%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP620+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 12:40:23 PM UTC 2026
% Result : Theorem 0.66s 0.63s
% Output : CNFRefutation 0.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 82 ( 26 unt; 0 def)
% Number of atoms : 693 ( 31 equ)
% Maximal formula atoms : 231 ( 8 avg)
% Number of connectives : 992 ( 381 ~; 424 |; 136 &)
% ( 8 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 38 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 130 ( 2 sgn 79 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t7_autgroup,conjecture,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> m2_fraenkel(k2_funct_1(X2),u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_autgroup) ).
fof(dt_k1_autgroup,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> m1_fraenkel(k1_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_autgroup) ).
fof(fc1_struct_0,axiom,
! [X1] :
( ( l1_struct_0(X1)
& ~ v3_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(dt_l1_group_1,axiom,
! [X1] :
( l1_group_1(X1)
=> l1_struct_0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_group_1) ).
fof(redefinition_m2_fraenkel,axiom,
! [X1,X2,X3] :
( ( m1_fraenkel(X3,X1,X2)
& ~ v1_xboole_0(X2) )
=> ! [X4] :
( m2_fraenkel(X4,X1,X2,X3)
<=> m1_subset_1(X4,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_fraenkel) ).
fof(dt_m1_fraenkel,axiom,
! [X1,X2,X3] :
( m1_fraenkel(X3,X1,X2)
=> ( v1_fraenkel(X3)
& ~ v1_xboole_0(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_fraenkel) ).
fof(d1_autgroup,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1))
=> ( X2 = k1_autgroup(X1)
<=> ( ! [X3] :
( ( m2_relset_1(X3,u1_struct_0(X1),u1_struct_0(X1))
& v1_group_6(X3,X1,X1)
& v1_funct_2(X3,u1_struct_0(X1),u1_struct_0(X1))
& v1_funct_1(X3) )
=> ( r2_hidden(X3,X2)
<=> ( v3_group_6(X3,X1,X1)
& v2_funct_1(X3) ) ) )
& ! [X3] :
( m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),X2)
=> ( m2_relset_1(X3,u1_struct_0(X1),u1_struct_0(X1))
& v1_group_6(X3,X1,X1)
& v1_funct_2(X3,u1_struct_0(X1),u1_struct_0(X1))
& v1_funct_1(X3) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_autgroup) ).
fof(t73_group_6,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( l1_group_1(X2)
& v4_group_1(X2)
& v3_group_1(X2)
& ~ v3_struct_0(X2) )
=> ! [X3] :
( ( m2_relset_1(X3,u1_struct_0(X2),u1_struct_0(X1))
& v1_group_6(X3,X2,X1)
& v1_funct_2(X3,u1_struct_0(X2),u1_struct_0(X1))
& v1_funct_1(X3) )
=> ! [X4] :
( ( m2_relset_1(X4,u1_struct_0(X1),u1_struct_0(X2))
& v1_group_6(X4,X1,X2)
& v1_funct_2(X4,u1_struct_0(X1),u1_struct_0(X2))
& v1_funct_1(X4) )
=> ( ( X4 = k2_funct_1(X3)
& v4_group_6(X3,X2,X1) )
=> v4_group_6(X4,X1,X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_group_6) ).
fof(t6_autgroup,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> ( m2_relset_1(k2_funct_1(X2),u1_struct_0(X1),u1_struct_0(X1))
& v1_group_6(k2_funct_1(X2),X1,X1)
& v1_funct_2(k2_funct_1(X2),u1_struct_0(X1),u1_struct_0(X1))
& v1_funct_1(k2_funct_1(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_autgroup) ).
fof(t5_autgroup,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( m2_relset_1(X2,u1_struct_0(X1),u1_struct_0(X1))
& v1_group_6(X2,X1,X1)
& v1_funct_2(X2,u1_struct_0(X1),u1_struct_0(X1))
& v1_funct_1(X2) )
=> ( r2_hidden(X2,k1_autgroup(X1))
<=> v4_group_6(X2,X1,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_autgroup) ).
fof(t2_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,X2)
=> ( r2_hidden(X1,X2)
| v1_xboole_0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(t1_subset,axiom,
! [X1,X2] :
( r2_hidden(X1,X2)
=> m1_subset_1(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(c_0_12,negated_conjecture,
~ ! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> m2_fraenkel(k2_funct_1(X2),u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1)) ) ),
inference(assume_negation,[status(cth)],[t7_autgroup]) ).
fof(c_0_13,negated_conjecture,
~ ! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> m2_fraenkel(k2_funct_1(X2),u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1)) ) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_14,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> m1_fraenkel(k1_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k1_autgroup]) ).
fof(c_0_15,plain,
! [X1] :
( ( l1_struct_0(X1)
& ~ v3_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).
fof(c_0_16,plain,
! [X43] :
( l1_struct_0(X43)
| ~ l1_group_1(X43) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_group_1])])]) ).
fof(c_0_17,negated_conjecture,
( ~ m2_fraenkel(k2_funct_1(esk2_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k1_autgroup(esk1_0))
& m2_fraenkel(esk2_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0),k1_autgroup(esk1_0))
& l1_group_1(esk1_0)
& v4_group_1(esk1_0)
& v3_group_1(esk1_0)
& v1_group_1(esk1_0)
& ~ v3_struct_0(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
fof(c_0_18,plain,
! [X1,X2,X3] :
( ( m1_fraenkel(X3,X1,X2)
& ~ v1_xboole_0(X2) )
=> ! [X4] :
( m2_fraenkel(X4,X1,X2,X3)
<=> m1_subset_1(X4,X3) ) ),
inference(fof_simplification,[status(thm)],[redefinition_m2_fraenkel]) ).
fof(c_0_19,plain,
! [X41] :
( m1_fraenkel(k1_autgroup(X41),u1_struct_0(X41),u1_struct_0(X41))
| ~ l1_group_1(X41)
| ~ v4_group_1(X41)
| ~ v3_group_1(X41)
| ~ v1_group_1(X41)
| v3_struct_0(X41) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
fof(c_0_20,plain,
! [X74] :
( ~ v1_xboole_0(u1_struct_0(X74))
| ~ l1_struct_0(X74)
| v3_struct_0(X74) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
cnf(c_0_21,plain,
( ~ l1_group_1(X1)
| l1_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_23,plain,
! [X1,X2,X3] :
( m1_fraenkel(X3,X1,X2)
=> ( v1_fraenkel(X3)
& ~ v1_xboole_0(X3) ) ),
inference(fof_simplification,[status(thm)],[dt_m1_fraenkel]) ).
fof(c_0_24,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1))
=> ( X2 = k1_autgroup(X1)
<=> ( ! [X3] :
( ( m2_relset_1(X3,u1_struct_0(X1),u1_struct_0(X1))
& v1_group_6(X3,X1,X1)
& v1_funct_2(X3,u1_struct_0(X1),u1_struct_0(X1))
& v1_funct_1(X3) )
=> ( r2_hidden(X3,X2)
<=> ( v3_group_6(X3,X1,X1)
& v2_funct_1(X3) ) ) )
& ! [X3] :
( m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),X2)
=> ( m2_relset_1(X3,u1_struct_0(X1),u1_struct_0(X1))
& v1_group_6(X3,X1,X1)
& v1_funct_2(X3,u1_struct_0(X1),u1_struct_0(X1))
& v1_funct_1(X3) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d1_autgroup]) ).
fof(c_0_25,plain,
! [X101,X102,X103,X104] :
( ( ~ m1_fraenkel(X103,X101,X102)
| v1_xboole_0(X102)
| m2_fraenkel(X104,X101,X102,X103)
| ~ m1_subset_1(X104,X103) )
& ( ~ m1_fraenkel(X103,X101,X102)
| v1_xboole_0(X102)
| m1_subset_1(X104,X103)
| ~ m2_fraenkel(X104,X101,X102,X103) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])])]) ).
cnf(c_0_26,plain,
( ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| m1_fraenkel(k1_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,negated_conjecture,
v1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_28,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_29,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_30,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_31,plain,
( ~ v1_xboole_0(u1_struct_0(X1))
| ~ l1_struct_0(X1)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_32,negated_conjecture,
l1_struct_0(esk1_0),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_33,plain,
! [X44,X45,X46] :
( ( ~ m1_fraenkel(X46,X44,X45)
| v1_fraenkel(X46) )
& ( ~ m1_fraenkel(X46,X44,X45)
| ~ v1_xboole_0(X46) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])]) ).
fof(c_0_34,plain,
! [X33,X34,X35,X36] :
( ( ~ l1_group_1(X33)
| ~ v4_group_1(X33)
| ~ v3_group_1(X33)
| ~ v1_group_1(X33)
| v3_struct_0(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| X34 = k1_autgroup(X33)
| ~ m2_relset_1(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33))
| ~ v1_group_6(esk3_2(X33,X34),X33,X33)
| ~ v1_funct_2(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33))
| ~ v1_funct_1(esk3_2(X33,X34))
| r2_hidden(esk4_2(X33,X34),X34)
| v3_group_6(esk4_2(X33,X34),X33,X33) )
& ( ~ l1_group_1(X33)
| ~ v4_group_1(X33)
| ~ v3_group_1(X33)
| ~ v1_group_1(X33)
| v3_struct_0(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| X34 = k1_autgroup(X33)
| ~ m2_relset_1(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33))
| ~ v1_group_6(esk3_2(X33,X34),X33,X33)
| ~ v1_funct_2(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33))
| ~ v1_funct_1(esk3_2(X33,X34))
| r2_hidden(esk4_2(X33,X34),X34)
| v2_funct_1(esk4_2(X33,X34)) )
& ( ~ l1_group_1(X33)
| ~ v4_group_1(X33)
| ~ v3_group_1(X33)
| ~ v1_group_1(X33)
| v3_struct_0(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| X34 = k1_autgroup(X33)
| ~ m2_relset_1(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33))
| ~ v1_group_6(esk3_2(X33,X34),X33,X33)
| ~ v1_funct_2(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33))
| ~ v1_funct_1(esk3_2(X33,X34))
| ~ v3_group_6(esk4_2(X33,X34),X33,X33)
| ~ v2_funct_1(esk4_2(X33,X34))
| ~ r2_hidden(esk4_2(X33,X34),X34) )
& ( ~ l1_group_1(X33)
| ~ v4_group_1(X33)
| ~ v3_group_1(X33)
| ~ v1_group_1(X33)
| v3_struct_0(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| X34 = k1_autgroup(X33)
| ~ m2_relset_1(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33))
| ~ v1_group_6(esk3_2(X33,X34),X33,X33)
| ~ v1_funct_2(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33))
| ~ v1_funct_1(esk3_2(X33,X34))
| m2_relset_1(esk4_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33)) )
& ( ~ l1_group_1(X33)
| ~ v4_group_1(X33)
| ~ v3_group_1(X33)
| ~ v1_group_1(X33)
| v3_struct_0(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| X34 = k1_autgroup(X33)
| ~ m2_relset_1(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33))
| ~ v1_group_6(esk3_2(X33,X34),X33,X33)
| ~ v1_funct_2(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33))
| ~ v1_funct_1(esk3_2(X33,X34))
| v1_group_6(esk4_2(X33,X34),X33,X33) )
& ( ~ l1_group_1(X33)
| ~ v4_group_1(X33)
| ~ v3_group_1(X33)
| ~ v1_group_1(X33)
| v3_struct_0(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| X34 = k1_autgroup(X33)
| ~ m2_relset_1(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33))
| ~ v1_group_6(esk3_2(X33,X34),X33,X33)
| ~ v1_funct_2(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33))
| ~ v1_funct_1(esk3_2(X33,X34))
| v1_funct_2(esk4_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33)) )
& ( ~ l1_group_1(X33)
| ~ v4_group_1(X33)
| ~ v3_group_1(X33)
| ~ v1_group_1(X33)
| v3_struct_0(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| X34 = k1_autgroup(X33)
| ~ m2_relset_1(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33))
| ~ v1_group_6(esk3_2(X33,X34),X33,X33)
| ~ v1_funct_2(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33))
| ~ v1_funct_1(esk3_2(X33,X34))
| v1_funct_1(esk4_2(X33,X34)) )
& ( ~ l1_group_1(X33)
| ~ v4_group_1(X33)
| ~ v3_group_1(X33)
| ~ v1_group_1(X33)
| v3_struct_0(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| X34 = k1_autgroup(X33)
| m2_fraenkel(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33),X34)
| r2_hidden(esk4_2(X33,X34),X34)
| v3_group_6(esk4_2(X33,X34),X33,X33) )
& ( ~ l1_group_1(X33)
| ~ v4_group_1(X33)
| ~ v3_group_1(X33)
| ~ v1_group_1(X33)
| v3_struct_0(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| X34 = k1_autgroup(X33)
| m2_fraenkel(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33),X34)
| r2_hidden(esk4_2(X33,X34),X34)
| v2_funct_1(esk4_2(X33,X34)) )
& ( ~ l1_group_1(X33)
| ~ v4_group_1(X33)
| ~ v3_group_1(X33)
| ~ v1_group_1(X33)
| v3_struct_0(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| X34 = k1_autgroup(X33)
| m2_fraenkel(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33),X34)
| ~ v3_group_6(esk4_2(X33,X34),X33,X33)
| ~ v2_funct_1(esk4_2(X33,X34))
| ~ r2_hidden(esk4_2(X33,X34),X34) )
& ( ~ l1_group_1(X33)
| ~ v4_group_1(X33)
| ~ v3_group_1(X33)
| ~ v1_group_1(X33)
| v3_struct_0(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| X34 = k1_autgroup(X33)
| m2_fraenkel(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33),X34)
| m2_relset_1(esk4_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33)) )
& ( ~ l1_group_1(X33)
| ~ v4_group_1(X33)
| ~ v3_group_1(X33)
| ~ v1_group_1(X33)
| v3_struct_0(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| X34 = k1_autgroup(X33)
| m2_fraenkel(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33),X34)
| v1_group_6(esk4_2(X33,X34),X33,X33) )
& ( ~ l1_group_1(X33)
| ~ v4_group_1(X33)
| ~ v3_group_1(X33)
| ~ v1_group_1(X33)
| v3_struct_0(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| X34 = k1_autgroup(X33)
| m2_fraenkel(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33),X34)
| v1_funct_2(esk4_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33)) )
& ( ~ l1_group_1(X33)
| ~ v4_group_1(X33)
| ~ v3_group_1(X33)
| ~ v1_group_1(X33)
| v3_struct_0(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| X34 = k1_autgroup(X33)
| m2_fraenkel(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33),X34)
| v1_funct_1(esk4_2(X33,X34)) )
& ( ~ l1_group_1(X33)
| ~ v4_group_1(X33)
| ~ v3_group_1(X33)
| ~ v1_group_1(X33)
| v3_struct_0(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| X34 != k1_autgroup(X33)
| ~ m2_relset_1(X36,u1_struct_0(X33),u1_struct_0(X33))
| ~ v1_group_6(X36,X33,X33)
| ~ v1_funct_2(X36,u1_struct_0(X33),u1_struct_0(X33))
| ~ v1_funct_1(X36)
| r2_hidden(X36,X34)
| ~ v3_group_6(X36,X33,X33)
| ~ v2_funct_1(X36) )
& ( ~ l1_group_1(X33)
| ~ v4_group_1(X33)
| ~ v3_group_1(X33)
| ~ v1_group_1(X33)
| v3_struct_0(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| X34 != k1_autgroup(X33)
| ~ m2_relset_1(X36,u1_struct_0(X33),u1_struct_0(X33))
| ~ v1_group_6(X36,X33,X33)
| ~ v1_funct_2(X36,u1_struct_0(X33),u1_struct_0(X33))
| ~ v1_funct_1(X36)
| ~ r2_hidden(X36,X34)
| v3_group_6(X36,X33,X33) )
& ( ~ l1_group_1(X33)
| ~ v4_group_1(X33)
| ~ v3_group_1(X33)
| ~ v1_group_1(X33)
| v3_struct_0(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| X34 != k1_autgroup(X33)
| ~ m2_relset_1(X36,u1_struct_0(X33),u1_struct_0(X33))
| ~ v1_group_6(X36,X33,X33)
| ~ v1_funct_2(X36,u1_struct_0(X33),u1_struct_0(X33))
| ~ v1_funct_1(X36)
| ~ r2_hidden(X36,X34)
| v2_funct_1(X36) )
& ( ~ l1_group_1(X33)
| ~ v4_group_1(X33)
| ~ v3_group_1(X33)
| ~ v1_group_1(X33)
| v3_struct_0(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| X34 != k1_autgroup(X33)
| ~ m2_fraenkel(X35,u1_struct_0(X33),u1_struct_0(X33),X34)
| m2_relset_1(X35,u1_struct_0(X33),u1_struct_0(X33)) )
& ( ~ l1_group_1(X33)
| ~ v4_group_1(X33)
| ~ v3_group_1(X33)
| ~ v1_group_1(X33)
| v3_struct_0(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| X34 != k1_autgroup(X33)
| ~ m2_fraenkel(X35,u1_struct_0(X33),u1_struct_0(X33),X34)
| v1_group_6(X35,X33,X33) )
& ( ~ l1_group_1(X33)
| ~ v4_group_1(X33)
| ~ v3_group_1(X33)
| ~ v1_group_1(X33)
| v3_struct_0(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| X34 != k1_autgroup(X33)
| ~ m2_fraenkel(X35,u1_struct_0(X33),u1_struct_0(X33),X34)
| v1_funct_2(X35,u1_struct_0(X33),u1_struct_0(X33)) )
& ( ~ l1_group_1(X33)
| ~ v4_group_1(X33)
| ~ v3_group_1(X33)
| ~ v1_group_1(X33)
| v3_struct_0(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| X34 != k1_autgroup(X33)
| ~ m2_fraenkel(X35,u1_struct_0(X33),u1_struct_0(X33),X34)
| v1_funct_1(X35) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])])])]) ).
fof(c_0_35,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( l1_group_1(X2)
& v4_group_1(X2)
& v3_group_1(X2)
& ~ v3_struct_0(X2) )
=> ! [X3] :
( ( m2_relset_1(X3,u1_struct_0(X2),u1_struct_0(X1))
& v1_group_6(X3,X2,X1)
& v1_funct_2(X3,u1_struct_0(X2),u1_struct_0(X1))
& v1_funct_1(X3) )
=> ! [X4] :
( ( m2_relset_1(X4,u1_struct_0(X1),u1_struct_0(X2))
& v1_group_6(X4,X1,X2)
& v1_funct_2(X4,u1_struct_0(X1),u1_struct_0(X2))
& v1_funct_1(X4) )
=> ( ( X4 = k2_funct_1(X3)
& v4_group_6(X3,X2,X1) )
=> v4_group_6(X4,X1,X2) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[t73_group_6]) ).
fof(c_0_36,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> ( m2_relset_1(k2_funct_1(X2),u1_struct_0(X1),u1_struct_0(X1))
& v1_group_6(k2_funct_1(X2),X1,X1)
& v1_funct_2(k2_funct_1(X2),u1_struct_0(X1),u1_struct_0(X1))
& v1_funct_1(k2_funct_1(X2)) ) ) ),
inference(fof_simplification,[status(thm)],[t6_autgroup]) ).
fof(c_0_37,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( m2_relset_1(X2,u1_struct_0(X1),u1_struct_0(X1))
& v1_group_6(X2,X1,X1)
& v1_funct_2(X2,u1_struct_0(X1),u1_struct_0(X1))
& v1_funct_1(X2) )
=> ( r2_hidden(X2,k1_autgroup(X1))
<=> v4_group_6(X2,X1,X1) ) ) ),
inference(fof_simplification,[status(thm)],[t5_autgroup]) ).
fof(c_0_38,plain,
! [X111,X112] :
( r2_hidden(X111,X112)
| v1_xboole_0(X112)
| ~ m1_subset_1(X111,X112) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])])]) ).
cnf(c_0_39,plain,
( ~ m1_fraenkel(X4,X2,X3)
| ~ m2_fraenkel(X1,X2,X3,X4)
| v1_xboole_0(X3)
| m1_subset_1(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_40,negated_conjecture,
m2_fraenkel(esk2_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0),k1_autgroup(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_41,negated_conjecture,
m1_fraenkel(k1_autgroup(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_22]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_42,negated_conjecture,
~ v1_xboole_0(u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_30]) ).
cnf(c_0_43,plain,
( ~ m1_fraenkel(X1,X2,X3)
| ~ v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_44,plain,
( ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ v1_group_1(X2)
| ~ m1_fraenkel(X3,u1_struct_0(X2),u1_struct_0(X2))
| X3 != k1_autgroup(X2)
| ~ m2_fraenkel(X1,u1_struct_0(X2),u1_struct_0(X2),X3)
| v3_struct_0(X2)
| v1_funct_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_45,plain,
! [X126,X127,X128,X129] :
( v4_group_6(X129,X126,X127)
| X129 != k2_funct_1(X128)
| ~ v4_group_6(X128,X127,X126)
| ~ m2_relset_1(X129,u1_struct_0(X126),u1_struct_0(X127))
| ~ v1_group_6(X129,X126,X127)
| ~ v1_funct_2(X129,u1_struct_0(X126),u1_struct_0(X127))
| ~ v1_funct_1(X129)
| ~ m2_relset_1(X128,u1_struct_0(X127),u1_struct_0(X126))
| ~ v1_group_6(X128,X127,X126)
| ~ v1_funct_2(X128,u1_struct_0(X127),u1_struct_0(X126))
| ~ v1_funct_1(X128)
| ~ l1_group_1(X127)
| ~ v4_group_1(X127)
| ~ v3_group_1(X127)
| v3_struct_0(X127)
| ~ l1_group_1(X126)
| ~ v4_group_1(X126)
| ~ v3_group_1(X126)
| v3_struct_0(X126) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])])]) ).
fof(c_0_46,plain,
! [X123,X124] :
( ( ~ l1_group_1(X123)
| ~ v4_group_1(X123)
| ~ v3_group_1(X123)
| ~ v1_group_1(X123)
| v3_struct_0(X123)
| ~ m2_fraenkel(X124,u1_struct_0(X123),u1_struct_0(X123),k1_autgroup(X123))
| m2_relset_1(k2_funct_1(X124),u1_struct_0(X123),u1_struct_0(X123)) )
& ( ~ l1_group_1(X123)
| ~ v4_group_1(X123)
| ~ v3_group_1(X123)
| ~ v1_group_1(X123)
| v3_struct_0(X123)
| ~ m2_fraenkel(X124,u1_struct_0(X123),u1_struct_0(X123),k1_autgroup(X123))
| v1_group_6(k2_funct_1(X124),X123,X123) )
& ( ~ l1_group_1(X123)
| ~ v4_group_1(X123)
| ~ v3_group_1(X123)
| ~ v1_group_1(X123)
| v3_struct_0(X123)
| ~ m2_fraenkel(X124,u1_struct_0(X123),u1_struct_0(X123),k1_autgroup(X123))
| v1_funct_2(k2_funct_1(X124),u1_struct_0(X123),u1_struct_0(X123)) )
& ( ~ l1_group_1(X123)
| ~ v4_group_1(X123)
| ~ v3_group_1(X123)
| ~ v1_group_1(X123)
| v3_struct_0(X123)
| ~ m2_fraenkel(X124,u1_struct_0(X123),u1_struct_0(X123),k1_autgroup(X123))
| v1_funct_1(k2_funct_1(X124)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])])])]) ).
fof(c_0_47,plain,
! [X118,X119] :
( ( ~ l1_group_1(X118)
| ~ v4_group_1(X118)
| ~ v3_group_1(X118)
| ~ v1_group_1(X118)
| v3_struct_0(X118)
| ~ m2_relset_1(X119,u1_struct_0(X118),u1_struct_0(X118))
| ~ v1_group_6(X119,X118,X118)
| ~ v1_funct_2(X119,u1_struct_0(X118),u1_struct_0(X118))
| ~ v1_funct_1(X119)
| r2_hidden(X119,k1_autgroup(X118))
| ~ v4_group_6(X119,X118,X118) )
& ( ~ l1_group_1(X118)
| ~ v4_group_1(X118)
| ~ v3_group_1(X118)
| ~ v1_group_1(X118)
| v3_struct_0(X118)
| ~ m2_relset_1(X119,u1_struct_0(X118),u1_struct_0(X118))
| ~ v1_group_6(X119,X118,X118)
| ~ v1_funct_2(X119,u1_struct_0(X118),u1_struct_0(X118))
| ~ v1_funct_1(X119)
| v4_group_6(X119,X118,X118)
| ~ r2_hidden(X119,k1_autgroup(X118)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])])])]) ).
cnf(c_0_48,plain,
( ~ m1_subset_1(X1,X2)
| r2_hidden(X1,X2)
| v1_xboole_0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_49,negated_conjecture,
m1_subset_1(esk2_0,k1_autgroup(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]),c_0_42]) ).
cnf(c_0_50,negated_conjecture,
~ v1_xboole_0(k1_autgroup(esk1_0)),
inference(spm,[status(thm)],[c_0_43,c_0_41]) ).
cnf(c_0_51,plain,
( ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ v1_group_1(X2)
| ~ m1_fraenkel(X3,u1_struct_0(X2),u1_struct_0(X2))
| X3 != k1_autgroup(X2)
| ~ m2_fraenkel(X1,u1_struct_0(X2),u1_struct_0(X2),X3)
| v3_struct_0(X2)
| m2_relset_1(X1,u1_struct_0(X2),u1_struct_0(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_52,plain,
( ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ v1_group_1(X2)
| ~ m1_fraenkel(X3,u1_struct_0(X2),u1_struct_0(X2))
| X3 != k1_autgroup(X2)
| ~ m2_fraenkel(X1,u1_struct_0(X2),u1_struct_0(X2),X3)
| v3_struct_0(X2)
| v1_group_6(X1,X2,X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_53,plain,
( ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ v1_group_1(X2)
| ~ m1_fraenkel(X3,u1_struct_0(X2),u1_struct_0(X2))
| X3 != k1_autgroup(X2)
| ~ m2_fraenkel(X1,u1_struct_0(X2),u1_struct_0(X2),X3)
| v3_struct_0(X2)
| v1_funct_2(X1,u1_struct_0(X2),u1_struct_0(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_54,negated_conjecture,
( ~ m1_fraenkel(k1_autgroup(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| v1_funct_1(esk2_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_40]),c_0_22]),c_0_28]),c_0_29]),c_0_27])]),c_0_30]) ).
cnf(c_0_55,plain,
( X4 != k2_funct_1(X3)
| ~ v4_group_6(X3,X2,X1)
| ~ m2_relset_1(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_group_6(X4,X1,X2)
| ~ v1_funct_2(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_funct_1(X4)
| ~ m2_relset_1(X3,u1_struct_0(X2),u1_struct_0(X1))
| ~ v1_group_6(X3,X2,X1)
| ~ v1_funct_2(X3,u1_struct_0(X2),u1_struct_0(X1))
| ~ v1_funct_1(X3)
| ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| v4_group_6(X4,X1,X2)
| v3_struct_0(X2)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_56,plain,
( ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ v1_group_1(X2)
| ~ m2_fraenkel(X1,u1_struct_0(X2),u1_struct_0(X2),k1_autgroup(X2))
| v3_struct_0(X2)
| m2_relset_1(k2_funct_1(X1),u1_struct_0(X2),u1_struct_0(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_57,plain,
( ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ v1_group_1(X2)
| ~ m2_relset_1(X1,u1_struct_0(X2),u1_struct_0(X2))
| ~ v1_group_6(X1,X2,X2)
| ~ v1_funct_2(X1,u1_struct_0(X2),u1_struct_0(X2))
| ~ v1_funct_1(X1)
| ~ r2_hidden(X1,k1_autgroup(X2))
| v3_struct_0(X2)
| v4_group_6(X1,X2,X2) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_58,negated_conjecture,
r2_hidden(esk2_0,k1_autgroup(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
cnf(c_0_59,negated_conjecture,
m2_relset_1(esk2_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_40]),c_0_22]),c_0_28]),c_0_29]),c_0_27])]),c_0_30]),c_0_41])]) ).
cnf(c_0_60,negated_conjecture,
v1_group_6(esk2_0,esk1_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_40]),c_0_22]),c_0_28]),c_0_29]),c_0_27])]),c_0_30]),c_0_41])]) ).
cnf(c_0_61,negated_conjecture,
v1_funct_2(esk2_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_40]),c_0_22]),c_0_28]),c_0_29]),c_0_27])]),c_0_30]),c_0_41])]) ).
cnf(c_0_62,negated_conjecture,
v1_funct_1(esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_41])]) ).
cnf(c_0_63,plain,
( ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ v1_group_1(X2)
| ~ m2_fraenkel(X1,u1_struct_0(X2),u1_struct_0(X2),k1_autgroup(X2))
| v3_struct_0(X2)
| v1_group_6(k2_funct_1(X1),X2,X2) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_64,plain,
( ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ v1_group_1(X2)
| ~ m2_fraenkel(X1,u1_struct_0(X2),u1_struct_0(X2),k1_autgroup(X2))
| v3_struct_0(X2)
| v1_funct_2(k2_funct_1(X1),u1_struct_0(X2),u1_struct_0(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_65,plain,
( ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ v1_group_1(X2)
| ~ m2_fraenkel(X1,u1_struct_0(X2),u1_struct_0(X2),k1_autgroup(X2))
| v3_struct_0(X2)
| v1_funct_1(k2_funct_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_66,plain,
( ~ v3_group_1(X2)
| ~ v3_group_1(X3)
| ~ v4_group_1(X2)
| ~ v4_group_1(X3)
| ~ l1_group_1(X2)
| ~ l1_group_1(X3)
| ~ v1_funct_1(X1)
| ~ v1_funct_1(k2_funct_1(X1))
| ~ v1_funct_2(X1,u1_struct_0(X3),u1_struct_0(X2))
| ~ v1_funct_2(k2_funct_1(X1),u1_struct_0(X2),u1_struct_0(X3))
| ~ v1_group_6(X1,X3,X2)
| ~ v1_group_6(k2_funct_1(X1),X2,X3)
| ~ m2_relset_1(X1,u1_struct_0(X3),u1_struct_0(X2))
| ~ m2_relset_1(k2_funct_1(X1),u1_struct_0(X2),u1_struct_0(X3))
| ~ v4_group_6(X1,X3,X2)
| v3_struct_0(X2)
| v3_struct_0(X3)
| v4_group_6(k2_funct_1(X1),X2,X3) ),
inference(er,[status(thm)],[c_0_55]) ).
cnf(c_0_67,negated_conjecture,
m2_relset_1(k2_funct_1(esk2_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_40]),c_0_22]),c_0_28]),c_0_29]),c_0_27])]),c_0_30]) ).
cnf(c_0_68,negated_conjecture,
v4_group_6(esk2_0,esk1_0,esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]),c_0_60]),c_0_61]),c_0_62]),c_0_22]),c_0_28]),c_0_29]),c_0_27])]),c_0_30]) ).
cnf(c_0_69,negated_conjecture,
v1_group_6(k2_funct_1(esk2_0),esk1_0,esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_40]),c_0_22]),c_0_28]),c_0_29]),c_0_27])]),c_0_30]) ).
cnf(c_0_70,negated_conjecture,
v1_funct_2(k2_funct_1(esk2_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_40]),c_0_22]),c_0_28]),c_0_29]),c_0_27])]),c_0_30]) ).
cnf(c_0_71,negated_conjecture,
v1_funct_1(k2_funct_1(esk2_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_40]),c_0_22]),c_0_28]),c_0_29]),c_0_27])]),c_0_30]) ).
fof(c_0_72,plain,
! [X109,X110] :
( m1_subset_1(X109,X110)
| ~ r2_hidden(X109,X110) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])])]) ).
cnf(c_0_73,plain,
( ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ v1_group_1(X2)
| ~ m2_relset_1(X1,u1_struct_0(X2),u1_struct_0(X2))
| ~ v1_group_6(X1,X2,X2)
| ~ v1_funct_2(X1,u1_struct_0(X2),u1_struct_0(X2))
| ~ v1_funct_1(X1)
| ~ v4_group_6(X1,X2,X2)
| v3_struct_0(X2)
| r2_hidden(X1,k1_autgroup(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_74,negated_conjecture,
v4_group_6(k2_funct_1(esk2_0),esk1_0,esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]),c_0_59]),c_0_69]),c_0_60]),c_0_70]),c_0_61]),c_0_71]),c_0_62]),c_0_22]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_75,plain,
( ~ r2_hidden(X1,X2)
| m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_76,negated_conjecture,
r2_hidden(k2_funct_1(esk2_0),k1_autgroup(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_67]),c_0_69]),c_0_70]),c_0_71]),c_0_22]),c_0_28]),c_0_29]),c_0_27])]),c_0_30]) ).
cnf(c_0_77,plain,
( ~ m1_fraenkel(X2,X3,X4)
| ~ m1_subset_1(X1,X2)
| v1_xboole_0(X4)
| m2_fraenkel(X1,X3,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_78,negated_conjecture,
m1_subset_1(k2_funct_1(esk2_0),k1_autgroup(esk1_0)),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_79,negated_conjecture,
( ~ m1_fraenkel(k1_autgroup(esk1_0),X2,X1)
| m2_fraenkel(k2_funct_1(esk2_0),X2,X1,k1_autgroup(esk1_0))
| v1_xboole_0(X1) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_80,negated_conjecture,
~ m2_fraenkel(k2_funct_1(esk2_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k1_autgroup(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_81,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_41]),c_0_42]),c_0_80]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP620+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.45 % Computer : n011.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Sun Sep 20 20:18:55 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.50 Running first-order theorem proving
% 0.20/0.50 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.66/0.63 % Version: 3.5.1
% 0.66/0.63 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.66/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.66/0.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.66/0.63 % Starting new_bool_3 with 300s (1) cores
% 0.66/0.63 % Starting new_bool_1 with 300s (1) cores
% 0.66/0.63 % Starting sh5l with 300s (1) cores
% 0.66/0.63 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 92099 completed with status 0
% 0.66/0.63 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.66/0.63 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.66/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.66/0.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.66/0.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.66/0.63 % No SInE strategy applied
% 0.66/0.63 % Search class: FGHSM-FSLM31-SFFFFFNN
% 0.66/0.63 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.66/0.63 % Starting SubtermCWHack with 136s (1) cores
% 0.66/0.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.66/0.63 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_S0e with 136s (1) cores
% 0.66/0.63 % Starting G-E--_208_C18_F1_AE_CS_SP_PI_S0a with 136s (1) cores
% 0.66/0.63 % Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 0.66/0.63 % G-E--_208_C18_F1_AE_CS_SP_PI_S0a with pid 92109 completed with status 0
% 0.66/0.63 % Result found by G-E--_208_C18_F1_AE_CS_SP_PI_S0a
% 0.66/0.63 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.66/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.66/0.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.66/0.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.66/0.63 % No SInE strategy applied
% 0.66/0.63 % Search class: FGHSM-FSLM31-SFFFFFNN
% 0.66/0.63 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.66/0.63 % Starting SubtermCWHack with 136s (1) cores
% 0.66/0.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.66/0.63 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_S0e with 136s (1) cores
% 0.66/0.63 % Starting G-E--_208_C18_F1_AE_CS_SP_PI_S0a with 136s (1) cores
% 0.66/0.63 % Preprocessing time : 0.002 s
% 0.66/0.63
% 0.66/0.63 % Proof found!
% 0.66/0.63 % SZS status Theorem
% 0.66/0.63 % SZS output start CNFRefutation
% See solution above
% 0.66/0.63 % Parsed axioms : 69
% 0.66/0.63 % Removed by relevancy pruning/SinE : 0
% 0.66/0.63 % Initial clauses : 154
% 0.66/0.63 % Removed in clause preprocessing : 15
% 0.66/0.63 % Initial clauses in saturation : 139
% 0.66/0.63 % Processed clauses : 1054
% 0.66/0.63 % ...of these trivial : 34
% 0.66/0.63 % ...subsumed : 113
% 0.66/0.63 % ...remaining for further processing : 907
% 0.66/0.63 % Other redundant clauses eliminated : 0
% 0.66/0.63 % Clauses deleted for lack of memory : 0
% 0.66/0.63 % Backward-subsumed : 9
% 0.66/0.63 % Backward-rewritten : 23
% 0.66/0.63 % Generated clauses : 1368
% 0.66/0.63 % ...of the previous two non-redundant : 1201
% 0.66/0.63 % ...aggressively subsumed : 0
% 0.66/0.63 % Contextual simplify-reflections : 2
% 0.66/0.63 % Paramodulations : 1359
% 0.66/0.63 % Factorizations : 0
% 0.66/0.63 % NegExts : 0
% 0.66/0.63 % Equation resolutions : 9
% 0.66/0.63 % Disequality decompositions : 0
% 0.66/0.63 % Total rewrite steps : 1202
% 0.66/0.63 % ...of those cached : 946
% 0.66/0.63 % Propositional unsat checks : 0
% 0.66/0.63 % Propositional check models : 0
% 0.66/0.63 % Propositional check unsatisfiable : 0
% 0.66/0.63 % Propositional clauses : 0
% 0.66/0.63 % Propositional clauses after purity: 0
% 0.66/0.63 % Propositional unsat core size : 0
% 0.66/0.63 % Propositional preprocessing time : 0.000
% 0.66/0.63 % Propositional encoding time : 0.000
% 0.66/0.63 % Propositional solver time : 0.000
% 0.66/0.63 % Success case prop preproc time : 0.000
% 0.66/0.63 % Success case prop encoding time : 0.000
% 0.66/0.63 % Success case prop solver time : 0.000
% 0.66/0.63 % Current number of processed clauses : 875
% 0.66/0.63 % Positive orientable unit clauses : 437
% 0.66/0.63 % Positive unorientable unit clauses: 0
% 0.66/0.63 % Negative unit clauses : 43
% 0.66/0.63 % Non-unit-clauses : 395
% 0.66/0.63 % Current number of unprocessed clauses: 269
% 0.66/0.63 % ...number of literals in the above : 1480
% 0.66/0.63 % Current number of archived formulas : 0
% 0.66/0.63 % Current number of archived clauses : 32
% 0.66/0.63 % Clause-clause subsumption calls (NU) : 34107
% 0.66/0.63 % Rec. Clause-clause subsumption calls : 10138
% 0.66/0.63 % Non-unit clause-clause subsumptions : 47
% 0.66/0.63 % Unit Clause-clause subsumption calls : 27484
% 0.66/0.63 % Rewrite failures with RHS unbound : 0
% 0.66/0.63 % BW rewrite match attempts : 7558
% 0.66/0.63 % BW rewrite match successes : 13
% 0.66/0.63 % Condensation attempts : 0
% 0.66/0.63 % Condensation successes : 0
% 0.66/0.63 % Termbank termtop insertions : 45501
% 0.66/0.63 % Search garbage collected termcells : 2141
% 0.66/0.63
% 0.66/0.63 % -------------------------------------------------
% 0.66/0.63 % User time : 0.073 s
% 0.66/0.63 % System time : 0.008 s
% 0.66/0.63 % Total time : 0.081 s
% 0.66/0.63 % Maximum resident set size: 3968 pages
% 0.66/0.63
% 0.66/0.63 % -------------------------------------------------
% 0.66/0.63 % User time : 0.459 s
% 0.66/0.63 % System time : 0.035 s
% 0.66/0.63 % Total time : 0.494 s
% 0.66/0.63 % Maximum resident set size: 4608 pages
% 0.66/0.63 % E exiting
%------------------------------------------------------------------------------