%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG218+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 12:53:50 PM UTC 2026
% Result : Theorem 17.74s 3.26s
% Output : CNFRefutation 17.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 16
% Syntax : Number of formulae : 181 ( 66 unt; 0 def)
% Number of atoms : 795 ( 101 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 1027 ( 413 ~; 427 |; 158 &)
% ( 5 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 5 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 : 27 ( 25 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 194 ( 0 sgn 185 !; 9 ?; 83 :)
% 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)))
=> ~ ( X2 != k7_rlvect_2(X1,k1_rlvect_1(X1))
& X2 != k1_xboole_0
& k1_rmod_5(X0,X1,X2) = k1_rmod_2(X0,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_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)))
=> ~ ( X2 != k7_rlvect_2(X1,k1_rlvect_1(X1))
& X2 != k1_xboole_0
& k1_rmod_5(X0,X1,X2) = k1_rmod_2(X0,X1) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f9,axiom,
! [X0,X1] :
( X1 = k1_tarski(X0)
<=> ! [X2] :
( r2_hidden(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f12,axiom,
! [X0] :
( l2_struct_0(X0)
=> m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_rlvect_1) ).
fof(f20,axiom,
! [X0] :
( l1_group_1(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_group_1) ).
fof(f21,axiom,
! [X0] :
( l1_rlvect_1(X0)
=> l2_struct_0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_rlvect_1) ).
fof(f23,axiom,
! [X0] :
( l1_vectsp_1(X0)
=> l1_group_1(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_vectsp_1) ).
fof(f24,axiom,
! [X0] :
( l1_struct_0(X0)
=> ! [X1] :
( l1_vectsp_2(X1,X0)
=> l1_rlvect_1(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_vectsp_2) ).
fof(f25,axiom,
! [X0] :
( l2_struct_0(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_struct_0) ).
fof(f26,axiom,
! [X0] :
( l2_vectsp_1(X0)
=> ( l2_struct_0(X0)
& l1_vectsp_1(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_vectsp_1) ).
fof(f27,axiom,
! [X0] :
( l3_vectsp_1(X0)
=> ( l2_vectsp_1(X0)
& l1_rlvect_1(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_vectsp_1) ).
fof(f46,axiom,
! [X0] :
? [X1] : m1_subset_1(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f68,axiom,
! [X0,X1] :
( ( m1_subset_1(X1,u1_struct_0(X0))
& l1_struct_0(X0)
& ~ v3_struct_0(X0) )
=> k7_rlvect_2(X0,X1) = k1_tarski(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_rlvect_2) ).
fof(f71,axiom,
! [X0,X1] :
( ( l3_vectsp_1(X1)
& v2_vectsp_2(X1)
& ~ v10_vectsp_1(X1)
& v8_vectsp_1(X1)
& v7_vectsp_1(X1)
& v6_vectsp_1(X1)
& v7_group_1(X1)
& v4_group_1(X1)
& v6_rlvect_1(X1)
& v5_rlvect_1(X1)
& v4_rlvect_1(X1)
& v3_rlvect_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( l1_vectsp_2(X2,X1)
& v5_vectsp_2(X2,X1)
& v6_rlvect_1(X2)
& v5_rlvect_1(X2)
& v4_rlvect_1(X2)
& v3_rlvect_1(X2)
& ~ v3_struct_0(X2) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
=> ( r2_hidden(X0,X3)
=> r1_rlvect_1(k1_rmod_5(X1,X2,X3),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_rmod_5) ).
fof(f73,axiom,
! [X0,X1] :
( m1_subset_1(X0,X1)
=> ( r2_hidden(X0,X1)
| v1_xboole_0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f75,axiom,
! [X0,X1] :
( ( l3_vectsp_1(X1)
& v8_vectsp_1(X1)
& v7_vectsp_1(X1)
& v6_vectsp_1(X1)
& v4_group_1(X1)
& v6_rlvect_1(X1)
& v5_rlvect_1(X1)
& v4_rlvect_1(X1)
& v3_rlvect_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( l1_vectsp_2(X2,X1)
& v5_vectsp_2(X2,X1)
& v6_rlvect_1(X2)
& v5_rlvect_1(X2)
& v4_rlvect_1(X2)
& v3_rlvect_1(X2)
& ~ v3_struct_0(X2) )
=> ( r1_rlvect_1(k1_rmod_2(X1,X2),X0)
<=> X0 = k1_rlvect_1(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_rmod_2) ).
fof(f78,axiom,
! [X0] :
( v1_xboole_0(X0)
=> X0 = k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f87,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)))
& X2 != k7_rlvect_2(X1,k1_rlvect_1(X1))
& X2 != k1_xboole_0
& k1_rmod_5(X0,X1,X2) = k1_rmod_2(X0,X1) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f88,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)))
& X2 != k7_rlvect_2(X1,k1_rlvect_1(X1))
& X2 != k1_xboole_0
& k1_rmod_5(X0,X1,X2) = k1_rmod_2(X0,X1) ) ) ),
inference(flattening,[],[f87]) ).
fof(f99,plain,
! [X0] :
( ~ l2_struct_0(X0)
| m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f12]) ).
fof(f106,plain,
! [X0] :
( ~ l1_group_1(X0)
| l1_struct_0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f107,plain,
! [X0] :
( ~ l1_rlvect_1(X0)
| l2_struct_0(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f108,plain,
! [X0] :
( ~ l1_vectsp_1(X0)
| l1_group_1(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f109,plain,
! [X0] :
( ~ l1_struct_0(X0)
| ! [X1] :
( ~ l1_vectsp_2(X1,X0)
| l1_rlvect_1(X1) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f110,plain,
! [X0] :
( ~ l2_struct_0(X0)
| l1_struct_0(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f111,plain,
! [X0] :
( ~ l2_vectsp_1(X0)
| ( l2_struct_0(X0)
& l1_vectsp_1(X0) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f112,plain,
! [X0] :
( ~ l3_vectsp_1(X0)
| ( l2_vectsp_1(X0)
& l1_rlvect_1(X0) ) ),
inference(ennf_transformation,[],[f27]) ).
fof(f144,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0)
| k7_rlvect_2(X0,X1) = k1_tarski(X1) ),
inference(ennf_transformation,[],[f68]) ).
fof(f145,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0)
| k7_rlvect_2(X0,X1) = k1_tarski(X1) ),
inference(flattening,[],[f144]) ).
fof(f146,plain,
! [X0,X1] :
( ~ l3_vectsp_1(X1)
| ~ v2_vectsp_2(X1)
| v10_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v7_group_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ! [X2] :
( ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v3_rlvect_1(X2)
| v3_struct_0(X2)
| ! [X3] :
( ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
| ~ r2_hidden(X0,X3)
| r1_rlvect_1(k1_rmod_5(X1,X2,X3),X0) ) ) ),
inference(ennf_transformation,[],[f71]) ).
fof(f147,plain,
! [X0,X1] :
( ~ l3_vectsp_1(X1)
| ~ v2_vectsp_2(X1)
| v10_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v7_group_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ! [X2] :
( ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v3_rlvect_1(X2)
| v3_struct_0(X2)
| ! [X3] :
( ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
| ~ r2_hidden(X0,X3)
| r1_rlvect_1(k1_rmod_5(X1,X2,X3),X0) ) ) ),
inference(flattening,[],[f146]) ).
fof(f149,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(ennf_transformation,[],[f73]) ).
fof(f150,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(flattening,[],[f149]) ).
fof(f151,plain,
! [X0,X1] :
( ~ l3_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ! [X2] :
( ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v3_rlvect_1(X2)
| v3_struct_0(X2)
| ( r1_rlvect_1(k1_rmod_2(X1,X2),X0)
<=> X0 = k1_rlvect_1(X2) ) ) ),
inference(ennf_transformation,[],[f75]) ).
fof(f152,plain,
! [X0,X1] :
( ~ l3_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ! [X2] :
( ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v3_rlvect_1(X2)
| v3_struct_0(X2)
| ( r1_rlvect_1(k1_rmod_2(X1,X2),X0)
<=> X0 = k1_rlvect_1(X2) ) ) ),
inference(flattening,[],[f151]) ).
fof(f156,plain,
! [X0] :
( ~ v1_xboole_0(X0)
| X0 = k1_xboole_0 ),
inference(ennf_transformation,[],[f78]) ).
fof(f159,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)))
& sK2 != k7_rlvect_2(sK1,k1_rlvect_1(sK1))
& k1_xboole_0 != sK2
& k1_rmod_5(sK0,sK1,sK2) = k1_rmod_2(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f88]) ).
fof(f162,plain,
! [X0,X1] :
( ( k1_tarski(X0) != X1
| ! [X2] :
( ( ~ r2_hidden(X2,X1)
| X2 = X0 )
& ( X0 != X2
| r2_hidden(X2,X1) ) ) )
& ( ? [X2] :
( ( r2_hidden(X2,X1)
| X2 = X0 )
& ( ~ r2_hidden(X2,X1)
| X0 != X2 ) )
| X1 = k1_tarski(X0) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f163,plain,
! [X0,X1] :
( ( k1_tarski(X0) != X1
| ! [X3] :
( ( ~ r2_hidden(X3,X1)
| X0 = X3 )
& ( X0 != X3
| r2_hidden(X3,X1) ) ) )
& ( ? [X2] :
( ( r2_hidden(X2,X1)
| X2 = X0 )
& ( ~ r2_hidden(X2,X1)
| X0 != X2 ) )
| X1 = k1_tarski(X0) ) ),
inference(rectify,[],[f162]) ).
fof(f164,plain,
! [X0,X1] :
( ( k1_tarski(X0) != X1
| ! [X3] :
( ( ~ r2_hidden(X3,X1)
| X0 = X3 )
& ( X0 != X3
| r2_hidden(X3,X1) ) ) )
& ( ( ( r2_hidden(sK3(X0,X1),X1)
| sK3(X0,X1) = X0 )
& ( ~ r2_hidden(sK3(X0,X1),X1)
| sK3(X0,X1) != X0 ) )
| X1 = k1_tarski(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f163]) ).
fof(f178,plain,
! [X0] : m1_subset_1(sK15(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X1,sK15(X0))],[f46]) ).
fof(f195,plain,
! [X0,X1] :
( ~ l3_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ! [X2] :
( ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v3_rlvect_1(X2)
| v3_struct_0(X2)
| ( ( ~ r1_rlvect_1(k1_rmod_2(X1,X2),X0)
| X0 = k1_rlvect_1(X2) )
& ( k1_rlvect_1(X2) != X0
| r1_rlvect_1(k1_rmod_2(X1,X2),X0) ) ) ) ),
inference(nnf_transformation,[],[f152]) ).
fof(f196,plain,
l3_vectsp_1(sK0),
inference(cnf_transformation,[],[f159]) ).
fof(f197,plain,
v2_vectsp_2(sK0),
inference(cnf_transformation,[],[f159]) ).
fof(f198,plain,
~ v10_vectsp_1(sK0),
inference(cnf_transformation,[],[f159]) ).
fof(f199,plain,
v8_vectsp_1(sK0),
inference(cnf_transformation,[],[f159]) ).
fof(f200,plain,
v7_vectsp_1(sK0),
inference(cnf_transformation,[],[f159]) ).
fof(f201,plain,
v6_vectsp_1(sK0),
inference(cnf_transformation,[],[f159]) ).
fof(f202,plain,
v7_group_1(sK0),
inference(cnf_transformation,[],[f159]) ).
fof(f203,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f159]) ).
fof(f204,plain,
v6_rlvect_1(sK0),
inference(cnf_transformation,[],[f159]) ).
fof(f205,plain,
v5_rlvect_1(sK0),
inference(cnf_transformation,[],[f159]) ).
fof(f206,plain,
v4_rlvect_1(sK0),
inference(cnf_transformation,[],[f159]) ).
fof(f207,plain,
v3_rlvect_1(sK0),
inference(cnf_transformation,[],[f159]) ).
fof(f208,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f159]) ).
fof(f209,plain,
l1_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f159]) ).
fof(f210,plain,
v5_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f159]) ).
fof(f211,plain,
v6_rlvect_1(sK1),
inference(cnf_transformation,[],[f159]) ).
fof(f212,plain,
v5_rlvect_1(sK1),
inference(cnf_transformation,[],[f159]) ).
fof(f213,plain,
v4_rlvect_1(sK1),
inference(cnf_transformation,[],[f159]) ).
fof(f214,plain,
v3_rlvect_1(sK1),
inference(cnf_transformation,[],[f159]) ).
fof(f215,plain,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f159]) ).
fof(f216,plain,
m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1))),
inference(cnf_transformation,[],[f159]) ).
fof(f217,plain,
sK2 != k7_rlvect_2(sK1,k1_rlvect_1(sK1)),
inference(cnf_transformation,[],[f159]) ).
fof(f218,plain,
k1_xboole_0 != sK2,
inference(cnf_transformation,[],[f159]) ).
fof(f219,plain,
k1_rmod_5(sK0,sK1,sK2) = k1_rmod_2(sK0,sK1),
inference(cnf_transformation,[],[f159]) ).
fof(f233,plain,
! [X0,X1] :
( r2_hidden(sK3(X0,X1),X1)
| sK3(X0,X1) = X0
| k1_tarski(X0) = X1 ),
inference(cnf_transformation,[],[f164]) ).
fof(f234,plain,
! [X0,X1] :
( ~ r2_hidden(sK3(X0,X1),X1)
| sK3(X0,X1) != X0
| k1_tarski(X0) = X1 ),
inference(cnf_transformation,[],[f164]) ).
fof(f240,plain,
! [X0] :
( ~ l2_struct_0(X0)
| m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f99]) ).
fof(f246,plain,
! [X0] :
( ~ l1_group_1(X0)
| l1_struct_0(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f247,plain,
! [X0] :
( ~ l1_rlvect_1(X0)
| l2_struct_0(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f248,plain,
! [X0] :
( ~ l1_vectsp_1(X0)
| l1_group_1(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f249,plain,
! [X0,X1] :
( ~ l1_struct_0(X0)
| ~ l1_vectsp_2(X1,X0)
| l1_rlvect_1(X1) ),
inference(cnf_transformation,[],[f109]) ).
fof(f250,plain,
! [X0] :
( ~ l2_struct_0(X0)
| l1_struct_0(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f252,plain,
! [X0] :
( ~ l2_vectsp_1(X0)
| l1_vectsp_1(X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f253,plain,
! [X0] :
( ~ l3_vectsp_1(X0)
| l2_vectsp_1(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f280,plain,
! [X0] : m1_subset_1(sK15(X0),X0),
inference(cnf_transformation,[],[f178]) ).
fof(f335,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0)
| k7_rlvect_2(X0,X1) = k1_tarski(X1) ),
inference(cnf_transformation,[],[f145]) ).
fof(f339,plain,
! [X2,X3,X0,X1] :
( ~ l3_vectsp_1(X1)
| ~ v2_vectsp_2(X1)
| v10_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v7_group_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v3_rlvect_1(X2)
| v3_struct_0(X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
| ~ r2_hidden(X0,X3)
| r1_rlvect_1(k1_rmod_5(X1,X2,X3),X0) ),
inference(cnf_transformation,[],[f147]) ).
fof(f341,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f150]) ).
fof(f344,plain,
! [X2,X0,X1] :
( ~ l3_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v3_rlvect_1(X2)
| v3_struct_0(X2)
| ~ r1_rlvect_1(k1_rmod_2(X1,X2),X0)
| k1_rlvect_1(X2) = X0 ),
inference(cnf_transformation,[],[f195]) ).
fof(f348,plain,
! [X0] :
( ~ v1_xboole_0(X0)
| k1_xboole_0 = X0 ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_49,negated_conjecture,
k1_rmod_5(sK0,sK1,sK2) = k1_rmod_2(sK0,sK1),
inference(cnf_transformation,[],[f219]) ).
tcf(c_50,negated_conjecture,
sK2 != k1_xboole_0,
inference(cnf_transformation,[],[f218]) ).
tcf(c_51,negated_conjecture,
k7_rlvect_2(sK1,k1_rlvect_1(sK1)) != sK2,
inference(cnf_transformation,[],[f217]) ).
tcf(c_52,negated_conjecture,
m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1))),
inference(cnf_transformation,[],[f216]) ).
tcf(c_53,negated_conjecture,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f215]) ).
tcf(c_54,negated_conjecture,
v3_rlvect_1(sK1),
inference(cnf_transformation,[],[f214]) ).
tcf(c_55,negated_conjecture,
v4_rlvect_1(sK1),
inference(cnf_transformation,[],[f213]) ).
tcf(c_56,negated_conjecture,
v5_rlvect_1(sK1),
inference(cnf_transformation,[],[f212]) ).
tcf(c_57,negated_conjecture,
v6_rlvect_1(sK1),
inference(cnf_transformation,[],[f211]) ).
tcf(c_58,negated_conjecture,
v5_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f210]) ).
tcf(c_59,negated_conjecture,
l1_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f209]) ).
tcf(c_60,negated_conjecture,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f208]) ).
tcf(c_61,negated_conjecture,
v3_rlvect_1(sK0),
inference(cnf_transformation,[],[f207]) ).
tcf(c_62,negated_conjecture,
v4_rlvect_1(sK0),
inference(cnf_transformation,[],[f206]) ).
tcf(c_63,negated_conjecture,
v5_rlvect_1(sK0),
inference(cnf_transformation,[],[f205]) ).
tcf(c_64,negated_conjecture,
v6_rlvect_1(sK0),
inference(cnf_transformation,[],[f204]) ).
tcf(c_65,negated_conjecture,
v4_group_1(sK0),
inference(cnf_transformation,[],[f203]) ).
tcf(c_66,negated_conjecture,
v7_group_1(sK0),
inference(cnf_transformation,[],[f202]) ).
tcf(c_67,negated_conjecture,
v6_vectsp_1(sK0),
inference(cnf_transformation,[],[f201]) ).
tcf(c_68,negated_conjecture,
v7_vectsp_1(sK0),
inference(cnf_transformation,[],[f200]) ).
tcf(c_69,negated_conjecture,
v8_vectsp_1(sK0),
inference(cnf_transformation,[],[f199]) ).
tcf(c_70,negated_conjecture,
~ v10_vectsp_1(sK0),
inference(cnf_transformation,[],[f198]) ).
tcf(c_71,negated_conjecture,
v2_vectsp_2(sK0),
inference(cnf_transformation,[],[f197]) ).
tcf(c_72,negated_conjecture,
l3_vectsp_1(sK0),
inference(cnf_transformation,[],[f196]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( ( k1_tarski(X0) = X1 )
| ~ r2_hidden(sK3(X0,X1),X1)
| ( sK3(X0,X1) != X0 ) ),
inference(cnf_transformation,[],[f234]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] :
( r2_hidden(sK3(X0,X1),X1)
| ( k1_tarski(X0) = X1 )
| ( sK3(X0,X1) = X0 ) ),
inference(cnf_transformation,[],[f233]) ).
tcf(c_89,plain,
! [X0: $i] :
( m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0))
| ~ l2_struct_0(X0) ),
inference(cnf_transformation,[],[f240]) ).
tcf(c_95,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f246]) ).
tcf(c_96,plain,
! [X0: $i] :
( l2_struct_0(X0)
| ~ l1_rlvect_1(X0) ),
inference(cnf_transformation,[],[f247]) ).
tcf(c_97,plain,
! [X0: $i] :
( l1_group_1(X0)
| ~ l1_vectsp_1(X0) ),
inference(cnf_transformation,[],[f248]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( l1_rlvect_1(X0)
| ~ l1_struct_0(X1)
| ~ l1_vectsp_2(X0,X1) ),
inference(cnf_transformation,[],[f249]) ).
tcf(c_99,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l2_struct_0(X0) ),
inference(cnf_transformation,[],[f250]) ).
tcf(c_100,plain,
! [X0: $i] :
( l1_vectsp_1(X0)
| ~ l2_vectsp_1(X0) ),
inference(cnf_transformation,[],[f252]) ).
tcf(c_103,plain,
! [X0: $i] :
( l2_vectsp_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(cnf_transformation,[],[f253]) ).
tcf(c_129,plain,
! [X0: $i] : m1_subset_1(sK15(X0),X0),
inference(cnf_transformation,[],[f280]) ).
tcf(c_184,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| ( k7_rlvect_2(X1,X0) = k1_tarski(X0) )
| ~ l1_struct_0(X1)
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f335]) ).
tcf(c_188,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v10_vectsp_1(X2)
| v3_struct_0(X2)
| v3_struct_0(X1)
| r1_rlvect_1(k1_rmod_5(X2,X1,X0),X3)
| ~ 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)
| ~ r2_hidden(X3,X0)
| ~ l1_vectsp_2(X1,X2)
| ~ v5_vectsp_2(X1,X2)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(cnf_transformation,[],[f339]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X1)
| r2_hidden(X0,X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f341]) ).
tcf(c_194,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| v3_struct_0(X0)
| ( k1_rlvect_1(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)
| ~ v5_vectsp_2(X1,X0)
| ~ r1_rlvect_1(k1_rmod_2(X0,X1),X2) ),
inference(cnf_transformation,[],[f344]) ).
tcf(c_197,plain,
! [X0: $i] :
( ( X0 = k1_xboole_0 )
| ~ v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f348]) ).
tcf(c_311,plain,
! [X0: $i] :
( ~ l2_struct_0(X0)
| l1_struct_0(X0) ),
inference(prop_impl_just,[status(thm)],[c_99]) ).
tcf(c_312,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l2_struct_0(X0) ),
inference(renaming,[status(thm)],[c_311]) ).
tcf(c_313,plain,
! [X0: $i] :
( ~ l1_group_1(X0)
| l1_struct_0(X0) ),
inference(prop_impl_just,[status(thm)],[c_95]) ).
tcf(c_314,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(renaming,[status(thm)],[c_313]) ).
tcf(c_323,plain,
! [X0: $i] :
( l1_group_1(X0)
| ~ l1_vectsp_1(X0) ),
inference(prop_impl_just,[status(thm)],[c_97]) ).
tcf(c_325,plain,
! [X0: $i] :
( ~ l2_vectsp_1(X0)
| l1_vectsp_1(X0) ),
inference(prop_impl_just,[status(thm)],[c_100]) ).
tcf(c_326,plain,
! [X0: $i] :
( l1_vectsp_1(X0)
| ~ l2_vectsp_1(X0) ),
inference(renaming,[status(thm)],[c_325]) ).
tcf(c_337,plain,
! [X0: $i] :
( m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0))
| ~ l2_struct_0(X0) ),
inference(prop_impl_just,[status(thm)],[c_89]) ).
tcf(c_341,plain,
! [X0: $i] :
( ~ l1_rlvect_1(X0)
| l2_struct_0(X0) ),
inference(prop_impl_just,[status(thm)],[c_96]) ).
tcf(c_342,plain,
! [X0: $i] :
( l2_struct_0(X0)
| ~ l1_rlvect_1(X0) ),
inference(renaming,[status(thm)],[c_341]) ).
tcf(c_347,plain,
! [X0: $i] :
( l2_vectsp_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(prop_impl_just,[status(thm)],[c_103]) ).
tcf(c_3236,plain,
! [X0: $i,X1: $i] :
( l1_struct_0(X1)
| ~ l1_vectsp_1(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_323,c_314]) ).
tcf(c_3237,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l1_vectsp_1(X0) ),
inference(unflattening,[status(thm)],[c_3236]) ).
tcf(c_3262,plain,
! [X0: $i,X1: $i] :
( l1_vectsp_1(X1)
| ~ l3_vectsp_1(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_347,c_326]) ).
tcf(c_3263,plain,
! [X0: $i] :
( l1_vectsp_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(unflattening,[status(thm)],[c_3262]) ).
tcf(c_3605,plain,
! [X0: $i,X1: $i] :
( l1_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_3263,c_3237]) ).
tcf(c_3606,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l3_vectsp_1(X0) ),
inference(unflattening,[status(thm)],[c_3605]) ).
tcf(c_3743,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X2)
| v3_struct_0(X0)
| r1_rlvect_1(k1_rmod_5(X0,X2,X1),X3)
| ~ l3_vectsp_1(X0)
| ~ v2_vectsp_2(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_group_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X2)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X2)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X2)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X2)
| ~ v3_rlvect_1(X0)
| ~ r2_hidden(X3,X1)
| ~ 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_70,c_188]) ).
tcf(c_3744,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(sK0)
| v3_struct_0(X1)
| r1_rlvect_1(k1_rmod_5(sK0,X1,X0),X2)
| ~ l3_vectsp_1(sK0)
| ~ v2_vectsp_2(sK0)
| ~ v8_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| ~ l1_vectsp_2(X1,sK0)
| ~ v5_vectsp_2(X1,sK0)
| ~ r2_hidden(X2,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(unflattening,[status(thm)],[c_3743]) ).
tcf(c_3745,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ 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)
| ~ r2_hidden(X2,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1)))
| r1_rlvect_1(k1_rmod_5(sK0,X1,X0),X2)
| v3_struct_0(X1) ),
inference(global_subsumption_just,[status(thm)],[c_3744,c_72,c_71,c_69,c_68,c_67,c_66,c_65,c_64,c_63,c_62,c_61,c_60,c_3744]) ).
tcf(c_3746,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| r1_rlvect_1(k1_rmod_5(sK0,X1,X0),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)
| ~ r2_hidden(X2,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(renaming,[status(thm)],[c_3745]) ).
tcf(c_4383,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| v3_struct_0(X0)
| ( k1_rlvect_1(X1) = X2 )
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v6_rlvect_1(X1)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X1)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X1)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X1)
| ~ v3_rlvect_1(X0)
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ r1_rlvect_1(k1_rmod_2(X0,X1),X2)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_65,c_194]) ).
tcf(c_4384,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| v3_struct_0(X0)
| ( k1_rlvect_1(X0) = X1 )
| ~ l3_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| ~ l1_vectsp_2(X0,sK0)
| ~ v5_vectsp_2(X0,sK0)
| ~ r1_rlvect_1(k1_rmod_2(sK0,X0),X1) ),
inference(unflattening,[status(thm)],[c_4383]) ).
tcf(c_4386,plain,
! [X0: $i,X1: $i] :
( ~ r1_rlvect_1(k1_rmod_2(sK0,X0),X1)
| ~ v5_vectsp_2(X0,sK0)
| ~ l1_vectsp_2(X0,sK0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ( k1_rlvect_1(X0) = X1 )
| v3_struct_0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_4384,c_72,c_69,c_68,c_67,c_64,c_63,c_62,c_61,c_60,c_4384]) ).
tcf(c_4387,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| ( k1_rlvect_1(X0) = X1 )
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| ~ l1_vectsp_2(X0,sK0)
| ~ v5_vectsp_2(X0,sK0)
| ~ r1_rlvect_1(k1_rmod_2(sK0,X0),X1) ),
inference(renaming,[status(thm)],[c_4386]) ).
tcf(c_5281,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_72,c_3606]) ).
tcf(c_5282,plain,
l1_struct_0(sK0),
inference(unflattening,[status(thm)],[c_5281]) ).
tcf(c_5325,plain,
! [X0: $i,X1: $i] :
( l1_struct_0(X1)
| ~ l1_rlvect_1(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_342,c_312]) ).
tcf(c_5326,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l1_rlvect_1(X0) ),
inference(unflattening,[status(thm)],[c_5325]) ).
tcf(c_5333,plain,
! [X0: $i,X1: $i] :
( m1_subset_1(k1_rlvect_1(X1),u1_struct_0(X1))
| ~ l1_rlvect_1(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_342,c_337]) ).
tcf(c_5334,plain,
! [X0: $i] :
( m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0))
| ~ l1_rlvect_1(X0) ),
inference(unflattening,[status(thm)],[c_5333]) ).
tcf(c_9911,plain,
( l1_rlvect_1(sK1)
| ~ l1_struct_0(sK0) ),
inference(superposition,[status(thm)],[c_59,c_98]) ).
tcf(c_9914,plain,
l1_rlvect_1(sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_9911,c_5282]) ).
tcf(c_10054,plain,
l1_struct_0(sK1),
inference(superposition,[status(thm)],[c_9914,c_5326]) ).
tcf(c_10114,plain,
! [X0: $i] :
( v1_xboole_0(X0)
| r2_hidden(sK15(X0),X0) ),
inference(superposition,[status(thm)],[c_129,c_190]) ).
tcf(c_10236,plain,
! [X0: $i] :
( v3_struct_0(sK1)
| r1_rlvect_1(k1_rmod_2(sK0,sK1),X0)
| ~ v6_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| ~ l1_vectsp_2(sK1,sK0)
| ~ v5_vectsp_2(sK1,sK0)
| ~ r2_hidden(X0,sK2)
| ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1))) ),
inference(superposition,[status(thm)],[c_49,c_3746]) ).
tcf(c_10237,plain,
! [X0: $i] :
( r1_rlvect_1(k1_rmod_2(sK0,sK1),X0)
| ~ r2_hidden(X0,sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10236,c_53,c_57,c_56,c_55,c_54,c_59,c_58,c_52]) ).
tcf(c_12940,plain,
! [X0: $i] :
( v3_struct_0(sK1)
| ( k1_rlvect_1(sK1) = X0 )
| ~ v6_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| ~ l1_vectsp_2(sK1,sK0)
| ~ v5_vectsp_2(sK1,sK0)
| ~ r2_hidden(X0,sK2) ),
inference(superposition,[status(thm)],[c_10237,c_4387]) ).
tcf(c_12941,plain,
! [X0: $i] :
( ( k1_rlvect_1(sK1) = X0 )
| ~ r2_hidden(X0,sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12940,c_53,c_57,c_56,c_55,c_54,c_59,c_58]) ).
tcf(c_12944,plain,
! [X0: $i] :
( ( k1_tarski(X0) = sK2 )
| ( sK3(X0,sK2) = X0 )
| ( sK3(X0,sK2) = k1_rlvect_1(sK1) ) ),
inference(superposition,[status(thm)],[c_81,c_12941]) ).
tcf(c_12948,plain,
( v1_xboole_0(sK2)
| ( k1_rlvect_1(sK1) = sK15(sK2) ) ),
inference(superposition,[status(thm)],[c_10114,c_12941]) ).
tcf(c_12965,plain,
( ( sK2 = k1_xboole_0 )
| ( k1_rlvect_1(sK1) = sK15(sK2) ) ),
inference(superposition,[status(thm)],[c_12948,c_197]) ).
tcf(c_12966,plain,
k1_rlvect_1(sK1) = sK15(sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_12965,c_50]) ).
tcf(c_12967,plain,
k7_rlvect_2(sK1,sK15(sK2)) != sK2,
inference(superposition,[status(thm)],[c_12966,c_51]) ).
tcf(c_12968,plain,
( m1_subset_1(sK15(sK2),u1_struct_0(sK1))
| ~ l1_rlvect_1(sK1) ),
inference(superposition,[status(thm)],[c_12966,c_5334]) ).
tcf(c_12970,plain,
m1_subset_1(sK15(sK2),u1_struct_0(sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_12968,c_9914]) ).
tcf(c_12972,plain,
( v3_struct_0(sK1)
| ( k7_rlvect_2(sK1,sK15(sK2)) = k1_tarski(sK15(sK2)) )
| ~ l1_struct_0(sK1) ),
inference(superposition,[status(thm)],[c_12970,c_184]) ).
tcf(c_12975,plain,
k7_rlvect_2(sK1,sK15(sK2)) = k1_tarski(sK15(sK2)),
inference(forward_subsumption_resolution,[status(thm)],[c_12972,c_53,c_10054]) ).
tcf(c_12985,plain,
! [X0: $i] :
( ( k1_tarski(X0) = sK2 )
| ( sK3(X0,sK2) = X0 )
| ( sK3(X0,sK2) = sK15(sK2) ) ),
inference(demodulation,[status(thm)],[c_12944,c_12966]) ).
tcf(c_13003,plain,
! [X0: $i] :
( ( k1_tarski(X0) = sK2 )
| ( sK3(X0,sK2) = X0 )
| ( sK15(sK2) != X0 ) ),
inference(equality_factoring,[status(thm)],[c_12985]) ).
tcf(c_13005,plain,
k1_tarski(sK15(sK2)) != sK2,
inference(demodulation,[status(thm)],[c_12967,c_12975]) ).
tcf(c_13015,plain,
( ( k1_tarski(sK15(sK2)) = sK2 )
| ( sK3(sK15(sK2),sK2) = sK15(sK2) ) ),
inference(equality_resolution,[status(thm)],[c_13003]) ).
tcf(c_13016,plain,
sK3(sK15(sK2),sK2) = sK15(sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_13015,c_13005]) ).
tcf(c_13035,plain,
( ( k1_tarski(sK15(sK2)) = sK2 )
| ~ r2_hidden(sK3(sK15(sK2),sK2),sK2) ),
inference(superposition,[status(thm)],[c_13016,c_80]) ).
tcf(c_13038,plain,
~ r2_hidden(sK3(sK15(sK2),sK2),sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_13035,c_13005]) ).
tcf(c_13039,plain,
~ r2_hidden(sK15(sK2),sK2),
inference(demodulation,[status(thm)],[c_13038,c_13016]) ).
tcf(c_13101,plain,
v1_xboole_0(sK2),
inference(superposition,[status(thm)],[c_10114,c_13039]) ).
tcf(c_13103,plain,
sK2 = k1_xboole_0,
inference(superposition,[status(thm)],[c_13101,c_197]) ).
tcf(c_13104,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_13103,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG218+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 05:12:28 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.40 Running first-order theorem proving
% 0.03/0.40 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
% 0.03/0.41
% 0.03/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.41
% 0.03/0.41 % Detected problem language: tptp
% 0.03/0.42 % Proving...
% 17.74/3.26 % SZS status Started for theBenchmark.p
% 17.74/3.26 % SZS status Theorem for theBenchmark.p
% 17.74/3.26
% 17.74/3.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 17.74/3.26
% 17.74/3.26 % ------ iProver source info
% 17.74/3.26
% 17.74/3.26 % git: date: 2026-07-19 20:42:38 +0200
% 17.74/3.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 17.74/3.26 % git: non_committed_changes: false
% 17.74/3.26
% 17.74/3.26 % ------ Parsing...
% 17.74/3.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 17.74/3.26
% 17.74/3.26 % ------ 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 %
% 17.74/3.26
% 17.74/3.26 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 17.74/3.26
% 17.74/3.26 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 17.74/3.26 % ------ Proving...
% 17.74/3.26 % ------ Problem Properties
% 17.74/3.26
% 17.74/3.26 %
% 17.74/3.26 % clauses 144
% 17.74/3.26 % conjectures 16
% 17.74/3.26 % EPR 52
% 17.74/3.26 % Horn 114
% 17.74/3.26 % unary 67
% 17.74/3.26 % binary 25
% 17.74/3.26 % lits 457
% 17.74/3.26 % lits eq 24
% 17.74/3.26 % fd_pure 0
% 17.74/3.26 % fd_pseudo 0
% 17.74/3.26 % fd_cond 1
% 17.74/3.26 % fd_pseudo_cond 10
% 17.74/3.26 % AC symbols 0
% 17.74/3.26
% 17.74/3.26 % ------ Input Options Time Limit: Unbounded
% 17.74/3.26
% 17.74/3.26
% 17.74/3.26 % ------
% 17.74/3.26 % Current options:
% 17.74/3.26 % ------
% 17.74/3.26
% 17.74/3.26
% 17.74/3.26 %
% 17.74/3.26
% 17.74/3.26 % ------ Proving...
% 17.74/3.26 %
% 17.74/3.26
% 17.74/3.26 % SZS status Theorem for theBenchmark.p
% 17.74/3.26
% 17.74/3.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.74/3.26
% 17.74/3.26
%------------------------------------------------------------------------------