TSTP Solution File: GRP631+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP631+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 00:22:02 EDT 2023
% Result : Theorem 6.53s 6.65s
% Output : CNFRefutation 6.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 84
% Syntax : Number of formulae : 170 ( 24 unt; 66 typ; 0 def)
% Number of atoms : 341 ( 51 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 355 ( 118 ~; 127 |; 85 &)
% ( 1 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 90 ( 50 >; 40 *; 0 +; 0 <<)
% Number of predicates : 29 ( 27 usr; 1 prp; 0-4 aty)
% Number of functors : 39 ( 39 usr; 16 con; 0-6 aty)
% Number of variables : 153 ( 2 sgn; 86 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
v3_struct_0: $i > $o ).
tff(decl_23,type,
v1_group_1: $i > $o ).
tff(decl_24,type,
v3_group_1: $i > $o ).
tff(decl_25,type,
v4_group_1: $i > $o ).
tff(decl_26,type,
l1_group_1: $i > $o ).
tff(decl_27,type,
u1_struct_0: $i > $i ).
tff(decl_28,type,
m1_subset_1: ( $i * $i ) > $o ).
tff(decl_29,type,
k2_group_1: $i > $i ).
tff(decl_30,type,
k6_autgroup: ( $i * $i ) > $i ).
tff(decl_31,type,
k7_funct_2: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_32,type,
u1_group_1: $i > $i ).
tff(decl_33,type,
g1_group_1: ( $i * $i ) > $i ).
tff(decl_34,type,
r2_hidden: ( $i * $i ) > $o ).
tff(decl_35,type,
v1_fraenkel: $i > $o ).
tff(decl_36,type,
v1_relat_1: $i > $o ).
tff(decl_37,type,
v1_funct_1: $i > $o ).
tff(decl_38,type,
v1_xboole_0: $i > $o ).
tff(decl_39,type,
m1_relset_1: ( $i * $i * $i ) > $o ).
tff(decl_40,type,
v1_partfun1: ( $i * $i * $i ) > $o ).
tff(decl_41,type,
v1_funct_2: ( $i * $i * $i ) > $o ).
tff(decl_42,type,
v2_group_1: $i > $o ).
tff(decl_43,type,
v3_relat_2: $i > $o ).
tff(decl_44,type,
v8_relat_2: $i > $o ).
tff(decl_45,type,
v1_relat_2: $i > $o ).
tff(decl_46,type,
k2_zfmisc_1: ( $i * $i ) > $i ).
tff(decl_47,type,
k1_zfmisc_1: $i > $i ).
tff(decl_48,type,
v2_funct_1: $i > $o ).
tff(decl_49,type,
v3_funct_2: ( $i * $i * $i ) > $o ).
tff(decl_50,type,
v2_funct_2: ( $i * $i * $i ) > $o ).
tff(decl_51,type,
k4_autgroup: $i > $i ).
tff(decl_52,type,
m1_fraenkel: ( $i * $i * $i ) > $o ).
tff(decl_53,type,
k5_relat_1: ( $i * $i ) > $i ).
tff(decl_54,type,
m2_fraenkel: ( $i * $i * $i * $i ) > $o ).
tff(decl_55,type,
k6_partfun1: $i > $i ).
tff(decl_56,type,
m2_relset_1: ( $i * $i * $i ) > $o ).
tff(decl_57,type,
k6_relat_1: $i > $i ).
tff(decl_58,type,
k7_relset_1: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_59,type,
l1_struct_0: $i > $o ).
tff(decl_60,type,
k1_xboole_0: $i ).
tff(decl_61,type,
v4_relat_2: $i > $o ).
tff(decl_62,type,
r1_tarski: ( $i * $i ) > $o ).
tff(decl_63,type,
esk1_0: $i ).
tff(decl_64,type,
esk2_0: $i ).
tff(decl_65,type,
esk3_0: $i ).
tff(decl_66,type,
esk4_0: $i ).
tff(decl_67,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_68,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_69,type,
esk7_1: $i > $i ).
tff(decl_70,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_71,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_72,type,
esk10_0: $i ).
tff(decl_73,type,
esk11_0: $i ).
tff(decl_74,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_75,type,
esk13_0: $i ).
tff(decl_76,type,
esk14_0: $i ).
tff(decl_77,type,
esk15_0: $i ).
tff(decl_78,type,
esk16_0: $i ).
tff(decl_79,type,
esk17_1: $i > $i ).
tff(decl_80,type,
esk18_0: $i ).
tff(decl_81,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_82,type,
esk20_0: $i ).
tff(decl_83,type,
esk21_0: $i ).
tff(decl_84,type,
esk22_0: $i ).
tff(decl_85,type,
esk23_1: $i > $i ).
tff(decl_86,type,
esk24_0: $i ).
tff(decl_87,type,
esk25_1: $i > $i ).
fof(dt_k6_autgroup,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1)
& m1_subset_1(X2,u1_struct_0(X1)) )
=> m2_fraenkel(k6_autgroup(X1,X2),u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_autgroup) ).
fof(t29_autgroup,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ( k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_autgroup(X1,k2_group_1(X1)),k6_autgroup(X1,X2)) = k6_autgroup(X1,X2)
& k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_autgroup(X1,X2),k6_autgroup(X1,k2_group_1(X1))) = k6_autgroup(X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_autgroup) ).
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/sandbox2/benchmark/theBenchmark.p',dt_m2_fraenkel) ).
fof(dt_k4_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(k4_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_autgroup) ).
fof(fc2_funct_1,axiom,
! [X1] :
( v1_relat_1(k6_relat_1(X1))
& v1_funct_1(k6_relat_1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(redefinition_k6_partfun1,axiom,
! [X1] : k6_partfun1(X1) = k6_relat_1(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_partfun1) ).
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_k6_partfun1,axiom,
! [X1] :
( v1_partfun1(k6_partfun1(X1),X1,X1)
& m2_relset_1(k6_partfun1(X1),X1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_partfun1) ).
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(cc1_funct_2,axiom,
! [X1,X2,X3] :
( m1_relset_1(X3,X1,X2)
=> ( ( v1_funct_1(X3)
& v1_partfun1(X3,X1,X2) )
=> ( v1_funct_1(X3)
& v1_funct_2(X3,X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_2) ).
fof(redefinition_k7_relset_1,axiom,
! [X1,X2,X3,X4,X5,X6] :
( ( m1_relset_1(X5,X1,X2)
& m1_relset_1(X6,X3,X4) )
=> k7_relset_1(X1,X2,X3,X4,X5,X6) = k5_relat_1(X5,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_relset_1) ).
fof(t6_boole,axiom,
! [X1] :
( v1_xboole_0(X1)
=> X1 = k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(rc2_funct_1,axiom,
? [X1] :
( v1_relat_1(X1)
& v1_xboole_0(X1)
& v1_funct_1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(t24_autgroup,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> k6_autgroup(X1,k2_group_1(X1)) = k6_partfun1(u1_struct_0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_autgroup) ).
fof(t23_funct_2,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
=> ( k7_relset_1(X1,X1,X1,X2,k6_partfun1(X1),X3) = X3
& k7_relset_1(X1,X2,X2,X2,X3,k6_partfun1(X2)) = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_2) ).
fof(rc1_partfun1,axiom,
? [X1] :
( v1_relat_1(X1)
& v1_funct_1(X1)
& v2_funct_1(X1)
& v1_xboole_0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_partfun1) ).
fof(fc1_struct_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(dt_l1_group_1,axiom,
! [X1] :
( l1_group_1(X1)
=> l1_struct_0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_group_1) ).
fof(c_0_18,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1)
& m1_subset_1(X2,u1_struct_0(X1)) )
=> m2_fraenkel(k6_autgroup(X1,X2),u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k6_autgroup]) ).
fof(c_0_19,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ( k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_autgroup(X1,k2_group_1(X1)),k6_autgroup(X1,X2)) = k6_autgroup(X1,X2)
& k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_autgroup(X1,X2),k6_autgroup(X1,k2_group_1(X1))) = k6_autgroup(X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t29_autgroup])]) ).
fof(c_0_20,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_21,plain,
! [X44,X45] :
( v3_struct_0(X44)
| ~ v1_group_1(X44)
| ~ v3_group_1(X44)
| ~ v4_group_1(X44)
| ~ l1_group_1(X44)
| ~ m1_subset_1(X45,u1_struct_0(X44))
| m2_fraenkel(k6_autgroup(X44,X45),u1_struct_0(X44),u1_struct_0(X44),k4_autgroup(X44)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])]) ).
fof(c_0_22,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)
& m1_subset_1(esk2_0,u1_struct_0(esk1_0))
& ( k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_autgroup(esk1_0,k2_group_1(esk1_0)),k6_autgroup(esk1_0,esk2_0)) != k6_autgroup(esk1_0,esk2_0)
| k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_autgroup(esk1_0,esk2_0),k6_autgroup(esk1_0,k2_group_1(esk1_0))) != k6_autgroup(esk1_0,esk2_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
fof(c_0_23,plain,
! [X63,X64,X65,X66] :
( ( v1_funct_1(X66)
| ~ m2_fraenkel(X66,X63,X64,X65)
| v1_xboole_0(X64)
| ~ m1_fraenkel(X65,X63,X64) )
& ( v1_funct_2(X66,X63,X64)
| ~ m2_fraenkel(X66,X63,X64,X65)
| v1_xboole_0(X64)
| ~ m1_fraenkel(X65,X63,X64) )
& ( m2_relset_1(X66,X63,X64)
| ~ m2_fraenkel(X66,X63,X64,X65)
| v1_xboole_0(X64)
| ~ m1_fraenkel(X65,X63,X64) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).
cnf(c_0_24,plain,
( v3_struct_0(X1)
| m2_fraenkel(k6_autgroup(X1,X2),u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,negated_conjecture,
m1_subset_1(esk2_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,negated_conjecture,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,negated_conjecture,
v1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_31,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> m1_fraenkel(k4_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k4_autgroup]) ).
fof(c_0_32,plain,
! [X93] :
( v1_relat_1(k6_relat_1(X93))
& v1_funct_1(k6_relat_1(X93)) ),
inference(variable_rename,[status(thm)],[fc2_funct_1]) ).
fof(c_0_33,plain,
! [X122] : k6_partfun1(X122) = k6_relat_1(X122),
inference(variable_rename,[status(thm)],[redefinition_k6_partfun1]) ).
fof(c_0_34,plain,
! [X138,X139,X140] :
( ( ~ m2_relset_1(X140,X138,X139)
| m1_relset_1(X140,X138,X139) )
& ( ~ m1_relset_1(X140,X138,X139)
| m2_relset_1(X140,X138,X139) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
fof(c_0_35,plain,
! [X46] :
( v1_partfun1(k6_partfun1(X46),X46,X46)
& m2_relset_1(k6_partfun1(X46),X46,X46) ),
inference(variable_rename,[status(thm)],[dt_k6_partfun1]) ).
cnf(c_0_36,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_23]) ).
cnf(c_0_37,negated_conjecture,
m2_fraenkel(k6_autgroup(esk1_0,esk2_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k4_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(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
fof(c_0_38,plain,
! [X41] :
( v3_struct_0(X41)
| ~ v1_group_1(X41)
| ~ v3_group_1(X41)
| ~ v4_group_1(X41)
| ~ l1_group_1(X41)
| m1_fraenkel(k4_autgroup(X41),u1_struct_0(X41),u1_struct_0(X41)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])]) ).
fof(c_0_39,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_40,plain,
! [X15,X16,X17] :
( ( v1_funct_1(X17)
| ~ v1_funct_1(X17)
| ~ v1_partfun1(X17,X15,X16)
| ~ m1_relset_1(X17,X15,X16) )
& ( v1_funct_2(X17,X15,X16)
| ~ v1_funct_1(X17)
| ~ v1_partfun1(X17,X15,X16)
| ~ m1_relset_1(X17,X15,X16) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_funct_2])])]) ).
cnf(c_0_41,plain,
v1_funct_1(k6_relat_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_42,plain,
k6_partfun1(X1) = k6_relat_1(X1),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_43,plain,
( m1_relset_1(X1,X2,X3)
| ~ m2_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_44,plain,
m2_relset_1(k6_partfun1(X1),X1,X1),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_45,plain,
! [X128,X129,X130,X131,X132,X133] :
( ~ m1_relset_1(X132,X128,X129)
| ~ m1_relset_1(X133,X130,X131)
| k7_relset_1(X128,X129,X130,X131,X132,X133) = k5_relat_1(X132,X133) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k7_relset_1])]) ).
cnf(c_0_46,negated_conjecture,
( m2_relset_1(k6_autgroup(esk1_0,esk2_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| v1_xboole_0(u1_struct_0(esk1_0))
| ~ m1_fraenkel(k4_autgroup(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_47,plain,
( v3_struct_0(X1)
| m1_fraenkel(k4_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_38]) ).
fof(c_0_48,plain,
! [X158] :
( ~ v1_xboole_0(X158)
| X158 = k1_xboole_0 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_49,plain,
( v1_relat_1(esk16_0)
& v1_xboole_0(esk16_0)
& v1_funct_1(esk16_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_funct_1])]) ).
fof(c_0_50,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> k6_autgroup(X1,k2_group_1(X1)) = k6_partfun1(u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[t24_autgroup]) ).
fof(c_0_51,plain,
! [X123,X124,X125,X126,X127] :
( v1_xboole_0(X124)
| ~ v1_funct_1(X126)
| ~ v1_funct_2(X126,X123,X124)
| ~ m1_relset_1(X126,X123,X124)
| ~ v1_funct_1(X127)
| ~ v1_funct_2(X127,X124,X125)
| ~ m1_relset_1(X127,X124,X125)
| k7_funct_2(X123,X124,X125,X126,X127) = k5_relat_1(X126,X127) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])]) ).
cnf(c_0_52,plain,
( v1_funct_2(X1,X2,X3)
| ~ v1_funct_1(X1)
| ~ v1_partfun1(X1,X2,X3)
| ~ m1_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_53,plain,
v1_partfun1(k6_partfun1(X1),X1,X1),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_54,plain,
v1_funct_1(k6_partfun1(X1)),
inference(rw,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_55,plain,
m1_relset_1(k6_partfun1(X1),X1,X1),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_56,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_23]) ).
cnf(c_0_57,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_23]) ).
fof(c_0_58,plain,
! [X144,X145,X146] :
( ( k7_relset_1(X144,X144,X144,X145,k6_partfun1(X144),X146) = X146
| ~ m2_relset_1(X146,X144,X145) )
& ( k7_relset_1(X144,X145,X145,X145,X146,k6_partfun1(X145)) = X146
| ~ m2_relset_1(X146,X144,X145) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_funct_2])])]) ).
cnf(c_0_59,plain,
( k7_relset_1(X2,X3,X5,X6,X1,X4) = k5_relat_1(X1,X4)
| ~ m1_relset_1(X1,X2,X3)
| ~ m1_relset_1(X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_60,negated_conjecture,
( m2_relset_1(k6_autgroup(esk1_0,esk2_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_61,plain,
( X1 = k1_xboole_0
| ~ v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_62,plain,
v1_xboole_0(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
fof(c_0_63,plain,
! [X147] :
( v3_struct_0(X147)
| ~ v1_group_1(X147)
| ~ v3_group_1(X147)
| ~ v4_group_1(X147)
| ~ l1_group_1(X147)
| k6_autgroup(X147,k2_group_1(X147)) = k6_partfun1(u1_struct_0(X147)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_50])]) ).
cnf(c_0_64,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_51]) ).
cnf(c_0_65,plain,
v1_funct_2(k6_partfun1(X1),X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54])]),c_0_55])]) ).
cnf(c_0_66,negated_conjecture,
( v1_funct_2(k6_autgroup(esk1_0,esk2_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| v1_xboole_0(u1_struct_0(esk1_0))
| ~ m1_fraenkel(k4_autgroup(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_56,c_0_37]) ).
cnf(c_0_67,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk1_0))
| v1_funct_1(k6_autgroup(esk1_0,esk2_0))
| ~ m1_fraenkel(k4_autgroup(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_57,c_0_37]) ).
cnf(c_0_68,plain,
( k7_relset_1(X1,X2,X2,X2,X3,k6_partfun1(X2)) = X3
| ~ m2_relset_1(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_69,plain,
( k7_relset_1(X1,X2,X3,X3,X4,k6_partfun1(X3)) = k5_relat_1(X4,k6_partfun1(X3))
| ~ m1_relset_1(X4,X1,X2) ),
inference(spm,[status(thm)],[c_0_59,c_0_55]) ).
cnf(c_0_70,negated_conjecture,
( m1_relset_1(k6_autgroup(esk1_0,esk2_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_43,c_0_60]) ).
cnf(c_0_71,plain,
k1_xboole_0 = esk16_0,
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
fof(c_0_72,plain,
( v1_relat_1(esk14_0)
& v1_funct_1(esk14_0)
& v2_funct_1(esk14_0)
& v1_xboole_0(esk14_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_partfun1])]) ).
cnf(c_0_73,negated_conjecture,
( k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_autgroup(esk1_0,k2_group_1(esk1_0)),k6_autgroup(esk1_0,esk2_0)) != k6_autgroup(esk1_0,esk2_0)
| k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_autgroup(esk1_0,esk2_0),k6_autgroup(esk1_0,k2_group_1(esk1_0))) != k6_autgroup(esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_74,plain,
( v3_struct_0(X1)
| k6_autgroup(X1,k2_group_1(X1)) = k6_partfun1(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_63]) ).
cnf(c_0_75,plain,
( k7_funct_2(X1,X2,X2,X3,k6_partfun1(X2)) = k5_relat_1(X3,k6_partfun1(X2))
| v1_xboole_0(X2)
| ~ v1_funct_2(X3,X1,X2)
| ~ m1_relset_1(X3,X1,X2)
| ~ v1_funct_1(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_55]),c_0_54])]) ).
cnf(c_0_76,negated_conjecture,
( v1_funct_2(k6_autgroup(esk1_0,esk2_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_47]),c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_77,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk1_0))
| v1_funct_1(k6_autgroup(esk1_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(spm,[status(thm)],[c_0_67,c_0_47]),c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_78,negated_conjecture,
( k7_relset_1(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_autgroup(esk1_0,esk2_0),k6_partfun1(u1_struct_0(esk1_0))) = k6_autgroup(esk1_0,esk2_0)
| v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_68,c_0_60]) ).
cnf(c_0_79,negated_conjecture,
( k7_relset_1(u1_struct_0(esk1_0),u1_struct_0(esk1_0),X1,X1,k6_autgroup(esk1_0,esk2_0),k6_partfun1(X1)) = k5_relat_1(k6_autgroup(esk1_0,esk2_0),k6_partfun1(X1))
| v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_80,plain,
( k7_relset_1(X1,X1,X1,X2,k6_partfun1(X1),X3) = X3
| ~ m2_relset_1(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_81,negated_conjecture,
( k7_relset_1(X1,X2,u1_struct_0(esk1_0),u1_struct_0(esk1_0),X3,k6_autgroup(esk1_0,esk2_0)) = k5_relat_1(X3,k6_autgroup(esk1_0,esk2_0))
| v1_xboole_0(u1_struct_0(esk1_0))
| ~ m1_relset_1(X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_59,c_0_70]) ).
cnf(c_0_82,plain,
( X1 = esk16_0
| ~ v1_xboole_0(X1) ),
inference(rw,[status(thm)],[c_0_61,c_0_71]) ).
cnf(c_0_83,plain,
v1_xboole_0(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_84,negated_conjecture,
( k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_autgroup(esk1_0,esk2_0),k6_partfun1(u1_struct_0(esk1_0))) != k6_autgroup(esk1_0,esk2_0)
| k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_partfun1(u1_struct_0(esk1_0)),k6_autgroup(esk1_0,esk2_0)) != k6_autgroup(esk1_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(spm,[status(thm)],[c_0_73,c_0_74]),c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_85,negated_conjecture,
( k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_autgroup(esk1_0,esk2_0),k6_partfun1(u1_struct_0(esk1_0))) = k5_relat_1(k6_autgroup(esk1_0,esk2_0),k6_partfun1(u1_struct_0(esk1_0)))
| v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77]),c_0_70]) ).
cnf(c_0_86,negated_conjecture,
( k5_relat_1(k6_autgroup(esk1_0,esk2_0),k6_partfun1(u1_struct_0(esk1_0))) = k6_autgroup(esk1_0,esk2_0)
| v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_87,negated_conjecture,
( k7_funct_2(X1,u1_struct_0(esk1_0),u1_struct_0(esk1_0),X2,k6_autgroup(esk1_0,esk2_0)) = k5_relat_1(X2,k6_autgroup(esk1_0,esk2_0))
| v1_xboole_0(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(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_76]),c_0_77]),c_0_70]) ).
cnf(c_0_88,negated_conjecture,
( k7_relset_1(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_partfun1(u1_struct_0(esk1_0)),k6_autgroup(esk1_0,esk2_0)) = k6_autgroup(esk1_0,esk2_0)
| v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_80,c_0_60]) ).
cnf(c_0_89,negated_conjecture,
( k7_relset_1(X1,X1,u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_partfun1(X1),k6_autgroup(esk1_0,esk2_0)) = k5_relat_1(k6_partfun1(X1),k6_autgroup(esk1_0,esk2_0))
| v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_81,c_0_55]) ).
fof(c_0_90,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).
cnf(c_0_91,plain,
esk16_0 = esk14_0,
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_92,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk1_0))
| k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_partfun1(u1_struct_0(esk1_0)),k6_autgroup(esk1_0,esk2_0)) != k6_autgroup(esk1_0,esk2_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86]) ).
cnf(c_0_93,negated_conjecture,
( k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_partfun1(u1_struct_0(esk1_0)),k6_autgroup(esk1_0,esk2_0)) = k5_relat_1(k6_partfun1(u1_struct_0(esk1_0)),k6_autgroup(esk1_0,esk2_0))
| v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_65]),c_0_55]),c_0_54])]) ).
cnf(c_0_94,negated_conjecture,
( k5_relat_1(k6_partfun1(u1_struct_0(esk1_0)),k6_autgroup(esk1_0,esk2_0)) = k6_autgroup(esk1_0,esk2_0)
| v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
fof(c_0_95,plain,
! [X92] :
( v3_struct_0(X92)
| ~ l1_struct_0(X92)
| ~ v1_xboole_0(u1_struct_0(X92)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_90])]) ).
cnf(c_0_96,plain,
( X1 = esk14_0
| ~ v1_xboole_0(X1) ),
inference(rw,[status(thm)],[c_0_82,c_0_91]) ).
cnf(c_0_97,negated_conjecture,
v1_xboole_0(u1_struct_0(esk1_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_94]) ).
cnf(c_0_98,plain,
( v3_struct_0(X1)
| ~ l1_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_99,negated_conjecture,
u1_struct_0(esk1_0) = esk14_0,
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
fof(c_0_100,plain,
! [X59] :
( ~ l1_group_1(X59)
| l1_struct_0(X59) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_group_1])]) ).
cnf(c_0_101,negated_conjecture,
~ l1_struct_0(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_83])]),c_0_30]) ).
cnf(c_0_102,plain,
( l1_struct_0(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_103,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.09 % Problem : GRP631+1 : TPTP v8.1.2. Released v3.4.0.
% 0.07/0.10 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Mon Aug 28 19:53:46 EDT 2023
% 0.10/0.29 % CPUTime :
% 0.14/0.47 start to proof: theBenchmark
% 6.53/6.65 % Version : CSE_E---1.5
% 6.53/6.65 % Problem : theBenchmark.p
% 6.53/6.65 % Proof found
% 6.53/6.65 % SZS status Theorem for theBenchmark.p
% 6.53/6.65 % SZS output start Proof
% See solution above
% 6.53/6.66 % Total time : 6.170000 s
% 6.53/6.66 % SZS output end Proof
% 6.53/6.66 % Total time : 6.173000 s
%------------------------------------------------------------------------------