TSTP Solution File: GRP642+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP642+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n007.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 00:22:22 EDT 2023
% Result : Theorem 0.52s 0.57s
% Output : CNFRefutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 50
% Syntax : Number of formulae : 83 ( 14 unt; 43 typ; 0 def)
% Number of atoms : 214 ( 18 equ)
% Maximal formula atoms : 38 ( 5 avg)
% Number of connectives : 277 ( 103 ~; 100 |; 53 &)
% ( 2 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 55 ( 35 >; 20 *; 0 +; 0 <<)
% Number of predicates : 19 ( 17 usr; 1 prp; 0-3 aty)
% Number of functors : 26 ( 26 usr; 8 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn; 27 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
v3_struct_0: $i > $o ).
tff(decl_23,type,
v3_group_1: $i > $o ).
tff(decl_24,type,
v4_group_1: $i > $o ).
tff(decl_25,type,
l1_group_1: $i > $o ).
tff(decl_26,type,
v1_group_1: $i > $o ).
tff(decl_27,type,
m1_group_2: ( $i * $i ) > $o ).
tff(decl_28,type,
k1_latsubgr: $i > $i ).
tff(decl_29,type,
k1_funct_1: ( $i * $i ) > $i ).
tff(decl_30,type,
k1_xboole_0: $i ).
tff(decl_31,type,
u1_struct_0: $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,
m1_relset_1: ( $i * $i * $i ) > $o ).
tff(decl_36,type,
v1_funct_1: $i > $o ).
tff(decl_37,type,
v1_partfun1: ( $i * $i * $i ) > $o ).
tff(decl_38,type,
v1_funct_2: ( $i * $i * $i ) > $o ).
tff(decl_39,type,
k2_zfmisc_1: ( $i * $i ) > $i ).
tff(decl_40,type,
k1_zfmisc_1: $i > $i ).
tff(decl_41,type,
m1_subset_1: ( $i * $i ) > $o ).
tff(decl_42,type,
v1_relat_1: $i > $o ).
tff(decl_43,type,
v1_xboole_0: $i > $o ).
tff(decl_44,type,
k1_group_3: $i > $i ).
tff(decl_45,type,
m2_relset_1: ( $i * $i * $i ) > $o ).
tff(decl_46,type,
l1_struct_0: $i > $o ).
tff(decl_47,type,
r1_tarski: ( $i * $i ) > $o ).
tff(decl_48,type,
esk1_0: $i ).
tff(decl_49,type,
esk2_0: $i ).
tff(decl_50,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_51,type,
esk4_0: $i ).
tff(decl_52,type,
esk5_0: $i ).
tff(decl_53,type,
esk6_1: $i > $i ).
tff(decl_54,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk8_1: $i > $i ).
tff(decl_56,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_57,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_58,type,
esk11_1: $i > $i ).
tff(decl_59,type,
esk12_0: $i ).
tff(decl_60,type,
esk13_2: ( $i * $i ) > $i ).
tff(decl_61,type,
esk14_1: $i > $i ).
tff(decl_62,type,
esk15_0: $i ).
tff(decl_63,type,
esk16_0: $i ).
tff(decl_64,type,
esk17_1: $i > $i ).
fof(d1_latsubgr,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
& m2_relset_1(X2,k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1))) )
=> ( X2 = k1_latsubgr(X1)
<=> ! [X3] :
( ( v1_group_1(X3)
& m1_group_2(X3,X1) )
=> k1_funct_1(X2,X3) = u1_struct_0(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_latsubgr) ).
fof(dt_k1_latsubgr,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ( v1_funct_1(k1_latsubgr(X1))
& v1_funct_2(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
& m2_relset_1(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_latsubgr) ).
fof(dt_m1_group_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> ( ~ v3_struct_0(X2)
& v3_group_1(X2)
& l1_group_1(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_group_2) ).
fof(t20_latsubgr,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( ( v1_group_1(X2)
& m1_group_2(X2,X1) )
=> k1_funct_1(k1_latsubgr(X1),X2) != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_latsubgr) ).
fof(fc1_struct_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(dt_l1_group_1,axiom,
! [X1] :
( l1_group_1(X1)
=> l1_struct_0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_group_1) ).
fof(fc1_xboole_0,axiom,
v1_xboole_0(k1_xboole_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(c_0_7,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
& m2_relset_1(X2,k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1))) )
=> ( X2 = k1_latsubgr(X1)
<=> ! [X3] :
( ( v1_group_1(X3)
& m1_group_2(X3,X1) )
=> k1_funct_1(X2,X3) = u1_struct_0(X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[d1_latsubgr]) ).
fof(c_0_8,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ( v1_funct_1(k1_latsubgr(X1))
& v1_funct_2(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
& m2_relset_1(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1))) ) ),
inference(fof_simplification,[status(thm)],[dt_k1_latsubgr]) ).
fof(c_0_9,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> ( ~ v3_struct_0(X2)
& v3_group_1(X2)
& l1_group_1(X2) ) ) ),
inference(fof_simplification,[status(thm)],[dt_m1_group_2]) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( ( v1_group_1(X2)
& m1_group_2(X2,X1) )
=> k1_funct_1(k1_latsubgr(X1),X2) != k1_xboole_0 ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t20_latsubgr])]) ).
fof(c_0_11,plain,
! [X22,X23,X24] :
( ( X23 != k1_latsubgr(X22)
| ~ v1_group_1(X24)
| ~ m1_group_2(X24,X22)
| k1_funct_1(X23,X24) = u1_struct_0(X24)
| ~ v1_funct_1(X23)
| ~ v1_funct_2(X23,k1_group_3(X22),k1_zfmisc_1(u1_struct_0(X22)))
| ~ m2_relset_1(X23,k1_group_3(X22),k1_zfmisc_1(u1_struct_0(X22)))
| v3_struct_0(X22)
| ~ v3_group_1(X22)
| ~ v4_group_1(X22)
| ~ l1_group_1(X22) )
& ( v1_group_1(esk3_2(X22,X23))
| X23 = k1_latsubgr(X22)
| ~ v1_funct_1(X23)
| ~ v1_funct_2(X23,k1_group_3(X22),k1_zfmisc_1(u1_struct_0(X22)))
| ~ m2_relset_1(X23,k1_group_3(X22),k1_zfmisc_1(u1_struct_0(X22)))
| v3_struct_0(X22)
| ~ v3_group_1(X22)
| ~ v4_group_1(X22)
| ~ l1_group_1(X22) )
& ( m1_group_2(esk3_2(X22,X23),X22)
| X23 = k1_latsubgr(X22)
| ~ v1_funct_1(X23)
| ~ v1_funct_2(X23,k1_group_3(X22),k1_zfmisc_1(u1_struct_0(X22)))
| ~ m2_relset_1(X23,k1_group_3(X22),k1_zfmisc_1(u1_struct_0(X22)))
| v3_struct_0(X22)
| ~ v3_group_1(X22)
| ~ v4_group_1(X22)
| ~ l1_group_1(X22) )
& ( k1_funct_1(X23,esk3_2(X22,X23)) != u1_struct_0(esk3_2(X22,X23))
| X23 = k1_latsubgr(X22)
| ~ v1_funct_1(X23)
| ~ v1_funct_2(X23,k1_group_3(X22),k1_zfmisc_1(u1_struct_0(X22)))
| ~ m2_relset_1(X23,k1_group_3(X22),k1_zfmisc_1(u1_struct_0(X22)))
| v3_struct_0(X22)
| ~ v3_group_1(X22)
| ~ v4_group_1(X22)
| ~ l1_group_1(X22) ) ),
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_7])])])])]) ).
fof(c_0_12,plain,
! [X28] :
( ( v1_funct_1(k1_latsubgr(X28))
| v3_struct_0(X28)
| ~ v3_group_1(X28)
| ~ v4_group_1(X28)
| ~ l1_group_1(X28) )
& ( v1_funct_2(k1_latsubgr(X28),k1_group_3(X28),k1_zfmisc_1(u1_struct_0(X28)))
| v3_struct_0(X28)
| ~ v3_group_1(X28)
| ~ v4_group_1(X28)
| ~ l1_group_1(X28) )
& ( m2_relset_1(k1_latsubgr(X28),k1_group_3(X28),k1_zfmisc_1(u1_struct_0(X28)))
| v3_struct_0(X28)
| ~ v3_group_1(X28)
| ~ v4_group_1(X28)
| ~ l1_group_1(X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_13,plain,
! [X30,X31] :
( ( ~ v3_struct_0(X31)
| ~ m1_group_2(X31,X30)
| v3_struct_0(X30)
| ~ v3_group_1(X30)
| ~ l1_group_1(X30) )
& ( v3_group_1(X31)
| ~ m1_group_2(X31,X30)
| v3_struct_0(X30)
| ~ v3_group_1(X30)
| ~ l1_group_1(X30) )
& ( l1_group_1(X31)
| ~ m1_group_2(X31,X30)
| v3_struct_0(X30)
| ~ v3_group_1(X30)
| ~ l1_group_1(X30) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
fof(c_0_14,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v3_group_1(esk1_0)
& v4_group_1(esk1_0)
& l1_group_1(esk1_0)
& v1_group_1(esk2_0)
& m1_group_2(esk2_0,esk1_0)
& k1_funct_1(k1_latsubgr(esk1_0),esk2_0) = k1_xboole_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_15,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_16,plain,
( k1_funct_1(X1,X3) = u1_struct_0(X3)
| v3_struct_0(X2)
| X1 != k1_latsubgr(X2)
| ~ v1_group_1(X3)
| ~ m1_group_2(X3,X2)
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k1_group_3(X2),k1_zfmisc_1(u1_struct_0(X2)))
| ~ m2_relset_1(X1,k1_group_3(X2),k1_zfmisc_1(u1_struct_0(X2)))
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( v1_funct_1(k1_latsubgr(X1))
| v3_struct_0(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( v1_funct_2(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
| v3_struct_0(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
( m2_relset_1(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
| v3_struct_0(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_20,plain,
! [X29] :
( ~ l1_group_1(X29)
| l1_struct_0(X29) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_group_1])]) ).
cnf(c_0_21,plain,
( l1_group_1(X1)
| v3_struct_0(X2)
| ~ m1_group_2(X1,X2)
| ~ v3_group_1(X2)
| ~ l1_group_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,negated_conjecture,
m1_group_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,negated_conjecture,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_25,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_26,plain,
! [X49] :
( v3_struct_0(X49)
| ~ l1_struct_0(X49)
| ~ v1_xboole_0(u1_struct_0(X49)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])]) ).
cnf(c_0_27,plain,
( k1_funct_1(k1_latsubgr(X1),X2) = u1_struct_0(X2)
| v3_struct_0(X1)
| ~ m1_group_2(X2,X1)
| ~ v1_group_1(X2)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_16]),c_0_17]),c_0_18]),c_0_19]) ).
cnf(c_0_28,negated_conjecture,
k1_funct_1(k1_latsubgr(esk1_0),esk2_0) = k1_xboole_0,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_29,negated_conjecture,
v1_group_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_30,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_31,plain,
( l1_struct_0(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_32,negated_conjecture,
l1_group_1(esk2_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_24])]),c_0_25]) ).
cnf(c_0_33,plain,
( v3_struct_0(X2)
| ~ v3_struct_0(X1)
| ~ m1_group_2(X1,X2)
| ~ v3_group_1(X2)
| ~ l1_group_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_34,plain,
( v3_struct_0(X1)
| ~ l1_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,negated_conjecture,
u1_struct_0(esk2_0) = k1_xboole_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_27,c_0_22]),c_0_28]),c_0_29]),c_0_23]),c_0_30]),c_0_24])]),c_0_25]) ).
cnf(c_0_36,negated_conjecture,
l1_struct_0(esk2_0),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,plain,
v1_xboole_0(k1_xboole_0),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]) ).
cnf(c_0_38,negated_conjecture,
~ v3_struct_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_33,c_0_22]),c_0_23]),c_0_24])]),c_0_25]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_37])]),c_0_38]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP642+1 : TPTP v8.1.2. Released v3.4.0.
% 0.06/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n007.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 21:51:58 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.52/0.55 start to proof: theBenchmark
% 0.52/0.57 % Version : CSE_E---1.5
% 0.52/0.57 % Problem : theBenchmark.p
% 0.52/0.57 % Proof found
% 0.52/0.57 % SZS status Theorem for theBenchmark.p
% 0.52/0.57 % SZS output start Proof
% See solution above
% 0.52/0.58 % Total time : 0.012000 s
% 0.52/0.58 % SZS output end Proof
% 0.52/0.58 % Total time : 0.016000 s
%------------------------------------------------------------------------------