TSTP Solution File: ALG219+1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : ALG219+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 3 02:04:19 EDT 2024
% Result : Theorem 7.78s 1.66s
% Output : CNFRefutation 7.78s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% 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)))
=> ( u1_struct_0(X1) = X2
=> ( 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)))
=> ( u1_struct_0(X1) = X2
=> ( k1_rmod_5(X0,X1,X2) = X1
| k1_rlvect_1(X0) = k2_group_1(X0) ) ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f3,axiom,
! [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 ) ),
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) )
=> 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) ) ),
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) )
=> ( u1_struct_0(X3) = X2
=> ( 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] :
( ? [X1] :
( ? [X2] :
( k1_rmod_5(X0,X1,X2) != X1
& k1_rlvect_1(X0) != k2_group_1(X0)
& u1_struct_0(X1) = X2
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(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) )
& 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) ),
inference(ennf_transformation,[],[f2]) ).
fof(f80,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( k1_rmod_5(X0,X1,X2) != X1
& k1_rlvect_1(X0) != k2_group_1(X0)
& u1_struct_0(X1) = X2
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(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) )
& 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) ),
inference(flattening,[],[f79]) ).
fof(f81,plain,
! [X0,X1] :
( g1_vectsp_2(X0,u1_struct_0(X1),u1_rlvect_1(X1),u2_struct_0(X1),u1_vectsp_2(X0,X1)) = X1
| ~ v3_vectsp_2(X1,X0)
| ~ l1_vectsp_2(X1,X0)
| ~ l1_struct_0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f82,plain,
! [X0,X1] :
( g1_vectsp_2(X0,u1_struct_0(X1),u1_rlvect_1(X1),u2_struct_0(X1),u1_vectsp_2(X0,X1)) = X1
| ~ v3_vectsp_2(X1,X0)
| ~ l1_vectsp_2(X1,X0)
| ~ l1_struct_0(X0) ),
inference(flattening,[],[f81]) ).
fof(f88,plain,
! [X0] :
( ! [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)
| ~ 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) ),
inference(ennf_transformation,[],[f8]) ).
fof(f89,plain,
! [X0] :
( ! [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)
| ~ 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) ),
inference(flattening,[],[f88]) ).
fof(f97,plain,
! [X0,X1] :
( ( m1_rmod_2(k2_rmod_2(X0,X1),X0,X1)
& v3_vectsp_2(k2_rmod_2(X0,X1),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)
| ~ 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) ),
inference(ennf_transformation,[],[f15]) ).
fof(f98,plain,
! [X0,X1] :
( ( m1_rmod_2(k2_rmod_2(X0,X1),X0,X1)
& v3_vectsp_2(k2_rmod_2(X0,X1),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)
| ~ 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) ),
inference(flattening,[],[f97]) ).
fof(f99,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f101,plain,
! [X0] :
( l1_group_1(X0)
| ~ l1_vectsp_1(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f104,plain,
! [X0] :
( ( l2_struct_0(X0)
& l1_vectsp_1(X0) )
| ~ l2_vectsp_1(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f105,plain,
! [X0] :
( ( l2_vectsp_1(X0)
& l1_rlvect_1(X0) )
| ~ l3_vectsp_1(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f135,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( k1_rmod_5(X0,X1,X2) = X3
| k1_rlvect_1(X0) = k2_group_1(X0)
| u1_struct_0(X3) != X2
| ~ m1_rmod_2(X3,X0,X1)
| ~ v3_vectsp_2(X3,X0) )
| ~ 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) ),
inference(ennf_transformation,[],[f65]) ).
fof(f136,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( k1_rmod_5(X0,X1,X2) = X3
| k1_rlvect_1(X0) = k2_group_1(X0)
| u1_struct_0(X3) != X2
| ~ m1_rmod_2(X3,X0,X1)
| ~ v3_vectsp_2(X3,X0) )
| ~ 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) ),
inference(flattening,[],[f135]) ).
fof(f140,plain,
! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ),
inference(ennf_transformation,[],[f75]) ).
fof(f147,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( k1_rmod_5(X0,X1,X2) != X1
& k1_rlvect_1(X0) != k2_group_1(X0)
& u1_struct_0(X1) = X2
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(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) )
& 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] :
( ? [X2] :
( k1_rmod_5(sK0,X1,X2) != X1
& k1_rlvect_1(sK0) != k2_group_1(sK0)
& u1_struct_0(X1) = X2
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
& l1_vectsp_2(X1,sK0)
& v5_vectsp_2(X1,sK0)
& v3_vectsp_2(X1,sK0)
& v6_rlvect_1(X1)
& v5_rlvect_1(X1)
& v4_rlvect_1(X1)
& v3_rlvect_1(X1)
& ~ v3_struct_0(X1) )
& 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) ) ),
introduced(choice_axiom,[]) ).
fof(f148,plain,
( ? [X1] :
( ? [X2] :
( k1_rmod_5(sK0,X1,X2) != X1
& k1_rlvect_1(sK0) != k2_group_1(sK0)
& u1_struct_0(X1) = X2
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
& l1_vectsp_2(X1,sK0)
& v5_vectsp_2(X1,sK0)
& v3_vectsp_2(X1,sK0)
& v6_rlvect_1(X1)
& v5_rlvect_1(X1)
& v4_rlvect_1(X1)
& v3_rlvect_1(X1)
& ~ v3_struct_0(X1) )
=> ( ? [X2] :
( sK1 != k1_rmod_5(sK0,sK1,X2)
& k1_rlvect_1(sK0) != k2_group_1(sK0)
& u1_struct_0(sK1) = X2
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(sK1))) )
& 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) ) ),
introduced(choice_axiom,[]) ).
fof(f149,plain,
( ? [X2] :
( sK1 != k1_rmod_5(sK0,sK1,X2)
& k1_rlvect_1(sK0) != k2_group_1(sK0)
& u1_struct_0(sK1) = X2
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(sK1))) )
=> ( sK1 != k1_rmod_5(sK0,sK1,sK2)
& k1_rlvect_1(sK0) != k2_group_1(sK0)
& u1_struct_0(sK1) = sK2
& m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1))) ) ),
introduced(choice_axiom,[]) ).
fof(f150,plain,
( sK1 != k1_rmod_5(sK0,sK1,sK2)
& k1_rlvect_1(sK0) != k2_group_1(sK0)
& u1_struct_0(sK1) = sK2
& m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
& 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)
& 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) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f80,f149,f148,f147]) ).
fof(f200,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f150]) ).
fof(f201,plain,
v3_rlvect_1(sK0),
inference(cnf_transformation,[],[f150]) ).
fof(f202,plain,
v4_rlvect_1(sK0),
inference(cnf_transformation,[],[f150]) ).
fof(f203,plain,
v5_rlvect_1(sK0),
inference(cnf_transformation,[],[f150]) ).
fof(f204,plain,
v6_rlvect_1(sK0),
inference(cnf_transformation,[],[f150]) ).
fof(f205,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f150]) ).
fof(f206,plain,
v7_group_1(sK0),
inference(cnf_transformation,[],[f150]) ).
fof(f207,plain,
v6_vectsp_1(sK0),
inference(cnf_transformation,[],[f150]) ).
fof(f208,plain,
v7_vectsp_1(sK0),
inference(cnf_transformation,[],[f150]) ).
fof(f209,plain,
v8_vectsp_1(sK0),
inference(cnf_transformation,[],[f150]) ).
fof(f210,plain,
~ v10_vectsp_1(sK0),
inference(cnf_transformation,[],[f150]) ).
fof(f211,plain,
v2_vectsp_2(sK0),
inference(cnf_transformation,[],[f150]) ).
fof(f212,plain,
l3_vectsp_1(sK0),
inference(cnf_transformation,[],[f150]) ).
fof(f213,plain,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f150]) ).
fof(f214,plain,
v3_rlvect_1(sK1),
inference(cnf_transformation,[],[f150]) ).
fof(f215,plain,
v4_rlvect_1(sK1),
inference(cnf_transformation,[],[f150]) ).
fof(f216,plain,
v5_rlvect_1(sK1),
inference(cnf_transformation,[],[f150]) ).
fof(f217,plain,
v6_rlvect_1(sK1),
inference(cnf_transformation,[],[f150]) ).
fof(f218,plain,
v3_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f150]) ).
fof(f219,plain,
v5_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f150]) ).
fof(f220,plain,
l1_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f150]) ).
fof(f222,plain,
u1_struct_0(sK1) = sK2,
inference(cnf_transformation,[],[f150]) ).
fof(f223,plain,
k1_rlvect_1(sK0) != k2_group_1(sK0),
inference(cnf_transformation,[],[f150]) ).
fof(f224,plain,
sK1 != k1_rmod_5(sK0,sK1,sK2),
inference(cnf_transformation,[],[f150]) ).
fof(f225,plain,
! [X0,X1] :
( g1_vectsp_2(X0,u1_struct_0(X1),u1_rlvect_1(X1),u2_struct_0(X1),u1_vectsp_2(X0,X1)) = X1
| ~ v3_vectsp_2(X1,X0)
| ~ l1_vectsp_2(X1,X0)
| ~ l1_struct_0(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f233,plain,
! [X0,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)
| ~ 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) ),
inference(cnf_transformation,[],[f89]) ).
fof(f241,plain,
! [X0,X1] :
( m1_rmod_2(k2_rmod_2(X0,X1),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) ),
inference(cnf_transformation,[],[f98]) ).
fof(f242,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f244,plain,
! [X0] :
( l1_group_1(X0)
| ~ l1_vectsp_1(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f247,plain,
! [X0] :
( l1_vectsp_1(X0)
| ~ l2_vectsp_1(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f250,plain,
! [X0] :
( l2_vectsp_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f330,plain,
! [X0] : r1_tarski(X0,X0),
inference(cnf_transformation,[],[f74]) ).
fof(f331,plain,
! [X2,X3,X0,X1] :
( k1_rmod_5(X0,X1,X2) = X3
| k1_rlvect_1(X0) = k2_group_1(X0)
| u1_struct_0(X3) != X2
| ~ m1_rmod_2(X3,X0,X1)
| ~ v3_vectsp_2(X3,X0)
| ~ 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) ),
inference(cnf_transformation,[],[f136]) ).
fof(f334,plain,
! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f140]) ).
fof(f340,plain,
! [X3,X0,X1] :
( k1_rmod_5(X0,X1,u1_struct_0(X3)) = X3
| k1_rlvect_1(X0) = k2_group_1(X0)
| ~ m1_rmod_2(X3,X0,X1)
| ~ v3_vectsp_2(X3,X0)
| ~ m1_subset_1(u1_struct_0(X3),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) ),
inference(equality_resolution,[],[f331]) ).
cnf(c_49,negated_conjecture,
k1_rmod_5(sK0,sK1,sK2) != sK1,
inference(cnf_transformation,[],[f224]) ).
cnf(c_50,negated_conjecture,
k1_rlvect_1(sK0) != k2_group_1(sK0),
inference(cnf_transformation,[],[f223]) ).
cnf(c_51,negated_conjecture,
u1_struct_0(sK1) = sK2,
inference(cnf_transformation,[],[f222]) ).
cnf(c_53,negated_conjecture,
l1_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f220]) ).
cnf(c_54,negated_conjecture,
v5_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f219]) ).
cnf(c_55,negated_conjecture,
v3_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f218]) ).
cnf(c_56,negated_conjecture,
v6_rlvect_1(sK1),
inference(cnf_transformation,[],[f217]) ).
cnf(c_57,negated_conjecture,
v5_rlvect_1(sK1),
inference(cnf_transformation,[],[f216]) ).
cnf(c_58,negated_conjecture,
v4_rlvect_1(sK1),
inference(cnf_transformation,[],[f215]) ).
cnf(c_59,negated_conjecture,
v3_rlvect_1(sK1),
inference(cnf_transformation,[],[f214]) ).
cnf(c_60,negated_conjecture,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f213]) ).
cnf(c_61,negated_conjecture,
l3_vectsp_1(sK0),
inference(cnf_transformation,[],[f212]) ).
cnf(c_62,negated_conjecture,
v2_vectsp_2(sK0),
inference(cnf_transformation,[],[f211]) ).
cnf(c_63,negated_conjecture,
~ v10_vectsp_1(sK0),
inference(cnf_transformation,[],[f210]) ).
cnf(c_64,negated_conjecture,
v8_vectsp_1(sK0),
inference(cnf_transformation,[],[f209]) ).
cnf(c_65,negated_conjecture,
v7_vectsp_1(sK0),
inference(cnf_transformation,[],[f208]) ).
cnf(c_66,negated_conjecture,
v6_vectsp_1(sK0),
inference(cnf_transformation,[],[f207]) ).
cnf(c_67,negated_conjecture,
v7_group_1(sK0),
inference(cnf_transformation,[],[f206]) ).
cnf(c_68,negated_conjecture,
v4_group_1(sK0),
inference(cnf_transformation,[],[f205]) ).
cnf(c_69,negated_conjecture,
v6_rlvect_1(sK0),
inference(cnf_transformation,[],[f204]) ).
cnf(c_70,negated_conjecture,
v5_rlvect_1(sK0),
inference(cnf_transformation,[],[f203]) ).
cnf(c_71,negated_conjecture,
v4_rlvect_1(sK0),
inference(cnf_transformation,[],[f202]) ).
cnf(c_72,negated_conjecture,
v3_rlvect_1(sK0),
inference(cnf_transformation,[],[f201]) ).
cnf(c_73,negated_conjecture,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f200]) ).
cnf(c_74,plain,
( ~ l1_vectsp_2(X0,X1)
| ~ v3_vectsp_2(X0,X1)
| ~ l1_struct_0(X1)
| g1_vectsp_2(X1,u1_struct_0(X0),u1_rlvect_1(X0),u2_struct_0(X0),u1_vectsp_2(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f225]) ).
cnf(c_78,plain,
( ~ l1_vectsp_2(X0,X1)
| ~ v5_vectsp_2(X0,X1)
| ~ v6_rlvect_1(X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X0)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X0)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X0)
| ~ v3_rlvect_1(X1)
| ~ l3_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v4_group_1(X1)
| 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)
| v3_struct_0(X0)
| v3_struct_0(X1) ),
inference(cnf_transformation,[],[f233]) ).
cnf(c_85,plain,
( ~ l1_vectsp_2(X0,X1)
| ~ v5_vectsp_2(X0,X1)
| ~ v6_rlvect_1(X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X0)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X0)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X0)
| ~ v3_rlvect_1(X1)
| ~ l3_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v4_group_1(X1)
| m1_rmod_2(k2_rmod_2(X1,X0),X1,X0)
| v3_struct_0(X0)
| v3_struct_0(X1) ),
inference(cnf_transformation,[],[f241]) ).
cnf(c_87,plain,
( ~ l1_group_1(X0)
| l1_struct_0(X0) ),
inference(cnf_transformation,[],[f242]) ).
cnf(c_89,plain,
( ~ l1_vectsp_1(X0)
| l1_group_1(X0) ),
inference(cnf_transformation,[],[f244]) ).
cnf(c_93,plain,
( ~ l2_vectsp_1(X0)
| l1_vectsp_1(X0) ),
inference(cnf_transformation,[],[f247]) ).
cnf(c_94,plain,
( ~ l3_vectsp_1(X0)
| l2_vectsp_1(X0) ),
inference(cnf_transformation,[],[f250]) ).
cnf(c_175,plain,
r1_tarski(X0,X0),
inference(cnf_transformation,[],[f330]) ).
cnf(c_176,plain,
( ~ m1_subset_1(u1_struct_0(X0),k1_zfmisc_1(u1_struct_0(X1)))
| ~ m1_rmod_2(X0,X2,X1)
| ~ l1_vectsp_2(X1,X2)
| ~ v5_vectsp_2(X1,X2)
| ~ v3_vectsp_2(X0,X2)
| ~ v6_rlvect_1(X1)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X1)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X1)
| ~ v4_rlvect_1(X2)
| ~ v3_rlvect_1(X1)
| ~ v3_rlvect_1(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)
| k1_rmod_5(X2,X1,u1_struct_0(X0)) = X0
| k1_rlvect_1(X2) = k2_group_1(X2)
| v3_struct_0(X1)
| v3_struct_0(X2)
| v10_vectsp_1(X2) ),
inference(cnf_transformation,[],[f340]) ).
cnf(c_179,plain,
( ~ r1_tarski(X0,X1)
| m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[],[f334]) ).
cnf(c_285,plain,
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(prop_impl_just,[status(thm)],[c_87]) ).
cnf(c_286,plain,
( ~ l1_group_1(X0)
| l1_struct_0(X0) ),
inference(renaming,[status(thm)],[c_285]) ).
cnf(c_295,plain,
( ~ l1_vectsp_1(X0)
| l1_group_1(X0) ),
inference(prop_impl_just,[status(thm)],[c_89]) ).
cnf(c_297,plain,
( l1_vectsp_1(X0)
| ~ l2_vectsp_1(X0) ),
inference(prop_impl_just,[status(thm)],[c_93]) ).
cnf(c_298,plain,
( ~ l2_vectsp_1(X0)
| l1_vectsp_1(X0) ),
inference(renaming,[status(thm)],[c_297]) ).
cnf(c_301,plain,
( ~ l3_vectsp_1(X0)
| l2_vectsp_1(X0) ),
inference(prop_impl_just,[status(thm)],[c_94]) ).
cnf(c_345,plain,
( ~ r1_tarski(X0,X1)
| m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(prop_impl_just,[status(thm)],[c_179]) ).
cnf(c_3802,plain,
( X0 != X1
| X0 != X2
| m1_subset_1(X1,k1_zfmisc_1(X2)) ),
inference(resolution_lifted,[status(thm)],[c_175,c_345]) ).
cnf(c_3803,plain,
m1_subset_1(X0,k1_zfmisc_1(X0)),
inference(unflattening,[status(thm)],[c_3802]) ).
cnf(c_3809,plain,
( X0 != X1
| ~ l3_vectsp_1(X0)
| l1_vectsp_1(X1) ),
inference(resolution_lifted,[status(thm)],[c_301,c_298]) ).
cnf(c_3810,plain,
( ~ l3_vectsp_1(X0)
| l1_vectsp_1(X0) ),
inference(unflattening,[status(thm)],[c_3809]) ).
cnf(c_3843,plain,
( X0 != X1
| ~ l1_vectsp_1(X0)
| l1_struct_0(X1) ),
inference(resolution_lifted,[status(thm)],[c_295,c_286]) ).
cnf(c_3844,plain,
( ~ l1_vectsp_1(X0)
| l1_struct_0(X0) ),
inference(unflattening,[status(thm)],[c_3843]) ).
cnf(c_4215,plain,
( X0 != X1
| ~ l3_vectsp_1(X0)
| l1_struct_0(X1) ),
inference(resolution_lifted,[status(thm)],[c_3810,c_3844]) ).
cnf(c_4216,plain,
( ~ l3_vectsp_1(X0)
| l1_struct_0(X0) ),
inference(unflattening,[status(thm)],[c_4215]) ).
cnf(c_4376,plain,
( X0 != sK0
| ~ m1_subset_1(u1_struct_0(X1),k1_zfmisc_1(u1_struct_0(X2)))
| ~ m1_rmod_2(X1,X0,X2)
| ~ l1_vectsp_2(X2,X0)
| ~ v5_vectsp_2(X2,X0)
| ~ v3_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X0)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X0)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X0)
| ~ v4_rlvect_1(X2)
| ~ v3_rlvect_1(X0)
| ~ v3_rlvect_1(X2)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_group_1(X0)
| ~ v4_group_1(X0)
| k1_rmod_5(X0,X2,u1_struct_0(X1)) = X1
| k1_rlvect_1(X0) = k2_group_1(X0)
| v3_struct_0(X0)
| v3_struct_0(X2)
| v10_vectsp_1(X0) ),
inference(resolution_lifted,[status(thm)],[c_62,c_176]) ).
cnf(c_4377,plain,
( ~ m1_subset_1(u1_struct_0(X0),k1_zfmisc_1(u1_struct_0(X1)))
| ~ m1_rmod_2(X0,sK0,X1)
| ~ l1_vectsp_2(X1,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ v3_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| ~ v6_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| ~ l3_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_group_1(sK0)
| ~ v4_group_1(sK0)
| k1_rmod_5(sK0,X1,u1_struct_0(X0)) = X0
| k1_rlvect_1(sK0) = k2_group_1(sK0)
| v3_struct_0(X1)
| v3_struct_0(sK0)
| v10_vectsp_1(sK0) ),
inference(unflattening,[status(thm)],[c_4376]) ).
cnf(c_4379,plain,
( k1_rmod_5(sK0,X1,u1_struct_0(X0)) = X0
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v3_vectsp_2(X0,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ l1_vectsp_2(X1,sK0)
| ~ m1_rmod_2(X0,sK0,X1)
| ~ m1_subset_1(u1_struct_0(X0),k1_zfmisc_1(u1_struct_0(X1)))
| v3_struct_0(X1) ),
inference(global_subsumption_just,[status(thm)],[c_4377,c_72,c_71,c_70,c_69,c_68,c_67,c_66,c_65,c_64,c_61,c_73,c_63,c_50,c_4377]) ).
cnf(c_4380,plain,
( ~ m1_subset_1(u1_struct_0(X0),k1_zfmisc_1(u1_struct_0(X1)))
| ~ m1_rmod_2(X0,sK0,X1)
| ~ l1_vectsp_2(X1,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ v3_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| k1_rmod_5(sK0,X1,u1_struct_0(X0)) = X0
| v3_struct_0(X1) ),
inference(renaming,[status(thm)],[c_4379]) ).
cnf(c_5917,plain,
( X0 != sK0
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X0)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X0)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X0)
| ~ v3_rlvect_1(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| m1_rmod_2(k2_rmod_2(X0,X1),X0,X1)
| v3_struct_0(X0)
| v3_struct_0(X1) ),
inference(resolution_lifted,[status(thm)],[c_65,c_85]) ).
cnf(c_5918,plain,
( ~ l1_vectsp_2(X0,sK0)
| ~ v5_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| ~ v6_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| ~ l3_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v4_group_1(sK0)
| m1_rmod_2(k2_rmod_2(sK0,X0),sK0,X0)
| v3_struct_0(X0)
| v3_struct_0(sK0) ),
inference(unflattening,[status(thm)],[c_5917]) ).
cnf(c_5920,plain,
( v3_struct_0(X0)
| m1_rmod_2(k2_rmod_2(sK0,X0),sK0,X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_vectsp_2(X0,sK0)
| ~ l1_vectsp_2(X0,sK0) ),
inference(global_subsumption_just,[status(thm)],[c_5918,c_72,c_71,c_70,c_69,c_68,c_66,c_64,c_61,c_73,c_5918]) ).
cnf(c_5921,plain,
( ~ l1_vectsp_2(X0,sK0)
| ~ v5_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| m1_rmod_2(k2_rmod_2(sK0,X0),sK0,X0)
| v3_struct_0(X0) ),
inference(renaming,[status(thm)],[c_5920]) ).
cnf(c_5947,plain,
( X0 != sK0
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X0)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X0)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X0)
| ~ v3_rlvect_1(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(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)
| v3_struct_0(X0)
| v3_struct_0(X1) ),
inference(resolution_lifted,[status(thm)],[c_65,c_78]) ).
cnf(c_5948,plain,
( ~ l1_vectsp_2(X0,sK0)
| ~ v5_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| ~ v6_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| ~ l3_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v4_group_1(sK0)
| 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)
| v3_struct_0(sK0) ),
inference(unflattening,[status(thm)],[c_5947]) ).
cnf(c_5950,plain,
( 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)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_vectsp_2(X0,sK0)
| ~ l1_vectsp_2(X0,sK0) ),
inference(global_subsumption_just,[status(thm)],[c_5948,c_72,c_71,c_70,c_69,c_68,c_66,c_64,c_61,c_73,c_5948]) ).
cnf(c_5951,plain,
( ~ l1_vectsp_2(X0,sK0)
| ~ v5_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_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(renaming,[status(thm)],[c_5950]) ).
cnf(c_6158,plain,
( X0 != sK0
| l1_struct_0(X0) ),
inference(resolution_lifted,[status(thm)],[c_61,c_4216]) ).
cnf(c_6159,plain,
l1_struct_0(sK0),
inference(unflattening,[status(thm)],[c_6158]) ).
cnf(c_20155,plain,
u1_struct_0(sK1) = sP0_iProver_def,
definition ).
cnf(c_20158,plain,
k1_rmod_5(sK0,sK1,sK2) = sP3_iProver_def,
definition ).
cnf(c_20164,negated_conjecture,
~ v3_struct_0(sK1),
inference(demodulation,[status(thm)],[c_60]) ).
cnf(c_20165,negated_conjecture,
v3_rlvect_1(sK1),
inference(demodulation,[status(thm)],[c_59]) ).
cnf(c_20166,negated_conjecture,
v4_rlvect_1(sK1),
inference(demodulation,[status(thm)],[c_58]) ).
cnf(c_20167,negated_conjecture,
v5_rlvect_1(sK1),
inference(demodulation,[status(thm)],[c_57]) ).
cnf(c_20168,negated_conjecture,
v6_rlvect_1(sK1),
inference(demodulation,[status(thm)],[c_56]) ).
cnf(c_20169,negated_conjecture,
v3_vectsp_2(sK1,sK0),
inference(demodulation,[status(thm)],[c_55]) ).
cnf(c_20170,negated_conjecture,
v5_vectsp_2(sK1,sK0),
inference(demodulation,[status(thm)],[c_54]) ).
cnf(c_20171,negated_conjecture,
l1_vectsp_2(sK1,sK0),
inference(demodulation,[status(thm)],[c_53]) ).
cnf(c_20172,negated_conjecture,
sP0_iProver_def = sK2,
inference(demodulation,[status(thm)],[c_51,c_20155]) ).
cnf(c_20174,negated_conjecture,
sP3_iProver_def != sK1,
inference(demodulation,[status(thm)],[c_49,c_20158]) ).
cnf(c_23079,plain,
k1_rmod_5(sK0,sK1,sP0_iProver_def) = sP3_iProver_def,
inference(light_normalisation,[status(thm)],[c_20158,c_20172]) ).
cnf(c_23721,plain,
( ~ l1_vectsp_2(sK1,sK0)
| ~ v6_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v3_rlvect_1(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)
| v3_struct_0(sK1) ),
inference(superposition,[status(thm)],[c_20170,c_5951]) ).
cnf(c_23726,plain,
( ~ l1_vectsp_2(sK1,sK0)
| ~ v6_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| g1_vectsp_2(sK0,sP0_iProver_def,u1_rlvect_1(sK1),u2_struct_0(sK1),u1_vectsp_2(sK0,sK1)) = k2_rmod_2(sK0,sK1)
| v3_struct_0(sK1) ),
inference(light_normalisation,[status(thm)],[c_23721,c_20155]) ).
cnf(c_23727,plain,
g1_vectsp_2(sK0,sP0_iProver_def,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_23726,c_20164,c_20165,c_20166,c_20167,c_20168,c_20171]) ).
cnf(c_23768,plain,
( ~ m1_subset_1(u1_struct_0(X0),k1_zfmisc_1(sP0_iProver_def))
| ~ m1_rmod_2(X0,sK0,sK1)
| ~ v3_vectsp_2(X0,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ v5_vectsp_2(sK1,sK0)
| ~ v6_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| k1_rmod_5(sK0,sK1,u1_struct_0(X0)) = X0
| v3_struct_0(sK1) ),
inference(superposition,[status(thm)],[c_20155,c_4380]) ).
cnf(c_23779,plain,
( ~ m1_subset_1(u1_struct_0(X0),k1_zfmisc_1(sP0_iProver_def))
| ~ m1_rmod_2(X0,sK0,sK1)
| ~ v3_vectsp_2(X0,sK0)
| k1_rmod_5(sK0,sK1,u1_struct_0(X0)) = X0 ),
inference(forward_subsumption_resolution,[status(thm)],[c_23768,c_20164,c_20165,c_20166,c_20167,c_20168,c_20170,c_20171]) ).
cnf(c_23807,plain,
( ~ m1_subset_1(sP0_iProver_def,k1_zfmisc_1(sP0_iProver_def))
| ~ m1_rmod_2(sK1,sK0,sK1)
| ~ v3_vectsp_2(sK1,sK0)
| k1_rmod_5(sK0,sK1,u1_struct_0(sK1)) = sK1 ),
inference(superposition,[status(thm)],[c_20155,c_23779]) ).
cnf(c_23808,plain,
( ~ m1_subset_1(sP0_iProver_def,k1_zfmisc_1(sP0_iProver_def))
| ~ m1_rmod_2(sK1,sK0,sK1)
| ~ v3_vectsp_2(sK1,sK0)
| sK1 = sP3_iProver_def ),
inference(light_normalisation,[status(thm)],[c_23807,c_20155,c_23079]) ).
cnf(c_23809,plain,
( ~ m1_rmod_2(sK1,sK0,sK1)
| sK1 = sP3_iProver_def ),
inference(forward_subsumption_resolution,[status(thm)],[c_23808,c_20169,c_3803]) ).
cnf(c_25469,plain,
( ~ l1_vectsp_2(sK1,sK0)
| ~ l1_struct_0(sK0)
| g1_vectsp_2(sK0,u1_struct_0(sK1),u1_rlvect_1(sK1),u2_struct_0(sK1),u1_vectsp_2(sK0,sK1)) = sK1 ),
inference(superposition,[status(thm)],[c_20169,c_74]) ).
cnf(c_25479,plain,
( ~ l1_vectsp_2(sK1,sK0)
| ~ l1_struct_0(sK0)
| k2_rmod_2(sK0,sK1) = sK1 ),
inference(light_normalisation,[status(thm)],[c_25469,c_20155,c_23727]) ).
cnf(c_25480,plain,
k2_rmod_2(sK0,sK1) = sK1,
inference(forward_subsumption_resolution,[status(thm)],[c_25479,c_6159,c_20171]) ).
cnf(c_25719,plain,
( ~ l1_vectsp_2(sK1,sK0)
| ~ v5_vectsp_2(sK1,sK0)
| ~ v6_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| m1_rmod_2(sK1,sK0,sK1)
| v3_struct_0(sK1) ),
inference(superposition,[status(thm)],[c_25480,c_5921]) ).
cnf(c_25721,plain,
m1_rmod_2(sK1,sK0,sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_25719,c_20164,c_20165,c_20166,c_20167,c_20168,c_20170,c_20171]) ).
cnf(c_25722,plain,
sK1 = sP3_iProver_def,
inference(backward_subsumption_resolution,[status(thm)],[c_23809,c_25721]) ).
cnf(c_25743,plain,
sP3_iProver_def != sP3_iProver_def,
inference(demodulation,[status(thm)],[c_20174,c_25722]) ).
cnf(c_25753,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_25743]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG219+1 : TPTP v8.1.2. Released v3.4.0.
% 0.03/0.12 % Command : run_iprover %s %d THM
% 0.11/0.33 % Computer : n017.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu May 2 22:16:36 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.18/0.45 Running first-order theorem proving
% 0.18/0.45 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.78/1.66 % SZS status Started for theBenchmark.p
% 7.78/1.66 % SZS status Theorem for theBenchmark.p
% 7.78/1.66
% 7.78/1.66 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 7.78/1.66
% 7.78/1.66 ------ iProver source info
% 7.78/1.66
% 7.78/1.66 git: date: 2024-05-02 19:28:25 +0000
% 7.78/1.66 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 7.78/1.66 git: non_committed_changes: false
% 7.78/1.66
% 7.78/1.66 ------ Parsing...
% 7.78/1.66 ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.78/1.66
% 7.78/1.66 ------ 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
% 7.78/1.66
% 7.78/1.66 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 7.78/1.66
% 7.78/1.66 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.78/1.66 ------ Proving...
% 7.78/1.66 ------ Problem Properties
% 7.78/1.66
% 7.78/1.66
% 7.78/1.66 clauses 137
% 7.78/1.66 conjectures 16
% 7.78/1.66 EPR 50
% 7.78/1.66 Horn 109
% 7.78/1.66 unary 70
% 7.78/1.66 binary 24
% 7.78/1.66 lits 424
% 7.78/1.66 lits eq 22
% 7.78/1.66 fd_pure 0
% 7.78/1.66 fd_pseudo 0
% 7.78/1.66 fd_cond 1
% 7.78/1.66 fd_pseudo_cond 6
% 7.78/1.66 AC symbols 0
% 7.78/1.66
% 7.78/1.66 ------ Schedule dynamic 5 is on
% 7.78/1.66
% 7.78/1.66 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.78/1.66
% 7.78/1.66
% 7.78/1.66 ------
% 7.78/1.66 Current options:
% 7.78/1.66 ------
% 7.78/1.66
% 7.78/1.66
% 7.78/1.66
% 7.78/1.66
% 7.78/1.66 ------ Proving...
% 7.78/1.66
% 7.78/1.66
% 7.78/1.66 % SZS status Theorem for theBenchmark.p
% 7.78/1.66
% 7.78/1.66 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.78/1.66
% 7.78/1.66
%------------------------------------------------------------------------------