%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG219+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n016.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 12:53:50 PM UTC 2026
% Result : Theorem 3.01s 1.73s
% Output : CNFRefutation 3.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 13
% Syntax : Number of formulae : 161 ( 74 unt; 2 def)
% Number of atoms : 908 ( 86 equ)
% Maximal formula atoms : 26 ( 5 avg)
% Number of connectives : 1240 ( 512 ~; 536 |; 168 &)
% ( 1 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 6 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 : 29 ( 27 usr; 3 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-5 aty)
% Number of variables : 142 ( 1 sgn 136 !; 6 ?; 63 :)
% 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)))
=> ( X2 = u1_struct_0(X1)
=> ( k1_rmod_5(X0,X1,X2) = X1
| k1_rlvect_1(X0) = k2_group_1(X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_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)))
=> ( X2 = u1_struct_0(X1)
=> ( k1_rmod_5(X0,X1,X2) = X1
| k1_rlvect_1(X0) = k2_group_1(X0) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
! [X0,X1] :
( ( l1_vectsp_2(X1,X0)
& l1_struct_0(X0) )
=> ( v3_vectsp_2(X1,X0)
=> X1 = g1_vectsp_2(X0,u1_struct_0(X1),u1_rlvect_1(X1),u2_struct_0(X1),u1_vectsp_2(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v3_vectsp_2) ).
fof(f8,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)
& v6_rlvect_1(X1)
& v5_rlvect_1(X1)
& v4_rlvect_1(X1)
& v3_rlvect_1(X1)
& ~ v3_struct_0(X1) )
=> k2_rmod_2(X0,X1) = g1_vectsp_2(X0,u1_struct_0(X1),u1_rlvect_1(X1),u2_struct_0(X1),u1_vectsp_2(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_rmod_2) ).
fof(f15,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) )
=> ( m1_rmod_2(k2_rmod_2(X0,X1),X0,X1)
& v3_vectsp_2(k2_rmod_2(X0,X1),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_rmod_2) ).
fof(f17,axiom,
! [X0] :
( l1_group_1(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_group_1) ).
fof(f20,axiom,
! [X0] :
( l1_vectsp_1(X0)
=> l1_group_1(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_vectsp_1) ).
fof(f23,axiom,
! [X0] :
( l2_vectsp_1(X0)
=> ( l2_struct_0(X0)
& l1_vectsp_1(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_vectsp_1) ).
fof(f24,axiom,
! [X0] :
( l3_vectsp_1(X0)
=> ( l2_vectsp_1(X0)
& l1_rlvect_1(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_vectsp_1) ).
fof(f64,axiom,
! [X0,X1] : r1_tarski(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f65,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_rmod_2(X3,X0,X1)
& v3_vectsp_2(X3,X0) )
=> ( X2 = u1_struct_0(X3)
=> ( k1_rmod_5(X0,X1,X2) = X3
| k1_rlvect_1(X0) = k2_group_1(X0) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_rmod_5) ).
fof(f68,axiom,
! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
<=> r1_tarski(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f74,plain,
! [X0] : r1_tarski(X0,X0),
inference(rectify,[],[f64]) ).
fof(f75,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
=> m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(unused_predicate_definition_removal,[],[f68]) ).
fof(f79,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)))
& X2 = u1_struct_0(X1)
& k1_rmod_5(X0,X1,X2) != X1
& k1_rlvect_1(X0) != k2_group_1(X0) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f80,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)))
& X2 = u1_struct_0(X1)
& k1_rmod_5(X0,X1,X2) != X1
& k1_rlvect_1(X0) != k2_group_1(X0) ) ) ),
inference(flattening,[],[f79]) ).
fof(f81,plain,
! [X0,X1] :
( ~ l1_vectsp_2(X1,X0)
| ~ l1_struct_0(X0)
| ~ v3_vectsp_2(X1,X0)
| X1 = g1_vectsp_2(X0,u1_struct_0(X1),u1_rlvect_1(X1),u2_struct_0(X1),u1_vectsp_2(X0,X1)) ),
inference(ennf_transformation,[],[f3]) ).
fof(f82,plain,
! [X0,X1] :
( ~ l1_vectsp_2(X1,X0)
| ~ l1_struct_0(X0)
| ~ v3_vectsp_2(X1,X0)
| X1 = g1_vectsp_2(X0,u1_struct_0(X1),u1_rlvect_1(X1),u2_struct_0(X1),u1_vectsp_2(X0,X1)) ),
inference(flattening,[],[f81]) ).
fof(f88,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)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| k2_rmod_2(X0,X1) = g1_vectsp_2(X0,u1_struct_0(X1),u1_rlvect_1(X1),u2_struct_0(X1),u1_vectsp_2(X0,X1)) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f89,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)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| k2_rmod_2(X0,X1) = g1_vectsp_2(X0,u1_struct_0(X1),u1_rlvect_1(X1),u2_struct_0(X1),u1_vectsp_2(X0,X1)) ) ),
inference(flattening,[],[f88]) ).
fof(f97,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)
| ( m1_rmod_2(k2_rmod_2(X0,X1),X0,X1)
& v3_vectsp_2(k2_rmod_2(X0,X1),X0) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f98,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)
| ( m1_rmod_2(k2_rmod_2(X0,X1),X0,X1)
& v3_vectsp_2(k2_rmod_2(X0,X1),X0) ) ),
inference(flattening,[],[f97]) ).
fof(f99,plain,
! [X0] :
( ~ l1_group_1(X0)
| l1_struct_0(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f101,plain,
! [X0] :
( ~ l1_vectsp_1(X0)
| l1_group_1(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f104,plain,
! [X0] :
( ~ l2_vectsp_1(X0)
| ( l2_struct_0(X0)
& l1_vectsp_1(X0) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f105,plain,
! [X0] :
( ~ l3_vectsp_1(X0)
| ( l2_vectsp_1(X0)
& l1_rlvect_1(X0) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f135,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_rmod_2(X3,X0,X1)
| ~ v3_vectsp_2(X3,X0)
| u1_struct_0(X3) != X2
| k1_rmod_5(X0,X1,X2) = X3
| k1_rlvect_1(X0) = k2_group_1(X0) ) ) ) ),
inference(ennf_transformation,[],[f65]) ).
fof(f136,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_rmod_2(X3,X0,X1)
| ~ v3_vectsp_2(X3,X0)
| u1_struct_0(X3) != X2
| k1_rmod_5(X0,X1,X2) = X3
| k1_rlvect_1(X0) = k2_group_1(X0) ) ) ) ),
inference(flattening,[],[f135]) ).
fof(f140,plain,
! [X0,X1] :
( ~ r1_tarski(X0,X1)
| m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(ennf_transformation,[],[f75]) ).
fof(f147,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)))
& sK2 = u1_struct_0(sK1)
& sK1 != k1_rmod_5(sK0,sK1,sK2)
& k1_rlvect_1(sK0) != k2_group_1(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f80]) ).
fof(f173,plain,
l3_vectsp_1(sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f174,plain,
v2_vectsp_2(sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f175,plain,
~ v10_vectsp_1(sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f176,plain,
v8_vectsp_1(sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f177,plain,
v7_vectsp_1(sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f178,plain,
v6_vectsp_1(sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f179,plain,
v7_group_1(sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f180,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f181,plain,
v6_rlvect_1(sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f182,plain,
v5_rlvect_1(sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f183,plain,
v4_rlvect_1(sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f184,plain,
v3_rlvect_1(sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f185,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f186,plain,
l1_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f187,plain,
v5_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f188,plain,
v3_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f189,plain,
v6_rlvect_1(sK1),
inference(cnf_transformation,[],[f147]) ).
fof(f190,plain,
v5_rlvect_1(sK1),
inference(cnf_transformation,[],[f147]) ).
fof(f191,plain,
v4_rlvect_1(sK1),
inference(cnf_transformation,[],[f147]) ).
fof(f192,plain,
v3_rlvect_1(sK1),
inference(cnf_transformation,[],[f147]) ).
fof(f193,plain,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f147]) ).
fof(f195,plain,
sK2 = u1_struct_0(sK1),
inference(cnf_transformation,[],[f147]) ).
fof(f196,plain,
sK1 != k1_rmod_5(sK0,sK1,sK2),
inference(cnf_transformation,[],[f147]) ).
fof(f197,plain,
k1_rlvect_1(sK0) != k2_group_1(sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f198,plain,
! [X0,X1] :
( ~ l1_vectsp_2(X1,X0)
| ~ l1_struct_0(X0)
| ~ v3_vectsp_2(X1,X0)
| g1_vectsp_2(X0,u1_struct_0(X1),u1_rlvect_1(X1),u2_struct_0(X1),u1_vectsp_2(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f82]) ).
fof(f206,plain,
! [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)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| g1_vectsp_2(X0,u1_struct_0(X1),u1_rlvect_1(X1),u2_struct_0(X1),u1_vectsp_2(X0,X1)) = k2_rmod_2(X0,X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f213,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)
| m1_rmod_2(k2_rmod_2(X0,X1),X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f215,plain,
! [X0] :
( ~ l1_group_1(X0)
| l1_struct_0(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f217,plain,
! [X0] :
( ~ l1_vectsp_1(X0)
| l1_group_1(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f221,plain,
! [X0] :
( ~ l2_vectsp_1(X0)
| l1_vectsp_1(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f222,plain,
! [X0] :
( ~ l3_vectsp_1(X0)
| l2_vectsp_1(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f303,plain,
! [X0] : r1_tarski(X0,X0),
inference(cnf_transformation,[],[f74]) ).
fof(f304,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_rmod_2(X3,X0,X1)
| ~ v3_vectsp_2(X3,X0)
| u1_struct_0(X3) != X2
| k1_rmod_5(X0,X1,X2) = X3
| k1_rlvect_1(X0) = k2_group_1(X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f307,plain,
! [X0,X1] :
( ~ r1_tarski(X0,X1)
| m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[],[f140]) ).
fof(f313,plain,
! [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(u1_struct_0(X3),k1_zfmisc_1(u1_struct_0(X1)))
| ~ m1_rmod_2(X3,X0,X1)
| ~ v3_vectsp_2(X3,X0)
| k1_rmod_5(X0,X1,u1_struct_0(X3)) = X3
| k1_rlvect_1(X0) = k2_group_1(X0) ),
inference(equality_resolution,[],[f304]) ).
tcf(c_49,negated_conjecture,
k1_rlvect_1(sK0) != k2_group_1(sK0),
inference(cnf_transformation,[],[f197]) ).
tcf(c_50,negated_conjecture,
k1_rmod_5(sK0,sK1,sK2) != sK1,
inference(cnf_transformation,[],[f196]) ).
tcf(c_51,negated_conjecture,
u1_struct_0(sK1) = sK2,
inference(cnf_transformation,[],[f195]) ).
tcf(c_53,negated_conjecture,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f193]) ).
tcf(c_54,negated_conjecture,
v3_rlvect_1(sK1),
inference(cnf_transformation,[],[f192]) ).
tcf(c_55,negated_conjecture,
v4_rlvect_1(sK1),
inference(cnf_transformation,[],[f191]) ).
tcf(c_56,negated_conjecture,
v5_rlvect_1(sK1),
inference(cnf_transformation,[],[f190]) ).
tcf(c_57,negated_conjecture,
v6_rlvect_1(sK1),
inference(cnf_transformation,[],[f189]) ).
tcf(c_58,negated_conjecture,
v3_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f188]) ).
tcf(c_59,negated_conjecture,
v5_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f187]) ).
tcf(c_60,negated_conjecture,
l1_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f186]) ).
tcf(c_61,negated_conjecture,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f185]) ).
tcf(c_62,negated_conjecture,
v3_rlvect_1(sK0),
inference(cnf_transformation,[],[f184]) ).
tcf(c_63,negated_conjecture,
v4_rlvect_1(sK0),
inference(cnf_transformation,[],[f183]) ).
tcf(c_64,negated_conjecture,
v5_rlvect_1(sK0),
inference(cnf_transformation,[],[f182]) ).
tcf(c_65,negated_conjecture,
v6_rlvect_1(sK0),
inference(cnf_transformation,[],[f181]) ).
tcf(c_66,negated_conjecture,
v4_group_1(sK0),
inference(cnf_transformation,[],[f180]) ).
tcf(c_67,negated_conjecture,
v7_group_1(sK0),
inference(cnf_transformation,[],[f179]) ).
tcf(c_68,negated_conjecture,
v6_vectsp_1(sK0),
inference(cnf_transformation,[],[f178]) ).
tcf(c_69,negated_conjecture,
v7_vectsp_1(sK0),
inference(cnf_transformation,[],[f177]) ).
tcf(c_70,negated_conjecture,
v8_vectsp_1(sK0),
inference(cnf_transformation,[],[f176]) ).
tcf(c_71,negated_conjecture,
~ v10_vectsp_1(sK0),
inference(cnf_transformation,[],[f175]) ).
tcf(c_72,negated_conjecture,
v2_vectsp_2(sK0),
inference(cnf_transformation,[],[f174]) ).
tcf(c_73,negated_conjecture,
l3_vectsp_1(sK0),
inference(cnf_transformation,[],[f173]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( ( g1_vectsp_2(X1,u1_struct_0(X0),u1_rlvect_1(X0),u2_struct_0(X0),u1_vectsp_2(X1,X0)) = X0 )
| ~ l1_struct_0(X1)
| ~ l1_vectsp_2(X0,X1)
| ~ v3_vectsp_2(X0,X1) ),
inference(cnf_transformation,[],[f198]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v3_struct_0(X0)
| ( g1_vectsp_2(X1,u1_struct_0(X0),u1_rlvect_1(X0),u2_struct_0(X0),u1_vectsp_2(X1,X0)) = k2_rmod_2(X1,X0) )
| ~ l3_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X1)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X1)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X1)
| ~ v3_rlvect_1(X0)
| ~ l1_vectsp_2(X0,X1)
| ~ v5_vectsp_2(X0,X1) ),
inference(cnf_transformation,[],[f206]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v3_struct_0(X0)
| m1_rmod_2(k2_rmod_2(X1,X0),X1,X0)
| ~ l3_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X1)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X1)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X1)
| ~ v3_rlvect_1(X0)
| ~ l1_vectsp_2(X0,X1)
| ~ v5_vectsp_2(X0,X1) ),
inference(cnf_transformation,[],[f213]) ).
tcf(c_87,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f215]) ).
tcf(c_89,plain,
! [X0: $i] :
( l1_group_1(X0)
| ~ l1_vectsp_1(X0) ),
inference(cnf_transformation,[],[f217]) ).
tcf(c_92,plain,
! [X0: $i] :
( l1_vectsp_1(X0)
| ~ l2_vectsp_1(X0) ),
inference(cnf_transformation,[],[f221]) ).
tcf(c_95,plain,
! [X0: $i] :
( l2_vectsp_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(cnf_transformation,[],[f222]) ).
tcf(c_175,plain,
! [X0: $i] : r1_tarski(X0,X0),
inference(cnf_transformation,[],[f303]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i,X2: $i] :
( v10_vectsp_1(X2)
| v3_struct_0(X2)
| v3_struct_0(X1)
| ( k1_rlvect_1(X2) = k2_group_1(X2) )
| ( k1_rmod_5(X2,X1,u1_struct_0(X0)) = X0 )
| ~ 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)
| ~ v3_vectsp_2(X0,X2)
| ~ m1_rmod_2(X0,X2,X1)
| ~ m1_subset_1(u1_struct_0(X0),k1_zfmisc_1(u1_struct_0(X1))) ),
inference(cnf_transformation,[],[f313]) ).
tcf(c_179,plain,
! [X0: $i,X1: $i] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f307]) ).
tcf(c_285,plain,
! [X0: $i] :
( ~ l1_group_1(X0)
| l1_struct_0(X0) ),
inference(prop_impl_just,[status(thm)],[c_87]) ).
tcf(c_286,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(renaming,[status(thm)],[c_285]) ).
tcf(c_295,plain,
! [X0: $i] :
( l1_group_1(X0)
| ~ l1_vectsp_1(X0) ),
inference(prop_impl_just,[status(thm)],[c_89]) ).
tcf(c_297,plain,
! [X0: $i] :
( ~ l2_vectsp_1(X0)
| l1_vectsp_1(X0) ),
inference(prop_impl_just,[status(thm)],[c_92]) ).
tcf(c_298,plain,
! [X0: $i] :
( l1_vectsp_1(X0)
| ~ l2_vectsp_1(X0) ),
inference(renaming,[status(thm)],[c_297]) ).
tcf(c_301,plain,
! [X0: $i] :
( l2_vectsp_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(prop_impl_just,[status(thm)],[c_95]) ).
tcf(c_345,plain,
! [X0: $i,X1: $i] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_179]) ).
tcf(c_3802,plain,
! [X0: $i,X1: $i,X2: $i] :
( m1_subset_1(X1,k1_zfmisc_1(X2))
| ( X0 != X2 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_175,c_345]) ).
tcf(c_3803,plain,
! [X0: $i] : m1_subset_1(X0,k1_zfmisc_1(X0)),
inference(unflattening,[status(thm)],[c_3802]) ).
tcf(c_3818,plain,
! [X0: $i,X1: $i] :
( l1_vectsp_1(X1)
| ~ l3_vectsp_1(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_301,c_298]) ).
tcf(c_3819,plain,
! [X0: $i] :
( l1_vectsp_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(unflattening,[status(thm)],[c_3818]) ).
tcf(c_3843,plain,
! [X0: $i,X1: $i] :
( l1_struct_0(X1)
| ~ l1_vectsp_1(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_295,c_286]) ).
tcf(c_3844,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l1_vectsp_1(X0) ),
inference(unflattening,[status(thm)],[c_3843]) ).
tcf(c_4215,plain,
! [X0: $i,X1: $i] :
( l1_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_3819,c_3844]) ).
tcf(c_4216,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l3_vectsp_1(X0) ),
inference(unflattening,[status(thm)],[c_4215]) ).
tcf(c_4376,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X2)
| v3_struct_0(X0)
| ( k1_rlvect_1(X0) = k2_group_1(X0) )
| ( k1_rmod_5(X0,X2,u1_struct_0(X1)) = X1 )
| ~ l3_vectsp_1(X0)
| ~ v2_vectsp_2(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_group_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)
| ~ v3_vectsp_2(X1,X0)
| ~ m1_rmod_2(X1,X0,X2)
| ~ m1_subset_1(u1_struct_0(X1),k1_zfmisc_1(u1_struct_0(X2)))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_71,c_176]) ).
tcf(c_4377,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| v3_struct_0(X1)
| ( k1_rlvect_1(sK0) = k2_group_1(sK0) )
| ( k1_rmod_5(sK0,X1,u1_struct_0(X0)) = X0 )
| ~ l3_vectsp_1(sK0)
| ~ v2_vectsp_2(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)
| ~ 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(X0,sK0)
| ~ m1_rmod_2(X0,sK0,X1)
| ~ m1_subset_1(u1_struct_0(X0),k1_zfmisc_1(u1_struct_0(X1))) ),
inference(unflattening,[status(thm)],[c_4376]) ).
tcf(c_4379,plain,
! [X0: $i,X1: $i] :
( ( k1_rmod_5(sK0,X1,u1_struct_0(X0)) = X0 )
| ~ m1_subset_1(u1_struct_0(X0),k1_zfmisc_1(u1_struct_0(X1)))
| ~ m1_rmod_2(X0,sK0,X1)
| ~ v3_vectsp_2(X0,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)
| v3_struct_0(X1) ),
inference(global_subsumption_just,[status(thm)],[c_4377,c_73,c_72,c_70,c_69,c_68,c_67,c_66,c_65,c_64,c_63,c_62,c_61,c_49,c_4377]) ).
tcf(c_4380,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| ( k1_rmod_5(sK0,X1,u1_struct_0(X0)) = 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)
| ~ v3_vectsp_2(X0,sK0)
| ~ m1_rmod_2(X0,sK0,X1)
| ~ m1_subset_1(u1_struct_0(X0),k1_zfmisc_1(u1_struct_0(X1))) ),
inference(renaming,[status(thm)],[c_4379]) ).
tcf(c_5887,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v3_struct_0(X0)
| m1_rmod_2(k2_rmod_2(X0,X1),X0,X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v6_rlvect_1(X1)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X1)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X1)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X1)
| ~ v3_rlvect_1(X0)
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_66,c_86]) ).
tcf(c_5888,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| v3_struct_0(X0)
| m1_rmod_2(k2_rmod_2(sK0,X0),sK0,X0)
| ~ 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(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| ~ l1_vectsp_2(X0,sK0)
| ~ v5_vectsp_2(X0,sK0) ),
inference(unflattening,[status(thm)],[c_5887]) ).
tcf(c_5890,plain,
! [X0: $i] :
( ~ v5_vectsp_2(X0,sK0)
| ~ l1_vectsp_2(X0,sK0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| m1_rmod_2(k2_rmod_2(sK0,X0),sK0,X0)
| v3_struct_0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_5888,c_73,c_70,c_69,c_68,c_65,c_64,c_63,c_62,c_61,c_5888]) ).
tcf(c_5891,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m1_rmod_2(k2_rmod_2(sK0,X0),sK0,X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| ~ l1_vectsp_2(X0,sK0)
| ~ v5_vectsp_2(X0,sK0) ),
inference(renaming,[status(thm)],[c_5890]) ).
tcf(c_5947,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v3_struct_0(X0)
| ( g1_vectsp_2(X0,u1_struct_0(X1),u1_rlvect_1(X1),u2_struct_0(X1),u1_vectsp_2(X0,X1)) = k2_rmod_2(X0,X1) )
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v6_rlvect_1(X1)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X1)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X1)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X1)
| ~ v3_rlvect_1(X0)
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_66,c_78]) ).
tcf(c_5948,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| v3_struct_0(X0)
| ( g1_vectsp_2(sK0,u1_struct_0(X0),u1_rlvect_1(X0),u2_struct_0(X0),u1_vectsp_2(sK0,X0)) = k2_rmod_2(sK0,X0) )
| ~ 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(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| ~ l1_vectsp_2(X0,sK0)
| ~ v5_vectsp_2(X0,sK0) ),
inference(unflattening,[status(thm)],[c_5947]) ).
tcf(c_5950,plain,
! [X0: $i] :
( ~ v5_vectsp_2(X0,sK0)
| ~ l1_vectsp_2(X0,sK0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ( g1_vectsp_2(sK0,u1_struct_0(X0),u1_rlvect_1(X0),u2_struct_0(X0),u1_vectsp_2(sK0,X0)) = k2_rmod_2(sK0,X0) )
| v3_struct_0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_5948,c_73,c_70,c_69,c_68,c_65,c_64,c_63,c_62,c_61,c_5948]) ).
tcf(c_5951,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ( g1_vectsp_2(sK0,u1_struct_0(X0),u1_rlvect_1(X0),u2_struct_0(X0),u1_vectsp_2(sK0,X0)) = k2_rmod_2(sK0,X0) )
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| ~ l1_vectsp_2(X0,sK0)
| ~ v5_vectsp_2(X0,sK0) ),
inference(renaming,[status(thm)],[c_5950]) ).
tcf(c_6158,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_73,c_4216]) ).
tcf(c_6159,plain,
l1_struct_0(sK0),
inference(unflattening,[status(thm)],[c_6158]) ).
tcf(c_20161,definition,
iPr_def_16 = u1_struct_0(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_20162,definition,
iPr_def_17 = k1_rmod_5(sK0,sK1,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_20166,plain,
l1_struct_0(sK0),
inference(demodulation,[status(thm)],[c_6159]) ).
tcf(c_20168,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ( g1_vectsp_2(sK0,u1_struct_0(X0),u1_rlvect_1(X0),u2_struct_0(X0),u1_vectsp_2(sK0,X0)) = k2_rmod_2(sK0,X0) )
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| ~ l1_vectsp_2(X0,sK0)
| ~ v5_vectsp_2(X0,sK0) ),
inference(demodulation,[status(thm)],[c_5951]) ).
tcf(c_20170,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m1_rmod_2(k2_rmod_2(sK0,X0),sK0,X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| ~ l1_vectsp_2(X0,sK0)
| ~ v5_vectsp_2(X0,sK0) ),
inference(demodulation,[status(thm)],[c_5891]) ).
tcf(c_20204,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| ( k1_rmod_5(sK0,X1,u1_struct_0(X0)) = 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)
| ~ v3_vectsp_2(X0,sK0)
| ~ m1_rmod_2(X0,sK0,X1)
| ~ m1_subset_1(u1_struct_0(X0),k1_zfmisc_1(u1_struct_0(X1))) ),
inference(demodulation,[status(thm)],[c_4380]) ).
tcf(c_20210,negated_conjecture,
l1_vectsp_2(sK1,sK0),
inference(demodulation,[status(thm)],[c_60]) ).
tcf(c_20211,negated_conjecture,
v5_vectsp_2(sK1,sK0),
inference(demodulation,[status(thm)],[c_59]) ).
tcf(c_20212,negated_conjecture,
v3_vectsp_2(sK1,sK0),
inference(demodulation,[status(thm)],[c_58]) ).
tcf(c_20213,negated_conjecture,
v6_rlvect_1(sK1),
inference(demodulation,[status(thm)],[c_57]) ).
tcf(c_20214,negated_conjecture,
v5_rlvect_1(sK1),
inference(demodulation,[status(thm)],[c_56]) ).
tcf(c_20215,negated_conjecture,
v4_rlvect_1(sK1),
inference(demodulation,[status(thm)],[c_55]) ).
tcf(c_20216,negated_conjecture,
v3_rlvect_1(sK1),
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_20217,negated_conjecture,
~ v3_struct_0(sK1),
inference(demodulation,[status(thm)],[c_53]) ).
tcf(c_20218,negated_conjecture,
iPr_def_16 = sK2,
inference(demodulation,[status(thm)],[c_51,c_20161]) ).
tcf(c_20219,negated_conjecture,
iPr_def_17 != sK1,
inference(demodulation,[status(thm)],[c_50,c_20162]) ).
tcf(c_23260,plain,
k1_rmod_5(sK0,sK1,iPr_def_16) = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_20162,c_20218]) ).
tcf(c_23785,plain,
( v3_struct_0(sK1)
| ( g1_vectsp_2(sK0,u1_struct_0(sK1),u1_rlvect_1(sK1),u2_struct_0(sK1),u1_vectsp_2(sK0,sK1)) = k2_rmod_2(sK0,sK1) )
| ~ v6_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| ~ l1_vectsp_2(sK1,sK0) ),
inference(superposition,[status(thm)],[c_20211,c_20168]) ).
tcf(c_23791,plain,
( v3_struct_0(sK1)
| ( g1_vectsp_2(sK0,iPr_def_16,u1_rlvect_1(sK1),u2_struct_0(sK1),u1_vectsp_2(sK0,sK1)) = k2_rmod_2(sK0,sK1) )
| ~ v6_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| ~ l1_vectsp_2(sK1,sK0) ),
inference(light_normalisation,[status(thm)],[c_23785,c_20161]) ).
tcf(c_23792,plain,
g1_vectsp_2(sK0,iPr_def_16,u1_rlvect_1(sK1),u2_struct_0(sK1),u1_vectsp_2(sK0,sK1)) = k2_rmod_2(sK0,sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_23791,c_20217,c_20213,c_20214,c_20215,c_20216,c_20210]) ).
tcf(c_23833,plain,
! [X0: $i] :
( v3_struct_0(sK1)
| ( k1_rmod_5(sK0,sK1,u1_struct_0(X0)) = 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)
| ~ v3_vectsp_2(X0,sK0)
| ~ m1_rmod_2(X0,sK0,sK1)
| ~ m1_subset_1(u1_struct_0(X0),k1_zfmisc_1(iPr_def_16)) ),
inference(superposition,[status(thm)],[c_20161,c_20204]) ).
tcf(c_23852,plain,
! [X0: $i] :
( ( k1_rmod_5(sK0,sK1,u1_struct_0(X0)) = X0 )
| ~ v3_vectsp_2(X0,sK0)
| ~ m1_rmod_2(X0,sK0,sK1)
| ~ m1_subset_1(u1_struct_0(X0),k1_zfmisc_1(iPr_def_16)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23833,c_20217,c_20213,c_20214,c_20215,c_20216,c_20210,c_20211]) ).
tcf(c_23894,plain,
( ( k1_rmod_5(sK0,sK1,u1_struct_0(sK1)) = sK1 )
| ~ v3_vectsp_2(sK1,sK0)
| ~ m1_rmod_2(sK1,sK0,sK1)
| ~ m1_subset_1(iPr_def_16,k1_zfmisc_1(iPr_def_16)) ),
inference(superposition,[status(thm)],[c_20161,c_23852]) ).
tcf(c_23901,plain,
( ( sK1 = iPr_def_17 )
| ~ v3_vectsp_2(sK1,sK0)
| ~ m1_rmod_2(sK1,sK0,sK1)
| ~ m1_subset_1(iPr_def_16,k1_zfmisc_1(iPr_def_16)) ),
inference(light_normalisation,[status(thm)],[c_23894,c_20161,c_23260]) ).
tcf(c_23902,plain,
( ( sK1 = iPr_def_17 )
| ~ m1_rmod_2(sK1,sK0,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23901,c_20212,c_3803]) ).
tcf(c_24824,plain,
( ( g1_vectsp_2(sK0,u1_struct_0(sK1),u1_rlvect_1(sK1),u2_struct_0(sK1),u1_vectsp_2(sK0,sK1)) = sK1 )
| ~ l1_struct_0(sK0)
| ~ l1_vectsp_2(sK1,sK0) ),
inference(superposition,[status(thm)],[c_20212,c_74]) ).
tcf(c_24837,plain,
( ( k2_rmod_2(sK0,sK1) = sK1 )
| ~ l1_struct_0(sK0)
| ~ l1_vectsp_2(sK1,sK0) ),
inference(light_normalisation,[status(thm)],[c_24824,c_20161,c_23792]) ).
tcf(c_24838,plain,
k2_rmod_2(sK0,sK1) = sK1,
inference(forward_subsumption_resolution,[status(thm)],[c_24837,c_20166,c_20210]) ).
tcf(c_25041,plain,
( v3_struct_0(sK1)
| m1_rmod_2(sK1,sK0,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) ),
inference(superposition,[status(thm)],[c_24838,c_20170]) ).
tcf(c_25043,plain,
m1_rmod_2(sK1,sK0,sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_25041,c_20217,c_20213,c_20214,c_20215,c_20216,c_20210,c_20211]) ).
tcf(c_25044,plain,
sK1 = iPr_def_17,
inference(backward_subsumption_resolution,[status(thm)],[c_23902,c_25043]) ).
tcf(c_25067,plain,
iPr_def_17 != iPr_def_17,
inference(demodulation,[status(thm)],[c_20219,c_25044]) ).
tcf(c_25076,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_25067]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG219+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n016.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Fri Sep 25 05:12:43 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 3.01/1.73 % SZS status Started for theBenchmark.p
% 3.01/1.73 % SZS status Theorem for theBenchmark.p
% 3.01/1.73
% 3.01/1.73 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.01/1.73
% 3.01/1.73 % ------ iProver source info
% 3.01/1.73
% 3.01/1.73 % git: date: 2026-07-19 20:42:38 +0200
% 3.01/1.73 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.01/1.73 % git: non_committed_changes: false
% 3.01/1.73
% 3.01/1.73 % ------ Parsing...
% 3.01/1.73 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.01/1.73
% 3.01/1.73 % ------ Preprocessing... sup_sim: 1 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: 13 0s sf_e pe_s pe_e %
% 3.01/1.73
% 3.01/1.73 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.01/1.73
% 3.01/1.73 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.01/1.73 % ------ Proving...
% 3.01/1.73 % ------ Problem Properties
% 3.01/1.73
% 3.01/1.73 %
% 3.01/1.73 % clauses 141
% 3.01/1.73 % conjectures 16
% 3.01/1.73 % EPR 68
% 3.01/1.73 % Horn 113
% 3.01/1.73 % unary 74
% 3.01/1.73 % binary 24
% 3.01/1.73 % lits 428
% 3.01/1.73 % lits eq 26
% 3.01/1.73 % fd_pure 0
% 3.01/1.73 % fd_pseudo 0
% 3.01/1.73 % fd_cond 1
% 3.01/1.73 % fd_pseudo_cond 6
% 3.01/1.73 % AC symbols 0
% 3.01/1.73
% 3.01/1.73 % ------ Schedule dynamic 5 is on
% 3.01/1.73
% 3.01/1.73 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.01/1.73
% 3.01/1.73
% 3.01/1.73 % ------
% 3.01/1.73 % Current options:
% 3.01/1.73 % ------
% 3.01/1.73
% 3.01/1.73
% 3.01/1.73 %
% 3.01/1.73
% 3.01/1.73 % ------ Proving...
% 3.01/1.73 %
% 3.01/1.73
% 3.01/1.73 % SZS status Theorem for theBenchmark.p
% 3.01/1.73
% 3.01/1.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.01/1.74
% 3.01/1.74
%------------------------------------------------------------------------------