TSTP Solution File: GRP621+1 by E-SAT---3.1.00
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%------------------------------------------------------------------------------
% File : E-SAT---3.1.00
% Problem : GRP621+1 : TPTP v8.2.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n017.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 : Mon May 20 20:58:11 EDT 2024
% Result : Theorem 1.30s 0.65s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 18
% Syntax : Number of formulae : 123 ( 36 unt; 0 def)
% Number of atoms : 1041 ( 38 equ)
% Maximal formula atoms : 231 ( 8 avg)
% Number of connectives : 1484 ( 566 ~; 617 |; 243 &)
% ( 9 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 38 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 1 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-5 aty)
% Number of variables : 247 ( 4 sgn 150 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rc5_struct_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ? [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
& ~ v1_xboole_0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_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(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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',dt_k1_autgroup) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( r2_hidden(X1,X2)
& m1_subset_1(X2,k1_zfmisc_1(X3))
& v1_xboole_0(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
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(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : m1_subset_1(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
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(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(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/sandbox2/benchmark/theBenchmark.p',dt_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/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
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(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(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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
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/sandbox2/benchmark/theBenchmark.p',redefinition_k7_funct_2) ).
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/sandbox2/benchmark/theBenchmark.p',t74_group_6) ).
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/sandbox2/benchmark/theBenchmark.p',dt_k8_group_6) ).
fof(c_0_18,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ? [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
& ~ v1_xboole_0(X2) ) ),
inference(fof_simplification,[status(thm)],[rc5_struct_0]) ).
fof(c_0_19,plain,
! [X108] :
( ( m1_subset_1(esk27_1(X108),k1_zfmisc_1(u1_struct_0(X108)))
| v3_struct_0(X108)
| ~ l1_struct_0(X108) )
& ( ~ v1_xboole_0(esk27_1(X108))
| v3_struct_0(X108)
| ~ l1_struct_0(X108) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])])]) ).
fof(c_0_20,plain,
! [X50] :
( ~ l1_group_1(X50)
| l1_struct_0(X50) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_group_1])])]) ).
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])]) ).
cnf(c_0_22,plain,
( m1_subset_1(esk27_1(X1),k1_zfmisc_1(u1_struct_0(X1)))
| v3_struct_0(X1)
| ~ l1_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,plain,
( l1_struct_0(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_24,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(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])]) ).
fof(c_0_25,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_26,plain,
! [X139,X140,X141] :
( ~ r2_hidden(X139,X140)
| ~ m1_subset_1(X140,k1_zfmisc_1(X141))
| ~ v1_xboole_0(X141) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])])]) ).
cnf(c_0_27,plain,
( m1_subset_1(esk27_1(X1),k1_zfmisc_1(u1_struct_0(X1)))
| v3_struct_0(X1)
| ~ l1_group_1(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,negated_conjecture,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_30,plain,
! [X130,X131] :
( ~ m1_subset_1(X130,X131)
| v1_xboole_0(X131)
| r2_hidden(X130,X131) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])])]) ).
fof(c_0_31,plain,
! [X70] : m1_subset_1(esk10_1(X70),X70),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(c_0_32,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_33,plain,
! [X37] :
( v3_struct_0(X37)
| ~ v1_group_1(X37)
| ~ v3_group_1(X37)
| ~ v4_group_1(X37)
| ~ l1_group_1(X37)
| m1_fraenkel(k1_autgroup(X37),u1_struct_0(X37),u1_struct_0(X37)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])]) ).
cnf(c_0_34,plain,
( ~ r2_hidden(X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X3))
| ~ v1_xboole_0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,negated_conjecture,
m1_subset_1(esk27_1(esk1_0),k1_zfmisc_1(u1_struct_0(esk1_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_36,plain,
( v1_xboole_0(X2)
| r2_hidden(X1,X2)
| ~ m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,plain,
m1_subset_1(esk10_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_38,plain,
! [X29,X30,X31,X32] :
( ( v1_funct_1(X31)
| ~ m2_fraenkel(X31,u1_struct_0(X29),u1_struct_0(X29),X30)
| X30 != k1_autgroup(X29)
| ~ m1_fraenkel(X30,u1_struct_0(X29),u1_struct_0(X29))
| v3_struct_0(X29)
| ~ v1_group_1(X29)
| ~ v3_group_1(X29)
| ~ v4_group_1(X29)
| ~ l1_group_1(X29) )
& ( v1_funct_2(X31,u1_struct_0(X29),u1_struct_0(X29))
| ~ m2_fraenkel(X31,u1_struct_0(X29),u1_struct_0(X29),X30)
| X30 != k1_autgroup(X29)
| ~ m1_fraenkel(X30,u1_struct_0(X29),u1_struct_0(X29))
| v3_struct_0(X29)
| ~ v1_group_1(X29)
| ~ v3_group_1(X29)
| ~ v4_group_1(X29)
| ~ l1_group_1(X29) )
& ( v1_group_6(X31,X29,X29)
| ~ m2_fraenkel(X31,u1_struct_0(X29),u1_struct_0(X29),X30)
| X30 != k1_autgroup(X29)
| ~ m1_fraenkel(X30,u1_struct_0(X29),u1_struct_0(X29))
| v3_struct_0(X29)
| ~ v1_group_1(X29)
| ~ v3_group_1(X29)
| ~ v4_group_1(X29)
| ~ l1_group_1(X29) )
& ( m2_relset_1(X31,u1_struct_0(X29),u1_struct_0(X29))
| ~ m2_fraenkel(X31,u1_struct_0(X29),u1_struct_0(X29),X30)
| X30 != k1_autgroup(X29)
| ~ m1_fraenkel(X30,u1_struct_0(X29),u1_struct_0(X29))
| v3_struct_0(X29)
| ~ v1_group_1(X29)
| ~ v3_group_1(X29)
| ~ v4_group_1(X29)
| ~ l1_group_1(X29) )
& ( v2_funct_1(X32)
| ~ r2_hidden(X32,X30)
| ~ v1_funct_1(X32)
| ~ v1_funct_2(X32,u1_struct_0(X29),u1_struct_0(X29))
| ~ v1_group_6(X32,X29,X29)
| ~ m2_relset_1(X32,u1_struct_0(X29),u1_struct_0(X29))
| X30 != k1_autgroup(X29)
| ~ m1_fraenkel(X30,u1_struct_0(X29),u1_struct_0(X29))
| v3_struct_0(X29)
| ~ v1_group_1(X29)
| ~ v3_group_1(X29)
| ~ v4_group_1(X29)
| ~ l1_group_1(X29) )
& ( v3_group_6(X32,X29,X29)
| ~ r2_hidden(X32,X30)
| ~ v1_funct_1(X32)
| ~ v1_funct_2(X32,u1_struct_0(X29),u1_struct_0(X29))
| ~ v1_group_6(X32,X29,X29)
| ~ m2_relset_1(X32,u1_struct_0(X29),u1_struct_0(X29))
| X30 != k1_autgroup(X29)
| ~ m1_fraenkel(X30,u1_struct_0(X29),u1_struct_0(X29))
| v3_struct_0(X29)
| ~ v1_group_1(X29)
| ~ v3_group_1(X29)
| ~ v4_group_1(X29)
| ~ l1_group_1(X29) )
& ( ~ v2_funct_1(X32)
| ~ v3_group_6(X32,X29,X29)
| r2_hidden(X32,X30)
| ~ v1_funct_1(X32)
| ~ v1_funct_2(X32,u1_struct_0(X29),u1_struct_0(X29))
| ~ v1_group_6(X32,X29,X29)
| ~ m2_relset_1(X32,u1_struct_0(X29),u1_struct_0(X29))
| X30 != k1_autgroup(X29)
| ~ m1_fraenkel(X30,u1_struct_0(X29),u1_struct_0(X29))
| v3_struct_0(X29)
| ~ v1_group_1(X29)
| ~ v3_group_1(X29)
| ~ v4_group_1(X29)
| ~ l1_group_1(X29) )
& ( v1_funct_1(esk5_2(X29,X30))
| m2_fraenkel(esk4_2(X29,X30),u1_struct_0(X29),u1_struct_0(X29),X30)
| X30 = k1_autgroup(X29)
| ~ m1_fraenkel(X30,u1_struct_0(X29),u1_struct_0(X29))
| v3_struct_0(X29)
| ~ v1_group_1(X29)
| ~ v3_group_1(X29)
| ~ v4_group_1(X29)
| ~ l1_group_1(X29) )
& ( v1_funct_2(esk5_2(X29,X30),u1_struct_0(X29),u1_struct_0(X29))
| m2_fraenkel(esk4_2(X29,X30),u1_struct_0(X29),u1_struct_0(X29),X30)
| X30 = k1_autgroup(X29)
| ~ m1_fraenkel(X30,u1_struct_0(X29),u1_struct_0(X29))
| v3_struct_0(X29)
| ~ v1_group_1(X29)
| ~ v3_group_1(X29)
| ~ v4_group_1(X29)
| ~ l1_group_1(X29) )
& ( v1_group_6(esk5_2(X29,X30),X29,X29)
| m2_fraenkel(esk4_2(X29,X30),u1_struct_0(X29),u1_struct_0(X29),X30)
| X30 = k1_autgroup(X29)
| ~ m1_fraenkel(X30,u1_struct_0(X29),u1_struct_0(X29))
| v3_struct_0(X29)
| ~ v1_group_1(X29)
| ~ v3_group_1(X29)
| ~ v4_group_1(X29)
| ~ l1_group_1(X29) )
& ( m2_relset_1(esk5_2(X29,X30),u1_struct_0(X29),u1_struct_0(X29))
| m2_fraenkel(esk4_2(X29,X30),u1_struct_0(X29),u1_struct_0(X29),X30)
| X30 = k1_autgroup(X29)
| ~ m1_fraenkel(X30,u1_struct_0(X29),u1_struct_0(X29))
| v3_struct_0(X29)
| ~ v1_group_1(X29)
| ~ v3_group_1(X29)
| ~ v4_group_1(X29)
| ~ l1_group_1(X29) )
& ( ~ r2_hidden(esk5_2(X29,X30),X30)
| ~ v2_funct_1(esk5_2(X29,X30))
| ~ v3_group_6(esk5_2(X29,X30),X29,X29)
| m2_fraenkel(esk4_2(X29,X30),u1_struct_0(X29),u1_struct_0(X29),X30)
| X30 = k1_autgroup(X29)
| ~ m1_fraenkel(X30,u1_struct_0(X29),u1_struct_0(X29))
| v3_struct_0(X29)
| ~ v1_group_1(X29)
| ~ v3_group_1(X29)
| ~ v4_group_1(X29)
| ~ l1_group_1(X29) )
& ( v2_funct_1(esk5_2(X29,X30))
| r2_hidden(esk5_2(X29,X30),X30)
| m2_fraenkel(esk4_2(X29,X30),u1_struct_0(X29),u1_struct_0(X29),X30)
| X30 = k1_autgroup(X29)
| ~ m1_fraenkel(X30,u1_struct_0(X29),u1_struct_0(X29))
| v3_struct_0(X29)
| ~ v1_group_1(X29)
| ~ v3_group_1(X29)
| ~ v4_group_1(X29)
| ~ l1_group_1(X29) )
& ( v3_group_6(esk5_2(X29,X30),X29,X29)
| r2_hidden(esk5_2(X29,X30),X30)
| m2_fraenkel(esk4_2(X29,X30),u1_struct_0(X29),u1_struct_0(X29),X30)
| X30 = k1_autgroup(X29)
| ~ m1_fraenkel(X30,u1_struct_0(X29),u1_struct_0(X29))
| v3_struct_0(X29)
| ~ v1_group_1(X29)
| ~ v3_group_1(X29)
| ~ v4_group_1(X29)
| ~ l1_group_1(X29) )
& ( v1_funct_1(esk5_2(X29,X30))
| ~ v1_funct_1(esk4_2(X29,X30))
| ~ v1_funct_2(esk4_2(X29,X30),u1_struct_0(X29),u1_struct_0(X29))
| ~ v1_group_6(esk4_2(X29,X30),X29,X29)
| ~ m2_relset_1(esk4_2(X29,X30),u1_struct_0(X29),u1_struct_0(X29))
| X30 = k1_autgroup(X29)
| ~ m1_fraenkel(X30,u1_struct_0(X29),u1_struct_0(X29))
| v3_struct_0(X29)
| ~ v1_group_1(X29)
| ~ v3_group_1(X29)
| ~ v4_group_1(X29)
| ~ l1_group_1(X29) )
& ( v1_funct_2(esk5_2(X29,X30),u1_struct_0(X29),u1_struct_0(X29))
| ~ v1_funct_1(esk4_2(X29,X30))
| ~ v1_funct_2(esk4_2(X29,X30),u1_struct_0(X29),u1_struct_0(X29))
| ~ v1_group_6(esk4_2(X29,X30),X29,X29)
| ~ m2_relset_1(esk4_2(X29,X30),u1_struct_0(X29),u1_struct_0(X29))
| X30 = k1_autgroup(X29)
| ~ m1_fraenkel(X30,u1_struct_0(X29),u1_struct_0(X29))
| v3_struct_0(X29)
| ~ v1_group_1(X29)
| ~ v3_group_1(X29)
| ~ v4_group_1(X29)
| ~ l1_group_1(X29) )
& ( v1_group_6(esk5_2(X29,X30),X29,X29)
| ~ v1_funct_1(esk4_2(X29,X30))
| ~ v1_funct_2(esk4_2(X29,X30),u1_struct_0(X29),u1_struct_0(X29))
| ~ v1_group_6(esk4_2(X29,X30),X29,X29)
| ~ m2_relset_1(esk4_2(X29,X30),u1_struct_0(X29),u1_struct_0(X29))
| X30 = k1_autgroup(X29)
| ~ m1_fraenkel(X30,u1_struct_0(X29),u1_struct_0(X29))
| v3_struct_0(X29)
| ~ v1_group_1(X29)
| ~ v3_group_1(X29)
| ~ v4_group_1(X29)
| ~ l1_group_1(X29) )
& ( m2_relset_1(esk5_2(X29,X30),u1_struct_0(X29),u1_struct_0(X29))
| ~ v1_funct_1(esk4_2(X29,X30))
| ~ v1_funct_2(esk4_2(X29,X30),u1_struct_0(X29),u1_struct_0(X29))
| ~ v1_group_6(esk4_2(X29,X30),X29,X29)
| ~ m2_relset_1(esk4_2(X29,X30),u1_struct_0(X29),u1_struct_0(X29))
| X30 = k1_autgroup(X29)
| ~ m1_fraenkel(X30,u1_struct_0(X29),u1_struct_0(X29))
| v3_struct_0(X29)
| ~ v1_group_1(X29)
| ~ v3_group_1(X29)
| ~ v4_group_1(X29)
| ~ l1_group_1(X29) )
& ( ~ r2_hidden(esk5_2(X29,X30),X30)
| ~ v2_funct_1(esk5_2(X29,X30))
| ~ v3_group_6(esk5_2(X29,X30),X29,X29)
| ~ v1_funct_1(esk4_2(X29,X30))
| ~ v1_funct_2(esk4_2(X29,X30),u1_struct_0(X29),u1_struct_0(X29))
| ~ v1_group_6(esk4_2(X29,X30),X29,X29)
| ~ m2_relset_1(esk4_2(X29,X30),u1_struct_0(X29),u1_struct_0(X29))
| X30 = k1_autgroup(X29)
| ~ m1_fraenkel(X30,u1_struct_0(X29),u1_struct_0(X29))
| v3_struct_0(X29)
| ~ v1_group_1(X29)
| ~ v3_group_1(X29)
| ~ v4_group_1(X29)
| ~ l1_group_1(X29) )
& ( v2_funct_1(esk5_2(X29,X30))
| r2_hidden(esk5_2(X29,X30),X30)
| ~ v1_funct_1(esk4_2(X29,X30))
| ~ v1_funct_2(esk4_2(X29,X30),u1_struct_0(X29),u1_struct_0(X29))
| ~ v1_group_6(esk4_2(X29,X30),X29,X29)
| ~ m2_relset_1(esk4_2(X29,X30),u1_struct_0(X29),u1_struct_0(X29))
| X30 = k1_autgroup(X29)
| ~ m1_fraenkel(X30,u1_struct_0(X29),u1_struct_0(X29))
| v3_struct_0(X29)
| ~ v1_group_1(X29)
| ~ v3_group_1(X29)
| ~ v4_group_1(X29)
| ~ l1_group_1(X29) )
& ( v3_group_6(esk5_2(X29,X30),X29,X29)
| r2_hidden(esk5_2(X29,X30),X30)
| ~ v1_funct_1(esk4_2(X29,X30))
| ~ v1_funct_2(esk4_2(X29,X30),u1_struct_0(X29),u1_struct_0(X29))
| ~ v1_group_6(esk4_2(X29,X30),X29,X29)
| ~ m2_relset_1(esk4_2(X29,X30),u1_struct_0(X29),u1_struct_0(X29))
| X30 = k1_autgroup(X29)
| ~ m1_fraenkel(X30,u1_struct_0(X29),u1_struct_0(X29))
| v3_struct_0(X29)
| ~ v1_group_1(X29)
| ~ v3_group_1(X29)
| ~ v4_group_1(X29)
| ~ l1_group_1(X29) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])])])])]) ).
cnf(c_0_39,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_33]) ).
cnf(c_0_40,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_41,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_42,negated_conjecture,
v1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_43,negated_conjecture,
( ~ v1_xboole_0(u1_struct_0(esk1_0))
| ~ r2_hidden(X1,esk27_1(esk1_0)) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_44,plain,
( v1_xboole_0(X1)
| r2_hidden(esk10_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
fof(c_0_45,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_46,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_47,plain,
! [X124,X125,X126] :
( ( ~ m2_relset_1(X126,X124,X125)
| m1_relset_1(X126,X124,X125) )
& ( ~ m1_relset_1(X126,X124,X125)
| m2_relset_1(X126,X124,X125) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])])]) ).
cnf(c_0_48,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_38]) ).
cnf(c_0_49,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_24]) ).
cnf(c_0_50,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_39,c_0_28]),c_0_40]),c_0_41]),c_0_42])]),c_0_29]) ).
cnf(c_0_51,plain,
( v3_struct_0(X1)
| ~ v1_xboole_0(esk27_1(X1))
| ~ l1_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_52,negated_conjecture,
( v1_xboole_0(esk27_1(esk1_0))
| ~ v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
fof(c_0_53,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_54,plain,
! [X120,X121,X122,X123] :
( ( ~ m2_fraenkel(X123,X120,X121,X122)
| m1_subset_1(X123,X122)
| v1_xboole_0(X121)
| ~ m1_fraenkel(X122,X120,X121) )
& ( ~ m1_subset_1(X123,X122)
| m2_fraenkel(X123,X120,X121,X122)
| v1_xboole_0(X121)
| ~ m1_fraenkel(X122,X120,X121) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])])])]) ).
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] :
( ( 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_56,plain,
! [X40,X41,X42,X43,X44] :
( ( v1_funct_1(k7_funct_2(X40,X41,X42,X43,X44))
| v1_xboole_0(X41)
| ~ v1_funct_1(X43)
| ~ v1_funct_2(X43,X40,X41)
| ~ m1_relset_1(X43,X40,X41)
| ~ v1_funct_1(X44)
| ~ v1_funct_2(X44,X41,X42)
| ~ m1_relset_1(X44,X41,X42) )
& ( v1_funct_2(k7_funct_2(X40,X41,X42,X43,X44),X40,X42)
| v1_xboole_0(X41)
| ~ v1_funct_1(X43)
| ~ v1_funct_2(X43,X40,X41)
| ~ m1_relset_1(X43,X40,X41)
| ~ v1_funct_1(X44)
| ~ v1_funct_2(X44,X41,X42)
| ~ m1_relset_1(X44,X41,X42) )
& ( m2_relset_1(k7_funct_2(X40,X41,X42,X43,X44),X40,X42)
| v1_xboole_0(X41)
| ~ v1_funct_1(X43)
| ~ v1_funct_2(X43,X40,X41)
| ~ m1_relset_1(X43,X40,X41)
| ~ v1_funct_1(X44)
| ~ v1_funct_2(X44,X41,X42)
| ~ m1_relset_1(X44,X41,X42) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_46])])])]) ).
cnf(c_0_57,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_38]) ).
cnf(c_0_58,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_38]) ).
cnf(c_0_59,plain,
( m1_relset_1(X1,X2,X3)
| ~ m2_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_60,negated_conjecture,
m2_relset_1(esk2_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_28]),c_0_40]),c_0_41]),c_0_42])]),c_0_29]),c_0_50])]) ).
cnf(c_0_61,negated_conjecture,
( ~ l1_struct_0(esk1_0)
| ~ v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_29]) ).
fof(c_0_62,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]) ).
fof(c_0_63,plain,
! [X51,X52,X53] :
( ( ~ v1_xboole_0(X53)
| ~ m1_fraenkel(X53,X51,X52) )
& ( v1_fraenkel(X53)
| ~ m1_fraenkel(X53,X51,X52) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_53])])])]) ).
cnf(c_0_64,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_54]) ).
fof(c_0_65,plain,
! [X128,X129] :
( ~ r2_hidden(X128,X129)
| m1_subset_1(X128,X129) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])])]) ).
fof(c_0_66,plain,
! [X137,X138] :
( ( ~ r2_hidden(X138,k1_autgroup(X137))
| v4_group_6(X138,X137,X137)
| ~ v1_funct_1(X138)
| ~ v1_funct_2(X138,u1_struct_0(X137),u1_struct_0(X137))
| ~ v1_group_6(X138,X137,X137)
| ~ m2_relset_1(X138,u1_struct_0(X137),u1_struct_0(X137))
| v3_struct_0(X137)
| ~ v1_group_1(X137)
| ~ v3_group_1(X137)
| ~ v4_group_1(X137)
| ~ l1_group_1(X137) )
& ( ~ v4_group_6(X138,X137,X137)
| r2_hidden(X138,k1_autgroup(X137))
| ~ v1_funct_1(X138)
| ~ v1_funct_2(X138,u1_struct_0(X137),u1_struct_0(X137))
| ~ v1_group_6(X138,X137,X137)
| ~ m2_relset_1(X138,u1_struct_0(X137),u1_struct_0(X137))
| v3_struct_0(X137)
| ~ v1_group_1(X137)
| ~ v3_group_1(X137)
| ~ v4_group_1(X137)
| ~ l1_group_1(X137) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])])])]) ).
cnf(c_0_67,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_56]) ).
cnf(c_0_68,negated_conjecture,
v1_funct_2(esk2_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_49]),c_0_28]),c_0_40]),c_0_41]),c_0_42])]),c_0_29]),c_0_50])]) ).
cnf(c_0_69,negated_conjecture,
v1_funct_1(esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_49]),c_0_28]),c_0_40]),c_0_41]),c_0_42])]),c_0_29]),c_0_50])]) ).
cnf(c_0_70,negated_conjecture,
m1_relset_1(esk2_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0)),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_71,negated_conjecture,
~ v1_xboole_0(u1_struct_0(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_23]),c_0_28])]) ).
cnf(c_0_72,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_56]) ).
cnf(c_0_73,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_24]) ).
fof(c_0_74,plain,
! [X115,X116,X117,X118,X119] :
( v3_struct_0(X115)
| ~ v3_group_1(X115)
| ~ v4_group_1(X115)
| ~ l1_group_1(X115)
| v3_struct_0(X116)
| ~ v3_group_1(X116)
| ~ v4_group_1(X116)
| ~ l1_group_1(X116)
| v3_struct_0(X117)
| ~ v3_group_1(X117)
| ~ v4_group_1(X117)
| ~ l1_group_1(X117)
| ~ v1_funct_1(X118)
| ~ v1_funct_2(X118,u1_struct_0(X115),u1_struct_0(X116))
| ~ v1_group_6(X118,X115,X116)
| ~ m1_relset_1(X118,u1_struct_0(X115),u1_struct_0(X116))
| ~ v1_funct_1(X119)
| ~ v1_funct_2(X119,u1_struct_0(X116),u1_struct_0(X117))
| ~ v1_group_6(X119,X116,X117)
| ~ m1_relset_1(X119,u1_struct_0(X116),u1_struct_0(X117))
| k8_group_6(X115,X116,X117,X118,X119) = k5_relat_1(X118,X119) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_62])])]) ).
cnf(c_0_75,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_38]) ).
cnf(c_0_76,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_54]) ).
cnf(c_0_77,plain,
( ~ v1_xboole_0(X1)
| ~ m1_fraenkel(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_78,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk1_0))
| m2_fraenkel(X1,u1_struct_0(esk1_0),u1_struct_0(esk1_0),k1_autgroup(esk1_0))
| ~ m1_subset_1(X1,k1_autgroup(esk1_0)) ),
inference(spm,[status(thm)],[c_0_64,c_0_50]) ).
cnf(c_0_79,plain,
( m1_subset_1(X1,X2)
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_80,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_66]) ).
cnf(c_0_81,negated_conjecture,
( m2_relset_1(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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69])]),c_0_70])]),c_0_71]) ).
cnf(c_0_82,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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_68]),c_0_69])]),c_0_70])]),c_0_71]) ).
cnf(c_0_83,plain,
( v1_funct_1(k7_funct_2(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) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_84,negated_conjecture,
m2_relset_1(esk3_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_73]),c_0_28]),c_0_40]),c_0_41]),c_0_42])]),c_0_29]),c_0_50])]) ).
fof(c_0_85,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_86,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]) ).
cnf(c_0_87,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_74]) ).
cnf(c_0_88,negated_conjecture,
v1_group_6(esk2_0,esk1_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_49]),c_0_28]),c_0_40]),c_0_41]),c_0_42])]),c_0_29]),c_0_50])]) ).
cnf(c_0_89,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_66]) ).
cnf(c_0_90,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_76,c_0_49]),c_0_50])]),c_0_71]) ).
cnf(c_0_91,negated_conjecture,
~ v1_xboole_0(k1_autgroup(esk1_0)),
inference(spm,[status(thm)],[c_0_77,c_0_50]) ).
cnf(c_0_92,negated_conjecture,
v1_group_6(esk3_0,esk1_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_73]),c_0_28]),c_0_40]),c_0_41]),c_0_42])]),c_0_29]),c_0_50])]) ).
cnf(c_0_93,negated_conjecture,
v1_funct_2(esk3_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_73]),c_0_28]),c_0_40]),c_0_41]),c_0_42])]),c_0_29]),c_0_50])]) ).
cnf(c_0_94,negated_conjecture,
v1_funct_1(esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_73]),c_0_28]),c_0_40]),c_0_41]),c_0_42])]),c_0_29]),c_0_50])]) ).
cnf(c_0_95,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_76,c_0_73]),c_0_50])]),c_0_71]) ).
fof(c_0_96,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]) ).
cnf(c_0_97,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk1_0))
| m2_fraenkel(X1,u1_struct_0(esk1_0),u1_struct_0(esk1_0),k1_autgroup(esk1_0))
| ~ r2_hidden(X1,k1_autgroup(esk1_0)) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_98,negated_conjecture,
( r2_hidden(k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),X1,esk2_0),k1_autgroup(esk1_0))
| ~ v4_group_6(k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),X1,esk2_0),esk1_0,esk1_0)
| ~ v1_group_6(k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),X1,esk2_0),esk1_0,esk1_0)
| ~ v1_funct_2(X1,u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| ~ m1_relset_1(X1,u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| ~ v1_funct_1(k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),X1,esk2_0))
| ~ v1_funct_1(X1) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_28]),c_0_40]),c_0_41]),c_0_42])]),c_0_29]),c_0_82]) ).
cnf(c_0_99,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk1_0))
| v1_funct_1(k7_funct_2(X1,u1_struct_0(esk1_0),u1_struct_0(esk1_0),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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_68]),c_0_69])]),c_0_70])]) ).
cnf(c_0_100,negated_conjecture,
m1_relset_1(esk3_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0)),
inference(spm,[status(thm)],[c_0_59,c_0_84]) ).
fof(c_0_101,plain,
! [X110,X111,X112,X113,X114] :
( v1_xboole_0(X111)
| ~ v1_funct_1(X113)
| ~ v1_funct_2(X113,X110,X111)
| ~ m1_relset_1(X113,X110,X111)
| ~ v1_funct_1(X114)
| ~ v1_funct_2(X114,X111,X112)
| ~ m1_relset_1(X114,X111,X112)
| k7_funct_2(X110,X111,X112,X113,X114) = k5_relat_1(X113,X114) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_85])])]) ).
fof(c_0_102,plain,
! [X143,X144,X145,X146,X147] :
( v3_struct_0(X143)
| ~ v3_group_1(X143)
| ~ v4_group_1(X143)
| ~ l1_group_1(X143)
| v3_struct_0(X144)
| ~ v3_group_1(X144)
| ~ v4_group_1(X144)
| ~ l1_group_1(X144)
| v3_struct_0(X145)
| ~ v3_group_1(X145)
| ~ v4_group_1(X145)
| ~ l1_group_1(X145)
| ~ v1_funct_1(X146)
| ~ v1_funct_2(X146,u1_struct_0(X143),u1_struct_0(X144))
| ~ v1_group_6(X146,X143,X144)
| ~ m2_relset_1(X146,u1_struct_0(X143),u1_struct_0(X144))
| ~ v1_funct_1(X147)
| ~ v1_funct_2(X147,u1_struct_0(X144),u1_struct_0(X145))
| ~ v1_group_6(X147,X144,X145)
| ~ m2_relset_1(X147,u1_struct_0(X144),u1_struct_0(X145))
| ~ v4_group_6(X146,X143,X144)
| ~ v4_group_6(X147,X144,X145)
| v4_group_6(k8_group_6(X143,X144,X145,X146,X147),X143,X145) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_86])])])]) ).
cnf(c_0_103,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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_68]),c_0_88]),c_0_69]),c_0_28]),c_0_40]),c_0_41])]),c_0_29]),c_0_70])]) ).
cnf(c_0_104,negated_conjecture,
( v4_group_6(esk2_0,esk1_0,esk1_0)
| ~ r2_hidden(esk2_0,k1_autgroup(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_60]),c_0_88]),c_0_68]),c_0_69]),c_0_28]),c_0_40]),c_0_41]),c_0_42])]),c_0_29]) ).
cnf(c_0_105,negated_conjecture,
r2_hidden(esk2_0,k1_autgroup(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_90]),c_0_91]) ).
cnf(c_0_106,negated_conjecture,
( v4_group_6(esk3_0,esk1_0,esk1_0)
| ~ r2_hidden(esk3_0,k1_autgroup(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_84]),c_0_92]),c_0_93]),c_0_94]),c_0_28]),c_0_40]),c_0_41]),c_0_42])]),c_0_29]) ).
cnf(c_0_107,negated_conjecture,
r2_hidden(esk3_0,k1_autgroup(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_95]),c_0_91]) ).
fof(c_0_108,plain,
! [X45,X46,X47,X48,X49] :
( ( v1_funct_1(k8_group_6(X45,X46,X47,X48,X49))
| v3_struct_0(X45)
| ~ v3_group_1(X45)
| ~ v4_group_1(X45)
| ~ l1_group_1(X45)
| v3_struct_0(X46)
| ~ v3_group_1(X46)
| ~ v4_group_1(X46)
| ~ l1_group_1(X46)
| v3_struct_0(X47)
| ~ v3_group_1(X47)
| ~ v4_group_1(X47)
| ~ l1_group_1(X47)
| ~ v1_funct_1(X48)
| ~ v1_funct_2(X48,u1_struct_0(X45),u1_struct_0(X46))
| ~ v1_group_6(X48,X45,X46)
| ~ m1_relset_1(X48,u1_struct_0(X45),u1_struct_0(X46))
| ~ v1_funct_1(X49)
| ~ v1_funct_2(X49,u1_struct_0(X46),u1_struct_0(X47))
| ~ v1_group_6(X49,X46,X47)
| ~ m1_relset_1(X49,u1_struct_0(X46),u1_struct_0(X47)) )
& ( v1_funct_2(k8_group_6(X45,X46,X47,X48,X49),u1_struct_0(X45),u1_struct_0(X47))
| v3_struct_0(X45)
| ~ v3_group_1(X45)
| ~ v4_group_1(X45)
| ~ l1_group_1(X45)
| v3_struct_0(X46)
| ~ v3_group_1(X46)
| ~ v4_group_1(X46)
| ~ l1_group_1(X46)
| v3_struct_0(X47)
| ~ v3_group_1(X47)
| ~ v4_group_1(X47)
| ~ l1_group_1(X47)
| ~ v1_funct_1(X48)
| ~ v1_funct_2(X48,u1_struct_0(X45),u1_struct_0(X46))
| ~ v1_group_6(X48,X45,X46)
| ~ m1_relset_1(X48,u1_struct_0(X45),u1_struct_0(X46))
| ~ v1_funct_1(X49)
| ~ v1_funct_2(X49,u1_struct_0(X46),u1_struct_0(X47))
| ~ v1_group_6(X49,X46,X47)
| ~ m1_relset_1(X49,u1_struct_0(X46),u1_struct_0(X47)) )
& ( v1_group_6(k8_group_6(X45,X46,X47,X48,X49),X45,X47)
| v3_struct_0(X45)
| ~ v3_group_1(X45)
| ~ v4_group_1(X45)
| ~ l1_group_1(X45)
| v3_struct_0(X46)
| ~ v3_group_1(X46)
| ~ v4_group_1(X46)
| ~ l1_group_1(X46)
| v3_struct_0(X47)
| ~ v3_group_1(X47)
| ~ v4_group_1(X47)
| ~ l1_group_1(X47)
| ~ v1_funct_1(X48)
| ~ v1_funct_2(X48,u1_struct_0(X45),u1_struct_0(X46))
| ~ v1_group_6(X48,X45,X46)
| ~ m1_relset_1(X48,u1_struct_0(X45),u1_struct_0(X46))
| ~ v1_funct_1(X49)
| ~ v1_funct_2(X49,u1_struct_0(X46),u1_struct_0(X47))
| ~ v1_group_6(X49,X46,X47)
| ~ m1_relset_1(X49,u1_struct_0(X46),u1_struct_0(X47)) )
& ( m2_relset_1(k8_group_6(X45,X46,X47,X48,X49),u1_struct_0(X45),u1_struct_0(X47))
| v3_struct_0(X45)
| ~ v3_group_1(X45)
| ~ v4_group_1(X45)
| ~ l1_group_1(X45)
| v3_struct_0(X46)
| ~ v3_group_1(X46)
| ~ v4_group_1(X46)
| ~ l1_group_1(X46)
| v3_struct_0(X47)
| ~ v3_group_1(X47)
| ~ v4_group_1(X47)
| ~ l1_group_1(X47)
| ~ v1_funct_1(X48)
| ~ v1_funct_2(X48,u1_struct_0(X45),u1_struct_0(X46))
| ~ v1_group_6(X48,X45,X46)
| ~ m1_relset_1(X48,u1_struct_0(X45),u1_struct_0(X46))
| ~ v1_funct_1(X49)
| ~ v1_funct_2(X49,u1_struct_0(X46),u1_struct_0(X47))
| ~ v1_group_6(X49,X46,X47)
| ~ m1_relset_1(X49,u1_struct_0(X46),u1_struct_0(X47)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_96])])])]) ).
cnf(c_0_109,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_24]) ).
cnf(c_0_110,negated_conjecture,
( m2_fraenkel(k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),X1,esk2_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k1_autgroup(esk1_0))
| ~ v4_group_6(k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),X1,esk2_0),esk1_0,esk1_0)
| ~ v1_group_6(k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),X1,esk2_0),esk1_0,esk1_0)
| ~ v1_funct_2(X1,u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| ~ m1_relset_1(X1,u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| ~ v1_funct_1(k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),X1,esk2_0))
| ~ v1_funct_1(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_71]) ).
cnf(c_0_111,negated_conjecture,
v1_funct_1(k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),esk3_0,esk2_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_93]),c_0_100]),c_0_94])]),c_0_71]) ).
cnf(c_0_112,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_101]) ).
cnf(c_0_113,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_102]) ).
cnf(c_0_114,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_103,c_0_93]),c_0_92]),c_0_100]),c_0_94]),c_0_28]),c_0_40]),c_0_41])]),c_0_29]) ).
cnf(c_0_115,negated_conjecture,
v4_group_6(esk2_0,esk1_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_104,c_0_105])]) ).
cnf(c_0_116,negated_conjecture,
v4_group_6(esk3_0,esk1_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_106,c_0_107])]) ).
cnf(c_0_117,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_108]) ).
cnf(c_0_118,negated_conjecture,
( ~ v4_group_6(k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),esk3_0,esk2_0),esk1_0,esk1_0)
| ~ v1_group_6(k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),esk3_0,esk2_0),esk1_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_109,c_0_110]),c_0_93]),c_0_100]),c_0_111]),c_0_94])]) ).
cnf(c_0_119,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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_68]),c_0_69])]),c_0_70])]),c_0_71]) ).
cnf(c_0_120,negated_conjecture,
v4_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(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_113,c_0_114]),c_0_115]),c_0_116]),c_0_60]),c_0_84]),c_0_88]),c_0_92]),c_0_68]),c_0_93]),c_0_69]),c_0_94]),c_0_28]),c_0_40]),c_0_41])]),c_0_29]) ).
cnf(c_0_121,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_114]),c_0_88]),c_0_92]),c_0_68]),c_0_93]),c_0_70]),c_0_100]),c_0_69]),c_0_94]),c_0_28]),c_0_40]),c_0_41])]),c_0_29]) ).
cnf(c_0_122,negated_conjecture,
$false,
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(spm,[status(thm)],[c_0_118,c_0_119]),c_0_120]),c_0_121]),c_0_93]),c_0_100]),c_0_94])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP621+1 : TPTP v8.2.0. Released v3.4.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.15/0.35 % Computer : n017.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sun May 19 04:54:53 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.21/0.49 Running first-order model finding
% 0.21/0.49 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.30/0.65 # Version: 3.1.0
% 1.30/0.65 # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.30/0.65 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.30/0.65 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.30/0.65 # Starting new_bool_3 with 300s (1) cores
% 1.30/0.65 # Starting new_bool_1 with 300s (1) cores
% 1.30/0.65 # Starting sh5l with 300s (1) cores
% 1.30/0.65 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 8330 completed with status 0
% 1.30/0.65 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 1.30/0.65 # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.30/0.65 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.30/0.65 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.30/0.65 # No SInE strategy applied
% 1.30/0.65 # Search class: FGHSM-FSLM32-SFFFFFNN
% 1.30/0.65 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.30/0.65 # Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 633s (1) cores
% 1.30/0.65 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.30/0.65 # Starting U----_213g_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.30/0.65 # Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 1.30/0.65 # Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 1.30/0.65 # G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with pid 8340 completed with status 0
% 1.30/0.65 # Result found by G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN
% 1.30/0.65 # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.30/0.65 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.30/0.65 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.30/0.65 # No SInE strategy applied
% 1.30/0.65 # Search class: FGHSM-FSLM32-SFFFFFNN
% 1.30/0.65 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.30/0.65 # Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 633s (1) cores
% 1.30/0.65 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.30/0.65 # Starting U----_213g_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.30/0.65 # Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 1.30/0.65 # Preprocessing time : 0.011 s
% 1.30/0.65
% 1.30/0.65 # Proof found!
% 1.30/0.65 # SZS status Theorem
% 1.30/0.65 # SZS output start CNFRefutation
% See solution above
% 1.30/0.65 # Parsed axioms : 71
% 1.30/0.65 # Removed by relevancy pruning/SinE : 0
% 1.30/0.65 # Initial clauses : 156
% 1.30/0.65 # Removed in clause preprocessing : 15
% 1.30/0.65 # Initial clauses in saturation : 141
% 1.30/0.65 # Processed clauses : 724
% 1.30/0.65 # ...of these trivial : 14
% 1.30/0.65 # ...subsumed : 93
% 1.30/0.65 # ...remaining for further processing : 617
% 1.30/0.65 # Other redundant clauses eliminated : 2
% 1.30/0.65 # Clauses deleted for lack of memory : 0
% 1.30/0.65 # Backward-subsumed : 22
% 1.30/0.65 # Backward-rewritten : 34
% 1.30/0.65 # Generated clauses : 1385
% 1.30/0.65 # ...of the previous two non-redundant : 1274
% 1.30/0.65 # ...aggressively subsumed : 0
% 1.30/0.65 # Contextual simplify-reflections : 29
% 1.30/0.65 # Paramodulations : 1364
% 1.30/0.65 # Factorizations : 6
% 1.30/0.65 # NegExts : 0
% 1.30/0.65 # Equation resolutions : 11
% 1.30/0.65 # Disequality decompositions : 0
% 1.30/0.65 # Total rewrite steps : 2167
% 1.30/0.65 # ...of those cached : 2051
% 1.30/0.65 # Propositional unsat checks : 0
% 1.30/0.65 # Propositional check models : 0
% 1.30/0.65 # Propositional check unsatisfiable : 0
% 1.30/0.65 # Propositional clauses : 0
% 1.30/0.65 # Propositional clauses after purity: 0
% 1.30/0.65 # Propositional unsat core size : 0
% 1.30/0.65 # Propositional preprocessing time : 0.000
% 1.30/0.65 # Propositional encoding time : 0.000
% 1.30/0.65 # Propositional solver time : 0.000
% 1.30/0.65 # Success case prop preproc time : 0.000
% 1.30/0.65 # Success case prop encoding time : 0.000
% 1.30/0.65 # Success case prop solver time : 0.000
% 1.30/0.65 # Current number of processed clauses : 557
% 1.30/0.65 # Positive orientable unit clauses : 141
% 1.30/0.65 # Positive unorientable unit clauses: 0
% 1.30/0.65 # Negative unit clauses : 20
% 1.30/0.65 # Non-unit-clauses : 396
% 1.30/0.65 # Current number of unprocessed clauses: 667
% 1.30/0.65 # ...number of literals in the above : 4318
% 1.30/0.65 # Current number of archived formulas : 0
% 1.30/0.65 # Current number of archived clauses : 60
% 1.30/0.65 # Clause-clause subsumption calls (NU) : 87640
% 1.30/0.65 # Rec. Clause-clause subsumption calls : 8155
% 1.30/0.65 # Non-unit clause-clause subsumptions : 106
% 1.30/0.65 # Unit Clause-clause subsumption calls : 5189
% 1.30/0.65 # Rewrite failures with RHS unbound : 0
% 1.30/0.65 # BW rewrite match attempts : 29
% 1.30/0.65 # BW rewrite match successes : 15
% 1.30/0.65 # Condensation attempts : 0
% 1.30/0.65 # Condensation successes : 0
% 1.30/0.65 # Termbank termtop insertions : 66059
% 1.30/0.65 # Search garbage collected termcells : 2420
% 1.30/0.65
% 1.30/0.65 # -------------------------------------------------
% 1.30/0.65 # User time : 0.119 s
% 1.30/0.65 # System time : 0.012 s
% 1.30/0.65 # Total time : 0.131 s
% 1.30/0.65 # Maximum resident set size: 2320 pages
% 1.30/0.65
% 1.30/0.65 # -------------------------------------------------
% 1.30/0.65 # User time : 0.632 s
% 1.30/0.65 # System time : 0.034 s
% 1.30/0.65 # Total time : 0.666 s
% 1.30/0.65 # Maximum resident set size: 1776 pages
% 1.30/0.65 % E---3.1 exiting
%------------------------------------------------------------------------------