TSTP Solution File: ALG219+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ALG219+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 : n026.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 : Wed Aug 30 16:06:44 EDT 2023
% Result : Theorem 0.19s 0.71s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 83
% Syntax : Number of formulae : 144 ( 30 unt; 72 typ; 0 def)
% Number of atoms : 499 ( 39 equ)
% Maximal formula atoms : 36 ( 6 avg)
% Number of connectives : 656 ( 229 ~; 225 |; 171 &)
% ( 1 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 84 ( 57 >; 27 *; 0 +; 0 <<)
% Number of predicates : 35 ( 33 usr; 1 prp; 0-3 aty)
% Number of functors : 39 ( 39 usr; 15 con; 0-5 aty)
% Number of variables : 78 ( 1 sgn; 49 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
v3_struct_0: $i > $o ).
tff(decl_23,type,
v3_rlvect_1: $i > $o ).
tff(decl_24,type,
v4_rlvect_1: $i > $o ).
tff(decl_25,type,
v5_rlvect_1: $i > $o ).
tff(decl_26,type,
v6_rlvect_1: $i > $o ).
tff(decl_27,type,
v4_group_1: $i > $o ).
tff(decl_28,type,
v7_group_1: $i > $o ).
tff(decl_29,type,
v6_vectsp_1: $i > $o ).
tff(decl_30,type,
v7_vectsp_1: $i > $o ).
tff(decl_31,type,
v8_vectsp_1: $i > $o ).
tff(decl_32,type,
v10_vectsp_1: $i > $o ).
tff(decl_33,type,
v2_vectsp_2: $i > $o ).
tff(decl_34,type,
l3_vectsp_1: $i > $o ).
tff(decl_35,type,
v3_vectsp_2: ( $i * $i ) > $o ).
tff(decl_36,type,
v5_vectsp_2: ( $i * $i ) > $o ).
tff(decl_37,type,
l1_vectsp_2: ( $i * $i ) > $o ).
tff(decl_38,type,
u1_struct_0: $i > $i ).
tff(decl_39,type,
k1_zfmisc_1: $i > $i ).
tff(decl_40,type,
m1_subset_1: ( $i * $i ) > $o ).
tff(decl_41,type,
k1_rlvect_1: $i > $i ).
tff(decl_42,type,
k2_group_1: $i > $i ).
tff(decl_43,type,
k1_rmod_5: ( $i * $i * $i ) > $i ).
tff(decl_44,type,
l1_struct_0: $i > $o ).
tff(decl_45,type,
u1_rlvect_1: $i > $i ).
tff(decl_46,type,
u2_struct_0: $i > $i ).
tff(decl_47,type,
u1_vectsp_2: ( $i * $i ) > $i ).
tff(decl_48,type,
g1_vectsp_2: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_49,type,
r2_hidden: ( $i * $i ) > $o ).
tff(decl_50,type,
k2_zfmisc_1: ( $i * $i ) > $i ).
tff(decl_51,type,
v1_relat_1: $i > $o ).
tff(decl_52,type,
l1_vectsp_1: $i > $o ).
tff(decl_53,type,
v2_group_1: $i > $o ).
tff(decl_54,type,
k2_rmod_2: ( $i * $i ) > $i ).
tff(decl_55,type,
v1_funct_1: $i > $o ).
tff(decl_56,type,
v1_funct_2: ( $i * $i * $i ) > $o ).
tff(decl_57,type,
m1_relset_1: ( $i * $i * $i ) > $o ).
tff(decl_58,type,
l2_struct_0: $i > $o ).
tff(decl_59,type,
m1_rmod_2: ( $i * $i * $i ) > $o ).
tff(decl_60,type,
l1_group_1: $i > $o ).
tff(decl_61,type,
l1_rlvect_1: $i > $o ).
tff(decl_62,type,
l2_vectsp_1: $i > $o ).
tff(decl_63,type,
m2_relset_1: ( $i * $i * $i ) > $o ).
tff(decl_64,type,
v1_xboole_0: $i > $o ).
tff(decl_65,type,
k1_xboole_0: $i ).
tff(decl_66,type,
r1_tarski: ( $i * $i ) > $o ).
tff(decl_67,type,
esk1_0: $i ).
tff(decl_68,type,
esk2_0: $i ).
tff(decl_69,type,
esk3_0: $i ).
tff(decl_70,type,
esk4_0: $i ).
tff(decl_71,type,
esk5_0: $i ).
tff(decl_72,type,
esk6_0: $i ).
tff(decl_73,type,
esk7_0: $i ).
tff(decl_74,type,
esk8_1: $i > $i ).
tff(decl_75,type,
esk9_0: $i ).
tff(decl_76,type,
esk10_0: $i ).
tff(decl_77,type,
esk11_0: $i ).
tff(decl_78,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_79,type,
esk13_2: ( $i * $i ) > $i ).
tff(decl_80,type,
esk14_1: $i > $i ).
tff(decl_81,type,
esk15_2: ( $i * $i ) > $i ).
tff(decl_82,type,
esk16_1: $i > $i ).
tff(decl_83,type,
esk17_1: $i > $i ).
tff(decl_84,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_85,type,
esk19_1: $i > $i ).
tff(decl_86,type,
esk20_0: $i ).
tff(decl_87,type,
esk21_1: $i > $i ).
tff(decl_88,type,
esk22_0: $i ).
tff(decl_89,type,
esk23_0: $i ).
tff(decl_90,type,
esk24_0: $i ).
tff(decl_91,type,
esk25_1: $i > $i ).
tff(decl_92,type,
esk26_1: $i > $i ).
tff(decl_93,type,
esk27_1: $i > $i ).
fof(d4_rmod_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v4_group_1(X1)
& v6_vectsp_1(X1)
& v7_vectsp_1(X1)
& v8_vectsp_1(X1)
& l3_vectsp_1(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v5_vectsp_2(X2,X1)
& l1_vectsp_2(X2,X1) )
=> k2_rmod_2(X1,X2) = g1_vectsp_2(X1,u1_struct_0(X2),u1_rlvect_1(X2),u2_struct_0(X2),u1_vectsp_2(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_rmod_2) ).
fof(t14_rmod_5,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v4_group_1(X1)
& v7_group_1(X1)
& v6_vectsp_1(X1)
& v7_vectsp_1(X1)
& v8_vectsp_1(X1)
& ~ v10_vectsp_1(X1)
& v2_vectsp_2(X1)
& l3_vectsp_1(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v3_vectsp_2(X2,X1)
& v5_vectsp_2(X2,X1)
& l1_vectsp_2(X2,X1) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
=> ( X3 = u1_struct_0(X2)
=> ( k1_rlvect_1(X1) = k2_group_1(X1)
| k1_rmod_5(X1,X2,X3) = X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_rmod_5) ).
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(dt_l1_vectsp_1,axiom,
! [X1] :
( l1_vectsp_1(X1)
=> l1_group_1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_vectsp_1) ).
fof(dt_l2_vectsp_1,axiom,
! [X1] :
( l2_vectsp_1(X1)
=> ( l1_vectsp_1(X1)
& l2_struct_0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_vectsp_1) ).
fof(dt_l3_vectsp_1,axiom,
! [X1] :
( l3_vectsp_1(X1)
=> ( l1_rlvect_1(X1)
& l2_vectsp_1(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_vectsp_1) ).
fof(t13_rmod_5,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v4_group_1(X1)
& v7_group_1(X1)
& v6_vectsp_1(X1)
& v7_vectsp_1(X1)
& v8_vectsp_1(X1)
& ~ v10_vectsp_1(X1)
& v2_vectsp_2(X1)
& l3_vectsp_1(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v5_vectsp_2(X2,X1)
& l1_vectsp_2(X2,X1) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
=> ! [X4] :
( ( v3_vectsp_2(X4,X1)
& m1_rmod_2(X4,X1,X2) )
=> ( X3 = u1_struct_0(X4)
=> ( k1_rlvect_1(X1) = k2_group_1(X1)
| k1_rmod_5(X1,X2,X3) = X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_rmod_5) ).
fof(abstractness_v3_vectsp_2,axiom,
! [X1,X2] :
( ( l1_struct_0(X1)
& l1_vectsp_2(X2,X1) )
=> ( v3_vectsp_2(X2,X1)
=> X2 = g1_vectsp_2(X1,u1_struct_0(X2),u1_rlvect_1(X2),u2_struct_0(X2),u1_vectsp_2(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v3_vectsp_2) ).
fof(dt_k2_rmod_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v4_group_1(X1)
& v6_vectsp_1(X1)
& v7_vectsp_1(X1)
& v8_vectsp_1(X1)
& l3_vectsp_1(X1)
& ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v5_vectsp_2(X2,X1)
& l1_vectsp_2(X2,X1) )
=> ( v3_vectsp_2(k2_rmod_2(X1,X2),X1)
& m1_rmod_2(k2_rmod_2(X1,X2),X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_rmod_2) ).
fof(t3_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,k1_zfmisc_1(X2))
<=> r1_tarski(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : r1_tarski(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(c_0_11,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v4_group_1(X1)
& v6_vectsp_1(X1)
& v7_vectsp_1(X1)
& v8_vectsp_1(X1)
& l3_vectsp_1(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v5_vectsp_2(X2,X1)
& l1_vectsp_2(X2,X1) )
=> k2_rmod_2(X1,X2) = g1_vectsp_2(X1,u1_struct_0(X2),u1_rlvect_1(X2),u2_struct_0(X2),u1_vectsp_2(X1,X2)) ) ),
inference(fof_simplification,[status(thm)],[d4_rmod_2]) ).
fof(c_0_12,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v4_group_1(X1)
& v7_group_1(X1)
& v6_vectsp_1(X1)
& v7_vectsp_1(X1)
& v8_vectsp_1(X1)
& ~ v10_vectsp_1(X1)
& v2_vectsp_2(X1)
& l3_vectsp_1(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v3_vectsp_2(X2,X1)
& v5_vectsp_2(X2,X1)
& l1_vectsp_2(X2,X1) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
=> ( X3 = u1_struct_0(X2)
=> ( k1_rlvect_1(X1) = k2_group_1(X1)
| k1_rmod_5(X1,X2,X3) = X2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t14_rmod_5])]) ).
fof(c_0_13,plain,
! [X37] :
( ~ l1_group_1(X37)
| l1_struct_0(X37) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_group_1])]) ).
fof(c_0_14,plain,
! [X39] :
( ~ l1_vectsp_1(X39)
| l1_group_1(X39) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_vectsp_1])]) ).
fof(c_0_15,plain,
! [X43] :
( ( l1_vectsp_1(X43)
| ~ l2_vectsp_1(X43) )
& ( l2_struct_0(X43)
| ~ l2_vectsp_1(X43) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_vectsp_1])])]) ).
fof(c_0_16,plain,
! [X44] :
( ( l1_rlvect_1(X44)
| ~ l3_vectsp_1(X44) )
& ( l2_vectsp_1(X44)
| ~ l3_vectsp_1(X44) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_vectsp_1])])]) ).
fof(c_0_17,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v4_group_1(X1)
& v7_group_1(X1)
& v6_vectsp_1(X1)
& v7_vectsp_1(X1)
& v8_vectsp_1(X1)
& ~ v10_vectsp_1(X1)
& v2_vectsp_2(X1)
& l3_vectsp_1(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v5_vectsp_2(X2,X1)
& l1_vectsp_2(X2,X1) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
=> ! [X4] :
( ( v3_vectsp_2(X4,X1)
& m1_rmod_2(X4,X1,X2) )
=> ( X3 = u1_struct_0(X4)
=> ( k1_rlvect_1(X1) = k2_group_1(X1)
| k1_rmod_5(X1,X2,X3) = X4 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[t13_rmod_5]) ).
fof(c_0_18,plain,
! [X23,X24] :
( v3_struct_0(X23)
| ~ v3_rlvect_1(X23)
| ~ v4_rlvect_1(X23)
| ~ v5_rlvect_1(X23)
| ~ v6_rlvect_1(X23)
| ~ v4_group_1(X23)
| ~ v6_vectsp_1(X23)
| ~ v7_vectsp_1(X23)
| ~ v8_vectsp_1(X23)
| ~ l3_vectsp_1(X23)
| v3_struct_0(X24)
| ~ v3_rlvect_1(X24)
| ~ v4_rlvect_1(X24)
| ~ v5_rlvect_1(X24)
| ~ v6_rlvect_1(X24)
| ~ v5_vectsp_2(X24,X23)
| ~ l1_vectsp_2(X24,X23)
| k2_rmod_2(X23,X24) = g1_vectsp_2(X23,u1_struct_0(X24),u1_rlvect_1(X24),u2_struct_0(X24),u1_vectsp_2(X23,X24)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_19,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v3_rlvect_1(esk1_0)
& v4_rlvect_1(esk1_0)
& v5_rlvect_1(esk1_0)
& v6_rlvect_1(esk1_0)
& v4_group_1(esk1_0)
& v7_group_1(esk1_0)
& v6_vectsp_1(esk1_0)
& v7_vectsp_1(esk1_0)
& v8_vectsp_1(esk1_0)
& ~ v10_vectsp_1(esk1_0)
& v2_vectsp_2(esk1_0)
& l3_vectsp_1(esk1_0)
& ~ v3_struct_0(esk2_0)
& v3_rlvect_1(esk2_0)
& v4_rlvect_1(esk2_0)
& v5_rlvect_1(esk2_0)
& v6_rlvect_1(esk2_0)
& v3_vectsp_2(esk2_0,esk1_0)
& v5_vectsp_2(esk2_0,esk1_0)
& l1_vectsp_2(esk2_0,esk1_0)
& m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk2_0)))
& esk3_0 = u1_struct_0(esk2_0)
& k1_rlvect_1(esk1_0) != k2_group_1(esk1_0)
& k1_rmod_5(esk1_0,esk2_0,esk3_0) != esk2_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
fof(c_0_20,plain,
! [X14,X15] :
( ~ l1_struct_0(X14)
| ~ l1_vectsp_2(X15,X14)
| ~ v3_vectsp_2(X15,X14)
| X15 = g1_vectsp_2(X14,u1_struct_0(X15),u1_rlvect_1(X15),u2_struct_0(X15),u1_vectsp_2(X14,X15)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[abstractness_v3_vectsp_2])]) ).
cnf(c_0_21,plain,
( l1_struct_0(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,plain,
( l1_group_1(X1)
| ~ l1_vectsp_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,plain,
( l1_vectsp_1(X1)
| ~ l2_vectsp_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
( l2_vectsp_1(X1)
| ~ l3_vectsp_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_25,plain,
! [X119,X120,X121,X122] :
( v3_struct_0(X119)
| ~ v3_rlvect_1(X119)
| ~ v4_rlvect_1(X119)
| ~ v5_rlvect_1(X119)
| ~ v6_rlvect_1(X119)
| ~ v4_group_1(X119)
| ~ v7_group_1(X119)
| ~ v6_vectsp_1(X119)
| ~ v7_vectsp_1(X119)
| ~ v8_vectsp_1(X119)
| v10_vectsp_1(X119)
| ~ v2_vectsp_2(X119)
| ~ l3_vectsp_1(X119)
| v3_struct_0(X120)
| ~ v3_rlvect_1(X120)
| ~ v4_rlvect_1(X120)
| ~ v5_rlvect_1(X120)
| ~ v6_rlvect_1(X120)
| ~ v5_vectsp_2(X120,X119)
| ~ l1_vectsp_2(X120,X119)
| ~ m1_subset_1(X121,k1_zfmisc_1(u1_struct_0(X120)))
| ~ v3_vectsp_2(X122,X119)
| ~ m1_rmod_2(X122,X119,X120)
| X121 != u1_struct_0(X122)
| k1_rlvect_1(X119) = k2_group_1(X119)
| k1_rmod_5(X119,X120,X121) = X122 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).
fof(c_0_26,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v4_group_1(X1)
& v6_vectsp_1(X1)
& v7_vectsp_1(X1)
& v8_vectsp_1(X1)
& l3_vectsp_1(X1)
& ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v5_vectsp_2(X2,X1)
& l1_vectsp_2(X2,X1) )
=> ( v3_vectsp_2(k2_rmod_2(X1,X2),X1)
& m1_rmod_2(k2_rmod_2(X1,X2),X1,X2) ) ),
inference(fof_simplification,[status(thm)],[dt_k2_rmod_2]) ).
cnf(c_0_27,plain,
( v3_struct_0(X1)
| v3_struct_0(X2)
| k2_rmod_2(X1,X2) = g1_vectsp_2(X1,u1_struct_0(X2),u1_rlvect_1(X2),u2_struct_0(X2),u1_vectsp_2(X1,X2))
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v4_group_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ l3_vectsp_1(X1)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_vectsp_2(X2,X1)
| ~ l1_vectsp_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,negated_conjecture,
esk3_0 = u1_struct_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,negated_conjecture,
v6_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_30,negated_conjecture,
v5_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_31,negated_conjecture,
v4_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_32,negated_conjecture,
v3_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_33,negated_conjecture,
~ v3_struct_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_34,plain,
( X2 = g1_vectsp_2(X1,u1_struct_0(X2),u1_rlvect_1(X2),u2_struct_0(X2),u1_vectsp_2(X1,X2))
| ~ l1_struct_0(X1)
| ~ l1_vectsp_2(X2,X1)
| ~ v3_vectsp_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_35,plain,
( l1_struct_0(X1)
| ~ l1_vectsp_1(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_36,plain,
( l1_vectsp_1(X1)
| ~ l3_vectsp_1(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_37,plain,
( v3_struct_0(X1)
| v10_vectsp_1(X1)
| v3_struct_0(X2)
| k1_rlvect_1(X1) = k2_group_1(X1)
| k1_rmod_5(X1,X2,X3) = X4
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v4_group_1(X1)
| ~ v7_group_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v2_vectsp_2(X1)
| ~ l3_vectsp_1(X1)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_vectsp_2(X2,X1)
| ~ l1_vectsp_2(X2,X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
| ~ v3_vectsp_2(X4,X1)
| ~ m1_rmod_2(X4,X1,X2)
| X3 != u1_struct_0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_38,plain,
! [X127,X128] :
( ( ~ m1_subset_1(X127,k1_zfmisc_1(X128))
| r1_tarski(X127,X128) )
& ( ~ r1_tarski(X127,X128)
| m1_subset_1(X127,k1_zfmisc_1(X128)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(c_0_39,plain,
! [X118] : r1_tarski(X118,X118),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(c_0_40,plain,
! [X35,X36] :
( ( v3_vectsp_2(k2_rmod_2(X35,X36),X35)
| v3_struct_0(X35)
| ~ v3_rlvect_1(X35)
| ~ v4_rlvect_1(X35)
| ~ v5_rlvect_1(X35)
| ~ v6_rlvect_1(X35)
| ~ v4_group_1(X35)
| ~ v6_vectsp_1(X35)
| ~ v7_vectsp_1(X35)
| ~ v8_vectsp_1(X35)
| ~ l3_vectsp_1(X35)
| v3_struct_0(X36)
| ~ v3_rlvect_1(X36)
| ~ v4_rlvect_1(X36)
| ~ v5_rlvect_1(X36)
| ~ v6_rlvect_1(X36)
| ~ v5_vectsp_2(X36,X35)
| ~ l1_vectsp_2(X36,X35) )
& ( m1_rmod_2(k2_rmod_2(X35,X36),X35,X36)
| v3_struct_0(X35)
| ~ v3_rlvect_1(X35)
| ~ v4_rlvect_1(X35)
| ~ v5_rlvect_1(X35)
| ~ v6_rlvect_1(X35)
| ~ v4_group_1(X35)
| ~ v6_vectsp_1(X35)
| ~ v7_vectsp_1(X35)
| ~ v8_vectsp_1(X35)
| ~ l3_vectsp_1(X35)
| v3_struct_0(X36)
| ~ v3_rlvect_1(X36)
| ~ v4_rlvect_1(X36)
| ~ v5_rlvect_1(X36)
| ~ v6_rlvect_1(X36)
| ~ v5_vectsp_2(X36,X35)
| ~ l1_vectsp_2(X36,X35) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])]) ).
cnf(c_0_41,negated_conjecture,
( g1_vectsp_2(X1,esk3_0,u1_rlvect_1(esk2_0),u2_struct_0(esk2_0),u1_vectsp_2(X1,esk2_0)) = k2_rmod_2(X1,esk2_0)
| v3_struct_0(X1)
| ~ l1_vectsp_2(esk2_0,X1)
| ~ v5_vectsp_2(esk2_0,X1)
| ~ l3_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30]),c_0_31]),c_0_32])]),c_0_33]) ).
cnf(c_0_42,negated_conjecture,
( g1_vectsp_2(X1,esk3_0,u1_rlvect_1(esk2_0),u2_struct_0(esk2_0),u1_vectsp_2(X1,esk2_0)) = esk2_0
| ~ l1_struct_0(X1)
| ~ l1_vectsp_2(esk2_0,X1)
| ~ v3_vectsp_2(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_28]) ).
cnf(c_0_43,plain,
( l1_struct_0(X1)
| ~ l3_vectsp_1(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_44,negated_conjecture,
( k1_rmod_5(X1,esk2_0,X2) = X3
| k2_group_1(X1) = k1_rlvect_1(X1)
| v10_vectsp_1(X1)
| v3_struct_0(X1)
| X2 != u1_struct_0(X3)
| ~ m1_rmod_2(X3,X1,esk2_0)
| ~ m1_subset_1(X2,k1_zfmisc_1(esk3_0))
| ~ l1_vectsp_2(esk2_0,X1)
| ~ v5_vectsp_2(esk2_0,X1)
| ~ v3_vectsp_2(X3,X1)
| ~ l3_vectsp_1(X1)
| ~ v2_vectsp_2(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v7_group_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_28]),c_0_29]),c_0_30]),c_0_31]),c_0_32])]),c_0_33]) ).
cnf(c_0_45,negated_conjecture,
v3_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_46,negated_conjecture,
l1_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_47,negated_conjecture,
v5_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_48,negated_conjecture,
l3_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_49,negated_conjecture,
v2_vectsp_2(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_50,negated_conjecture,
v8_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_51,negated_conjecture,
v7_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_52,negated_conjecture,
v6_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_53,negated_conjecture,
v7_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_54,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_55,negated_conjecture,
v6_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_56,negated_conjecture,
v5_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_57,negated_conjecture,
v4_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_58,negated_conjecture,
v3_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_59,negated_conjecture,
k1_rlvect_1(esk1_0) != k2_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_60,negated_conjecture,
~ v10_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_61,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_62,plain,
( m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r1_tarski(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_63,plain,
r1_tarski(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_64,plain,
( m1_rmod_2(k2_rmod_2(X1,X2),X1,X2)
| v3_struct_0(X1)
| v3_struct_0(X2)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v4_group_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ l3_vectsp_1(X1)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_vectsp_2(X2,X1)
| ~ l1_vectsp_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_65,negated_conjecture,
( k2_rmod_2(X1,esk2_0) = esk2_0
| v3_struct_0(X1)
| ~ l1_vectsp_2(esk2_0,X1)
| ~ v5_vectsp_2(esk2_0,X1)
| ~ v3_vectsp_2(esk2_0,X1)
| ~ l3_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
cnf(c_0_66,negated_conjecture,
k1_rmod_5(esk1_0,esk2_0,esk3_0) != esk2_0,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_67,negated_conjecture,
( k1_rmod_5(esk1_0,esk2_0,X1) = esk2_0
| X1 != esk3_0
| ~ m1_rmod_2(esk2_0,esk1_0,esk2_0)
| ~ m1_subset_1(X1,k1_zfmisc_1(esk3_0)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(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_44,c_0_45]),c_0_28]),c_0_46]),c_0_47]),c_0_48]),c_0_49]),c_0_50]),c_0_51]),c_0_52]),c_0_53]),c_0_54]),c_0_55]),c_0_56]),c_0_57]),c_0_58])]),c_0_59]),c_0_60]),c_0_61]) ).
cnf(c_0_68,plain,
m1_subset_1(X1,k1_zfmisc_1(X1)),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_69,negated_conjecture,
( m1_rmod_2(esk2_0,X1,esk2_0)
| v3_struct_0(X1)
| ~ l1_vectsp_2(esk2_0,X1)
| ~ v5_vectsp_2(esk2_0,X1)
| ~ v3_vectsp_2(esk2_0,X1)
| ~ l3_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_29]),c_0_30]),c_0_31]),c_0_32])]),c_0_33]) ).
cnf(c_0_70,negated_conjecture,
~ m1_rmod_2(esk2_0,esk1_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68])]) ).
cnf(c_0_71,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_45]),c_0_46]),c_0_47]),c_0_48]),c_0_50]),c_0_51]),c_0_52]),c_0_54]),c_0_55]),c_0_56]),c_0_57]),c_0_58])]),c_0_70]),c_0_61]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG219+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.16/0.34 % Computer : n026.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon Aug 28 03:18:19 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 0.19/0.71 % Version : CSE_E---1.5
% 0.19/0.71 % Problem : theBenchmark.p
% 0.19/0.71 % Proof found
% 0.19/0.71 % SZS status Theorem for theBenchmark.p
% 0.19/0.71 % SZS output start Proof
% See solution above
% 0.19/0.72 % Total time : 0.134000 s
% 0.19/0.72 % SZS output end Proof
% 0.19/0.72 % Total time : 0.139000 s
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