(sK1_skl)
| ~ l1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ l1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f303,f371]) ).
fof(f1596,plain,
( ~ sQ13_spl
| sQ42_spl
| ~ sQ126_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ122_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f1593,f321,f327,f330,f333,f311,f316,f1388,f348,f353,f360,f365,f1403,f498,f370]) ).
fof(f1601,plain,
( v1_funct_1(sK1_skl)
| ~ sP0_prd(sK1_skl,k1_autgroup(sK0_skl),sK0_skl) ),
inference(resolution,[status(thm)],[f293,f78]) ).
fof(f1604,definition,
( sQ133_spl
<=> sP0_prd(sK1_skl,k1_autgroup(sK0_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition]) ).
fof(f1606,plain,
( sQ133_spl
| ~ sP0_prd(sK1_skl,k1_autgroup(sK0_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f1604]) ).
fof(f1607,plain,
( sQ2_spl
| ~ sQ133_spl ),
inference(split_clause,[status(thm)],[f1601,f1604,f311]) ).
fof(f1608,plain,
( v1_funct_2(sK1_skl,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl))
| ~ sP0_prd(sK1_skl,k1_autgroup(sK0_skl),sK0_skl) ),
inference(resolution,[status(thm)],[f294,f78]) ).
fof(f1611,plain,
( sQ3_spl
| ~ sQ133_spl ),
inference(split_clause,[status(thm)],[f1608,f1604,f316]) ).
fof(f1612,plain,
( sQ133_spl
| ~ l1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| ~ v1_group_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f1606,f509]) ).
fof(f1613,plain,
( sQ133_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f1612,f321,f324,f327,f330,f333,f1604]) ).
fof(f1637,plain,
( v1_group_6(sK1_skl,sK0_skl,sK0_skl)
| ~ sP0_prd(sK1_skl,k1_autgroup(sK0_skl),sK0_skl) ),
inference(resolution,[status(thm)],[f295,f78]) ).
fof(f1640,plain,
( sQ122_spl
| ~ sQ133_spl ),
inference(split_clause,[status(thm)],[f1637,f1604,f1388]) ).
fof(f1641,plain,
( m2_relset_1(sK1_skl,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl))
| ~ sP0_prd(sK1_skl,k1_autgroup(sK0_skl),sK0_skl) ),
inference(resolution,[status(thm)],[f296,f78]) ).
fof(f1644,plain,
( sQ9_spl
| ~ sQ133_spl ),
inference(split_clause,[status(thm)],[f1641,f1604,f348]) ).
fof(f1687,plain,
( ~ sQ44_spl
| m1_subset_1(k2_funct_1(sK1_skl),k1_autgroup(sK0_skl)) ),
inference(resolution,[status(thm)],[f513,f259]) ).
fof(f1690,plain,
( ~ sQ44_spl
| sQ129_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1687,f1466]) ).
fof(f1691,plain,
( ~ sQ44_spl
| sQ129_spl ),
inference(contradiction_clause,[status(thm)],[f1690]) ).
fof(f1692,plain,
$false,
inference(sat_refutation,[status(thm)],[f336,f338,f340,f342,f344,f346,f356,f363,f368,f373,f494,f504,f506,f521,f1061,f1063,f1065,f1401,f1402,f1409,f1412,f1443,f1453,f1467,f1485,f1497,f1596,f1607,f1611,f1613,f1640,f1644,f1691]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP620+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:20:14 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.54 % Refutation found
% 0.09/0.54 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.72/0.57 % Elapsed time: 0.192794 seconds
% 0.72/0.57 % CPU time: 1.222517 seconds
% 0.72/0.57 % Total memory used: 113.809 MB
% 0.72/0.57 % Net memory used: 113.098 MB
%------------------------------------------------------------------------------