TSTP Solution File: ALG215+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ALG215+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 : n012.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 16:06:41 EDT 2023
% Result : Theorem 50.91s 50.99s
% Output : CNFRefutation 50.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 83
% Syntax : Number of formulae : 128 ( 24 unt; 76 typ; 0 def)
% Number of atoms : 521 ( 18 equ)
% Maximal formula atoms : 82 ( 10 avg)
% Number of connectives : 749 ( 280 ~; 290 |; 147 &)
% ( 4 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 112 ( 62 >; 50 *; 0 +; 0 <<)
% Number of predicates : 36 ( 34 usr; 1 prp; 0-4 aty)
% Number of functors : 42 ( 42 usr; 14 con; 0-4 aty)
% Number of variables : 77 ( 3 sgn; 46 !; 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,
v6_vectsp_1: $i > $o ).
tff(decl_29,type,
v7_vectsp_1: $i > $o ).
tff(decl_30,type,
v8_vectsp_1: $i > $o ).
tff(decl_31,type,
l3_vectsp_1: $i > $o ).
tff(decl_32,type,
v5_vectsp_2: ( $i * $i ) > $o ).
tff(decl_33,type,
l1_vectsp_2: ( $i * $i ) > $o ).
tff(decl_34,type,
u1_struct_0: $i > $i ).
tff(decl_35,type,
k1_subset_1: $i > $i ).
tff(decl_36,type,
v1_rmod_5: ( $i * $i * $i ) > $o ).
tff(decl_37,type,
r2_hidden: ( $i * $i ) > $o ).
tff(decl_38,type,
k2_zfmisc_1: ( $i * $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,
v1_relat_1: $i > $o ).
tff(decl_42,type,
m2_rmod_4: ( $i * $i * $i * $i ) > $o ).
tff(decl_43,type,
k5_rmod_4: ( $i * $i * $i ) > $i ).
tff(decl_44,type,
k1_rlvect_1: $i > $i ).
tff(decl_45,type,
k2_rmod_4: ( $i * $i * $i ) > $i ).
tff(decl_46,type,
k1_xboole_0: $i ).
tff(decl_47,type,
m1_rmod_4: ( $i * $i * $i ) > $o ).
tff(decl_48,type,
a_3_0_rmod_4: ( $i * $i * $i ) > $i ).
tff(decl_49,type,
r1_tarski: ( $i * $i ) > $o ).
tff(decl_50,type,
v1_xboole_0: $i > $o ).
tff(decl_51,type,
k1_fraenkel: ( $i * $i ) > $i ).
tff(decl_52,type,
m1_fraenkel: ( $i * $i * $i ) > $o ).
tff(decl_53,type,
l2_struct_0: $i > $o ).
tff(decl_54,type,
v1_finset_1: $i > $o ).
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,
k8_funct_2: ( $i * $i * $i * $i ) > $i ).
tff(decl_59,type,
l1_group_1: $i > $o ).
tff(decl_60,type,
l1_struct_0: $i > $o ).
tff(decl_61,type,
l1_rlvect_1: $i > $o ).
tff(decl_62,type,
l1_vectsp_1: $i > $o ).
tff(decl_63,type,
l2_vectsp_1: $i > $o ).
tff(decl_64,type,
v1_fraenkel: $i > $o ).
tff(decl_65,type,
m2_fraenkel: ( $i * $i * $i * $i ) > $o ).
tff(decl_66,type,
m2_relset_1: ( $i * $i * $i ) > $o ).
tff(decl_67,type,
k1_funct_2: ( $i * $i ) > $i ).
tff(decl_68,type,
k1_funct_1: ( $i * $i ) > $i ).
tff(decl_69,type,
esk1_0: $i ).
tff(decl_70,type,
esk2_0: $i ).
tff(decl_71,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_72,type,
esk4_0: $i ).
tff(decl_73,type,
esk5_0: $i ).
tff(decl_74,type,
esk6_0: $i ).
tff(decl_75,type,
esk7_0: $i ).
tff(decl_76,type,
esk8_1: $i > $i ).
tff(decl_77,type,
esk9_0: $i ).
tff(decl_78,type,
esk10_0: $i ).
tff(decl_79,type,
esk11_0: $i ).
tff(decl_80,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_81,type,
esk13_2: ( $i * $i ) > $i ).
tff(decl_82,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_83,type,
esk15_1: $i > $i ).
tff(decl_84,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_85,type,
esk17_2: ( $i * $i ) > $i ).
tff(decl_86,type,
esk18_3: ( $i * $i * $i ) > $i ).
tff(decl_87,type,
esk19_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_88,type,
esk20_1: $i > $i ).
tff(decl_89,type,
esk21_0: $i ).
tff(decl_90,type,
esk22_1: $i > $i ).
tff(decl_91,type,
esk23_1: $i > $i ).
tff(decl_92,type,
esk24_0: $i ).
tff(decl_93,type,
esk25_0: $i ).
tff(decl_94,type,
esk26_0: $i ).
tff(decl_95,type,
esk27_1: $i > $i ).
tff(decl_96,type,
esk28_1: $i > $i ).
tff(decl_97,type,
esk29_2: ( $i * $i ) > $i ).
fof(d7_rmod_4,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) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
=> ! [X4] :
( m1_rmod_4(X4,X1,X2)
=> ( m2_rmod_4(X4,X1,X2,X3)
<=> r1_tarski(k2_rmod_4(X1,X2,X4),X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_rmod_4) ).
fof(dt_m2_rmod_4,axiom,
! [X1,X2,X3] :
( ( ~ 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)
& m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2))) )
=> ! [X4] :
( m2_rmod_4(X4,X1,X2,X3)
=> m1_rmod_4(X4,X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_rmod_4) ).
fof(t6_boole,axiom,
! [X1] :
( v1_xboole_0(X1)
=> X1 = k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(dt_k1_subset_1,axiom,
! [X1] :
( v1_xboole_0(k1_subset_1(X1))
& m1_subset_1(k1_subset_1(X1),k1_zfmisc_1(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_subset_1) ).
fof(t3_xboole_1,axiom,
! [X1] :
( r1_tarski(X1,k1_xboole_0)
=> X1 = k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(d1_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)
& 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) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
=> ( v1_rmod_5(X3,X1,X2)
<=> ! [X4] :
( m2_rmod_4(X4,X1,X2,X3)
=> ( k5_rmod_4(X1,X2,X4) = k1_rlvect_1(X2)
=> k2_rmod_4(X1,X2,X4) = k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_rmod_5) ).
fof(t4_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)
& 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) )
=> v1_rmod_5(k1_subset_1(u1_struct_0(X2)),X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_rmod_5) ).
fof(c_0_7,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) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
=> ! [X4] :
( m1_rmod_4(X4,X1,X2)
=> ( m2_rmod_4(X4,X1,X2,X3)
<=> r1_tarski(k2_rmod_4(X1,X2,X4),X3) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d7_rmod_4]) ).
fof(c_0_8,plain,
! [X1,X2,X3] :
( ( ~ 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)
& m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2))) )
=> ! [X4] :
( m2_rmod_4(X4,X1,X2,X3)
=> m1_rmod_4(X4,X1,X2) ) ),
inference(fof_simplification,[status(thm)],[dt_m2_rmod_4]) ).
fof(c_0_9,plain,
! [X149] :
( ~ v1_xboole_0(X149)
| X149 = k1_xboole_0 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_10,plain,
! [X28] :
( v1_xboole_0(k1_subset_1(X28))
& m1_subset_1(k1_subset_1(X28),k1_zfmisc_1(X28)) ),
inference(variable_rename,[status(thm)],[dt_k1_subset_1]) ).
fof(c_0_11,plain,
! [X21,X22,X23,X24] :
( ( ~ m2_rmod_4(X24,X21,X22,X23)
| r1_tarski(k2_rmod_4(X21,X22,X24),X23)
| ~ m1_rmod_4(X24,X21,X22)
| ~ m1_subset_1(X23,k1_zfmisc_1(u1_struct_0(X22)))
| v3_struct_0(X22)
| ~ v3_rlvect_1(X22)
| ~ v4_rlvect_1(X22)
| ~ v5_rlvect_1(X22)
| ~ v6_rlvect_1(X22)
| ~ v5_vectsp_2(X22,X21)
| ~ l1_vectsp_2(X22,X21)
| v3_struct_0(X21)
| ~ v3_rlvect_1(X21)
| ~ v4_rlvect_1(X21)
| ~ v5_rlvect_1(X21)
| ~ v6_rlvect_1(X21)
| ~ v4_group_1(X21)
| ~ v6_vectsp_1(X21)
| ~ v7_vectsp_1(X21)
| ~ v8_vectsp_1(X21)
| ~ l3_vectsp_1(X21) )
& ( ~ r1_tarski(k2_rmod_4(X21,X22,X24),X23)
| m2_rmod_4(X24,X21,X22,X23)
| ~ m1_rmod_4(X24,X21,X22)
| ~ m1_subset_1(X23,k1_zfmisc_1(u1_struct_0(X22)))
| v3_struct_0(X22)
| ~ v3_rlvect_1(X22)
| ~ v4_rlvect_1(X22)
| ~ v5_rlvect_1(X22)
| ~ v6_rlvect_1(X22)
| ~ v5_vectsp_2(X22,X21)
| ~ l1_vectsp_2(X22,X21)
| v3_struct_0(X21)
| ~ v3_rlvect_1(X21)
| ~ v4_rlvect_1(X21)
| ~ v5_rlvect_1(X21)
| ~ v6_rlvect_1(X21)
| ~ v4_group_1(X21)
| ~ v6_vectsp_1(X21)
| ~ v7_vectsp_1(X21)
| ~ v8_vectsp_1(X21)
| ~ l3_vectsp_1(X21) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
fof(c_0_12,plain,
! [X60,X61,X62,X63] :
( v3_struct_0(X60)
| ~ v3_rlvect_1(X60)
| ~ v4_rlvect_1(X60)
| ~ v5_rlvect_1(X60)
| ~ v6_rlvect_1(X60)
| ~ v4_group_1(X60)
| ~ v6_vectsp_1(X60)
| ~ v7_vectsp_1(X60)
| ~ v8_vectsp_1(X60)
| ~ l3_vectsp_1(X60)
| v3_struct_0(X61)
| ~ v3_rlvect_1(X61)
| ~ v4_rlvect_1(X61)
| ~ v5_rlvect_1(X61)
| ~ v6_rlvect_1(X61)
| ~ v5_vectsp_2(X61,X60)
| ~ l1_vectsp_2(X61,X60)
| ~ m1_subset_1(X62,k1_zfmisc_1(u1_struct_0(X61)))
| ~ m2_rmod_4(X63,X60,X61,X62)
| m1_rmod_4(X63,X60,X61) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
cnf(c_0_13,plain,
( X1 = k1_xboole_0
| ~ v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
v1_xboole_0(k1_subset_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,plain,
! [X142] :
( ~ r1_tarski(X142,k1_xboole_0)
| X142 = k1_xboole_0 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_xboole_1])]) ).
cnf(c_0_16,plain,
( r1_tarski(k2_rmod_4(X2,X3,X1),X4)
| v3_struct_0(X3)
| v3_struct_0(X2)
| ~ m2_rmod_4(X1,X2,X3,X4)
| ~ m1_rmod_4(X1,X2,X3)
| ~ m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X3)))
| ~ v3_rlvect_1(X3)
| ~ v4_rlvect_1(X3)
| ~ v5_rlvect_1(X3)
| ~ v6_rlvect_1(X3)
| ~ v5_vectsp_2(X3,X2)
| ~ l1_vectsp_2(X3,X2)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v4_group_1(X2)
| ~ v6_vectsp_1(X2)
| ~ v7_vectsp_1(X2)
| ~ v8_vectsp_1(X2)
| ~ l3_vectsp_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( v3_struct_0(X1)
| v3_struct_0(X2)
| m1_rmod_4(X4,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)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
| ~ m2_rmod_4(X4,X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
m1_subset_1(k1_subset_1(X1),k1_zfmisc_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,plain,
k1_subset_1(X1) = k1_xboole_0,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_20,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) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
=> ( v1_rmod_5(X3,X1,X2)
<=> ! [X4] :
( m2_rmod_4(X4,X1,X2,X3)
=> ( k5_rmod_4(X1,X2,X4) = k1_rlvect_1(X2)
=> k2_rmod_4(X1,X2,X4) = k1_xboole_0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d1_rmod_5]) ).
fof(c_0_21,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)
& 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) )
=> v1_rmod_5(k1_subset_1(u1_struct_0(X2)),X1,X2) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t4_rmod_5])]) ).
cnf(c_0_22,plain,
( X1 = k1_xboole_0
| ~ r1_tarski(X1,k1_xboole_0) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
( r1_tarski(k2_rmod_4(X1,X2,X3),X4)
| v3_struct_0(X1)
| v3_struct_0(X2)
| ~ m2_rmod_4(X3,X1,X2,X4)
| ~ m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))
| ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ l3_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(X2)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X2)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X2)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X2)
| ~ v3_rlvect_1(X1) ),
inference(csr,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,plain,
m1_subset_1(k1_xboole_0,k1_zfmisc_1(X1)),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_25,plain,
! [X13,X14,X15,X16] :
( ( ~ v1_rmod_5(X15,X13,X14)
| ~ m2_rmod_4(X16,X13,X14,X15)
| k5_rmod_4(X13,X14,X16) != k1_rlvect_1(X14)
| k2_rmod_4(X13,X14,X16) = k1_xboole_0
| ~ m1_subset_1(X15,k1_zfmisc_1(u1_struct_0(X14)))
| v3_struct_0(X14)
| ~ v3_rlvect_1(X14)
| ~ v4_rlvect_1(X14)
| ~ v5_rlvect_1(X14)
| ~ v6_rlvect_1(X14)
| ~ v5_vectsp_2(X14,X13)
| ~ l1_vectsp_2(X14,X13)
| v3_struct_0(X13)
| ~ v3_rlvect_1(X13)
| ~ v4_rlvect_1(X13)
| ~ v5_rlvect_1(X13)
| ~ v6_rlvect_1(X13)
| ~ v4_group_1(X13)
| ~ v6_vectsp_1(X13)
| ~ v7_vectsp_1(X13)
| ~ v8_vectsp_1(X13)
| ~ l3_vectsp_1(X13) )
& ( m2_rmod_4(esk3_3(X13,X14,X15),X13,X14,X15)
| v1_rmod_5(X15,X13,X14)
| ~ m1_subset_1(X15,k1_zfmisc_1(u1_struct_0(X14)))
| v3_struct_0(X14)
| ~ v3_rlvect_1(X14)
| ~ v4_rlvect_1(X14)
| ~ v5_rlvect_1(X14)
| ~ v6_rlvect_1(X14)
| ~ v5_vectsp_2(X14,X13)
| ~ l1_vectsp_2(X14,X13)
| v3_struct_0(X13)
| ~ v3_rlvect_1(X13)
| ~ v4_rlvect_1(X13)
| ~ v5_rlvect_1(X13)
| ~ v6_rlvect_1(X13)
| ~ v4_group_1(X13)
| ~ v6_vectsp_1(X13)
| ~ v7_vectsp_1(X13)
| ~ v8_vectsp_1(X13)
| ~ l3_vectsp_1(X13) )
& ( k5_rmod_4(X13,X14,esk3_3(X13,X14,X15)) = k1_rlvect_1(X14)
| v1_rmod_5(X15,X13,X14)
| ~ m1_subset_1(X15,k1_zfmisc_1(u1_struct_0(X14)))
| v3_struct_0(X14)
| ~ v3_rlvect_1(X14)
| ~ v4_rlvect_1(X14)
| ~ v5_rlvect_1(X14)
| ~ v6_rlvect_1(X14)
| ~ v5_vectsp_2(X14,X13)
| ~ l1_vectsp_2(X14,X13)
| v3_struct_0(X13)
| ~ v3_rlvect_1(X13)
| ~ v4_rlvect_1(X13)
| ~ v5_rlvect_1(X13)
| ~ v6_rlvect_1(X13)
| ~ v4_group_1(X13)
| ~ v6_vectsp_1(X13)
| ~ v7_vectsp_1(X13)
| ~ v8_vectsp_1(X13)
| ~ l3_vectsp_1(X13) )
& ( k2_rmod_4(X13,X14,esk3_3(X13,X14,X15)) != k1_xboole_0
| v1_rmod_5(X15,X13,X14)
| ~ m1_subset_1(X15,k1_zfmisc_1(u1_struct_0(X14)))
| v3_struct_0(X14)
| ~ v3_rlvect_1(X14)
| ~ v4_rlvect_1(X14)
| ~ v5_rlvect_1(X14)
| ~ v6_rlvect_1(X14)
| ~ v5_vectsp_2(X14,X13)
| ~ l1_vectsp_2(X14,X13)
| v3_struct_0(X13)
| ~ v3_rlvect_1(X13)
| ~ v4_rlvect_1(X13)
| ~ v5_rlvect_1(X13)
| ~ v6_rlvect_1(X13)
| ~ v4_group_1(X13)
| ~ v6_vectsp_1(X13)
| ~ v7_vectsp_1(X13)
| ~ v8_vectsp_1(X13)
| ~ l3_vectsp_1(X13) ) ),
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_20])])])])]) ).
fof(c_0_26,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)
& v6_vectsp_1(esk1_0)
& v7_vectsp_1(esk1_0)
& v8_vectsp_1(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)
& v5_vectsp_2(esk2_0,esk1_0)
& l1_vectsp_2(esk2_0,esk1_0)
& ~ v1_rmod_5(k1_subset_1(u1_struct_0(esk2_0)),esk1_0,esk2_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
cnf(c_0_27,plain,
( k2_rmod_4(X1,X2,X3) = k1_xboole_0
| v3_struct_0(X1)
| v3_struct_0(X2)
| ~ m2_rmod_4(X3,X1,X2,k1_xboole_0)
| ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ l3_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(X2)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X2)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X2)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X2)
| ~ v3_rlvect_1(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_28,plain,
( m2_rmod_4(esk3_3(X1,X2,X3),X1,X2,X3)
| v1_rmod_5(X3,X1,X2)
| v3_struct_0(X2)
| v3_struct_0(X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_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_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) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,negated_conjecture,
~ v1_rmod_5(k1_subset_1(u1_struct_0(esk2_0)),esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_30,plain,
( v1_rmod_5(X3,X1,X2)
| v3_struct_0(X2)
| v3_struct_0(X1)
| k2_rmod_4(X1,X2,esk3_3(X1,X2,X3)) != k1_xboole_0
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_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_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) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
( k2_rmod_4(X1,X2,esk3_3(X1,X2,k1_xboole_0)) = k1_xboole_0
| v1_rmod_5(k1_xboole_0,X1,X2)
| v3_struct_0(X2)
| v3_struct_0(X1)
| ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ l3_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(X2)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X2)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X2)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X2)
| ~ v3_rlvect_1(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_24])]) ).
cnf(c_0_32,negated_conjecture,
~ v1_rmod_5(k1_xboole_0,esk1_0,esk2_0),
inference(rw,[status(thm)],[c_0_29,c_0_19]) ).
cnf(c_0_33,plain,
( v1_rmod_5(k1_xboole_0,X1,X2)
| v3_struct_0(X1)
| v3_struct_0(X2)
| ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ l3_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(X2)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X2)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X2)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X2)
| ~ v3_rlvect_1(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_24])]) ).
cnf(c_0_34,negated_conjecture,
l1_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,negated_conjecture,
v5_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_36,negated_conjecture,
l3_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_37,negated_conjecture,
v8_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_38,negated_conjecture,
v7_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_39,negated_conjecture,
v6_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_40,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_41,negated_conjecture,
v6_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_42,negated_conjecture,
v6_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_43,negated_conjecture,
v5_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_44,negated_conjecture,
v5_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_45,negated_conjecture,
v4_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_46,negated_conjecture,
v4_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_47,negated_conjecture,
v3_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_48,negated_conjecture,
v3_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_49,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_50,negated_conjecture,
~ v3_struct_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_51,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_35]),c_0_36]),c_0_37]),c_0_38]),c_0_39]),c_0_40]),c_0_41]),c_0_42]),c_0_43]),c_0_44]),c_0_45]),c_0_46]),c_0_47]),c_0_48])]),c_0_49]),c_0_50]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG215+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 06:01:09 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.58 start to proof: theBenchmark
% 50.91/50.99 % Version : CSE_E---1.5
% 50.91/50.99 % Problem : theBenchmark.p
% 50.91/50.99 % Proof found
% 50.91/50.99 % SZS status Theorem for theBenchmark.p
% 50.91/50.99 % SZS output start Proof
% See solution above
% 50.91/51.00 % Total time : 50.403000 s
% 50.91/51.00 % SZS output end Proof
% 50.91/51.00 % Total time : 50.410000 s
%------------------------------------------------------------------------------