%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG222+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 : n009.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 7.41s 1.97s
% Output : CNFRefutation 7.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 9
% Syntax : Number of formulae : 126 ( 57 unt; 0 def)
% Number of atoms : 895 ( 15 equ)
% Maximal formula atoms : 24 ( 7 avg)
% Number of connectives : 1329 ( 560 ~; 565 |; 180 &)
% ( 1 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 8 avg)
% Maximal term depth : 4 ( 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 : 10 ( 10 usr; 4 con; 0-4 aty)
% Number of variables : 186 ( 0 sgn 178 !; 8 ?; 79 :)
% 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)
& 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)))
=> m1_rmod_2(k1_rmod_5(X0,X1,k5_subset_1(u1_struct_0(X1),X2,X3)),X0,k2_rmod_3(X0,X1,k1_rmod_5(X0,X1,X2),k1_rmod_5(X0,X1,X3))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_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)
& 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)))
=> m1_rmod_2(k1_rmod_5(X0,X1,k5_subset_1(u1_struct_0(X1),X2,X3)),X0,k2_rmod_3(X0,X1,k1_rmod_5(X0,X1,X2),k1_rmod_5(X0,X1,X3))) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f8,axiom,
! [X0,X1] : k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f11,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(f17,axiom,
! [X0,X1,X2] :
( ( m1_subset_1(X2,k1_zfmisc_1(X0))
& m1_subset_1(X1,k1_zfmisc_1(X0)) )
=> m1_subset_1(k5_subset_1(X0,X1,X2),k1_zfmisc_1(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_subset_1) ).
fof(f66,axiom,
! [X0,X1,X2] :
( ( m1_subset_1(X2,k1_zfmisc_1(X0))
& m1_subset_1(X1,k1_zfmisc_1(X0)) )
=> k5_subset_1(X0,X1,X2) = k3_xboole_0(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
fof(f69,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(f70,axiom,
! [X0,X1] : r1_tarski(k3_xboole_0(X0,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
fof(f72,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) )
=> ! [X2] :
( m1_rmod_2(X2,X0,X1)
=> ! [X3] :
( m1_rmod_2(X3,X0,X1)
=> ! [X4] :
( m1_rmod_2(X4,X0,X1)
=> ( ( m1_rmod_2(X2,X0,X4)
& m1_rmod_2(X2,X0,X3) )
=> m1_rmod_2(X2,X0,k2_rmod_3(X0,X1,X3,X4)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_rmod_3) ).
fof(f75,axiom,
! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
<=> r1_tarski(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f85,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) ),
inference(pure_predicate_removal,[],[f11]) ).
fof(f89,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)))
& ~ m1_rmod_2(k1_rmod_5(X0,X1,k5_subset_1(u1_struct_0(X1),X2,X3)),X0,k2_rmod_3(X0,X1,k1_rmod_5(X0,X1,X2),k1_rmod_5(X0,X1,X3))) ) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f90,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)))
& ~ m1_rmod_2(k1_rmod_5(X0,X1,k5_subset_1(u1_struct_0(X1),X2,X3)),X0,k2_rmod_3(X0,X1,k1_rmod_5(X0,X1,X2),k1_rmod_5(X0,X1,X3))) ) ) ) ),
inference(flattening,[],[f89]) ).
fof(f107,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| k5_subset_1(X0,X1,X2) = k3_xboole_0(X1,X2) ),
inference(ennf_transformation,[],[f66]) ).
fof(f108,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| k5_subset_1(X0,X1,X2) = k3_xboole_0(X1,X2) ),
inference(flattening,[],[f107]) ).
fof(f111,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| m1_subset_1(k5_subset_1(X0,X1,X2),k1_zfmisc_1(X0)) ),
inference(ennf_transformation,[],[f17]) ).
fof(f112,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| m1_subset_1(k5_subset_1(X0,X1,X2),k1_zfmisc_1(X0)) ),
inference(flattening,[],[f111]) ).
fof(f115,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,[],[f69]) ).
fof(f116,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,[],[f115]) ).
fof(f117,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) ),
inference(ennf_transformation,[],[f85]) ).
fof(f118,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) ),
inference(flattening,[],[f117]) ).
fof(f119,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)
| ! [X2] :
( ~ m1_rmod_2(X2,X0,X1)
| ! [X3] :
( ~ m1_rmod_2(X3,X0,X1)
| ! [X4] :
( ~ m1_rmod_2(X4,X0,X1)
| ~ m1_rmod_2(X2,X0,X4)
| ~ m1_rmod_2(X2,X0,X3)
| m1_rmod_2(X2,X0,k2_rmod_3(X0,X1,X3,X4)) ) ) ) ) ),
inference(ennf_transformation,[],[f72]) ).
fof(f120,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)
| ! [X2] :
( ~ m1_rmod_2(X2,X0,X1)
| ! [X3] :
( ~ m1_rmod_2(X3,X0,X1)
| ! [X4] :
( ~ m1_rmod_2(X4,X0,X1)
| ~ m1_rmod_2(X2,X0,X4)
| ~ m1_rmod_2(X2,X0,X3)
| m1_rmod_2(X2,X0,k2_rmod_3(X0,X1,X3,X4)) ) ) ) ) ),
inference(flattening,[],[f119]) ).
fof(f126,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)
& 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)))
& ~ m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k2_rmod_3(sK0,sK1,k1_rmod_5(sK0,sK1,sK2),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)],[f90]) ).
fof(f143,plain,
! [X0,X1] :
( ( ~ m1_subset_1(X0,k1_zfmisc_1(X1))
| r1_tarski(X0,X1) )
& ( ~ r1_tarski(X0,X1)
| m1_subset_1(X0,k1_zfmisc_1(X1)) ) ),
inference(nnf_transformation,[],[f75]) ).
fof(f144,plain,
l3_vectsp_1(sK0),
inference(cnf_transformation,[],[f126]) ).
fof(f145,plain,
v2_vectsp_2(sK0),
inference(cnf_transformation,[],[f126]) ).
fof(f146,plain,
~ v10_vectsp_1(sK0),
inference(cnf_transformation,[],[f126]) ).
fof(f147,plain,
v8_vectsp_1(sK0),
inference(cnf_transformation,[],[f126]) ).
fof(f148,plain,
v7_vectsp_1(sK0),
inference(cnf_transformation,[],[f126]) ).
fof(f149,plain,
v6_vectsp_1(sK0),
inference(cnf_transformation,[],[f126]) ).
fof(f150,plain,
v7_group_1(sK0),
inference(cnf_transformation,[],[f126]) ).
fof(f151,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f126]) ).
fof(f152,plain,
v6_rlvect_1(sK0),
inference(cnf_transformation,[],[f126]) ).
fof(f153,plain,
v5_rlvect_1(sK0),
inference(cnf_transformation,[],[f126]) ).
fof(f154,plain,
v4_rlvect_1(sK0),
inference(cnf_transformation,[],[f126]) ).
fof(f155,plain,
v3_rlvect_1(sK0),
inference(cnf_transformation,[],[f126]) ).
fof(f156,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f126]) ).
fof(f157,plain,
l1_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f126]) ).
fof(f158,plain,
v5_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f126]) ).
fof(f159,plain,
v6_rlvect_1(sK1),
inference(cnf_transformation,[],[f126]) ).
fof(f160,plain,
v5_rlvect_1(sK1),
inference(cnf_transformation,[],[f126]) ).
fof(f161,plain,
v4_rlvect_1(sK1),
inference(cnf_transformation,[],[f126]) ).
fof(f162,plain,
v3_rlvect_1(sK1),
inference(cnf_transformation,[],[f126]) ).
fof(f163,plain,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f126]) ).
fof(f164,plain,
m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1))),
inference(cnf_transformation,[],[f126]) ).
fof(f165,plain,
m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1))),
inference(cnf_transformation,[],[f126]) ).
fof(f166,plain,
~ m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k2_rmod_3(sK0,sK1,k1_rmod_5(sK0,sK1,sK2),k1_rmod_5(sK0,sK1,sK3))),
inference(cnf_transformation,[],[f126]) ).
fof(f207,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| k5_subset_1(X0,X1,X2) = k3_xboole_0(X1,X2) ),
inference(cnf_transformation,[],[f108]) ).
fof(f209,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| m1_subset_1(k5_subset_1(X0,X1,X2),k1_zfmisc_1(X0)) ),
inference(cnf_transformation,[],[f112]) ).
fof(f211,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,[],[f116]) ).
fof(f212,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,[],[f118]) ).
fof(f213,plain,
! [X2,X3,X0,X1,X4] :
( ~ 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)
| ~ m1_rmod_2(X2,X0,X1)
| ~ m1_rmod_2(X3,X0,X1)
| ~ m1_rmod_2(X4,X0,X1)
| ~ m1_rmod_2(X2,X0,X4)
| ~ m1_rmod_2(X2,X0,X3)
| m1_rmod_2(X2,X0,k2_rmod_3(X0,X1,X3,X4)) ),
inference(cnf_transformation,[],[f120]) ).
fof(f223,plain,
! [X0,X1] : r1_tarski(k3_xboole_0(X0,X1),X0),
inference(cnf_transformation,[],[f70]) ).
fof(f225,plain,
! [X0,X1] : k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0),
inference(cnf_transformation,[],[f8]) ).
fof(f226,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,k1_zfmisc_1(X1))
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f143]) ).
fof(f227,plain,
! [X0,X1] :
( ~ r1_tarski(X0,X1)
| m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_49,negated_conjecture,
~ m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k2_rmod_3(sK0,sK1,k1_rmod_5(sK0,sK1,sK2),k1_rmod_5(sK0,sK1,sK3))),
inference(cnf_transformation,[],[f166]) ).
tcf(c_50,negated_conjecture,
m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1))),
inference(cnf_transformation,[],[f165]) ).
tcf(c_51,negated_conjecture,
m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1))),
inference(cnf_transformation,[],[f164]) ).
tcf(c_52,negated_conjecture,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f163]) ).
tcf(c_53,negated_conjecture,
v3_rlvect_1(sK1),
inference(cnf_transformation,[],[f162]) ).
tcf(c_54,negated_conjecture,
v4_rlvect_1(sK1),
inference(cnf_transformation,[],[f161]) ).
tcf(c_55,negated_conjecture,
v5_rlvect_1(sK1),
inference(cnf_transformation,[],[f160]) ).
tcf(c_56,negated_conjecture,
v6_rlvect_1(sK1),
inference(cnf_transformation,[],[f159]) ).
tcf(c_57,negated_conjecture,
v5_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f158]) ).
tcf(c_58,negated_conjecture,
l1_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f157]) ).
tcf(c_59,negated_conjecture,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f156]) ).
tcf(c_60,negated_conjecture,
v3_rlvect_1(sK0),
inference(cnf_transformation,[],[f155]) ).
tcf(c_61,negated_conjecture,
v4_rlvect_1(sK0),
inference(cnf_transformation,[],[f154]) ).
tcf(c_62,negated_conjecture,
v5_rlvect_1(sK0),
inference(cnf_transformation,[],[f153]) ).
tcf(c_63,negated_conjecture,
v6_rlvect_1(sK0),
inference(cnf_transformation,[],[f152]) ).
tcf(c_64,negated_conjecture,
v4_group_1(sK0),
inference(cnf_transformation,[],[f151]) ).
tcf(c_65,negated_conjecture,
v7_group_1(sK0),
inference(cnf_transformation,[],[f150]) ).
tcf(c_66,negated_conjecture,
v6_vectsp_1(sK0),
inference(cnf_transformation,[],[f149]) ).
tcf(c_67,negated_conjecture,
v7_vectsp_1(sK0),
inference(cnf_transformation,[],[f148]) ).
tcf(c_68,negated_conjecture,
v8_vectsp_1(sK0),
inference(cnf_transformation,[],[f147]) ).
tcf(c_69,negated_conjecture,
~ v10_vectsp_1(sK0),
inference(cnf_transformation,[],[f146]) ).
tcf(c_70,negated_conjecture,
v2_vectsp_2(sK0),
inference(cnf_transformation,[],[f145]) ).
tcf(c_71,negated_conjecture,
l3_vectsp_1(sK0),
inference(cnf_transformation,[],[f144]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( k5_subset_1(X1,X0,X2) = k3_xboole_0(X0,X2) )
| ~ m1_subset_1(X2,k1_zfmisc_1(X1))
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[],[f207]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i,X2: $i] :
( m1_subset_1(k5_subset_1(X1,X0,X2),k1_zfmisc_1(X1))
| ~ m1_subset_1(X2,k1_zfmisc_1(X1))
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[],[f209]) ).
tcf(c_116,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)
| ~ r1_tarski(X0,X2)
| ~ l1_vectsp_2(X1,X3)
| ~ v5_vectsp_2(X1,X3)
| ~ 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,[],[f211]) ).
tcf(c_117,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,[],[f212]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( v3_struct_0(X2)
| v3_struct_0(X1)
| m1_rmod_2(X0,X1,k2_rmod_3(X1,X2,X3,X4))
| ~ 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(X4,X1,X2)
| ~ m1_rmod_2(X3,X1,X2)
| ~ m1_rmod_2(X0,X1,X4)
| ~ m1_rmod_2(X0,X1,X3)
| ~ m1_rmod_2(X0,X1,X2) ),
inference(cnf_transformation,[],[f213]) ).
tcf(c_128,plain,
! [X0: $i,X1: $i] : r1_tarski(k3_xboole_0(X0,X1),X0),
inference(cnf_transformation,[],[f223]) ).
tcf(c_130,plain,
! [X0: $i,X1: $i] : k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0),
inference(cnf_transformation,[],[f225]) ).
tcf(c_131,plain,
! [X0: $i,X1: $i] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f227]) ).
tcf(c_132,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X0,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[],[f226]) ).
tcf(c_184,plain,
! [X0: $i,X1: $i] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_131]) ).
tcf(c_368,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( k5_subset_1(X1,X2,X0) = k3_xboole_0(X2,X0) )
| ~ r1_tarski(X2,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(bin_hyper_res,[status(thm)],[c_112,c_184]) ).
tcf(c_370,plain,
! [X0: $i,X1: $i,X2: $i] :
( m1_subset_1(k5_subset_1(X1,X2,X0),k1_zfmisc_1(X1))
| ~ r1_tarski(X2,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(bin_hyper_res,[status(thm)],[c_114,c_184]) ).
tcf(c_2770,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)
| ~ r1_tarski(X1,X3)
| ~ l1_vectsp_2(X2,X0)
| ~ v5_vectsp_2(X2,X0)
| ~ 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_65,c_116]) ).
tcf(c_2771,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_2770]) ).
tcf(c_2773,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_2771,c_71,c_70,c_68,c_67,c_66,c_64,c_63,c_62,c_61,c_60,c_69,c_59,c_2771]) ).
tcf(c_2809,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_65,c_117]) ).
tcf(c_2810,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_2809]) ).
tcf(c_2812,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_2810,c_71,c_70,c_68,c_67,c_66,c_64,c_63,c_62,c_61,c_60,c_69,c_59,c_2810]) ).
tcf(c_3282,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( v3_struct_0(X2)
| v3_struct_0(X0)
| m1_rmod_2(X1,X0,k2_rmod_3(X0,X2,X3,X4))
| ~ 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(X4,X0,X2)
| ~ m1_rmod_2(X3,X0,X2)
| ~ m1_rmod_2(X1,X0,X4)
| ~ m1_rmod_2(X1,X0,X3)
| ~ m1_rmod_2(X1,X0,X2)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_64,c_118]) ).
tcf(c_3283,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(sK0)
| v3_struct_0(X1)
| m1_rmod_2(X0,sK0,k2_rmod_3(sK0,X1,X2,X3))
| ~ 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(X3,sK0,X1)
| ~ m1_rmod_2(X2,sK0,X1)
| ~ m1_rmod_2(X0,sK0,X3)
| ~ m1_rmod_2(X0,sK0,X2)
| ~ m1_rmod_2(X0,sK0,X1) ),
inference(unflattening,[status(thm)],[c_3282]) ).
tcf(c_3285,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ m1_rmod_2(X0,sK0,X1)
| ~ m1_rmod_2(X0,sK0,X2)
| ~ m1_rmod_2(X0,sK0,X3)
| ~ m1_rmod_2(X2,sK0,X1)
| ~ m1_rmod_2(X3,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)
| m1_rmod_2(X0,sK0,k2_rmod_3(sK0,X1,X2,X3))
| v3_struct_0(X1) ),
inference(global_subsumption_just,[status(thm)],[c_3283,c_71,c_68,c_67,c_66,c_63,c_62,c_61,c_60,c_59,c_3283]) ).
tcf(c_3286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X1)
| m1_rmod_2(X0,sK0,k2_rmod_3(sK0,X1,X2,X3))
| ~ 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(X3,sK0,X1)
| ~ m1_rmod_2(X2,sK0,X1)
| ~ m1_rmod_2(X0,sK0,X3)
| ~ m1_rmod_2(X0,sK0,X2)
| ~ m1_rmod_2(X0,sK0,X1) ),
inference(renaming,[status(thm)],[c_3285]) ).
tcf(c_3906,plain,
! [X0: $i,X1: $i] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_131]) ).
tcf(c_4040,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( k5_subset_1(X1,X2,X0) = k3_xboole_0(X2,X0) )
| ~ r1_tarski(X2,X1)
| ~ r1_tarski(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_368,c_3906]) ).
tcf(c_4042,plain,
! [X0: $i,X1: $i,X2: $i] :
( m1_subset_1(k5_subset_1(X1,X2,X0),k1_zfmisc_1(X1))
| ~ r1_tarski(X2,X1)
| ~ r1_tarski(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_370,c_3906]) ).
tcf(c_6995,plain,
! [X0: $i,X1: $i] : r1_tarski(k3_xboole_0(X0,X1),X1),
inference(superposition,[status(thm)],[c_130,c_128]) ).
tcf(c_7005,plain,
r1_tarski(sK3,u1_struct_0(sK1)),
inference(superposition,[status(thm)],[c_50,c_132]) ).
tcf(c_7006,plain,
r1_tarski(sK2,u1_struct_0(sK1)),
inference(superposition,[status(thm)],[c_51,c_132]) ).
tcf(c_7471,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)
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,sK3),sK0,sK1)
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,sK2),sK0,sK1)
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,sK1)
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK3))
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK2)) ),
inference(superposition,[status(thm)],[c_3286,c_49]) ).
tcf(c_7479,plain,
( ~ m1_rmod_2(k1_rmod_5(sK0,sK1,sK3),sK0,sK1)
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,sK2),sK0,sK1)
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,sK1)
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK3))
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7471,c_52,c_56,c_55,c_54,c_53,c_58,c_57]) ).
tcf(c_7635,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)
| ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ r1_tarski(k5_subset_1(u1_struct_0(sK1),sK2,sK3),sK2)
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,sK3),sK0,sK1)
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,sK2),sK0,sK1)
| ~ m1_subset_1(k5_subset_1(u1_struct_0(sK1),sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,sK1)
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK3)) ),
inference(superposition,[status(thm)],[c_2773,c_7479]) ).
tcf(c_7636,plain,
( ~ r1_tarski(k5_subset_1(u1_struct_0(sK1),sK2,sK3),sK2)
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,sK3),sK0,sK1)
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,sK2),sK0,sK1)
| ~ m1_subset_1(k5_subset_1(u1_struct_0(sK1),sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,sK1)
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7635,c_52,c_56,c_55,c_54,c_53,c_58,c_57,c_51]) ).
tcf(c_7692,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)
| ~ m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ r1_tarski(k5_subset_1(u1_struct_0(sK1),sK2,sK3),sK3)
| ~ r1_tarski(k5_subset_1(u1_struct_0(sK1),sK2,sK3),sK2)
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,sK3),sK0,sK1)
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,sK2),sK0,sK1)
| ~ m1_subset_1(k5_subset_1(u1_struct_0(sK1),sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,sK1) ),
inference(superposition,[status(thm)],[c_2773,c_7636]) ).
tcf(c_7693,plain,
( ~ r1_tarski(k5_subset_1(u1_struct_0(sK1),sK2,sK3),sK3)
| ~ r1_tarski(k5_subset_1(u1_struct_0(sK1),sK2,sK3),sK2)
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,sK3),sK0,sK1)
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,sK2),sK0,sK1)
| ~ m1_subset_1(k5_subset_1(u1_struct_0(sK1),sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7692,c_52,c_56,c_55,c_54,c_53,c_58,c_57,c_50]) ).
tcf(c_7712,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)
| ~ r1_tarski(k5_subset_1(u1_struct_0(sK1),sK2,sK3),sK3)
| ~ r1_tarski(k5_subset_1(u1_struct_0(sK1),sK2,sK3),sK2)
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,sK3),sK0,sK1)
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,sK2),sK0,sK1)
| ~ m1_subset_1(k5_subset_1(u1_struct_0(sK1),sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1))) ),
inference(superposition,[status(thm)],[c_2812,c_7693]) ).
tcf(c_7713,plain,
( ~ r1_tarski(k5_subset_1(u1_struct_0(sK1),sK2,sK3),sK3)
| ~ r1_tarski(k5_subset_1(u1_struct_0(sK1),sK2,sK3),sK2)
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,sK3),sK0,sK1)
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,sK2),sK0,sK1)
| ~ m1_subset_1(k5_subset_1(u1_struct_0(sK1),sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7712,c_52,c_56,c_55,c_54,c_53,c_58,c_57]) ).
tcf(c_8107,plain,
( ~ r1_tarski(sK3,u1_struct_0(sK1))
| ~ r1_tarski(sK2,u1_struct_0(sK1))
| ~ r1_tarski(k5_subset_1(u1_struct_0(sK1),sK2,sK3),sK3)
| ~ r1_tarski(k5_subset_1(u1_struct_0(sK1),sK2,sK3),sK2)
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,sK3),sK0,sK1)
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,sK2),sK0,sK1) ),
inference(superposition,[status(thm)],[c_4042,c_7713]) ).
tcf(c_8133,plain,
( ~ r1_tarski(k5_subset_1(u1_struct_0(sK1),sK2,sK3),sK3)
| ~ r1_tarski(k5_subset_1(u1_struct_0(sK1),sK2,sK3),sK2)
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,sK3),sK0,sK1)
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,sK2),sK0,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8107,c_7005,c_7006]) ).
tcf(c_8219,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)
| ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ r1_tarski(k5_subset_1(u1_struct_0(sK1),sK2,sK3),sK3)
| ~ r1_tarski(k5_subset_1(u1_struct_0(sK1),sK2,sK3),sK2)
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,sK3),sK0,sK1) ),
inference(superposition,[status(thm)],[c_2812,c_8133]) ).
tcf(c_8220,plain,
( ~ r1_tarski(k5_subset_1(u1_struct_0(sK1),sK2,sK3),sK3)
| ~ r1_tarski(k5_subset_1(u1_struct_0(sK1),sK2,sK3),sK2)
| ~ m1_rmod_2(k1_rmod_5(sK0,sK1,sK3),sK0,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8219,c_52,c_56,c_55,c_54,c_53,c_58,c_57,c_51]) ).
tcf(c_8233,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)
| ~ m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ r1_tarski(k5_subset_1(u1_struct_0(sK1),sK2,sK3),sK3)
| ~ r1_tarski(k5_subset_1(u1_struct_0(sK1),sK2,sK3),sK2) ),
inference(superposition,[status(thm)],[c_2812,c_8220]) ).
tcf(c_8234,plain,
( ~ r1_tarski(k5_subset_1(u1_struct_0(sK1),sK2,sK3),sK3)
| ~ r1_tarski(k5_subset_1(u1_struct_0(sK1),sK2,sK3),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8233,c_52,c_56,c_55,c_54,c_53,c_58,c_57,c_50]) ).
tcf(c_8543,plain,
! [X0: $i] :
( ( k5_subset_1(u1_struct_0(sK1),X0,sK3) = k3_xboole_0(X0,sK3) )
| ~ r1_tarski(X0,u1_struct_0(sK1)) ),
inference(superposition,[status(thm)],[c_7005,c_4040]) ).
tcf(c_8699,plain,
k5_subset_1(u1_struct_0(sK1),sK2,sK3) = k3_xboole_0(sK2,sK3),
inference(superposition,[status(thm)],[c_7006,c_8543]) ).
tcf(c_8711,plain,
( ~ r1_tarski(k3_xboole_0(sK2,sK3),sK3)
| ~ r1_tarski(k3_xboole_0(sK2,sK3),sK2) ),
inference(demodulation,[status(thm)],[c_8234,c_8699]) ).
tcf(c_8726,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_8711,c_6995,c_128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ALG222+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.19/0.44 % Computer : n009.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Fri Sep 25 05:09:31 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.23/0.51 Running first-order theorem proving
% 0.23/0.51 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
% 0.23/0.52
% 0.23/0.52 % ======== iProver multi-core TPTP/SMT =========
% 0.23/0.52
% 0.23/0.52 % Detected problem language: tptp
% 0.23/0.54 % Proving...
% 7.41/1.97 % SZS status Started for theBenchmark.p
% 7.41/1.97 % SZS status Theorem for theBenchmark.p
% 7.41/1.97
% 7.41/1.97 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.41/1.97
% 7.41/1.97 % ------ iProver source info
% 7.41/1.97
% 7.41/1.97 % git: date: 2026-07-19 20:42:38 +0200
% 7.41/1.97 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.41/1.97 % git: non_committed_changes: false
% 7.41/1.97
% 7.41/1.97 % ------ Parsing...
% 7.41/1.97 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.41/1.97
% 7.41/1.97 % ------ 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: 10 0s sf_e pe_s pe_e %
% 7.41/1.97
% 7.41/1.97 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.41/1.97
% 7.41/1.97 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.41/1.97 % ------ Proving...
% 7.41/1.97 % ------ Problem Properties
% 7.41/1.97
% 7.41/1.97 %
% 7.41/1.97 % clauses 81
% 7.41/1.97 % conjectures 15
% 7.41/1.97 % EPR 24
% 7.41/1.97 % Horn 62
% 7.41/1.97 % unary 50
% 7.41/1.97 % binary 7
% 7.41/1.97 % lits 249
% 7.41/1.97 % lits eq 6
% 7.41/1.97 % fd_pure 0
% 7.41/1.97 % fd_pseudo 0
% 7.41/1.97 % fd_cond 0
% 7.41/1.97 % fd_pseudo_cond 1
% 7.41/1.97 % AC symbols 0
% 7.41/1.97
% 7.41/1.97 % ------ Schedule dynamic 5 is on
% 7.41/1.97
% 7.41/1.97 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.41/1.97
% 7.41/1.97
% 7.41/1.97 % ------
% 7.41/1.97 % Current options:
% 7.41/1.97 % ------
% 7.41/1.97
% 7.41/1.97
% 7.41/1.97 %
% 7.41/1.97
% 7.41/1.97 % ------ Proving...
% 7.41/1.97 %
% 7.41/1.97
% 7.41/1.97 % SZS status Theorem for theBenchmark.p
% 7.41/1.97
% 7.41/1.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.41/1.98
% 7.41/1.98
%------------------------------------------------------------------------------