%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG219+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 : n002.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 11:55:38 AM UTC 2026
% Result : Theorem 0.16s 0.68s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 88 ( 44 unt; 0 def)
% Number of atoms : 811 ( 41 equ)
% Maximal formula atoms : 133 ( 9 avg)
% Number of connectives : 1158 ( 435 ~; 447 |; 238 &)
% ( 1 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-5 aty)
% Number of variables : 103 ( 1 sgn 59 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t14_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)))
=> ( X3 = u1_struct_0(X2)
=> ( k1_rmod_5(X1,X2,X3) = X2
| k1_rlvect_1(X1) = k2_group_1(X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_rmod_5) ).
fof(dt_l3_vectsp_1,axiom,
! [X1] :
( l3_vectsp_1(X1)
=> ( l2_vectsp_1(X1)
& l1_rlvect_1(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_vectsp_1) ).
fof(dt_l1_rlvect_1,axiom,
! [X1] :
( l1_rlvect_1(X1)
=> l2_struct_0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_rlvect_1) ).
fof(dt_k2_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) )
=> ( m1_rmod_2(k2_rmod_2(X1,X2),X1,X2)
& v3_vectsp_2(k2_rmod_2(X1,X2),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_rmod_2) ).
fof(dt_l2_struct_0,axiom,
! [X1] :
( l2_struct_0(X1)
=> l1_struct_0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_struct_0) ).
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(d4_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)
& v6_rlvect_1(X2)
& v5_rlvect_1(X2)
& v4_rlvect_1(X2)
& v3_rlvect_1(X2)
& ~ 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)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_rmod_2) ).
fof(abstractness_v3_vectsp_2,axiom,
! [X1,X2] :
( ( l1_vectsp_2(X2,X1)
& l1_struct_0(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/sandbox2/benchmark/theBenchmark.p',abstractness_v3_vectsp_2) ).
fof(t13_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_rmod_2(X4,X1,X2)
& v3_vectsp_2(X4,X1) )
=> ( X3 = u1_struct_0(X4)
=> ( k1_rmod_5(X1,X2,X3) = X4
| k1_rlvect_1(X1) = k2_group_1(X1) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_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(reflexivity_r1_tarski,axiom,
! [X1,X2] : r1_tarski(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(c_0_11,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)))
=> ( X3 = u1_struct_0(X2)
=> ( k1_rmod_5(X1,X2,X3) = X2
| k1_rlvect_1(X1) = k2_group_1(X1) ) ) ) ) ),
inference(assume_negation,[status(cth)],[t14_rmod_5]) ).
fof(c_0_12,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)))
=> ( X3 = u1_struct_0(X2)
=> ( k1_rmod_5(X1,X2,X3) = X2
| k1_rlvect_1(X1) = k2_group_1(X1) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_13,plain,
! [X44] :
( ( ~ l3_vectsp_1(X44)
| l2_vectsp_1(X44) )
& ( ~ l3_vectsp_1(X44)
| l1_rlvect_1(X44) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_vectsp_1])])])]) ).
fof(c_0_14,negated_conjecture,
( k1_rmod_5(esk1_0,esk2_0,esk3_0) != esk2_0
& k1_rlvect_1(esk1_0) != k2_group_1(esk1_0)
& esk3_0 = 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_12])])])]) ).
fof(c_0_15,plain,
! [X38] :
( l2_struct_0(X38)
| ~ l1_rlvect_1(X38) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_rlvect_1])])]) ).
cnf(c_0_16,plain,
( ~ l3_vectsp_1(X1)
| l1_rlvect_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
l3_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_18,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) )
=> ( m1_rmod_2(k2_rmod_2(X1,X2),X1,X2)
& v3_vectsp_2(k2_rmod_2(X1,X2),X1) ) ),
inference(fof_simplification,[status(thm)],[dt_k2_rmod_2]) ).
fof(c_0_19,plain,
! [X42] :
( l1_struct_0(X42)
| ~ l2_struct_0(X42) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_struct_0])])]) ).
cnf(c_0_20,plain,
( ~ l1_rlvect_1(X1)
| l2_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
l1_rlvect_1(esk1_0),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_22,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_23,plain,
! [X35,X36] :
( ( ~ l1_vectsp_2(X36,X35)
| ~ v5_vectsp_2(X36,X35)
| ~ v6_rlvect_1(X36)
| ~ v5_rlvect_1(X36)
| ~ v4_rlvect_1(X36)
| ~ v3_rlvect_1(X36)
| v3_struct_0(X36)
| ~ l3_vectsp_1(X35)
| ~ v8_vectsp_1(X35)
| ~ v7_vectsp_1(X35)
| ~ v6_vectsp_1(X35)
| ~ v4_group_1(X35)
| ~ v6_rlvect_1(X35)
| ~ v5_rlvect_1(X35)
| ~ v4_rlvect_1(X35)
| ~ v3_rlvect_1(X35)
| v3_struct_0(X35)
| m1_rmod_2(k2_rmod_2(X35,X36),X35,X36) )
& ( ~ l1_vectsp_2(X36,X35)
| ~ v5_vectsp_2(X36,X35)
| ~ v6_rlvect_1(X36)
| ~ v5_rlvect_1(X36)
| ~ v4_rlvect_1(X36)
| ~ v3_rlvect_1(X36)
| v3_struct_0(X36)
| ~ l3_vectsp_1(X35)
| ~ v8_vectsp_1(X35)
| ~ v7_vectsp_1(X35)
| ~ v6_vectsp_1(X35)
| ~ v4_group_1(X35)
| ~ v6_rlvect_1(X35)
| ~ v5_rlvect_1(X35)
| ~ v4_rlvect_1(X35)
| ~ v3_rlvect_1(X35)
| v3_struct_0(X35)
| v3_vectsp_2(k2_rmod_2(X35,X36),X35) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])]) ).
fof(c_0_24,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)
& v6_rlvect_1(X2)
& v5_rlvect_1(X2)
& v4_rlvect_1(X2)
& v3_rlvect_1(X2)
& ~ 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)) ) ),
inference(fof_simplification,[status(thm)],[d4_rmod_2]) ).
fof(c_0_25,plain,
! [X14,X15] :
( X15 = g1_vectsp_2(X14,u1_struct_0(X15),u1_rlvect_1(X15),u2_struct_0(X15),u1_vectsp_2(X14,X15))
| ~ v3_vectsp_2(X15,X14)
| ~ l1_vectsp_2(X15,X14)
| ~ l1_struct_0(X14) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[abstractness_v3_vectsp_2])])]) ).
cnf(c_0_26,plain,
( ~ l2_struct_0(X1)
| l1_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,negated_conjecture,
l2_struct_0(esk1_0),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_28,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_rmod_2(X4,X1,X2)
& v3_vectsp_2(X4,X1) )
=> ( X3 = u1_struct_0(X4)
=> ( k1_rmod_5(X1,X2,X3) = X4
| k1_rlvect_1(X1) = k2_group_1(X1) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[t13_rmod_5]) ).
fof(c_0_29,plain,
! [X45,X46,X47] :
( ( ~ l1_vectsp_2(X46,X45)
| ~ v5_vectsp_2(X46,X45)
| ~ v6_rlvect_1(X46)
| ~ v5_rlvect_1(X46)
| ~ v4_rlvect_1(X46)
| ~ v3_rlvect_1(X46)
| v3_struct_0(X46)
| ~ l3_vectsp_1(X45)
| ~ v8_vectsp_1(X45)
| ~ v7_vectsp_1(X45)
| ~ v6_vectsp_1(X45)
| ~ v4_group_1(X45)
| ~ v6_rlvect_1(X45)
| ~ v5_rlvect_1(X45)
| ~ v4_rlvect_1(X45)
| ~ v3_rlvect_1(X45)
| v3_struct_0(X45)
| ~ m1_rmod_2(X47,X45,X46)
| l1_vectsp_2(X47,X45) )
& ( ~ l1_vectsp_2(X46,X45)
| ~ v5_vectsp_2(X46,X45)
| ~ v6_rlvect_1(X46)
| ~ v5_rlvect_1(X46)
| ~ v4_rlvect_1(X46)
| ~ v3_rlvect_1(X46)
| v3_struct_0(X46)
| ~ l3_vectsp_1(X45)
| ~ v8_vectsp_1(X45)
| ~ v7_vectsp_1(X45)
| ~ v6_vectsp_1(X45)
| ~ v4_group_1(X45)
| ~ v6_rlvect_1(X45)
| ~ v5_rlvect_1(X45)
| ~ v4_rlvect_1(X45)
| ~ v3_rlvect_1(X45)
| v3_struct_0(X45)
| ~ m1_rmod_2(X47,X45,X46)
| v5_vectsp_2(X47,X45) )
& ( ~ l1_vectsp_2(X46,X45)
| ~ v5_vectsp_2(X46,X45)
| ~ v6_rlvect_1(X46)
| ~ v5_rlvect_1(X46)
| ~ v4_rlvect_1(X46)
| ~ v3_rlvect_1(X46)
| v3_struct_0(X46)
| ~ l3_vectsp_1(X45)
| ~ v8_vectsp_1(X45)
| ~ v7_vectsp_1(X45)
| ~ v6_vectsp_1(X45)
| ~ v4_group_1(X45)
| ~ v6_rlvect_1(X45)
| ~ v5_rlvect_1(X45)
| ~ v4_rlvect_1(X45)
| ~ v3_rlvect_1(X45)
| v3_struct_0(X45)
| ~ m1_rmod_2(X47,X45,X46)
| v6_rlvect_1(X47) )
& ( ~ l1_vectsp_2(X46,X45)
| ~ v5_vectsp_2(X46,X45)
| ~ v6_rlvect_1(X46)
| ~ v5_rlvect_1(X46)
| ~ v4_rlvect_1(X46)
| ~ v3_rlvect_1(X46)
| v3_struct_0(X46)
| ~ l3_vectsp_1(X45)
| ~ v8_vectsp_1(X45)
| ~ v7_vectsp_1(X45)
| ~ v6_vectsp_1(X45)
| ~ v4_group_1(X45)
| ~ v6_rlvect_1(X45)
| ~ v5_rlvect_1(X45)
| ~ v4_rlvect_1(X45)
| ~ v3_rlvect_1(X45)
| v3_struct_0(X45)
| ~ m1_rmod_2(X47,X45,X46)
| v5_rlvect_1(X47) )
& ( ~ l1_vectsp_2(X46,X45)
| ~ v5_vectsp_2(X46,X45)
| ~ v6_rlvect_1(X46)
| ~ v5_rlvect_1(X46)
| ~ v4_rlvect_1(X46)
| ~ v3_rlvect_1(X46)
| v3_struct_0(X46)
| ~ l3_vectsp_1(X45)
| ~ v8_vectsp_1(X45)
| ~ v7_vectsp_1(X45)
| ~ v6_vectsp_1(X45)
| ~ v4_group_1(X45)
| ~ v6_rlvect_1(X45)
| ~ v5_rlvect_1(X45)
| ~ v4_rlvect_1(X45)
| ~ v3_rlvect_1(X45)
| v3_struct_0(X45)
| ~ m1_rmod_2(X47,X45,X46)
| v4_rlvect_1(X47) )
& ( ~ l1_vectsp_2(X46,X45)
| ~ v5_vectsp_2(X46,X45)
| ~ v6_rlvect_1(X46)
| ~ v5_rlvect_1(X46)
| ~ v4_rlvect_1(X46)
| ~ v3_rlvect_1(X46)
| v3_struct_0(X46)
| ~ l3_vectsp_1(X45)
| ~ v8_vectsp_1(X45)
| ~ v7_vectsp_1(X45)
| ~ v6_vectsp_1(X45)
| ~ v4_group_1(X45)
| ~ v6_rlvect_1(X45)
| ~ v5_rlvect_1(X45)
| ~ v4_rlvect_1(X45)
| ~ v3_rlvect_1(X45)
| v3_struct_0(X45)
| ~ m1_rmod_2(X47,X45,X46)
| v3_rlvect_1(X47) )
& ( ~ l1_vectsp_2(X46,X45)
| ~ v5_vectsp_2(X46,X45)
| ~ v6_rlvect_1(X46)
| ~ v5_rlvect_1(X46)
| ~ v4_rlvect_1(X46)
| ~ v3_rlvect_1(X46)
| v3_struct_0(X46)
| ~ l3_vectsp_1(X45)
| ~ v8_vectsp_1(X45)
| ~ v7_vectsp_1(X45)
| ~ v6_vectsp_1(X45)
| ~ v4_group_1(X45)
| ~ v6_rlvect_1(X45)
| ~ v5_rlvect_1(X45)
| ~ v4_rlvect_1(X45)
| ~ v3_rlvect_1(X45)
| v3_struct_0(X45)
| ~ m1_rmod_2(X47,X45,X46)
| ~ v3_struct_0(X47) ) ),
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_22])])])])]) ).
cnf(c_0_30,plain,
( ~ 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)
| ~ 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(X2)
| v3_struct_0(X1)
| m1_rmod_2(k2_rmod_2(X1,X2),X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,negated_conjecture,
v5_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_32,negated_conjecture,
l1_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_33,negated_conjecture,
v8_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_34,negated_conjecture,
v7_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_35,negated_conjecture,
v6_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_36,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_37,negated_conjecture,
v6_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_38,negated_conjecture,
v6_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_39,negated_conjecture,
v5_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_40,negated_conjecture,
v5_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_41,negated_conjecture,
v4_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_42,negated_conjecture,
v4_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_43,negated_conjecture,
v3_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_44,negated_conjecture,
v3_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_45,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_46,negated_conjecture,
~ v3_struct_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_47,plain,
! [X23,X24] :
( 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))
| ~ l1_vectsp_2(X24,X23)
| ~ v5_vectsp_2(X24,X23)
| ~ v6_rlvect_1(X24)
| ~ v5_rlvect_1(X24)
| ~ v4_rlvect_1(X24)
| ~ v3_rlvect_1(X24)
| v3_struct_0(X24)
| ~ l3_vectsp_1(X23)
| ~ v8_vectsp_1(X23)
| ~ v7_vectsp_1(X23)
| ~ v6_vectsp_1(X23)
| ~ v4_group_1(X23)
| ~ v6_rlvect_1(X23)
| ~ v5_rlvect_1(X23)
| ~ v4_rlvect_1(X23)
| ~ v3_rlvect_1(X23)
| v3_struct_0(X23) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])]) ).
cnf(c_0_48,plain,
( ~ v3_vectsp_2(X2,X1)
| ~ l1_vectsp_2(X2,X1)
| ~ l1_struct_0(X1)
| X2 = g1_vectsp_2(X1,u1_struct_0(X2),u1_rlvect_1(X2),u2_struct_0(X2),u1_vectsp_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_49,negated_conjecture,
v3_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_50,negated_conjecture,
esk3_0 = u1_struct_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_51,negated_conjecture,
l1_struct_0(esk1_0),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_52,plain,
! [X119,X120,X121,X122] :
( k1_rmod_5(X119,X120,X121) = X122
| k1_rlvect_1(X119) = k2_group_1(X119)
| X121 != u1_struct_0(X122)
| ~ m1_rmod_2(X122,X119,X120)
| ~ v3_vectsp_2(X122,X119)
| ~ m1_subset_1(X121,k1_zfmisc_1(u1_struct_0(X120)))
| ~ l1_vectsp_2(X120,X119)
| ~ v5_vectsp_2(X120,X119)
| ~ v6_rlvect_1(X120)
| ~ v5_rlvect_1(X120)
| ~ v4_rlvect_1(X120)
| ~ v3_rlvect_1(X120)
| v3_struct_0(X120)
| ~ l3_vectsp_1(X119)
| ~ v2_vectsp_2(X119)
| v10_vectsp_1(X119)
| ~ v8_vectsp_1(X119)
| ~ v7_vectsp_1(X119)
| ~ v6_vectsp_1(X119)
| ~ v7_group_1(X119)
| ~ v4_group_1(X119)
| ~ v6_rlvect_1(X119)
| ~ v5_rlvect_1(X119)
| ~ v4_rlvect_1(X119)
| ~ v3_rlvect_1(X119)
| v3_struct_0(X119) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])])]) ).
cnf(c_0_53,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_29]) ).
cnf(c_0_54,negated_conjecture,
m1_rmod_2(k2_rmod_2(esk1_0,esk2_0),esk1_0,esk2_0),
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_30,c_0_31]),c_0_32]),c_0_17]),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]) ).
cnf(c_0_55,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_29]) ).
cnf(c_0_56,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_29]) ).
cnf(c_0_57,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_29]) ).
cnf(c_0_58,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_29]) ).
cnf(c_0_59,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_29]) ).
cnf(c_0_60,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_29]) ).
cnf(c_0_61,plain,
( ~ 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)
| ~ 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)
| 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_struct_0(X2)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_62,negated_conjecture,
g1_vectsp_2(esk1_0,esk3_0,u1_rlvect_1(esk2_0),u2_struct_0(esk2_0),u1_vectsp_2(esk1_0,esk2_0)) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_32])]),c_0_51])]) ).
cnf(c_0_63,plain,
( X3 != u1_struct_0(X4)
| ~ m1_rmod_2(X4,X1,X2)
| ~ v3_vectsp_2(X4,X1)
| ~ 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)
| k1_rmod_5(X1,X2,X3) = X4
| k1_rlvect_1(X1) = k2_group_1(X1)
| v3_struct_0(X2)
| v10_vectsp_1(X1)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_64,plain,
( ~ 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)
| ~ 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(X2)
| v3_struct_0(X1)
| v3_vectsp_2(k2_rmod_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_65,negated_conjecture,
v5_vectsp_2(k2_rmod_2(esk1_0,esk2_0),esk1_0),
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_53,c_0_54]),c_0_32]),c_0_31]),c_0_17]),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]) ).
cnf(c_0_66,negated_conjecture,
v6_rlvect_1(k2_rmod_2(esk1_0,esk2_0)),
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_55,c_0_54]),c_0_32]),c_0_31]),c_0_17]),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]) ).
cnf(c_0_67,negated_conjecture,
v5_rlvect_1(k2_rmod_2(esk1_0,esk2_0)),
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_56,c_0_54]),c_0_32]),c_0_31]),c_0_17]),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]) ).
cnf(c_0_68,negated_conjecture,
v4_rlvect_1(k2_rmod_2(esk1_0,esk2_0)),
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_57,c_0_54]),c_0_32]),c_0_31]),c_0_17]),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]) ).
cnf(c_0_69,negated_conjecture,
v3_rlvect_1(k2_rmod_2(esk1_0,esk2_0)),
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_58,c_0_54]),c_0_32]),c_0_31]),c_0_17]),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]) ).
cnf(c_0_70,negated_conjecture,
~ v3_struct_0(k2_rmod_2(esk1_0,esk2_0)),
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_59,c_0_54]),c_0_32]),c_0_31]),c_0_17]),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]) ).
cnf(c_0_71,negated_conjecture,
l1_vectsp_2(k2_rmod_2(esk1_0,esk2_0),esk1_0),
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_60,c_0_54]),c_0_32]),c_0_31]),c_0_17]),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]) ).
cnf(c_0_72,negated_conjecture,
k2_rmod_2(esk1_0,esk2_0) = esk2_0,
inference(rw,[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(spm,[status(thm)],[c_0_61,c_0_31]),c_0_50]),c_0_32]),c_0_17]),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_62]) ).
fof(c_0_73,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(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])]) ).
fof(c_0_74,plain,
! [X118] : r1_tarski(X118,X118),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_75,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)
| ~ v3_vectsp_2(X3,X1)
| ~ v5_vectsp_2(esk2_0,X1)
| ~ l1_vectsp_2(esk2_0,X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(esk3_0))
| ~ m1_rmod_2(X3,X1,esk2_0)
| X2 != u1_struct_0(X3)
| v3_struct_0(X1)
| v10_vectsp_1(X1)
| k2_group_1(X1) = k1_rlvect_1(X1)
| k1_rmod_5(X1,esk2_0,X2) = X3 ),
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_63,c_0_50]),c_0_37]),c_0_39]),c_0_41]),c_0_43])]),c_0_46]) ).
cnf(c_0_76,negated_conjecture,
v3_vectsp_2(k2_rmod_2(esk1_0,k2_rmod_2(esk1_0,esk2_0)),esk1_0),
inference(cn,[status(thm)],[inference(rw,[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(spm,[status(thm)],[c_0_64,c_0_65]),c_0_17]),c_0_33]),c_0_34]),c_0_35]),c_0_36]),c_0_66]),c_0_38]),c_0_67]),c_0_40]),c_0_68]),c_0_42]),c_0_69]),c_0_44])]),c_0_45]),c_0_70]),c_0_71])]) ).
cnf(c_0_77,negated_conjecture,
m1_rmod_2(esk2_0,esk1_0,esk2_0),
inference(rw,[status(thm)],[c_0_54,c_0_72]) ).
cnf(c_0_78,negated_conjecture,
v2_vectsp_2(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_79,negated_conjecture,
v7_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_80,negated_conjecture,
k1_rlvect_1(esk1_0) != k2_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_81,negated_conjecture,
~ v10_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_82,plain,
( ~ r1_tarski(X1,X2)
| m1_subset_1(X1,k1_zfmisc_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_83,plain,
r1_tarski(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_84,negated_conjecture,
( ~ m1_subset_1(X1,k1_zfmisc_1(esk3_0))
| X1 != esk3_0
| k1_rmod_5(esk1_0,esk2_0,X1) = 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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_72]),c_0_72]),c_0_72]),c_0_72]),c_0_50]),c_0_72]),c_0_72]),c_0_77]),c_0_32]),c_0_31]),c_0_17]),c_0_78]),c_0_33]),c_0_34]),c_0_35]),c_0_79]),c_0_36]),c_0_38]),c_0_40]),c_0_42]),c_0_44])]),c_0_80]),c_0_81]),c_0_45]) ).
cnf(c_0_85,plain,
m1_subset_1(X1,k1_zfmisc_1(X1)),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_86,negated_conjecture,
k1_rmod_5(esk1_0,esk2_0,esk3_0) != esk2_0,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_87,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG219+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.50 % Computer : n002.cluster.edu
% 0.10/0.50 % Model : x86_64 x86_64
% 0.10/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.50 % Memory : 8046.5625MB
% 0.10/0.50 % OS : Linux 6.8.0-71-generic
% 0.10/0.50 % CPULimit : 300
% 0.10/0.50 % WCLimit : 300
% 0.10/0.50 % DateTime : Mon Sep 21 13:06:22 UTC 2026
% 0.10/0.50 % CPUTime :
% 0.10/0.50 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.55 Running first-order theorem proving
% 0.10/0.55 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
% 0.16/0.68 % Version: 3.5.1
% 0.16/0.68 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/0.68 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.68 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.68 % Starting sh5l with 300s (1) cores
% 0.16/0.68 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 3344495 completed with status 0
% 0.16/0.68 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.16/0.68 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/0.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/0.68 % No SInE strategy applied
% 0.16/0.68 % Search class: FGHSM-FSLM31-SFFFFFNN
% 0.16/0.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.68 % Starting SubtermCWHack with 136s (1) cores
% 0.16/0.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.16/0.68 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_S0e with 136s (1) cores
% 0.16/0.68 % Starting G-E--_208_C18_F1_AE_CS_SP_PI_S0a with 136s (1) cores
% 0.16/0.68 % Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 0.16/0.68 % G-E--_208_C18_F1_AE_CS_SP_PI_S0a with pid 3344512 completed with status 0
% 0.16/0.68 % Result found by G-E--_208_C18_F1_AE_CS_SP_PI_S0a
% 0.16/0.68 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/0.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/0.68 % No SInE strategy applied
% 0.16/0.68 % Search class: FGHSM-FSLM31-SFFFFFNN
% 0.16/0.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.68 % Starting SubtermCWHack with 136s (1) cores
% 0.16/0.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.16/0.68 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_S0e with 136s (1) cores
% 0.16/0.68 % Starting G-E--_208_C18_F1_AE_CS_SP_PI_S0a with 136s (1) cores
% 0.16/0.68 % Preprocessing time : 0.004 s
% 0.16/0.68
% 0.16/0.68 % Proof found!
% 0.16/0.68 % SZS status Theorem
% 0.16/0.68 % SZS output start CNFRefutation
% See solution above
% 0.16/0.68 % Parsed axioms : 72
% 0.16/0.68 % Removed by relevancy pruning/SinE : 0
% 0.16/0.68 % Initial clauses : 151
% 0.16/0.68 % Removed in clause preprocessing : 11
% 0.16/0.68 % Initial clauses in saturation : 140
% 0.16/0.68 % Processed clauses : 870
% 0.16/0.68 % ...of these trivial : 60
% 0.16/0.68 % ...subsumed : 70
% 0.16/0.68 % ...remaining for further processing : 740
% 0.16/0.68 % Other redundant clauses eliminated : 0
% 0.16/0.68 % Clauses deleted for lack of memory : 0
% 0.16/0.68 % Backward-subsumed : 3
% 0.16/0.68 % Backward-rewritten : 27
% 0.16/0.68 % Generated clauses : 2109
% 0.16/0.68 % ...of the previous two non-redundant : 2003
% 0.16/0.68 % ...aggressively subsumed : 0
% 0.16/0.68 % Contextual simplify-reflections : 0
% 0.16/0.68 % Paramodulations : 2099
% 0.16/0.68 % Factorizations : 0
% 0.16/0.68 % NegExts : 0
% 0.16/0.68 % Equation resolutions : 10
% 0.16/0.68 % Disequality decompositions : 0
% 0.16/0.68 % Total rewrite steps : 3006
% 0.16/0.68 % ...of those cached : 2808
% 0.16/0.68 % Propositional unsat checks : 0
% 0.16/0.68 % Propositional check models : 0
% 0.16/0.68 % Propositional check unsatisfiable : 0
% 0.16/0.68 % Propositional clauses : 0
% 0.16/0.68 % Propositional clauses after purity: 0
% 0.16/0.68 % Propositional unsat core size : 0
% 0.16/0.68 % Propositional preprocessing time : 0.000
% 0.16/0.68 % Propositional encoding time : 0.000
% 0.16/0.68 % Propositional solver time : 0.000
% 0.16/0.68 % Success case prop preproc time : 0.000
% 0.16/0.68 % Success case prop encoding time : 0.000
% 0.16/0.68 % Success case prop solver time : 0.000
% 0.16/0.68 % Current number of processed clauses : 710
% 0.16/0.68 % Positive orientable unit clauses : 440
% 0.16/0.68 % Positive unorientable unit clauses: 0
% 0.16/0.68 % Negative unit clauses : 20
% 0.16/0.68 % Non-unit-clauses : 250
% 0.16/0.68 % Current number of unprocessed clauses: 1251
% 0.16/0.68 % ...number of literals in the above : 4379
% 0.16/0.68 % Current number of archived formulas : 0
% 0.16/0.68 % Current number of archived clauses : 30
% 0.16/0.68 % Clause-clause subsumption calls (NU) : 45647
% 0.16/0.68 % Rec. Clause-clause subsumption calls : 5341
% 0.16/0.68 % Non-unit clause-clause subsumptions : 42
% 0.16/0.68 % Unit Clause-clause subsumption calls : 15407
% 0.16/0.68 % Rewrite failures with RHS unbound : 0
% 0.16/0.68 % BW rewrite match attempts : 100
% 0.16/0.68 % BW rewrite match successes : 7
% 0.16/0.68 % Condensation attempts : 0
% 0.16/0.68 % Condensation successes : 0
% 0.16/0.68 % Termbank termtop insertions : 63997
% 0.16/0.68 % Search garbage collected termcells : 2458
% 0.16/0.68
% 0.16/0.68 % -------------------------------------------------
% 0.16/0.68 % User time : 0.104 s
% 0.16/0.68 % System time : 0.010 s
% 0.16/0.68 % Total time : 0.114 s
% 0.16/0.68 % Maximum resident set size: 4232 pages
% 0.16/0.68
% 0.16/0.68 % -------------------------------------------------
% 0.16/0.68 % User time : 0.494 s
% 0.16/0.68 % System time : 0.044 s
% 0.16/0.68 % Total time : 0.537 s
% 0.16/0.68 % Maximum resident set size: 4608 pages
% 0.16/0.68 % E exiting
%------------------------------------------------------------------------------