%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP624+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n013.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 : Fri Sep 25 01:34:54 PM UTC 2026
% Result : Theorem 6.84s 2.79s
% Output : CNFRefutation 6.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 125 ( 29 unt; 0 def)
% Number of atoms : 575 ( 61 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 775 ( 325 ~; 350 |; 74 &)
% ( 7 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-6 aty)
% Number of variables : 213 ( 0 sgn 203 !; 10 ?; 79 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
=> k1_binop_1(k2_autgroup(X0),X1,X2) = k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_autgroup) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
=> k1_binop_1(k2_autgroup(X0),X1,X2) = k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X2,X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f15,axiom,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( ( m2_relset_1(X1,k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
& v1_funct_2(X1,k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
& v1_funct_1(X1) )
=> ( X1 = k2_autgroup(X0)
<=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
=> ! [X3] :
( m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
=> k2_binop_1(k1_autgroup(X0),k1_autgroup(X0),k1_autgroup(X0),X1,X2,X3) = k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_autgroup) ).
fof(f18,axiom,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_autgroup) ).
fof(f24,axiom,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> ( m2_relset_1(k2_autgroup(X0),k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
& v1_funct_2(k2_autgroup(X0),k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
& v1_funct_1(k2_autgroup(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_autgroup) ).
fof(f32,axiom,
! [X0] :
( l1_group_1(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_group_1) ).
fof(f34,axiom,
! [X0,X1,X2] :
( m1_fraenkel(X2,X0,X1)
=> ( v1_fraenkel(X2)
& ~ v1_xboole_0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_fraenkel) ).
fof(f50,axiom,
! [X0] :
( ( l1_struct_0(X0)
& ~ v3_struct_0(X0) )
=> ~ v1_xboole_0(u1_struct_0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f67,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( m1_subset_1(X5,X1)
& m1_subset_1(X4,X0)
& m1_relset_1(X3,k2_zfmisc_1(X0,X1),X2)
& v1_funct_2(X3,k2_zfmisc_1(X0,X1),X2)
& v1_funct_1(X3)
& ~ v1_xboole_0(X1)
& ~ v1_xboole_0(X0) )
=> k2_binop_1(X0,X1,X2,X3,X4,X5) = k1_binop_1(X3,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).
fof(f69,axiom,
! [X0,X1,X2] :
( ( m1_fraenkel(X2,X0,X1)
& ~ v1_xboole_0(X1) )
=> ! [X3] :
( m2_fraenkel(X3,X0,X1,X2)
<=> m1_subset_1(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_fraenkel) ).
fof(f70,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
<=> m1_relset_1(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f72,axiom,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
=> m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_autgroup) ).
fof(f88,plain,
? [X0] :
( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
& ? [X2] :
( m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
& k1_binop_1(k2_autgroup(X0),X1,X2) != k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X2,X1) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f89,plain,
? [X0] :
( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
& ? [X2] :
( m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
& k1_binop_1(k2_autgroup(X0),X1,X2) != k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X2,X1) ) ) ),
inference(flattening,[],[f88]) ).
fof(f108,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_relset_1(X1,k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
| ~ v1_funct_2(X1,k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
| ~ v1_funct_1(X1)
| ( X1 = k2_autgroup(X0)
<=> ! [X2] :
( ~ m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ! [X3] :
( ~ m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| k2_binop_1(k1_autgroup(X0),k1_autgroup(X0),k1_autgroup(X0),X1,X2,X3) = k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X3,X2) ) ) ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f109,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_relset_1(X1,k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
| ~ v1_funct_2(X1,k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
| ~ v1_funct_1(X1)
| ( X1 = k2_autgroup(X0)
<=> ! [X2] :
( ~ m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ! [X3] :
( ~ m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| k2_binop_1(k1_autgroup(X0),k1_autgroup(X0),k1_autgroup(X0),X1,X2,X3) = k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X3,X2) ) ) ) ) ),
inference(flattening,[],[f108]) ).
fof(f112,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f18]) ).
fof(f113,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
inference(flattening,[],[f112]) ).
fof(f114,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ( m2_relset_1(k2_autgroup(X0),k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
& v1_funct_2(k2_autgroup(X0),k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
& v1_funct_1(k2_autgroup(X0)) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f115,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ( m2_relset_1(k2_autgroup(X0),k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
& v1_funct_2(k2_autgroup(X0),k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
& v1_funct_1(k2_autgroup(X0)) ) ),
inference(flattening,[],[f114]) ).
fof(f124,plain,
! [X0] :
( ~ l1_group_1(X0)
| l1_struct_0(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f125,plain,
! [X0,X1,X2] :
( ~ m1_fraenkel(X2,X0,X1)
| ( v1_fraenkel(X2)
& ~ v1_xboole_0(X2) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f136,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f50]) ).
fof(f137,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(flattening,[],[f136]) ).
fof(f142,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ m1_subset_1(X5,X1)
| ~ m1_subset_1(X4,X0)
| ~ m1_relset_1(X3,k2_zfmisc_1(X0,X1),X2)
| ~ v1_funct_2(X3,k2_zfmisc_1(X0,X1),X2)
| ~ v1_funct_1(X3)
| v1_xboole_0(X1)
| v1_xboole_0(X0)
| k2_binop_1(X0,X1,X2,X3,X4,X5) = k1_binop_1(X3,X4,X5) ),
inference(ennf_transformation,[],[f67]) ).
fof(f143,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ m1_subset_1(X5,X1)
| ~ m1_subset_1(X4,X0)
| ~ m1_relset_1(X3,k2_zfmisc_1(X0,X1),X2)
| ~ v1_funct_2(X3,k2_zfmisc_1(X0,X1),X2)
| ~ v1_funct_1(X3)
| v1_xboole_0(X1)
| v1_xboole_0(X0)
| k2_binop_1(X0,X1,X2,X3,X4,X5) = k1_binop_1(X3,X4,X5) ),
inference(flattening,[],[f142]) ).
fof(f146,plain,
! [X0,X1,X2] :
( ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1)
| ! [X3] :
( m2_fraenkel(X3,X0,X1,X2)
<=> m1_subset_1(X3,X2) ) ),
inference(ennf_transformation,[],[f69]) ).
fof(f147,plain,
! [X0,X1,X2] :
( ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1)
| ! [X3] :
( m2_fraenkel(X3,X0,X1,X2)
<=> m1_subset_1(X3,X2) ) ),
inference(flattening,[],[f146]) ).
fof(f148,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
| m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) ) ),
inference(ennf_transformation,[],[f72]) ).
fof(f149,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
| m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) ) ),
inference(flattening,[],[f148]) ).
fof(f160,plain,
( l1_group_1(sK0)
& v4_group_1(sK0)
& v3_group_1(sK0)
& v1_group_1(sK0)
& ~ v3_struct_0(sK0)
& m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
& m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
& k1_binop_1(k2_autgroup(sK0),sK1,sK2) != k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK2,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f89]) ).
fof(f161,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_relset_1(X1,k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
| ~ v1_funct_2(X1,k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
| ~ v1_funct_1(X1)
| ( ( k2_autgroup(X0) != X1
| ! [X2] :
( ~ m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ! [X3] :
( ~ m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| k2_binop_1(k1_autgroup(X0),k1_autgroup(X0),k1_autgroup(X0),X1,X2,X3) = k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X3,X2) ) ) )
& ( ? [X2] :
( m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
& ? [X3] :
( m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
& k2_binop_1(k1_autgroup(X0),k1_autgroup(X0),k1_autgroup(X0),X1,X2,X3) != k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X3,X2) ) )
| X1 = k2_autgroup(X0) ) ) ) ),
inference(nnf_transformation,[],[f109]) ).
fof(f162,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_relset_1(X1,k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
| ~ v1_funct_2(X1,k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
| ~ v1_funct_1(X1)
| ( ( k2_autgroup(X0) != X1
| ! [X4] :
( ~ m2_fraenkel(X4,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ! [X5] :
( ~ m2_fraenkel(X5,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| k2_binop_1(k1_autgroup(X0),k1_autgroup(X0),k1_autgroup(X0),X1,X4,X5) = k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X5,X4) ) ) )
& ( ? [X2] :
( m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
& ? [X3] :
( m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
& k2_binop_1(k1_autgroup(X0),k1_autgroup(X0),k1_autgroup(X0),X1,X2,X3) != k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X3,X2) ) )
| X1 = k2_autgroup(X0) ) ) ) ),
inference(rectify,[],[f161]) ).
fof(f163,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_relset_1(X1,k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
| ~ v1_funct_2(X1,k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
| ~ v1_funct_1(X1)
| ( ( k2_autgroup(X0) != X1
| ! [X4] :
( ~ m2_fraenkel(X4,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ! [X5] :
( ~ m2_fraenkel(X5,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| k2_binop_1(k1_autgroup(X0),k1_autgroup(X0),k1_autgroup(X0),X1,X4,X5) = k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X5,X4) ) ) )
& ( ( m2_fraenkel(sK3(X0,X1),u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
& m2_fraenkel(sK4(X0,X1),u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
& k2_binop_1(k1_autgroup(X0),k1_autgroup(X0),k1_autgroup(X0),X1,sK3(X0,X1),sK4(X0,X1)) != k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),sK4(X0,X1),sK3(X0,X1)) )
| X1 = k2_autgroup(X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X2,sK3(X0,X1)),skolemize(X3,sK4(X0,X1))],[f162]) ).
fof(f185,plain,
! [X0,X1,X2] :
( ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1)
| ! [X3] :
( ( ~ m2_fraenkel(X3,X0,X1,X2)
| m1_subset_1(X3,X2) )
& ( ~ m1_subset_1(X3,X2)
| m2_fraenkel(X3,X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f147]) ).
fof(f186,plain,
! [X0,X1,X2] :
( ( ~ m2_relset_1(X2,X0,X1)
| m1_relset_1(X2,X0,X1) )
& ( ~ m1_relset_1(X2,X0,X1)
| m2_relset_1(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f70]) ).
fof(f187,plain,
l1_group_1(sK0),
inference(cnf_transformation,[],[f160]) ).
fof(f188,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f160]) ).
fof(f189,plain,
v3_group_1(sK0),
inference(cnf_transformation,[],[f160]) ).
fof(f190,plain,
v1_group_1(sK0),
inference(cnf_transformation,[],[f160]) ).
fof(f191,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f160]) ).
fof(f192,plain,
m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)),
inference(cnf_transformation,[],[f160]) ).
fof(f193,plain,
m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)),
inference(cnf_transformation,[],[f160]) ).
fof(f194,plain,
k1_binop_1(k2_autgroup(sK0),sK1,sK2) != k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK2,sK1),
inference(cnf_transformation,[],[f160]) ).
fof(f215,plain,
! [X0,X1,X4,X5] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ~ m2_relset_1(X1,k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
| ~ v1_funct_2(X1,k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
| ~ v1_funct_1(X1)
| k2_autgroup(X0) != X1
| ~ m2_fraenkel(X4,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ~ m2_fraenkel(X5,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| k2_binop_1(k1_autgroup(X0),k1_autgroup(X0),k1_autgroup(X0),X1,X4,X5) = k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X5,X4) ),
inference(cnf_transformation,[],[f163]) ).
fof(f222,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f113]) ).
fof(f223,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| m2_relset_1(k2_autgroup(X0),k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0)) ),
inference(cnf_transformation,[],[f115]) ).
fof(f224,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| v1_funct_2(k2_autgroup(X0),k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0)) ),
inference(cnf_transformation,[],[f115]) ).
fof(f225,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| v1_funct_1(k2_autgroup(X0)) ),
inference(cnf_transformation,[],[f115]) ).
fof(f232,plain,
! [X0] :
( ~ l1_group_1(X0)
| l1_struct_0(X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f234,plain,
! [X2,X0,X1] :
( ~ m1_fraenkel(X2,X0,X1)
| ~ v1_xboole_0(X2) ),
inference(cnf_transformation,[],[f125]) ).
fof(f253,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f137]) ).
fof(f292,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ m1_subset_1(X5,X1)
| ~ m1_subset_1(X4,X0)
| ~ m1_relset_1(X3,k2_zfmisc_1(X0,X1),X2)
| ~ v1_funct_2(X3,k2_zfmisc_1(X0,X1),X2)
| ~ v1_funct_1(X3)
| v1_xboole_0(X1)
| v1_xboole_0(X0)
| k2_binop_1(X0,X1,X2,X3,X4,X5) = k1_binop_1(X3,X4,X5) ),
inference(cnf_transformation,[],[f143]) ).
fof(f294,plain,
! [X2,X3,X0,X1] :
( ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1)
| ~ m2_fraenkel(X3,X0,X1,X2)
| m1_subset_1(X3,X2) ),
inference(cnf_transformation,[],[f185]) ).
fof(f296,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f186]) ).
fof(f299,plain,
! [X0,X1] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
| m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) ),
inference(cnf_transformation,[],[f149]) ).
fof(f309,plain,
! [X0,X4,X5] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ~ m2_relset_1(k2_autgroup(X0),k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
| ~ v1_funct_2(k2_autgroup(X0),k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
| ~ v1_funct_1(k2_autgroup(X0))
| ~ m2_fraenkel(X4,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ~ m2_fraenkel(X5,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X5,X4) = k2_binop_1(k1_autgroup(X0),k1_autgroup(X0),k1_autgroup(X0),k2_autgroup(X0),X4,X5) ),
inference(equality_resolution,[],[f215]) ).
tcf(c_49,negated_conjecture,
k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK2,sK1) != k1_binop_1(k2_autgroup(sK0),sK1,sK2),
inference(cnf_transformation,[],[f194]) ).
tcf(c_50,negated_conjecture,
m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)),
inference(cnf_transformation,[],[f193]) ).
tcf(c_51,negated_conjecture,
m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)),
inference(cnf_transformation,[],[f192]) ).
tcf(c_52,negated_conjecture,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f191]) ).
tcf(c_53,negated_conjecture,
v1_group_1(sK0),
inference(cnf_transformation,[],[f190]) ).
tcf(c_54,negated_conjecture,
v3_group_1(sK0),
inference(cnf_transformation,[],[f189]) ).
tcf(c_55,negated_conjecture,
v4_group_1(sK0),
inference(cnf_transformation,[],[f188]) ).
tcf(c_56,negated_conjecture,
l1_group_1(sK0),
inference(cnf_transformation,[],[f187]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| ( k2_binop_1(k1_autgroup(X0),k1_autgroup(X0),k1_autgroup(X0),k2_autgroup(X0),X2,X1) = k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X1,X2) )
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| ~ v1_funct_1(k2_autgroup(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))
| ~ m2_relset_1(k2_autgroup(X0),k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
| ~ v1_funct_2(k2_autgroup(X0),k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0)) ),
inference(cnf_transformation,[],[f309]) ).
tcf(c_75,plain,
! [X0: $i] :
( v3_struct_0(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) ),
inference(cnf_transformation,[],[f222]) ).
tcf(c_76,plain,
! [X0: $i] :
( v3_struct_0(X0)
| v1_funct_1(k2_autgroup(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0) ),
inference(cnf_transformation,[],[f225]) ).
tcf(c_77,plain,
! [X0: $i] :
( v3_struct_0(X0)
| v1_funct_2(k2_autgroup(X0),k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0) ),
inference(cnf_transformation,[],[f224]) ).
tcf(c_78,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m2_relset_1(k2_autgroup(X0),k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0) ),
inference(cnf_transformation,[],[f223]) ).
tcf(c_85,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f232]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ v1_xboole_0(X0)
| ~ m1_fraenkel(X0,X1,X2) ),
inference(cnf_transformation,[],[f234]) ).
tcf(c_106,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ l1_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f253]) ).
tcf(c_145,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( v1_xboole_0(X2)
| v1_xboole_0(X1)
| ( k2_binop_1(X1,X2,X3,X0,X5,X4) = k1_binop_1(X0,X5,X4) )
| ~ v1_funct_1(X0)
| ~ m1_subset_1(X5,X1)
| ~ m1_subset_1(X4,X2)
| ~ m1_relset_1(X0,k2_zfmisc_1(X1,X2),X3)
| ~ v1_funct_2(X0,k2_zfmisc_1(X1,X2),X3) ),
inference(cnf_transformation,[],[f292]) ).
tcf(c_148,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X2)
| m1_subset_1(X0,X3)
| ~ m1_fraenkel(X3,X1,X2)
| ~ m2_fraenkel(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f294]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i,X2: $i] :
( m1_relset_1(X0,X1,X2)
| ~ m2_relset_1(X0,X1,X2) ),
inference(cnf_transformation,[],[f296]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m2_fraenkel(X0,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(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)) ),
inference(cnf_transformation,[],[f299]) ).
tcf(c_167,plain,
( l1_struct_0(sK0)
| ~ l1_group_1(sK0) ),
inference(instantiation,[status(thm)],[c_85]) ).
tcf(c_188,plain,
( v3_struct_0(sK0)
| ~ l1_struct_0(sK0)
| ~ v1_xboole_0(u1_struct_0(sK0)) ),
inference(instantiation,[status(thm)],[c_106]) ).
tcf(c_206,plain,
( v3_struct_0(sK0)
| v1_funct_1(k2_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v1_group_1(sK0) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_211,plain,
( v3_struct_0(sK0)
| m1_fraenkel(k1_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v1_group_1(sK0) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_215,plain,
( v3_struct_0(sK0)
| m2_relset_1(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v1_group_1(sK0) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_216,plain,
( v3_struct_0(sK0)
| v1_funct_2(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v1_group_1(sK0) ),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_237,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| ( k2_binop_1(k1_autgroup(X0),k1_autgroup(X0),k1_autgroup(X0),k2_autgroup(X0),X2,X1) = k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X1,X2) )
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ~ m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_72,c_76,c_78,c_77,c_72]) ).
tcf(c_238,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| ( k2_binop_1(k1_autgroup(X1),k1_autgroup(X1),k1_autgroup(X1),k2_autgroup(X1),X2,X0) = k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X0,X2) )
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| ~ m2_fraenkel(X0,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1)) ),
inference(renaming,[status(thm)],[c_237]) ).
tcf(c_266,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ m1_fraenkel(X0,X1,X2)
| ~ v1_xboole_0(X0) ),
inference(prop_impl_just,[status(thm)],[c_86]) ).
tcf(c_267,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ v1_xboole_0(X0)
| ~ m1_fraenkel(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_266]) ).
tcf(c_1281,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m2_relset_1(k2_autgroup(X0),k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v1_group_1(X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_78]) ).
tcf(c_1282,plain,
( v3_struct_0(sK0)
| m2_relset_1(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v1_group_1(sK0) ),
inference(unflattening,[status(thm)],[c_1281]) ).
tcf(c_1283,plain,
m2_relset_1(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0)),
inference(global_subsumption_just,[status(thm)],[c_1282,c_56,c_55,c_54,c_53,c_52,c_215]) ).
tcf(c_1302,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v1_group_1(X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_75]) ).
tcf(c_1303,plain,
( v3_struct_0(sK0)
| m1_fraenkel(k1_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v1_group_1(sK0) ),
inference(unflattening,[status(thm)],[c_1302]) ).
tcf(c_1304,plain,
m1_fraenkel(k1_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0)),
inference(global_subsumption_just,[status(thm)],[c_1303,c_56,c_55,c_54,c_53,c_52,c_211]) ).
tcf(c_1330,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| ( k2_binop_1(k1_autgroup(X0),k1_autgroup(X0),k1_autgroup(X0),k2_autgroup(X0),X2,X1) = k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X1,X2) )
| ~ l1_group_1(X0)
| ~ v4_group_1(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))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_238]) ).
tcf(c_1331,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| ( k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),X1,X0) = k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),X0,X1) )
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v1_group_1(sK0)
| ~ m2_fraenkel(X1,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)) ),
inference(unflattening,[status(thm)],[c_1330]) ).
tcf(c_1333,plain,
! [X0: $i,X1: $i] :
( ~ m2_fraenkel(X1,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ( k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),X1,X0) = k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),X0,X1) ) ),
inference(global_subsumption_just,[status(thm)],[c_1331,c_56,c_55,c_53,c_52,c_1331]) ).
tcf(c_1334,plain,
! [X0: $i,X1: $i] :
( ( k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),X1,X0) = k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),X0,X1) )
| ~ m2_fraenkel(X1,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)) ),
inference(renaming,[status(thm)],[c_1333]) ).
tcf(c_1345,plain,
! [X0: $i,X1: $i] :
( v3_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)
| ~ v1_group_1(X0)
| ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_152]) ).
tcf(c_1346,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v1_group_1(sK0)
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) ),
inference(unflattening,[status(thm)],[c_1345]) ).
tcf(c_1348,plain,
! [X0: $i] :
( ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)) ),
inference(global_subsumption_just,[status(thm)],[c_1346,c_56,c_55,c_53,c_52,c_1346]) ).
tcf(c_1349,plain,
! [X0: $i] :
( m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) ),
inference(renaming,[status(thm)],[c_1348]) ).
tcf(c_2467,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ v1_xboole_0(X0)
| ( k1_autgroup(sK0) != X0 )
| ( u1_struct_0(sK0) != X2 )
| ( u1_struct_0(sK0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_267,c_1304]) ).
tcf(c_2468,plain,
~ v1_xboole_0(k1_autgroup(sK0)),
inference(unflattening,[status(thm)],[c_2467]) ).
tcf(c_2626,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X1)
| m1_subset_1(X3,X2)
| ~ m2_fraenkel(X3,X0,X1,X2)
| ( k1_autgroup(sK0) != X2 )
| ( u1_struct_0(sK0) != X1 )
| ( u1_struct_0(sK0) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_148,c_1304]) ).
tcf(c_2627,plain,
! [X0: $i] :
( v1_xboole_0(u1_struct_0(sK0))
| m1_subset_1(X0,k1_autgroup(sK0))
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)) ),
inference(unflattening,[status(thm)],[c_2626]) ).
tcf(c_2629,plain,
! [X0: $i] :
( ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| m1_subset_1(X0,k1_autgroup(sK0)) ),
inference(global_subsumption_just,[status(thm)],[c_2627,c_56,c_52,c_167,c_188,c_2627]) ).
tcf(c_2630,plain,
! [X0: $i] :
( m1_subset_1(X0,k1_autgroup(sK0))
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)) ),
inference(renaming,[status(thm)],[c_2629]) ).
tcf(c_9509,plain,
m1_relset_1(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0)),
inference(superposition,[status(thm)],[c_1283,c_150]) ).
tcf(c_11358,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(k1_autgroup(sK0))
| ( k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),X1,X0) = k1_binop_1(k2_autgroup(sK0),X1,X0) )
| ~ v1_funct_1(k2_autgroup(sK0))
| ~ m1_subset_1(X1,k1_autgroup(sK0))
| ~ m1_subset_1(X0,k1_autgroup(sK0))
| ~ v1_funct_2(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0)) ),
inference(superposition,[status(thm)],[c_9509,c_145]) ).
tcf(c_13733,plain,
! [X0: $i,X1: $i] :
( ~ m1_subset_1(X1,k1_autgroup(sK0))
| ~ m1_subset_1(X0,k1_autgroup(sK0))
| ( k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),X1,X0) = k1_binop_1(k2_autgroup(sK0),X1,X0) ) ),
inference(global_subsumption_just,[status(thm)],[c_11358,c_56,c_55,c_54,c_53,c_52,c_206,c_216,c_2468,c_11358]) ).
tcf(c_13734,plain,
! [X0: $i,X1: $i] :
( ( k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),X1,X0) = k1_binop_1(k2_autgroup(sK0),X1,X0) )
| ~ m1_subset_1(X1,k1_autgroup(sK0))
| ~ m1_subset_1(X0,k1_autgroup(sK0)) ),
inference(renaming,[status(thm)],[c_13733]) ).
tcf(c_14028,plain,
m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)),
inference(superposition,[status(thm)],[c_50,c_1349]) ).
tcf(c_14029,plain,
m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)),
inference(superposition,[status(thm)],[c_51,c_1349]) ).
tcf(c_14033,plain,
! [X0: $i] :
( ( k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),sK1,X0) = k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),X0,sK1) )
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)) ),
inference(superposition,[status(thm)],[c_14029,c_1334]) ).
tcf(c_14050,plain,
m1_subset_1(sK2,k1_autgroup(sK0)),
inference(superposition,[status(thm)],[c_14028,c_2630]) ).
tcf(c_14051,plain,
m1_subset_1(sK1,k1_autgroup(sK0)),
inference(superposition,[status(thm)],[c_14029,c_2630]) ).
tcf(c_14105,plain,
k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),sK1,sK2) = k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK2,sK1),
inference(superposition,[status(thm)],[c_14028,c_14033]) ).
tcf(c_14199,plain,
m1_relset_1(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0)),
inference(superposition,[status(thm)],[c_1283,c_150]) ).
tcf(c_14415,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(k1_autgroup(sK0))
| ( k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),X1,X0) = k1_binop_1(k2_autgroup(sK0),X1,X0) )
| ~ v1_funct_1(k2_autgroup(sK0))
| ~ m1_subset_1(X1,k1_autgroup(sK0))
| ~ m1_subset_1(X0,k1_autgroup(sK0))
| ~ v1_funct_2(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0)) ),
inference(superposition,[status(thm)],[c_14199,c_145]) ).
tcf(c_14742,plain,
! [X0: $i,X1: $i] :
( ~ m1_subset_1(X1,k1_autgroup(sK0))
| ~ m1_subset_1(X0,k1_autgroup(sK0))
| ( k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),X1,X0) = k1_binop_1(k2_autgroup(sK0),X1,X0) ) ),
inference(global_subsumption_just,[status(thm)],[c_14415,c_13734]) ).
tcf(c_14743,plain,
! [X0: $i,X1: $i] :
( ( k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),X1,X0) = k1_binop_1(k2_autgroup(sK0),X1,X0) )
| ~ m1_subset_1(X1,k1_autgroup(sK0))
| ~ m1_subset_1(X0,k1_autgroup(sK0)) ),
inference(renaming,[status(thm)],[c_14742]) ).
tcf(c_14747,plain,
! [X0: $i] :
( ( k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),X0,sK2) = k1_binop_1(k2_autgroup(sK0),X0,sK2) )
| ~ m1_subset_1(X0,k1_autgroup(sK0)) ),
inference(superposition,[status(thm)],[c_14050,c_14743]) ).
tcf(c_14767,plain,
k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),sK1,sK2) = k1_binop_1(k2_autgroup(sK0),sK1,sK2),
inference(superposition,[status(thm)],[c_14051,c_14747]) ).
tcf(c_15063,plain,
k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK2,sK1) = k1_binop_1(k2_autgroup(sK0),sK1,sK2),
inference(superposition,[status(thm)],[c_14767,c_14105]) ).
tcf(c_15064,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_15063,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP624+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n013.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 15:17:06 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/0.40 Running first-order theorem proving
% 0.03/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.41
% 0.03/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.41
% 0.03/0.41 % Detected problem language: tptp
% 0.03/0.42 % Proving...
% 6.84/2.79 % SZS status Started for theBenchmark.p
% 6.84/2.79 % SZS status Theorem for theBenchmark.p
% 6.84/2.79
% 6.84/2.79 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.84/2.79
% 6.84/2.79 % ------ iProver source info
% 6.84/2.79
% 6.84/2.79 % git: date: 2026-07-19 20:42:38 +0200
% 6.84/2.79 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.84/2.79 % git: non_committed_changes: false
% 6.84/2.79
% 6.84/2.79 % ------ Parsing...
% 6.84/2.79 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.84/2.79
% 6.84/2.79 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e %
% 6.84/2.79
% 6.84/2.79 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 6.84/2.79
% 6.84/2.79 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 6.84/2.79 % ------ Proving...
% 6.84/2.79 % ------ Problem Properties
% 6.84/2.79
% 6.84/2.79 %
% 6.84/2.79 % clauses 142
% 6.84/2.79 % conjectures 6
% 6.84/2.79 % EPR 40
% 6.84/2.79 % Horn 122
% 6.84/2.79 % unary 66
% 6.84/2.79 % binary 38
% 6.84/2.79 % lits 310
% 6.84/2.79 % lits eq 22
% 6.84/2.79 % fd_pure 0
% 6.84/2.79 % fd_pseudo 0
% 6.84/2.79 % fd_cond 7
% 6.84/2.79 % fd_pseudo_cond 3
% 6.84/2.79 % AC symbols 0
% 6.84/2.79
% 6.84/2.79 % ------ Input Options Time Limit: Unbounded
% 6.84/2.79
% 6.84/2.79
% 6.84/2.79 % ------
% 6.84/2.79 % Current options:
% 6.84/2.79 % ------
% 6.84/2.79
% 6.84/2.79
% 6.84/2.79 %
% 6.84/2.79
% 6.84/2.79 % ------ Proving...
% 6.84/2.79 %
% 6.84/2.79
% 6.84/2.79 % SZS status Theorem for theBenchmark.p
% 6.84/2.79
% 6.84/2.79 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.84/2.79
% 6.84/2.79
%------------------------------------------------------------------------------