%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : ALG215+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n017.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 : 600s
% DateTime : Thu Jul 14 16:50:25 EDT 2022
% Result : Theorem 0.24s 1.40s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 59 ( 28 unt; 0 def)
% Number of atoms : 496 ( 22 equ)
% Maximal formula atoms : 82 ( 8 avg)
% Number of connectives : 736 ( 299 ~; 316 |; 102 &)
% ( 2 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 78 ( 4 sgn 39 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t8_boole,axiom,
! [X1,X2] :
~ ( v1_xboole_0(X1)
& X1 != X2
& v1_xboole_0(X2) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t8_boole) ).
fof(rc1_xboole_0,axiom,
? [X1] : v1_xboole_0(X1),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',rc1_xboole_0) ).
fof(t6_boole,axiom,
! [X1] :
( v1_xboole_0(X1)
=> X1 = k1_xboole_0 ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t6_boole) ).
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_m2_rmod_4) ).
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_k1_subset_1) ).
fof(t3_xboole_1,axiom,
! [X1] :
( r1_tarski(X1,k1_xboole_0)
=> X1 = k1_xboole_0 ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t4_rmod_5) ).
fof(c_0_9,plain,
! [X3,X4] :
( ~ v1_xboole_0(X3)
| X3 = X4
| ~ v1_xboole_0(X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(c_0_10,plain,
v1_xboole_0(esk13_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
fof(c_0_11,plain,
! [X2] :
( ~ v1_xboole_0(X2)
| X2 = k1_xboole_0 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_12,plain,
! [X5,X6,X7,X8] :
( ( ~ m2_rmod_4(X8,X5,X6,X7)
| r1_tarski(k2_rmod_4(X5,X6,X8),X7)
| ~ m1_rmod_4(X8,X5,X6)
| ~ m1_subset_1(X7,k1_zfmisc_1(u1_struct_0(X6)))
| v3_struct_0(X6)
| ~ v3_rlvect_1(X6)
| ~ v4_rlvect_1(X6)
| ~ v5_rlvect_1(X6)
| ~ v6_rlvect_1(X6)
| ~ v5_vectsp_2(X6,X5)
| ~ l1_vectsp_2(X6,X5)
| v3_struct_0(X5)
| ~ v3_rlvect_1(X5)
| ~ v4_rlvect_1(X5)
| ~ v5_rlvect_1(X5)
| ~ v6_rlvect_1(X5)
| ~ v4_group_1(X5)
| ~ v6_vectsp_1(X5)
| ~ v7_vectsp_1(X5)
| ~ v8_vectsp_1(X5)
| ~ l3_vectsp_1(X5) )
& ( ~ r1_tarski(k2_rmod_4(X5,X6,X8),X7)
| m2_rmod_4(X8,X5,X6,X7)
| ~ m1_rmod_4(X8,X5,X6)
| ~ m1_subset_1(X7,k1_zfmisc_1(u1_struct_0(X6)))
| v3_struct_0(X6)
| ~ v3_rlvect_1(X6)
| ~ v4_rlvect_1(X6)
| ~ v5_rlvect_1(X6)
| ~ v6_rlvect_1(X6)
| ~ v5_vectsp_2(X6,X5)
| ~ l1_vectsp_2(X6,X5)
| v3_struct_0(X5)
| ~ v3_rlvect_1(X5)
| ~ v4_rlvect_1(X5)
| ~ v5_rlvect_1(X5)
| ~ v6_rlvect_1(X5)
| ~ v4_group_1(X5)
| ~ v6_vectsp_1(X5)
| ~ v7_vectsp_1(X5)
| ~ v8_vectsp_1(X5)
| ~ l3_vectsp_1(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d7_rmod_4])])])])])])]) ).
fof(c_0_13,plain,
! [X5,X6,X7,X8] :
( v3_struct_0(X5)
| ~ v3_rlvect_1(X5)
| ~ v4_rlvect_1(X5)
| ~ v5_rlvect_1(X5)
| ~ v6_rlvect_1(X5)
| ~ v4_group_1(X5)
| ~ v6_vectsp_1(X5)
| ~ v7_vectsp_1(X5)
| ~ v8_vectsp_1(X5)
| ~ l3_vectsp_1(X5)
| v3_struct_0(X6)
| ~ v3_rlvect_1(X6)
| ~ v4_rlvect_1(X6)
| ~ v5_rlvect_1(X6)
| ~ v6_rlvect_1(X6)
| ~ v5_vectsp_2(X6,X5)
| ~ l1_vectsp_2(X6,X5)
| ~ m1_subset_1(X7,k1_zfmisc_1(u1_struct_0(X6)))
| ~ m2_rmod_4(X8,X5,X6,X7)
| m1_rmod_4(X8,X5,X6) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_m2_rmod_4])])])])])]) ).
cnf(c_0_14,plain,
( X2 = X1
| ~ v1_xboole_0(X1)
| ~ v1_xboole_0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
v1_xboole_0(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,plain,
! [X2,X2] :
( v1_xboole_0(k1_subset_1(X2))
& m1_subset_1(k1_subset_1(X2),k1_zfmisc_1(X2)) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[dt_k1_subset_1])])]) ).
fof(c_0_17,plain,
! [X2] :
( ~ r1_tarski(X2,k1_xboole_0)
| X2 = k1_xboole_0 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_xboole_1])]) ).
cnf(c_0_18,plain,
( X1 = k1_xboole_0
| ~ v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
( v3_struct_0(X1)
| v3_struct_0(X2)
| r1_tarski(k2_rmod_4(X1,X2,X4),X3)
| ~ 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)
| ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v3_rlvect_1(X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
| ~ m1_rmod_4(X4,X1,X2)
| ~ m2_rmod_4(X4,X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
( m1_rmod_4(X1,X2,X3)
| v3_struct_0(X3)
| v3_struct_0(X2)
| ~ m2_rmod_4(X1,X2,X3,X4)
| ~ m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X3)))
| ~ l1_vectsp_2(X3,X2)
| ~ v5_vectsp_2(X3,X2)
| ~ v6_rlvect_1(X3)
| ~ v5_rlvect_1(X3)
| ~ v4_rlvect_1(X3)
| ~ v3_rlvect_1(X3)
| ~ l3_vectsp_1(X2)
| ~ v8_vectsp_1(X2)
| ~ v7_vectsp_1(X2)
| ~ v6_vectsp_1(X2)
| ~ v4_group_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v3_rlvect_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_21,plain,
! [X5,X6,X7,X8] :
( ( ~ v1_rmod_5(X7,X5,X6)
| ~ m2_rmod_4(X8,X5,X6,X7)
| k5_rmod_4(X5,X6,X8) != k1_rlvect_1(X6)
| k2_rmod_4(X5,X6,X8) = k1_xboole_0
| ~ m1_subset_1(X7,k1_zfmisc_1(u1_struct_0(X6)))
| v3_struct_0(X6)
| ~ v3_rlvect_1(X6)
| ~ v4_rlvect_1(X6)
| ~ v5_rlvect_1(X6)
| ~ v6_rlvect_1(X6)
| ~ v5_vectsp_2(X6,X5)
| ~ l1_vectsp_2(X6,X5)
| v3_struct_0(X5)
| ~ v3_rlvect_1(X5)
| ~ v4_rlvect_1(X5)
| ~ v5_rlvect_1(X5)
| ~ v6_rlvect_1(X5)
| ~ v4_group_1(X5)
| ~ v6_vectsp_1(X5)
| ~ v7_vectsp_1(X5)
| ~ v8_vectsp_1(X5)
| ~ l3_vectsp_1(X5) )
& ( m2_rmod_4(esk3_3(X5,X6,X7),X5,X6,X7)
| v1_rmod_5(X7,X5,X6)
| ~ m1_subset_1(X7,k1_zfmisc_1(u1_struct_0(X6)))
| v3_struct_0(X6)
| ~ v3_rlvect_1(X6)
| ~ v4_rlvect_1(X6)
| ~ v5_rlvect_1(X6)
| ~ v6_rlvect_1(X6)
| ~ v5_vectsp_2(X6,X5)
| ~ l1_vectsp_2(X6,X5)
| v3_struct_0(X5)
| ~ v3_rlvect_1(X5)
| ~ v4_rlvect_1(X5)
| ~ v5_rlvect_1(X5)
| ~ v6_rlvect_1(X5)
| ~ v4_group_1(X5)
| ~ v6_vectsp_1(X5)
| ~ v7_vectsp_1(X5)
| ~ v8_vectsp_1(X5)
| ~ l3_vectsp_1(X5) )
& ( k5_rmod_4(X5,X6,esk3_3(X5,X6,X7)) = k1_rlvect_1(X6)
| v1_rmod_5(X7,X5,X6)
| ~ m1_subset_1(X7,k1_zfmisc_1(u1_struct_0(X6)))
| v3_struct_0(X6)
| ~ v3_rlvect_1(X6)
| ~ v4_rlvect_1(X6)
| ~ v5_rlvect_1(X6)
| ~ v6_rlvect_1(X6)
| ~ v5_vectsp_2(X6,X5)
| ~ l1_vectsp_2(X6,X5)
| v3_struct_0(X5)
| ~ v3_rlvect_1(X5)
| ~ v4_rlvect_1(X5)
| ~ v5_rlvect_1(X5)
| ~ v6_rlvect_1(X5)
| ~ v4_group_1(X5)
| ~ v6_vectsp_1(X5)
| ~ v7_vectsp_1(X5)
| ~ v8_vectsp_1(X5)
| ~ l3_vectsp_1(X5) )
& ( k2_rmod_4(X5,X6,esk3_3(X5,X6,X7)) != k1_xboole_0
| v1_rmod_5(X7,X5,X6)
| ~ m1_subset_1(X7,k1_zfmisc_1(u1_struct_0(X6)))
| v3_struct_0(X6)
| ~ v3_rlvect_1(X6)
| ~ v4_rlvect_1(X6)
| ~ v5_rlvect_1(X6)
| ~ v6_rlvect_1(X6)
| ~ v5_vectsp_2(X6,X5)
| ~ l1_vectsp_2(X6,X5)
| v3_struct_0(X5)
| ~ v3_rlvect_1(X5)
| ~ v4_rlvect_1(X5)
| ~ v5_rlvect_1(X5)
| ~ v6_rlvect_1(X5)
| ~ v4_group_1(X5)
| ~ v6_vectsp_1(X5)
| ~ v7_vectsp_1(X5)
| ~ v8_vectsp_1(X5)
| ~ l3_vectsp_1(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d1_rmod_5])])])])])])])]) ).
cnf(c_0_22,plain,
( X1 = esk13_0
| ~ v1_xboole_0(X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_23,plain,
v1_xboole_0(k1_subset_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_24,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(assume_negation,[status(cth)],[t4_rmod_5]) ).
cnf(c_0_25,plain,
( X1 = k1_xboole_0
| ~ r1_tarski(X1,k1_xboole_0) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,plain,
k1_xboole_0 = esk13_0,
inference(spm,[status(thm)],[c_0_18,c_0_15]) ).
cnf(c_0_27,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_19,c_0_20]) ).
cnf(c_0_28,plain,
( v3_struct_0(X1)
| v3_struct_0(X2)
| v1_rmod_5(X3,X1,X2)
| m2_rmod_4(esk3_3(X1,X2,X3),X1,X2,X3)
| ~ 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)
| ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v3_rlvect_1(X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,plain,
m1_subset_1(k1_subset_1(X1),k1_zfmisc_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_30,plain,
k1_subset_1(X1) = esk13_0,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_31,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(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_24])])])])])]) ).
cnf(c_0_32,plain,
( v3_struct_0(X1)
| v3_struct_0(X2)
| v1_rmod_5(X3,X1,X2)
| ~ 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)
| ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v3_rlvect_1(X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
| k2_rmod_4(X1,X2,esk3_3(X1,X2,X3)) != k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_33,plain,
( X1 = esk13_0
| ~ r1_tarski(X1,esk13_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_26]) ).
cnf(c_0_34,plain,
( r1_tarski(k2_rmod_4(X1,X2,esk3_3(X1,X2,X3)),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)))
| ~ 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(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_35,plain,
m1_subset_1(esk13_0,k1_zfmisc_1(X1)),
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,negated_conjecture,
~ v1_rmod_5(k1_subset_1(u1_struct_0(esk2_0)),esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_37,plain,
( v1_rmod_5(X1,X2,X3)
| v3_struct_0(X3)
| v3_struct_0(X2)
| k2_rmod_4(X2,X3,esk3_3(X2,X3,X1)) != esk13_0
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X3)))
| ~ l1_vectsp_2(X3,X2)
| ~ v5_vectsp_2(X3,X2)
| ~ l3_vectsp_1(X2)
| ~ v8_vectsp_1(X2)
| ~ v7_vectsp_1(X2)
| ~ v6_vectsp_1(X2)
| ~ v4_group_1(X2)
| ~ v6_rlvect_1(X3)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X3)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X3)
| ~ v4_rlvect_1(X2)
| ~ v3_rlvect_1(X3)
| ~ v3_rlvect_1(X2) ),
inference(rw,[status(thm)],[c_0_32,c_0_26]) ).
cnf(c_0_38,plain,
( k2_rmod_4(X1,X2,esk3_3(X1,X2,esk13_0)) = esk13_0
| v1_rmod_5(esk13_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_33,c_0_34]),c_0_35])]) ).
cnf(c_0_39,negated_conjecture,
~ v1_rmod_5(esk13_0,esk1_0,esk2_0),
inference(rw,[status(thm)],[c_0_36,c_0_30]) ).
cnf(c_0_40,plain,
( v1_rmod_5(esk13_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_37,c_0_38]),c_0_35])]) ).
cnf(c_0_41,negated_conjecture,
l1_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_42,negated_conjecture,
v5_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_43,negated_conjecture,
l3_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_44,negated_conjecture,
v8_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_45,negated_conjecture,
v7_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_46,negated_conjecture,
v6_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_47,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_48,negated_conjecture,
v6_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_49,negated_conjecture,
v6_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_50,negated_conjecture,
v5_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_51,negated_conjecture,
v5_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_52,negated_conjecture,
v4_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_53,negated_conjecture,
v4_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_54,negated_conjecture,
v3_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_55,negated_conjecture,
v3_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_56,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_57,negated_conjecture,
~ v3_struct_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_58,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_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]),c_0_51]),c_0_52]),c_0_53]),c_0_54]),c_0_55])]),c_0_56]),c_0_57]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG215+1 : TPTP v8.1.0. Released v3.4.0.
% 0.07/0.12 % Command : run_ET %s %d
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 9 06:35:49 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.24/1.40 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.24/1.40 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.24/1.40 # Preprocessing time : 0.021 s
% 0.24/1.40
% 0.24/1.40 # Proof found!
% 0.24/1.40 # SZS status Theorem
% 0.24/1.40 # SZS output start CNFRefutation
% See solution above
% 0.24/1.40 # Proof object total steps : 59
% 0.24/1.40 # Proof object clause steps : 40
% 0.24/1.40 # Proof object formula steps : 19
% 0.24/1.40 # Proof object conjectures : 23
% 0.24/1.40 # Proof object clause conjectures : 20
% 0.24/1.40 # Proof object formula conjectures : 3
% 0.24/1.40 # Proof object initial clauses used : 28
% 0.24/1.40 # Proof object initial formulas used : 9
% 0.24/1.40 # Proof object generating inferences : 7
% 0.24/1.40 # Proof object simplifying inferences : 28
% 0.24/1.40 # Training examples: 0 positive, 0 negative
% 0.24/1.40 # Parsed axioms : 77
% 0.24/1.40 # Removed by relevancy pruning/SinE : 46
% 0.24/1.40 # Initial clauses : 60
% 0.24/1.40 # Removed in clause preprocessing : 0
% 0.24/1.40 # Initial clauses in saturation : 60
% 0.24/1.40 # Processed clauses : 98
% 0.24/1.40 # ...of these trivial : 1
% 0.24/1.40 # ...subsumed : 2
% 0.24/1.40 # ...remaining for further processing : 95
% 0.24/1.40 # Other redundant clauses eliminated : 0
% 0.24/1.40 # Clauses deleted for lack of memory : 0
% 0.24/1.40 # Backward-subsumed : 3
% 0.24/1.40 # Backward-rewritten : 11
% 0.24/1.40 # Generated clauses : 68
% 0.24/1.40 # ...of the previous two non-trivial : 65
% 0.24/1.40 # Contextual simplify-reflections : 2
% 0.24/1.40 # Paramodulations : 68
% 0.24/1.40 # Factorizations : 0
% 0.24/1.40 # Equation resolutions : 0
% 0.24/1.40 # Current number of processed clauses : 81
% 0.24/1.40 # Positive orientable unit clauses : 32
% 0.24/1.40 # Positive unorientable unit clauses: 0
% 0.24/1.40 # Negative unit clauses : 9
% 0.24/1.40 # Non-unit-clauses : 40
% 0.24/1.40 # Current number of unprocessed clauses: 14
% 0.24/1.40 # ...number of literals in the above : 280
% 0.24/1.40 # Current number of archived formulas : 0
% 0.24/1.40 # Current number of archived clauses : 14
% 0.24/1.40 # Clause-clause subsumption calls (NU) : 7519
% 0.24/1.40 # Rec. Clause-clause subsumption calls : 102
% 0.24/1.40 # Non-unit clause-clause subsumptions : 7
% 0.24/1.40 # Unit Clause-clause subsumption calls : 167
% 0.24/1.40 # Rewrite failures with RHS unbound : 0
% 0.24/1.40 # BW rewrite match attempts : 11
% 0.24/1.40 # BW rewrite match successes : 5
% 0.24/1.40 # Condensation attempts : 0
% 0.24/1.40 # Condensation successes : 0
% 0.24/1.40 # Termbank termtop insertions : 10266
% 0.24/1.40
% 0.24/1.40 # -------------------------------------------------
% 0.24/1.40 # User time : 0.031 s
% 0.24/1.40 # System time : 0.006 s
% 0.24/1.40 # Total time : 0.037 s
% 0.24/1.40 # Maximum resident set size: 3440 pages
%------------------------------------------------------------------------------