TSTP Solution File: GRP624+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP624+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 : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 00:21:56 EDT 2023
% Result : Theorem 1.06s 1.12s
% Output : CNFRefutation 1.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 78
% Syntax : Number of formulae : 143 ( 11 unt; 64 typ; 0 def)
% Number of atoms : 420 ( 26 equ)
% Maximal formula atoms : 42 ( 5 avg)
% Number of connectives : 555 ( 214 ~; 206 |; 94 &)
% ( 5 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 89 ( 47 >; 42 *; 0 +; 0 <<)
% Number of predicates : 23 ( 21 usr; 1 prp; 0-4 aty)
% Number of functors : 43 ( 43 usr; 17 con; 0-6 aty)
% Number of variables : 137 ( 2 sgn; 90 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
v3_struct_0: $i > $o ).
tff(decl_23,type,
v1_group_1: $i > $o ).
tff(decl_24,type,
v3_group_1: $i > $o ).
tff(decl_25,type,
v4_group_1: $i > $o ).
tff(decl_26,type,
l1_group_1: $i > $o ).
tff(decl_27,type,
u1_struct_0: $i > $i ).
tff(decl_28,type,
k4_autgroup: $i > $i ).
tff(decl_29,type,
m2_fraenkel: ( $i * $i * $i * $i ) > $o ).
tff(decl_30,type,
k2_autgroup: $i > $i ).
tff(decl_31,type,
k1_binop_1: ( $i * $i * $i ) > $i ).
tff(decl_32,type,
k7_funct_2: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_33,type,
u1_group_1: $i > $i ).
tff(decl_34,type,
g1_group_1: ( $i * $i ) > $i ).
tff(decl_35,type,
r2_hidden: ( $i * $i ) > $o ).
tff(decl_36,type,
v1_fraenkel: $i > $o ).
tff(decl_37,type,
m1_subset_1: ( $i * $i ) > $o ).
tff(decl_38,type,
v1_relat_1: $i > $o ).
tff(decl_39,type,
v1_funct_1: $i > $o ).
tff(decl_40,type,
v1_xboole_0: $i > $o ).
tff(decl_41,type,
m1_relset_1: ( $i * $i * $i ) > $o ).
tff(decl_42,type,
v1_partfun1: ( $i * $i * $i ) > $o ).
tff(decl_43,type,
v1_funct_2: ( $i * $i * $i ) > $o ).
tff(decl_44,type,
v2_group_1: $i > $o ).
tff(decl_45,type,
k2_zfmisc_1: ( $i * $i ) > $i ).
tff(decl_46,type,
k1_zfmisc_1: $i > $i ).
tff(decl_47,type,
v2_funct_1: $i > $o ).
tff(decl_48,type,
k2_tarski: ( $i * $i ) > $i ).
tff(decl_49,type,
k4_tarski: ( $i * $i ) > $i ).
tff(decl_50,type,
k1_funct_1: ( $i * $i ) > $i ).
tff(decl_51,type,
k1_autgroup: $i > $i ).
tff(decl_52,type,
m2_relset_1: ( $i * $i * $i ) > $o ).
tff(decl_53,type,
k2_binop_1: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_54,type,
k1_tarski: $i > $i ).
tff(decl_55,type,
m1_fraenkel: ( $i * $i * $i ) > $o ).
tff(decl_56,type,
k5_relat_1: ( $i * $i ) > $i ).
tff(decl_57,type,
l1_struct_0: $i > $o ).
tff(decl_58,type,
k1_xboole_0: $i ).
tff(decl_59,type,
r1_tarski: ( $i * $i ) > $o ).
tff(decl_60,type,
esk1_0: $i ).
tff(decl_61,type,
esk2_0: $i ).
tff(decl_62,type,
esk3_0: $i ).
tff(decl_63,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_64,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_65,type,
esk6_0: $i ).
tff(decl_66,type,
esk7_0: $i ).
tff(decl_67,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_68,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_69,type,
esk10_1: $i > $i ).
tff(decl_70,type,
esk11_3: ( $i * $i * $i ) > $i ).
tff(decl_71,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_72,type,
esk13_0: $i ).
tff(decl_73,type,
esk14_0: $i ).
tff(decl_74,type,
esk15_2: ( $i * $i ) > $i ).
tff(decl_75,type,
esk16_0: $i ).
tff(decl_76,type,
esk17_0: $i ).
tff(decl_77,type,
esk18_0: $i ).
tff(decl_78,type,
esk19_0: $i ).
tff(decl_79,type,
esk20_0: $i ).
tff(decl_80,type,
esk21_2: ( $i * $i ) > $i ).
tff(decl_81,type,
esk22_0: $i ).
tff(decl_82,type,
esk23_0: $i ).
tff(decl_83,type,
esk24_0: $i ).
tff(decl_84,type,
esk25_0: $i ).
tff(decl_85,type,
esk26_1: $i > $i ).
fof(dt_m1_fraenkel,axiom,
! [X1,X2,X3] :
( m1_fraenkel(X3,X1,X2)
=> ( ~ v1_xboole_0(X3)
& v1_fraenkel(X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_fraenkel) ).
fof(dt_k1_autgroup,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> m1_fraenkel(k1_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_autgroup) ).
fof(redefinition_k2_binop_1,axiom,
! [X1,X2,X3,X4,X5,X6] :
( ( ~ v1_xboole_0(X1)
& ~ v1_xboole_0(X2)
& v1_funct_1(X4)
& v1_funct_2(X4,k2_zfmisc_1(X1,X2),X3)
& m1_relset_1(X4,k2_zfmisc_1(X1,X2),X3)
& m1_subset_1(X5,X1)
& m1_subset_1(X6,X2) )
=> k2_binop_1(X1,X2,X3,X4,X5,X6) = k1_binop_1(X4,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).
fof(d2_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,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
& m2_relset_1(X2,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1)) )
=> ( X2 = k2_autgroup(X1)
<=> ! [X3] :
( m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> ! [X4] :
( m2_fraenkel(X4,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> k2_binop_1(k1_autgroup(X1),k1_autgroup(X1),k1_autgroup(X1),X2,X3,X4) = k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X4,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_autgroup) ).
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_k2_autgroup,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ( v1_funct_1(k2_autgroup(X1))
& v1_funct_2(k2_autgroup(X1),k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
& m2_relset_1(k2_autgroup(X1),k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_autgroup) ).
fof(fc1_group_1,axiom,
! [X1,X2] :
( ( ~ v1_xboole_0(X1)
& v1_funct_1(X2)
& v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)
& m1_relset_1(X2,k2_zfmisc_1(X1,X1),X1) )
=> ( ~ v3_struct_0(g1_group_1(X1,X2))
& v1_group_1(g1_group_1(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_group_1) ).
fof(dt_u1_group_1,axiom,
! [X1] :
( l1_group_1(X1)
=> ( v1_funct_1(u1_group_1(X1))
& v1_funct_2(u1_group_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
& m2_relset_1(u1_group_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_group_1) ).
fof(t15_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),k4_autgroup(X1))
=> ! [X3] :
( m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
=> k1_binop_1(k2_autgroup(X1),X2,X3) = k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X3,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_autgroup) ).
fof(t13_autgroup,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
=> m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_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(abstractness_v1_group_1,axiom,
! [X1] :
( l1_group_1(X1)
=> ( v1_group_1(X1)
=> X1 = g1_group_1(u1_struct_0(X1),u1_group_1(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v1_group_1) ).
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_14,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_15,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_16,plain,
! [X1,X2,X3,X4,X5,X6] :
( ( ~ v1_xboole_0(X1)
& ~ v1_xboole_0(X2)
& v1_funct_1(X4)
& v1_funct_2(X4,k2_zfmisc_1(X1,X2),X3)
& m1_relset_1(X4,k2_zfmisc_1(X1,X2),X3)
& m1_subset_1(X5,X1)
& m1_subset_1(X6,X2) )
=> k2_binop_1(X1,X2,X3,X4,X5,X6) = k1_binop_1(X4,X5,X6) ),
inference(fof_simplification,[status(thm)],[redefinition_k2_binop_1]) ).
fof(c_0_17,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,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
& m2_relset_1(X2,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1)) )
=> ( X2 = k2_autgroup(X1)
<=> ! [X3] :
( m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> ! [X4] :
( m2_fraenkel(X4,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> k2_binop_1(k1_autgroup(X1),k1_autgroup(X1),k1_autgroup(X1),X2,X3,X4) = k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X4,X3) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d2_autgroup]) ).
fof(c_0_18,plain,
! [X62,X63,X64] :
( ( ~ v1_xboole_0(X64)
| ~ m1_fraenkel(X64,X62,X63) )
& ( v1_fraenkel(X64)
| ~ m1_fraenkel(X64,X62,X63) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
fof(c_0_19,plain,
! [X45] :
( v3_struct_0(X45)
| ~ v1_group_1(X45)
| ~ v3_group_1(X45)
| ~ v4_group_1(X45)
| ~ l1_group_1(X45)
| m1_fraenkel(k1_autgroup(X45),u1_struct_0(X45),u1_struct_0(X45)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])]) ).
fof(c_0_20,plain,
! [X118,X119,X120,X121,X122,X123] :
( v1_xboole_0(X118)
| v1_xboole_0(X119)
| ~ v1_funct_1(X121)
| ~ v1_funct_2(X121,k2_zfmisc_1(X118,X119),X120)
| ~ m1_relset_1(X121,k2_zfmisc_1(X118,X119),X120)
| ~ m1_subset_1(X122,X118)
| ~ m1_subset_1(X123,X119)
| k2_binop_1(X118,X119,X120,X121,X122,X123) = k1_binop_1(X121,X122,X123) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])]) ).
fof(c_0_21,plain,
! [X35,X36,X37,X38] :
( ( X36 != k2_autgroup(X35)
| ~ m2_fraenkel(X37,u1_struct_0(X35),u1_struct_0(X35),k1_autgroup(X35))
| ~ m2_fraenkel(X38,u1_struct_0(X35),u1_struct_0(X35),k1_autgroup(X35))
| k2_binop_1(k1_autgroup(X35),k1_autgroup(X35),k1_autgroup(X35),X36,X37,X38) = k7_funct_2(u1_struct_0(X35),u1_struct_0(X35),u1_struct_0(X35),X38,X37)
| ~ v1_funct_1(X36)
| ~ v1_funct_2(X36,k2_zfmisc_1(k1_autgroup(X35),k1_autgroup(X35)),k1_autgroup(X35))
| ~ m2_relset_1(X36,k2_zfmisc_1(k1_autgroup(X35),k1_autgroup(X35)),k1_autgroup(X35))
| v3_struct_0(X35)
| ~ v1_group_1(X35)
| ~ v3_group_1(X35)
| ~ v4_group_1(X35)
| ~ l1_group_1(X35) )
& ( m2_fraenkel(esk4_2(X35,X36),u1_struct_0(X35),u1_struct_0(X35),k1_autgroup(X35))
| X36 = k2_autgroup(X35)
| ~ v1_funct_1(X36)
| ~ v1_funct_2(X36,k2_zfmisc_1(k1_autgroup(X35),k1_autgroup(X35)),k1_autgroup(X35))
| ~ m2_relset_1(X36,k2_zfmisc_1(k1_autgroup(X35),k1_autgroup(X35)),k1_autgroup(X35))
| v3_struct_0(X35)
| ~ v1_group_1(X35)
| ~ v3_group_1(X35)
| ~ v4_group_1(X35)
| ~ l1_group_1(X35) )
& ( m2_fraenkel(esk5_2(X35,X36),u1_struct_0(X35),u1_struct_0(X35),k1_autgroup(X35))
| X36 = k2_autgroup(X35)
| ~ v1_funct_1(X36)
| ~ v1_funct_2(X36,k2_zfmisc_1(k1_autgroup(X35),k1_autgroup(X35)),k1_autgroup(X35))
| ~ m2_relset_1(X36,k2_zfmisc_1(k1_autgroup(X35),k1_autgroup(X35)),k1_autgroup(X35))
| v3_struct_0(X35)
| ~ v1_group_1(X35)
| ~ v3_group_1(X35)
| ~ v4_group_1(X35)
| ~ l1_group_1(X35) )
& ( k2_binop_1(k1_autgroup(X35),k1_autgroup(X35),k1_autgroup(X35),X36,esk4_2(X35,X36),esk5_2(X35,X36)) != k7_funct_2(u1_struct_0(X35),u1_struct_0(X35),u1_struct_0(X35),esk5_2(X35,X36),esk4_2(X35,X36))
| X36 = k2_autgroup(X35)
| ~ v1_funct_1(X36)
| ~ v1_funct_2(X36,k2_zfmisc_1(k1_autgroup(X35),k1_autgroup(X35)),k1_autgroup(X35))
| ~ m2_relset_1(X36,k2_zfmisc_1(k1_autgroup(X35),k1_autgroup(X35)),k1_autgroup(X35))
| v3_struct_0(X35)
| ~ v1_group_1(X35)
| ~ v3_group_1(X35)
| ~ v4_group_1(X35)
| ~ l1_group_1(X35) ) ),
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_17])])])])]) ).
fof(c_0_22,plain,
! [X133,X134,X135] :
( ( ~ m2_relset_1(X135,X133,X134)
| m1_relset_1(X135,X133,X134) )
& ( ~ m1_relset_1(X135,X133,X134)
| m2_relset_1(X135,X133,X134) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
cnf(c_0_23,plain,
( ~ v1_xboole_0(X1)
| ~ m1_fraenkel(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,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_19]) ).
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) )
=> ( v1_funct_1(k2_autgroup(X1))
& v1_funct_2(k2_autgroup(X1),k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
& m2_relset_1(k2_autgroup(X1),k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1)) ) ),
inference(fof_simplification,[status(thm)],[dt_k2_autgroup]) ).
fof(c_0_26,plain,
! [X1,X2] :
( ( ~ v1_xboole_0(X1)
& v1_funct_1(X2)
& v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)
& m1_relset_1(X2,k2_zfmisc_1(X1,X1),X1) )
=> ( ~ v3_struct_0(g1_group_1(X1,X2))
& v1_group_1(g1_group_1(X1,X2)) ) ),
inference(fof_simplification,[status(thm)],[fc1_group_1]) ).
fof(c_0_27,plain,
! [X72] :
( ( v1_funct_1(u1_group_1(X72))
| ~ l1_group_1(X72) )
& ( v1_funct_2(u1_group_1(X72),k2_zfmisc_1(u1_struct_0(X72),u1_struct_0(X72)),u1_struct_0(X72))
| ~ l1_group_1(X72) )
& ( m2_relset_1(u1_group_1(X72),k2_zfmisc_1(u1_struct_0(X72),u1_struct_0(X72)),u1_struct_0(X72))
| ~ l1_group_1(X72) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_group_1])])]) ).
fof(c_0_28,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),k4_autgroup(X1))
=> ! [X3] :
( m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
=> k1_binop_1(k2_autgroup(X1),X2,X3) = k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X3,X2) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t15_autgroup])]) ).
cnf(c_0_29,plain,
( v1_xboole_0(X1)
| v1_xboole_0(X2)
| k2_binop_1(X1,X2,X4,X3,X5,X6) = k1_binop_1(X3,X5,X6)
| ~ v1_funct_1(X3)
| ~ v1_funct_2(X3,k2_zfmisc_1(X1,X2),X4)
| ~ m1_relset_1(X3,k2_zfmisc_1(X1,X2),X4)
| ~ m1_subset_1(X5,X1)
| ~ m1_subset_1(X6,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,plain,
( k2_binop_1(k1_autgroup(X2),k1_autgroup(X2),k1_autgroup(X2),X1,X3,X4) = k7_funct_2(u1_struct_0(X2),u1_struct_0(X2),u1_struct_0(X2),X4,X3)
| v3_struct_0(X2)
| X1 != k2_autgroup(X2)
| ~ m2_fraenkel(X3,u1_struct_0(X2),u1_struct_0(X2),k1_autgroup(X2))
| ~ m2_fraenkel(X4,u1_struct_0(X2),u1_struct_0(X2),k1_autgroup(X2))
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k2_zfmisc_1(k1_autgroup(X2),k1_autgroup(X2)),k1_autgroup(X2))
| ~ m2_relset_1(X1,k2_zfmisc_1(k1_autgroup(X2),k1_autgroup(X2)),k1_autgroup(X2))
| ~ v1_group_1(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_31,plain,
( m1_relset_1(X1,X2,X3)
| ~ m2_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_32,plain,
( v3_struct_0(X1)
| ~ v1_xboole_0(k1_autgroup(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
fof(c_0_33,plain,
! [X46] :
( ( v1_funct_1(k2_autgroup(X46))
| v3_struct_0(X46)
| ~ v1_group_1(X46)
| ~ v3_group_1(X46)
| ~ v4_group_1(X46)
| ~ l1_group_1(X46) )
& ( v1_funct_2(k2_autgroup(X46),k2_zfmisc_1(k1_autgroup(X46),k1_autgroup(X46)),k1_autgroup(X46))
| v3_struct_0(X46)
| ~ v1_group_1(X46)
| ~ v3_group_1(X46)
| ~ v4_group_1(X46)
| ~ l1_group_1(X46) )
& ( m2_relset_1(k2_autgroup(X46),k2_zfmisc_1(k1_autgroup(X46),k1_autgroup(X46)),k1_autgroup(X46))
| v3_struct_0(X46)
| ~ v1_group_1(X46)
| ~ v3_group_1(X46)
| ~ v4_group_1(X46)
| ~ l1_group_1(X46) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])]) ).
fof(c_0_34,plain,
! [X92,X93] :
( ( ~ v3_struct_0(g1_group_1(X92,X93))
| v1_xboole_0(X92)
| ~ v1_funct_1(X93)
| ~ v1_funct_2(X93,k2_zfmisc_1(X92,X92),X92)
| ~ m1_relset_1(X93,k2_zfmisc_1(X92,X92),X92) )
& ( v1_group_1(g1_group_1(X92,X93))
| v1_xboole_0(X92)
| ~ v1_funct_1(X93)
| ~ v1_funct_2(X93,k2_zfmisc_1(X92,X92),X92)
| ~ m1_relset_1(X93,k2_zfmisc_1(X92,X92),X92) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])]) ).
cnf(c_0_35,plain,
( m2_relset_1(u1_group_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_36,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),k4_autgroup(esk1_0))
& m2_fraenkel(esk3_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0),k4_autgroup(esk1_0))
& k1_binop_1(k2_autgroup(esk1_0),esk2_0,esk3_0) != k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),esk3_0,esk2_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])]) ).
cnf(c_0_37,plain,
( k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X2,X3) = k1_binop_1(X4,X3,X2)
| v3_struct_0(X1)
| X4 != k2_autgroup(X1)
| ~ m2_relset_1(X4,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
| ~ v1_funct_2(X4,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
| ~ v1_funct_1(X4)
| ~ m1_subset_1(X2,k1_autgroup(X1))
| ~ m1_subset_1(X3,k1_autgroup(X1))
| ~ m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| ~ m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32]) ).
cnf(c_0_38,plain,
( m2_relset_1(k2_autgroup(X1),k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
| v3_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_39,plain,
( v1_funct_1(k2_autgroup(X1))
| v3_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,plain,
( v1_funct_2(k2_autgroup(X1),k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
| v3_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]) ).
fof(c_0_41,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
=> m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1)) ) ),
inference(fof_simplification,[status(thm)],[t13_autgroup]) ).
fof(c_0_42,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]) ).
cnf(c_0_43,plain,
( v1_xboole_0(X1)
| ~ v3_struct_0(g1_group_1(X1,X2))
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)
| ~ m1_relset_1(X2,k2_zfmisc_1(X1,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_44,plain,
( v1_funct_2(u1_group_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_45,plain,
( v1_funct_1(u1_group_1(X1))
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_46,plain,
( m1_relset_1(u1_group_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ l1_group_1(X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_35]) ).
fof(c_0_47,plain,
! [X10] :
( ~ l1_group_1(X10)
| ~ v1_group_1(X10)
| X10 = g1_group_1(u1_struct_0(X10),u1_group_1(X10)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[abstractness_v1_group_1])]) ).
cnf(c_0_48,negated_conjecture,
k1_binop_1(k2_autgroup(esk1_0),esk2_0,esk3_0) != k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_49,plain,
( k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X2,X3) = k1_binop_1(k2_autgroup(X1),X3,X2)
| v3_struct_0(X1)
| ~ m1_subset_1(X2,k1_autgroup(X1))
| ~ m1_subset_1(X3,k1_autgroup(X1))
| ~ m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| ~ m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_40]) ).
cnf(c_0_50,negated_conjecture,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_51,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_52,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_53,negated_conjecture,
v1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_54,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_55,plain,
! [X137,X138] :
( v3_struct_0(X137)
| ~ v1_group_1(X137)
| ~ v3_group_1(X137)
| ~ v4_group_1(X137)
| ~ l1_group_1(X137)
| ~ m2_fraenkel(X138,u1_struct_0(X137),u1_struct_0(X137),k4_autgroup(X137))
| m2_fraenkel(X138,u1_struct_0(X137),u1_struct_0(X137),k1_autgroup(X137)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])]) ).
fof(c_0_56,plain,
! [X129,X130,X131,X132] :
( ( ~ m2_fraenkel(X132,X129,X130,X131)
| m1_subset_1(X132,X131)
| v1_xboole_0(X130)
| ~ m1_fraenkel(X131,X129,X130) )
& ( ~ m1_subset_1(X132,X131)
| m2_fraenkel(X132,X129,X130,X131)
| v1_xboole_0(X130)
| ~ m1_fraenkel(X131,X129,X130) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])])]) ).
cnf(c_0_57,plain,
( v1_xboole_0(u1_struct_0(X1))
| ~ l1_group_1(X1)
| ~ v3_struct_0(g1_group_1(u1_struct_0(X1),u1_group_1(X1))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_46]) ).
cnf(c_0_58,plain,
( X1 = g1_group_1(u1_struct_0(X1),u1_group_1(X1))
| ~ l1_group_1(X1)
| ~ v1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
fof(c_0_59,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_60,negated_conjecture,
( ~ m1_subset_1(esk3_0,k1_autgroup(esk1_0))
| ~ m1_subset_1(esk2_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(esk2_0,u1_struct_0(esk1_0),u1_struct_0(esk1_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(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_51]),c_0_52]),c_0_53])]),c_0_54]) ).
cnf(c_0_61,plain,
( v3_struct_0(X1)
| m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_62,negated_conjecture,
m2_fraenkel(esk3_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0),k4_autgroup(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_63,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_56]) ).
cnf(c_0_64,plain,
( v1_xboole_0(u1_struct_0(X1))
| ~ l1_group_1(X1)
| ~ v1_group_1(X1)
| ~ v3_struct_0(X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
fof(c_0_65,plain,
! [X94] :
( v3_struct_0(X94)
| ~ l1_struct_0(X94)
| ~ v1_xboole_0(u1_struct_0(X94)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_59])]) ).
cnf(c_0_66,negated_conjecture,
( ~ m1_subset_1(esk3_0,k1_autgroup(esk1_0))
| ~ m1_subset_1(esk2_0,k1_autgroup(esk1_0))
| ~ m2_fraenkel(esk2_0,u1_struct_0(esk1_0),u1_struct_0(esk1_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(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]),c_0_50]),c_0_51]),c_0_52]),c_0_53])]),c_0_54]) ).
cnf(c_0_67,negated_conjecture,
m2_fraenkel(esk2_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0),k4_autgroup(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_68,plain,
( v1_xboole_0(u1_struct_0(X1))
| m1_subset_1(X2,k1_autgroup(X1))
| ~ m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_61]),c_0_24]),c_0_64]) ).
cnf(c_0_69,plain,
( v3_struct_0(X1)
| ~ l1_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_70,negated_conjecture,
( ~ m1_subset_1(esk3_0,k1_autgroup(esk1_0))
| ~ m1_subset_1(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(spm,[status(thm)],[c_0_66,c_0_61]),c_0_67]),c_0_50]),c_0_51]),c_0_52]),c_0_53])]),c_0_54]) ).
cnf(c_0_71,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk1_0))
| m1_subset_1(esk3_0,k1_autgroup(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_68,c_0_62]),c_0_50]),c_0_51]),c_0_52]),c_0_53])]) ).
cnf(c_0_72,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk1_0))
| m1_subset_1(esk2_0,k1_autgroup(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_68,c_0_67]),c_0_50]),c_0_51]),c_0_52]),c_0_53])]) ).
cnf(c_0_73,negated_conjecture,
( ~ l1_struct_0(esk1_0)
| ~ v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_54,c_0_69]) ).
cnf(c_0_74,negated_conjecture,
v1_xboole_0(u1_struct_0(esk1_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]) ).
fof(c_0_75,plain,
! [X61] :
( ~ l1_group_1(X61)
| l1_struct_0(X61) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_group_1])]) ).
cnf(c_0_76,negated_conjecture,
~ l1_struct_0(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_74])]) ).
cnf(c_0_77,plain,
( l1_struct_0(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_78,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_50])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP624+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 23:56:25 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 1.06/1.11 % Version : CSE_E---1.5
% 1.06/1.11 % Problem : theBenchmark.p
% 1.06/1.12 % Proof found
% 1.06/1.12 % SZS status Theorem for theBenchmark.p
% 1.06/1.12 % SZS output start Proof
% See solution above
% 1.06/1.13 % Total time : 0.553000 s
% 1.06/1.13 % SZS output end Proof
% 1.06/1.13 % Total time : 0.557000 s
%------------------------------------------------------------------------------