%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG219+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 11:48:59 AM UTC 2026
% Result : Theorem 0.19s 5.52s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 39
% Syntax : Number of formulae : 188 ( 51 unt; 31 def)
% Number of atoms : 810 ( 58 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 1018 ( 396 ~; 429 |; 141 &)
% ( 31 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 55 ( 53 usr; 32 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-5 aty)
% Number of variables : 67 ( 64 !; 3 ?)
% 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)))
=> ( C = u1_struct_0(B)
=> ( k1_rmod_5(A,B,C) = B
| k1_rlvect_1(A) = k2_group_1(A) ) ) ) ) ),
file('/export/starexec/sandbox/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)))
=> ( C = u1_struct_0(B)
=> ( k1_rmod_5(A,B,C) = B
| k1_rlvect_1(A) = k2_group_1(A) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
! [A,B] :
( ( l1_vectsp_2(B,A)
& l1_struct_0(A) )
=> ( v3_vectsp_2(B,A)
=> B = g1_vectsp_2(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u1_vectsp_2(A,B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,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)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B) )
=> k2_rmod_2(A,B) = g1_vectsp_2(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u1_vectsp_2(A,B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,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) )
=> ( m1_rmod_2(k2_rmod_2(A,B),A,B)
& v3_vectsp_2(k2_rmod_2(A,B),A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A] :
( l1_rlvect_1(A)
=> l2_struct_0(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [A] :
( l2_struct_0(A)
=> l1_struct_0(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [A] :
( l3_vectsp_1(A)
=> ( l2_vectsp_1(A)
& l1_rlvect_1(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f65,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_rmod_2(D,A,B)
& v3_vectsp_2(D,A) )
=> ( C = u1_struct_0(D)
=> ( k1_rmod_5(A,B,C) = D
| k1_rlvect_1(A) = k2_group_1(A) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f74,plain,
? [A] :
( ? [B] :
( ? [C] :
( k1_rmod_5(A,B,C) != B
& k1_rlvect_1(A) != k2_group_1(A)
& C = 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(f75,plain,
( k1_rmod_5(sK0_skl,sK1_skl,sK2_skl) != sK1_skl
& k1_rlvect_1(sK0_skl) != k2_group_1(sK0_skl)
& sK2_skl = 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]),skolemize(A,sK0_skl),skolemize(B,sK1_skl),skolemize(C,sK2_skl)],[f74]) ).
fof(f76,plain,
~ v3_struct_0(sK0_skl),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f77,plain,
v3_rlvect_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f78,plain,
v4_rlvect_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f79,plain,
v5_rlvect_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f80,plain,
v6_rlvect_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f81,plain,
v4_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f82,plain,
v7_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f83,plain,
v6_vectsp_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f84,plain,
v7_vectsp_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f85,plain,
v8_vectsp_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f86,plain,
~ v10_vectsp_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f87,plain,
v2_vectsp_2(sK0_skl),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f88,plain,
l3_vectsp_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f89,plain,
~ v3_struct_0(sK1_skl),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f90,plain,
v3_rlvect_1(sK1_skl),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f91,plain,
v4_rlvect_1(sK1_skl),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f92,plain,
v5_rlvect_1(sK1_skl),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f93,plain,
v6_rlvect_1(sK1_skl),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f94,plain,
v3_vectsp_2(sK1_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f95,plain,
v5_vectsp_2(sK1_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f96,plain,
l1_vectsp_2(sK1_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f97,plain,
m1_subset_1(sK2_skl,k1_zfmisc_1(u1_struct_0(sK1_skl))),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f98,plain,
sK2_skl = u1_struct_0(sK1_skl),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f99,plain,
k1_rlvect_1(sK0_skl) != k2_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f100,plain,
k1_rmod_5(sK0_skl,sK1_skl,sK2_skl) != sK1_skl,
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f101,plain,
! [A,B] :
( B = g1_vectsp_2(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u1_vectsp_2(A,B))
| ~ v3_vectsp_2(B,A)
| ~ l1_vectsp_2(B,A)
| ~ l1_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f102,plain,
! [X0,X1] :
( X1 = g1_vectsp_2(X0,u1_struct_0(X1),u1_rlvect_1(X1),u2_struct_0(X1),u1_vectsp_2(X0,X1))
| ~ v3_vectsp_2(X1,X0)
| ~ l1_vectsp_2(X1,X0)
| ~ l1_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f118,plain,
! [A] :
( ! [B] :
( k2_rmod_2(A,B) = g1_vectsp_2(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u1_vectsp_2(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)],[f8]) ).
fof(f119,plain,
! [X0,X1] :
( k2_rmod_2(X0,X1) = g1_vectsp_2(X0,u1_struct_0(X1),u1_rlvect_1(X1),u2_struct_0(X1),u1_vectsp_2(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)],[f118]) ).
fof(f130,plain,
! [A,B] :
( ( m1_rmod_2(k2_rmod_2(A,B),A,B)
& v3_vectsp_2(k2_rmod_2(A,B),A) )
| ~ 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)],[f15]) ).
fof(f132,plain,
! [X0,X1] :
( m1_rmod_2(k2_rmod_2(X0,X1),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)],[f130]) ).
fof(f135,plain,
! [A] :
( l2_struct_0(A)
| ~ l1_rlvect_1(A) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f136,plain,
! [X0] :
( l2_struct_0(X0)
| ~ l1_rlvect_1(X0) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f141,plain,
! [A] :
( l1_struct_0(A)
| ~ l2_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f142,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l2_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f146,plain,
! [A] :
( ( l2_vectsp_1(A)
& l1_rlvect_1(A) )
| ~ l3_vectsp_1(A) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f147,plain,
! [X0] :
( l1_rlvect_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f274,plain,
! [A] :
( ! [B] :
( ! [C] :
( ! [D] :
( k1_rmod_5(A,B,C) = D
| k1_rlvect_1(A) = k2_group_1(A)
| C != u1_struct_0(D)
| ~ m1_rmod_2(D,A,B)
| ~ v3_vectsp_2(D,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)],[f65]) ).
fof(f275,plain,
! [X0,X1,X2,X3] :
( k1_rmod_5(X0,X1,X2) = X3
| k1_rlvect_1(X0) = k2_group_1(X0)
| X2 != u1_struct_0(X3)
| ~ m1_rmod_2(X3,X0,X1)
| ~ v3_vectsp_2(X3,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)],[f274]) ).
fof(f298,plain,
! [X0,X1,X2] :
( k1_rmod_5(X0,X1,u1_struct_0(X2)) = X2
| k1_rlvect_1(X0) = k2_group_1(X0)
| ~ m1_rmod_2(X2,X0,X1)
| ~ v3_vectsp_2(X2,X0)
| ~ m1_subset_1(u1_struct_0(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(destructive_equality_resolution,[status(thm)],[f275]) ).
fof(f299,plain,
m1_subset_1(sK2_skl,k1_zfmisc_1(sK2_skl)),
inference(forward_demodulation,[status(thm)],[f98,f97]) ).
fof(f309,definition,
( sQ2_spl
<=> v3_struct_0(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f310,plain,
( ~ sQ2_spl
| v3_struct_0(sK1_skl) ),
inference(component_clause,[status(thm)],[f309]) ).
fof(f319,plain,
! [X0,X1] :
( k1_rmod_5(sK0_skl,X0,u1_struct_0(X1)) = X1
| k1_rlvect_1(sK0_skl) = k2_group_1(sK0_skl)
| ~ m1_rmod_2(X1,sK0_skl,X0)
| ~ v3_vectsp_2(X1,sK0_skl)
| ~ m1_subset_1(u1_struct_0(X1),k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_vectsp_2(X0,sK0_skl)
| ~ v5_vectsp_2(X0,sK0_skl)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ 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)
| ~ 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)],[f298,f81]) ).
fof(f320,definition,
( sQ5_spl
<=> v3_struct_0(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f321,plain,
( ~ sQ5_spl
| v3_struct_0(sK0_skl) ),
inference(component_clause,[status(thm)],[f320]) ).
fof(f323,definition,
( sQ6_spl
<=> v3_rlvect_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f325,plain,
( sQ6_spl
| ~ v3_rlvect_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f323]) ).
fof(f326,definition,
( sQ7_spl
<=> v4_rlvect_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f328,plain,
( sQ7_spl
| ~ v4_rlvect_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f326]) ).
fof(f329,definition,
( sQ8_spl
<=> v5_rlvect_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f331,plain,
( sQ8_spl
| ~ v5_rlvect_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f329]) ).
fof(f332,definition,
( sQ9_spl
<=> v6_rlvect_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f334,plain,
( sQ9_spl
| ~ v6_rlvect_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f332]) ).
fof(f335,definition,
( sQ10_spl
<=> v7_group_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f337,plain,
( sQ10_spl
| ~ v7_group_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f335]) ).
fof(f338,definition,
( sQ11_spl
<=> v6_vectsp_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f340,plain,
( sQ11_spl
| ~ v6_vectsp_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f338]) ).
fof(f341,definition,
( sQ12_spl
<=> v7_vectsp_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f343,plain,
( sQ12_spl
| ~ v7_vectsp_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f341]) ).
fof(f344,definition,
( sQ13_spl
<=> v8_vectsp_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f346,plain,
( sQ13_spl
| ~ v8_vectsp_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f344]) ).
fof(f347,definition,
( sQ14_spl
<=> v10_vectsp_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f348,plain,
( ~ sQ14_spl
| v10_vectsp_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f347]) ).
fof(f350,definition,
( sQ15_spl
<=> v2_vectsp_2(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f352,plain,
( sQ15_spl
| ~ v2_vectsp_2(sK0_skl) ),
inference(component_clause,[status(thm)],[f350]) ).
fof(f353,definition,
( sQ16_spl
<=> l3_vectsp_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f355,plain,
( sQ16_spl
| ~ l3_vectsp_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f353]) ).
fof(f356,definition,
! [X0,X1] :
( sQ17_spl
<=> ( k1_rmod_5(sK0_skl,X0,u1_struct_0(X1)) = X1
| ~ m1_rmod_2(X1,sK0_skl,X0)
| ~ v3_vectsp_2(X1,sK0_skl)
| ~ m1_subset_1(u1_struct_0(X1),k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_vectsp_2(X0,sK0_skl)
| ~ v5_vectsp_2(X0,sK0_skl)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f357,plain,
! [X0,X1] :
( ~ sQ17_spl
| k1_rmod_5(sK0_skl,X0,u1_struct_0(X1)) = X1
| ~ m1_rmod_2(X1,sK0_skl,X0)
| ~ v3_vectsp_2(X1,sK0_skl)
| ~ m1_subset_1(u1_struct_0(X1),k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_vectsp_2(X0,sK0_skl)
| ~ v5_vectsp_2(X0,sK0_skl)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(component_clause,[status(thm)],[f356]) ).
fof(f359,definition,
( sQ18_spl
<=> k1_rlvect_1(sK0_skl) = k2_group_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f360,plain,
( ~ sQ18_spl
| k1_rlvect_1(sK0_skl) = k2_group_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f359]) ).
fof(f362,plain,
( 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 ),
inference(split_clause,[status(thm)],[f319,f320,f323,f326,f329,f332,f335,f338,f341,f344,f347,f350,f353,f356,f359]) ).
fof(f363,plain,
( ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f360,f99]) ).
fof(f364,plain,
~ sQ18_spl,
inference(contradiction_clause,[status(thm)],[f363]) ).
fof(f365,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f355,f88]) ).
fof(f366,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f365]) ).
fof(f367,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f352,f87]) ).
fof(f368,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f367]) ).
fof(f369,plain,
( ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f348,f86]) ).
fof(f370,plain,
~ sQ14_spl,
inference(contradiction_clause,[status(thm)],[f369]) ).
fof(f371,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f346,f85]) ).
fof(f372,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f371]) ).
fof(f373,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f343,f84]) ).
fof(f374,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f373]) ).
fof(f375,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f340,f83]) ).
fof(f376,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f375]) ).
fof(f377,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f337,f82]) ).
fof(f378,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f377]) ).
fof(f379,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f334,f80]) ).
fof(f380,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f379]) ).
fof(f381,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f331,f79]) ).
fof(f382,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f381]) ).
fof(f383,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f328,f78]) ).
fof(f384,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f383]) ).
fof(f385,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f325,f77]) ).
fof(f386,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f385]) ).
fof(f387,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f321,f76]) ).
fof(f388,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f387]) ).
fof(f389,plain,
! [X0] :
( ~ sQ17_spl
| k1_rmod_5(sK0_skl,sK1_skl,u1_struct_0(X0)) = X0
| ~ m1_rmod_2(X0,sK0_skl,sK1_skl)
| ~ v3_vectsp_2(X0,sK0_skl)
| ~ m1_subset_1(u1_struct_0(X0),k1_zfmisc_1(u1_struct_0(sK1_skl)))
| ~ l1_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) ),
inference(resolution,[status(thm)],[f357,f95]) ).
fof(f390,definition,
( sQ19_spl
<=> v3_rlvect_1(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f392,plain,
( sQ19_spl
| ~ v3_rlvect_1(sK1_skl) ),
inference(component_clause,[status(thm)],[f390]) ).
fof(f393,definition,
( sQ20_spl
<=> v4_rlvect_1(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f395,plain,
( sQ20_spl
| ~ v4_rlvect_1(sK1_skl) ),
inference(component_clause,[status(thm)],[f393]) ).
fof(f396,definition,
( sQ21_spl
<=> v5_rlvect_1(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f398,plain,
( sQ21_spl
| ~ v5_rlvect_1(sK1_skl) ),
inference(component_clause,[status(thm)],[f396]) ).
fof(f399,definition,
( sQ22_spl
<=> v6_rlvect_1(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f401,plain,
( sQ22_spl
| ~ v6_rlvect_1(sK1_skl) ),
inference(component_clause,[status(thm)],[f399]) ).
fof(f402,definition,
( sQ23_spl
<=> l1_vectsp_2(sK1_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f404,plain,
( sQ23_spl
| ~ l1_vectsp_2(sK1_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f402]) ).
fof(f405,definition,
! [X0] :
( sQ24_spl
<=> ( k1_rmod_5(sK0_skl,sK1_skl,u1_struct_0(X0)) = X0
| ~ m1_rmod_2(X0,sK0_skl,sK1_skl)
| ~ v3_vectsp_2(X0,sK0_skl)
| ~ m1_subset_1(u1_struct_0(X0),k1_zfmisc_1(u1_struct_0(sK1_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f406,plain,
! [X0] :
( ~ sQ24_spl
| k1_rmod_5(sK0_skl,sK1_skl,u1_struct_0(X0)) = X0
| ~ m1_rmod_2(X0,sK0_skl,sK1_skl)
| ~ v3_vectsp_2(X0,sK0_skl)
| ~ m1_subset_1(u1_struct_0(X0),k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
inference(component_clause,[status(thm)],[f405]) ).
fof(f408,plain,
( ~ sQ17_spl
| sQ24_spl
| ~ sQ23_spl
| ~ sQ22_spl
| ~ sQ21_spl
| ~ sQ20_spl
| ~ sQ19_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f389,f309,f390,f393,f396,f399,f402,f405,f356]) ).
fof(f409,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f310,f89]) ).
fof(f410,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f409]) ).
fof(f411,plain,
! [X0] :
( ~ sQ24_spl
| k1_rmod_5(sK0_skl,sK1_skl,u1_struct_0(X0)) = X0
| ~ m1_rmod_2(X0,sK0_skl,sK1_skl)
| ~ v3_vectsp_2(X0,sK0_skl)
| ~ m1_subset_1(u1_struct_0(X0),k1_zfmisc_1(sK2_skl)) ),
inference(forward_demodulation,[status(thm)],[f98,f406]) ).
fof(f414,plain,
( sK1_skl = g1_vectsp_2(sK0_skl,u1_struct_0(sK1_skl),u1_rlvect_1(sK1_skl),u2_struct_0(sK1_skl),u1_vectsp_2(sK0_skl,sK1_skl))
| ~ v3_vectsp_2(sK1_skl,sK0_skl)
| ~ l1_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f102,f96]) ).
fof(f415,definition,
( sQ25_spl
<=> l1_struct_0(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f417,plain,
( sQ25_spl
| ~ l1_struct_0(sK0_skl) ),
inference(component_clause,[status(thm)],[f415]) ).
fof(f418,definition,
( sQ26_spl
<=> v3_vectsp_2(sK1_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f420,plain,
( sQ26_spl
| ~ v3_vectsp_2(sK1_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f418]) ).
fof(f421,definition,
( sQ27_spl
<=> sK1_skl = g1_vectsp_2(sK0_skl,u1_struct_0(sK1_skl),u1_rlvect_1(sK1_skl),u2_struct_0(sK1_skl),u1_vectsp_2(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f422,plain,
( ~ sQ27_spl
| sK1_skl = g1_vectsp_2(sK0_skl,u1_struct_0(sK1_skl),u1_rlvect_1(sK1_skl),u2_struct_0(sK1_skl),u1_vectsp_2(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f421]) ).
fof(f424,plain,
( sQ27_spl
| ~ sQ26_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f414,f415,f418,f421]) ).
fof(f425,plain,
( ~ sQ27_spl
| sK1_skl = g1_vectsp_2(sK0_skl,sK2_skl,u1_rlvect_1(sK1_skl),u2_struct_0(sK1_skl),u1_vectsp_2(sK0_skl,sK1_skl)) ),
inference(forward_demodulation,[status(thm)],[f98,f422]) ).
fof(f426,plain,
( sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f420,f94]) ).
fof(f427,plain,
sQ26_spl,
inference(contradiction_clause,[status(thm)],[f426]) ).
fof(f429,plain,
( ~ sQ24_spl
| k1_rmod_5(sK0_skl,sK1_skl,u1_struct_0(sK1_skl)) = sK1_skl
| ~ m1_rmod_2(sK1_skl,sK0_skl,sK1_skl)
| ~ v3_vectsp_2(sK1_skl,sK0_skl)
| ~ m1_subset_1(sK2_skl,k1_zfmisc_1(sK2_skl)) ),
inference(paramodulation,[status(thm)],[f98,f411]) ).
fof(f430,definition,
( sQ28_spl
<=> m1_subset_1(sK2_skl,k1_zfmisc_1(sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f432,plain,
( sQ28_spl
| ~ m1_subset_1(sK2_skl,k1_zfmisc_1(sK2_skl)) ),
inference(component_clause,[status(thm)],[f430]) ).
fof(f433,definition,
( sQ29_spl
<=> m1_rmod_2(sK1_skl,sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f435,plain,
( sQ29_spl
| ~ m1_rmod_2(sK1_skl,sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f433]) ).
fof(f436,definition,
( sQ30_spl
<=> k1_rmod_5(sK0_skl,sK1_skl,u1_struct_0(sK1_skl)) = sK1_skl ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f437,plain,
( ~ sQ30_spl
| k1_rmod_5(sK0_skl,sK1_skl,u1_struct_0(sK1_skl)) = sK1_skl ),
inference(component_clause,[status(thm)],[f436]) ).
fof(f439,plain,
( ~ sQ24_spl
| sQ30_spl
| ~ sQ29_spl
| ~ sQ26_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f429,f430,f418,f433,f436,f405]) ).
fof(f440,plain,
( ~ sQ30_spl
| k1_rmod_5(sK0_skl,sK1_skl,sK2_skl) = sK1_skl ),
inference(forward_demodulation,[status(thm)],[f98,f437]) ).
fof(f441,plain,
( ~ sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f440,f100]) ).
fof(f442,plain,
~ sQ30_spl,
inference(contradiction_clause,[status(thm)],[f441]) ).
fof(f443,plain,
( sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f432,f299]) ).
fof(f444,plain,
sQ28_spl,
inference(contradiction_clause,[status(thm)],[f443]) ).
fof(f445,plain,
( sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f404,f96]) ).
fof(f446,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f445]) ).
fof(f448,plain,
( sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f401,f93]) ).
fof(f449,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f448]) ).
fof(f450,plain,
( sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f398,f92]) ).
fof(f451,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f450]) ).
fof(f452,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f395,f91]) ).
fof(f453,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f452]) ).
fof(f454,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f392,f90]) ).
fof(f455,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f454]) ).
fof(f458,plain,
( sQ25_spl
| ~ l2_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f142,f417]) ).
fof(f459,plain,
( sQ25_spl
| ~ l1_rlvect_1(sK0_skl) ),
inference(resolution,[status(thm)],[f458,f136]) ).
fof(f463,plain,
l1_rlvect_1(sK0_skl),
inference(resolution,[status(thm)],[f147,f88]) ).
fof(f464,plain,
( sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f463,f459]) ).
fof(f465,plain,
sQ25_spl,
inference(contradiction_clause,[status(thm)],[f464]) ).
fof(f474,plain,
! [X0] :
( k2_rmod_2(sK0_skl,X0) = g1_vectsp_2(sK0_skl,u1_struct_0(X0),u1_rlvect_1(X0),u2_struct_0(X0),u1_vectsp_2(sK0_skl,X0))
| ~ l1_vectsp_2(X0,sK0_skl)
| ~ v5_vectsp_2(X0,sK0_skl)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ l3_vectsp_1(sK0_skl)
| ~ v8_vectsp_1(sK0_skl)
| ~ v7_vectsp_1(sK0_skl)
| ~ v6_vectsp_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)],[f119,f81]) ).
fof(f475,definition,
! [X0] :
( sQ31_spl
<=> ( k2_rmod_2(sK0_skl,X0) = g1_vectsp_2(sK0_skl,u1_struct_0(X0),u1_rlvect_1(X0),u2_struct_0(X0),u1_vectsp_2(sK0_skl,X0))
| ~ l1_vectsp_2(X0,sK0_skl)
| ~ v5_vectsp_2(X0,sK0_skl)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f476,plain,
! [X0] :
( ~ sQ31_spl
| k2_rmod_2(sK0_skl,X0) = g1_vectsp_2(sK0_skl,u1_struct_0(X0),u1_rlvect_1(X0),u2_struct_0(X0),u1_vectsp_2(sK0_skl,X0))
| ~ l1_vectsp_2(X0,sK0_skl)
| ~ v5_vectsp_2(X0,sK0_skl)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(component_clause,[status(thm)],[f475]) ).
fof(f478,plain,
( sQ31_spl
| ~ sQ16_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f474,f320,f323,f326,f329,f332,f338,f341,f344,f353,f475]) ).
fof(f479,plain,
( ~ sQ31_spl
| k2_rmod_2(sK0_skl,sK1_skl) = g1_vectsp_2(sK0_skl,u1_struct_0(sK1_skl),u1_rlvect_1(sK1_skl),u2_struct_0(sK1_skl),u1_vectsp_2(sK0_skl,sK1_skl))
| ~ l1_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) ),
inference(resolution,[status(thm)],[f476,f95]) ).
fof(f480,definition,
( sQ32_spl
<=> k2_rmod_2(sK0_skl,sK1_skl) = g1_vectsp_2(sK0_skl,u1_struct_0(sK1_skl),u1_rlvect_1(sK1_skl),u2_struct_0(sK1_skl),u1_vectsp_2(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f481,plain,
( ~ sQ32_spl
| k2_rmod_2(sK0_skl,sK1_skl) = g1_vectsp_2(sK0_skl,u1_struct_0(sK1_skl),u1_rlvect_1(sK1_skl),u2_struct_0(sK1_skl),u1_vectsp_2(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f480]) ).
fof(f483,plain,
( ~ sQ31_spl
| sQ32_spl
| ~ sQ23_spl
| ~ sQ22_spl
| ~ sQ21_spl
| ~ sQ20_spl
| ~ sQ19_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f479,f309,f390,f393,f396,f399,f402,f480,f475]) ).
fof(f484,plain,
( ~ sQ32_spl
| k2_rmod_2(sK0_skl,sK1_skl) = g1_vectsp_2(sK0_skl,sK2_skl,u1_rlvect_1(sK1_skl),u2_struct_0(sK1_skl),u1_vectsp_2(sK0_skl,sK1_skl)) ),
inference(forward_demodulation,[status(thm)],[f98,f481]) ).
fof(f485,plain,
( ~ sQ32_spl
| ~ sQ27_spl
| k2_rmod_2(sK0_skl,sK1_skl) = sK1_skl ),
inference(forward_demodulation,[status(thm)],[f425,f484]) ).
fof(f510,plain,
! [X0] :
( m1_rmod_2(k2_rmod_2(sK0_skl,X0),sK0_skl,X0)
| ~ l1_vectsp_2(X0,sK0_skl)
| ~ v5_vectsp_2(X0,sK0_skl)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ l3_vectsp_1(sK0_skl)
| ~ v8_vectsp_1(sK0_skl)
| ~ v7_vectsp_1(sK0_skl)
| ~ v6_vectsp_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)],[f132,f81]) ).
fof(f511,definition,
! [X0] :
( sQ35_spl
<=> ( m1_rmod_2(k2_rmod_2(sK0_skl,X0),sK0_skl,X0)
| ~ l1_vectsp_2(X0,sK0_skl)
| ~ v5_vectsp_2(X0,sK0_skl)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f512,plain,
! [X0] :
( ~ sQ35_spl
| m1_rmod_2(k2_rmod_2(sK0_skl,X0),sK0_skl,X0)
| ~ l1_vectsp_2(X0,sK0_skl)
| ~ v5_vectsp_2(X0,sK0_skl)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(component_clause,[status(thm)],[f511]) ).
fof(f514,plain,
( sQ35_spl
| ~ sQ16_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f510,f320,f323,f326,f329,f332,f338,f341,f344,f353,f511]) ).
fof(f515,plain,
( ~ sQ35_spl
| m1_rmod_2(k2_rmod_2(sK0_skl,sK1_skl),sK0_skl,sK1_skl)
| ~ l1_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) ),
inference(resolution,[status(thm)],[f512,f95]) ).
fof(f516,definition,
( sQ36_spl
<=> m1_rmod_2(k2_rmod_2(sK0_skl,sK1_skl),sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f517,plain,
( ~ sQ36_spl
| m1_rmod_2(k2_rmod_2(sK0_skl,sK1_skl),sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f516]) ).
fof(f519,plain,
( ~ sQ35_spl
| sQ36_spl
| ~ sQ23_spl
| ~ sQ22_spl
| ~ sQ21_spl
| ~ sQ20_spl
| ~ sQ19_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f515,f309,f390,f393,f396,f399,f402,f516,f511]) ).
fof(f520,plain,
( ~ sQ36_spl
| ~ sQ32_spl
| ~ sQ27_spl
| m1_rmod_2(sK1_skl,sK0_skl,sK1_skl) ),
inference(forward_demodulation,[status(thm)],[f485,f517]) ).
fof(f521,plain,
( ~ sQ36_spl
| ~ sQ32_spl
| ~ sQ27_spl
| sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f520,f435]) ).
fof(f522,plain,
( ~ sQ36_spl
| ~ sQ32_spl
| ~ sQ27_spl
| sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f521]) ).
fof(f523,plain,
$false,
inference(sat_refutation,[status(thm)],[f362,f364,f366,f368,f370,f372,f374,f376,f378,f380,f382,f384,f386,f388,f408,f410,f424,f427,f439,f442,f444,f446,f449,f451,f453,f455,f465,f478,f483,f514,f519,f522]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG219+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/5.42 % Computer : n020.cluster.edu
% 0.15/5.42 % Model : x86_64 x86_64
% 0.15/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.42 % Memory : 8046.5625MB
% 0.15/5.42 % OS : Linux 6.8.0-71-generic
% 0.15/5.42 % CPULimit : 300
% 0.15/5.42 % WCLimit : 300
% 0.15/5.42 % DateTime : Mon Sep 21 13:04:23 UTC 2026
% 0.15/5.42 % CPUTime :
% 0.15/5.45 % Drodi V4.1.1
% 0.19/5.52 % Refutation found
% 0.19/5.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/5.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/5.54 % Elapsed time: 0.107740 seconds
% 0.19/5.54 % CPU time: 0.367120 seconds
% 0.19/5.54 % Total memory used: 78.160 MB
% 0.19/5.54 % Net memory used: 77.797 MB
%------------------------------------------------------------------------------