%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP624+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 : n011.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 12:34:50 PM UTC 2026
% Result : Theorem 138.36s 17.94s
% Output : CNFRefutation 138.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 14
% Syntax : Number of formulae : 136 ( 28 unt; 0 def)
% Number of atoms : 617 ( 68 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 812 ( 331 ~; 387 |; 69 &)
% ( 5 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-4 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-6 aty)
% Number of variables : 176 ( 169 !; 7 ?)
% 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),k4_autgroup(A))
=> ! [C] :
( m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A))
=> k1_binop_1(k2_autgroup(A),B,C) = k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C,B) ) ) ),
file('/export/starexec/sandbox/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),k4_autgroup(A))
=> ! [C] :
( m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A))
=> k1_binop_1(k2_autgroup(A),B,C) = k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C,B) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
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] :
( ( m2_relset_1(B,k2_zfmisc_1(k1_autgroup(A),k1_autgroup(A)),k1_autgroup(A))
& v1_funct_2(B,k2_zfmisc_1(k1_autgroup(A),k1_autgroup(A)),k1_autgroup(A))
& v1_funct_1(B) )
=> ( B = k2_autgroup(A)
<=> ! [C] :
( m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A))
=> ! [D] :
( m2_fraenkel(D,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A))
=> k2_binop_1(k1_autgroup(A),k1_autgroup(A),k1_autgroup(A),B,C,D) = k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),D,C) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,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/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> ( m2_relset_1(k2_autgroup(A),k2_zfmisc_1(k1_autgroup(A),k1_autgroup(A)),k1_autgroup(A))
& v1_funct_2(k2_autgroup(A),k2_zfmisc_1(k1_autgroup(A),k1_autgroup(A)),k1_autgroup(A))
& v1_funct_1(k2_autgroup(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [A] :
( l1_group_1(A)
=> l1_struct_0(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [A,B,C] :
( m1_fraenkel(C,A,B)
=> ( v1_fraenkel(C)
& ~ v1_xboole_0(C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [A] :
( ( l1_struct_0(A)
& ~ v3_struct_0(A) )
=> ~ v1_xboole_0(u1_struct_0(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,axiom,
? [A] : v1_xboole_0(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f59,axiom,
? [A] :
( v1_funct_1(A)
& v1_xboole_0(A)
& v1_relat_1(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f67,axiom,
! [A,B,C,D,E,F] :
( ( m1_subset_1(F,B)
& m1_subset_1(E,A)
& m1_relset_1(D,k2_zfmisc_1(A,B),C)
& v1_funct_2(D,k2_zfmisc_1(A,B),C)
& v1_funct_1(D)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(A) )
=> k2_binop_1(A,B,C,D,E,F) = k1_binop_1(D,E,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f69,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/sandbox/benchmark/theBenchmark.p') ).
fof(f70,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
<=> m1_relset_1(C,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f72,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),k4_autgroup(A))
=> m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f78,axiom,
! [A] :
( v1_xboole_0(A)
=> A = k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f81,plain,
? [A] :
( ? [B] :
( ? [C] :
( k1_binop_1(k2_autgroup(A),B,C) != k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C,B)
& m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A)) )
& m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k4_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(f82,plain,
( k1_binop_1(k2_autgroup(sK0_skl),sK1_skl,sK2_skl) != k7_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),sK2_skl,sK1_skl)
& m2_fraenkel(sK2_skl,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k4_autgroup(sK0_skl))
& m2_fraenkel(sK1_skl,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k4_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,sK2_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl),skolemize(C,sK2_skl)],[f81]) ).
fof(f83,plain,
~ v3_struct_0(sK0_skl),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f84,plain,
v1_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f85,plain,
v3_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f86,plain,
v4_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f87,plain,
l1_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f88,plain,
m2_fraenkel(sK1_skl,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k4_autgroup(sK0_skl)),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f89,plain,
m2_fraenkel(sK2_skl,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k4_autgroup(sK0_skl)),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f90,plain,
k1_binop_1(k2_autgroup(sK0_skl),sK1_skl,sK2_skl) != k7_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),sK2_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f126,plain,
! [A] :
( ! [B] :
( ( B = k2_autgroup(A)
<=> ! [C] :
( ! [D] :
( k2_binop_1(k1_autgroup(A),k1_autgroup(A),k1_autgroup(A),B,C,D) = k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),D,C)
| ~ m2_fraenkel(D,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) )
| ~ m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) ) )
| ~ m2_relset_1(B,k2_zfmisc_1(k1_autgroup(A),k1_autgroup(A)),k1_autgroup(A))
| ~ v1_funct_2(B,k2_zfmisc_1(k1_autgroup(A),k1_autgroup(A)),k1_autgroup(A))
| ~ v1_funct_1(B) )
| ~ 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(f127,plain,
! [A] :
( ! [B] :
( ( ( ? [C] :
( ? [D] :
( k2_binop_1(k1_autgroup(A),k1_autgroup(A),k1_autgroup(A),B,C,D) != k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),D,C)
& m2_fraenkel(D,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) )
& m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) )
| B = k2_autgroup(A) )
& ( ! [C] :
( ! [D] :
( k2_binop_1(k1_autgroup(A),k1_autgroup(A),k1_autgroup(A),B,C,D) = k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),D,C)
| ~ m2_fraenkel(D,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) )
| ~ m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) )
| B != k2_autgroup(A) ) )
| ~ m2_relset_1(B,k2_zfmisc_1(k1_autgroup(A),k1_autgroup(A)),k1_autgroup(A))
| ~ v1_funct_2(B,k2_zfmisc_1(k1_autgroup(A),k1_autgroup(A)),k1_autgroup(A))
| ~ v1_funct_1(B) )
| ~ 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)],[f126]) ).
fof(f128,plain,
! [A] :
( ! [B] :
( ( ( ( k2_binop_1(k1_autgroup(A),k1_autgroup(A),k1_autgroup(A),B,sK3_skl(B,A),sK4_skl(B,A)) != k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),sK4_skl(B,A),sK3_skl(B,A))
& m2_fraenkel(sK4_skl(B,A),u1_struct_0(A),u1_struct_0(A),k1_autgroup(A))
& m2_fraenkel(sK3_skl(B,A),u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) )
| B = k2_autgroup(A) )
& ( ! [C] :
( ! [D] :
( k2_binop_1(k1_autgroup(A),k1_autgroup(A),k1_autgroup(A),B,C,D) = k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),D,C)
| ~ m2_fraenkel(D,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) )
| ~ m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) )
| B != k2_autgroup(A) ) )
| ~ m2_relset_1(B,k2_zfmisc_1(k1_autgroup(A),k1_autgroup(A)),k1_autgroup(A))
| ~ v1_funct_2(B,k2_zfmisc_1(k1_autgroup(A),k1_autgroup(A)),k1_autgroup(A))
| ~ v1_funct_1(B) )
| ~ 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,[sK3_skl,sK4_skl]),skolemize(C,sK3_skl(B,A)),skolemize(D,sK4_skl(B,A))],[f127]) ).
fof(f129,plain,
! [X0,X1,X2,X3] :
( v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ~ v1_funct_2(X3,k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
| ~ v3_group_1(X0)
| ~ m2_relset_1(X3,k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
| X3 != k2_autgroup(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ v1_funct_1(X3)
| k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X1,X2) = k2_binop_1(k1_autgroup(X0),k1_autgroup(X0),k1_autgroup(X0),X3,X2,X1) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f137,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)],[f18]) ).
fof(f138,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v4_group_1(X0)
| ~ v1_group_1(X0) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f139,plain,
! [A] :
( ( m2_relset_1(k2_autgroup(A),k2_zfmisc_1(k1_autgroup(A),k1_autgroup(A)),k1_autgroup(A))
& v1_funct_2(k2_autgroup(A),k2_zfmisc_1(k1_autgroup(A),k1_autgroup(A)),k1_autgroup(A))
& v1_funct_1(k2_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)],[f24]) ).
fof(f140,plain,
! [X0] :
( v1_funct_1(k2_autgroup(X0))
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f141,plain,
! [X0] :
( ~ v4_group_1(X0)
| v1_funct_2(k2_autgroup(X0),k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
| v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f142,plain,
! [X0] :
( v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| m2_relset_1(k2_autgroup(X0),k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
| ~ v1_group_1(X0) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f153,plain,
! [A] :
( l1_struct_0(A)
| ~ l1_group_1(A) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f154,plain,
! [X0] :
( ~ l1_group_1(X0)
| l1_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f155,plain,
! [A,B,C] :
( ( v1_fraenkel(C)
& ~ v1_xboole_0(C) )
| ~ m1_fraenkel(C,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f156,plain,
! [C] :
( ( v1_fraenkel(C)
& ~ v1_xboole_0(C) )
| ! [A,B] : ~ m1_fraenkel(C,A,B) ),
inference(miniscoping,[status(thm)],[f155]) ).
fof(f157,plain,
! [X0,X1,X2] :
( ~ v1_xboole_0(X0)
| ~ m1_fraenkel(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f156]) ).
fof(f190,plain,
! [A] :
( ~ v1_xboole_0(u1_struct_0(A))
| ~ l1_struct_0(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f191,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f215,plain,
v1_xboole_0(sK17_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl]),skolemize(A,sK17_skl)],[f58]) ).
fof(f216,plain,
v1_xboole_0(sK17_skl),
inference(cnf_transformation,[status(thm)],[f215]) ).
fof(f217,plain,
( v1_funct_1(sK18_skl)
& v1_xboole_0(sK18_skl)
& v1_relat_1(sK18_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18_skl]),skolemize(A,sK18_skl)],[f59]) ).
fof(f219,plain,
v1_xboole_0(sK18_skl),
inference(cnf_transformation,[status(thm)],[f217]) ).
fof(f249,plain,
! [A,B,C,D,E,F] :
( k2_binop_1(A,B,C,D,E,F) = k1_binop_1(D,E,F)
| ~ m1_subset_1(F,B)
| ~ m1_subset_1(E,A)
| ~ m1_relset_1(D,k2_zfmisc_1(A,B),C)
| ~ v1_funct_2(D,k2_zfmisc_1(A,B),C)
| ~ v1_funct_1(D)
| v1_xboole_0(B)
| v1_xboole_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f67]) ).
fof(f250,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ m1_subset_1(X2,X4)
| ~ m1_subset_1(X3,X0)
| ~ v1_funct_2(X1,k2_zfmisc_1(X4,X0),X5)
| v1_xboole_0(X4)
| ~ m1_relset_1(X1,k2_zfmisc_1(X4,X0),X5)
| k1_binop_1(X1,X2,X3) = k2_binop_1(X4,X0,X5,X1,X2,X3)
| ~ v1_funct_1(X1)
| v1_xboole_0(X0) ),
inference(cnf_transformation,[status(thm)],[f249]) ).
fof(f253,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)],[f69]) ).
fof(f254,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)],[f253]) ).
fof(f255,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)],[f254]) ).
fof(f256,plain,
! [X0,X1,X2,X3] :
( ~ m1_fraenkel(X3,X1,X2)
| m1_subset_1(X0,X3)
| v1_xboole_0(X2)
| ~ m2_fraenkel(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f258,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)],[f70]) ).
fof(f259,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)],[f258]) ).
fof(f260,plain,
! [X0,X1,X2] :
( ~ m2_relset_1(X0,X1,X2)
| m1_relset_1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f259]) ).
fof(f264,plain,
! [A] :
( ! [B] :
( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A))
| ~ m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k4_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)],[f72]) ).
fof(f265,plain,
! [X0,X1] :
( ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ m2_fraenkel(X0,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
| v3_struct_0(X1)
| m2_fraenkel(X0,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1)) ),
inference(cnf_transformation,[status(thm)],[f264]) ).
fof(f280,plain,
! [A] :
( A = k1_xboole_0
| ~ v1_xboole_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f78]) ).
fof(f281,plain,
! [X0] :
( ~ v1_xboole_0(X0)
| X0 = k1_xboole_0 ),
inference(cnf_transformation,[status(thm)],[f280]) ).
fof(f296,plain,
! [X0,X1,X2] :
( ~ v1_funct_2(X0,k2_zfmisc_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl)),k1_autgroup(sK0_skl))
| ~ l1_group_1(sK0_skl)
| ~ v1_group_1(sK0_skl)
| ~ m2_fraenkel(X2,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl))
| k7_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),X1,X2) = k2_binop_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),X0,X2,X1)
| ~ m2_fraenkel(X1,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl))
| ~ v4_group_1(sK0_skl)
| ~ m2_relset_1(X0,k2_zfmisc_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl)),k1_autgroup(sK0_skl))
| ~ v1_funct_1(X0)
| k2_autgroup(sK0_skl) != X0
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f85,f129]) ).
fof(f304,plain,
! [X0,X1,X2] :
( ~ v1_funct_1(X0)
| ~ v1_funct_2(X0,k2_zfmisc_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl)),k1_autgroup(sK0_skl))
| k7_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),X2,X1) = k2_binop_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),X0,X1,X2)
| ~ l1_group_1(sK0_skl)
| ~ m2_fraenkel(X2,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl))
| ~ v1_group_1(sK0_skl)
| ~ m2_fraenkel(X1,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl))
| ~ m2_relset_1(X0,k2_zfmisc_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl)),k1_autgroup(sK0_skl))
| k2_autgroup(sK0_skl) != X0
| v3_struct_0(sK0_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f296,f86]) ).
fof(f333,plain,
! [X0,X1,X2] :
( ~ v1_funct_1(X0)
| ~ v1_funct_2(X0,k2_zfmisc_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl)),k1_autgroup(sK0_skl))
| ~ m2_fraenkel(X1,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl))
| ~ v1_group_1(sK0_skl)
| ~ m2_fraenkel(X2,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl))
| k2_binop_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),X0,X1,X2) = k7_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),X2,X1)
| k2_autgroup(sK0_skl) != X0
| ~ m2_relset_1(X0,k2_zfmisc_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl)),k1_autgroup(sK0_skl))
| v3_struct_0(sK0_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f304,f87]) ).
fof(f337,plain,
! [X0] :
( ~ v4_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| ~ v1_group_1(sK0_skl)
| ~ m2_fraenkel(X0,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k4_autgroup(sK0_skl))
| v3_struct_0(sK0_skl)
| m2_fraenkel(X0,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl)) ),
inference(resolution,[status(thm)],[f87,f265]) ).
fof(f339,plain,
! [X0] :
( ~ v1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| m2_fraenkel(X0,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl))
| ~ m2_fraenkel(X0,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k4_autgroup(sK0_skl))
| v3_struct_0(sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f337,f85]) ).
fof(f382,plain,
! [X0,X1,X2] :
( ~ m2_fraenkel(X2,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl))
| ~ v1_funct_2(X0,k2_zfmisc_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl)),k1_autgroup(sK0_skl))
| k2_autgroup(sK0_skl) != X0
| ~ m2_relset_1(X0,k2_zfmisc_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl)),k1_autgroup(sK0_skl))
| ~ v1_group_1(sK0_skl)
| k7_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),X1,X2) = k2_binop_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),X0,X2,X1)
| ~ m2_fraenkel(X1,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl))
| ~ v1_funct_1(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f333,f83]) ).
fof(f383,plain,
! [X0,X1,X2] :
( ~ m2_fraenkel(X2,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl))
| ~ m2_relset_1(X0,k2_zfmisc_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl)),k1_autgroup(sK0_skl))
| k2_binop_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),X0,X1,X2) = k7_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),X2,X1)
| X0 != k2_autgroup(sK0_skl)
| ~ m2_fraenkel(X1,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl))
| ~ v1_funct_2(X0,k2_zfmisc_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl)),k1_autgroup(sK0_skl))
| ~ v1_funct_1(X0) ),
inference(resolution,[status(thm)],[f382,f84]) ).
fof(f398,plain,
! [X0] :
( m2_fraenkel(X0,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl))
| ~ v1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ m2_fraenkel(X0,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k4_autgroup(sK0_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f339,f83]) ).
fof(f399,plain,
! [X0] :
( m2_fraenkel(X0,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl))
| ~ v4_group_1(sK0_skl)
| ~ m2_fraenkel(X0,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k4_autgroup(sK0_skl)) ),
inference(resolution,[status(thm)],[f398,f84]) ).
fof(f400,plain,
! [X0] :
( ~ m2_fraenkel(X0,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k4_autgroup(sK0_skl))
| m2_fraenkel(X0,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f399,f86]) ).
fof(f476,plain,
m2_fraenkel(sK2_skl,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl)),
inference(resolution,[status(thm)],[f400,f89]) ).
fof(f477,plain,
m2_fraenkel(sK1_skl,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl)),
inference(resolution,[status(thm)],[f400,f88]) ).
fof(f524,plain,
( v1_xboole_0(u1_struct_0(sK0_skl))
| ~ m1_fraenkel(k1_autgroup(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl))
| m1_subset_1(sK1_skl,k1_autgroup(sK0_skl)) ),
inference(resolution,[status(thm)],[f477,f256]) ).
fof(f526,plain,
( ~ l1_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v1_group_1(sK0_skl)
| v1_xboole_0(u1_struct_0(sK0_skl))
| m1_subset_1(sK1_skl,k1_autgroup(sK0_skl)) ),
inference(resolution,[status(thm)],[f524,f138]) ).
fof(f527,plain,
( ~ v4_group_1(sK0_skl)
| v1_xboole_0(u1_struct_0(sK0_skl))
| ~ l1_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| m1_subset_1(sK1_skl,k1_autgroup(sK0_skl))
| v3_struct_0(sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f526,f84]) ).
fof(f530,plain,
( ~ v4_group_1(sK0_skl)
| v1_xboole_0(u1_struct_0(sK0_skl))
| ~ l1_group_1(sK0_skl)
| m1_subset_1(sK1_skl,k1_autgroup(sK0_skl))
| ~ v3_group_1(sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f527,f83]) ).
fof(f531,plain,
( ~ v4_group_1(sK0_skl)
| v1_xboole_0(u1_struct_0(sK0_skl))
| m1_subset_1(sK1_skl,k1_autgroup(sK0_skl))
| ~ v3_group_1(sK0_skl) ),
inference(resolution,[status(thm)],[f530,f87]) ).
fof(f532,plain,
( m1_subset_1(sK1_skl,k1_autgroup(sK0_skl))
| v1_xboole_0(u1_struct_0(sK0_skl))
| ~ v4_group_1(sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f531,f85]) ).
fof(f533,plain,
( m1_subset_1(sK1_skl,k1_autgroup(sK0_skl))
| v1_xboole_0(u1_struct_0(sK0_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f532,f86]) ).
fof(f554,plain,
! [X0,X1] :
( k7_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),sK2_skl,X1) = k2_binop_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),X0,X1,sK2_skl)
| ~ v1_funct_1(X0)
| ~ m2_relset_1(X0,k2_zfmisc_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl)),k1_autgroup(sK0_skl))
| ~ m2_fraenkel(X1,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl))
| k2_autgroup(sK0_skl) != X0
| ~ v1_funct_2(X0,k2_zfmisc_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl)),k1_autgroup(sK0_skl)) ),
inference(resolution,[status(thm)],[f476,f383]) ).
fof(f556,plain,
( v1_xboole_0(u1_struct_0(sK0_skl))
| m1_subset_1(sK2_skl,k1_autgroup(sK0_skl))
| ~ m1_fraenkel(k1_autgroup(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl)) ),
inference(resolution,[status(thm)],[f476,f256]) ).
fof(f569,plain,
! [X0] :
( ~ v4_group_1(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ l1_group_1(sK0_skl)
| ~ v1_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| k7_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),sK2_skl,X0) = k2_binop_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k2_autgroup(sK0_skl),X0,sK2_skl)
| ~ v1_funct_1(k2_autgroup(sK0_skl))
| ~ m2_relset_1(k2_autgroup(sK0_skl),k2_zfmisc_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl)),k1_autgroup(sK0_skl))
| ~ m2_fraenkel(X0,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl))
| k2_autgroup(sK0_skl) != k2_autgroup(sK0_skl) ),
inference(resolution,[status(thm)],[f554,f141]) ).
fof(f570,plain,
! [X0] :
( ~ v4_group_1(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ l1_group_1(sK0_skl)
| ~ v1_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| k7_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),sK2_skl,X0) = k2_binop_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k2_autgroup(sK0_skl),X0,sK2_skl)
| ~ v1_funct_1(k2_autgroup(sK0_skl))
| ~ m2_relset_1(k2_autgroup(sK0_skl),k2_zfmisc_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl)),k1_autgroup(sK0_skl))
| ~ m2_fraenkel(X0,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl)) ),
inference(trivial_equality_resolution,[status(thm)],[f569]) ).
fof(f571,plain,
! [X0] :
( ~ l1_group_1(sK0_skl)
| ~ v1_funct_1(k2_autgroup(sK0_skl))
| k7_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),sK2_skl,X0) = k2_binop_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k2_autgroup(sK0_skl),X0,sK2_skl)
| ~ v3_group_1(sK0_skl)
| ~ m2_fraenkel(X0,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl))
| v3_struct_0(sK0_skl)
| ~ v1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f570,f142]) ).
fof(f573,plain,
( ~ l1_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v1_group_1(sK0_skl)
| v1_xboole_0(u1_struct_0(sK0_skl))
| m1_subset_1(sK2_skl,k1_autgroup(sK0_skl)) ),
inference(resolution,[status(thm)],[f556,f138]) ).
fof(f574,plain,
( ~ l1_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ v4_group_1(sK0_skl)
| v1_xboole_0(u1_struct_0(sK0_skl))
| m1_subset_1(sK2_skl,k1_autgroup(sK0_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f573,f84]) ).
fof(f575,plain,
( ~ v3_group_1(sK0_skl)
| ~ l1_group_1(sK0_skl)
| m1_subset_1(sK2_skl,k1_autgroup(sK0_skl))
| v1_xboole_0(u1_struct_0(sK0_skl))
| v3_struct_0(sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f574,f86]) ).
fof(f576,plain,
( ~ v3_group_1(sK0_skl)
| m1_subset_1(sK2_skl,k1_autgroup(sK0_skl))
| v1_xboole_0(u1_struct_0(sK0_skl))
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f575,f87]) ).
fof(f577,plain,
( v1_xboole_0(u1_struct_0(sK0_skl))
| ~ v3_group_1(sK0_skl)
| m1_subset_1(sK2_skl,k1_autgroup(sK0_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f576,f83]) ).
fof(f578,plain,
( v1_xboole_0(u1_struct_0(sK0_skl))
| m1_subset_1(sK2_skl,k1_autgroup(sK0_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f577,f85]) ).
fof(f764,plain,
k1_xboole_0 = sK17_skl,
inference(resolution,[status(thm)],[f281,f216]) ).
fof(f766,plain,
sK18_skl = k1_xboole_0,
inference(resolution,[status(thm)],[f281,f219]) ).
fof(f777,plain,
! [X0] :
( ~ v1_funct_1(k2_autgroup(sK0_skl))
| ~ v3_group_1(sK0_skl)
| k7_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),sK2_skl,X0) = k2_binop_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k2_autgroup(sK0_skl),X0,sK2_skl)
| ~ m2_fraenkel(X0,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl))
| ~ l1_group_1(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ v1_group_1(sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f571,f86]) ).
fof(f779,plain,
! [X0] :
( ~ v1_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)
| k7_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),sK2_skl,X0) = k2_binop_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k2_autgroup(sK0_skl),X0,sK2_skl)
| ~ m2_fraenkel(X0,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl))
| ~ l1_group_1(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ v1_group_1(sK0_skl) ),
inference(resolution,[status(thm)],[f777,f140]) ).
fof(f780,plain,
! [X0] :
( ~ v4_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| k7_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),sK2_skl,X0) = k2_binop_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k2_autgroup(sK0_skl),X0,sK2_skl)
| ~ m2_fraenkel(X0,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl))
| ~ l1_group_1(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ v1_group_1(sK0_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f779]) ).
fof(f781,plain,
! [X0] :
( ~ v4_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ m2_fraenkel(X0,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl))
| k2_binop_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k2_autgroup(sK0_skl),X0,sK2_skl) = k7_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),sK2_skl,X0)
| ~ l1_group_1(sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f780,f84]) ).
fof(f792,plain,
! [X0] :
( ~ v1_xboole_0(X0)
| X0 = sK18_skl ),
inference(backward_demodulation,[status(thm)],[f766,f281]) ).
fof(f828,plain,
! [X0] :
( ~ v3_group_1(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ m2_fraenkel(X0,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl))
| ~ v4_group_1(sK0_skl)
| k7_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),sK2_skl,X0) = k2_binop_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k2_autgroup(sK0_skl),X0,sK2_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f781,f87]) ).
fof(f829,plain,
! [X0] :
( v3_struct_0(sK0_skl)
| ~ m2_fraenkel(X0,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl))
| ~ v4_group_1(sK0_skl)
| k7_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),sK2_skl,X0) = k2_binop_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k2_autgroup(sK0_skl),X0,sK2_skl) ),
inference(resolution,[status(thm)],[f828,f85]) ).
fof(f830,plain,
! [X0] :
( ~ m2_fraenkel(X0,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl))
| k7_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),sK2_skl,X0) = k2_binop_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k2_autgroup(sK0_skl),X0,sK2_skl)
| v3_struct_0(sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f829,f86]) ).
fof(f831,plain,
! [X0] :
( ~ m2_fraenkel(X0,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),k1_autgroup(sK0_skl))
| k7_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),sK2_skl,X0) = k2_binop_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k2_autgroup(sK0_skl),X0,sK2_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f830,f83]) ).
fof(f833,plain,
k7_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),sK2_skl,sK1_skl) = k2_binop_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k2_autgroup(sK0_skl),sK1_skl,sK2_skl),
inference(resolution,[status(thm)],[f831,f477]) ).
fof(f897,plain,
sK18_skl = sK17_skl,
inference(backward_demodulation,[status(thm)],[f764,f766]) ).
fof(f1073,plain,
! [X0] :
( sK17_skl = X0
| ~ v1_xboole_0(X0) ),
inference(forward_demodulation,[status(thm)],[f897,f792]) ).
fof(f1574,plain,
! [X0] :
( ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| m1_relset_1(k2_autgroup(X0),k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
| v3_struct_0(X0) ),
inference(resolution,[status(thm)],[f260,f142]) ).
fof(f1583,plain,
( ~ v1_group_1(sK0_skl)
| ~ l1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| m1_relset_1(k2_autgroup(sK0_skl),k2_zfmisc_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl)),k1_autgroup(sK0_skl))
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f1574,f85]) ).
fof(f1585,plain,
( ~ v4_group_1(sK0_skl)
| ~ v1_group_1(sK0_skl)
| m1_relset_1(k2_autgroup(sK0_skl),k2_zfmisc_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl)),k1_autgroup(sK0_skl))
| ~ l1_group_1(sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f1583,f83]) ).
fof(f1624,plain,
( m1_relset_1(k2_autgroup(sK0_skl),k2_zfmisc_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl)),k1_autgroup(sK0_skl))
| ~ v1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f1585,f87]) ).
fof(f1625,plain,
( m1_relset_1(k2_autgroup(sK0_skl),k2_zfmisc_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl)),k1_autgroup(sK0_skl))
| ~ v4_group_1(sK0_skl) ),
inference(resolution,[status(thm)],[f1624,f84]) ).
fof(f1626,plain,
m1_relset_1(k2_autgroup(sK0_skl),k2_zfmisc_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl)),k1_autgroup(sK0_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f1625,f86]) ).
fof(f1707,plain,
l1_struct_0(sK0_skl),
inference(resolution,[status(thm)],[f154,f87]) ).
fof(f1719,plain,
( ~ v1_xboole_0(u1_struct_0(sK0_skl))
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f1707,f191]) ).
fof(f1722,plain,
~ v1_xboole_0(u1_struct_0(sK0_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f1719,f83]) ).
fof(f1780,plain,
m1_subset_1(sK2_skl,k1_autgroup(sK0_skl)),
inference(backward_subsumption_resolution,[status(thm)],[f578,f1722]) ).
fof(f1783,plain,
m1_subset_1(sK1_skl,k1_autgroup(sK0_skl)),
inference(backward_subsumption_resolution,[status(thm)],[f533,f1722]) ).
fof(f2039,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,k1_autgroup(sK0_skl))
| ~ m1_subset_1(X1,k1_autgroup(sK0_skl))
| ~ v1_funct_2(k2_autgroup(sK0_skl),k2_zfmisc_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl)),k1_autgroup(sK0_skl))
| v1_xboole_0(k1_autgroup(sK0_skl))
| k1_binop_1(k2_autgroup(sK0_skl),X0,X1) = k2_binop_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k2_autgroup(sK0_skl),X0,X1)
| ~ v1_funct_1(k2_autgroup(sK0_skl))
| v1_xboole_0(k1_autgroup(sK0_skl)) ),
inference(resolution,[status(thm)],[f1626,f250]) ).
fof(f2046,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,k1_autgroup(sK0_skl))
| ~ m1_subset_1(X1,k1_autgroup(sK0_skl))
| ~ v1_funct_1(k2_autgroup(sK0_skl))
| k2_binop_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k2_autgroup(sK0_skl),X0,X1) = k1_binop_1(k2_autgroup(sK0_skl),X0,X1)
| v1_xboole_0(k1_autgroup(sK0_skl))
| ~ v1_funct_2(k2_autgroup(sK0_skl),k2_zfmisc_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl)),k1_autgroup(sK0_skl)) ),
inference(duplicate_literals_removal,[status(thm)],[f2039]) ).
fof(f2081,plain,
! [X0,X1] :
( ~ v1_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ l1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ m1_subset_1(X0,k1_autgroup(sK0_skl))
| ~ m1_subset_1(X1,k1_autgroup(sK0_skl))
| k2_binop_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k2_autgroup(sK0_skl),X0,X1) = k1_binop_1(k2_autgroup(sK0_skl),X0,X1)
| v1_xboole_0(k1_autgroup(sK0_skl))
| ~ v1_funct_2(k2_autgroup(sK0_skl),k2_zfmisc_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl)),k1_autgroup(sK0_skl)) ),
inference(resolution,[status(thm)],[f2046,f140]) ).
fof(f2082,plain,
! [X0,X1] :
( v3_struct_0(sK0_skl)
| ~ m1_subset_1(X0,k1_autgroup(sK0_skl))
| ~ v1_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| ~ l1_group_1(sK0_skl)
| v1_xboole_0(k1_autgroup(sK0_skl))
| ~ v4_group_1(sK0_skl)
| ~ m1_subset_1(X1,k1_autgroup(sK0_skl))
| k2_binop_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k2_autgroup(sK0_skl),X0,X1) = k1_binop_1(k2_autgroup(sK0_skl),X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f2081,f141]) ).
fof(f2156,plain,
! [X0,X1] :
( v1_xboole_0(k1_autgroup(sK0_skl))
| ~ v3_group_1(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ l1_group_1(sK0_skl)
| k2_binop_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k2_autgroup(sK0_skl),X1,X0) = k1_binop_1(k2_autgroup(sK0_skl),X1,X0)
| ~ m1_subset_1(X1,k1_autgroup(sK0_skl))
| ~ v1_group_1(sK0_skl)
| ~ m1_subset_1(X0,k1_autgroup(sK0_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f2082,f86]) ).
fof(f2157,plain,
! [X0,X1] :
( v1_xboole_0(k1_autgroup(sK0_skl))
| ~ v3_group_1(sK0_skl)
| v3_struct_0(sK0_skl)
| k2_binop_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k2_autgroup(sK0_skl),X1,X0) = k1_binop_1(k2_autgroup(sK0_skl),X1,X0)
| ~ m1_subset_1(X1,k1_autgroup(sK0_skl))
| ~ v1_group_1(sK0_skl)
| ~ m1_subset_1(X0,k1_autgroup(sK0_skl)) ),
inference(resolution,[status(thm)],[f2156,f87]) ).
fof(f2158,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,k1_autgroup(sK0_skl))
| ~ m1_subset_1(X0,k1_autgroup(sK0_skl))
| k1_binop_1(k2_autgroup(sK0_skl),X0,X1) = k2_binop_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k2_autgroup(sK0_skl),X0,X1)
| v3_struct_0(sK0_skl)
| v1_xboole_0(k1_autgroup(sK0_skl))
| ~ v3_group_1(sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f2157,f84]) ).
fof(f2987,plain,
! [X0,X1] :
( v1_xboole_0(k1_autgroup(sK0_skl))
| ~ m1_subset_1(X1,k1_autgroup(sK0_skl))
| v3_struct_0(sK0_skl)
| ~ m1_subset_1(X0,k1_autgroup(sK0_skl))
| k2_binop_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k2_autgroup(sK0_skl),X0,X1) = k1_binop_1(k2_autgroup(sK0_skl),X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f2158,f85]) ).
fof(f3065,plain,
! [X0] :
( v1_xboole_0(k1_autgroup(sK0_skl))
| v3_struct_0(sK0_skl)
| ~ m1_subset_1(X0,k1_autgroup(sK0_skl))
| k2_binop_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k2_autgroup(sK0_skl),X0,sK2_skl) = k1_binop_1(k2_autgroup(sK0_skl),X0,sK2_skl) ),
inference(resolution,[status(thm)],[f1780,f2987]) ).
fof(f3070,plain,
! [X0] :
( k1_binop_1(k2_autgroup(sK0_skl),X0,sK2_skl) = k2_binop_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k2_autgroup(sK0_skl),X0,sK2_skl)
| ~ m1_subset_1(X0,k1_autgroup(sK0_skl))
| v1_xboole_0(k1_autgroup(sK0_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f3065,f83]) ).
fof(f3082,plain,
( k1_binop_1(k2_autgroup(sK0_skl),sK1_skl,sK2_skl) = k2_binop_1(k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k1_autgroup(sK0_skl),k2_autgroup(sK0_skl),sK1_skl,sK2_skl)
| v1_xboole_0(k1_autgroup(sK0_skl)) ),
inference(resolution,[status(thm)],[f1783,f3070]) ).
fof(f3091,plain,
( k1_binop_1(k2_autgroup(sK0_skl),sK1_skl,sK2_skl) = k7_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),u1_struct_0(sK0_skl),sK2_skl,sK1_skl)
| v1_xboole_0(k1_autgroup(sK0_skl)) ),
inference(forward_demodulation,[status(thm)],[f833,f3082]) ).
fof(f3092,plain,
v1_xboole_0(k1_autgroup(sK0_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f3091,f90]) ).
fof(f3167,plain,
sK17_skl = k1_autgroup(sK0_skl),
inference(resolution,[status(thm)],[f3092,f1073]) ).
fof(f3310,plain,
( ~ l1_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| m1_fraenkel(sK17_skl,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl))
| v3_struct_0(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v1_group_1(sK0_skl) ),
inference(paramodulation,[status(thm)],[f3167,f138]) ).
fof(f3324,plain,
( ~ v3_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ l1_group_1(sK0_skl)
| m1_fraenkel(sK17_skl,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl))
| v3_struct_0(sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f3310,f84]) ).
fof(f3934,plain,
( ~ l1_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| m1_fraenkel(sK17_skl,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f3324,f83]) ).
fof(f3935,plain,
( ~ l1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| m1_fraenkel(sK17_skl,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl)) ),
inference(resolution,[status(thm)],[f3934,f85]) ).
fof(f3937,plain,
( m1_fraenkel(sK17_skl,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl))
| ~ l1_group_1(sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f3935,f86]) ).
fof(f4187,plain,
m1_fraenkel(sK17_skl,u1_struct_0(sK0_skl),u1_struct_0(sK0_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f3937,f87]) ).
fof(f4197,plain,
~ v1_xboole_0(sK17_skl),
inference(resolution,[status(thm)],[f4187,f157]) ).
fof(f4204,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f4197,f216]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP624+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n011.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 20:19:11 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 138.36/17.94 % Refutation found
% 138.36/17.94 % SZS status Theorem for theBenchmark: Theorem is valid
% 138.36/17.94 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 78.29/18.12 % Elapsed time: 17.726745 seconds
% 78.29/18.12 % CPU time: 139.332969 seconds
% 78.29/18.12 % Total memory used: 713.919 MB
% 78.29/18.12 % Net memory used: 686.918 MB
%------------------------------------------------------------------------------