%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG220+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 : Thu Sep 24 11:49:00 AM UTC 2026
% Result : Theorem 0.14s 5.46s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 46
% Syntax : Number of formulae : 224 ( 64 unt; 35 def)
% Number of atoms : 1244 ( 21 equ)
% Maximal formula atoms : 29 ( 5 avg)
% Number of connectives : 1725 ( 705 ~; 770 |; 188 &)
% ( 36 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 61 ( 59 usr; 36 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 128 ( 124 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [A] :
( ( l3_vectsp_1(A)
& v2_vectsp_2(A)
& ~ v10_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v7_group_1(A)
& v4_group_1(A)
& v6_rlvect_1(A)
& v5_rlvect_1(A)
& v4_rlvect_1(A)
& v3_rlvect_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& v3_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( r1_tarski(C,D)
& k1_rmod_5(A,B,C) = B )
=> k1_rmod_5(A,B,D) = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [A] :
( ( l3_vectsp_1(A)
& v2_vectsp_2(A)
& ~ v10_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v7_group_1(A)
& v4_group_1(A)
& v6_rlvect_1(A)
& v5_rlvect_1(A)
& v4_rlvect_1(A)
& v3_rlvect_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& v3_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( r1_tarski(C,D)
& k1_rmod_5(A,B,C) = B )
=> k1_rmod_5(A,B,D) = B ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f9,axiom,
! [A,B,C] :
( ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& l1_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B)
& l3_vectsp_1(A)
& v2_vectsp_2(A)
& ~ v10_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v7_group_1(A)
& v4_group_1(A)
& v6_rlvect_1(A)
& v5_rlvect_1(A)
& v4_rlvect_1(A)
& v3_rlvect_1(A)
& ~ v3_struct_0(A) )
=> ( m1_rmod_2(k1_rmod_5(A,B,C),A,B)
& v3_vectsp_2(k1_rmod_5(A,B,C),A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A] :
( l1_rlvect_1(A)
=> l2_struct_0(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A] :
( l2_struct_0(A)
=> l1_struct_0(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [A] :
( l2_vectsp_1(A)
=> ( l2_struct_0(A)
& l1_vectsp_1(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A] :
( l3_vectsp_1(A)
=> ( l2_vectsp_1(A)
& l1_rlvect_1(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [A,B] :
( ( l1_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B)
& l3_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v4_group_1(A)
& v6_rlvect_1(A)
& v5_rlvect_1(A)
& v4_rlvect_1(A)
& v3_rlvect_1(A)
& ~ v3_struct_0(A) )
=> ! [C] :
( m1_rmod_2(C,A,B)
=> ( l1_vectsp_2(C,A)
& v5_vectsp_2(C,A)
& v6_rlvect_1(C)
& v5_rlvect_1(C)
& v4_rlvect_1(C)
& v3_rlvect_1(C)
& ~ v3_struct_0(C) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f60,axiom,
! [A,B] : r1_tarski(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f61,axiom,
! [A] :
( ( l3_vectsp_1(A)
& v2_vectsp_2(A)
& ~ v10_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v7_group_1(A)
& v4_group_1(A)
& v6_rlvect_1(A)
& v5_rlvect_1(A)
& v4_rlvect_1(A)
& v3_rlvect_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( r1_tarski(C,D)
=> m1_rmod_2(k1_rmod_5(A,B,C),A,k1_rmod_5(A,B,D)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f64,axiom,
! [A] :
( ( l3_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v4_group_1(A)
& v6_rlvect_1(A)
& v5_rlvect_1(A)
& v4_rlvect_1(A)
& v3_rlvect_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& v3_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( ( l1_vectsp_2(C,A)
& v5_vectsp_2(C,A)
& v3_vectsp_2(C,A)
& v6_rlvect_1(C)
& v5_rlvect_1(C)
& v4_rlvect_1(C)
& v3_rlvect_1(C)
& ~ v3_struct_0(C) )
=> ( ( m1_rmod_2(B,A,C)
& m1_rmod_2(C,A,B) )
=> C = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f65,axiom,
! [A,B] :
( m1_subset_1(A,k1_zfmisc_1(B))
<=> r1_tarski(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f71,plain,
? [A] :
( ? [B] :
( ? [C] :
( ? [D] :
( k1_rmod_5(A,B,D) != B
& r1_tarski(C,D)
& k1_rmod_5(A,B,C) = B
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
& l1_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& v3_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B) )
& l3_vectsp_1(A)
& v2_vectsp_2(A)
& ~ v10_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v7_group_1(A)
& v4_group_1(A)
& v6_rlvect_1(A)
& v5_rlvect_1(A)
& v4_rlvect_1(A)
& v3_rlvect_1(A)
& ~ v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f72,plain,
( k1_rmod_5(sK0_skl,sK1_skl,sK3_skl) != sK1_skl
& r1_tarski(sK2_skl,sK3_skl)
& k1_rmod_5(sK0_skl,sK1_skl,sK2_skl) = sK1_skl
& m1_subset_1(sK3_skl,k1_zfmisc_1(u1_struct_0(sK1_skl)))
& m1_subset_1(sK2_skl,k1_zfmisc_1(u1_struct_0(sK1_skl)))
& l1_vectsp_2(sK1_skl,sK0_skl)
& v5_vectsp_2(sK1_skl,sK0_skl)
& v3_vectsp_2(sK1_skl,sK0_skl)
& v6_rlvect_1(sK1_skl)
& v5_rlvect_1(sK1_skl)
& v4_rlvect_1(sK1_skl)
& v3_rlvect_1(sK1_skl)
& ~ v3_struct_0(sK1_skl)
& l3_vectsp_1(sK0_skl)
& v2_vectsp_2(sK0_skl)
& ~ v10_vectsp_1(sK0_skl)
& v8_vectsp_1(sK0_skl)
& v7_vectsp_1(sK0_skl)
& v6_vectsp_1(sK0_skl)
& v7_group_1(sK0_skl)
& v4_group_1(sK0_skl)
& v6_rlvect_1(sK0_skl)
& v5_rlvect_1(sK0_skl)
& v4_rlvect_1(sK0_skl)
& v3_rlvect_1(sK0_skl)
& ~ v3_struct_0(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl),skolemize(C,sK2_skl),skolemize(D,sK3_skl)],[f71]) ).
fof(f73,plain,
~ v3_struct_0(sK0_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f74,plain,
v3_rlvect_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f75,plain,
v4_rlvect_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f76,plain,
v5_rlvect_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f77,plain,
v6_rlvect_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f78,plain,
v4_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f79,plain,
v7_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f80,plain,
v6_vectsp_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f81,plain,
v7_vectsp_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f82,plain,
v8_vectsp_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f83,plain,
~ v10_vectsp_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f84,plain,
v2_vectsp_2(sK0_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f85,plain,
l3_vectsp_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f86,plain,
~ v3_struct_0(sK1_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f87,plain,
v3_rlvect_1(sK1_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f88,plain,
v4_rlvect_1(sK1_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f89,plain,
v5_rlvect_1(sK1_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f90,plain,
v6_rlvect_1(sK1_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f91,plain,
v3_vectsp_2(sK1_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f92,plain,
v5_vectsp_2(sK1_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f93,plain,
l1_vectsp_2(sK1_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f94,plain,
m1_subset_1(sK2_skl,k1_zfmisc_1(u1_struct_0(sK1_skl))),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f95,plain,
m1_subset_1(sK3_skl,k1_zfmisc_1(u1_struct_0(sK1_skl))),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f96,plain,
k1_rmod_5(sK0_skl,sK1_skl,sK2_skl) = sK1_skl,
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f97,plain,
r1_tarski(sK2_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f98,plain,
k1_rmod_5(sK0_skl,sK1_skl,sK3_skl) != sK1_skl,
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f119,plain,
! [A,B,C] :
( ( m1_rmod_2(k1_rmod_5(A,B,C),A,B)
& v3_vectsp_2(k1_rmod_5(A,B,C),A) )
| ~ m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
| ~ l1_vectsp_2(B,A)
| ~ v5_vectsp_2(B,A)
| ~ v6_rlvect_1(B)
| ~ v5_rlvect_1(B)
| ~ v4_rlvect_1(B)
| ~ v3_rlvect_1(B)
| v3_struct_0(B)
| ~ l3_vectsp_1(A)
| ~ v2_vectsp_2(A)
| v10_vectsp_1(A)
| ~ v8_vectsp_1(A)
| ~ v7_vectsp_1(A)
| ~ v6_vectsp_1(A)
| ~ v7_group_1(A)
| ~ v4_group_1(A)
| ~ v6_rlvect_1(A)
| ~ v5_rlvect_1(A)
| ~ v4_rlvect_1(A)
| ~ v3_rlvect_1(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f120,plain,
! [X0,X1,X2] :
( v3_vectsp_2(k1_rmod_5(X0,X1,X2),X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v2_vectsp_2(X0)
| v10_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_group_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f121,plain,
! [X0,X1,X2] :
( m1_rmod_2(k1_rmod_5(X0,X1,X2),X0,X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v2_vectsp_2(X0)
| v10_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_group_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f124,plain,
! [A] :
( l2_struct_0(A)
| ~ l1_rlvect_1(A) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f125,plain,
! [X0] :
( l2_struct_0(X0)
| ~ l1_rlvect_1(X0) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f130,plain,
! [A] :
( l1_struct_0(A)
| ~ l2_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f131,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l2_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f132,plain,
! [A] :
( ( l2_struct_0(A)
& l1_vectsp_1(A) )
| ~ l2_vectsp_1(A) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f133,plain,
! [X0] :
( l1_vectsp_1(X0)
| ~ l2_vectsp_1(X0) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f135,plain,
! [A] :
( ( l2_vectsp_1(A)
& l1_rlvect_1(A) )
| ~ l3_vectsp_1(A) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f136,plain,
! [X0] :
( l1_rlvect_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f137,plain,
! [X0] :
( l2_vectsp_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f138,plain,
! [A,B] :
( ! [C] :
( ( l1_vectsp_2(C,A)
& v5_vectsp_2(C,A)
& v6_rlvect_1(C)
& v5_rlvect_1(C)
& v4_rlvect_1(C)
& v3_rlvect_1(C)
& ~ v3_struct_0(C) )
| ~ m1_rmod_2(C,A,B) )
| ~ l1_vectsp_2(B,A)
| ~ v5_vectsp_2(B,A)
| ~ v6_rlvect_1(B)
| ~ v5_rlvect_1(B)
| ~ v4_rlvect_1(B)
| ~ v3_rlvect_1(B)
| v3_struct_0(B)
| ~ l3_vectsp_1(A)
| ~ v8_vectsp_1(A)
| ~ v7_vectsp_1(A)
| ~ v6_vectsp_1(A)
| ~ v4_group_1(A)
| ~ v6_rlvect_1(A)
| ~ v5_rlvect_1(A)
| ~ v4_rlvect_1(A)
| ~ v3_rlvect_1(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f139,plain,
! [X0,X1,X2] :
( ~ v3_struct_0(X2)
| ~ m1_rmod_2(X2,X0,X1)
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f140,plain,
! [X0,X1,X2] :
( v3_rlvect_1(X2)
| ~ m1_rmod_2(X2,X0,X1)
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f141,plain,
! [X0,X1,X2] :
( v4_rlvect_1(X2)
| ~ m1_rmod_2(X2,X0,X1)
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f142,plain,
! [X0,X1,X2] :
( v5_rlvect_1(X2)
| ~ m1_rmod_2(X2,X0,X1)
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f143,plain,
! [X0,X1,X2] :
( v6_rlvect_1(X2)
| ~ m1_rmod_2(X2,X0,X1)
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f144,plain,
! [X0,X1,X2] :
( v5_vectsp_2(X2,X0)
| ~ m1_rmod_2(X2,X0,X1)
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f145,plain,
! [X0,X1,X2] :
( l1_vectsp_2(X2,X0)
| ~ m1_rmod_2(X2,X0,X1)
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f261,plain,
! [A] : r1_tarski(A,A),
inference(miniscoping,[status(thm)],[f60]) ).
fof(f262,plain,
! [X0] : r1_tarski(X0,X0),
inference(cnf_transformation,[status(thm)],[f261]) ).
fof(f263,plain,
! [A] :
( ! [B] :
( ! [C] :
( ! [D] :
( m1_rmod_2(k1_rmod_5(A,B,C),A,k1_rmod_5(A,B,D))
| ~ r1_tarski(C,D)
| ~ m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
| ~ m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
| ~ l1_vectsp_2(B,A)
| ~ v5_vectsp_2(B,A)
| ~ v6_rlvect_1(B)
| ~ v5_rlvect_1(B)
| ~ v4_rlvect_1(B)
| ~ v3_rlvect_1(B)
| v3_struct_0(B) )
| ~ l3_vectsp_1(A)
| ~ v2_vectsp_2(A)
| v10_vectsp_1(A)
| ~ v8_vectsp_1(A)
| ~ v7_vectsp_1(A)
| ~ v6_vectsp_1(A)
| ~ v7_group_1(A)
| ~ v4_group_1(A)
| ~ v6_rlvect_1(A)
| ~ v5_rlvect_1(A)
| ~ v4_rlvect_1(A)
| ~ v3_rlvect_1(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f61]) ).
fof(f264,plain,
! [X0,X1,X2,X3] :
( m1_rmod_2(k1_rmod_5(X0,X1,X2),X0,k1_rmod_5(X0,X1,X3))
| ~ r1_tarski(X2,X3)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v2_vectsp_2(X0)
| v10_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_group_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f263]) ).
fof(f269,plain,
! [A] :
( ! [B] :
( ! [C] :
( C = B
| ~ m1_rmod_2(B,A,C)
| ~ m1_rmod_2(C,A,B)
| ~ l1_vectsp_2(C,A)
| ~ v5_vectsp_2(C,A)
| ~ v3_vectsp_2(C,A)
| ~ v6_rlvect_1(C)
| ~ v5_rlvect_1(C)
| ~ v4_rlvect_1(C)
| ~ v3_rlvect_1(C)
| v3_struct_0(C) )
| ~ l1_vectsp_2(B,A)
| ~ v5_vectsp_2(B,A)
| ~ v3_vectsp_2(B,A)
| ~ v6_rlvect_1(B)
| ~ v5_rlvect_1(B)
| ~ v4_rlvect_1(B)
| ~ v3_rlvect_1(B)
| v3_struct_0(B) )
| ~ l3_vectsp_1(A)
| ~ v8_vectsp_1(A)
| ~ v7_vectsp_1(A)
| ~ v6_vectsp_1(A)
| ~ v4_group_1(A)
| ~ v6_rlvect_1(A)
| ~ v5_rlvect_1(A)
| ~ v4_rlvect_1(A)
| ~ v3_rlvect_1(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f64]) ).
fof(f270,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ m1_rmod_2(X1,X0,X2)
| ~ m1_rmod_2(X2,X0,X1)
| ~ l1_vectsp_2(X2,X0)
| ~ v5_vectsp_2(X2,X0)
| ~ v3_vectsp_2(X2,X0)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v3_rlvect_1(X2)
| v3_struct_0(X2)
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v3_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f271,plain,
! [A,B] :
( ( ~ r1_tarski(A,B)
| m1_subset_1(A,k1_zfmisc_1(B)) )
& ( r1_tarski(A,B)
| ~ m1_subset_1(A,k1_zfmisc_1(B)) ) ),
inference(NNF_transformation,[status(thm)],[f65]) ).
fof(f272,plain,
( ! [A,B] :
( ~ r1_tarski(A,B)
| m1_subset_1(A,k1_zfmisc_1(B)) )
& ! [A,B] :
( r1_tarski(A,B)
| ~ m1_subset_1(A,k1_zfmisc_1(B)) ) ),
inference(miniscoping,[status(thm)],[f271]) ).
fof(f273,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[status(thm)],[f272]) ).
fof(f290,definition,
( sQ0_spl
<=> l1_struct_0(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f292,plain,
( sQ0_spl
| ~ l1_struct_0(sK0_skl) ),
inference(component_clause,[status(thm)],[f290]) ).
fof(f293,definition,
( sQ1_spl
<=> v3_vectsp_2(sK1_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f295,plain,
( sQ1_spl
| ~ v3_vectsp_2(sK1_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f293]) ).
fof(f301,plain,
r1_tarski(sK2_skl,u1_struct_0(sK1_skl)),
inference(resolution,[status(thm)],[f273,f94]) ).
fof(f302,plain,
! [X0] :
( v3_vectsp_2(k1_rmod_5(sK0_skl,sK1_skl,X0),sK0_skl)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl)))
| ~ v5_vectsp_2(sK1_skl,sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl)
| ~ v4_rlvect_1(sK1_skl)
| ~ v3_rlvect_1(sK1_skl)
| v3_struct_0(sK1_skl)
| ~ l3_vectsp_1(sK0_skl)
| ~ v2_vectsp_2(sK0_skl)
| v10_vectsp_1(sK0_skl)
| ~ v8_vectsp_1(sK0_skl)
| ~ v7_vectsp_1(sK0_skl)
| ~ v6_vectsp_1(sK0_skl)
| ~ v7_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v6_rlvect_1(sK0_skl)
| ~ v5_rlvect_1(sK0_skl)
| ~ v4_rlvect_1(sK0_skl)
| ~ v3_rlvect_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f120,f93]) ).
fof(f303,definition,
( sQ3_spl
<=> v3_struct_0(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f304,plain,
( ~ sQ3_spl
| v3_struct_0(sK0_skl) ),
inference(component_clause,[status(thm)],[f303]) ).
fof(f306,definition,
( sQ4_spl
<=> v3_rlvect_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f308,plain,
( sQ4_spl
| ~ v3_rlvect_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f306]) ).
fof(f309,definition,
( sQ5_spl
<=> v4_rlvect_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f311,plain,
( sQ5_spl
| ~ v4_rlvect_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f309]) ).
fof(f312,definition,
( sQ6_spl
<=> v5_rlvect_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f314,plain,
( sQ6_spl
| ~ v5_rlvect_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f312]) ).
fof(f315,definition,
( sQ7_spl
<=> v6_rlvect_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f317,plain,
( sQ7_spl
| ~ v6_rlvect_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f315]) ).
fof(f318,definition,
( sQ8_spl
<=> v4_group_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f320,plain,
( sQ8_spl
| ~ v4_group_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f318]) ).
fof(f321,definition,
( sQ9_spl
<=> v7_group_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f323,plain,
( sQ9_spl
| ~ v7_group_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f321]) ).
fof(f324,definition,
( sQ10_spl
<=> v6_vectsp_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f326,plain,
( sQ10_spl
| ~ v6_vectsp_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f324]) ).
fof(f327,definition,
( sQ11_spl
<=> v7_vectsp_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f329,plain,
( sQ11_spl
| ~ v7_vectsp_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f327]) ).
fof(f330,definition,
( sQ12_spl
<=> v8_vectsp_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f332,plain,
( sQ12_spl
| ~ v8_vectsp_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f330]) ).
fof(f333,definition,
( sQ13_spl
<=> v10_vectsp_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f334,plain,
( ~ sQ13_spl
| v10_vectsp_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f333]) ).
fof(f336,definition,
( sQ14_spl
<=> v2_vectsp_2(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f338,plain,
( sQ14_spl
| ~ v2_vectsp_2(sK0_skl) ),
inference(component_clause,[status(thm)],[f336]) ).
fof(f339,definition,
( sQ15_spl
<=> l3_vectsp_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f341,plain,
( sQ15_spl
| ~ l3_vectsp_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f339]) ).
fof(f342,definition,
( sQ16_spl
<=> v3_struct_0(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f343,plain,
( ~ sQ16_spl
| v3_struct_0(sK1_skl) ),
inference(component_clause,[status(thm)],[f342]) ).
fof(f345,definition,
( sQ17_spl
<=> v3_rlvect_1(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f347,plain,
( sQ17_spl
| ~ v3_rlvect_1(sK1_skl) ),
inference(component_clause,[status(thm)],[f345]) ).
fof(f348,definition,
( sQ18_spl
<=> v4_rlvect_1(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f350,plain,
( sQ18_spl
| ~ v4_rlvect_1(sK1_skl) ),
inference(component_clause,[status(thm)],[f348]) ).
fof(f351,definition,
( sQ19_spl
<=> v5_rlvect_1(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f353,plain,
( sQ19_spl
| ~ v5_rlvect_1(sK1_skl) ),
inference(component_clause,[status(thm)],[f351]) ).
fof(f354,definition,
( sQ20_spl
<=> v6_rlvect_1(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f356,plain,
( sQ20_spl
| ~ v6_rlvect_1(sK1_skl) ),
inference(component_clause,[status(thm)],[f354]) ).
fof(f357,definition,
( sQ21_spl
<=> v5_vectsp_2(sK1_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f359,plain,
( sQ21_spl
| ~ v5_vectsp_2(sK1_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f357]) ).
fof(f360,definition,
! [X0] :
( sQ22_spl
<=> ( v3_vectsp_2(k1_rmod_5(sK0_skl,sK1_skl,X0),sK0_skl)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f361,plain,
! [X0] :
( ~ sQ22_spl
| v3_vectsp_2(k1_rmod_5(sK0_skl,sK1_skl,X0),sK0_skl)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
inference(component_clause,[status(thm)],[f360]) ).
fof(f363,plain,
( sQ22_spl
| ~ sQ21_spl
| ~ sQ20_spl
| ~ sQ19_spl
| ~ sQ18_spl
| ~ sQ17_spl
| sQ16_spl
| ~ sQ15_spl
| ~ sQ14_spl
| sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f302,f303,f306,f309,f312,f315,f318,f321,f324,f327,f330,f333,f336,f339,f342,f345,f348,f351,f354,f357,f360]) ).
fof(f364,plain,
( sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f359,f92]) ).
fof(f365,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f364]) ).
fof(f366,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f356,f90]) ).
fof(f367,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f366]) ).
fof(f368,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f353,f89]) ).
fof(f369,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f368]) ).
fof(f370,plain,
( sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f350,f88]) ).
fof(f371,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f370]) ).
fof(f372,plain,
( sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f347,f87]) ).
fof(f373,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f372]) ).
fof(f374,plain,
( ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f343,f86]) ).
fof(f375,plain,
~ sQ16_spl,
inference(contradiction_clause,[status(thm)],[f374]) ).
fof(f376,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f341,f85]) ).
fof(f377,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f376]) ).
fof(f378,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f338,f84]) ).
fof(f379,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f378]) ).
fof(f380,plain,
( ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f334,f83]) ).
fof(f381,plain,
~ sQ13_spl,
inference(contradiction_clause,[status(thm)],[f380]) ).
fof(f382,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f332,f82]) ).
fof(f383,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f382]) ).
fof(f384,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f329,f81]) ).
fof(f385,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f384]) ).
fof(f386,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f326,f80]) ).
fof(f387,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f386]) ).
fof(f388,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f323,f79]) ).
fof(f389,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f388]) ).
fof(f390,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f320,f78]) ).
fof(f391,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f390]) ).
fof(f392,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f317,f77]) ).
fof(f393,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f392]) ).
fof(f394,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f314,f76]) ).
fof(f395,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f394]) ).
fof(f396,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f311,f75]) ).
fof(f397,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f396]) ).
fof(f398,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f308,f74]) ).
fof(f399,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f398]) ).
fof(f400,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f304,f73]) ).
fof(f401,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f400]) ).
fof(f402,plain,
! [X0] :
( m1_rmod_2(k1_rmod_5(sK0_skl,sK1_skl,X0),sK0_skl,sK1_skl)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl)))
| ~ v5_vectsp_2(sK1_skl,sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl)
| ~ v4_rlvect_1(sK1_skl)
| ~ v3_rlvect_1(sK1_skl)
| v3_struct_0(sK1_skl)
| ~ l3_vectsp_1(sK0_skl)
| ~ v2_vectsp_2(sK0_skl)
| v10_vectsp_1(sK0_skl)
| ~ v8_vectsp_1(sK0_skl)
| ~ v7_vectsp_1(sK0_skl)
| ~ v6_vectsp_1(sK0_skl)
| ~ v7_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v6_rlvect_1(sK0_skl)
| ~ v5_rlvect_1(sK0_skl)
| ~ v4_rlvect_1(sK0_skl)
| ~ v3_rlvect_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f121,f93]) ).
fof(f403,definition,
! [X0] :
( sQ23_spl
<=> ( m1_rmod_2(k1_rmod_5(sK0_skl,sK1_skl,X0),sK0_skl,sK1_skl)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f404,plain,
! [X0] :
( ~ sQ23_spl
| m1_rmod_2(k1_rmod_5(sK0_skl,sK1_skl,X0),sK0_skl,sK1_skl)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
inference(component_clause,[status(thm)],[f403]) ).
fof(f406,plain,
( sQ23_spl
| ~ sQ21_spl
| ~ sQ20_spl
| ~ sQ19_spl
| ~ sQ18_spl
| ~ sQ17_spl
| sQ16_spl
| ~ sQ15_spl
| ~ sQ14_spl
| sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f402,f303,f306,f309,f312,f315,f318,f321,f324,f327,f330,f333,f336,f339,f342,f345,f348,f351,f354,f357,f403]) ).
fof(f408,definition,
( sQ24_spl
<=> l1_vectsp_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f410,plain,
( sQ24_spl
| ~ l1_vectsp_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f408]) ).
fof(f421,plain,
! [X0,X1] :
( m1_rmod_2(k1_rmod_5(sK0_skl,sK1_skl,X0),sK0_skl,k1_rmod_5(sK0_skl,sK1_skl,X1))
| ~ r1_tarski(X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(sK1_skl)))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl)))
| ~ v5_vectsp_2(sK1_skl,sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl)
| ~ v4_rlvect_1(sK1_skl)
| ~ v3_rlvect_1(sK1_skl)
| v3_struct_0(sK1_skl)
| ~ l3_vectsp_1(sK0_skl)
| ~ v2_vectsp_2(sK0_skl)
| v10_vectsp_1(sK0_skl)
| ~ v8_vectsp_1(sK0_skl)
| ~ v7_vectsp_1(sK0_skl)
| ~ v6_vectsp_1(sK0_skl)
| ~ v7_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v6_rlvect_1(sK0_skl)
| ~ v5_rlvect_1(sK0_skl)
| ~ v4_rlvect_1(sK0_skl)
| ~ v3_rlvect_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f264,f93]) ).
fof(f422,definition,
! [X0,X1] :
( sQ26_spl
<=> ( m1_rmod_2(k1_rmod_5(sK0_skl,sK1_skl,X0),sK0_skl,k1_rmod_5(sK0_skl,sK1_skl,X1))
| ~ r1_tarski(X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(sK1_skl)))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f423,plain,
! [X0,X1] :
( ~ sQ26_spl
| m1_rmod_2(k1_rmod_5(sK0_skl,sK1_skl,X0),sK0_skl,k1_rmod_5(sK0_skl,sK1_skl,X1))
| ~ r1_tarski(X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(sK1_skl)))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
inference(component_clause,[status(thm)],[f422]) ).
fof(f425,plain,
( sQ26_spl
| ~ sQ21_spl
| ~ sQ20_spl
| ~ sQ19_spl
| ~ sQ18_spl
| ~ sQ17_spl
| sQ16_spl
| ~ sQ15_spl
| ~ sQ14_spl
| sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f421,f303,f306,f309,f312,f315,f318,f321,f324,f327,f330,f333,f336,f339,f342,f345,f348,f351,f354,f357,f422]) ).
fof(f431,plain,
( ~ sQ22_spl
| v3_vectsp_2(k1_rmod_5(sK0_skl,sK1_skl,sK3_skl),sK0_skl) ),
inference(resolution,[status(thm)],[f361,f95]) ).
fof(f437,plain,
( ~ sQ23_spl
| m1_rmod_2(k1_rmod_5(sK0_skl,sK1_skl,sK3_skl),sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f404,f95]) ).
fof(f445,definition,
( sQ27_spl
<=> l1_vectsp_2(sK1_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f447,plain,
( sQ27_spl
| ~ l1_vectsp_2(sK1_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f445]) ).
fof(f455,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f295,f91]) ).
fof(f456,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f455]) ).
fof(f458,plain,
! [X0] :
( ~ sQ26_spl
| m1_rmod_2(k1_rmod_5(sK0_skl,sK1_skl,sK2_skl),sK0_skl,k1_rmod_5(sK0_skl,sK1_skl,X0))
| ~ r1_tarski(sK2_skl,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
inference(resolution,[status(thm)],[f423,f94]) ).
fof(f460,plain,
! [X0] :
( ~ sQ26_spl
| m1_rmod_2(sK1_skl,sK0_skl,k1_rmod_5(sK0_skl,sK1_skl,X0))
| ~ r1_tarski(sK2_skl,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
inference(forward_demodulation,[status(thm)],[f96,f458]) ).
fof(f477,definition,
( sQ35_spl
<=> v3_vectsp_2(k1_rmod_5(sK0_skl,sK1_skl,sK3_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f479,plain,
( sQ35_spl
| ~ v3_vectsp_2(k1_rmod_5(sK0_skl,sK1_skl,sK3_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f477]) ).
fof(f480,definition,
( sQ36_spl
<=> v5_vectsp_2(k1_rmod_5(sK0_skl,sK1_skl,sK3_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f483,definition,
( sQ37_spl
<=> l1_vectsp_2(k1_rmod_5(sK0_skl,sK1_skl,sK3_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f486,definition,
( sQ38_spl
<=> m1_rmod_2(sK1_skl,sK0_skl,k1_rmod_5(sK0_skl,sK1_skl,sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f489,definition,
( sQ39_spl
<=> k1_rmod_5(sK0_skl,sK1_skl,sK3_skl) = sK1_skl ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f490,plain,
( ~ sQ39_spl
| k1_rmod_5(sK0_skl,sK1_skl,sK3_skl) = sK1_skl ),
inference(component_clause,[status(thm)],[f489]) ).
fof(f493,plain,
( sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f447,f93]) ).
fof(f494,plain,
sQ27_spl,
inference(contradiction_clause,[status(thm)],[f493]) ).
fof(f497,plain,
( ~ sQ39_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f490,f98]) ).
fof(f498,plain,
~ sQ39_spl,
inference(contradiction_clause,[status(thm)],[f497]) ).
fof(f574,plain,
( ~ sQ26_spl
| m1_rmod_2(sK1_skl,sK0_skl,k1_rmod_5(sK0_skl,sK1_skl,sK3_skl))
| ~ r1_tarski(sK2_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f460,f95]) ).
fof(f577,definition,
( sQ57_spl
<=> r1_tarski(sK2_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f579,plain,
( sQ57_spl
| ~ r1_tarski(sK2_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f577]) ).
fof(f580,plain,
( ~ sQ26_spl
| sQ38_spl
| ~ sQ57_spl ),
inference(split_clause,[status(thm)],[f574,f577,f486,f422]) ).
fof(f581,definition,
( sQ58_spl
<=> r1_tarski(sK2_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f583,plain,
( sQ58_spl
| ~ r1_tarski(sK2_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f581]) ).
fof(f588,definition,
( sQ60_spl
<=> r1_tarski(sK2_skl,u1_struct_0(sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f590,plain,
( sQ60_spl
| ~ r1_tarski(sK2_skl,u1_struct_0(sK1_skl)) ),
inference(component_clause,[status(thm)],[f588]) ).
fof(f592,plain,
( sQ57_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f579,f97]) ).
fof(f593,plain,
sQ57_spl,
inference(contradiction_clause,[status(thm)],[f592]) ).
fof(f594,plain,
( sQ58_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f583,f262]) ).
fof(f595,plain,
sQ58_spl,
inference(contradiction_clause,[status(thm)],[f594]) ).
fof(f596,plain,
( sQ60_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f590,f301]) ).
fof(f597,plain,
sQ60_spl,
inference(contradiction_clause,[status(thm)],[f596]) ).
fof(f601,plain,
l1_rlvect_1(sK0_skl),
inference(resolution,[status(thm)],[f136,f85]) ).
fof(f603,plain,
l2_vectsp_1(sK0_skl),
inference(resolution,[status(thm)],[f137,f85]) ).
fof(f604,plain,
l2_struct_0(sK0_skl),
inference(resolution,[status(thm)],[f601,f125]) ).
fof(f606,plain,
l1_vectsp_1(sK0_skl),
inference(resolution,[status(thm)],[f603,f133]) ).
fof(f607,plain,
( sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f606,f410]) ).
fof(f608,plain,
sQ24_spl,
inference(contradiction_clause,[status(thm)],[f607]) ).
fof(f609,plain,
l1_struct_0(sK0_skl),
inference(resolution,[status(thm)],[f604,f131]) ).
fof(f610,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f609,f292]) ).
fof(f611,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f610]) ).
fof(f615,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ m1_rmod_2(X1,X0,X2)
| ~ m1_rmod_2(X2,X0,X1)
| ~ l1_vectsp_2(X2,X0)
| ~ v5_vectsp_2(X2,X0)
| ~ v3_vectsp_2(X2,X0)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v3_rlvect_1(X2)
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v3_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f270,f139]) ).
fof(f634,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ m1_rmod_2(X1,X0,X2)
| ~ m1_rmod_2(X2,X0,X1)
| ~ l1_vectsp_2(X2,X0)
| ~ v5_vectsp_2(X2,X0)
| ~ v3_vectsp_2(X2,X0)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v3_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f615,f140]) ).
fof(f641,plain,
( sQ35_spl
| ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f479,f431]) ).
fof(f642,plain,
( sQ35_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f641]) ).
fof(f660,definition,
( sQ65_spl
<=> r1_tarski(u1_struct_0(sK1_skl),u1_struct_0(sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f662,plain,
( sQ65_spl
| ~ r1_tarski(u1_struct_0(sK1_skl),u1_struct_0(sK1_skl)) ),
inference(component_clause,[status(thm)],[f660]) ).
fof(f667,plain,
( sQ65_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f662,f262]) ).
fof(f668,plain,
sQ65_spl,
inference(contradiction_clause,[status(thm)],[f667]) ).
fof(f673,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ m1_rmod_2(X1,X0,X2)
| ~ m1_rmod_2(X2,X0,X1)
| ~ l1_vectsp_2(X2,X0)
| ~ v5_vectsp_2(X2,X0)
| ~ v3_vectsp_2(X2,X0)
| ~ v6_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v3_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f634,f142]) ).
fof(f677,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ m1_rmod_2(X1,X0,X2)
| ~ m1_rmod_2(X2,X0,X1)
| ~ l1_vectsp_2(X2,X0)
| ~ v5_vectsp_2(X2,X0)
| ~ v3_vectsp_2(X2,X0)
| ~ v6_rlvect_1(X2)
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v3_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f673,f141]) ).
fof(f688,plain,
( ~ sQ23_spl
| v5_vectsp_2(k1_rmod_5(sK0_skl,sK1_skl,sK3_skl),sK0_skl)
| ~ l1_vectsp_2(sK1_skl,sK0_skl)
| ~ v5_vectsp_2(sK1_skl,sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl)
| ~ v4_rlvect_1(sK1_skl)
| ~ v3_rlvect_1(sK1_skl)
| v3_struct_0(sK1_skl)
| ~ l3_vectsp_1(sK0_skl)
| ~ v8_vectsp_1(sK0_skl)
| ~ v7_vectsp_1(sK0_skl)
| ~ v6_vectsp_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v6_rlvect_1(sK0_skl)
| ~ v5_rlvect_1(sK0_skl)
| ~ v4_rlvect_1(sK0_skl)
| ~ v3_rlvect_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f144,f437]) ).
fof(f691,plain,
( ~ sQ23_spl
| sQ36_spl
| ~ sQ27_spl
| ~ sQ21_spl
| ~ sQ20_spl
| ~ sQ19_spl
| ~ sQ18_spl
| ~ sQ17_spl
| sQ16_spl
| ~ sQ15_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f688,f303,f306,f309,f312,f315,f318,f324,f327,f330,f339,f342,f345,f348,f351,f354,f357,f445,f480,f403]) ).
fof(f705,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ m1_rmod_2(X1,X0,X2)
| ~ m1_rmod_2(X2,X0,X1)
| ~ l1_vectsp_2(X2,X0)
| ~ v5_vectsp_2(X2,X0)
| ~ v3_vectsp_2(X2,X0)
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v3_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f677,f143]) ).
fof(f708,plain,
( ~ sQ23_spl
| k1_rmod_5(sK0_skl,sK1_skl,sK3_skl) = sK1_skl
| ~ m1_rmod_2(sK1_skl,sK0_skl,k1_rmod_5(sK0_skl,sK1_skl,sK3_skl))
| ~ l1_vectsp_2(k1_rmod_5(sK0_skl,sK1_skl,sK3_skl),sK0_skl)
| ~ v5_vectsp_2(k1_rmod_5(sK0_skl,sK1_skl,sK3_skl),sK0_skl)
| ~ v3_vectsp_2(k1_rmod_5(sK0_skl,sK1_skl,sK3_skl),sK0_skl)
| ~ l1_vectsp_2(sK1_skl,sK0_skl)
| ~ v5_vectsp_2(sK1_skl,sK0_skl)
| ~ v3_vectsp_2(sK1_skl,sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl)
| ~ v4_rlvect_1(sK1_skl)
| ~ v3_rlvect_1(sK1_skl)
| v3_struct_0(sK1_skl)
| ~ l3_vectsp_1(sK0_skl)
| ~ v8_vectsp_1(sK0_skl)
| ~ v7_vectsp_1(sK0_skl)
| ~ v6_vectsp_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v6_rlvect_1(sK0_skl)
| ~ v5_rlvect_1(sK0_skl)
| ~ v4_rlvect_1(sK0_skl)
| ~ v3_rlvect_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f705,f437]) ).
fof(f715,plain,
( ~ sQ23_spl
| sQ39_spl
| ~ sQ38_spl
| ~ sQ37_spl
| ~ sQ36_spl
| ~ sQ35_spl
| ~ sQ27_spl
| ~ sQ21_spl
| ~ sQ1_spl
| ~ sQ20_spl
| ~ sQ19_spl
| ~ sQ18_spl
| ~ sQ17_spl
| sQ16_spl
| ~ sQ15_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f708,f303,f306,f309,f312,f315,f318,f324,f327,f330,f339,f342,f345,f348,f351,f354,f293,f357,f445,f477,f480,f483,f486,f489,f403]) ).
fof(f740,plain,
( ~ sQ23_spl
| l1_vectsp_2(k1_rmod_5(sK0_skl,sK1_skl,sK3_skl),sK0_skl)
| ~ l1_vectsp_2(sK1_skl,sK0_skl)
| ~ v5_vectsp_2(sK1_skl,sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl)
| ~ v4_rlvect_1(sK1_skl)
| ~ v3_rlvect_1(sK1_skl)
| v3_struct_0(sK1_skl)
| ~ l3_vectsp_1(sK0_skl)
| ~ v8_vectsp_1(sK0_skl)
| ~ v7_vectsp_1(sK0_skl)
| ~ v6_vectsp_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v6_rlvect_1(sK0_skl)
| ~ v5_rlvect_1(sK0_skl)
| ~ v4_rlvect_1(sK0_skl)
| ~ v3_rlvect_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f145,f437]) ).
fof(f746,plain,
( ~ sQ23_spl
| sQ37_spl
| ~ sQ27_spl
| ~ sQ21_spl
| ~ sQ20_spl
| ~ sQ19_spl
| ~ sQ18_spl
| ~ sQ17_spl
| sQ16_spl
| ~ sQ15_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f740,f303,f306,f309,f312,f315,f318,f324,f327,f330,f339,f342,f345,f348,f351,f354,f357,f445,f483,f403]) ).
fof(f748,plain,
$false,
inference(sat_refutation,[status(thm)],[f363,f365,f367,f369,f371,f373,f375,f377,f379,f381,f383,f385,f387,f389,f391,f393,f395,f397,f399,f401,f406,f425,f456,f494,f498,f580,f593,f595,f597,f608,f611,f642,f668,f691,f715,f746]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG220+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n018.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Mon Sep 21 13:06:50 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.14/5.40 % Drodi V4.1.1
% 0.14/5.46 % Refutation found
% 0.14/5.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/5.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.48 % Elapsed time: 0.091018 seconds
% 0.14/5.48 % CPU time: 0.509495 seconds
% 0.14/5.48 % Total memory used: 116.439 MB
% 0.14/5.48 % Net memory used: 115.439 MB
%------------------------------------------------------------------------------