%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG220+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 11:55:39 AM UTC 2026
% Result : Theorem 0.16s 0.69s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 66 ( 30 unt; 0 def)
% Number of atoms : 871 ( 15 equ)
% Maximal formula atoms : 133 ( 13 avg)
% Number of connectives : 1295 ( 490 ~; 502 |; 263 &)
% ( 1 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 11 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 101 ( 0 sgn 55 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t16_rmod_5,conjecture,
! [X1] :
( ( l3_vectsp_1(X1)
& v2_vectsp_2(X1)
& ~ v10_vectsp_1(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)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( l1_vectsp_2(X2,X1)
& v5_vectsp_2(X2,X1)
& v3_vectsp_2(X2,X1)
& v6_rlvect_1(X2)
& v5_rlvect_1(X2)
& v4_rlvect_1(X2)
& v3_rlvect_1(X2)
& ~ v3_struct_0(X2) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))
=> ( ( r1_tarski(X3,X4)
& k1_rmod_5(X1,X2,X3) = X2 )
=> k1_rmod_5(X1,X2,X4) = X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_rmod_5) ).
fof(t15_rmod_5,axiom,
! [X1] :
( ( l3_vectsp_1(X1)
& v2_vectsp_2(X1)
& ~ v10_vectsp_1(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)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( 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)
& ~ v3_struct_0(X2) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))
=> ( r1_tarski(X3,X4)
=> m1_rmod_2(k1_rmod_5(X1,X2,X3),X1,k1_rmod_5(X1,X2,X4)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_rmod_5) ).
fof(t33_rmod_2,axiom,
! [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)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( l1_vectsp_2(X2,X1)
& v5_vectsp_2(X2,X1)
& v3_vectsp_2(X2,X1)
& v6_rlvect_1(X2)
& v5_rlvect_1(X2)
& v4_rlvect_1(X2)
& v3_rlvect_1(X2)
& ~ v3_struct_0(X2) )
=> ! [X3] :
( ( l1_vectsp_2(X3,X1)
& v5_vectsp_2(X3,X1)
& v3_vectsp_2(X3,X1)
& v6_rlvect_1(X3)
& v5_rlvect_1(X3)
& v4_rlvect_1(X3)
& v3_rlvect_1(X3)
& ~ v3_struct_0(X3) )
=> ( ( m1_rmod_2(X2,X1,X3)
& m1_rmod_2(X3,X1,X2) )
=> X3 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_rmod_2) ).
fof(dt_m1_rmod_2,axiom,
! [X1,X2] :
( ( 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)
& ~ v3_struct_0(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)
& ~ v3_struct_0(X1) )
=> ! [X3] :
( m1_rmod_2(X3,X1,X2)
=> ( l1_vectsp_2(X3,X1)
& v5_vectsp_2(X3,X1)
& v6_rlvect_1(X3)
& v5_rlvect_1(X3)
& v4_rlvect_1(X3)
& v3_rlvect_1(X3)
& ~ v3_struct_0(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_rmod_2) ).
fof(dt_k1_rmod_5,axiom,
! [X1,X2,X3] :
( ( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
& 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)
& ~ v3_struct_0(X2)
& l3_vectsp_1(X1)
& v2_vectsp_2(X1)
& ~ v10_vectsp_1(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)
& ~ v3_struct_0(X1) )
=> ( m1_rmod_2(k1_rmod_5(X1,X2,X3),X1,X2)
& v3_vectsp_2(k1_rmod_5(X1,X2,X3),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_rmod_5) ).
fof(t3_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,k1_zfmisc_1(X2))
<=> r1_tarski(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ( l3_vectsp_1(X1)
& v2_vectsp_2(X1)
& ~ v10_vectsp_1(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)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( l1_vectsp_2(X2,X1)
& v5_vectsp_2(X2,X1)
& v3_vectsp_2(X2,X1)
& v6_rlvect_1(X2)
& v5_rlvect_1(X2)
& v4_rlvect_1(X2)
& v3_rlvect_1(X2)
& ~ v3_struct_0(X2) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))
=> ( ( r1_tarski(X3,X4)
& k1_rmod_5(X1,X2,X3) = X2 )
=> k1_rmod_5(X1,X2,X4) = X2 ) ) ) ) ),
inference(assume_negation,[status(cth)],[t16_rmod_5]) ).
fof(c_0_7,plain,
! [X1] :
( ( l3_vectsp_1(X1)
& v2_vectsp_2(X1)
& ~ v10_vectsp_1(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)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( 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)
& ~ v3_struct_0(X2) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))
=> ( r1_tarski(X3,X4)
=> m1_rmod_2(k1_rmod_5(X1,X2,X3),X1,k1_rmod_5(X1,X2,X4)) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[t15_rmod_5]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1] :
( ( l3_vectsp_1(X1)
& v2_vectsp_2(X1)
& ~ v10_vectsp_1(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)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( l1_vectsp_2(X2,X1)
& v5_vectsp_2(X2,X1)
& v3_vectsp_2(X2,X1)
& v6_rlvect_1(X2)
& v5_rlvect_1(X2)
& v4_rlvect_1(X2)
& v3_rlvect_1(X2)
& ~ v3_struct_0(X2) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))
=> ( ( r1_tarski(X3,X4)
& k1_rmod_5(X1,X2,X3) = X2 )
=> k1_rmod_5(X1,X2,X4) = X2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [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)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( l1_vectsp_2(X2,X1)
& v5_vectsp_2(X2,X1)
& v3_vectsp_2(X2,X1)
& v6_rlvect_1(X2)
& v5_rlvect_1(X2)
& v4_rlvect_1(X2)
& v3_rlvect_1(X2)
& ~ v3_struct_0(X2) )
=> ! [X3] :
( ( l1_vectsp_2(X3,X1)
& v5_vectsp_2(X3,X1)
& v3_vectsp_2(X3,X1)
& v6_rlvect_1(X3)
& v5_rlvect_1(X3)
& v4_rlvect_1(X3)
& v3_rlvect_1(X3)
& ~ v3_struct_0(X3) )
=> ( ( m1_rmod_2(X2,X1,X3)
& m1_rmod_2(X3,X1,X2) )
=> X3 = X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[t33_rmod_2]) ).
fof(c_0_10,plain,
! [X1,X2] :
( ( 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)
& ~ v3_struct_0(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)
& ~ v3_struct_0(X1) )
=> ! [X3] :
( m1_rmod_2(X3,X1,X2)
=> ( l1_vectsp_2(X3,X1)
& v5_vectsp_2(X3,X1)
& v6_rlvect_1(X3)
& v5_rlvect_1(X3)
& v4_rlvect_1(X3)
& v3_rlvect_1(X3)
& ~ v3_struct_0(X3) ) ) ),
inference(fof_simplification,[status(thm)],[dt_m1_rmod_2]) ).
fof(c_0_11,plain,
! [X18,X19,X20,X21] :
( m1_rmod_2(k1_rmod_5(X18,X19,X20),X18,k1_rmod_5(X18,X19,X21))
| ~ r1_tarski(X20,X21)
| ~ m1_subset_1(X21,k1_zfmisc_1(u1_struct_0(X19)))
| ~ m1_subset_1(X20,k1_zfmisc_1(u1_struct_0(X19)))
| ~ l1_vectsp_2(X19,X18)
| ~ v5_vectsp_2(X19,X18)
| ~ v6_rlvect_1(X19)
| ~ v5_rlvect_1(X19)
| ~ v4_rlvect_1(X19)
| ~ v3_rlvect_1(X19)
| v3_struct_0(X19)
| ~ l3_vectsp_1(X18)
| ~ v2_vectsp_2(X18)
| v10_vectsp_1(X18)
| ~ v8_vectsp_1(X18)
| ~ v7_vectsp_1(X18)
| ~ v6_vectsp_1(X18)
| ~ v7_group_1(X18)
| ~ v4_group_1(X18)
| ~ v6_rlvect_1(X18)
| ~ v5_rlvect_1(X18)
| ~ v4_rlvect_1(X18)
| ~ v3_rlvect_1(X18)
| v3_struct_0(X18) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
fof(c_0_12,negated_conjecture,
( k1_rmod_5(esk1_0,esk2_0,esk4_0) != esk2_0
& r1_tarski(esk3_0,esk4_0)
& k1_rmod_5(esk1_0,esk2_0,esk3_0) = esk2_0
& m1_subset_1(esk4_0,k1_zfmisc_1(u1_struct_0(esk2_0)))
& m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk2_0)))
& l1_vectsp_2(esk2_0,esk1_0)
& v5_vectsp_2(esk2_0,esk1_0)
& v3_vectsp_2(esk2_0,esk1_0)
& v6_rlvect_1(esk2_0)
& v5_rlvect_1(esk2_0)
& v4_rlvect_1(esk2_0)
& v3_rlvect_1(esk2_0)
& ~ v3_struct_0(esk2_0)
& l3_vectsp_1(esk1_0)
& v2_vectsp_2(esk1_0)
& ~ v10_vectsp_1(esk1_0)
& v8_vectsp_1(esk1_0)
& v7_vectsp_1(esk1_0)
& v6_vectsp_1(esk1_0)
& v7_group_1(esk1_0)
& v4_group_1(esk1_0)
& v6_rlvect_1(esk1_0)
& v5_rlvect_1(esk1_0)
& v4_rlvect_1(esk1_0)
& v3_rlvect_1(esk1_0)
& ~ v3_struct_0(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
fof(c_0_13,plain,
! [X50,X51,X52] :
( X52 = X51
| ~ m1_rmod_2(X51,X50,X52)
| ~ m1_rmod_2(X52,X50,X51)
| ~ l1_vectsp_2(X52,X50)
| ~ v5_vectsp_2(X52,X50)
| ~ v3_vectsp_2(X52,X50)
| ~ v6_rlvect_1(X52)
| ~ v5_rlvect_1(X52)
| ~ v4_rlvect_1(X52)
| ~ v3_rlvect_1(X52)
| v3_struct_0(X52)
| ~ l1_vectsp_2(X51,X50)
| ~ v5_vectsp_2(X51,X50)
| ~ v3_vectsp_2(X51,X50)
| ~ v6_rlvect_1(X51)
| ~ v5_rlvect_1(X51)
| ~ v4_rlvect_1(X51)
| ~ v3_rlvect_1(X51)
| v3_struct_0(X51)
| ~ l3_vectsp_1(X50)
| ~ v8_vectsp_1(X50)
| ~ v7_vectsp_1(X50)
| ~ v6_vectsp_1(X50)
| ~ v4_group_1(X50)
| ~ v6_rlvect_1(X50)
| ~ v5_rlvect_1(X50)
| ~ v4_rlvect_1(X50)
| ~ v3_rlvect_1(X50)
| v3_struct_0(X50) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
fof(c_0_14,plain,
! [X39,X40,X41] :
( ( ~ l1_vectsp_2(X40,X39)
| ~ v5_vectsp_2(X40,X39)
| ~ v6_rlvect_1(X40)
| ~ v5_rlvect_1(X40)
| ~ v4_rlvect_1(X40)
| ~ v3_rlvect_1(X40)
| v3_struct_0(X40)
| ~ l3_vectsp_1(X39)
| ~ v8_vectsp_1(X39)
| ~ v7_vectsp_1(X39)
| ~ v6_vectsp_1(X39)
| ~ v4_group_1(X39)
| ~ v6_rlvect_1(X39)
| ~ v5_rlvect_1(X39)
| ~ v4_rlvect_1(X39)
| ~ v3_rlvect_1(X39)
| v3_struct_0(X39)
| ~ m1_rmod_2(X41,X39,X40)
| l1_vectsp_2(X41,X39) )
& ( ~ l1_vectsp_2(X40,X39)
| ~ v5_vectsp_2(X40,X39)
| ~ v6_rlvect_1(X40)
| ~ v5_rlvect_1(X40)
| ~ v4_rlvect_1(X40)
| ~ v3_rlvect_1(X40)
| v3_struct_0(X40)
| ~ l3_vectsp_1(X39)
| ~ v8_vectsp_1(X39)
| ~ v7_vectsp_1(X39)
| ~ v6_vectsp_1(X39)
| ~ v4_group_1(X39)
| ~ v6_rlvect_1(X39)
| ~ v5_rlvect_1(X39)
| ~ v4_rlvect_1(X39)
| ~ v3_rlvect_1(X39)
| v3_struct_0(X39)
| ~ m1_rmod_2(X41,X39,X40)
| v5_vectsp_2(X41,X39) )
& ( ~ l1_vectsp_2(X40,X39)
| ~ v5_vectsp_2(X40,X39)
| ~ v6_rlvect_1(X40)
| ~ v5_rlvect_1(X40)
| ~ v4_rlvect_1(X40)
| ~ v3_rlvect_1(X40)
| v3_struct_0(X40)
| ~ l3_vectsp_1(X39)
| ~ v8_vectsp_1(X39)
| ~ v7_vectsp_1(X39)
| ~ v6_vectsp_1(X39)
| ~ v4_group_1(X39)
| ~ v6_rlvect_1(X39)
| ~ v5_rlvect_1(X39)
| ~ v4_rlvect_1(X39)
| ~ v3_rlvect_1(X39)
| v3_struct_0(X39)
| ~ m1_rmod_2(X41,X39,X40)
| v6_rlvect_1(X41) )
& ( ~ l1_vectsp_2(X40,X39)
| ~ v5_vectsp_2(X40,X39)
| ~ v6_rlvect_1(X40)
| ~ v5_rlvect_1(X40)
| ~ v4_rlvect_1(X40)
| ~ v3_rlvect_1(X40)
| v3_struct_0(X40)
| ~ l3_vectsp_1(X39)
| ~ v8_vectsp_1(X39)
| ~ v7_vectsp_1(X39)
| ~ v6_vectsp_1(X39)
| ~ v4_group_1(X39)
| ~ v6_rlvect_1(X39)
| ~ v5_rlvect_1(X39)
| ~ v4_rlvect_1(X39)
| ~ v3_rlvect_1(X39)
| v3_struct_0(X39)
| ~ m1_rmod_2(X41,X39,X40)
| v5_rlvect_1(X41) )
& ( ~ l1_vectsp_2(X40,X39)
| ~ v5_vectsp_2(X40,X39)
| ~ v6_rlvect_1(X40)
| ~ v5_rlvect_1(X40)
| ~ v4_rlvect_1(X40)
| ~ v3_rlvect_1(X40)
| v3_struct_0(X40)
| ~ l3_vectsp_1(X39)
| ~ v8_vectsp_1(X39)
| ~ v7_vectsp_1(X39)
| ~ v6_vectsp_1(X39)
| ~ v4_group_1(X39)
| ~ v6_rlvect_1(X39)
| ~ v5_rlvect_1(X39)
| ~ v4_rlvect_1(X39)
| ~ v3_rlvect_1(X39)
| v3_struct_0(X39)
| ~ m1_rmod_2(X41,X39,X40)
| v4_rlvect_1(X41) )
& ( ~ l1_vectsp_2(X40,X39)
| ~ v5_vectsp_2(X40,X39)
| ~ v6_rlvect_1(X40)
| ~ v5_rlvect_1(X40)
| ~ v4_rlvect_1(X40)
| ~ v3_rlvect_1(X40)
| v3_struct_0(X40)
| ~ l3_vectsp_1(X39)
| ~ v8_vectsp_1(X39)
| ~ v7_vectsp_1(X39)
| ~ v6_vectsp_1(X39)
| ~ v4_group_1(X39)
| ~ v6_rlvect_1(X39)
| ~ v5_rlvect_1(X39)
| ~ v4_rlvect_1(X39)
| ~ v3_rlvect_1(X39)
| v3_struct_0(X39)
| ~ m1_rmod_2(X41,X39,X40)
| v3_rlvect_1(X41) )
& ( ~ l1_vectsp_2(X40,X39)
| ~ v5_vectsp_2(X40,X39)
| ~ v6_rlvect_1(X40)
| ~ v5_rlvect_1(X40)
| ~ v4_rlvect_1(X40)
| ~ v3_rlvect_1(X40)
| v3_struct_0(X40)
| ~ l3_vectsp_1(X39)
| ~ v8_vectsp_1(X39)
| ~ v7_vectsp_1(X39)
| ~ v6_vectsp_1(X39)
| ~ v4_group_1(X39)
| ~ v6_rlvect_1(X39)
| ~ v5_rlvect_1(X39)
| ~ v4_rlvect_1(X39)
| ~ v3_rlvect_1(X39)
| v3_struct_0(X39)
| ~ m1_rmod_2(X41,X39,X40)
| ~ v3_struct_0(X41) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])])]) ).
cnf(c_0_15,plain,
( ~ r1_tarski(X3,X4)
| ~ m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
| ~ 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)
| ~ 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)
| m1_rmod_2(k1_rmod_5(X1,X2,X3),X1,k1_rmod_5(X1,X2,X4))
| v3_struct_0(X2)
| v10_vectsp_1(X1)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
k1_rmod_5(esk1_0,esk2_0,esk3_0) = esk2_0,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,negated_conjecture,
m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
l1_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
v5_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,negated_conjecture,
l3_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,negated_conjecture,
v2_vectsp_2(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_22,negated_conjecture,
v8_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_23,negated_conjecture,
v7_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_24,negated_conjecture,
v6_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_25,negated_conjecture,
v7_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_26,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_27,negated_conjecture,
v6_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_28,negated_conjecture,
v6_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_29,negated_conjecture,
v5_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_30,negated_conjecture,
v5_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_31,negated_conjecture,
v4_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_32,negated_conjecture,
v4_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_33,negated_conjecture,
v3_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_34,negated_conjecture,
v3_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_35,negated_conjecture,
~ v10_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_36,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_37,negated_conjecture,
~ v3_struct_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_38,plain,
! [X1,X2,X3] :
( ( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
& 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)
& ~ v3_struct_0(X2)
& l3_vectsp_1(X1)
& v2_vectsp_2(X1)
& ~ v10_vectsp_1(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)
& ~ v3_struct_0(X1) )
=> ( m1_rmod_2(k1_rmod_5(X1,X2,X3),X1,X2)
& v3_vectsp_2(k1_rmod_5(X1,X2,X3),X1) ) ),
inference(fof_simplification,[status(thm)],[dt_k1_rmod_5]) ).
cnf(c_0_39,plain,
( ~ m1_rmod_2(X2,X1,X3)
| ~ m1_rmod_2(X3,X1,X2)
| ~ l1_vectsp_2(X3,X1)
| ~ v5_vectsp_2(X3,X1)
| ~ v3_vectsp_2(X3,X1)
| ~ v6_rlvect_1(X3)
| ~ v5_rlvect_1(X3)
| ~ v4_rlvect_1(X3)
| ~ v3_rlvect_1(X3)
| ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ v3_vectsp_2(X2,X1)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v3_rlvect_1(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)
| X3 = X2
| v3_struct_0(X3)
| v3_struct_0(X2)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_40,plain,
( ~ 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)
| ~ m1_rmod_2(X1,X2,X3)
| v3_struct_0(X3)
| v3_struct_0(X2)
| v3_rlvect_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_41,plain,
( ~ 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)
| ~ m1_rmod_2(X1,X2,X3)
| v3_struct_0(X3)
| v3_struct_0(X2)
| v4_rlvect_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_42,plain,
( ~ 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)
| ~ m1_rmod_2(X1,X2,X3)
| v3_struct_0(X3)
| v3_struct_0(X2)
| v5_rlvect_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_43,plain,
( ~ 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)
| ~ m1_rmod_2(X1,X2,X3)
| v3_struct_0(X3)
| v3_struct_0(X2)
| v6_rlvect_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_44,plain,
( ~ 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)
| ~ m1_rmod_2(X1,X2,X3)
| v3_struct_0(X3)
| v3_struct_0(X2)
| v5_vectsp_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_45,plain,
( ~ 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)
| ~ m1_rmod_2(X1,X2,X3)
| v3_struct_0(X3)
| v3_struct_0(X2)
| l1_vectsp_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_46,plain,
( ~ 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)
| ~ m1_rmod_2(X1,X2,X3)
| ~ v3_struct_0(X1)
| v3_struct_0(X3)
| v3_struct_0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_47,negated_conjecture,
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(esk2_0)))
| ~ r1_tarski(esk3_0,X1)
| m1_rmod_2(esk2_0,esk1_0,k1_rmod_5(esk1_0,esk2_0,X1)) ),
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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18]),c_0_19]),c_0_20]),c_0_21]),c_0_22]),c_0_23]),c_0_24]),c_0_25]),c_0_26]),c_0_27]),c_0_28]),c_0_29]),c_0_30]),c_0_31]),c_0_32]),c_0_33]),c_0_34])]),c_0_35]),c_0_36]),c_0_37]) ).
cnf(c_0_48,negated_conjecture,
m1_subset_1(esk4_0,k1_zfmisc_1(u1_struct_0(esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_49,negated_conjecture,
r1_tarski(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_50,plain,
! [X15,X16,X17] :
( ( ~ m1_subset_1(X17,k1_zfmisc_1(u1_struct_0(X16)))
| ~ l1_vectsp_2(X16,X15)
| ~ v5_vectsp_2(X16,X15)
| ~ v6_rlvect_1(X16)
| ~ v5_rlvect_1(X16)
| ~ v4_rlvect_1(X16)
| ~ v3_rlvect_1(X16)
| v3_struct_0(X16)
| ~ l3_vectsp_1(X15)
| ~ v2_vectsp_2(X15)
| v10_vectsp_1(X15)
| ~ v8_vectsp_1(X15)
| ~ v7_vectsp_1(X15)
| ~ v6_vectsp_1(X15)
| ~ v7_group_1(X15)
| ~ v4_group_1(X15)
| ~ v6_rlvect_1(X15)
| ~ v5_rlvect_1(X15)
| ~ v4_rlvect_1(X15)
| ~ v3_rlvect_1(X15)
| v3_struct_0(X15)
| m1_rmod_2(k1_rmod_5(X15,X16,X17),X15,X16) )
& ( ~ m1_subset_1(X17,k1_zfmisc_1(u1_struct_0(X16)))
| ~ l1_vectsp_2(X16,X15)
| ~ v5_vectsp_2(X16,X15)
| ~ v6_rlvect_1(X16)
| ~ v5_rlvect_1(X16)
| ~ v4_rlvect_1(X16)
| ~ v3_rlvect_1(X16)
| v3_struct_0(X16)
| ~ l3_vectsp_1(X15)
| ~ v2_vectsp_2(X15)
| v10_vectsp_1(X15)
| ~ v8_vectsp_1(X15)
| ~ v7_vectsp_1(X15)
| ~ v6_vectsp_1(X15)
| ~ v7_group_1(X15)
| ~ v4_group_1(X15)
| ~ v6_rlvect_1(X15)
| ~ v5_rlvect_1(X15)
| ~ v4_rlvect_1(X15)
| ~ v3_rlvect_1(X15)
| v3_struct_0(X15)
| v3_vectsp_2(k1_rmod_5(X15,X16,X17),X15) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])])]) ).
fof(c_0_51,plain,
! [X23,X24] :
( ( m1_subset_1(X23,k1_zfmisc_1(X24))
| ~ r1_tarski(X23,X24) )
& ( r1_tarski(X23,X24)
| ~ m1_subset_1(X23,k1_zfmisc_1(X24)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])]) ).
cnf(c_0_52,plain,
( ~ v3_rlvect_1(X3)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X3)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X3)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X3)
| ~ v6_rlvect_1(X2)
| ~ v4_group_1(X3)
| ~ v6_vectsp_1(X3)
| ~ v7_vectsp_1(X3)
| ~ v8_vectsp_1(X3)
| ~ l3_vectsp_1(X3)
| ~ v3_vectsp_2(X1,X3)
| ~ v3_vectsp_2(X2,X3)
| ~ v5_vectsp_2(X2,X3)
| ~ l1_vectsp_2(X2,X3)
| ~ m1_rmod_2(X1,X3,X2)
| ~ m1_rmod_2(X2,X3,X1)
| v3_struct_0(X2)
| v3_struct_0(X3)
| X1 = X2 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[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]) ).
cnf(c_0_53,negated_conjecture,
m1_rmod_2(esk2_0,esk1_0,k1_rmod_5(esk1_0,esk2_0,esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49])]) ).
cnf(c_0_54,negated_conjecture,
v3_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_55,negated_conjecture,
k1_rmod_5(esk1_0,esk2_0,esk4_0) != esk2_0,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_56,plain,
( ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
| ~ 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)
| ~ 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)
| v3_struct_0(X2)
| v10_vectsp_1(X1)
| v3_struct_0(X1)
| v3_vectsp_2(k1_rmod_5(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_57,plain,
( ~ r1_tarski(X1,X2)
| m1_subset_1(X1,k1_zfmisc_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_58,plain,
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| r1_tarski(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_59,negated_conjecture,
( ~ v3_vectsp_2(k1_rmod_5(esk1_0,esk2_0,esk4_0),esk1_0)
| ~ m1_rmod_2(k1_rmod_5(esk1_0,esk2_0,esk4_0),esk1_0,esk2_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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_18]),c_0_19]),c_0_54]),c_0_20]),c_0_22]),c_0_23]),c_0_24]),c_0_26]),c_0_27]),c_0_28]),c_0_29]),c_0_30]),c_0_31]),c_0_32]),c_0_33]),c_0_34])]),c_0_55]),c_0_36]),c_0_37]) ).
cnf(c_0_60,plain,
( ~ v3_rlvect_1(X1)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X1)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X1)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X1)
| ~ v6_rlvect_1(X2)
| ~ 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)
| ~ v5_vectsp_2(X2,X1)
| ~ l1_vectsp_2(X2,X1)
| ~ r1_tarski(X3,u1_struct_0(X2))
| v3_struct_0(X1)
| v3_struct_0(X2)
| v10_vectsp_1(X1)
| v3_vectsp_2(k1_rmod_5(X1,X2,X3),X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_61,negated_conjecture,
r1_tarski(esk4_0,u1_struct_0(esk2_0)),
inference(spm,[status(thm)],[c_0_58,c_0_48]) ).
cnf(c_0_62,plain,
( ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
| ~ 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)
| ~ 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)
| v3_struct_0(X2)
| v10_vectsp_1(X1)
| v3_struct_0(X1)
| m1_rmod_2(k1_rmod_5(X1,X2,X3),X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_63,negated_conjecture,
~ m1_rmod_2(k1_rmod_5(esk1_0,esk2_0,esk4_0),esk1_0,esk2_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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]),c_0_18]),c_0_19]),c_0_20]),c_0_21]),c_0_22]),c_0_23]),c_0_24]),c_0_25]),c_0_26]),c_0_27]),c_0_28]),c_0_29]),c_0_30]),c_0_31]),c_0_32]),c_0_33]),c_0_34])]),c_0_35]),c_0_37]),c_0_36]) ).
cnf(c_0_64,negated_conjecture,
( ~ 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)
| ~ v5_vectsp_2(esk2_0,X1)
| ~ l1_vectsp_2(esk2_0,X1)
| v3_struct_0(X1)
| v10_vectsp_1(X1)
| m1_rmod_2(k1_rmod_5(X1,esk2_0,esk4_0),X1,esk2_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_62,c_0_48]),c_0_27]),c_0_29]),c_0_31]),c_0_33])]),c_0_37]) ).
cnf(c_0_65,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(spm,[status(thm)],[c_0_63,c_0_64]),c_0_18]),c_0_19]),c_0_20]),c_0_21]),c_0_22]),c_0_23]),c_0_24]),c_0_25]),c_0_26]),c_0_28]),c_0_30]),c_0_32]),c_0_34])]),c_0_35]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG220+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.59 % Computer : n007.cluster.edu
% 0.11/0.59 % Model : x86_64 x86_64
% 0.11/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.59 % Memory : 8046.5625MB
% 0.11/0.59 % OS : Linux 6.8.0-71-generic
% 0.11/0.59 % CPULimit : 300
% 0.11/0.59 % WCLimit : 300
% 0.11/0.59 % DateTime : Mon Sep 21 13:02:52 UTC 2026
% 0.11/0.59 % CPUTime :
% 0.11/0.59 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.63 Running first-order theorem proving
% 0.16/0.63 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.69 % Version: 3.5.1
% 0.16/0.69 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/0.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.69 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/0.69 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.69 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.69 % Starting sh5l with 300s (1) cores
% 0.16/0.69 % new_bool_1 with pid 1142246 completed with status 0
% 0.16/0.69 % Result found by new_bool_1
% 0.16/0.69 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/0.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.69 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/0.69 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.69 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.69 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/0.69 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.69 % Search class: FGHSM-FSMM31-SFFFFFNN
% 0.16/0.69 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.69 % Starting SubtermCWHack with 31s (1) cores
% 0.16/0.69 % SubtermCWHack with pid 1142251 completed with status 0
% 0.16/0.69 % Result found by SubtermCWHack
% 0.16/0.69 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/0.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.69 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/0.69 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.69 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.69 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/0.69 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.69 % Search class: FGHSM-FSMM31-SFFFFFNN
% 0.16/0.69 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.69 % Starting SubtermCWHack with 31s (1) cores
% 0.16/0.69 % Preprocessing time : 0.003 s
% 0.16/0.69
% 0.16/0.69 % Proof found!
% 0.16/0.69 % SZS status Theorem
% 0.16/0.69 % SZS output start CNFRefutation
% See solution above
% 0.16/0.69 % Parsed axioms : 69
% 0.16/0.69 % Removed by relevancy pruning/SinE : 43
% 0.16/0.69 % Initial clauses : 85
% 0.16/0.69 % Removed in clause preprocessing : 0
% 0.16/0.69 % Initial clauses in saturation : 85
% 0.16/0.69 % Processed clauses : 178
% 0.16/0.69 % ...of these trivial : 0
% 0.16/0.69 % ...subsumed : 10
% 0.16/0.69 % ...remaining for further processing : 168
% 0.16/0.69 % Other redundant clauses eliminated : 0
% 0.16/0.69 % Clauses deleted for lack of memory : 0
% 0.16/0.69 % Backward-subsumed : 1
% 0.16/0.69 % Backward-rewritten : 2
% 0.16/0.69 % Generated clauses : 172
% 0.16/0.69 % ...of the previous two non-redundant : 139
% 0.16/0.69 % ...aggressively subsumed : 0
% 0.16/0.69 % Contextual simplify-reflections : 7
% 0.16/0.69 % Paramodulations : 172
% 0.16/0.69 % Factorizations : 0
% 0.16/0.69 % NegExts : 0
% 0.16/0.69 % Equation resolutions : 0
% 0.16/0.69 % Disequality decompositions : 0
% 0.16/0.69 % Total rewrite steps : 1095
% 0.16/0.69 % ...of those cached : 1060
% 0.16/0.69 % Propositional unsat checks : 0
% 0.16/0.69 % Propositional check models : 0
% 0.16/0.69 % Propositional check unsatisfiable : 0
% 0.16/0.69 % Propositional clauses : 0
% 0.16/0.69 % Propositional clauses after purity: 0
% 0.16/0.69 % Propositional unsat core size : 0
% 0.16/0.69 % Propositional preprocessing time : 0.000
% 0.16/0.69 % Propositional encoding time : 0.000
% 0.16/0.69 % Propositional solver time : 0.000
% 0.16/0.69 % Success case prop preproc time : 0.000
% 0.16/0.69 % Success case prop encoding time : 0.000
% 0.16/0.69 % Success case prop solver time : 0.000
% 0.16/0.69 % Current number of processed clauses : 165
% 0.16/0.69 % Positive orientable unit clauses : 43
% 0.16/0.69 % Positive unorientable unit clauses: 0
% 0.16/0.69 % Negative unit clauses : 9
% 0.16/0.69 % Non-unit-clauses : 113
% 0.16/0.69 % Current number of unprocessed clauses: 45
% 0.16/0.69 % ...number of literals in the above : 843
% 0.16/0.69 % Current number of archived formulas : 0
% 0.16/0.69 % Current number of archived clauses : 3
% 0.16/0.69 % Clause-clause subsumption calls (NU) : 18862
% 0.16/0.69 % Rec. Clause-clause subsumption calls : 520
% 0.16/0.69 % Non-unit clause-clause subsumptions : 15
% 0.16/0.69 % Unit Clause-clause subsumption calls : 43
% 0.16/0.69 % Rewrite failures with RHS unbound : 0
% 0.16/0.69 % BW rewrite match attempts : 5
% 0.16/0.69 % BW rewrite match successes : 1
% 0.16/0.69 % Condensation attempts : 0
% 0.16/0.69 % Condensation successes : 0
% 0.16/0.69 % Termbank termtop insertions : 22470
% 0.16/0.69 % Search garbage collected termcells : 1952
% 0.16/0.69
% 0.16/0.69 % -------------------------------------------------
% 0.16/0.69 % User time : 0.035 s
% 0.16/0.69 % System time : 0.004 s
% 0.16/0.69 % Total time : 0.038 s
% 0.16/0.69 % Maximum resident set size: 3972 pages
% 0.16/0.69
% 0.16/0.69 % -------------------------------------------------
% 0.16/0.69 % User time : 0.038 s
% 0.16/0.69 % System time : 0.008 s
% 0.16/0.69 % Total time : 0.046 s
% 0.16/0.69 % Maximum resident set size: 4608 pages
% 0.16/0.69 % E exiting
%------------------------------------------------------------------------------