%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP620+1 : TPTP v9.2.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n005.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 : Tue May 5 04:26:32 PM UTC 2026
% Result : Theorem 1.34s 1.74s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 82 ( 17 unt; 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 predicates : 21 ( 19 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 133 ( 2 sgn 77 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',t73_group_6) ).
fof(t1_subset,axiom,
! [X1,X2] :
( r2_hidden(X1,X2)
=> m1_subset_1(X1,X2) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(dt_l1_group_1,axiom,
! [X1] :
( l1_group_1(X1)
=> l1_struct_0(X1) ),
file('/export/starexec/sandbox2/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,
! [X229,X230,X231,X232] :
( ( ~ m2_fraenkel(X232,X229,X230,X231)
| m1_subset_1(X232,X231)
| v1_xboole_0(X230)
| ~ m1_fraenkel(X231,X229,X230) )
& ( ~ m1_subset_1(X232,X231)
| m2_fraenkel(X232,X229,X230,X231)
| v1_xboole_0(X230)
| ~ m1_fraenkel(X231,X229,X230) ) ),
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,
! [X161,X162,X163,X164] :
( ( v1_funct_1(X163)
| ~ m2_fraenkel(X163,u1_struct_0(X161),u1_struct_0(X161),X162)
| X162 != k1_autgroup(X161)
| ~ m1_fraenkel(X162,u1_struct_0(X161),u1_struct_0(X161))
| v3_struct_0(X161)
| ~ v1_group_1(X161)
| ~ v3_group_1(X161)
| ~ v4_group_1(X161)
| ~ l1_group_1(X161) )
& ( v1_funct_2(X163,u1_struct_0(X161),u1_struct_0(X161))
| ~ m2_fraenkel(X163,u1_struct_0(X161),u1_struct_0(X161),X162)
| X162 != k1_autgroup(X161)
| ~ m1_fraenkel(X162,u1_struct_0(X161),u1_struct_0(X161))
| v3_struct_0(X161)
| ~ v1_group_1(X161)
| ~ v3_group_1(X161)
| ~ v4_group_1(X161)
| ~ l1_group_1(X161) )
& ( v1_group_6(X163,X161,X161)
| ~ m2_fraenkel(X163,u1_struct_0(X161),u1_struct_0(X161),X162)
| X162 != k1_autgroup(X161)
| ~ m1_fraenkel(X162,u1_struct_0(X161),u1_struct_0(X161))
| v3_struct_0(X161)
| ~ v1_group_1(X161)
| ~ v3_group_1(X161)
| ~ v4_group_1(X161)
| ~ l1_group_1(X161) )
& ( m2_relset_1(X163,u1_struct_0(X161),u1_struct_0(X161))
| ~ m2_fraenkel(X163,u1_struct_0(X161),u1_struct_0(X161),X162)
| X162 != k1_autgroup(X161)
| ~ m1_fraenkel(X162,u1_struct_0(X161),u1_struct_0(X161))
| v3_struct_0(X161)
| ~ v1_group_1(X161)
| ~ v3_group_1(X161)
| ~ v4_group_1(X161)
| ~ l1_group_1(X161) )
& ( v2_funct_1(X164)
| ~ r2_hidden(X164,X162)
| ~ v1_funct_1(X164)
| ~ v1_funct_2(X164,u1_struct_0(X161),u1_struct_0(X161))
| ~ v1_group_6(X164,X161,X161)
| ~ m2_relset_1(X164,u1_struct_0(X161),u1_struct_0(X161))
| X162 != k1_autgroup(X161)
| ~ m1_fraenkel(X162,u1_struct_0(X161),u1_struct_0(X161))
| v3_struct_0(X161)
| ~ v1_group_1(X161)
| ~ v3_group_1(X161)
| ~ v4_group_1(X161)
| ~ l1_group_1(X161) )
& ( v3_group_6(X164,X161,X161)
| ~ r2_hidden(X164,X162)
| ~ v1_funct_1(X164)
| ~ v1_funct_2(X164,u1_struct_0(X161),u1_struct_0(X161))
| ~ v1_group_6(X164,X161,X161)
| ~ m2_relset_1(X164,u1_struct_0(X161),u1_struct_0(X161))
| X162 != k1_autgroup(X161)
| ~ m1_fraenkel(X162,u1_struct_0(X161),u1_struct_0(X161))
| v3_struct_0(X161)
| ~ v1_group_1(X161)
| ~ v3_group_1(X161)
| ~ v4_group_1(X161)
| ~ l1_group_1(X161) )
& ( ~ v2_funct_1(X164)
| ~ v3_group_6(X164,X161,X161)
| r2_hidden(X164,X162)
| ~ v1_funct_1(X164)
| ~ v1_funct_2(X164,u1_struct_0(X161),u1_struct_0(X161))
| ~ v1_group_6(X164,X161,X161)
| ~ m2_relset_1(X164,u1_struct_0(X161),u1_struct_0(X161))
| X162 != k1_autgroup(X161)
| ~ m1_fraenkel(X162,u1_struct_0(X161),u1_struct_0(X161))
| v3_struct_0(X161)
| ~ v1_group_1(X161)
| ~ v3_group_1(X161)
| ~ v4_group_1(X161)
| ~ l1_group_1(X161) )
& ( v1_funct_1(esk4_2(X161,X162))
| m2_fraenkel(esk3_2(X161,X162),u1_struct_0(X161),u1_struct_0(X161),X162)
| X162 = k1_autgroup(X161)
| ~ m1_fraenkel(X162,u1_struct_0(X161),u1_struct_0(X161))
| v3_struct_0(X161)
| ~ v1_group_1(X161)
| ~ v3_group_1(X161)
| ~ v4_group_1(X161)
| ~ l1_group_1(X161) )
& ( v1_funct_2(esk4_2(X161,X162),u1_struct_0(X161),u1_struct_0(X161))
| m2_fraenkel(esk3_2(X161,X162),u1_struct_0(X161),u1_struct_0(X161),X162)
| X162 = k1_autgroup(X161)
| ~ m1_fraenkel(X162,u1_struct_0(X161),u1_struct_0(X161))
| v3_struct_0(X161)
| ~ v1_group_1(X161)
| ~ v3_group_1(X161)
| ~ v4_group_1(X161)
| ~ l1_group_1(X161) )
& ( v1_group_6(esk4_2(X161,X162),X161,X161)
| m2_fraenkel(esk3_2(X161,X162),u1_struct_0(X161),u1_struct_0(X161),X162)
| X162 = k1_autgroup(X161)
| ~ m1_fraenkel(X162,u1_struct_0(X161),u1_struct_0(X161))
| v3_struct_0(X161)
| ~ v1_group_1(X161)
| ~ v3_group_1(X161)
| ~ v4_group_1(X161)
| ~ l1_group_1(X161) )
& ( m2_relset_1(esk4_2(X161,X162),u1_struct_0(X161),u1_struct_0(X161))
| m2_fraenkel(esk3_2(X161,X162),u1_struct_0(X161),u1_struct_0(X161),X162)
| X162 = k1_autgroup(X161)
| ~ m1_fraenkel(X162,u1_struct_0(X161),u1_struct_0(X161))
| v3_struct_0(X161)
| ~ v1_group_1(X161)
| ~ v3_group_1(X161)
| ~ v4_group_1(X161)
| ~ l1_group_1(X161) )
& ( ~ r2_hidden(esk4_2(X161,X162),X162)
| ~ v2_funct_1(esk4_2(X161,X162))
| ~ v3_group_6(esk4_2(X161,X162),X161,X161)
| m2_fraenkel(esk3_2(X161,X162),u1_struct_0(X161),u1_struct_0(X161),X162)
| X162 = k1_autgroup(X161)
| ~ m1_fraenkel(X162,u1_struct_0(X161),u1_struct_0(X161))
| v3_struct_0(X161)
| ~ v1_group_1(X161)
| ~ v3_group_1(X161)
| ~ v4_group_1(X161)
| ~ l1_group_1(X161) )
& ( v2_funct_1(esk4_2(X161,X162))
| r2_hidden(esk4_2(X161,X162),X162)
| m2_fraenkel(esk3_2(X161,X162),u1_struct_0(X161),u1_struct_0(X161),X162)
| X162 = k1_autgroup(X161)
| ~ m1_fraenkel(X162,u1_struct_0(X161),u1_struct_0(X161))
| v3_struct_0(X161)
| ~ v1_group_1(X161)
| ~ v3_group_1(X161)
| ~ v4_group_1(X161)
| ~ l1_group_1(X161) )
& ( v3_group_6(esk4_2(X161,X162),X161,X161)
| r2_hidden(esk4_2(X161,X162),X162)
| m2_fraenkel(esk3_2(X161,X162),u1_struct_0(X161),u1_struct_0(X161),X162)
| X162 = k1_autgroup(X161)
| ~ m1_fraenkel(X162,u1_struct_0(X161),u1_struct_0(X161))
| v3_struct_0(X161)
| ~ v1_group_1(X161)
| ~ v3_group_1(X161)
| ~ v4_group_1(X161)
| ~ l1_group_1(X161) )
& ( v1_funct_1(esk4_2(X161,X162))
| ~ v1_funct_1(esk3_2(X161,X162))
| ~ v1_funct_2(esk3_2(X161,X162),u1_struct_0(X161),u1_struct_0(X161))
| ~ v1_group_6(esk3_2(X161,X162),X161,X161)
| ~ m2_relset_1(esk3_2(X161,X162),u1_struct_0(X161),u1_struct_0(X161))
| X162 = k1_autgroup(X161)
| ~ m1_fraenkel(X162,u1_struct_0(X161),u1_struct_0(X161))
| v3_struct_0(X161)
| ~ v1_group_1(X161)
| ~ v3_group_1(X161)
| ~ v4_group_1(X161)
| ~ l1_group_1(X161) )
& ( v1_funct_2(esk4_2(X161,X162),u1_struct_0(X161),u1_struct_0(X161))
| ~ v1_funct_1(esk3_2(X161,X162))
| ~ v1_funct_2(esk3_2(X161,X162),u1_struct_0(X161),u1_struct_0(X161))
| ~ v1_group_6(esk3_2(X161,X162),X161,X161)
| ~ m2_relset_1(esk3_2(X161,X162),u1_struct_0(X161),u1_struct_0(X161))
| X162 = k1_autgroup(X161)
| ~ m1_fraenkel(X162,u1_struct_0(X161),u1_struct_0(X161))
| v3_struct_0(X161)
| ~ v1_group_1(X161)
| ~ v3_group_1(X161)
| ~ v4_group_1(X161)
| ~ l1_group_1(X161) )
& ( v1_group_6(esk4_2(X161,X162),X161,X161)
| ~ v1_funct_1(esk3_2(X161,X162))
| ~ v1_funct_2(esk3_2(X161,X162),u1_struct_0(X161),u1_struct_0(X161))
| ~ v1_group_6(esk3_2(X161,X162),X161,X161)
| ~ m2_relset_1(esk3_2(X161,X162),u1_struct_0(X161),u1_struct_0(X161))
| X162 = k1_autgroup(X161)
| ~ m1_fraenkel(X162,u1_struct_0(X161),u1_struct_0(X161))
| v3_struct_0(X161)
| ~ v1_group_1(X161)
| ~ v3_group_1(X161)
| ~ v4_group_1(X161)
| ~ l1_group_1(X161) )
& ( m2_relset_1(esk4_2(X161,X162),u1_struct_0(X161),u1_struct_0(X161))
| ~ v1_funct_1(esk3_2(X161,X162))
| ~ v1_funct_2(esk3_2(X161,X162),u1_struct_0(X161),u1_struct_0(X161))
| ~ v1_group_6(esk3_2(X161,X162),X161,X161)
| ~ m2_relset_1(esk3_2(X161,X162),u1_struct_0(X161),u1_struct_0(X161))
| X162 = k1_autgroup(X161)
| ~ m1_fraenkel(X162,u1_struct_0(X161),u1_struct_0(X161))
| v3_struct_0(X161)
| ~ v1_group_1(X161)
| ~ v3_group_1(X161)
| ~ v4_group_1(X161)
| ~ l1_group_1(X161) )
& ( ~ r2_hidden(esk4_2(X161,X162),X162)
| ~ v2_funct_1(esk4_2(X161,X162))
| ~ v3_group_6(esk4_2(X161,X162),X161,X161)
| ~ v1_funct_1(esk3_2(X161,X162))
| ~ v1_funct_2(esk3_2(X161,X162),u1_struct_0(X161),u1_struct_0(X161))
| ~ v1_group_6(esk3_2(X161,X162),X161,X161)
| ~ m2_relset_1(esk3_2(X161,X162),u1_struct_0(X161),u1_struct_0(X161))
| X162 = k1_autgroup(X161)
| ~ m1_fraenkel(X162,u1_struct_0(X161),u1_struct_0(X161))
| v3_struct_0(X161)
| ~ v1_group_1(X161)
| ~ v3_group_1(X161)
| ~ v4_group_1(X161)
| ~ l1_group_1(X161) )
& ( v2_funct_1(esk4_2(X161,X162))
| r2_hidden(esk4_2(X161,X162),X162)
| ~ v1_funct_1(esk3_2(X161,X162))
| ~ v1_funct_2(esk3_2(X161,X162),u1_struct_0(X161),u1_struct_0(X161))
| ~ v1_group_6(esk3_2(X161,X162),X161,X161)
| ~ m2_relset_1(esk3_2(X161,X162),u1_struct_0(X161),u1_struct_0(X161))
| X162 = k1_autgroup(X161)
| ~ m1_fraenkel(X162,u1_struct_0(X161),u1_struct_0(X161))
| v3_struct_0(X161)
| ~ v1_group_1(X161)
| ~ v3_group_1(X161)
| ~ v4_group_1(X161)
| ~ l1_group_1(X161) )
& ( v3_group_6(esk4_2(X161,X162),X161,X161)
| r2_hidden(esk4_2(X161,X162),X162)
| ~ v1_funct_1(esk3_2(X161,X162))
| ~ v1_funct_2(esk3_2(X161,X162),u1_struct_0(X161),u1_struct_0(X161))
| ~ v1_group_6(esk3_2(X161,X162),X161,X161)
| ~ m2_relset_1(esk3_2(X161,X162),u1_struct_0(X161),u1_struct_0(X161))
| X162 = k1_autgroup(X161)
| ~ m1_fraenkel(X162,u1_struct_0(X161),u1_struct_0(X161))
| v3_struct_0(X161)
| ~ v1_group_1(X161)
| ~ v3_group_1(X161)
| ~ v4_group_1(X161)
| ~ l1_group_1(X161) ) ),
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,
! [X239,X240] :
( ~ m1_subset_1(X239,X240)
| v1_xboole_0(X240)
| r2_hidden(X239,X240) ),
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,
! [X172,X173,X174] :
( ( ~ v1_xboole_0(X174)
| ~ m1_fraenkel(X174,X172,X173) )
& ( v1_fraenkel(X174)
| ~ m1_fraenkel(X174,X172,X173) ) ),
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,
! [X169] :
( v3_struct_0(X169)
| ~ v1_group_1(X169)
| ~ v3_group_1(X169)
| ~ v4_group_1(X169)
| ~ l1_group_1(X169)
| m1_fraenkel(k1_autgroup(X169),u1_struct_0(X169),u1_struct_0(X169)) ),
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,
! [X246,X247] :
( ( ~ r2_hidden(X247,k1_autgroup(X246))
| v4_group_6(X247,X246,X246)
| ~ v1_funct_1(X247)
| ~ v1_funct_2(X247,u1_struct_0(X246),u1_struct_0(X246))
| ~ v1_group_6(X247,X246,X246)
| ~ m2_relset_1(X247,u1_struct_0(X246),u1_struct_0(X246))
| v3_struct_0(X246)
| ~ v1_group_1(X246)
| ~ v3_group_1(X246)
| ~ v4_group_1(X246)
| ~ l1_group_1(X246) )
& ( ~ v4_group_6(X247,X246,X246)
| r2_hidden(X247,k1_autgroup(X246))
| ~ v1_funct_1(X247)
| ~ v1_funct_2(X247,u1_struct_0(X246),u1_struct_0(X246))
| ~ v1_group_6(X247,X246,X246)
| ~ m2_relset_1(X247,u1_struct_0(X246),u1_struct_0(X246))
| v3_struct_0(X246)
| ~ v1_group_1(X246)
| ~ v3_group_1(X246)
| ~ v4_group_1(X246)
| ~ l1_group_1(X246) ) ),
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,
! [X254,X255,X256,X257] :
( v3_struct_0(X254)
| ~ v3_group_1(X254)
| ~ v4_group_1(X254)
| ~ l1_group_1(X254)
| v3_struct_0(X255)
| ~ v3_group_1(X255)
| ~ v4_group_1(X255)
| ~ l1_group_1(X255)
| ~ v1_funct_1(X256)
| ~ v1_funct_2(X256,u1_struct_0(X255),u1_struct_0(X254))
| ~ v1_group_6(X256,X255,X254)
| ~ m2_relset_1(X256,u1_struct_0(X255),u1_struct_0(X254))
| ~ v1_funct_1(X257)
| ~ v1_funct_2(X257,u1_struct_0(X254),u1_struct_0(X255))
| ~ v1_group_6(X257,X254,X255)
| ~ m2_relset_1(X257,u1_struct_0(X254),u1_struct_0(X255))
| ~ v4_group_6(X256,X255,X254)
| X257 != k2_funct_1(X256)
| v4_group_6(X257,X254,X255) ),
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,
! [X237,X238] :
( ~ r2_hidden(X237,X238)
| m1_subset_1(X237,X238) ),
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,
! [X251,X252] :
( ( v1_funct_1(k2_funct_1(X252))
| ~ m2_fraenkel(X252,u1_struct_0(X251),u1_struct_0(X251),k1_autgroup(X251))
| v3_struct_0(X251)
| ~ v1_group_1(X251)
| ~ v3_group_1(X251)
| ~ v4_group_1(X251)
| ~ l1_group_1(X251) )
& ( v1_funct_2(k2_funct_1(X252),u1_struct_0(X251),u1_struct_0(X251))
| ~ m2_fraenkel(X252,u1_struct_0(X251),u1_struct_0(X251),k1_autgroup(X251))
| v3_struct_0(X251)
| ~ v1_group_1(X251)
| ~ v3_group_1(X251)
| ~ v4_group_1(X251)
| ~ l1_group_1(X251) )
& ( v1_group_6(k2_funct_1(X252),X251,X251)
| ~ m2_fraenkel(X252,u1_struct_0(X251),u1_struct_0(X251),k1_autgroup(X251))
| v3_struct_0(X251)
| ~ v1_group_1(X251)
| ~ v3_group_1(X251)
| ~ v4_group_1(X251)
| ~ l1_group_1(X251) )
& ( m2_relset_1(k2_funct_1(X252),u1_struct_0(X251),u1_struct_0(X251))
| ~ m2_fraenkel(X252,u1_struct_0(X251),u1_struct_0(X251),k1_autgroup(X251))
| v3_struct_0(X251)
| ~ v1_group_1(X251)
| ~ v3_group_1(X251)
| ~ v4_group_1(X251)
| ~ l1_group_1(X251) ) ),
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,
! [X202] :
( v3_struct_0(X202)
| ~ l1_struct_0(X202)
| ~ v1_xboole_0(u1_struct_0(X202)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_61])]) ).
fof(c_0_69,plain,
! [X171] :
( ~ l1_group_1(X171)
| l1_struct_0(X171) ),
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
% 0.00/0.12 % Problem : GRP620+1 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n005.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 18:46:15 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.34/1.74 % Version : CSE_E---1.7
% 1.34/1.74 % Problem : theBenchmark.p
% 1.34/1.74 % SZS status Theorem for theBenchmark.p
% 1.34/1.74 % SZS output start CNFRefutation
% See solution above
% 1.34/1.75 % Total time : 1.372s
%------------------------------------------------------------------------------