%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP621+1 : TPTP v9.2.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n004.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 04:26:33 PM UTC 2026
% Result : Theorem 8.30s 5.78s
% Output : CNFRefutation 8.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 21
% Syntax : Number of formulae : 136 ( 40 unt; 0 def)
% Number of atoms : 1079 ( 36 equ)
% Maximal formula atoms : 231 ( 7 avg)
% Number of connectives : 1518 ( 575 ~; 623 |; 253 &)
% ( 9 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 38 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-5 aty)
% Number of variables : 281 ( 14 sgn 174 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t8_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))
=> ! [X3] :
( m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> m2_fraenkel(k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X3,X2),u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_autgroup) ).
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(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(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(dt_m2_fraenkel,axiom,
! [X1,X2,X3] :
( ( ~ v1_xboole_0(X2)
& m1_fraenkel(X3,X1,X2) )
=> ! [X4] :
( m2_fraenkel(X4,X1,X2,X3)
=> ( v1_funct_1(X4)
& v1_funct_2(X4,X1,X2)
& m2_relset_1(X4,X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_fraenkel) ).
fof(cc1_fraenkel,axiom,
! [X1] :
( v1_fraenkel(X1)
=> ! [X2] :
( m1_subset_1(X2,X1)
=> ( v1_relat_1(X2)
& v1_funct_1(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_fraenkel) ).
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(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(redefinition_k7_funct_2,axiom,
! [X1,X2,X3,X4,X5] :
( ( ~ v1_xboole_0(X2)
& v1_funct_1(X4)
& v1_funct_2(X4,X1,X2)
& m1_relset_1(X4,X1,X2)
& v1_funct_1(X5)
& v1_funct_2(X5,X2,X3)
& m1_relset_1(X5,X2,X3) )
=> k7_funct_2(X1,X2,X3,X4,X5) = k5_relat_1(X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_funct_2) ).
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
<=> m1_relset_1(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(dt_k7_funct_2,axiom,
! [X1,X2,X3,X4,X5] :
( ( ~ v1_xboole_0(X2)
& v1_funct_1(X4)
& v1_funct_2(X4,X1,X2)
& m1_relset_1(X4,X1,X2)
& v1_funct_1(X5)
& v1_funct_2(X5,X2,X3)
& m1_relset_1(X5,X2,X3) )
=> ( v1_funct_1(k7_funct_2(X1,X2,X3,X4,X5))
& v1_funct_2(k7_funct_2(X1,X2,X3,X4,X5),X1,X3)
& m2_relset_1(k7_funct_2(X1,X2,X3,X4,X5),X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_funct_2) ).
fof(fc1_funct_1,axiom,
! [X1,X2] :
( ( v1_relat_1(X1)
& v1_funct_1(X1)
& v1_relat_1(X2)
& v1_funct_1(X2) )
=> ( v1_relat_1(k5_relat_1(X1,X2))
& v1_funct_1(k5_relat_1(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(cc1_relset_1,axiom,
! [X1,X2,X3] :
( m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
=> v1_relat_1(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(dt_m2_relset_1,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
=> m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(redefinition_k8_group_6,axiom,
! [X1,X2,X3,X4,X5] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1)
& ~ v3_struct_0(X2)
& v3_group_1(X2)
& v4_group_1(X2)
& l1_group_1(X2)
& ~ v3_struct_0(X3)
& v3_group_1(X3)
& v4_group_1(X3)
& l1_group_1(X3)
& v1_funct_1(X4)
& v1_funct_2(X4,u1_struct_0(X1),u1_struct_0(X2))
& v1_group_6(X4,X1,X2)
& m1_relset_1(X4,u1_struct_0(X1),u1_struct_0(X2))
& v1_funct_1(X5)
& v1_funct_2(X5,u1_struct_0(X2),u1_struct_0(X3))
& v1_group_6(X5,X2,X3)
& m1_relset_1(X5,u1_struct_0(X2),u1_struct_0(X3)) )
=> k8_group_6(X1,X2,X3,X4,X5) = k5_relat_1(X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_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(dt_k8_group_6,axiom,
! [X1,X2,X3,X4,X5] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1)
& ~ v3_struct_0(X2)
& v3_group_1(X2)
& v4_group_1(X2)
& l1_group_1(X2)
& ~ v3_struct_0(X3)
& v3_group_1(X3)
& v4_group_1(X3)
& l1_group_1(X3)
& v1_funct_1(X4)
& v1_funct_2(X4,u1_struct_0(X1),u1_struct_0(X2))
& v1_group_6(X4,X1,X2)
& m1_relset_1(X4,u1_struct_0(X1),u1_struct_0(X2))
& v1_funct_1(X5)
& v1_funct_2(X5,u1_struct_0(X2),u1_struct_0(X3))
& v1_group_6(X5,X2,X3)
& m1_relset_1(X5,u1_struct_0(X2),u1_struct_0(X3)) )
=> ( v1_funct_1(k8_group_6(X1,X2,X3,X4,X5))
& v1_funct_2(k8_group_6(X1,X2,X3,X4,X5),u1_struct_0(X1),u1_struct_0(X3))
& v1_group_6(k8_group_6(X1,X2,X3,X4,X5),X1,X3)
& m2_relset_1(k8_group_6(X1,X2,X3,X4,X5),u1_struct_0(X1),u1_struct_0(X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_group_6) ).
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(t74_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] :
( ( ~ v3_struct_0(X3)
& v3_group_1(X3)
& v4_group_1(X3)
& l1_group_1(X3) )
=> ! [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)) )
=> ! [X5] :
( ( v1_funct_1(X5)
& v1_funct_2(X5,u1_struct_0(X2),u1_struct_0(X3))
& v1_group_6(X5,X2,X3)
& m2_relset_1(X5,u1_struct_0(X2),u1_struct_0(X3)) )
=> ( ( v4_group_6(X4,X1,X2)
& v4_group_6(X5,X2,X3) )
=> v4_group_6(k8_group_6(X1,X2,X3,X4,X5),X1,X3) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_group_6) ).
fof(c_0_21,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))
=> ! [X3] :
( m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> m2_fraenkel(k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X3,X2),u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1)) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t8_autgroup])]) ).
fof(c_0_22,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_23,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]) ).
fof(c_0_24,plain,
! [X195] :
( ~ l1_group_1(X195)
| l1_struct_0(X195) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_group_1])]) ).
fof(c_0_25,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(esk3_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0),k1_autgroup(esk1_0))
& ~ m2_fraenkel(k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),esk3_0,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_21])])]) ).
fof(c_0_26,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_27,plain,
! [X182] :
( v3_struct_0(X182)
| ~ v1_group_1(X182)
| ~ v3_group_1(X182)
| ~ v4_group_1(X182)
| ~ l1_group_1(X182)
| m1_fraenkel(k1_autgroup(X182),u1_struct_0(X182),u1_struct_0(X182)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])]) ).
fof(c_0_28,plain,
! [X228] :
( v3_struct_0(X228)
| ~ l1_struct_0(X228)
| ~ v1_xboole_0(u1_struct_0(X228)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])]) ).
cnf(c_0_29,plain,
( l1_struct_0(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,negated_conjecture,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_31,plain,
! [X265,X266,X267,X268] :
( ( ~ m2_fraenkel(X268,X265,X266,X267)
| m1_subset_1(X268,X267)
| v1_xboole_0(X266)
| ~ m1_fraenkel(X267,X265,X266) )
& ( ~ m1_subset_1(X268,X267)
| m2_fraenkel(X268,X265,X266,X267)
| v1_xboole_0(X266)
| ~ m1_fraenkel(X267,X265,X266) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])])]) ).
cnf(c_0_32,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_27]) ).
cnf(c_0_33,negated_conjecture,
v1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_34,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_35,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_36,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_37,plain,
( v3_struct_0(X1)
| ~ l1_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,negated_conjecture,
l1_struct_0(esk1_0),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
fof(c_0_39,plain,
! [X1,X2,X3] :
( ( ~ v1_xboole_0(X2)
& m1_fraenkel(X3,X1,X2) )
=> ! [X4] :
( m2_fraenkel(X4,X1,X2,X3)
=> ( v1_funct_1(X4)
& v1_funct_2(X4,X1,X2)
& m2_relset_1(X4,X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[dt_m2_fraenkel]) ).
fof(c_0_40,plain,
! [X157,X158] :
( ( v1_relat_1(X158)
| ~ m1_subset_1(X158,X157)
| ~ v1_fraenkel(X157) )
& ( v1_funct_1(X158)
| ~ m1_subset_1(X158,X157)
| ~ v1_fraenkel(X157) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_fraenkel])])])]) ).
cnf(c_0_41,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_31]) ).
cnf(c_0_42,negated_conjecture,
m2_fraenkel(esk3_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0),k1_autgroup(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_43,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_32,c_0_33]),c_0_30]),c_0_34]),c_0_35])]),c_0_36]) ).
cnf(c_0_44,negated_conjecture,
~ v1_xboole_0(u1_struct_0(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]) ).
fof(c_0_45,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_46,plain,
! [X199,X200,X201,X202] :
( ( v1_funct_1(X202)
| ~ m2_fraenkel(X202,X199,X200,X201)
| v1_xboole_0(X200)
| ~ m1_fraenkel(X201,X199,X200) )
& ( v1_funct_2(X202,X199,X200)
| ~ m2_fraenkel(X202,X199,X200,X201)
| v1_xboole_0(X200)
| ~ m1_fraenkel(X201,X199,X200) )
& ( m2_relset_1(X202,X199,X200)
| ~ m2_fraenkel(X202,X199,X200,X201)
| v1_xboole_0(X200)
| ~ m1_fraenkel(X201,X199,X200) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])])]) ).
cnf(c_0_47,plain,
( v1_relat_1(X1)
| ~ m1_subset_1(X1,X2)
| ~ v1_fraenkel(X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_48,negated_conjecture,
m1_subset_1(esk3_0,k1_autgroup(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]),c_0_44]) ).
fof(c_0_49,plain,
! [X196,X197,X198] :
( ( ~ v1_xboole_0(X198)
| ~ m1_fraenkel(X198,X196,X197) )
& ( v1_fraenkel(X198)
| ~ m1_fraenkel(X198,X196,X197) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])]) ).
cnf(c_0_50,plain,
( v1_funct_1(X1)
| v1_xboole_0(X3)
| ~ m2_fraenkel(X1,X2,X3,X4)
| ~ m1_fraenkel(X4,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
fof(c_0_51,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_52,plain,
! [X1,X2,X3,X4,X5] :
( ( ~ v1_xboole_0(X2)
& v1_funct_1(X4)
& v1_funct_2(X4,X1,X2)
& m1_relset_1(X4,X1,X2)
& v1_funct_1(X5)
& v1_funct_2(X5,X2,X3)
& m1_relset_1(X5,X2,X3) )
=> k7_funct_2(X1,X2,X3,X4,X5) = k5_relat_1(X4,X5) ),
inference(fof_simplification,[status(thm)],[redefinition_k7_funct_2]) ).
fof(c_0_53,plain,
! [X269,X270,X271] :
( ( ~ m2_relset_1(X271,X269,X270)
| m1_relset_1(X271,X269,X270) )
& ( ~ m1_relset_1(X271,X269,X270)
| m2_relset_1(X271,X269,X270) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
cnf(c_0_54,plain,
( m2_relset_1(X1,X2,X3)
| v1_xboole_0(X3)
| ~ m2_fraenkel(X1,X2,X3,X4)
| ~ m1_fraenkel(X4,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_55,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_25]) ).
fof(c_0_56,plain,
! [X1,X2,X3,X4,X5] :
( ( ~ v1_xboole_0(X2)
& v1_funct_1(X4)
& v1_funct_2(X4,X1,X2)
& m1_relset_1(X4,X1,X2)
& v1_funct_1(X5)
& v1_funct_2(X5,X2,X3)
& m1_relset_1(X5,X2,X3) )
=> ( v1_funct_1(k7_funct_2(X1,X2,X3,X4,X5))
& v1_funct_2(k7_funct_2(X1,X2,X3,X4,X5),X1,X3)
& m2_relset_1(k7_funct_2(X1,X2,X3,X4,X5),X1,X3) ) ),
inference(fof_simplification,[status(thm)],[dt_k7_funct_2]) ).
fof(c_0_57,plain,
! [X224,X225] :
( ( v1_relat_1(k5_relat_1(X224,X225))
| ~ v1_relat_1(X224)
| ~ v1_funct_1(X224)
| ~ v1_relat_1(X225)
| ~ v1_funct_1(X225) )
& ( v1_funct_1(k5_relat_1(X224,X225))
| ~ v1_relat_1(X224)
| ~ v1_funct_1(X224)
| ~ v1_relat_1(X225)
| ~ v1_funct_1(X225) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc1_funct_1])])]) ).
cnf(c_0_58,negated_conjecture,
( v1_relat_1(esk3_0)
| ~ v1_fraenkel(k1_autgroup(esk1_0)) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_59,plain,
( v1_fraenkel(X1)
| ~ m1_fraenkel(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_60,negated_conjecture,
( v1_funct_1(esk3_0)
| ~ m1_fraenkel(k1_autgroup(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_42]),c_0_44]) ).
fof(c_0_61,plain,
! [X174,X175,X176,X177] :
( ( v1_funct_1(X176)
| ~ m2_fraenkel(X176,u1_struct_0(X174),u1_struct_0(X174),X175)
| X175 != k1_autgroup(X174)
| ~ m1_fraenkel(X175,u1_struct_0(X174),u1_struct_0(X174))
| v3_struct_0(X174)
| ~ v1_group_1(X174)
| ~ v3_group_1(X174)
| ~ v4_group_1(X174)
| ~ l1_group_1(X174) )
& ( v1_funct_2(X176,u1_struct_0(X174),u1_struct_0(X174))
| ~ m2_fraenkel(X176,u1_struct_0(X174),u1_struct_0(X174),X175)
| X175 != k1_autgroup(X174)
| ~ m1_fraenkel(X175,u1_struct_0(X174),u1_struct_0(X174))
| v3_struct_0(X174)
| ~ v1_group_1(X174)
| ~ v3_group_1(X174)
| ~ v4_group_1(X174)
| ~ l1_group_1(X174) )
& ( v1_group_6(X176,X174,X174)
| ~ m2_fraenkel(X176,u1_struct_0(X174),u1_struct_0(X174),X175)
| X175 != k1_autgroup(X174)
| ~ m1_fraenkel(X175,u1_struct_0(X174),u1_struct_0(X174))
| v3_struct_0(X174)
| ~ v1_group_1(X174)
| ~ v3_group_1(X174)
| ~ v4_group_1(X174)
| ~ l1_group_1(X174) )
& ( m2_relset_1(X176,u1_struct_0(X174),u1_struct_0(X174))
| ~ m2_fraenkel(X176,u1_struct_0(X174),u1_struct_0(X174),X175)
| X175 != k1_autgroup(X174)
| ~ m1_fraenkel(X175,u1_struct_0(X174),u1_struct_0(X174))
| v3_struct_0(X174)
| ~ v1_group_1(X174)
| ~ v3_group_1(X174)
| ~ v4_group_1(X174)
| ~ l1_group_1(X174) )
& ( v2_funct_1(X177)
| ~ r2_hidden(X177,X175)
| ~ v1_funct_1(X177)
| ~ v1_funct_2(X177,u1_struct_0(X174),u1_struct_0(X174))
| ~ v1_group_6(X177,X174,X174)
| ~ m2_relset_1(X177,u1_struct_0(X174),u1_struct_0(X174))
| X175 != k1_autgroup(X174)
| ~ m1_fraenkel(X175,u1_struct_0(X174),u1_struct_0(X174))
| v3_struct_0(X174)
| ~ v1_group_1(X174)
| ~ v3_group_1(X174)
| ~ v4_group_1(X174)
| ~ l1_group_1(X174) )
& ( v3_group_6(X177,X174,X174)
| ~ r2_hidden(X177,X175)
| ~ v1_funct_1(X177)
| ~ v1_funct_2(X177,u1_struct_0(X174),u1_struct_0(X174))
| ~ v1_group_6(X177,X174,X174)
| ~ m2_relset_1(X177,u1_struct_0(X174),u1_struct_0(X174))
| X175 != k1_autgroup(X174)
| ~ m1_fraenkel(X175,u1_struct_0(X174),u1_struct_0(X174))
| v3_struct_0(X174)
| ~ v1_group_1(X174)
| ~ v3_group_1(X174)
| ~ v4_group_1(X174)
| ~ l1_group_1(X174) )
& ( ~ v2_funct_1(X177)
| ~ v3_group_6(X177,X174,X174)
| r2_hidden(X177,X175)
| ~ v1_funct_1(X177)
| ~ v1_funct_2(X177,u1_struct_0(X174),u1_struct_0(X174))
| ~ v1_group_6(X177,X174,X174)
| ~ m2_relset_1(X177,u1_struct_0(X174),u1_struct_0(X174))
| X175 != k1_autgroup(X174)
| ~ m1_fraenkel(X175,u1_struct_0(X174),u1_struct_0(X174))
| v3_struct_0(X174)
| ~ v1_group_1(X174)
| ~ v3_group_1(X174)
| ~ v4_group_1(X174)
| ~ l1_group_1(X174) )
& ( v1_funct_1(esk5_2(X174,X175))
| m2_fraenkel(esk4_2(X174,X175),u1_struct_0(X174),u1_struct_0(X174),X175)
| X175 = k1_autgroup(X174)
| ~ m1_fraenkel(X175,u1_struct_0(X174),u1_struct_0(X174))
| v3_struct_0(X174)
| ~ v1_group_1(X174)
| ~ v3_group_1(X174)
| ~ v4_group_1(X174)
| ~ l1_group_1(X174) )
& ( v1_funct_2(esk5_2(X174,X175),u1_struct_0(X174),u1_struct_0(X174))
| m2_fraenkel(esk4_2(X174,X175),u1_struct_0(X174),u1_struct_0(X174),X175)
| X175 = k1_autgroup(X174)
| ~ m1_fraenkel(X175,u1_struct_0(X174),u1_struct_0(X174))
| v3_struct_0(X174)
| ~ v1_group_1(X174)
| ~ v3_group_1(X174)
| ~ v4_group_1(X174)
| ~ l1_group_1(X174) )
& ( v1_group_6(esk5_2(X174,X175),X174,X174)
| m2_fraenkel(esk4_2(X174,X175),u1_struct_0(X174),u1_struct_0(X174),X175)
| X175 = k1_autgroup(X174)
| ~ m1_fraenkel(X175,u1_struct_0(X174),u1_struct_0(X174))
| v3_struct_0(X174)
| ~ v1_group_1(X174)
| ~ v3_group_1(X174)
| ~ v4_group_1(X174)
| ~ l1_group_1(X174) )
& ( m2_relset_1(esk5_2(X174,X175),u1_struct_0(X174),u1_struct_0(X174))
| m2_fraenkel(esk4_2(X174,X175),u1_struct_0(X174),u1_struct_0(X174),X175)
| X175 = k1_autgroup(X174)
| ~ m1_fraenkel(X175,u1_struct_0(X174),u1_struct_0(X174))
| v3_struct_0(X174)
| ~ v1_group_1(X174)
| ~ v3_group_1(X174)
| ~ v4_group_1(X174)
| ~ l1_group_1(X174) )
& ( ~ r2_hidden(esk5_2(X174,X175),X175)
| ~ v2_funct_1(esk5_2(X174,X175))
| ~ v3_group_6(esk5_2(X174,X175),X174,X174)
| m2_fraenkel(esk4_2(X174,X175),u1_struct_0(X174),u1_struct_0(X174),X175)
| X175 = k1_autgroup(X174)
| ~ m1_fraenkel(X175,u1_struct_0(X174),u1_struct_0(X174))
| v3_struct_0(X174)
| ~ v1_group_1(X174)
| ~ v3_group_1(X174)
| ~ v4_group_1(X174)
| ~ l1_group_1(X174) )
& ( v2_funct_1(esk5_2(X174,X175))
| r2_hidden(esk5_2(X174,X175),X175)
| m2_fraenkel(esk4_2(X174,X175),u1_struct_0(X174),u1_struct_0(X174),X175)
| X175 = k1_autgroup(X174)
| ~ m1_fraenkel(X175,u1_struct_0(X174),u1_struct_0(X174))
| v3_struct_0(X174)
| ~ v1_group_1(X174)
| ~ v3_group_1(X174)
| ~ v4_group_1(X174)
| ~ l1_group_1(X174) )
& ( v3_group_6(esk5_2(X174,X175),X174,X174)
| r2_hidden(esk5_2(X174,X175),X175)
| m2_fraenkel(esk4_2(X174,X175),u1_struct_0(X174),u1_struct_0(X174),X175)
| X175 = k1_autgroup(X174)
| ~ m1_fraenkel(X175,u1_struct_0(X174),u1_struct_0(X174))
| v3_struct_0(X174)
| ~ v1_group_1(X174)
| ~ v3_group_1(X174)
| ~ v4_group_1(X174)
| ~ l1_group_1(X174) )
& ( v1_funct_1(esk5_2(X174,X175))
| ~ v1_funct_1(esk4_2(X174,X175))
| ~ v1_funct_2(esk4_2(X174,X175),u1_struct_0(X174),u1_struct_0(X174))
| ~ v1_group_6(esk4_2(X174,X175),X174,X174)
| ~ m2_relset_1(esk4_2(X174,X175),u1_struct_0(X174),u1_struct_0(X174))
| X175 = k1_autgroup(X174)
| ~ m1_fraenkel(X175,u1_struct_0(X174),u1_struct_0(X174))
| v3_struct_0(X174)
| ~ v1_group_1(X174)
| ~ v3_group_1(X174)
| ~ v4_group_1(X174)
| ~ l1_group_1(X174) )
& ( v1_funct_2(esk5_2(X174,X175),u1_struct_0(X174),u1_struct_0(X174))
| ~ v1_funct_1(esk4_2(X174,X175))
| ~ v1_funct_2(esk4_2(X174,X175),u1_struct_0(X174),u1_struct_0(X174))
| ~ v1_group_6(esk4_2(X174,X175),X174,X174)
| ~ m2_relset_1(esk4_2(X174,X175),u1_struct_0(X174),u1_struct_0(X174))
| X175 = k1_autgroup(X174)
| ~ m1_fraenkel(X175,u1_struct_0(X174),u1_struct_0(X174))
| v3_struct_0(X174)
| ~ v1_group_1(X174)
| ~ v3_group_1(X174)
| ~ v4_group_1(X174)
| ~ l1_group_1(X174) )
& ( v1_group_6(esk5_2(X174,X175),X174,X174)
| ~ v1_funct_1(esk4_2(X174,X175))
| ~ v1_funct_2(esk4_2(X174,X175),u1_struct_0(X174),u1_struct_0(X174))
| ~ v1_group_6(esk4_2(X174,X175),X174,X174)
| ~ m2_relset_1(esk4_2(X174,X175),u1_struct_0(X174),u1_struct_0(X174))
| X175 = k1_autgroup(X174)
| ~ m1_fraenkel(X175,u1_struct_0(X174),u1_struct_0(X174))
| v3_struct_0(X174)
| ~ v1_group_1(X174)
| ~ v3_group_1(X174)
| ~ v4_group_1(X174)
| ~ l1_group_1(X174) )
& ( m2_relset_1(esk5_2(X174,X175),u1_struct_0(X174),u1_struct_0(X174))
| ~ v1_funct_1(esk4_2(X174,X175))
| ~ v1_funct_2(esk4_2(X174,X175),u1_struct_0(X174),u1_struct_0(X174))
| ~ v1_group_6(esk4_2(X174,X175),X174,X174)
| ~ m2_relset_1(esk4_2(X174,X175),u1_struct_0(X174),u1_struct_0(X174))
| X175 = k1_autgroup(X174)
| ~ m1_fraenkel(X175,u1_struct_0(X174),u1_struct_0(X174))
| v3_struct_0(X174)
| ~ v1_group_1(X174)
| ~ v3_group_1(X174)
| ~ v4_group_1(X174)
| ~ l1_group_1(X174) )
& ( ~ r2_hidden(esk5_2(X174,X175),X175)
| ~ v2_funct_1(esk5_2(X174,X175))
| ~ v3_group_6(esk5_2(X174,X175),X174,X174)
| ~ v1_funct_1(esk4_2(X174,X175))
| ~ v1_funct_2(esk4_2(X174,X175),u1_struct_0(X174),u1_struct_0(X174))
| ~ v1_group_6(esk4_2(X174,X175),X174,X174)
| ~ m2_relset_1(esk4_2(X174,X175),u1_struct_0(X174),u1_struct_0(X174))
| X175 = k1_autgroup(X174)
| ~ m1_fraenkel(X175,u1_struct_0(X174),u1_struct_0(X174))
| v3_struct_0(X174)
| ~ v1_group_1(X174)
| ~ v3_group_1(X174)
| ~ v4_group_1(X174)
| ~ l1_group_1(X174) )
& ( v2_funct_1(esk5_2(X174,X175))
| r2_hidden(esk5_2(X174,X175),X175)
| ~ v1_funct_1(esk4_2(X174,X175))
| ~ v1_funct_2(esk4_2(X174,X175),u1_struct_0(X174),u1_struct_0(X174))
| ~ v1_group_6(esk4_2(X174,X175),X174,X174)
| ~ m2_relset_1(esk4_2(X174,X175),u1_struct_0(X174),u1_struct_0(X174))
| X175 = k1_autgroup(X174)
| ~ m1_fraenkel(X175,u1_struct_0(X174),u1_struct_0(X174))
| v3_struct_0(X174)
| ~ v1_group_1(X174)
| ~ v3_group_1(X174)
| ~ v4_group_1(X174)
| ~ l1_group_1(X174) )
& ( v3_group_6(esk5_2(X174,X175),X174,X174)
| r2_hidden(esk5_2(X174,X175),X175)
| ~ v1_funct_1(esk4_2(X174,X175))
| ~ v1_funct_2(esk4_2(X174,X175),u1_struct_0(X174),u1_struct_0(X174))
| ~ v1_group_6(esk4_2(X174,X175),X174,X174)
| ~ m2_relset_1(esk4_2(X174,X175),u1_struct_0(X174),u1_struct_0(X174))
| X175 = k1_autgroup(X174)
| ~ m1_fraenkel(X175,u1_struct_0(X174),u1_struct_0(X174))
| v3_struct_0(X174)
| ~ v1_group_1(X174)
| ~ v3_group_1(X174)
| ~ v4_group_1(X174)
| ~ l1_group_1(X174) ) ),
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_51])])])])]) ).
fof(c_0_62,plain,
! [X255,X256,X257,X258,X259] :
( v1_xboole_0(X256)
| ~ v1_funct_1(X258)
| ~ v1_funct_2(X258,X255,X256)
| ~ m1_relset_1(X258,X255,X256)
| ~ v1_funct_1(X259)
| ~ v1_funct_2(X259,X256,X257)
| ~ m1_relset_1(X259,X256,X257)
| k7_funct_2(X255,X256,X257,X258,X259) = k5_relat_1(X258,X259) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])]) ).
cnf(c_0_63,plain,
( v1_funct_2(X1,X2,X3)
| v1_xboole_0(X3)
| ~ m2_fraenkel(X1,X2,X3,X4)
| ~ m1_fraenkel(X4,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_64,plain,
( m1_relset_1(X1,X2,X3)
| ~ m2_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_65,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(spm,[status(thm)],[c_0_54,c_0_55]),c_0_43])]),c_0_44]) ).
cnf(c_0_66,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(spm,[status(thm)],[c_0_50,c_0_55]),c_0_44]) ).
fof(c_0_67,plain,
! [X185,X186,X187,X188,X189] :
( ( v1_funct_1(k7_funct_2(X185,X186,X187,X188,X189))
| v1_xboole_0(X186)
| ~ v1_funct_1(X188)
| ~ v1_funct_2(X188,X185,X186)
| ~ m1_relset_1(X188,X185,X186)
| ~ v1_funct_1(X189)
| ~ v1_funct_2(X189,X186,X187)
| ~ m1_relset_1(X189,X186,X187) )
& ( v1_funct_2(k7_funct_2(X185,X186,X187,X188,X189),X185,X187)
| v1_xboole_0(X186)
| ~ v1_funct_1(X188)
| ~ v1_funct_2(X188,X185,X186)
| ~ m1_relset_1(X188,X185,X186)
| ~ v1_funct_1(X189)
| ~ v1_funct_2(X189,X186,X187)
| ~ m1_relset_1(X189,X186,X187) )
& ( m2_relset_1(k7_funct_2(X185,X186,X187,X188,X189),X185,X187)
| v1_xboole_0(X186)
| ~ v1_funct_1(X188)
| ~ v1_funct_2(X188,X185,X186)
| ~ m1_relset_1(X188,X185,X186)
| ~ v1_funct_1(X189)
| ~ v1_funct_2(X189,X186,X187)
| ~ m1_relset_1(X189,X186,X187) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_56])])]) ).
cnf(c_0_68,plain,
( v1_funct_1(k5_relat_1(X1,X2))
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X1)
| ~ v1_relat_1(X2)
| ~ v1_funct_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_69,negated_conjecture,
( v1_relat_1(esk3_0)
| ~ m1_fraenkel(k1_autgroup(esk1_0),X1,X2) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_70,negated_conjecture,
v1_funct_1(esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_43])]) ).
fof(c_0_71,plain,
! [X164,X165,X166] :
( ~ m1_subset_1(X166,k1_zfmisc_1(k2_zfmisc_1(X164,X165)))
| v1_relat_1(X166) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])]) ).
fof(c_0_72,plain,
! [X203,X204,X205] :
( ~ m2_relset_1(X205,X203,X204)
| m1_subset_1(X205,k1_zfmisc_1(k2_zfmisc_1(X203,X204))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_relset_1])]) ).
fof(c_0_73,plain,
! [X1,X2,X3,X4,X5] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1)
& ~ v3_struct_0(X2)
& v3_group_1(X2)
& v4_group_1(X2)
& l1_group_1(X2)
& ~ v3_struct_0(X3)
& v3_group_1(X3)
& v4_group_1(X3)
& l1_group_1(X3)
& v1_funct_1(X4)
& v1_funct_2(X4,u1_struct_0(X1),u1_struct_0(X2))
& v1_group_6(X4,X1,X2)
& m1_relset_1(X4,u1_struct_0(X1),u1_struct_0(X2))
& v1_funct_1(X5)
& v1_funct_2(X5,u1_struct_0(X2),u1_struct_0(X3))
& v1_group_6(X5,X2,X3)
& m1_relset_1(X5,u1_struct_0(X2),u1_struct_0(X3)) )
=> k8_group_6(X1,X2,X3,X4,X5) = k5_relat_1(X4,X5) ),
inference(fof_simplification,[status(thm)],[redefinition_k8_group_6]) ).
cnf(c_0_74,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_61]) ).
cnf(c_0_75,plain,
( v1_xboole_0(X1)
| k7_funct_2(X3,X1,X5,X2,X4) = k5_relat_1(X2,X4)
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,X3,X1)
| ~ m1_relset_1(X2,X3,X1)
| ~ v1_funct_1(X4)
| ~ v1_funct_2(X4,X1,X5)
| ~ m1_relset_1(X4,X1,X5) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_76,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(spm,[status(thm)],[c_0_63,c_0_55]),c_0_43])]),c_0_44]) ).
cnf(c_0_77,negated_conjecture,
m1_relset_1(esk2_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0)),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_78,negated_conjecture,
v1_funct_1(esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_43])]) ).
cnf(c_0_79,negated_conjecture,
m2_relset_1(esk3_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_42]),c_0_43])]),c_0_44]) ).
cnf(c_0_80,plain,
( v1_funct_2(k7_funct_2(X1,X2,X3,X4,X5),X1,X3)
| v1_xboole_0(X2)
| ~ v1_funct_1(X4)
| ~ v1_funct_2(X4,X1,X2)
| ~ m1_relset_1(X4,X1,X2)
| ~ v1_funct_1(X5)
| ~ v1_funct_2(X5,X2,X3)
| ~ m1_relset_1(X5,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_81,negated_conjecture,
( v1_funct_1(k5_relat_1(esk3_0,X1))
| ~ m1_fraenkel(k1_autgroup(esk1_0),X2,X3)
| ~ v1_funct_1(X1)
| ~ v1_relat_1(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70])]) ).
cnf(c_0_82,plain,
( v1_relat_1(X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_83,plain,
( m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))
| ~ m2_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_84,negated_conjecture,
~ m2_fraenkel(k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),esk3_0,esk2_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k1_autgroup(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_85,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_31]) ).
fof(c_0_86,plain,
! [X273,X274] :
( ~ r2_hidden(X273,X274)
| m1_subset_1(X273,X274) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(c_0_87,plain,
! [X1,X2,X3,X4,X5] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1)
& ~ v3_struct_0(X2)
& v3_group_1(X2)
& v4_group_1(X2)
& l1_group_1(X2)
& ~ v3_struct_0(X3)
& v3_group_1(X3)
& v4_group_1(X3)
& l1_group_1(X3)
& v1_funct_1(X4)
& v1_funct_2(X4,u1_struct_0(X1),u1_struct_0(X2))
& v1_group_6(X4,X1,X2)
& m1_relset_1(X4,u1_struct_0(X1),u1_struct_0(X2))
& v1_funct_1(X5)
& v1_funct_2(X5,u1_struct_0(X2),u1_struct_0(X3))
& v1_group_6(X5,X2,X3)
& m1_relset_1(X5,u1_struct_0(X2),u1_struct_0(X3)) )
=> ( v1_funct_1(k8_group_6(X1,X2,X3,X4,X5))
& v1_funct_2(k8_group_6(X1,X2,X3,X4,X5),u1_struct_0(X1),u1_struct_0(X3))
& v1_group_6(k8_group_6(X1,X2,X3,X4,X5),X1,X3)
& m2_relset_1(k8_group_6(X1,X2,X3,X4,X5),u1_struct_0(X1),u1_struct_0(X3)) ) ),
inference(fof_simplification,[status(thm)],[dt_k8_group_6]) ).
fof(c_0_88,plain,
! [X260,X261,X262,X263,X264] :
( v3_struct_0(X260)
| ~ v3_group_1(X260)
| ~ v4_group_1(X260)
| ~ l1_group_1(X260)
| v3_struct_0(X261)
| ~ v3_group_1(X261)
| ~ v4_group_1(X261)
| ~ l1_group_1(X261)
| v3_struct_0(X262)
| ~ v3_group_1(X262)
| ~ v4_group_1(X262)
| ~ l1_group_1(X262)
| ~ v1_funct_1(X263)
| ~ v1_funct_2(X263,u1_struct_0(X260),u1_struct_0(X261))
| ~ v1_group_6(X263,X260,X261)
| ~ m1_relset_1(X263,u1_struct_0(X260),u1_struct_0(X261))
| ~ v1_funct_1(X264)
| ~ v1_funct_2(X264,u1_struct_0(X261),u1_struct_0(X262))
| ~ v1_group_6(X264,X261,X262)
| ~ m1_relset_1(X264,u1_struct_0(X261),u1_struct_0(X262))
| k8_group_6(X260,X261,X262,X263,X264) = k5_relat_1(X263,X264) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_73])]) ).
cnf(c_0_89,plain,
( v1_group_6(X1,X2,X2)
| v3_struct_0(X2)
| ~ m2_fraenkel(X1,u1_struct_0(X2),u1_struct_0(X2),k1_autgroup(X2))
| ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ v1_group_1(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_74]),c_0_32]) ).
fof(c_0_90,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_91,plain,
! [X275,X276] :
( ~ m1_subset_1(X275,X276)
| v1_xboole_0(X276)
| r2_hidden(X275,X276) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
cnf(c_0_92,plain,
( ~ v1_xboole_0(X1)
| ~ m1_fraenkel(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_93,negated_conjecture,
( k7_funct_2(X1,u1_struct_0(esk1_0),u1_struct_0(esk1_0),X2,esk2_0) = k5_relat_1(X2,esk2_0)
| ~ v1_funct_2(X2,X1,u1_struct_0(esk1_0))
| ~ m1_relset_1(X2,X1,u1_struct_0(esk1_0))
| ~ v1_funct_1(X2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77]),c_0_78])]),c_0_44]) ).
cnf(c_0_94,negated_conjecture,
v1_funct_2(esk3_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_42]),c_0_43])]),c_0_44]) ).
cnf(c_0_95,negated_conjecture,
m1_relset_1(esk3_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0)),
inference(spm,[status(thm)],[c_0_64,c_0_79]) ).
cnf(c_0_96,negated_conjecture,
( v1_funct_2(k7_funct_2(X1,u1_struct_0(esk1_0),u1_struct_0(esk1_0),X2,esk2_0),X1,u1_struct_0(esk1_0))
| ~ v1_funct_2(X2,X1,u1_struct_0(esk1_0))
| ~ m1_relset_1(X2,X1,u1_struct_0(esk1_0))
| ~ v1_funct_1(X2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_77]),c_0_76]),c_0_78])]),c_0_44]) ).
cnf(c_0_97,negated_conjecture,
( v1_funct_1(k5_relat_1(esk3_0,X1))
| ~ v1_funct_1(X1)
| ~ v1_relat_1(X1) ),
inference(spm,[status(thm)],[c_0_81,c_0_43]) ).
cnf(c_0_98,plain,
( v1_relat_1(X1)
| ~ m2_relset_1(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_99,negated_conjecture,
~ m1_subset_1(k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),esk3_0,esk2_0),k1_autgroup(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_43])]),c_0_44]) ).
cnf(c_0_100,plain,
( m1_subset_1(X1,X2)
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
fof(c_0_101,plain,
! [X190,X191,X192,X193,X194] :
( ( v1_funct_1(k8_group_6(X190,X191,X192,X193,X194))
| v3_struct_0(X190)
| ~ v3_group_1(X190)
| ~ v4_group_1(X190)
| ~ l1_group_1(X190)
| v3_struct_0(X191)
| ~ v3_group_1(X191)
| ~ v4_group_1(X191)
| ~ l1_group_1(X191)
| v3_struct_0(X192)
| ~ v3_group_1(X192)
| ~ v4_group_1(X192)
| ~ l1_group_1(X192)
| ~ v1_funct_1(X193)
| ~ v1_funct_2(X193,u1_struct_0(X190),u1_struct_0(X191))
| ~ v1_group_6(X193,X190,X191)
| ~ m1_relset_1(X193,u1_struct_0(X190),u1_struct_0(X191))
| ~ v1_funct_1(X194)
| ~ v1_funct_2(X194,u1_struct_0(X191),u1_struct_0(X192))
| ~ v1_group_6(X194,X191,X192)
| ~ m1_relset_1(X194,u1_struct_0(X191),u1_struct_0(X192)) )
& ( v1_funct_2(k8_group_6(X190,X191,X192,X193,X194),u1_struct_0(X190),u1_struct_0(X192))
| v3_struct_0(X190)
| ~ v3_group_1(X190)
| ~ v4_group_1(X190)
| ~ l1_group_1(X190)
| v3_struct_0(X191)
| ~ v3_group_1(X191)
| ~ v4_group_1(X191)
| ~ l1_group_1(X191)
| v3_struct_0(X192)
| ~ v3_group_1(X192)
| ~ v4_group_1(X192)
| ~ l1_group_1(X192)
| ~ v1_funct_1(X193)
| ~ v1_funct_2(X193,u1_struct_0(X190),u1_struct_0(X191))
| ~ v1_group_6(X193,X190,X191)
| ~ m1_relset_1(X193,u1_struct_0(X190),u1_struct_0(X191))
| ~ v1_funct_1(X194)
| ~ v1_funct_2(X194,u1_struct_0(X191),u1_struct_0(X192))
| ~ v1_group_6(X194,X191,X192)
| ~ m1_relset_1(X194,u1_struct_0(X191),u1_struct_0(X192)) )
& ( v1_group_6(k8_group_6(X190,X191,X192,X193,X194),X190,X192)
| v3_struct_0(X190)
| ~ v3_group_1(X190)
| ~ v4_group_1(X190)
| ~ l1_group_1(X190)
| v3_struct_0(X191)
| ~ v3_group_1(X191)
| ~ v4_group_1(X191)
| ~ l1_group_1(X191)
| v3_struct_0(X192)
| ~ v3_group_1(X192)
| ~ v4_group_1(X192)
| ~ l1_group_1(X192)
| ~ v1_funct_1(X193)
| ~ v1_funct_2(X193,u1_struct_0(X190),u1_struct_0(X191))
| ~ v1_group_6(X193,X190,X191)
| ~ m1_relset_1(X193,u1_struct_0(X190),u1_struct_0(X191))
| ~ v1_funct_1(X194)
| ~ v1_funct_2(X194,u1_struct_0(X191),u1_struct_0(X192))
| ~ v1_group_6(X194,X191,X192)
| ~ m1_relset_1(X194,u1_struct_0(X191),u1_struct_0(X192)) )
& ( m2_relset_1(k8_group_6(X190,X191,X192,X193,X194),u1_struct_0(X190),u1_struct_0(X192))
| v3_struct_0(X190)
| ~ v3_group_1(X190)
| ~ v4_group_1(X190)
| ~ l1_group_1(X190)
| v3_struct_0(X191)
| ~ v3_group_1(X191)
| ~ v4_group_1(X191)
| ~ l1_group_1(X191)
| v3_struct_0(X192)
| ~ v3_group_1(X192)
| ~ v4_group_1(X192)
| ~ l1_group_1(X192)
| ~ v1_funct_1(X193)
| ~ v1_funct_2(X193,u1_struct_0(X190),u1_struct_0(X191))
| ~ v1_group_6(X193,X190,X191)
| ~ m1_relset_1(X193,u1_struct_0(X190),u1_struct_0(X191))
| ~ v1_funct_1(X194)
| ~ v1_funct_2(X194,u1_struct_0(X191),u1_struct_0(X192))
| ~ v1_group_6(X194,X191,X192)
| ~ m1_relset_1(X194,u1_struct_0(X191),u1_struct_0(X192)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_87])])]) ).
cnf(c_0_102,plain,
( v3_struct_0(X1)
| v3_struct_0(X2)
| v3_struct_0(X3)
| k8_group_6(X1,X2,X3,X4,X5) = k5_relat_1(X4,X5)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2)
| ~ v3_group_1(X3)
| ~ v4_group_1(X3)
| ~ l1_group_1(X3)
| ~ v1_funct_1(X4)
| ~ v1_funct_2(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_group_6(X4,X1,X2)
| ~ m1_relset_1(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_funct_1(X5)
| ~ v1_funct_2(X5,u1_struct_0(X2),u1_struct_0(X3))
| ~ v1_group_6(X5,X2,X3)
| ~ m1_relset_1(X5,u1_struct_0(X2),u1_struct_0(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_103,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_89,c_0_55]),c_0_30]),c_0_34]),c_0_35]),c_0_33])]),c_0_36]) ).
fof(c_0_104,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] :
( ( ~ v3_struct_0(X3)
& v3_group_1(X3)
& v4_group_1(X3)
& l1_group_1(X3) )
=> ! [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)) )
=> ! [X5] :
( ( v1_funct_1(X5)
& v1_funct_2(X5,u1_struct_0(X2),u1_struct_0(X3))
& v1_group_6(X5,X2,X3)
& m2_relset_1(X5,u1_struct_0(X2),u1_struct_0(X3)) )
=> ( ( v4_group_6(X4,X1,X2)
& v4_group_6(X5,X2,X3) )
=> v4_group_6(k8_group_6(X1,X2,X3,X4,X5),X1,X3) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[t74_group_6]) ).
fof(c_0_105,plain,
! [X282,X283] :
( ( ~ r2_hidden(X283,k1_autgroup(X282))
| v4_group_6(X283,X282,X282)
| ~ v1_funct_1(X283)
| ~ v1_funct_2(X283,u1_struct_0(X282),u1_struct_0(X282))
| ~ v1_group_6(X283,X282,X282)
| ~ m2_relset_1(X283,u1_struct_0(X282),u1_struct_0(X282))
| v3_struct_0(X282)
| ~ v1_group_1(X282)
| ~ v3_group_1(X282)
| ~ v4_group_1(X282)
| ~ l1_group_1(X282) )
& ( ~ v4_group_6(X283,X282,X282)
| r2_hidden(X283,k1_autgroup(X282))
| ~ v1_funct_1(X283)
| ~ v1_funct_2(X283,u1_struct_0(X282),u1_struct_0(X282))
| ~ v1_group_6(X283,X282,X282)
| ~ m2_relset_1(X283,u1_struct_0(X282),u1_struct_0(X282))
| v3_struct_0(X282)
| ~ v1_group_1(X282)
| ~ v3_group_1(X282)
| ~ v4_group_1(X282)
| ~ l1_group_1(X282) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_90])])])]) ).
cnf(c_0_106,plain,
( v1_xboole_0(X2)
| r2_hidden(X1,X2)
| ~ m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_107,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_41,c_0_55]),c_0_43])]),c_0_44]) ).
cnf(c_0_108,negated_conjecture,
~ v1_xboole_0(k1_autgroup(esk1_0)),
inference(spm,[status(thm)],[c_0_92,c_0_43]) ).
cnf(c_0_109,plain,
( m2_relset_1(k7_funct_2(X1,X2,X3,X4,X5),X1,X3)
| v1_xboole_0(X2)
| ~ v1_funct_1(X4)
| ~ v1_funct_2(X4,X1,X2)
| ~ m1_relset_1(X4,X1,X2)
| ~ v1_funct_1(X5)
| ~ v1_funct_2(X5,X2,X3)
| ~ m1_relset_1(X5,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_110,negated_conjecture,
k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),esk3_0,esk2_0) = k5_relat_1(esk3_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95]),c_0_70])]) ).
cnf(c_0_111,negated_conjecture,
v1_funct_2(k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),esk3_0,esk2_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_95]),c_0_94]),c_0_70])]) ).
cnf(c_0_112,negated_conjecture,
( v1_funct_1(k5_relat_1(esk3_0,X1))
| ~ m2_relset_1(X1,X2,X3)
| ~ v1_funct_1(X1) ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_113,negated_conjecture,
~ r2_hidden(k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),esk3_0,esk2_0),k1_autgroup(esk1_0)),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_114,plain,
( v1_group_6(k8_group_6(X1,X2,X3,X4,X5),X1,X3)
| v3_struct_0(X1)
| v3_struct_0(X2)
| v3_struct_0(X3)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2)
| ~ v3_group_1(X3)
| ~ v4_group_1(X3)
| ~ l1_group_1(X3)
| ~ v1_funct_1(X4)
| ~ v1_funct_2(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_group_6(X4,X1,X2)
| ~ m1_relset_1(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_funct_1(X5)
| ~ v1_funct_2(X5,u1_struct_0(X2),u1_struct_0(X3))
| ~ v1_group_6(X5,X2,X3)
| ~ m1_relset_1(X5,u1_struct_0(X2),u1_struct_0(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_115,negated_conjecture,
( k8_group_6(X1,esk1_0,esk1_0,X2,esk2_0) = k5_relat_1(X2,esk2_0)
| v3_struct_0(X1)
| ~ v1_group_6(X2,X1,esk1_0)
| ~ v1_funct_2(X2,u1_struct_0(X1),u1_struct_0(esk1_0))
| ~ m1_relset_1(X2,u1_struct_0(X1),u1_struct_0(esk1_0))
| ~ v1_funct_1(X2)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_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(spm,[status(thm)],[c_0_102,c_0_76]),c_0_103]),c_0_77]),c_0_78]),c_0_30]),c_0_34]),c_0_35])]),c_0_36]) ).
cnf(c_0_116,negated_conjecture,
v1_group_6(esk3_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_89,c_0_42]),c_0_30]),c_0_34]),c_0_35]),c_0_33])]),c_0_36]) ).
fof(c_0_117,plain,
! [X288,X289,X290,X291,X292] :
( v3_struct_0(X288)
| ~ v3_group_1(X288)
| ~ v4_group_1(X288)
| ~ l1_group_1(X288)
| v3_struct_0(X289)
| ~ v3_group_1(X289)
| ~ v4_group_1(X289)
| ~ l1_group_1(X289)
| v3_struct_0(X290)
| ~ v3_group_1(X290)
| ~ v4_group_1(X290)
| ~ l1_group_1(X290)
| ~ v1_funct_1(X291)
| ~ v1_funct_2(X291,u1_struct_0(X288),u1_struct_0(X289))
| ~ v1_group_6(X291,X288,X289)
| ~ m2_relset_1(X291,u1_struct_0(X288),u1_struct_0(X289))
| ~ v1_funct_1(X292)
| ~ v1_funct_2(X292,u1_struct_0(X289),u1_struct_0(X290))
| ~ v1_group_6(X292,X289,X290)
| ~ m2_relset_1(X292,u1_struct_0(X289),u1_struct_0(X290))
| ~ v4_group_6(X291,X288,X289)
| ~ v4_group_6(X292,X289,X290)
| v4_group_6(k8_group_6(X288,X289,X290,X291,X292),X288,X290) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_104])])]) ).
cnf(c_0_118,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_105]) ).
cnf(c_0_119,negated_conjecture,
r2_hidden(esk2_0,k1_autgroup(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_108]) ).
cnf(c_0_120,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_105]) ).
cnf(c_0_121,negated_conjecture,
m2_relset_1(k5_relat_1(esk3_0,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_76]),c_0_94]),c_0_77]),c_0_95]),c_0_78]),c_0_70])]),c_0_44]) ).
cnf(c_0_122,negated_conjecture,
v1_funct_2(k5_relat_1(esk3_0,esk2_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0)),
inference(rw,[status(thm)],[c_0_111,c_0_110]) ).
cnf(c_0_123,negated_conjecture,
v1_funct_1(k5_relat_1(esk3_0,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_65]),c_0_78])]) ).
cnf(c_0_124,negated_conjecture,
~ r2_hidden(k5_relat_1(esk3_0,esk2_0),k1_autgroup(esk1_0)),
inference(rw,[status(thm)],[c_0_113,c_0_110]) ).
cnf(c_0_125,negated_conjecture,
( v1_group_6(k8_group_6(X1,esk1_0,esk1_0,X2,esk2_0),X1,esk1_0)
| v3_struct_0(X1)
| ~ v1_group_6(X2,X1,esk1_0)
| ~ v1_funct_2(X2,u1_struct_0(X1),u1_struct_0(esk1_0))
| ~ m1_relset_1(X2,u1_struct_0(X1),u1_struct_0(esk1_0))
| ~ v1_funct_1(X2)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_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(spm,[status(thm)],[c_0_114,c_0_76]),c_0_103]),c_0_77]),c_0_78]),c_0_30]),c_0_34]),c_0_35])]),c_0_36]) ).
cnf(c_0_126,negated_conjecture,
k8_group_6(esk1_0,esk1_0,esk1_0,esk3_0,esk2_0) = k5_relat_1(esk3_0,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_94]),c_0_95]),c_0_70]),c_0_30]),c_0_34]),c_0_35])]),c_0_36]) ).
cnf(c_0_127,plain,
( v3_struct_0(X1)
| v3_struct_0(X2)
| v3_struct_0(X3)
| v4_group_6(k8_group_6(X1,X2,X3,X4,X5),X1,X3)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2)
| ~ v3_group_1(X3)
| ~ v4_group_1(X3)
| ~ l1_group_1(X3)
| ~ 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))
| ~ v1_funct_1(X5)
| ~ v1_funct_2(X5,u1_struct_0(X2),u1_struct_0(X3))
| ~ v1_group_6(X5,X2,X3)
| ~ m2_relset_1(X5,u1_struct_0(X2),u1_struct_0(X3))
| ~ v4_group_6(X4,X1,X2)
| ~ v4_group_6(X5,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_128,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_118,c_0_119]),c_0_65]),c_0_103]),c_0_76]),c_0_78]),c_0_30]),c_0_34]),c_0_35]),c_0_33])]),c_0_36]) ).
cnf(c_0_129,negated_conjecture,
r2_hidden(esk3_0,k1_autgroup(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_48]),c_0_108]) ).
cnf(c_0_130,negated_conjecture,
( ~ v4_group_6(k5_relat_1(esk3_0,esk2_0),esk1_0,esk1_0)
| ~ v1_group_6(k5_relat_1(esk3_0,esk2_0),esk1_0,esk1_0) ),
inference(sr,[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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_122]),c_0_123]),c_0_30]),c_0_34]),c_0_35]),c_0_33])]),c_0_124]),c_0_36]) ).
cnf(c_0_131,negated_conjecture,
v1_group_6(k5_relat_1(esk3_0,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(spm,[status(thm)],[c_0_125,c_0_116]),c_0_126]),c_0_94]),c_0_95]),c_0_70]),c_0_30]),c_0_34]),c_0_35])]),c_0_36]) ).
cnf(c_0_132,negated_conjecture,
( v4_group_6(k8_group_6(X1,esk1_0,esk1_0,X2,esk2_0),X1,esk1_0)
| v3_struct_0(X1)
| ~ v4_group_6(X2,X1,esk1_0)
| ~ m2_relset_1(X2,u1_struct_0(X1),u1_struct_0(esk1_0))
| ~ v1_group_6(X2,X1,esk1_0)
| ~ v1_funct_2(X2,u1_struct_0(X1),u1_struct_0(esk1_0))
| ~ v1_funct_1(X2)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_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_127,c_0_65]),c_0_128]),c_0_103]),c_0_76]),c_0_78]),c_0_30]),c_0_34]),c_0_35])]),c_0_36]) ).
cnf(c_0_133,negated_conjecture,
v4_group_6(esk3_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_118,c_0_129]),c_0_79]),c_0_116]),c_0_94]),c_0_70]),c_0_30]),c_0_34]),c_0_35]),c_0_33])]),c_0_36]) ).
cnf(c_0_134,negated_conjecture,
~ v4_group_6(k5_relat_1(esk3_0,esk2_0),esk1_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_130,c_0_131])]) ).
cnf(c_0_135,negated_conjecture,
$false,
inference(sr,[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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_116]),c_0_126]),c_0_133]),c_0_79]),c_0_94]),c_0_70]),c_0_30]),c_0_34]),c_0_35])]),c_0_134]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP621+1 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n004.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 18:46:17 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 8.30/5.78 % Version : CSE_E---1.7
% 8.30/5.78 % Problem : theBenchmark.p
% 8.30/5.78 % SZS status Theorem for theBenchmark.p
% 8.30/5.78 % SZS output start CNFRefutation
% See solution above
% 8.40/5.80 % Total time : 4.373s
%------------------------------------------------------------------------------