%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG215+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 : n015.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 12:53:49 PM UTC 2026
% Result : Theorem 4.54s 6.31s
% Output : CNFRefutation 4.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 95 ( 45 unt; 0 def)
% Number of atoms : 790 ( 44 equ)
% Maximal formula atoms : 26 ( 8 avg)
% Number of connectives : 1195 ( 500 ~; 533 |; 139 &)
% ( 6 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 8 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 : 20 ( 18 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 135 ( 0 sgn 129 !; 6 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [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) )
=> v1_rmod_5(k1_subset_1(u1_struct_0(X1)),X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_rmod_5) ).
fof(f2,negated_conjecture,
~ ! [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) )
=> v1_rmod_5(k1_subset_1(u1_struct_0(X1)),X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f5,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_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> ( v1_rmod_5(X2,X0,X1)
<=> ! [X3] :
( m2_rmod_4(X3,X0,X1,X2)
=> ( k5_rmod_4(X0,X1,X3) = k1_rlvect_1(X1)
=> k2_rmod_4(X0,X1,X3) = k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_rmod_5) ).
fof(f7,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_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> ! [X3] :
( m1_rmod_4(X3,X0,X1)
=> ( m2_rmod_4(X3,X0,X1,X2)
<=> r1_tarski(k2_rmod_4(X0,X1,X3),X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_rmod_4) ).
fof(f12,axiom,
! [X0] :
( m1_subset_1(k1_subset_1(X0),k1_zfmisc_1(X0))
& v1_xboole_0(k1_subset_1(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_subset_1) ).
fof(f33,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)
& 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) )
=> ! [X3] :
( m2_rmod_4(X3,X0,X1,X2)
=> m1_rmod_4(X3,X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_rmod_4) ).
fof(f73,axiom,
! [X0] :
( r1_tarski(X0,k1_xboole_0)
=> X0 = k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(f76,axiom,
! [X0] :
( v1_xboole_0(X0)
=> X0 = k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f81,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)
& ~ v1_rmod_5(k1_subset_1(u1_struct_0(X1)),X0,X1) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f82,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)
& ~ v1_rmod_5(k1_subset_1(u1_struct_0(X1)),X0,X1) ) ),
inference(flattening,[],[f81]) ).
fof(f91,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_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ( v1_rmod_5(X2,X0,X1)
<=> ! [X3] :
( ~ m2_rmod_4(X3,X0,X1,X2)
| k5_rmod_4(X0,X1,X3) != k1_rlvect_1(X1)
| k2_rmod_4(X0,X1,X3) = k1_xboole_0 ) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f92,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_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ( v1_rmod_5(X2,X0,X1)
<=> ! [X3] :
( ~ m2_rmod_4(X3,X0,X1,X2)
| k5_rmod_4(X0,X1,X3) != k1_rlvect_1(X1)
| k2_rmod_4(X0,X1,X3) = k1_xboole_0 ) ) ) ) ),
inference(flattening,[],[f91]) ).
fof(f101,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_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ! [X3] :
( ~ m1_rmod_4(X3,X0,X1)
| ( m2_rmod_4(X3,X0,X1,X2)
<=> r1_tarski(k2_rmod_4(X0,X1,X3),X2) ) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f102,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_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ! [X3] :
( ~ m1_rmod_4(X3,X0,X1)
| ( m2_rmod_4(X3,X0,X1,X2)
<=> r1_tarski(k2_rmod_4(X0,X1,X3),X2) ) ) ) ) ),
inference(flattening,[],[f101]) ).
fof(f103,plain,
! [X0] :
( ~ v1_xboole_0(X0)
| X0 = k1_xboole_0 ),
inference(ennf_transformation,[],[f76]) ).
fof(f104,plain,
! [X0] :
( ~ r1_tarski(X0,k1_xboole_0)
| X0 = k1_xboole_0 ),
inference(ennf_transformation,[],[f73]) ).
fof(f107,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)
| ~ 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)
| ! [X3] :
( ~ m2_rmod_4(X3,X0,X1,X2)
| m1_rmod_4(X3,X0,X1) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f108,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)
| ~ 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)
| ! [X3] :
( ~ m2_rmod_4(X3,X0,X1,X2)
| m1_rmod_4(X3,X0,X1) ) ),
inference(flattening,[],[f107]) ).
fof(f135,plain,
( l3_vectsp_1(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)
& ~ 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)
& ~ v1_rmod_5(k1_subset_1(u1_struct_0(sK1)),sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f82]) ).
fof(f141,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_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ( ( ~ v1_rmod_5(X2,X0,X1)
| ! [X3] :
( ~ m2_rmod_4(X3,X0,X1,X2)
| k5_rmod_4(X0,X1,X3) != k1_rlvect_1(X1)
| k2_rmod_4(X0,X1,X3) = k1_xboole_0 ) )
& ( ? [X3] :
( m2_rmod_4(X3,X0,X1,X2)
& k5_rmod_4(X0,X1,X3) = k1_rlvect_1(X1)
& k2_rmod_4(X0,X1,X3) != k1_xboole_0 )
| v1_rmod_5(X2,X0,X1) ) ) ) ) ),
inference(nnf_transformation,[],[f92]) ).
fof(f142,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_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ( ( ~ v1_rmod_5(X2,X0,X1)
| ! [X4] :
( ~ m2_rmod_4(X4,X0,X1,X2)
| k1_rlvect_1(X1) != k5_rmod_4(X0,X1,X4)
| k1_xboole_0 = k2_rmod_4(X0,X1,X4) ) )
& ( ? [X3] :
( m2_rmod_4(X3,X0,X1,X2)
& k5_rmod_4(X0,X1,X3) = k1_rlvect_1(X1)
& k2_rmod_4(X0,X1,X3) != k1_xboole_0 )
| v1_rmod_5(X2,X0,X1) ) ) ) ) ),
inference(rectify,[],[f141]) ).
fof(f143,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_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ( ( ~ v1_rmod_5(X2,X0,X1)
| ! [X4] :
( ~ m2_rmod_4(X4,X0,X1,X2)
| k1_rlvect_1(X1) != k5_rmod_4(X0,X1,X4)
| k1_xboole_0 = k2_rmod_4(X0,X1,X4) ) )
& ( ( m2_rmod_4(sK7(X0,X1,X2),X0,X1,X2)
& k1_rlvect_1(X1) = k5_rmod_4(X0,X1,sK7(X0,X1,X2))
& k1_xboole_0 != k2_rmod_4(X0,X1,sK7(X0,X1,X2)) )
| v1_rmod_5(X2,X0,X1) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X3,sK7(X0,X1,X2))],[f142]) ).
fof(f156,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_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ! [X3] :
( ~ m1_rmod_4(X3,X0,X1)
| ( ( ~ m2_rmod_4(X3,X0,X1,X2)
| r1_tarski(k2_rmod_4(X0,X1,X3),X2) )
& ( ~ r1_tarski(k2_rmod_4(X0,X1,X3),X2)
| m2_rmod_4(X3,X0,X1,X2) ) ) ) ) ) ),
inference(nnf_transformation,[],[f102]) ).
fof(f169,plain,
l3_vectsp_1(sK0),
inference(cnf_transformation,[],[f135]) ).
fof(f170,plain,
v8_vectsp_1(sK0),
inference(cnf_transformation,[],[f135]) ).
fof(f171,plain,
v7_vectsp_1(sK0),
inference(cnf_transformation,[],[f135]) ).
fof(f172,plain,
v6_vectsp_1(sK0),
inference(cnf_transformation,[],[f135]) ).
fof(f173,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f135]) ).
fof(f174,plain,
v6_rlvect_1(sK0),
inference(cnf_transformation,[],[f135]) ).
fof(f175,plain,
v5_rlvect_1(sK0),
inference(cnf_transformation,[],[f135]) ).
fof(f176,plain,
v4_rlvect_1(sK0),
inference(cnf_transformation,[],[f135]) ).
fof(f177,plain,
v3_rlvect_1(sK0),
inference(cnf_transformation,[],[f135]) ).
fof(f178,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f135]) ).
fof(f179,plain,
l1_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f135]) ).
fof(f180,plain,
v5_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f135]) ).
fof(f181,plain,
v6_rlvect_1(sK1),
inference(cnf_transformation,[],[f135]) ).
fof(f182,plain,
v5_rlvect_1(sK1),
inference(cnf_transformation,[],[f135]) ).
fof(f183,plain,
v4_rlvect_1(sK1),
inference(cnf_transformation,[],[f135]) ).
fof(f184,plain,
v3_rlvect_1(sK1),
inference(cnf_transformation,[],[f135]) ).
fof(f185,plain,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f135]) ).
fof(f186,plain,
~ v1_rmod_5(k1_subset_1(u1_struct_0(sK1)),sK0,sK1),
inference(cnf_transformation,[],[f135]) ).
fof(f190,plain,
! [X0] : m1_subset_1(k1_subset_1(X0),k1_zfmisc_1(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f191,plain,
! [X0] : v1_xboole_0(k1_subset_1(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f198,plain,
! [X2,X0,X1] :
( ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ 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)))
| m2_rmod_4(sK7(X0,X1,X2),X0,X1,X2)
| v1_rmod_5(X2,X0,X1) ),
inference(cnf_transformation,[],[f143]) ).
fof(f200,plain,
! [X2,X0,X1] :
( ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ 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)))
| k1_xboole_0 != k2_rmod_4(X0,X1,sK7(X0,X1,X2))
| v1_rmod_5(X2,X0,X1) ),
inference(cnf_transformation,[],[f143]) ).
fof(f221,plain,
! [X2,X3,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)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ m1_rmod_4(X3,X0,X1)
| ~ m2_rmod_4(X3,X0,X1,X2)
| r1_tarski(k2_rmod_4(X0,X1,X3),X2) ),
inference(cnf_transformation,[],[f156]) ).
fof(f223,plain,
! [X0] :
( ~ v1_xboole_0(X0)
| k1_xboole_0 = X0 ),
inference(cnf_transformation,[],[f103]) ).
fof(f224,plain,
! [X0] :
( ~ r1_tarski(X0,k1_xboole_0)
| k1_xboole_0 = X0 ),
inference(cnf_transformation,[],[f104]) ).
fof(f227,plain,
! [X2,X3,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)
| ~ 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)
| ~ m2_rmod_4(X3,X0,X1,X2)
| m1_rmod_4(X3,X0,X1) ),
inference(cnf_transformation,[],[f108]) ).
tcf(c_49,negated_conjecture,
~ v1_rmod_5(k1_subset_1(u1_struct_0(sK1)),sK0,sK1),
inference(cnf_transformation,[],[f186]) ).
tcf(c_50,negated_conjecture,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f185]) ).
tcf(c_51,negated_conjecture,
v3_rlvect_1(sK1),
inference(cnf_transformation,[],[f184]) ).
tcf(c_52,negated_conjecture,
v4_rlvect_1(sK1),
inference(cnf_transformation,[],[f183]) ).
tcf(c_53,negated_conjecture,
v5_rlvect_1(sK1),
inference(cnf_transformation,[],[f182]) ).
tcf(c_54,negated_conjecture,
v6_rlvect_1(sK1),
inference(cnf_transformation,[],[f181]) ).
tcf(c_55,negated_conjecture,
v5_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f180]) ).
tcf(c_56,negated_conjecture,
l1_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f179]) ).
tcf(c_57,negated_conjecture,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f178]) ).
tcf(c_58,negated_conjecture,
v3_rlvect_1(sK0),
inference(cnf_transformation,[],[f177]) ).
tcf(c_59,negated_conjecture,
v4_rlvect_1(sK0),
inference(cnf_transformation,[],[f176]) ).
tcf(c_60,negated_conjecture,
v5_rlvect_1(sK0),
inference(cnf_transformation,[],[f175]) ).
tcf(c_61,negated_conjecture,
v6_rlvect_1(sK0),
inference(cnf_transformation,[],[f174]) ).
tcf(c_62,negated_conjecture,
v4_group_1(sK0),
inference(cnf_transformation,[],[f173]) ).
tcf(c_63,negated_conjecture,
v6_vectsp_1(sK0),
inference(cnf_transformation,[],[f172]) ).
tcf(c_64,negated_conjecture,
v7_vectsp_1(sK0),
inference(cnf_transformation,[],[f171]) ).
tcf(c_65,negated_conjecture,
v8_vectsp_1(sK0),
inference(cnf_transformation,[],[f170]) ).
tcf(c_66,negated_conjecture,
l3_vectsp_1(sK0),
inference(cnf_transformation,[],[f169]) ).
tcf(c_70,plain,
! [X0: $i] : v1_xboole_0(k1_subset_1(X0)),
inference(cnf_transformation,[],[f191]) ).
tcf(c_71,plain,
! [X0: $i] : m1_subset_1(k1_subset_1(X0),k1_zfmisc_1(X0)),
inference(cnf_transformation,[],[f190]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| v3_struct_0(X0)
| v1_rmod_5(X2,X0,X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(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)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ( k2_rmod_4(X0,X1,sK7(X0,X1,X2)) != k1_xboole_0 ) ),
inference(cnf_transformation,[],[f200]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X2)
| v3_struct_0(X1)
| v1_rmod_5(X0,X2,X1)
| m2_rmod_4(sK7(X2,X1,X0),X2,X1,X0)
| ~ l3_vectsp_1(X2)
| ~ v8_vectsp_1(X2)
| ~ v7_vectsp_1(X2)
| ~ v6_vectsp_1(X2)
| ~ v4_group_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X2)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X2)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X2)
| ~ v3_rlvect_1(X1)
| ~ l1_vectsp_2(X1,X2)
| ~ v5_vectsp_2(X1,X2)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(cnf_transformation,[],[f198]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X2)
| v3_struct_0(X1)
| r1_tarski(k2_rmod_4(X1,X2,X0),X3)
| ~ 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_4(X0,X1,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
| ~ m2_rmod_4(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f221]) ).
tcf(c_103,plain,
! [X0: $i] :
( ( X0 = k1_xboole_0 )
| ~ v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f223]) ).
tcf(c_104,plain,
! [X0: $i] :
( ( X0 = k1_xboole_0 )
| ~ r1_tarski(X0,k1_xboole_0) ),
inference(cnf_transformation,[],[f224]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X2)
| v3_struct_0(X1)
| m1_rmod_4(X0,X1,X2)
| ~ l3_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(X2)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X2)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X2)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X2)
| ~ v3_rlvect_1(X1)
| ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
| ~ m2_rmod_4(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f227]) ).
tcf(c_204,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X2)
| v3_struct_0(X1)
| r1_tarski(k2_rmod_4(X1,X2,X0),X3)
| ~ 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)
| ~ m2_rmod_4(X0,X1,X2,X3)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2))) ),
inference(global_subsumption_just,[status(thm)],[c_102,c_107,c_102]) ).
tcf(c_205,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X2)
| v3_struct_0(X1)
| r1_tarski(k2_rmod_4(X1,X2,X0),X3)
| ~ 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_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
| ~ m2_rmod_4(X0,X1,X2,X3) ),
inference(renaming,[status(thm)],[c_204]) ).
tcf(c_3676,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| v3_struct_0(X0)
| v1_rmod_5(X2,X0,X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(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)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ( X1 != sK1 )
| ( X0 != sK0 )
| ( k2_rmod_4(X0,X1,sK7(X0,X1,X2)) != k1_xboole_0 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_77]) ).
tcf(c_3677,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| v3_struct_0(sK1)
| v1_rmod_5(X0,sK0,sK1)
| ~ l3_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v6_rlvect_1(sK1)
| ~ v5_rlvect_1(sK0)
| ~ v5_rlvect_1(sK1)
| ~ v4_rlvect_1(sK0)
| ~ v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK0)
| ~ v3_rlvect_1(sK1)
| ~ l1_vectsp_2(sK1,sK0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1)))
| ( k2_rmod_4(sK0,sK1,sK7(sK0,sK1,X0)) != k1_xboole_0 ) ),
inference(unflattening,[status(thm)],[c_3676]) ).
tcf(c_3679,plain,
! [X0: $i] :
( v1_rmod_5(X0,sK0,sK1)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1)))
| ( k2_rmod_4(sK0,sK1,sK7(sK0,sK1,X0)) != k1_xboole_0 ) ),
inference(global_subsumption_just,[status(thm)],[c_3677,c_66,c_65,c_64,c_63,c_62,c_61,c_60,c_59,c_58,c_54,c_53,c_52,c_51,c_57,c_56,c_50,c_3677]) ).
tcf(c_3725,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| v3_struct_0(X0)
| v1_rmod_5(X2,X1,X0)
| m2_rmod_4(sK7(X1,X0,X2),X1,X0,X2)
| ~ l3_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(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)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
| ( X1 != sK0 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_79]) ).
tcf(c_3726,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| v3_struct_0(sK1)
| v1_rmod_5(X0,sK0,sK1)
| m2_rmod_4(sK7(sK0,sK1,X0),sK0,sK1,X0)
| ~ l3_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v6_rlvect_1(sK1)
| ~ v5_rlvect_1(sK0)
| ~ v5_rlvect_1(sK1)
| ~ v4_rlvect_1(sK0)
| ~ v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK0)
| ~ v3_rlvect_1(sK1)
| ~ l1_vectsp_2(sK1,sK0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1))) ),
inference(unflattening,[status(thm)],[c_3725]) ).
tcf(c_3728,plain,
! [X0: $i] :
( v1_rmod_5(X0,sK0,sK1)
| m2_rmod_4(sK7(sK0,sK1,X0),sK0,sK1,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1))) ),
inference(global_subsumption_just,[status(thm)],[c_3726,c_66,c_65,c_64,c_63,c_62,c_61,c_60,c_59,c_58,c_54,c_53,c_52,c_51,c_57,c_56,c_50,c_3726]) ).
tcf(c_3755,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X1)
| v3_struct_0(X0)
| r1_tarski(k2_rmod_4(X1,X0,X2),X3)
| ~ 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)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m2_rmod_4(X2,X1,X0,X3)
| ( X1 != sK0 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_205]) ).
tcf(c_3756,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| v3_struct_0(sK1)
| r1_tarski(k2_rmod_4(sK0,sK1,X0),X1)
| ~ l3_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v6_rlvect_1(sK1)
| ~ v5_rlvect_1(sK0)
| ~ v5_rlvect_1(sK1)
| ~ v4_rlvect_1(sK0)
| ~ v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK0)
| ~ v3_rlvect_1(sK1)
| ~ l1_vectsp_2(sK1,sK0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m2_rmod_4(X0,sK0,sK1,X1) ),
inference(unflattening,[status(thm)],[c_3755]) ).
tcf(c_3758,plain,
! [X0: $i,X1: $i] :
( r1_tarski(k2_rmod_4(sK0,sK1,X0),X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m2_rmod_4(X0,sK0,sK1,X1) ),
inference(global_subsumption_just,[status(thm)],[c_3756,c_66,c_65,c_64,c_63,c_62,c_61,c_60,c_59,c_58,c_54,c_53,c_52,c_51,c_57,c_56,c_50,c_3756]) ).
tcf(c_4635,plain,
! [X0: $i,X1: $i,X2: $i] :
( v1_rmod_5(X0,sK0,sK1)
| r1_tarski(k2_rmod_4(sK0,sK1,X1),X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1)))
| ( sK0 != sK0 )
| ( sK1 != sK1 )
| ( X0 != X2 )
| ( sK7(sK0,sK1,X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_3758,c_3728]) ).
tcf(c_4636,plain,
! [X0: $i] :
( v1_rmod_5(X0,sK0,sK1)
| r1_tarski(k2_rmod_4(sK0,sK1,sK7(sK0,sK1,X0)),X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1))) ),
inference(unflattening,[status(thm)],[c_4635]) ).
tcf(c_9099,plain,
! [X0: $i] : k1_subset_1(X0) = k1_xboole_0,
inference(superposition,[status(thm)],[c_70,c_103]) ).
tcf(c_9105,plain,
~ v1_rmod_5(k1_xboole_0,sK0,sK1),
inference(demodulation,[status(thm)],[c_49,c_9099]) ).
tcf(c_9107,plain,
! [X0: $i] : m1_subset_1(k1_xboole_0,k1_zfmisc_1(X0)),
inference(demodulation,[status(thm)],[c_71,c_9099]) ).
tcf(c_9213,plain,
( v1_rmod_5(k1_xboole_0,sK0,sK1)
| ( k2_rmod_4(sK0,sK1,sK7(sK0,sK1,k1_xboole_0)) = k1_xboole_0 )
| ~ m1_subset_1(k1_xboole_0,k1_zfmisc_1(u1_struct_0(sK1))) ),
inference(superposition,[status(thm)],[c_4636,c_104]) ).
tcf(c_9214,plain,
k2_rmod_4(sK0,sK1,sK7(sK0,sK1,k1_xboole_0)) = k1_xboole_0,
inference(forward_subsumption_resolution,[status(thm)],[c_9213,c_9105,c_9107]) ).
tcf(c_9235,plain,
( v1_rmod_5(k1_xboole_0,sK0,sK1)
| ~ m1_subset_1(k1_xboole_0,k1_zfmisc_1(u1_struct_0(sK1))) ),
inference(superposition,[status(thm)],[c_9214,c_3679]) ).
tcf(c_9236,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_9235,c_9105,c_9107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG215+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/5.38 % Computer : n015.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Fri Sep 25 05:09:32 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/5.44
% 0.14/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.44
% 0.14/5.44 % Detected problem language: tptp
% 0.14/5.45 % Proving...
% 4.54/6.31 % SZS status Started for theBenchmark.p
% 4.54/6.31 % SZS status Theorem for theBenchmark.p
% 4.54/6.31
% 4.54/6.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.54/6.31
% 4.54/6.31 % ------ iProver source info
% 4.54/6.31
% 4.54/6.31 % git: date: 2026-07-19 20:42:38 +0200
% 4.54/6.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.54/6.31 % git: non_committed_changes: false
% 4.54/6.31
% 4.54/6.31 % ------ Parsing...
% 4.54/6.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.54/6.31
% 4.54/6.31 % ------ 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:16:0s pe_e sup_sim: 0 sf_s rm: 21 0s sf_e pe_s pe_e %
% 4.54/6.31
% 4.54/6.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.54/6.31
% 4.54/6.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.54/6.31 % ------ Proving...
% 4.54/6.31 % ------ Problem Properties
% 4.54/6.31
% 4.54/6.31 %
% 4.54/6.31 % clauses 86
% 4.54/6.31 % conjectures 1
% 4.54/6.31 % EPR 20
% 4.54/6.31 % Horn 74
% 4.54/6.31 % unary 43
% 4.54/6.31 % binary 21
% 4.54/6.31 % lits 160
% 4.54/6.31 % lits eq 18
% 4.54/6.31 % fd_pure 0
% 4.54/6.31 % fd_pseudo 0
% 4.54/6.31 % fd_cond 2
% 4.54/6.31 % fd_pseudo_cond 3
% 4.54/6.31 % AC symbols 0
% 4.54/6.31
% 4.54/6.31 % ------ Schedule dynamic 5 is on
% 4.54/6.31
% 4.54/6.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.54/6.31
% 4.54/6.31
% 4.54/6.31 % ------
% 4.54/6.31 % Current options:
% 4.54/6.31 % ------
% 4.54/6.31
% 4.54/6.31
% 4.54/6.31 %
% 4.54/6.31
% 4.54/6.31 % ------ Proving...
% 4.54/6.31 %
% 4.54/6.31
% 4.54/6.31 % SZS status Theorem for theBenchmark.p
% 4.54/6.31
% 4.54/6.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.54/6.31
% 4.54/6.31
%------------------------------------------------------------------------------