%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG214+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n012.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 2.72s 0.97s
% Output : CNFRefutation 2.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 6
% Syntax : Number of formulae : 128 ( 55 unt; 1 def)
% Number of atoms : 1164 ( 75 equ)
% Maximal formula atoms : 26 ( 9 avg)
% Number of connectives : 1778 ( 762 ~; 821 |; 166 &)
% ( 3 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 9 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 3 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 192 ( 0 sgn 182 !; 10 ?; 89 :)
% 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) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
=> ( ( v1_rmod_5(X3,X0,X1)
& r1_tarski(X2,X3) )
=> v1_rmod_5(X2,X0,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_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) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
=> ( ( v1_rmod_5(X3,X0,X1)
& r1_tarski(X2,X3) )
=> v1_rmod_5(X2,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/sandbox2/benchmark/theBenchmark.p',d1_rmod_5) ).
fof(f6,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_4(X2,X0,X1)
=> k2_rmod_4(X0,X1,X2) = a_3_0_rmod_4(X0,X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_rmod_4) ).
fof(f31,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/sandbox2/benchmark/theBenchmark.p',dt_m2_rmod_4) ).
fof(f68,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_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
=> ! [X4] :
( m2_rmod_4(X4,X0,X1,X2)
=> ( r1_tarski(X2,X3)
=> m2_rmod_4(X4,X0,X1,X3) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_rmod_4) ).
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)
& ? [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
& ? [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
& v1_rmod_5(X3,X0,X1)
& r1_tarski(X2,X3)
& ~ v1_rmod_5(X2,X0,X1) ) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f83,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_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
& v1_rmod_5(X3,X0,X1)
& r1_tarski(X2,X3)
& ~ v1_rmod_5(X2,X0,X1) ) ) ) ),
inference(flattening,[],[f82]) ).
fof(f85,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(f86,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,[],[f85]) ).
fof(f87,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_4(X2,X0,X1)
| k2_rmod_4(X0,X1,X2) = a_3_0_rmod_4(X0,X1,X2) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f88,plain,
! [X0] :
( ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ! [X2] :
( ~ m1_rmod_4(X2,X0,X1)
| k2_rmod_4(X0,X1,X2) = a_3_0_rmod_4(X0,X1,X2) ) ) ),
inference(flattening,[],[f87]) ).
fof(f110,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,[],[f31]) ).
fof(f111,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,[],[f110]) ).
fof(f137,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_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
| ! [X4] :
( ~ m2_rmod_4(X4,X0,X1,X2)
| ~ r1_tarski(X2,X3)
| m2_rmod_4(X4,X0,X1,X3) ) ) ) ) ),
inference(ennf_transformation,[],[f68]) ).
fof(f138,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_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
| ! [X4] :
( ~ m2_rmod_4(X4,X0,X1,X2)
| ~ r1_tarski(X2,X3)
| m2_rmod_4(X4,X0,X1,X3) ) ) ) ) ),
inference(flattening,[],[f137]) ).
fof(f148,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)
& m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
& m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1)))
& v1_rmod_5(sK3,sK0,sK1)
& r1_tarski(sK2,sK3)
& ~ v1_rmod_5(sK2,sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f83]) ).
fof(f149,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,[],[f86]) ).
fof(f150,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,[],[f149]) ).
fof(f151,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(sK4(X0,X1,X2),X0,X1,X2)
& k1_rlvect_1(X1) = k5_rmod_4(X0,X1,sK4(X0,X1,X2))
& k1_xboole_0 != k2_rmod_4(X0,X1,sK4(X0,X1,X2)) )
| v1_rmod_5(X2,X0,X1) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f150]) ).
fof(f184,plain,
l3_vectsp_1(sK0),
inference(cnf_transformation,[],[f148]) ).
fof(f185,plain,
v8_vectsp_1(sK0),
inference(cnf_transformation,[],[f148]) ).
fof(f186,plain,
v7_vectsp_1(sK0),
inference(cnf_transformation,[],[f148]) ).
fof(f187,plain,
v6_vectsp_1(sK0),
inference(cnf_transformation,[],[f148]) ).
fof(f188,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f148]) ).
fof(f189,plain,
v6_rlvect_1(sK0),
inference(cnf_transformation,[],[f148]) ).
fof(f190,plain,
v5_rlvect_1(sK0),
inference(cnf_transformation,[],[f148]) ).
fof(f191,plain,
v4_rlvect_1(sK0),
inference(cnf_transformation,[],[f148]) ).
fof(f192,plain,
v3_rlvect_1(sK0),
inference(cnf_transformation,[],[f148]) ).
fof(f193,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f148]) ).
fof(f194,plain,
l1_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f148]) ).
fof(f195,plain,
v5_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f148]) ).
fof(f196,plain,
v6_rlvect_1(sK1),
inference(cnf_transformation,[],[f148]) ).
fof(f197,plain,
v5_rlvect_1(sK1),
inference(cnf_transformation,[],[f148]) ).
fof(f198,plain,
v4_rlvect_1(sK1),
inference(cnf_transformation,[],[f148]) ).
fof(f199,plain,
v3_rlvect_1(sK1),
inference(cnf_transformation,[],[f148]) ).
fof(f200,plain,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f148]) ).
fof(f201,plain,
m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1))),
inference(cnf_transformation,[],[f148]) ).
fof(f202,plain,
m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1))),
inference(cnf_transformation,[],[f148]) ).
fof(f203,plain,
v1_rmod_5(sK3,sK0,sK1),
inference(cnf_transformation,[],[f148]) ).
fof(f204,plain,
r1_tarski(sK2,sK3),
inference(cnf_transformation,[],[f148]) ).
fof(f205,plain,
~ v1_rmod_5(sK2,sK0,sK1),
inference(cnf_transformation,[],[f148]) ).
fof(f207,plain,
! [X2,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_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ v1_rmod_5(X2,X0,X1)
| ~ 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) ),
inference(cnf_transformation,[],[f151]) ).
fof(f208,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(sK4(X0,X1,X2),X0,X1,X2)
| v1_rmod_5(X2,X0,X1) ),
inference(cnf_transformation,[],[f151]) ).
fof(f209,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_rlvect_1(X1) = k5_rmod_4(X0,X1,sK4(X0,X1,X2))
| v1_rmod_5(X2,X0,X1) ),
inference(cnf_transformation,[],[f151]) ).
fof(f210,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,sK4(X0,X1,X2))
| v1_rmod_5(X2,X0,X1) ),
inference(cnf_transformation,[],[f151]) ).
fof(f211,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_rmod_4(X2,X0,X1)
| k2_rmod_4(X0,X1,X2) = a_3_0_rmod_4(X0,X1,X2) ),
inference(cnf_transformation,[],[f88]) ).
fof(f232,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,[],[f111]) ).
fof(f280,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_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
| ~ m2_rmod_4(X4,X0,X1,X2)
| ~ r1_tarski(X2,X3)
| m2_rmod_4(X4,X0,X1,X3) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_49,negated_conjecture,
~ v1_rmod_5(sK2,sK0,sK1),
inference(cnf_transformation,[],[f205]) ).
tcf(c_50,negated_conjecture,
r1_tarski(sK2,sK3),
inference(cnf_transformation,[],[f204]) ).
tcf(c_51,negated_conjecture,
v1_rmod_5(sK3,sK0,sK1),
inference(cnf_transformation,[],[f203]) ).
tcf(c_52,negated_conjecture,
m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1))),
inference(cnf_transformation,[],[f202]) ).
tcf(c_53,negated_conjecture,
m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1))),
inference(cnf_transformation,[],[f201]) ).
tcf(c_54,negated_conjecture,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f200]) ).
tcf(c_55,negated_conjecture,
v3_rlvect_1(sK1),
inference(cnf_transformation,[],[f199]) ).
tcf(c_56,negated_conjecture,
v4_rlvect_1(sK1),
inference(cnf_transformation,[],[f198]) ).
tcf(c_57,negated_conjecture,
v5_rlvect_1(sK1),
inference(cnf_transformation,[],[f197]) ).
tcf(c_58,negated_conjecture,
v6_rlvect_1(sK1),
inference(cnf_transformation,[],[f196]) ).
tcf(c_59,negated_conjecture,
v5_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f195]) ).
tcf(c_60,negated_conjecture,
l1_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f194]) ).
tcf(c_61,negated_conjecture,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f193]) ).
tcf(c_62,negated_conjecture,
v3_rlvect_1(sK0),
inference(cnf_transformation,[],[f192]) ).
tcf(c_63,negated_conjecture,
v4_rlvect_1(sK0),
inference(cnf_transformation,[],[f191]) ).
tcf(c_64,negated_conjecture,
v5_rlvect_1(sK0),
inference(cnf_transformation,[],[f190]) ).
tcf(c_65,negated_conjecture,
v6_rlvect_1(sK0),
inference(cnf_transformation,[],[f189]) ).
tcf(c_66,negated_conjecture,
v4_group_1(sK0),
inference(cnf_transformation,[],[f188]) ).
tcf(c_67,negated_conjecture,
v6_vectsp_1(sK0),
inference(cnf_transformation,[],[f187]) ).
tcf(c_68,negated_conjecture,
v7_vectsp_1(sK0),
inference(cnf_transformation,[],[f186]) ).
tcf(c_69,negated_conjecture,
v8_vectsp_1(sK0),
inference(cnf_transformation,[],[f185]) ).
tcf(c_70,negated_conjecture,
l3_vectsp_1(sK0),
inference(cnf_transformation,[],[f184]) ).
tcf(c_72,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,sK4(X0,X1,X2)) != k1_xboole_0 ) ),
inference(cnf_transformation,[],[f210]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X2)
| v3_struct_0(X1)
| v1_rmod_5(X0,X2,X1)
| ( k5_rmod_4(X2,X1,sK4(X2,X1,X0)) = k1_rlvect_1(X1) )
| ~ 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,[],[f209]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X2)
| v3_struct_0(X1)
| v1_rmod_5(X0,X2,X1)
| m2_rmod_4(sK4(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,[],[f208]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X1)
| v3_struct_0(X0)
| ( k2_rmod_4(X0,X1,X2) = k1_xboole_0 )
| ~ 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)
| ~ v1_rmod_5(X3,X0,X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
| ~ m2_rmod_4(X2,X0,X1,X3)
| ( k5_rmod_4(X0,X1,X2) != k1_rlvect_1(X1) ) ),
inference(cnf_transformation,[],[f207]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X2)
| v3_struct_0(X1)
| ( k2_rmod_4(X1,X2,X0) = a_3_0_rmod_4(X1,X2,X0) )
| ~ 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) ),
inference(cnf_transformation,[],[f211]) ).
tcf(c_97,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,[],[f232]) ).
tcf(c_145,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( v3_struct_0(X2)
| v3_struct_0(X1)
| m2_rmod_4(X0,X1,X2,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)
| ~ r1_tarski(X3,X4)
| ~ m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
| ~ m2_rmod_4(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f280]) ).
tcf(c_4379,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X1)
| v3_struct_0(X0)
| ( k2_rmod_4(X0,X1,X2) = k1_xboole_0 )
| ~ 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)
| ~ v1_rmod_5(X3,X0,X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
| ~ m2_rmod_4(X2,X0,X1,X3)
| ( X1 != sK1 )
| ( X0 != sK0 )
| ( k5_rmod_4(X0,X1,X2) != k1_rlvect_1(X1) ) ),
inference(resolution_lifted,[status(thm)],[c_59,c_75]) ).
tcf(c_4380,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK1)
| v3_struct_0(sK0)
| ( k2_rmod_4(sK0,sK1,X0) = k1_xboole_0 )
| ~ l3_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_rlvect_1(sK1)
| ~ v6_rlvect_1(sK0)
| ~ v5_rlvect_1(sK1)
| ~ v5_rlvect_1(sK0)
| ~ v4_rlvect_1(sK1)
| ~ v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK1)
| ~ v3_rlvect_1(sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ v1_rmod_5(X1,sK0,sK1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m2_rmod_4(X0,sK0,sK1,X1)
| ( k5_rmod_4(sK0,sK1,X0) != k1_rlvect_1(sK1) ) ),
inference(unflattening,[status(thm)],[c_4379]) ).
tcf(c_4382,plain,
! [X0: $i,X1: $i] :
( ( k2_rmod_4(sK0,sK1,X0) = k1_xboole_0 )
| ~ v1_rmod_5(X1,sK0,sK1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m2_rmod_4(X0,sK0,sK1,X1)
| ( k5_rmod_4(sK0,sK1,X0) != k1_rlvect_1(sK1) ) ),
inference(global_subsumption_just,[status(thm)],[c_4380,c_70,c_69,c_68,c_67,c_66,c_65,c_64,c_63,c_62,c_58,c_57,c_56,c_55,c_61,c_60,c_54,c_4380]) ).
tcf(c_4400,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,sK4(X0,X1,X2)) != k1_xboole_0 ) ),
inference(resolution_lifted,[status(thm)],[c_59,c_72]) ).
tcf(c_4401,plain,
! [X0: $i] :
( v3_struct_0(sK1)
| v3_struct_0(sK0)
| 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(sK1)
| ~ v6_rlvect_1(sK0)
| ~ v5_rlvect_1(sK1)
| ~ v5_rlvect_1(sK0)
| ~ v4_rlvect_1(sK1)
| ~ v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK1)
| ~ v3_rlvect_1(sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1)))
| ( k2_rmod_4(sK0,sK1,sK4(sK0,sK1,X0)) != k1_xboole_0 ) ),
inference(unflattening,[status(thm)],[c_4400]) ).
tcf(c_4403,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,sK4(sK0,sK1,X0)) != k1_xboole_0 ) ),
inference(global_subsumption_just,[status(thm)],[c_4401,c_70,c_69,c_68,c_67,c_66,c_65,c_64,c_63,c_62,c_58,c_57,c_56,c_55,c_61,c_60,c_54,c_4401]) ).
tcf(c_4427,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| v3_struct_0(X0)
| v1_rmod_5(X2,X0,X1)
| m2_rmod_4(sK4(X0,X1,X2),X0,X1,X2)
| ~ 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 ) ),
inference(resolution_lifted,[status(thm)],[c_59,c_74]) ).
tcf(c_4428,plain,
! [X0: $i] :
( v3_struct_0(sK1)
| v3_struct_0(sK0)
| v1_rmod_5(X0,sK0,sK1)
| m2_rmod_4(sK4(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(sK1)
| ~ v6_rlvect_1(sK0)
| ~ v5_rlvect_1(sK1)
| ~ v5_rlvect_1(sK0)
| ~ v4_rlvect_1(sK1)
| ~ v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK1)
| ~ v3_rlvect_1(sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1))) ),
inference(unflattening,[status(thm)],[c_4427]) ).
tcf(c_4430,plain,
! [X0: $i] :
( v1_rmod_5(X0,sK0,sK1)
| m2_rmod_4(sK4(sK0,sK1,X0),sK0,sK1,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1))) ),
inference(global_subsumption_just,[status(thm)],[c_4428,c_70,c_69,c_68,c_67,c_66,c_65,c_64,c_63,c_62,c_58,c_57,c_56,c_55,c_61,c_60,c_54,c_4428]) ).
tcf(c_4442,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| v3_struct_0(X0)
| v1_rmod_5(X2,X0,X1)
| ( k5_rmod_4(X0,X1,sK4(X0,X1,X2)) = k1_rlvect_1(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 ) ),
inference(resolution_lifted,[status(thm)],[c_59,c_73]) ).
tcf(c_4443,plain,
! [X0: $i] :
( v3_struct_0(sK1)
| v3_struct_0(sK0)
| v1_rmod_5(X0,sK0,sK1)
| ( k5_rmod_4(sK0,sK1,sK4(sK0,sK1,X0)) = k1_rlvect_1(sK1) )
| ~ l3_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_rlvect_1(sK1)
| ~ v6_rlvect_1(sK0)
| ~ v5_rlvect_1(sK1)
| ~ v5_rlvect_1(sK0)
| ~ v4_rlvect_1(sK1)
| ~ v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK1)
| ~ v3_rlvect_1(sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1))) ),
inference(unflattening,[status(thm)],[c_4442]) ).
tcf(c_4445,plain,
! [X0: $i] :
( v1_rmod_5(X0,sK0,sK1)
| ( k5_rmod_4(sK0,sK1,sK4(sK0,sK1,X0)) = k1_rlvect_1(sK1) )
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1))) ),
inference(global_subsumption_just,[status(thm)],[c_4443,c_70,c_69,c_68,c_67,c_66,c_65,c_64,c_63,c_62,c_58,c_57,c_56,c_55,c_61,c_60,c_54,c_4443]) ).
tcf(c_4457,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( v3_struct_0(X1)
| v3_struct_0(X0)
| m2_rmod_4(X2,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(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)
| ~ r1_tarski(X3,X4)
| ~ m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X1)))
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
| ~ m2_rmod_4(X2,X0,X1,X3)
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_59,c_145]) ).
tcf(c_4458,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(sK1)
| v3_struct_0(sK0)
| m2_rmod_4(X0,sK0,sK1,X2)
| ~ l3_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_rlvect_1(sK1)
| ~ v6_rlvect_1(sK0)
| ~ v5_rlvect_1(sK1)
| ~ v5_rlvect_1(sK0)
| ~ v4_rlvect_1(sK1)
| ~ v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK1)
| ~ v3_rlvect_1(sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ r1_tarski(X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m2_rmod_4(X0,sK0,sK1,X1) ),
inference(unflattening,[status(thm)],[c_4457]) ).
tcf(c_4459,plain,
! [X0: $i,X1: $i,X2: $i] :
( m2_rmod_4(X0,sK0,sK1,X2)
| ~ r1_tarski(X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ 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_4458,c_70,c_69,c_68,c_67,c_66,c_65,c_64,c_63,c_62,c_58,c_57,c_56,c_55,c_61,c_60,c_54,c_4458]) ).
tcf(c_4524,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X1)
| v3_struct_0(X0)
| m1_rmod_4(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(X3,k1_zfmisc_1(u1_struct_0(X1)))
| ~ m2_rmod_4(X2,X0,X1,X3)
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_59,c_97]) ).
tcf(c_4525,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK1)
| v3_struct_0(sK0)
| m1_rmod_4(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(sK1)
| ~ v6_rlvect_1(sK0)
| ~ v5_rlvect_1(sK1)
| ~ v5_rlvect_1(sK0)
| ~ v4_rlvect_1(sK1)
| ~ v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK1)
| ~ v3_rlvect_1(sK0)
| ~ 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_4524]) ).
tcf(c_4527,plain,
! [X0: $i,X1: $i] :
( m1_rmod_4(X0,sK0,sK1)
| ~ 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_4525,c_70,c_69,c_68,c_67,c_66,c_65,c_64,c_63,c_62,c_58,c_57,c_56,c_55,c_61,c_60,c_54,c_4525]) ).
tcf(c_4575,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| v3_struct_0(X0)
| ( k2_rmod_4(X0,X1,X2) = a_3_0_rmod_4(X0,X1,X2) )
| ~ 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_rmod_4(X2,X0,X1)
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_59,c_76]) ).
tcf(c_4576,plain,
! [X0: $i] :
( v3_struct_0(sK1)
| v3_struct_0(sK0)
| ( k2_rmod_4(sK0,sK1,X0) = a_3_0_rmod_4(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(sK1)
| ~ v6_rlvect_1(sK0)
| ~ v5_rlvect_1(sK1)
| ~ v5_rlvect_1(sK0)
| ~ v4_rlvect_1(sK1)
| ~ v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK1)
| ~ v3_rlvect_1(sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ m1_rmod_4(X0,sK0,sK1) ),
inference(unflattening,[status(thm)],[c_4575]) ).
tcf(c_4578,plain,
! [X0: $i] :
( ( k2_rmod_4(sK0,sK1,X0) = a_3_0_rmod_4(sK0,sK1,X0) )
| ~ m1_rmod_4(X0,sK0,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_4576,c_70,c_69,c_68,c_67,c_66,c_65,c_64,c_63,c_62,c_58,c_57,c_56,c_55,c_61,c_60,c_54,c_4576]) ).
tcf(c_4968,plain,
! [X0: $i,X1: $i,X2: $i] :
( m2_rmod_4(X2,sK0,sK1,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m2_rmod_4(X2,sK0,sK1,X0)
| ( X1 != sK3 )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_4459]) ).
tcf(c_4969,plain,
! [X0: $i] :
( m2_rmod_4(X0,sK0,sK1,sK3)
| ~ m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m2_rmod_4(X0,sK0,sK1,sK2) ),
inference(unflattening,[status(thm)],[c_4968]) ).
tcf(c_4971,plain,
! [X0: $i] :
( m2_rmod_4(X0,sK0,sK1,sK3)
| ~ m2_rmod_4(X0,sK0,sK1,sK2) ),
inference(global_subsumption_just,[status(thm)],[c_4969,c_53,c_52,c_4969]) ).
tcf(c_6080,definition,
iPr_def_26 = k1_rlvect_1(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_26])],[]) ).
tcf(c_6101,plain,
! [X0: $i] :
( m2_rmod_4(X0,sK0,sK1,sK3)
| ~ m2_rmod_4(X0,sK0,sK1,sK2) ),
inference(demodulation,[status(thm)],[c_4971]) ).
tcf(c_6104,plain,
! [X0: $i] :
( ( k2_rmod_4(sK0,sK1,X0) = a_3_0_rmod_4(sK0,sK1,X0) )
| ~ m1_rmod_4(X0,sK0,sK1) ),
inference(demodulation,[status(thm)],[c_4578]) ).
tcf(c_6108,plain,
! [X0: $i,X1: $i] :
( m1_rmod_4(X0,sK0,sK1)
| ~ m1_subset_1(X1,iPr_def_22)
| ~ m2_rmod_4(X0,sK0,sK1,X1) ),
inference(demodulation,[status(thm)],[c_4527]) ).
tcf(c_6112,plain,
! [X0: $i] :
( v1_rmod_5(X0,sK0,sK1)
| ( k5_rmod_4(sK0,sK1,sK4(sK0,sK1,X0)) = iPr_def_26 )
| ~ m1_subset_1(X0,iPr_def_22) ),
inference(demodulation,[status(thm)],[c_4445,c_6080]) ).
tcf(c_6113,plain,
! [X0: $i] :
( v1_rmod_5(X0,sK0,sK1)
| m2_rmod_4(sK4(sK0,sK1,X0),sK0,sK1,X0)
| ~ m1_subset_1(X0,iPr_def_22) ),
inference(demodulation,[status(thm)],[c_4430]) ).
tcf(c_6115,plain,
! [X0: $i] :
( v1_rmod_5(X0,sK0,sK1)
| ~ m1_subset_1(X0,iPr_def_22)
| ( k2_rmod_4(sK0,sK1,sK4(sK0,sK1,X0)) != k1_xboole_0 ) ),
inference(demodulation,[status(thm)],[c_4403]) ).
tcf(c_6116,plain,
! [X0: $i,X1: $i] :
( ( k2_rmod_4(sK0,sK1,X0) = k1_xboole_0 )
| ~ m1_subset_1(X1,iPr_def_22)
| ~ v1_rmod_5(X1,sK0,sK1)
| ~ m2_rmod_4(X0,sK0,sK1,X1)
| ( k5_rmod_4(sK0,sK1,X0) != iPr_def_26 ) ),
inference(demodulation,[status(thm)],[c_4382]) ).
tcf(c_6122,negated_conjecture,
m1_subset_1(sK2,iPr_def_22),
inference(demodulation,[status(thm)],[c_53]) ).
tcf(c_6123,negated_conjecture,
m1_subset_1(sK3,iPr_def_22),
inference(demodulation,[status(thm)],[c_52]) ).
tcf(c_6124,negated_conjecture,
v1_rmod_5(sK3,sK0,sK1),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_6125,negated_conjecture,
~ v1_rmod_5(sK2,sK0,sK1),
inference(demodulation,[status(thm)],[c_49]) ).
tcf(c_7567,plain,
( v1_rmod_5(sK2,sK0,sK1)
| m2_rmod_4(sK4(sK0,sK1,sK2),sK0,sK1,sK3)
| ~ m1_subset_1(sK2,iPr_def_22) ),
inference(superposition,[status(thm)],[c_6113,c_6101]) ).
tcf(c_7571,plain,
m2_rmod_4(sK4(sK0,sK1,sK2),sK0,sK1,sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_7567,c_6125,c_6122]) ).
tcf(c_7573,plain,
( m1_rmod_4(sK4(sK0,sK1,sK2),sK0,sK1)
| ~ m1_subset_1(sK3,iPr_def_22) ),
inference(superposition,[status(thm)],[c_7571,c_6108]) ).
tcf(c_7574,plain,
m1_rmod_4(sK4(sK0,sK1,sK2),sK0,sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_7573,c_6123]) ).
tcf(c_7575,plain,
k2_rmod_4(sK0,sK1,sK4(sK0,sK1,sK2)) = a_3_0_rmod_4(sK0,sK1,sK4(sK0,sK1,sK2)),
inference(superposition,[status(thm)],[c_7574,c_6104]) ).
tcf(c_7589,plain,
( ( k5_rmod_4(sK0,sK1,sK4(sK0,sK1,sK2)) = iPr_def_26 )
| ~ m1_subset_1(sK2,iPr_def_22) ),
inference(superposition,[status(thm)],[c_6112,c_6125]) ).
tcf(c_7590,plain,
k5_rmod_4(sK0,sK1,sK4(sK0,sK1,sK2)) = iPr_def_26,
inference(forward_subsumption_resolution,[status(thm)],[c_7589,c_6122]) ).
tcf(c_7608,plain,
( v1_rmod_5(sK2,sK0,sK1)
| ~ m1_subset_1(sK2,iPr_def_22)
| ( a_3_0_rmod_4(sK0,sK1,sK4(sK0,sK1,sK2)) != k1_xboole_0 ) ),
inference(superposition,[status(thm)],[c_7575,c_6115]) ).
tcf(c_7609,plain,
a_3_0_rmod_4(sK0,sK1,sK4(sK0,sK1,sK2)) != k1_xboole_0,
inference(forward_subsumption_resolution,[status(thm)],[c_7608,c_6125,c_6122]) ).
tcf(c_7646,plain,
! [X0: $i] :
( ( k2_rmod_4(sK0,sK1,sK4(sK0,sK1,sK2)) = k1_xboole_0 )
| ~ m1_subset_1(X0,iPr_def_22)
| ~ v1_rmod_5(X0,sK0,sK1)
| ~ m2_rmod_4(sK4(sK0,sK1,sK2),sK0,sK1,X0) ),
inference(superposition,[status(thm)],[c_7590,c_6116]) ).
tcf(c_7647,plain,
! [X0: $i] :
( ( a_3_0_rmod_4(sK0,sK1,sK4(sK0,sK1,sK2)) = k1_xboole_0 )
| ~ m1_subset_1(X0,iPr_def_22)
| ~ v1_rmod_5(X0,sK0,sK1)
| ~ m2_rmod_4(sK4(sK0,sK1,sK2),sK0,sK1,X0) ),
inference(light_normalisation,[status(thm)],[c_7646,c_7575]) ).
tcf(c_7648,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,iPr_def_22)
| ~ v1_rmod_5(X0,sK0,sK1)
| ~ m2_rmod_4(sK4(sK0,sK1,sK2),sK0,sK1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7647,c_7609]) ).
tcf(c_7660,plain,
( ~ m1_subset_1(sK3,iPr_def_22)
| ~ v1_rmod_5(sK3,sK0,sK1) ),
inference(superposition,[status(thm)],[c_7571,c_7648]) ).
tcf(c_7661,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_7660,c_6123,c_6124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ALG214+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Fri Sep 25 05:05:08 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.04/0.32 Running first-order theorem proving
% 0.04/0.32 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.33
% 0.06/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.06/0.33
% 0.06/0.33 % Detected problem language: tptp
% 0.06/0.34 % Proving...
% 2.72/0.97 % SZS status Started for theBenchmark.p
% 2.72/0.97 % SZS status Theorem for theBenchmark.p
% 2.72/0.97
% 2.72/0.97 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.72/0.97
% 2.72/0.97 % ------ iProver source info
% 2.72/0.97
% 2.72/0.97 % git: date: 2026-07-19 20:42:38 +0200
% 2.72/0.97 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.72/0.97 % git: non_committed_changes: false
% 2.72/0.97
% 2.72/0.97 % ------ Parsing...
% 2.72/0.97 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.72/0.97
% 2.72/0.97 % ------ 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:16:0s pe_e %
% 2.72/0.97
% 2.72/0.97 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.72/0.97
% 2.72/0.97 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.72/0.97 % ------ Proving...
% 2.72/0.97 % ------ Problem Properties
% 2.72/0.97
% 2.72/0.97 %
% 2.72/0.97 % clauses 160
% 2.72/0.97 % conjectures 4
% 2.72/0.97 % EPR 47
% 2.72/0.97 % Horn 145
% 2.72/0.97 % unary 112
% 2.72/0.97 % binary 25
% 2.72/0.97 % lits 245
% 2.72/0.97 % lits eq 33
% 2.72/0.97 % fd_pure 0
% 2.72/0.97 % fd_pseudo 0
% 2.72/0.97 % fd_cond 1
% 2.72/0.97 % fd_pseudo_cond 3
% 2.72/0.97 % AC symbols 0
% 2.72/0.97
% 2.72/0.97 % ------ Schedule dynamic 5 is on
% 2.72/0.97
% 2.72/0.97 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.72/0.97
% 2.72/0.97
% 2.72/0.97 % ------
% 2.72/0.97 % Current options:
% 2.72/0.97 % ------
% 2.72/0.97
% 2.72/0.97
% 2.72/0.97 %
% 2.72/0.97
% 2.72/0.97 % ------ Proving...
% 2.72/0.97 %
% 2.72/0.97
% 2.72/0.97 % SZS status Theorem for theBenchmark.p
% 2.72/0.97
% 2.72/0.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.72/0.97
% 2.72/0.97
%------------------------------------------------------------------------------