TSTP Solution File: GRP620+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP620+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 00:21:53 EDT 2023
% Result : Theorem 0.58s 0.68s
% Output : CNFRefutation 0.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 71
% Syntax : Number of formulae : 141 ( 17 unt; 59 typ; 0 def)
% Number of atoms : 706 ( 34 equ)
% Maximal formula atoms : 231 ( 8 avg)
% Number of connectives : 1015 ( 391 ~; 443 |; 132 &)
% ( 8 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 38 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 79 ( 43 >; 36 *; 0 +; 0 <<)
% Number of predicates : 27 ( 25 usr; 1 prp; 0-4 aty)
% Number of functors : 34 ( 34 usr; 16 con; 0-3 aty)
% Number of variables : 133 ( 2 sgn; 77 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
v3_struct_0: $i > $o ).
tff(decl_23,type,
v1_group_1: $i > $o ).
tff(decl_24,type,
v3_group_1: $i > $o ).
tff(decl_25,type,
v4_group_1: $i > $o ).
tff(decl_26,type,
l1_group_1: $i > $o ).
tff(decl_27,type,
u1_struct_0: $i > $i ).
tff(decl_28,type,
k1_autgroup: $i > $i ).
tff(decl_29,type,
m2_fraenkel: ( $i * $i * $i * $i ) > $o ).
tff(decl_30,type,
k2_funct_1: $i > $i ).
tff(decl_31,type,
u1_group_1: $i > $i ).
tff(decl_32,type,
g1_group_1: ( $i * $i ) > $i ).
tff(decl_33,type,
r2_hidden: ( $i * $i ) > $o ).
tff(decl_34,type,
v1_fraenkel: $i > $o ).
tff(decl_35,type,
m1_subset_1: ( $i * $i ) > $o ).
tff(decl_36,type,
v1_relat_1: $i > $o ).
tff(decl_37,type,
v1_funct_1: $i > $o ).
tff(decl_38,type,
v1_xboole_0: $i > $o ).
tff(decl_39,type,
m1_relset_1: ( $i * $i * $i ) > $o ).
tff(decl_40,type,
v1_partfun1: ( $i * $i * $i ) > $o ).
tff(decl_41,type,
v1_funct_2: ( $i * $i * $i ) > $o ).
tff(decl_42,type,
v2_group_1: $i > $o ).
tff(decl_43,type,
k2_zfmisc_1: ( $i * $i ) > $i ).
tff(decl_44,type,
k1_zfmisc_1: $i > $i ).
tff(decl_45,type,
v2_funct_1: $i > $o ).
tff(decl_46,type,
v1_group_6: ( $i * $i * $i ) > $o ).
tff(decl_47,type,
m2_relset_1: ( $i * $i * $i ) > $o ).
tff(decl_48,type,
v2_group_6: ( $i * $i * $i ) > $o ).
tff(decl_49,type,
v4_group_6: ( $i * $i * $i ) > $o ).
tff(decl_50,type,
v3_group_6: ( $i * $i * $i ) > $o ).
tff(decl_51,type,
m1_fraenkel: ( $i * $i * $i ) > $o ).
tff(decl_52,type,
l1_struct_0: $i > $o ).
tff(decl_53,type,
k1_xboole_0: $i ).
tff(decl_54,type,
r1_tarski: ( $i * $i ) > $o ).
tff(decl_55,type,
esk1_0: $i ).
tff(decl_56,type,
esk2_0: $i ).
tff(decl_57,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_58,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_59,type,
esk5_0: $i ).
tff(decl_60,type,
esk6_0: $i ).
tff(decl_61,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_62,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_63,type,
esk9_1: $i > $i ).
tff(decl_64,type,
esk10_3: ( $i * $i * $i ) > $i ).
tff(decl_65,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_66,type,
esk12_0: $i ).
tff(decl_67,type,
esk13_0: $i ).
tff(decl_68,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_69,type,
esk15_0: $i ).
tff(decl_70,type,
esk16_0: $i ).
tff(decl_71,type,
esk17_0: $i ).
tff(decl_72,type,
esk18_0: $i ).
tff(decl_73,type,
esk19_0: $i ).
tff(decl_74,type,
esk20_2: ( $i * $i ) > $i ).
tff(decl_75,type,
esk21_2: ( $i * $i ) > $i ).
tff(decl_76,type,
esk22_0: $i ).
tff(decl_77,type,
esk23_0: $i ).
tff(decl_78,type,
esk24_0: $i ).
tff(decl_79,type,
esk25_0: $i ).
tff(decl_80,type,
esk26_1: $i > $i ).
fof(redefinition_m2_fraenkel,axiom,
! [X1,X2,X3] :
( ( ~ v1_xboole_0(X2)
& m1_fraenkel(X3,X1,X2) )
=> ! [X4] :
( m2_fraenkel(X4,X1,X2,X3)
<=> m1_subset_1(X4,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_fraenkel) ).
fof(t7_autgroup,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(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(d1_autgroup,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1))
=> ( X2 = k1_autgroup(X1)
<=> ( ! [X3] :
( m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),X2)
=> ( v1_funct_1(X3)
& v1_funct_2(X3,u1_struct_0(X1),u1_struct_0(X1))
& v1_group_6(X3,X1,X1)
& m2_relset_1(X3,u1_struct_0(X1),u1_struct_0(X1)) ) )
& ! [X3] :
( ( v1_funct_1(X3)
& v1_funct_2(X3,u1_struct_0(X1),u1_struct_0(X1))
& v1_group_6(X3,X1,X1)
& m2_relset_1(X3,u1_struct_0(X1),u1_struct_0(X1)) )
=> ( r2_hidden(X3,X2)
<=> ( v2_funct_1(X3)
& v3_group_6(X3,X1,X1) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_autgroup) ).
fof(dt_m1_fraenkel,axiom,
! [X1,X2,X3] :
( m1_fraenkel(X3,X1,X2)
=> ( ~ v1_xboole_0(X3)
& v1_fraenkel(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_fraenkel) ).
fof(dt_k1_autgroup,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(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(t5_autgroup,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,u1_struct_0(X1),u1_struct_0(X1))
& v1_group_6(X2,X1,X1)
& m2_relset_1(X2,u1_struct_0(X1),u1_struct_0(X1)) )
=> ( 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)
=> ( v1_xboole_0(X2)
| r2_hidden(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(t73_group_6,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v3_group_1(X2)
& v4_group_1(X2)
& l1_group_1(X2) )
=> ! [X3] :
( ( v1_funct_1(X3)
& v1_funct_2(X3,u1_struct_0(X2),u1_struct_0(X1))
& v1_group_6(X3,X2,X1)
& m2_relset_1(X3,u1_struct_0(X2),u1_struct_0(X1)) )
=> ! [X4] :
( ( v1_funct_1(X4)
& v1_funct_2(X4,u1_struct_0(X1),u1_struct_0(X2))
& v1_group_6(X4,X1,X2)
& m2_relset_1(X4,u1_struct_0(X1),u1_struct_0(X2)) )
=> ( ( v4_group_6(X3,X2,X1)
& X4 = k2_funct_1(X3) )
=> v4_group_6(X4,X1,X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_group_6) ).
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(t6_autgroup,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> ( v1_funct_1(k2_funct_1(X2))
& v1_funct_2(k2_funct_1(X2),u1_struct_0(X1),u1_struct_0(X1))
& v1_group_6(k2_funct_1(X2),X1,X1)
& m2_relset_1(k2_funct_1(X2),u1_struct_0(X1),u1_struct_0(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_autgroup) ).
fof(fc1_struct_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_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(c_0_12,plain,
! [X1,X2,X3] :
( ( ~ v1_xboole_0(X2)
& m1_fraenkel(X3,X1,X2) )
=> ! [X4] :
( m2_fraenkel(X4,X1,X2,X3)
<=> m1_subset_1(X4,X3) ) ),
inference(fof_simplification,[status(thm)],[redefinition_m2_fraenkel]) ).
fof(c_0_13,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(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)],[inference(assume_negation,[status(cth)],[t7_autgroup])]) ).
fof(c_0_14,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1))
=> ( X2 = k1_autgroup(X1)
<=> ( ! [X3] :
( m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),X2)
=> ( v1_funct_1(X3)
& v1_funct_2(X3,u1_struct_0(X1),u1_struct_0(X1))
& v1_group_6(X3,X1,X1)
& m2_relset_1(X3,u1_struct_0(X1),u1_struct_0(X1)) ) )
& ! [X3] :
( ( v1_funct_1(X3)
& v1_funct_2(X3,u1_struct_0(X1),u1_struct_0(X1))
& v1_group_6(X3,X1,X1)
& m2_relset_1(X3,u1_struct_0(X1),u1_struct_0(X1)) )
=> ( r2_hidden(X3,X2)
<=> ( v2_funct_1(X3)
& v3_group_6(X3,X1,X1) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d1_autgroup]) ).
fof(c_0_15,plain,
! [X101,X102,X103,X104] :
( ( ~ m2_fraenkel(X104,X101,X102,X103)
| m1_subset_1(X104,X103)
| v1_xboole_0(X102)
| ~ m1_fraenkel(X103,X101,X102) )
& ( ~ m1_subset_1(X104,X103)
| m2_fraenkel(X104,X101,X102,X103)
| v1_xboole_0(X102)
| ~ m1_fraenkel(X103,X101,X102) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).
fof(c_0_16,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v1_group_1(esk1_0)
& v3_group_1(esk1_0)
& v4_group_1(esk1_0)
& l1_group_1(esk1_0)
& m2_fraenkel(esk2_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0),k1_autgroup(esk1_0))
& ~ m2_fraenkel(k2_funct_1(esk2_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k1_autgroup(esk1_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_17,plain,
! [X1,X2,X3] :
( m1_fraenkel(X3,X1,X2)
=> ( ~ v1_xboole_0(X3)
& v1_fraenkel(X3) ) ),
inference(fof_simplification,[status(thm)],[dt_m1_fraenkel]) ).
fof(c_0_18,plain,
! [X33,X34,X35,X36] :
( ( v1_funct_1(X35)
| ~ m2_fraenkel(X35,u1_struct_0(X33),u1_struct_0(X33),X34)
| X34 != k1_autgroup(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| v3_struct_0(X33)
| ~ v1_group_1(X33)
| ~ v3_group_1(X33)
| ~ v4_group_1(X33)
| ~ l1_group_1(X33) )
& ( v1_funct_2(X35,u1_struct_0(X33),u1_struct_0(X33))
| ~ m2_fraenkel(X35,u1_struct_0(X33),u1_struct_0(X33),X34)
| X34 != k1_autgroup(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| v3_struct_0(X33)
| ~ v1_group_1(X33)
| ~ v3_group_1(X33)
| ~ v4_group_1(X33)
| ~ l1_group_1(X33) )
& ( v1_group_6(X35,X33,X33)
| ~ m2_fraenkel(X35,u1_struct_0(X33),u1_struct_0(X33),X34)
| X34 != k1_autgroup(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| v3_struct_0(X33)
| ~ v1_group_1(X33)
| ~ v3_group_1(X33)
| ~ v4_group_1(X33)
| ~ l1_group_1(X33) )
& ( m2_relset_1(X35,u1_struct_0(X33),u1_struct_0(X33))
| ~ m2_fraenkel(X35,u1_struct_0(X33),u1_struct_0(X33),X34)
| X34 != k1_autgroup(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| v3_struct_0(X33)
| ~ v1_group_1(X33)
| ~ v3_group_1(X33)
| ~ v4_group_1(X33)
| ~ l1_group_1(X33) )
& ( v2_funct_1(X36)
| ~ r2_hidden(X36,X34)
| ~ v1_funct_1(X36)
| ~ v1_funct_2(X36,u1_struct_0(X33),u1_struct_0(X33))
| ~ v1_group_6(X36,X33,X33)
| ~ m2_relset_1(X36,u1_struct_0(X33),u1_struct_0(X33))
| X34 != k1_autgroup(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| v3_struct_0(X33)
| ~ v1_group_1(X33)
| ~ v3_group_1(X33)
| ~ v4_group_1(X33)
| ~ l1_group_1(X33) )
& ( v3_group_6(X36,X33,X33)
| ~ r2_hidden(X36,X34)
| ~ v1_funct_1(X36)
| ~ v1_funct_2(X36,u1_struct_0(X33),u1_struct_0(X33))
| ~ v1_group_6(X36,X33,X33)
| ~ m2_relset_1(X36,u1_struct_0(X33),u1_struct_0(X33))
| X34 != k1_autgroup(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| v3_struct_0(X33)
| ~ v1_group_1(X33)
| ~ v3_group_1(X33)
| ~ v4_group_1(X33)
| ~ l1_group_1(X33) )
& ( ~ v2_funct_1(X36)
| ~ v3_group_6(X36,X33,X33)
| r2_hidden(X36,X34)
| ~ v1_funct_1(X36)
| ~ v1_funct_2(X36,u1_struct_0(X33),u1_struct_0(X33))
| ~ v1_group_6(X36,X33,X33)
| ~ m2_relset_1(X36,u1_struct_0(X33),u1_struct_0(X33))
| X34 != k1_autgroup(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| v3_struct_0(X33)
| ~ v1_group_1(X33)
| ~ v3_group_1(X33)
| ~ v4_group_1(X33)
| ~ l1_group_1(X33) )
& ( v1_funct_1(esk4_2(X33,X34))
| m2_fraenkel(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33),X34)
| X34 = k1_autgroup(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| v3_struct_0(X33)
| ~ v1_group_1(X33)
| ~ v3_group_1(X33)
| ~ v4_group_1(X33)
| ~ l1_group_1(X33) )
& ( v1_funct_2(esk4_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33))
| m2_fraenkel(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33),X34)
| X34 = k1_autgroup(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| v3_struct_0(X33)
| ~ v1_group_1(X33)
| ~ v3_group_1(X33)
| ~ v4_group_1(X33)
| ~ l1_group_1(X33) )
& ( v1_group_6(esk4_2(X33,X34),X33,X33)
| m2_fraenkel(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33),X34)
| X34 = k1_autgroup(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| v3_struct_0(X33)
| ~ v1_group_1(X33)
| ~ v3_group_1(X33)
| ~ v4_group_1(X33)
| ~ l1_group_1(X33) )
& ( m2_relset_1(esk4_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33))
| m2_fraenkel(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33),X34)
| X34 = k1_autgroup(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| v3_struct_0(X33)
| ~ v1_group_1(X33)
| ~ v3_group_1(X33)
| ~ v4_group_1(X33)
| ~ l1_group_1(X33) )
& ( ~ r2_hidden(esk4_2(X33,X34),X34)
| ~ v2_funct_1(esk4_2(X33,X34))
| ~ v3_group_6(esk4_2(X33,X34),X33,X33)
| m2_fraenkel(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33),X34)
| X34 = k1_autgroup(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| v3_struct_0(X33)
| ~ v1_group_1(X33)
| ~ v3_group_1(X33)
| ~ v4_group_1(X33)
| ~ l1_group_1(X33) )
& ( v2_funct_1(esk4_2(X33,X34))
| r2_hidden(esk4_2(X33,X34),X34)
| m2_fraenkel(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33),X34)
| X34 = k1_autgroup(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| v3_struct_0(X33)
| ~ v1_group_1(X33)
| ~ v3_group_1(X33)
| ~ v4_group_1(X33)
| ~ l1_group_1(X33) )
& ( v3_group_6(esk4_2(X33,X34),X33,X33)
| r2_hidden(esk4_2(X33,X34),X34)
| m2_fraenkel(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33),X34)
| X34 = k1_autgroup(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| v3_struct_0(X33)
| ~ v1_group_1(X33)
| ~ v3_group_1(X33)
| ~ v4_group_1(X33)
| ~ l1_group_1(X33) )
& ( v1_funct_1(esk4_2(X33,X34))
| ~ v1_funct_1(esk3_2(X33,X34))
| ~ v1_funct_2(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33))
| ~ v1_group_6(esk3_2(X33,X34),X33,X33)
| ~ m2_relset_1(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33))
| X34 = k1_autgroup(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| v3_struct_0(X33)
| ~ v1_group_1(X33)
| ~ v3_group_1(X33)
| ~ v4_group_1(X33)
| ~ l1_group_1(X33) )
& ( v1_funct_2(esk4_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33))
| ~ v1_funct_1(esk3_2(X33,X34))
| ~ v1_funct_2(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33))
| ~ v1_group_6(esk3_2(X33,X34),X33,X33)
| ~ m2_relset_1(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33))
| X34 = k1_autgroup(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| v3_struct_0(X33)
| ~ v1_group_1(X33)
| ~ v3_group_1(X33)
| ~ v4_group_1(X33)
| ~ l1_group_1(X33) )
& ( v1_group_6(esk4_2(X33,X34),X33,X33)
| ~ v1_funct_1(esk3_2(X33,X34))
| ~ v1_funct_2(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33))
| ~ v1_group_6(esk3_2(X33,X34),X33,X33)
| ~ m2_relset_1(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33))
| X34 = k1_autgroup(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| v3_struct_0(X33)
| ~ v1_group_1(X33)
| ~ v3_group_1(X33)
| ~ v4_group_1(X33)
| ~ l1_group_1(X33) )
& ( m2_relset_1(esk4_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33))
| ~ v1_funct_1(esk3_2(X33,X34))
| ~ v1_funct_2(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33))
| ~ v1_group_6(esk3_2(X33,X34),X33,X33)
| ~ m2_relset_1(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33))
| X34 = k1_autgroup(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| v3_struct_0(X33)
| ~ v1_group_1(X33)
| ~ v3_group_1(X33)
| ~ v4_group_1(X33)
| ~ l1_group_1(X33) )
& ( ~ r2_hidden(esk4_2(X33,X34),X34)
| ~ v2_funct_1(esk4_2(X33,X34))
| ~ v3_group_6(esk4_2(X33,X34),X33,X33)
| ~ v1_funct_1(esk3_2(X33,X34))
| ~ v1_funct_2(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33))
| ~ v1_group_6(esk3_2(X33,X34),X33,X33)
| ~ m2_relset_1(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33))
| X34 = k1_autgroup(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| v3_struct_0(X33)
| ~ v1_group_1(X33)
| ~ v3_group_1(X33)
| ~ v4_group_1(X33)
| ~ l1_group_1(X33) )
& ( v2_funct_1(esk4_2(X33,X34))
| r2_hidden(esk4_2(X33,X34),X34)
| ~ v1_funct_1(esk3_2(X33,X34))
| ~ v1_funct_2(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33))
| ~ v1_group_6(esk3_2(X33,X34),X33,X33)
| ~ m2_relset_1(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33))
| X34 = k1_autgroup(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| v3_struct_0(X33)
| ~ v1_group_1(X33)
| ~ v3_group_1(X33)
| ~ v4_group_1(X33)
| ~ l1_group_1(X33) )
& ( v3_group_6(esk4_2(X33,X34),X33,X33)
| r2_hidden(esk4_2(X33,X34),X34)
| ~ v1_funct_1(esk3_2(X33,X34))
| ~ v1_funct_2(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33))
| ~ v1_group_6(esk3_2(X33,X34),X33,X33)
| ~ m2_relset_1(esk3_2(X33,X34),u1_struct_0(X33),u1_struct_0(X33))
| X34 = k1_autgroup(X33)
| ~ m1_fraenkel(X34,u1_struct_0(X33),u1_struct_0(X33))
| v3_struct_0(X33)
| ~ v1_group_1(X33)
| ~ v3_group_1(X33)
| ~ v4_group_1(X33)
| ~ l1_group_1(X33) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])])]) ).
fof(c_0_19,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(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_20,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,u1_struct_0(X1),u1_struct_0(X1))
& v1_group_6(X2,X1,X1)
& m2_relset_1(X2,u1_struct_0(X1),u1_struct_0(X1)) )
=> ( r2_hidden(X2,k1_autgroup(X1))
<=> v4_group_6(X2,X1,X1) ) ) ),
inference(fof_simplification,[status(thm)],[t5_autgroup]) ).
fof(c_0_21,plain,
! [X111,X112] :
( ~ m1_subset_1(X111,X112)
| v1_xboole_0(X112)
| r2_hidden(X111,X112) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
cnf(c_0_22,plain,
( m1_subset_1(X1,X4)
| v1_xboole_0(X3)
| ~ m2_fraenkel(X1,X2,X3,X4)
| ~ m1_fraenkel(X4,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,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_16]) ).
fof(c_0_24,plain,
! [X44,X45,X46] :
( ( ~ v1_xboole_0(X46)
| ~ m1_fraenkel(X46,X44,X45) )
& ( v1_fraenkel(X46)
| ~ m1_fraenkel(X46,X44,X45) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).
cnf(c_0_25,plain,
( m2_relset_1(X1,u1_struct_0(X2),u1_struct_0(X2))
| v3_struct_0(X2)
| ~ m2_fraenkel(X1,u1_struct_0(X2),u1_struct_0(X2),X3)
| X3 != k1_autgroup(X2)
| ~ m1_fraenkel(X3,u1_struct_0(X2),u1_struct_0(X2))
| ~ v1_group_1(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,negated_conjecture,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_27,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_28,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_29,negated_conjecture,
v1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_30,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_31,plain,
! [X41] :
( v3_struct_0(X41)
| ~ v1_group_1(X41)
| ~ v3_group_1(X41)
| ~ v4_group_1(X41)
| ~ l1_group_1(X41)
| m1_fraenkel(k1_autgroup(X41),u1_struct_0(X41),u1_struct_0(X41)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])]) ).
cnf(c_0_32,plain,
( v1_group_6(X1,X2,X2)
| v3_struct_0(X2)
| ~ m2_fraenkel(X1,u1_struct_0(X2),u1_struct_0(X2),X3)
| X3 != k1_autgroup(X2)
| ~ m1_fraenkel(X3,u1_struct_0(X2),u1_struct_0(X2))
| ~ v1_group_1(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_33,plain,
( v1_funct_2(X1,u1_struct_0(X2),u1_struct_0(X2))
| v3_struct_0(X2)
| ~ m2_fraenkel(X1,u1_struct_0(X2),u1_struct_0(X2),X3)
| X3 != k1_autgroup(X2)
| ~ m1_fraenkel(X3,u1_struct_0(X2),u1_struct_0(X2))
| ~ v1_group_1(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_34,plain,
( v1_funct_1(X1)
| v3_struct_0(X2)
| ~ m2_fraenkel(X1,u1_struct_0(X2),u1_struct_0(X2),X3)
| X3 != k1_autgroup(X2)
| ~ m1_fraenkel(X3,u1_struct_0(X2),u1_struct_0(X2))
| ~ v1_group_1(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_35,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v3_group_1(X2)
& v4_group_1(X2)
& l1_group_1(X2) )
=> ! [X3] :
( ( v1_funct_1(X3)
& v1_funct_2(X3,u1_struct_0(X2),u1_struct_0(X1))
& v1_group_6(X3,X2,X1)
& m2_relset_1(X3,u1_struct_0(X2),u1_struct_0(X1)) )
=> ! [X4] :
( ( v1_funct_1(X4)
& v1_funct_2(X4,u1_struct_0(X1),u1_struct_0(X2))
& v1_group_6(X4,X1,X2)
& m2_relset_1(X4,u1_struct_0(X1),u1_struct_0(X2)) )
=> ( ( v4_group_6(X3,X2,X1)
& X4 = k2_funct_1(X3) )
=> v4_group_6(X4,X1,X2) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[t73_group_6]) ).
fof(c_0_36,plain,
! [X118,X119] :
( ( ~ r2_hidden(X119,k1_autgroup(X118))
| v4_group_6(X119,X118,X118)
| ~ v1_funct_1(X119)
| ~ v1_funct_2(X119,u1_struct_0(X118),u1_struct_0(X118))
| ~ v1_group_6(X119,X118,X118)
| ~ m2_relset_1(X119,u1_struct_0(X118),u1_struct_0(X118))
| v3_struct_0(X118)
| ~ v1_group_1(X118)
| ~ v3_group_1(X118)
| ~ v4_group_1(X118)
| ~ l1_group_1(X118) )
& ( ~ v4_group_6(X119,X118,X118)
| r2_hidden(X119,k1_autgroup(X118))
| ~ v1_funct_1(X119)
| ~ v1_funct_2(X119,u1_struct_0(X118),u1_struct_0(X118))
| ~ v1_group_6(X119,X118,X118)
| ~ m2_relset_1(X119,u1_struct_0(X118),u1_struct_0(X118))
| v3_struct_0(X118)
| ~ v1_group_1(X118)
| ~ v3_group_1(X118)
| ~ v4_group_1(X118)
| ~ l1_group_1(X118) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).
cnf(c_0_37,plain,
( v1_xboole_0(X2)
| r2_hidden(X1,X2)
| ~ m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_38,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk1_0))
| m1_subset_1(esk2_0,k1_autgroup(esk1_0))
| ~ m1_fraenkel(k1_autgroup(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_39,plain,
( ~ v1_xboole_0(X1)
| ~ m1_fraenkel(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_40,negated_conjecture,
( m2_relset_1(esk2_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| ~ 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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_23]),c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_41,plain,
( v3_struct_0(X1)
| m1_fraenkel(k1_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1))
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_42,negated_conjecture,
( v1_group_6(esk2_0,esk1_0,esk1_0)
| ~ 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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_23]),c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_43,negated_conjecture,
( v1_funct_2(esk2_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| ~ 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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_23]),c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_44,negated_conjecture,
( v1_funct_1(esk2_0)
| ~ 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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_23]),c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
fof(c_0_45,plain,
! [X126,X127,X128,X129] :
( v3_struct_0(X126)
| ~ v3_group_1(X126)
| ~ v4_group_1(X126)
| ~ l1_group_1(X126)
| v3_struct_0(X127)
| ~ v3_group_1(X127)
| ~ v4_group_1(X127)
| ~ l1_group_1(X127)
| ~ v1_funct_1(X128)
| ~ v1_funct_2(X128,u1_struct_0(X127),u1_struct_0(X126))
| ~ v1_group_6(X128,X127,X126)
| ~ m2_relset_1(X128,u1_struct_0(X127),u1_struct_0(X126))
| ~ v1_funct_1(X129)
| ~ v1_funct_2(X129,u1_struct_0(X126),u1_struct_0(X127))
| ~ v1_group_6(X129,X126,X127)
| ~ m2_relset_1(X129,u1_struct_0(X126),u1_struct_0(X127))
| ~ v4_group_6(X128,X127,X126)
| X129 != k2_funct_1(X128)
| v4_group_6(X129,X126,X127) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])]) ).
cnf(c_0_46,plain,
( v4_group_6(X1,X2,X2)
| v3_struct_0(X2)
| ~ r2_hidden(X1,k1_autgroup(X2))
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,u1_struct_0(X2),u1_struct_0(X2))
| ~ v1_group_6(X1,X2,X2)
| ~ m2_relset_1(X1,u1_struct_0(X2),u1_struct_0(X2))
| ~ v1_group_1(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_47,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk1_0))
| r2_hidden(esk2_0,k1_autgroup(esk1_0))
| ~ m1_fraenkel(k1_autgroup(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_48,negated_conjecture,
m2_relset_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_40,c_0_41]),c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_49,negated_conjecture,
v1_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(spm,[status(thm)],[c_0_42,c_0_41]),c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_50,negated_conjecture,
v1_funct_2(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_43,c_0_41]),c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_51,negated_conjecture,
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_41]),c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
fof(c_0_52,plain,
! [X109,X110] :
( ~ r2_hidden(X109,X110)
| m1_subset_1(X109,X110) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
cnf(c_0_53,plain,
( v3_struct_0(X1)
| v3_struct_0(X2)
| v4_group_6(X4,X1,X2)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2)
| ~ v1_funct_1(X3)
| ~ v1_funct_2(X3,u1_struct_0(X2),u1_struct_0(X1))
| ~ v1_group_6(X3,X2,X1)
| ~ m2_relset_1(X3,u1_struct_0(X2),u1_struct_0(X1))
| ~ v1_funct_1(X4)
| ~ v1_funct_2(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_group_6(X4,X1,X2)
| ~ m2_relset_1(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v4_group_6(X3,X2,X1)
| X4 != k2_funct_1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_54,negated_conjecture,
( v4_group_6(esk2_0,esk1_0,esk1_0)
| v1_xboole_0(u1_struct_0(esk1_0))
| ~ 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(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_46,c_0_47]),c_0_48]),c_0_49]),c_0_50]),c_0_51]),c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
fof(c_0_55,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> ( v1_funct_1(k2_funct_1(X2))
& v1_funct_2(k2_funct_1(X2),u1_struct_0(X1),u1_struct_0(X1))
& v1_group_6(k2_funct_1(X2),X1,X1)
& m2_relset_1(k2_funct_1(X2),u1_struct_0(X1),u1_struct_0(X1)) ) ) ),
inference(fof_simplification,[status(thm)],[t6_autgroup]) ).
cnf(c_0_56,plain,
( m2_fraenkel(X1,X3,X4,X2)
| v1_xboole_0(X4)
| ~ m1_subset_1(X1,X2)
| ~ m1_fraenkel(X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_57,plain,
( m1_subset_1(X1,X2)
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_58,plain,
( r2_hidden(X1,k1_autgroup(X2))
| v3_struct_0(X2)
| ~ v4_group_6(X1,X2,X2)
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,u1_struct_0(X2),u1_struct_0(X2))
| ~ v1_group_6(X1,X2,X2)
| ~ m2_relset_1(X1,u1_struct_0(X2),u1_struct_0(X2))
| ~ v1_group_1(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_59,negated_conjecture,
( v4_group_6(X1,esk1_0,esk1_0)
| v1_xboole_0(u1_struct_0(esk1_0))
| X1 != k2_funct_1(esk2_0)
| ~ m1_fraenkel(k1_autgroup(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| ~ m2_relset_1(X1,u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| ~ v1_group_6(X1,esk1_0,esk1_0)
| ~ v1_funct_2(X1,u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| ~ v1_funct_1(X1) ),
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(spm,[status(thm)],[c_0_53,c_0_54]),c_0_48]),c_0_49]),c_0_50]),c_0_51]),c_0_26]),c_0_27]),c_0_28])]),c_0_30]) ).
fof(c_0_60,plain,
! [X123,X124] :
( ( v1_funct_1(k2_funct_1(X124))
| ~ m2_fraenkel(X124,u1_struct_0(X123),u1_struct_0(X123),k1_autgroup(X123))
| v3_struct_0(X123)
| ~ v1_group_1(X123)
| ~ v3_group_1(X123)
| ~ v4_group_1(X123)
| ~ l1_group_1(X123) )
& ( v1_funct_2(k2_funct_1(X124),u1_struct_0(X123),u1_struct_0(X123))
| ~ m2_fraenkel(X124,u1_struct_0(X123),u1_struct_0(X123),k1_autgroup(X123))
| v3_struct_0(X123)
| ~ v1_group_1(X123)
| ~ v3_group_1(X123)
| ~ v4_group_1(X123)
| ~ l1_group_1(X123) )
& ( v1_group_6(k2_funct_1(X124),X123,X123)
| ~ m2_fraenkel(X124,u1_struct_0(X123),u1_struct_0(X123),k1_autgroup(X123))
| v3_struct_0(X123)
| ~ v1_group_1(X123)
| ~ v3_group_1(X123)
| ~ v4_group_1(X123)
| ~ l1_group_1(X123) )
& ( m2_relset_1(k2_funct_1(X124),u1_struct_0(X123),u1_struct_0(X123))
| ~ m2_fraenkel(X124,u1_struct_0(X123),u1_struct_0(X123),k1_autgroup(X123))
| v3_struct_0(X123)
| ~ v1_group_1(X123)
| ~ v3_group_1(X123)
| ~ v4_group_1(X123)
| ~ l1_group_1(X123) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])])]) ).
fof(c_0_61,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).
cnf(c_0_62,plain,
( v1_xboole_0(X1)
| m2_fraenkel(X2,X3,X1,X4)
| ~ m1_fraenkel(X4,X3,X1)
| ~ r2_hidden(X2,X4) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_63,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk1_0))
| r2_hidden(X1,k1_autgroup(esk1_0))
| X1 != k2_funct_1(esk2_0)
| ~ m1_fraenkel(k1_autgroup(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| ~ m2_relset_1(X1,u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| ~ v1_group_6(X1,esk1_0,esk1_0)
| ~ v1_funct_2(X1,u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| ~ v1_funct_1(X1) ),
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_58,c_0_59]),c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_64,plain,
( m2_relset_1(k2_funct_1(X1),u1_struct_0(X2),u1_struct_0(X2))
| v3_struct_0(X2)
| ~ m2_fraenkel(X1,u1_struct_0(X2),u1_struct_0(X2),k1_autgroup(X2))
| ~ v1_group_1(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_65,plain,
( v1_group_6(k2_funct_1(X1),X2,X2)
| v3_struct_0(X2)
| ~ m2_fraenkel(X1,u1_struct_0(X2),u1_struct_0(X2),k1_autgroup(X2))
| ~ v1_group_1(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_66,plain,
( v1_funct_2(k2_funct_1(X1),u1_struct_0(X2),u1_struct_0(X2))
| v3_struct_0(X2)
| ~ m2_fraenkel(X1,u1_struct_0(X2),u1_struct_0(X2),k1_autgroup(X2))
| ~ v1_group_1(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_67,plain,
( v1_funct_1(k2_funct_1(X1))
| v3_struct_0(X2)
| ~ m2_fraenkel(X1,u1_struct_0(X2),u1_struct_0(X2),k1_autgroup(X2))
| ~ v1_group_1(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
fof(c_0_68,plain,
! [X74] :
( v3_struct_0(X74)
| ~ l1_struct_0(X74)
| ~ v1_xboole_0(u1_struct_0(X74)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_61])]) ).
fof(c_0_69,plain,
! [X43] :
( ~ l1_group_1(X43)
| l1_struct_0(X43) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_group_1])]) ).
cnf(c_0_70,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_16]) ).
cnf(c_0_71,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk1_0))
| v1_xboole_0(X1)
| m2_fraenkel(X2,X3,X1,k1_autgroup(esk1_0))
| X2 != k2_funct_1(esk2_0)
| ~ m1_fraenkel(k1_autgroup(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| ~ m1_fraenkel(k1_autgroup(esk1_0),X3,X1)
| ~ m2_relset_1(X2,u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| ~ v1_group_6(X2,esk1_0,esk1_0)
| ~ v1_funct_2(X2,u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| ~ v1_funct_1(X2) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_72,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_64,c_0_23]),c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_73,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_65,c_0_23]),c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_74,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_66,c_0_23]),c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_75,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_67,c_0_23]),c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_76,plain,
( v3_struct_0(X1)
| ~ l1_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_77,plain,
( l1_struct_0(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_78,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk1_0))
| ~ m1_fraenkel(k1_autgroup(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0)) ),
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_70,c_0_71]),c_0_72]),c_0_73]),c_0_74]),c_0_75])]) ).
cnf(c_0_79,plain,
( v3_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1))
| ~ l1_group_1(X1) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_80,negated_conjecture,
v1_xboole_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_78,c_0_41]),c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_81,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_26])]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP620+1 : TPTP v8.1.2. Released v3.4.0.
% 0.10/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.33 % Computer : n009.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon Aug 28 21:53:05 EDT 2023
% 0.14/0.33 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.58/0.68 % Version : CSE_E---1.5
% 0.58/0.68 % Problem : theBenchmark.p
% 0.58/0.68 % Proof found
% 0.58/0.68 % SZS status Theorem for theBenchmark.p
% 0.58/0.68 % SZS output start Proof
% See solution above
% 0.58/0.69 % Total time : 0.116000 s
% 0.58/0.69 % SZS output end Proof
% 0.58/0.69 % Total time : 0.120000 s
%------------------------------------------------------------------------------