%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG220+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n010.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 : Fri Sep 25 12:53:51 PM UTC 2026
% Result : Theorem 8.03s 1.81s
% Output : CNFRefutation 8.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 165 ( 58 unt; 0 def)
% Number of atoms : 1862 ( 47 equ)
% Maximal formula atoms : 29 ( 11 avg)
% Number of connectives : 3033 (1336 ~;1461 |; 214 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 12 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 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 : 251 ( 0 sgn 243 !; 8 ?; 162 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( l3_vectsp_1(X0)
& v2_vectsp_2(X0)
& ~ v10_vectsp_1(X0)
& v8_vectsp_1(X0)
& v7_vectsp_1(X0)
& v6_vectsp_1(X0)
& v7_group_1(X0)
& v4_group_1(X0)
& v6_rlvect_1(X0)
& v5_rlvect_1(X0)
& v4_rlvect_1(X0)
& v3_rlvect_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( ( l1_vectsp_2(X1,X0)
& v5_vectsp_2(X1,X0)
& v3_vectsp_2(X1,X0)
& v6_rlvect_1(X1)
& v5_rlvect_1(X1)
& v4_rlvect_1(X1)
& v3_rlvect_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
=> ( ( r1_tarski(X2,X3)
& k1_rmod_5(X0,X1,X2) = X1 )
=> k1_rmod_5(X0,X1,X3) = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_rmod_5) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( l3_vectsp_1(X0)
& v2_vectsp_2(X0)
& ~ v10_vectsp_1(X0)
& v8_vectsp_1(X0)
& v7_vectsp_1(X0)
& v6_vectsp_1(X0)
& v7_group_1(X0)
& v4_group_1(X0)
& v6_rlvect_1(X0)
& v5_rlvect_1(X0)
& v4_rlvect_1(X0)
& v3_rlvect_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( ( l1_vectsp_2(X1,X0)
& v5_vectsp_2(X1,X0)
& v3_vectsp_2(X1,X0)
& v6_rlvect_1(X1)
& v5_rlvect_1(X1)
& v4_rlvect_1(X1)
& v3_rlvect_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
=> ( ( r1_tarski(X2,X3)
& k1_rmod_5(X0,X1,X2) = X1 )
=> k1_rmod_5(X0,X1,X3) = X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f9,axiom,
! [X0,X1,X2] :
( ( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
& l1_vectsp_2(X1,X0)
& v5_vectsp_2(X1,X0)
& v6_rlvect_1(X1)
& v5_rlvect_1(X1)
& v4_rlvect_1(X1)
& v3_rlvect_1(X1)
& ~ v3_struct_0(X1)
& l3_vectsp_1(X0)
& v2_vectsp_2(X0)
& ~ v10_vectsp_1(X0)
& v8_vectsp_1(X0)
& v7_vectsp_1(X0)
& v6_vectsp_1(X0)
& v7_group_1(X0)
& v4_group_1(X0)
& v6_rlvect_1(X0)
& v5_rlvect_1(X0)
& v4_rlvect_1(X0)
& v3_rlvect_1(X0)
& ~ v3_struct_0(X0) )
=> ( m1_rmod_2(k1_rmod_5(X0,X1,X2),X0,X1)
& v3_vectsp_2(k1_rmod_5(X0,X1,X2),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_rmod_5) ).
fof(f22,axiom,
! [X0,X1] :
( ( l1_vectsp_2(X1,X0)
& v5_vectsp_2(X1,X0)
& v6_rlvect_1(X1)
& v5_rlvect_1(X1)
& v4_rlvect_1(X1)
& v3_rlvect_1(X1)
& ~ v3_struct_0(X1)
& l3_vectsp_1(X0)
& v8_vectsp_1(X0)
& v7_vectsp_1(X0)
& v6_vectsp_1(X0)
& v4_group_1(X0)
& v6_rlvect_1(X0)
& v5_rlvect_1(X0)
& v4_rlvect_1(X0)
& v3_rlvect_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X2] :
( m1_rmod_2(X2,X0,X1)
=> ( l1_vectsp_2(X2,X0)
& v5_vectsp_2(X2,X0)
& v6_rlvect_1(X2)
& v5_rlvect_1(X2)
& v4_rlvect_1(X2)
& v3_rlvect_1(X2)
& ~ v3_struct_0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_rmod_2) ).
fof(f61,axiom,
! [X0] :
( ( l3_vectsp_1(X0)
& v2_vectsp_2(X0)
& ~ v10_vectsp_1(X0)
& v8_vectsp_1(X0)
& v7_vectsp_1(X0)
& v6_vectsp_1(X0)
& v7_group_1(X0)
& v4_group_1(X0)
& v6_rlvect_1(X0)
& v5_rlvect_1(X0)
& v4_rlvect_1(X0)
& v3_rlvect_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( ( l1_vectsp_2(X1,X0)
& v5_vectsp_2(X1,X0)
& v6_rlvect_1(X1)
& v5_rlvect_1(X1)
& v4_rlvect_1(X1)
& v3_rlvect_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
=> ( r1_tarski(X2,X3)
=> m1_rmod_2(k1_rmod_5(X0,X1,X2),X0,k1_rmod_5(X0,X1,X3)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_rmod_5) ).
fof(f64,axiom,
! [X0] :
( ( l3_vectsp_1(X0)
& v8_vectsp_1(X0)
& v7_vectsp_1(X0)
& v6_vectsp_1(X0)
& v4_group_1(X0)
& v6_rlvect_1(X0)
& v5_rlvect_1(X0)
& v4_rlvect_1(X0)
& v3_rlvect_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( ( l1_vectsp_2(X1,X0)
& v5_vectsp_2(X1,X0)
& v3_vectsp_2(X1,X0)
& 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,X0)
& v5_vectsp_2(X2,X0)
& v3_vectsp_2(X2,X0)
& v6_rlvect_1(X2)
& v5_rlvect_1(X2)
& v4_rlvect_1(X2)
& v3_rlvect_1(X2)
& ~ v3_struct_0(X2) )
=> ( ( m1_rmod_2(X1,X0,X2)
& m1_rmod_2(X2,X0,X1) )
=> X2 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_rmod_2) ).
fof(f75,plain,
? [X0] :
( l3_vectsp_1(X0)
& v2_vectsp_2(X0)
& ~ v10_vectsp_1(X0)
& v8_vectsp_1(X0)
& v7_vectsp_1(X0)
& v6_vectsp_1(X0)
& v7_group_1(X0)
& v4_group_1(X0)
& v6_rlvect_1(X0)
& v5_rlvect_1(X0)
& v4_rlvect_1(X0)
& v3_rlvect_1(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( l1_vectsp_2(X1,X0)
& v5_vectsp_2(X1,X0)
& v3_vectsp_2(X1,X0)
& v6_rlvect_1(X1)
& v5_rlvect_1(X1)
& v4_rlvect_1(X1)
& v3_rlvect_1(X1)
& ~ v3_struct_0(X1)
& ? [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
& ? [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
& r1_tarski(X2,X3)
& k1_rmod_5(X0,X1,X2) = X1
& k1_rmod_5(X0,X1,X3) != X1 ) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f76,plain,
? [X0] :
( l3_vectsp_1(X0)
& v2_vectsp_2(X0)
& ~ v10_vectsp_1(X0)
& v8_vectsp_1(X0)
& v7_vectsp_1(X0)
& v6_vectsp_1(X0)
& v7_group_1(X0)
& v4_group_1(X0)
& v6_rlvect_1(X0)
& v5_rlvect_1(X0)
& v4_rlvect_1(X0)
& v3_rlvect_1(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( l1_vectsp_2(X1,X0)
& v5_vectsp_2(X1,X0)
& v3_vectsp_2(X1,X0)
& v6_rlvect_1(X1)
& v5_rlvect_1(X1)
& v4_rlvect_1(X1)
& v3_rlvect_1(X1)
& ~ v3_struct_0(X1)
& ? [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
& ? [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
& r1_tarski(X2,X3)
& k1_rmod_5(X0,X1,X2) = X1
& k1_rmod_5(X0,X1,X3) != X1 ) ) ) ),
inference(flattening,[],[f75]) ).
fof(f78,plain,
! [X0] :
( ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v3_vectsp_2(X1,X0)
| ~ 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,X0)
| ~ v5_vectsp_2(X2,X0)
| ~ v3_vectsp_2(X2,X0)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v3_rlvect_1(X2)
| v3_struct_0(X2)
| ~ m1_rmod_2(X1,X0,X2)
| ~ m1_rmod_2(X2,X0,X1)
| X2 = X1 ) ) ),
inference(ennf_transformation,[],[f64]) ).
fof(f79,plain,
! [X0] :
( ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v3_vectsp_2(X1,X0)
| ~ 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,X0)
| ~ v5_vectsp_2(X2,X0)
| ~ v3_vectsp_2(X2,X0)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v3_rlvect_1(X2)
| v3_struct_0(X2)
| ~ m1_rmod_2(X1,X0,X2)
| ~ m1_rmod_2(X2,X0,X1)
| X2 = X1 ) ) ),
inference(flattening,[],[f78]) ).
fof(f94,plain,
! [X0,X1] :
( ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ! [X2] :
( ~ m1_rmod_2(X2,X0,X1)
| ( l1_vectsp_2(X2,X0)
& v5_vectsp_2(X2,X0)
& v6_rlvect_1(X2)
& v5_rlvect_1(X2)
& v4_rlvect_1(X2)
& v3_rlvect_1(X2)
& ~ v3_struct_0(X2) ) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f95,plain,
! [X0,X1] :
( ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ! [X2] :
( ~ m1_rmod_2(X2,X0,X1)
| ( l1_vectsp_2(X2,X0)
& v5_vectsp_2(X2,X0)
& v6_rlvect_1(X2)
& v5_rlvect_1(X2)
& v4_rlvect_1(X2)
& v3_rlvect_1(X2)
& ~ v3_struct_0(X2) ) ) ),
inference(flattening,[],[f94]) ).
fof(f96,plain,
! [X0] :
( ~ l3_vectsp_1(X0)
| ~ v2_vectsp_2(X0)
| v10_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_group_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ! [X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ! [X3] :
( ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
| ~ r1_tarski(X2,X3)
| m1_rmod_2(k1_rmod_5(X0,X1,X2),X0,k1_rmod_5(X0,X1,X3)) ) ) ) ),
inference(ennf_transformation,[],[f61]) ).
fof(f97,plain,
! [X0] :
( ~ l3_vectsp_1(X0)
| ~ v2_vectsp_2(X0)
| v10_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_group_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ! [X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ! [X3] :
( ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
| ~ r1_tarski(X2,X3)
| m1_rmod_2(k1_rmod_5(X0,X1,X2),X0,k1_rmod_5(X0,X1,X3)) ) ) ) ),
inference(flattening,[],[f96]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v2_vectsp_2(X0)
| v10_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_group_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ( m1_rmod_2(k1_rmod_5(X0,X1,X2),X0,X1)
& v3_vectsp_2(k1_rmod_5(X0,X1,X2),X0) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v2_vectsp_2(X0)
| v10_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_group_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ( m1_rmod_2(k1_rmod_5(X0,X1,X2),X0,X1)
& v3_vectsp_2(k1_rmod_5(X0,X1,X2),X0) ) ),
inference(flattening,[],[f98]) ).
fof(f105,plain,
( l3_vectsp_1(sK0)
& v2_vectsp_2(sK0)
& ~ v10_vectsp_1(sK0)
& v8_vectsp_1(sK0)
& v7_vectsp_1(sK0)
& v6_vectsp_1(sK0)
& v7_group_1(sK0)
& v4_group_1(sK0)
& v6_rlvect_1(sK0)
& v5_rlvect_1(sK0)
& v4_rlvect_1(sK0)
& v3_rlvect_1(sK0)
& ~ v3_struct_0(sK0)
& l1_vectsp_2(sK1,sK0)
& v5_vectsp_2(sK1,sK0)
& v3_vectsp_2(sK1,sK0)
& v6_rlvect_1(sK1)
& v5_rlvect_1(sK1)
& v4_rlvect_1(sK1)
& v3_rlvect_1(sK1)
& ~ v3_struct_0(sK1)
& m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
& m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1)))
& r1_tarski(sK2,sK3)
& sK1 = k1_rmod_5(sK0,sK1,sK2)
& sK1 != k1_rmod_5(sK0,sK1,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f76]) ).
fof(f126,plain,
l3_vectsp_1(sK0),
inference(cnf_transformation,[],[f105]) ).
fof(f127,plain,
v2_vectsp_2(sK0),
inference(cnf_transformation,[],[f105]) ).
fof(f128,plain,
~ v10_vectsp_1(sK0),
inference(cnf_transformation,[],[f105]) ).
fof(f129,plain,
v8_vectsp_1(sK0),
inference(cnf_transformation,[],[f105]) ).
fof(f130,plain,
v7_vectsp_1(sK0),
inference(cnf_transformation,[],[f105]) ).
fof(f131,plain,
v6_vectsp_1(sK0),
inference(cnf_transformation,[],[f105]) ).
fof(f132,plain,
v7_group_1(sK0),
inference(cnf_transformation,[],[f105]) ).
fof(f133,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f105]) ).
fof(f134,plain,
v6_rlvect_1(sK0),
inference(cnf_transformation,[],[f105]) ).
fof(f135,plain,
v5_rlvect_1(sK0),
inference(cnf_transformation,[],[f105]) ).
fof(f136,plain,
v4_rlvect_1(sK0),
inference(cnf_transformation,[],[f105]) ).
fof(f137,plain,
v3_rlvect_1(sK0),
inference(cnf_transformation,[],[f105]) ).
fof(f138,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f105]) ).
fof(f139,plain,
l1_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f105]) ).
fof(f140,plain,
v5_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f105]) ).
fof(f141,plain,
v3_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f105]) ).
fof(f142,plain,
v6_rlvect_1(sK1),
inference(cnf_transformation,[],[f105]) ).
fof(f143,plain,
v5_rlvect_1(sK1),
inference(cnf_transformation,[],[f105]) ).
fof(f144,plain,
v4_rlvect_1(sK1),
inference(cnf_transformation,[],[f105]) ).
fof(f145,plain,
v3_rlvect_1(sK1),
inference(cnf_transformation,[],[f105]) ).
fof(f146,plain,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f105]) ).
fof(f147,plain,
m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1))),
inference(cnf_transformation,[],[f105]) ).
fof(f148,plain,
m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1))),
inference(cnf_transformation,[],[f105]) ).
fof(f149,plain,
r1_tarski(sK2,sK3),
inference(cnf_transformation,[],[f105]) ).
fof(f150,plain,
sK1 = k1_rmod_5(sK0,sK1,sK2),
inference(cnf_transformation,[],[f105]) ).
fof(f151,plain,
sK1 != k1_rmod_5(sK0,sK1,sK3),
inference(cnf_transformation,[],[f105]) ).
fof(f153,plain,
! [X2,X0,X1] :
( ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v3_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l1_vectsp_2(X2,X0)
| ~ v5_vectsp_2(X2,X0)
| ~ v3_vectsp_2(X2,X0)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v3_rlvect_1(X2)
| v3_struct_0(X2)
| ~ m1_rmod_2(X1,X0,X2)
| ~ m1_rmod_2(X2,X0,X1)
| X1 = X2 ),
inference(cnf_transformation,[],[f79]) ).
fof(f190,plain,
! [X2,X0,X1] :
( ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ m1_rmod_2(X2,X0,X1)
| l1_vectsp_2(X2,X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f191,plain,
! [X2,X0,X1] :
( ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ m1_rmod_2(X2,X0,X1)
| v5_vectsp_2(X2,X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f192,plain,
! [X2,X0,X1] :
( ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ m1_rmod_2(X2,X0,X1)
| v6_rlvect_1(X2) ),
inference(cnf_transformation,[],[f95]) ).
fof(f193,plain,
! [X2,X0,X1] :
( ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ m1_rmod_2(X2,X0,X1)
| v5_rlvect_1(X2) ),
inference(cnf_transformation,[],[f95]) ).
fof(f194,plain,
! [X2,X0,X1] :
( ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ m1_rmod_2(X2,X0,X1)
| v4_rlvect_1(X2) ),
inference(cnf_transformation,[],[f95]) ).
fof(f195,plain,
! [X2,X0,X1] :
( ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ m1_rmod_2(X2,X0,X1)
| v3_rlvect_1(X2) ),
inference(cnf_transformation,[],[f95]) ).
fof(f196,plain,
! [X2,X0,X1] :
( ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ m1_rmod_2(X2,X0,X1)
| ~ v3_struct_0(X2) ),
inference(cnf_transformation,[],[f95]) ).
fof(f197,plain,
! [X2,X3,X0,X1] :
( ~ l3_vectsp_1(X0)
| ~ v2_vectsp_2(X0)
| v10_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_group_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
| ~ r1_tarski(X2,X3)
| m1_rmod_2(k1_rmod_5(X0,X1,X2),X0,k1_rmod_5(X0,X1,X3)) ),
inference(cnf_transformation,[],[f97]) ).
fof(f198,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v2_vectsp_2(X0)
| v10_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_group_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| m1_rmod_2(k1_rmod_5(X0,X1,X2),X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f199,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v2_vectsp_2(X0)
| v10_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_group_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| v3_vectsp_2(k1_rmod_5(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_49,negated_conjecture,
k1_rmod_5(sK0,sK1,sK3) != sK1,
inference(cnf_transformation,[],[f151]) ).
tcf(c_50,negated_conjecture,
k1_rmod_5(sK0,sK1,sK2) = sK1,
inference(cnf_transformation,[],[f150]) ).
tcf(c_51,negated_conjecture,
r1_tarski(sK2,sK3),
inference(cnf_transformation,[],[f149]) ).
tcf(c_52,negated_conjecture,
m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1))),
inference(cnf_transformation,[],[f148]) ).
tcf(c_53,negated_conjecture,
m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1))),
inference(cnf_transformation,[],[f147]) ).
tcf(c_54,negated_conjecture,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f146]) ).
tcf(c_55,negated_conjecture,
v3_rlvect_1(sK1),
inference(cnf_transformation,[],[f145]) ).
tcf(c_56,negated_conjecture,
v4_rlvect_1(sK1),
inference(cnf_transformation,[],[f144]) ).
tcf(c_57,negated_conjecture,
v5_rlvect_1(sK1),
inference(cnf_transformation,[],[f143]) ).
tcf(c_58,negated_conjecture,
v6_rlvect_1(sK1),
inference(cnf_transformation,[],[f142]) ).
tcf(c_59,negated_conjecture,
v3_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f141]) ).
tcf(c_60,negated_conjecture,
v5_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f140]) ).
tcf(c_61,negated_conjecture,
l1_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f139]) ).
tcf(c_62,negated_conjecture,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f138]) ).
tcf(c_63,negated_conjecture,
v3_rlvect_1(sK0),
inference(cnf_transformation,[],[f137]) ).
tcf(c_64,negated_conjecture,
v4_rlvect_1(sK0),
inference(cnf_transformation,[],[f136]) ).
tcf(c_65,negated_conjecture,
v5_rlvect_1(sK0),
inference(cnf_transformation,[],[f135]) ).
tcf(c_66,negated_conjecture,
v6_rlvect_1(sK0),
inference(cnf_transformation,[],[f134]) ).
tcf(c_67,negated_conjecture,
v4_group_1(sK0),
inference(cnf_transformation,[],[f133]) ).
tcf(c_68,negated_conjecture,
v7_group_1(sK0),
inference(cnf_transformation,[],[f132]) ).
tcf(c_69,negated_conjecture,
v6_vectsp_1(sK0),
inference(cnf_transformation,[],[f131]) ).
tcf(c_70,negated_conjecture,
v7_vectsp_1(sK0),
inference(cnf_transformation,[],[f130]) ).
tcf(c_71,negated_conjecture,
v8_vectsp_1(sK0),
inference(cnf_transformation,[],[f129]) ).
tcf(c_72,negated_conjecture,
~ v10_vectsp_1(sK0),
inference(cnf_transformation,[],[f128]) ).
tcf(c_73,negated_conjecture,
v2_vectsp_2(sK0),
inference(cnf_transformation,[],[f127]) ).
tcf(c_74,negated_conjecture,
l3_vectsp_1(sK0),
inference(cnf_transformation,[],[f126]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X2)
| v3_struct_0(X1)
| v3_struct_0(X0)
| ( X0 = X2 )
| ~ 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)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X2)
| ~ v5_rlvect_1(X1)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X2)
| ~ v4_rlvect_1(X1)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X2)
| ~ v3_rlvect_1(X1)
| ~ v3_rlvect_1(X0)
| ~ l1_vectsp_2(X2,X1)
| ~ l1_vectsp_2(X0,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X0,X1)
| ~ v3_vectsp_2(X2,X1)
| ~ v3_vectsp_2(X0,X1)
| ~ m1_rmod_2(X2,X1,X0)
| ~ m1_rmod_2(X0,X1,X2) ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X2)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(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)
| ~ v3_struct_0(X0)
| ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ m1_rmod_2(X0,X1,X2) ),
inference(cnf_transformation,[],[f196]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_rlvect_1(X0)
| v3_struct_0(X2)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(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)
| ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ m1_rmod_2(X0,X1,X2) ),
inference(cnf_transformation,[],[f195]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i,X2: $i] :
( v4_rlvect_1(X0)
| v3_struct_0(X2)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(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)
| ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ m1_rmod_2(X0,X1,X2) ),
inference(cnf_transformation,[],[f194]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i,X2: $i] :
( v5_rlvect_1(X0)
| v3_struct_0(X2)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(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)
| ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ m1_rmod_2(X0,X1,X2) ),
inference(cnf_transformation,[],[f193]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i,X2: $i] :
( v6_rlvect_1(X0)
| v3_struct_0(X2)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(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)
| ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ m1_rmod_2(X0,X1,X2) ),
inference(cnf_transformation,[],[f192]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X2)
| v3_struct_0(X1)
| v5_vectsp_2(X0,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)
| ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ m1_rmod_2(X0,X1,X2) ),
inference(cnf_transformation,[],[f191]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X2)
| v3_struct_0(X1)
| l1_vectsp_2(X0,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)
| ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ m1_rmod_2(X0,X1,X2) ),
inference(cnf_transformation,[],[f190]) ).
tcf(c_120,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v10_vectsp_1(X3)
| v3_struct_0(X3)
| v3_struct_0(X1)
| m1_rmod_2(k1_rmod_5(X3,X1,X0),X3,k1_rmod_5(X3,X1,X2))
| ~ l3_vectsp_1(X3)
| ~ v2_vectsp_2(X3)
| ~ v8_vectsp_1(X3)
| ~ v7_vectsp_1(X3)
| ~ v6_vectsp_1(X3)
| ~ v7_group_1(X3)
| ~ v4_group_1(X3)
| ~ v6_rlvect_1(X3)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X3)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X3)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X3)
| ~ v3_rlvect_1(X1)
| ~ l1_vectsp_2(X1,X3)
| ~ v5_vectsp_2(X1,X3)
| ~ r1_tarski(X0,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(cnf_transformation,[],[f197]) ).
tcf(c_121,plain,
! [X0: $i,X1: $i,X2: $i] :
( v10_vectsp_1(X2)
| v3_struct_0(X2)
| v3_struct_0(X1)
| v3_vectsp_2(k1_rmod_5(X2,X1,X0),X2)
| ~ l3_vectsp_1(X2)
| ~ v2_vectsp_2(X2)
| ~ v8_vectsp_1(X2)
| ~ v7_vectsp_1(X2)
| ~ v6_vectsp_1(X2)
| ~ v7_group_1(X2)
| ~ v4_group_1(X2)
| ~ 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)
| ~ l1_vectsp_2(X1,X2)
| ~ v5_vectsp_2(X1,X2)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(cnf_transformation,[],[f199]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i,X2: $i] :
( v10_vectsp_1(X2)
| v3_struct_0(X2)
| v3_struct_0(X1)
| m1_rmod_2(k1_rmod_5(X2,X1,X0),X2,X1)
| ~ l3_vectsp_1(X2)
| ~ v2_vectsp_2(X2)
| ~ v8_vectsp_1(X2)
| ~ v7_vectsp_1(X2)
| ~ v6_vectsp_1(X2)
| ~ v7_group_1(X2)
| ~ v4_group_1(X2)
| ~ 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)
| ~ l1_vectsp_2(X1,X2)
| ~ v5_vectsp_2(X1,X2)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(cnf_transformation,[],[f198]) ).
tcf(c_191,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X2)
| v3_struct_0(X1)
| ~ v5_rlvect_1(X2)
| ~ v5_rlvect_1(X1)
| ~ v3_rlvect_1(X2)
| ~ v3_rlvect_1(X1)
| ~ v5_vectsp_2(X2,X1)
| ~ m1_rmod_2(X0,X1,X2)
| ~ m1_rmod_2(X2,X1,X0)
| ~ v3_vectsp_2(X0,X1)
| ~ v3_vectsp_2(X2,X1)
| ~ l1_vectsp_2(X2,X1)
| ~ v4_rlvect_1(X1)
| ~ v4_rlvect_1(X2)
| ~ v6_rlvect_1(X1)
| ~ v6_rlvect_1(X2)
| ~ v4_group_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ l3_vectsp_1(X1)
| ( X0 = X2 ) ),
inference(global_subsumption_just,[status(thm)],[c_76,c_117,c_116,c_115,c_114,c_119,c_118,c_113,c_76]) ).
tcf(c_192,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X2)
| v3_struct_0(X1)
| ( X0 = X2 )
| ~ 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)
| ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ v3_vectsp_2(X2,X1)
| ~ v3_vectsp_2(X0,X1)
| ~ m1_rmod_2(X2,X1,X0)
| ~ m1_rmod_2(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_191]) ).
tcf(c_2999,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v10_vectsp_1(X0)
| v3_struct_0(X2)
| v3_struct_0(X0)
| m1_rmod_2(k1_rmod_5(X0,X2,X1),X0,k1_rmod_5(X0,X2,X3))
| ~ l3_vectsp_1(X0)
| ~ v2_vectsp_2(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X2)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X2)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X2)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X2)
| ~ v3_rlvect_1(X0)
| ~ l1_vectsp_2(X2,X0)
| ~ v5_vectsp_2(X2,X0)
| ~ r1_tarski(X1,X3)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_68,c_120]) ).
tcf(c_3000,plain,
! [X0: $i,X1: $i,X2: $i] :
( v10_vectsp_1(sK0)
| v3_struct_0(sK0)
| v3_struct_0(X1)
| m1_rmod_2(k1_rmod_5(sK0,X1,X0),sK0,k1_rmod_5(sK0,X1,X2))
| ~ l3_vectsp_1(sK0)
| ~ v2_vectsp_2(sK0)
| ~ v8_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| ~ l1_vectsp_2(X1,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ r1_tarski(X0,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(unflattening,[status(thm)],[c_2999]) ).
tcf(c_3002,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| m1_rmod_2(k1_rmod_5(sK0,X1,X0),sK0,k1_rmod_5(sK0,X1,X2))
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| ~ l1_vectsp_2(X1,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ r1_tarski(X0,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(global_subsumption_just,[status(thm)],[c_3000,c_74,c_73,c_71,c_70,c_69,c_67,c_66,c_65,c_64,c_63,c_72,c_62,c_3000]) ).
tcf(c_3038,plain,
! [X0: $i,X1: $i,X2: $i] :
( v10_vectsp_1(X0)
| v3_struct_0(X2)
| v3_struct_0(X0)
| m1_rmod_2(k1_rmod_5(X0,X2,X1),X0,X2)
| ~ l3_vectsp_1(X0)
| ~ v2_vectsp_2(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X2)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X2)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X2)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X2)
| ~ v3_rlvect_1(X0)
| ~ l1_vectsp_2(X2,X0)
| ~ v5_vectsp_2(X2,X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_68,c_122]) ).
tcf(c_3039,plain,
! [X0: $i,X1: $i] :
( v10_vectsp_1(sK0)
| v3_struct_0(sK0)
| v3_struct_0(X1)
| m1_rmod_2(k1_rmod_5(sK0,X1,X0),sK0,X1)
| ~ l3_vectsp_1(sK0)
| ~ v2_vectsp_2(sK0)
| ~ v8_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| ~ l1_vectsp_2(X1,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(unflattening,[status(thm)],[c_3038]) ).
tcf(c_3041,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m1_rmod_2(k1_rmod_5(sK0,X1,X0),sK0,X1)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| ~ l1_vectsp_2(X1,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(global_subsumption_just,[status(thm)],[c_3039,c_74,c_73,c_71,c_70,c_69,c_67,c_66,c_65,c_64,c_63,c_72,c_62,c_3039]) ).
tcf(c_3071,plain,
! [X0: $i,X1: $i,X2: $i] :
( v10_vectsp_1(X0)
| v3_struct_0(X2)
| v3_struct_0(X0)
| v3_vectsp_2(k1_rmod_5(X0,X2,X1),X0)
| ~ l3_vectsp_1(X0)
| ~ v2_vectsp_2(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X2)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X2)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X2)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X2)
| ~ v3_rlvect_1(X0)
| ~ l1_vectsp_2(X2,X0)
| ~ v5_vectsp_2(X2,X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_68,c_121]) ).
tcf(c_3072,plain,
! [X0: $i,X1: $i] :
( v10_vectsp_1(sK0)
| v3_struct_0(sK0)
| v3_struct_0(X1)
| v3_vectsp_2(k1_rmod_5(sK0,X1,X0),sK0)
| ~ l3_vectsp_1(sK0)
| ~ v2_vectsp_2(sK0)
| ~ v8_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| ~ l1_vectsp_2(X1,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(unflattening,[status(thm)],[c_3071]) ).
tcf(c_3074,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v3_vectsp_2(k1_rmod_5(sK0,X1,X0),sK0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| ~ l1_vectsp_2(X1,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(global_subsumption_just,[status(thm)],[c_3072,c_74,c_73,c_71,c_70,c_69,c_67,c_66,c_65,c_64,c_63,c_72,c_62,c_3072]) ).
tcf(c_3390,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X2)
| v3_struct_0(X0)
| ( X1 = X2 )
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v6_rlvect_1(X2)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X2)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X2)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X2)
| ~ v3_rlvect_1(X0)
| ~ l1_vectsp_2(X2,X0)
| ~ v5_vectsp_2(X2,X0)
| ~ v3_vectsp_2(X2,X0)
| ~ v3_vectsp_2(X1,X0)
| ~ m1_rmod_2(X2,X0,X1)
| ~ m1_rmod_2(X1,X0,X2)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_67,c_192]) ).
tcf(c_3391,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| v3_struct_0(X1)
| ( X0 = X1 )
| ~ l3_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| ~ l1_vectsp_2(X1,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ v3_vectsp_2(X1,sK0)
| ~ v3_vectsp_2(X0,sK0)
| ~ m1_rmod_2(X1,sK0,X0)
| ~ m1_rmod_2(X0,sK0,X1) ),
inference(unflattening,[status(thm)],[c_3390]) ).
tcf(c_3393,plain,
! [X0: $i,X1: $i] :
( ~ m1_rmod_2(X0,sK0,X1)
| ~ m1_rmod_2(X1,sK0,X0)
| ~ v3_vectsp_2(X0,sK0)
| ~ v3_vectsp_2(X1,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ l1_vectsp_2(X1,sK0)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ( X0 = X1 )
| v3_struct_0(X1) ),
inference(global_subsumption_just,[status(thm)],[c_3391,c_74,c_71,c_70,c_69,c_66,c_65,c_64,c_63,c_62,c_3391]) ).
tcf(c_3394,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| ( X0 = X1 )
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| ~ l1_vectsp_2(X1,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ v3_vectsp_2(X1,sK0)
| ~ v3_vectsp_2(X0,sK0)
| ~ m1_rmod_2(X1,sK0,X0)
| ~ m1_rmod_2(X0,sK0,X1) ),
inference(renaming,[status(thm)],[c_3393]) ).
tcf(c_3432,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X2)
| v3_struct_0(X0)
| l1_vectsp_2(X1,X0)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v6_rlvect_1(X2)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X2)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X2)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X2)
| ~ v3_rlvect_1(X0)
| ~ l1_vectsp_2(X2,X0)
| ~ v5_vectsp_2(X2,X0)
| ~ m1_rmod_2(X1,X0,X2)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_67,c_119]) ).
tcf(c_3433,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| v3_struct_0(X1)
| l1_vectsp_2(X0,sK0)
| ~ l3_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| ~ l1_vectsp_2(X1,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ m1_rmod_2(X0,sK0,X1) ),
inference(unflattening,[status(thm)],[c_3432]) ).
tcf(c_3434,plain,
! [X0: $i,X1: $i] :
( ~ m1_rmod_2(X0,sK0,X1)
| ~ v5_vectsp_2(X1,sK0)
| ~ l1_vectsp_2(X1,sK0)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| l1_vectsp_2(X0,sK0)
| v3_struct_0(X1) ),
inference(global_subsumption_just,[status(thm)],[c_3433,c_74,c_71,c_70,c_69,c_66,c_65,c_64,c_63,c_62,c_3433]) ).
tcf(c_3435,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| l1_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| ~ l1_vectsp_2(X1,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ m1_rmod_2(X0,sK0,X1) ),
inference(renaming,[status(thm)],[c_3434]) ).
tcf(c_3463,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X2)
| v3_struct_0(X0)
| v5_vectsp_2(X1,X0)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v6_rlvect_1(X2)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X2)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X2)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X2)
| ~ v3_rlvect_1(X0)
| ~ l1_vectsp_2(X2,X0)
| ~ v5_vectsp_2(X2,X0)
| ~ m1_rmod_2(X1,X0,X2)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_67,c_118]) ).
tcf(c_3464,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| v3_struct_0(X1)
| v5_vectsp_2(X0,sK0)
| ~ l3_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| ~ l1_vectsp_2(X1,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ m1_rmod_2(X0,sK0,X1) ),
inference(unflattening,[status(thm)],[c_3463]) ).
tcf(c_3465,plain,
! [X0: $i,X1: $i] :
( ~ m1_rmod_2(X0,sK0,X1)
| ~ v5_vectsp_2(X1,sK0)
| ~ l1_vectsp_2(X1,sK0)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| v5_vectsp_2(X0,sK0)
| v3_struct_0(X1) ),
inference(global_subsumption_just,[status(thm)],[c_3464,c_74,c_71,c_70,c_69,c_66,c_65,c_64,c_63,c_62,c_3464]) ).
tcf(c_3466,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v5_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| ~ l1_vectsp_2(X1,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ m1_rmod_2(X0,sK0,X1) ),
inference(renaming,[status(thm)],[c_3465]) ).
tcf(c_3494,plain,
! [X0: $i,X1: $i,X2: $i] :
( v6_rlvect_1(X1)
| v3_struct_0(X2)
| v3_struct_0(X0)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v6_rlvect_1(X2)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X2)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X2)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X2)
| ~ v3_rlvect_1(X0)
| ~ l1_vectsp_2(X2,X0)
| ~ v5_vectsp_2(X2,X0)
| ~ m1_rmod_2(X1,X0,X2)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_67,c_117]) ).
tcf(c_3495,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| v6_rlvect_1(X0)
| v3_struct_0(X1)
| ~ l3_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| ~ l1_vectsp_2(X1,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ m1_rmod_2(X0,sK0,X1) ),
inference(unflattening,[status(thm)],[c_3494]) ).
tcf(c_3496,plain,
! [X0: $i,X1: $i] :
( ~ m1_rmod_2(X0,sK0,X1)
| ~ v5_vectsp_2(X1,sK0)
| ~ l1_vectsp_2(X1,sK0)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| v3_struct_0(X1)
| v6_rlvect_1(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3495,c_74,c_71,c_70,c_69,c_66,c_65,c_64,c_63,c_62,c_3495]) ).
tcf(c_3497,plain,
! [X0: $i,X1: $i] :
( v6_rlvect_1(X0)
| v3_struct_0(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| ~ l1_vectsp_2(X1,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ m1_rmod_2(X0,sK0,X1) ),
inference(renaming,[status(thm)],[c_3496]) ).
tcf(c_3525,plain,
! [X0: $i,X1: $i,X2: $i] :
( v5_rlvect_1(X1)
| v3_struct_0(X2)
| v3_struct_0(X0)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v6_rlvect_1(X2)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X2)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X2)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X2)
| ~ v3_rlvect_1(X0)
| ~ l1_vectsp_2(X2,X0)
| ~ v5_vectsp_2(X2,X0)
| ~ m1_rmod_2(X1,X0,X2)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_67,c_116]) ).
tcf(c_3526,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| v5_rlvect_1(X0)
| v3_struct_0(X1)
| ~ l3_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| ~ l1_vectsp_2(X1,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ m1_rmod_2(X0,sK0,X1) ),
inference(unflattening,[status(thm)],[c_3525]) ).
tcf(c_3527,plain,
! [X0: $i,X1: $i] :
( ~ m1_rmod_2(X0,sK0,X1)
| ~ v5_vectsp_2(X1,sK0)
| ~ l1_vectsp_2(X1,sK0)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| v3_struct_0(X1)
| v5_rlvect_1(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3526,c_74,c_71,c_70,c_69,c_66,c_65,c_64,c_63,c_62,c_3526]) ).
tcf(c_3528,plain,
! [X0: $i,X1: $i] :
( v5_rlvect_1(X0)
| v3_struct_0(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| ~ l1_vectsp_2(X1,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ m1_rmod_2(X0,sK0,X1) ),
inference(renaming,[status(thm)],[c_3527]) ).
tcf(c_3556,plain,
! [X0: $i,X1: $i,X2: $i] :
( v4_rlvect_1(X1)
| v3_struct_0(X2)
| v3_struct_0(X0)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v6_rlvect_1(X2)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X2)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X2)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X2)
| ~ v3_rlvect_1(X0)
| ~ l1_vectsp_2(X2,X0)
| ~ v5_vectsp_2(X2,X0)
| ~ m1_rmod_2(X1,X0,X2)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_67,c_115]) ).
tcf(c_3557,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| v4_rlvect_1(X0)
| v3_struct_0(X1)
| ~ l3_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| ~ l1_vectsp_2(X1,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ m1_rmod_2(X0,sK0,X1) ),
inference(unflattening,[status(thm)],[c_3556]) ).
tcf(c_3558,plain,
! [X0: $i,X1: $i] :
( ~ m1_rmod_2(X0,sK0,X1)
| ~ v5_vectsp_2(X1,sK0)
| ~ l1_vectsp_2(X1,sK0)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| v3_struct_0(X1)
| v4_rlvect_1(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3557,c_74,c_71,c_70,c_69,c_66,c_65,c_64,c_63,c_62,c_3557]) ).
tcf(c_3559,plain,
! [X0: $i,X1: $i] :
( v4_rlvect_1(X0)
| v3_struct_0(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| ~ l1_vectsp_2(X1,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ m1_rmod_2(X0,sK0,X1) ),
inference(renaming,[status(thm)],[c_3558]) ).
tcf(c_3587,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_rlvect_1(X1)
| v3_struct_0(X2)
| v3_struct_0(X0)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v6_rlvect_1(X2)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X2)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X2)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X2)
| ~ v3_rlvect_1(X0)
| ~ l1_vectsp_2(X2,X0)
| ~ v5_vectsp_2(X2,X0)
| ~ m1_rmod_2(X1,X0,X2)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_67,c_114]) ).
tcf(c_3588,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| v3_rlvect_1(X0)
| v3_struct_0(X1)
| ~ l3_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| ~ l1_vectsp_2(X1,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ m1_rmod_2(X0,sK0,X1) ),
inference(unflattening,[status(thm)],[c_3587]) ).
tcf(c_3589,plain,
! [X0: $i,X1: $i] :
( ~ m1_rmod_2(X0,sK0,X1)
| ~ v5_vectsp_2(X1,sK0)
| ~ l1_vectsp_2(X1,sK0)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| v3_struct_0(X1)
| v3_rlvect_1(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3588,c_74,c_71,c_70,c_69,c_66,c_65,c_64,c_63,c_62,c_3588]) ).
tcf(c_3590,plain,
! [X0: $i,X1: $i] :
( v3_rlvect_1(X0)
| v3_struct_0(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| ~ l1_vectsp_2(X1,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ m1_rmod_2(X0,sK0,X1) ),
inference(renaming,[status(thm)],[c_3589]) ).
tcf(c_3618,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X2)
| v3_struct_0(X0)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v6_rlvect_1(X2)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X2)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X2)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X2)
| ~ v3_rlvect_1(X0)
| ~ v3_struct_0(X1)
| ~ l1_vectsp_2(X2,X0)
| ~ v5_vectsp_2(X2,X0)
| ~ m1_rmod_2(X1,X0,X2)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_67,c_113]) ).
tcf(c_3619,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| v3_struct_0(X1)
| ~ l3_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| ~ v3_struct_0(X0)
| ~ l1_vectsp_2(X1,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ m1_rmod_2(X0,sK0,X1) ),
inference(unflattening,[status(thm)],[c_3618]) ).
tcf(c_3620,plain,
! [X0: $i,X1: $i] :
( ~ m1_rmod_2(X0,sK0,X1)
| ~ v5_vectsp_2(X1,sK0)
| ~ l1_vectsp_2(X1,sK0)
| ~ v3_struct_0(X0)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| v3_struct_0(X1) ),
inference(global_subsumption_just,[status(thm)],[c_3619,c_74,c_71,c_70,c_69,c_66,c_65,c_64,c_63,c_62,c_3619]) ).
tcf(c_3621,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| ~ v3_struct_0(X0)
| ~ l1_vectsp_2(X1,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ m1_rmod_2(X0,sK0,X1) ),
inference(renaming,[status(thm)],[c_3620]) ).
tcf(c_7426,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| ~ l1_vectsp_2(X1,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ v3_struct_0(k1_rmod_5(sK0,X1,X0))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(superposition,[status(thm)],[c_3041,c_3621]) ).
tcf(c_7427,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v5_vectsp_2(k1_rmod_5(sK0,X1,X0),sK0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| ~ l1_vectsp_2(X1,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(superposition,[status(thm)],[c_3041,c_3466]) ).
tcf(c_7428,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| l1_vectsp_2(k1_rmod_5(sK0,X1,X0),sK0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| ~ l1_vectsp_2(X1,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(superposition,[status(thm)],[c_3041,c_3435]) ).
tcf(c_7429,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v3_rlvect_1(k1_rmod_5(sK0,X1,X0))
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| ~ l1_vectsp_2(X1,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(superposition,[status(thm)],[c_3041,c_3590]) ).
tcf(c_7430,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v4_rlvect_1(k1_rmod_5(sK0,X1,X0))
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| ~ l1_vectsp_2(X1,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(superposition,[status(thm)],[c_3041,c_3559]) ).
tcf(c_7431,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v5_rlvect_1(k1_rmod_5(sK0,X1,X0))
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| ~ l1_vectsp_2(X1,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(superposition,[status(thm)],[c_3041,c_3528]) ).
tcf(c_7432,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v6_rlvect_1(k1_rmod_5(sK0,X1,X0))
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| ~ l1_vectsp_2(X1,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(superposition,[status(thm)],[c_3041,c_3497]) ).
tcf(c_7598,plain,
! [X0: $i] :
( v3_struct_0(sK1)
| m1_rmod_2(sK1,sK0,k1_rmod_5(sK0,sK1,X0))
| ~ v6_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| ~ l1_vectsp_2(sK1,sK0)
| ~ v5_vectsp_2(sK1,sK0)
| ~ r1_tarski(sK2,X0)
| ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1))) ),
inference(superposition,[status(thm)],[c_50,c_3002]) ).
tcf(c_7612,plain,
! [X0: $i] :
( m1_rmod_2(sK1,sK0,k1_rmod_5(sK0,sK1,X0))
| ~ r1_tarski(sK2,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7598,c_54,c_58,c_57,c_56,c_55,c_61,c_60,c_53]) ).
tcf(c_8055,plain,
! [X0: $i] :
( v3_struct_0(k1_rmod_5(sK0,sK1,X0))
| ( k1_rmod_5(sK0,sK1,X0) = sK1 )
| ~ v3_vectsp_2(sK1,sK0)
| ~ r1_tarski(sK2,X0)
| ~ v6_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ v5_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ v4_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ v3_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ l1_vectsp_2(k1_rmod_5(sK0,sK1,X0),sK0)
| ~ v5_vectsp_2(k1_rmod_5(sK0,sK1,X0),sK0)
| ~ v3_vectsp_2(k1_rmod_5(sK0,sK1,X0),sK0)
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,X0),sK0,sK1) ),
inference(superposition,[status(thm)],[c_7612,c_3394]) ).
tcf(c_8063,plain,
! [X0: $i] :
( v3_struct_0(k1_rmod_5(sK0,sK1,X0))
| ( k1_rmod_5(sK0,sK1,X0) = sK1 )
| ~ r1_tarski(sK2,X0)
| ~ v6_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ v5_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ v4_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ v3_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ l1_vectsp_2(k1_rmod_5(sK0,sK1,X0),sK0)
| ~ v5_vectsp_2(k1_rmod_5(sK0,sK1,X0),sK0)
| ~ v3_vectsp_2(k1_rmod_5(sK0,sK1,X0),sK0)
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,X0),sK0,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8055,c_59]) ).
tcf(c_8119,plain,
! [X0: $i] :
( v3_struct_0(sK1)
| v3_struct_0(k1_rmod_5(sK0,sK1,X0))
| ( k1_rmod_5(sK0,sK1,X0) = sK1 )
| ~ v6_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| ~ l1_vectsp_2(sK1,sK0)
| ~ v5_vectsp_2(sK1,sK0)
| ~ r1_tarski(sK2,X0)
| ~ v6_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ v5_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ v4_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ v3_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ l1_vectsp_2(k1_rmod_5(sK0,sK1,X0),sK0)
| ~ v5_vectsp_2(k1_rmod_5(sK0,sK1,X0),sK0)
| ~ v3_vectsp_2(k1_rmod_5(sK0,sK1,X0),sK0) ),
inference(superposition,[status(thm)],[c_3041,c_8063]) ).
tcf(c_8134,plain,
! [X0: $i] :
( v3_struct_0(k1_rmod_5(sK0,sK1,X0))
| ( k1_rmod_5(sK0,sK1,X0) = sK1 )
| ~ r1_tarski(sK2,X0)
| ~ v6_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ v5_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ v4_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ v3_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ l1_vectsp_2(k1_rmod_5(sK0,sK1,X0),sK0)
| ~ v5_vectsp_2(k1_rmod_5(sK0,sK1,X0),sK0)
| ~ v3_vectsp_2(k1_rmod_5(sK0,sK1,X0),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8119,c_54,c_58,c_57,c_56,c_55,c_61,c_60]) ).
tcf(c_8180,plain,
! [X0: $i] :
( v3_struct_0(sK1)
| v3_struct_0(k1_rmod_5(sK0,sK1,X0))
| ( k1_rmod_5(sK0,sK1,X0) = sK1 )
| ~ v6_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| ~ l1_vectsp_2(sK1,sK0)
| ~ v5_vectsp_2(sK1,sK0)
| ~ r1_tarski(sK2,X0)
| ~ v6_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ v5_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ v4_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ v3_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ l1_vectsp_2(k1_rmod_5(sK0,sK1,X0),sK0)
| ~ v5_vectsp_2(k1_rmod_5(sK0,sK1,X0),sK0) ),
inference(superposition,[status(thm)],[c_3074,c_8134]) ).
tcf(c_8182,plain,
! [X0: $i] :
( v3_struct_0(k1_rmod_5(sK0,sK1,X0))
| ( k1_rmod_5(sK0,sK1,X0) = sK1 )
| ~ r1_tarski(sK2,X0)
| ~ v6_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ v5_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ v4_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ v3_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ l1_vectsp_2(k1_rmod_5(sK0,sK1,X0),sK0)
| ~ v5_vectsp_2(k1_rmod_5(sK0,sK1,X0),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8180,c_54,c_58,c_57,c_56,c_55,c_61,c_60]) ).
tcf(c_8407,plain,
( v3_struct_0(sK1)
| v3_rlvect_1(k1_rmod_5(sK0,sK1,sK3))
| ~ v6_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| ~ l1_vectsp_2(sK1,sK0)
| ~ v5_vectsp_2(sK1,sK0) ),
inference(superposition,[status(thm)],[c_52,c_7429]) ).
tcf(c_8424,plain,
v3_rlvect_1(k1_rmod_5(sK0,sK1,sK3)),
inference(forward_subsumption_resolution,[status(thm)],[c_8407,c_54,c_58,c_57,c_56,c_55,c_61,c_60]) ).
tcf(c_8599,plain,
( v3_struct_0(sK1)
| v4_rlvect_1(k1_rmod_5(sK0,sK1,sK3))
| ~ v6_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| ~ l1_vectsp_2(sK1,sK0)
| ~ v5_vectsp_2(sK1,sK0) ),
inference(superposition,[status(thm)],[c_52,c_7430]) ).
tcf(c_8616,plain,
v4_rlvect_1(k1_rmod_5(sK0,sK1,sK3)),
inference(forward_subsumption_resolution,[status(thm)],[c_8599,c_54,c_58,c_57,c_56,c_55,c_61,c_60]) ).
tcf(c_8681,plain,
( v3_struct_0(sK1)
| v5_rlvect_1(k1_rmod_5(sK0,sK1,sK3))
| ~ v6_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| ~ l1_vectsp_2(sK1,sK0)
| ~ v5_vectsp_2(sK1,sK0) ),
inference(superposition,[status(thm)],[c_52,c_7431]) ).
tcf(c_8698,plain,
v5_rlvect_1(k1_rmod_5(sK0,sK1,sK3)),
inference(forward_subsumption_resolution,[status(thm)],[c_8681,c_54,c_58,c_57,c_56,c_55,c_61,c_60]) ).
tcf(c_8763,plain,
( v3_struct_0(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| ~ l1_vectsp_2(sK1,sK0)
| ~ v5_vectsp_2(sK1,sK0)
| ~ v3_struct_0(k1_rmod_5(sK0,sK1,sK3)) ),
inference(superposition,[status(thm)],[c_52,c_7426]) ).
tcf(c_8780,plain,
~ v3_struct_0(k1_rmod_5(sK0,sK1,sK3)),
inference(forward_subsumption_resolution,[status(thm)],[c_8763,c_54,c_58,c_57,c_56,c_55,c_61,c_60]) ).
tcf(c_8957,plain,
( v3_struct_0(sK1)
| v6_rlvect_1(k1_rmod_5(sK0,sK1,sK3))
| ~ v6_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| ~ l1_vectsp_2(sK1,sK0)
| ~ v5_vectsp_2(sK1,sK0) ),
inference(superposition,[status(thm)],[c_52,c_7432]) ).
tcf(c_8974,plain,
v6_rlvect_1(k1_rmod_5(sK0,sK1,sK3)),
inference(forward_subsumption_resolution,[status(thm)],[c_8957,c_54,c_58,c_57,c_56,c_55,c_61,c_60]) ).
tcf(c_9044,plain,
! [X0: $i] :
( v3_struct_0(sK1)
| v3_struct_0(k1_rmod_5(sK0,sK1,X0))
| ( k1_rmod_5(sK0,sK1,X0) = sK1 )
| ~ v6_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| ~ l1_vectsp_2(sK1,sK0)
| ~ v5_vectsp_2(sK1,sK0)
| ~ r1_tarski(sK2,X0)
| ~ v6_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ v5_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ v4_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ v3_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ l1_vectsp_2(k1_rmod_5(sK0,sK1,X0),sK0) ),
inference(superposition,[status(thm)],[c_7427,c_8182]) ).
tcf(c_9045,plain,
! [X0: $i] :
( v3_struct_0(k1_rmod_5(sK0,sK1,X0))
| ( k1_rmod_5(sK0,sK1,X0) = sK1 )
| ~ r1_tarski(sK2,X0)
| ~ v6_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ v5_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ v4_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ v3_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ l1_vectsp_2(k1_rmod_5(sK0,sK1,X0),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9044,c_54,c_58,c_57,c_56,c_55,c_61,c_60]) ).
tcf(c_9107,plain,
! [X0: $i] :
( v3_struct_0(sK1)
| v3_struct_0(k1_rmod_5(sK0,sK1,X0))
| ( k1_rmod_5(sK0,sK1,X0) = sK1 )
| ~ v6_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| ~ l1_vectsp_2(sK1,sK0)
| ~ v5_vectsp_2(sK1,sK0)
| ~ r1_tarski(sK2,X0)
| ~ v6_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ v5_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ v4_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ v3_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1))) ),
inference(superposition,[status(thm)],[c_7428,c_9045]) ).
tcf(c_9108,plain,
! [X0: $i] :
( v3_struct_0(k1_rmod_5(sK0,sK1,X0))
| ( k1_rmod_5(sK0,sK1,X0) = sK1 )
| ~ r1_tarski(sK2,X0)
| ~ v6_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ v5_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ v4_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ v3_rlvect_1(k1_rmod_5(sK0,sK1,X0))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9107,c_54,c_58,c_57,c_56,c_55,c_61,c_60]) ).
tcf(c_9134,plain,
( v3_struct_0(k1_rmod_5(sK0,sK1,sK3))
| ( k1_rmod_5(sK0,sK1,sK3) = sK1 )
| ~ r1_tarski(sK2,sK3)
| ~ v6_rlvect_1(k1_rmod_5(sK0,sK1,sK3))
| ~ v5_rlvect_1(k1_rmod_5(sK0,sK1,sK3))
| ~ v4_rlvect_1(k1_rmod_5(sK0,sK1,sK3))
| ~ v3_rlvect_1(k1_rmod_5(sK0,sK1,sK3)) ),
inference(superposition,[status(thm)],[c_52,c_9108]) ).
tcf(c_9140,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_9134,c_8780,c_49,c_51,c_8974,c_8698,c_8616,c_8424]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG220+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.38 % Computer : n010.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Fri Sep 25 05:08:43 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.43
% 0.13/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.43
% 0.13/0.44 % Detected problem language: tptp
% 0.13/0.45 % Proving...
% 8.03/1.81 % SZS status Started for theBenchmark.p
% 8.03/1.81 % SZS status Theorem for theBenchmark.p
% 8.03/1.81
% 8.03/1.81 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.03/1.81
% 8.03/1.81 % ------ iProver source info
% 8.03/1.81
% 8.03/1.81 % git: date: 2026-07-19 20:42:38 +0200
% 8.03/1.81 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.03/1.81 % git: non_committed_changes: false
% 8.03/1.81
% 8.03/1.81 % ------ Parsing...
% 8.03/1.81 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.03/1.81
% 8.03/1.81 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 12 0s sf_e pe_s pe_e %
% 8.03/1.81
% 8.03/1.81 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.03/1.81
% 8.03/1.81 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 8.03/1.81 % ------ Proving...
% 8.03/1.81 % ------ Problem Properties
% 8.03/1.81
% 8.03/1.81 %
% 8.03/1.81 % clauses 85
% 8.03/1.81 % conjectures 18
% 8.03/1.81 % EPR 27
% 8.03/1.81 % Horn 64
% 8.03/1.81 % unary 56
% 8.03/1.81 % binary 7
% 8.03/1.81 % lits 252
% 8.03/1.81 % lits eq 4
% 8.03/1.81 % fd_pure 0
% 8.03/1.81 % fd_pseudo 0
% 8.03/1.81 % fd_cond 0
% 8.03/1.81 % fd_pseudo_cond 2
% 8.03/1.81 % AC symbols 0
% 8.03/1.81
% 8.03/1.81 % ------ Schedule dynamic 5 is on
% 8.03/1.81
% 8.03/1.81 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 8.03/1.81
% 8.03/1.81
% 8.03/1.81 % ------
% 8.03/1.81 % Current options:
% 8.03/1.81 % ------
% 8.03/1.81
% 8.03/1.81
% 8.03/1.81 %
% 8.03/1.81
% 8.03/1.81 % ------ Proving...
% 8.03/1.81 %
% 8.03/1.81
% 8.03/1.81 % SZS status Theorem for theBenchmark.p
% 8.03/1.81
% 8.03/1.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.03/1.81
% 8.03/1.81
%------------------------------------------------------------------------------