%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG214+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 : n009.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 11:48:58 AM UTC 2026
% Result : Theorem 0.14s 5.61s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 31
% Syntax : Number of formulae : 153 ( 44 unt; 28 def)
% Number of atoms : 805 ( 28 equ)
% Maximal formula atoms : 26 ( 5 avg)
% Number of connectives : 1105 ( 453 ~; 491 |; 110 &)
% ( 30 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 46 ( 44 usr; 29 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 80 ( 75 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [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) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( v1_rmod_5(D,A,B)
& r1_tarski(C,D) )
=> v1_rmod_5(C,A,B) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [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) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( v1_rmod_5(D,A,B)
& r1_tarski(C,D) )
=> v1_rmod_5(C,A,B) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f5,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) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ( v1_rmod_5(C,A,B)
<=> ! [D] :
( m2_rmod_4(D,A,B,C)
=> ( k5_rmod_4(A,B,D) = k1_rlvect_1(B)
=> k2_rmod_4(A,B,D) = k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f68,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) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ! [E] :
( m2_rmod_4(E,A,B,C)
=> ( r1_tarski(C,D)
=> m2_rmod_4(E,A,B,D) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f77,plain,
? [A] :
( ? [B] :
( ? [C] :
( ? [D] :
( ~ v1_rmod_5(C,A,B)
& v1_rmod_5(D,A,B)
& 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)
& 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)],[f2]) ).
fof(f78,plain,
( ~ v1_rmod_5(sK2_skl,sK0_skl,sK1_skl)
& v1_rmod_5(sK3_skl,sK0_skl,sK1_skl)
& r1_tarski(sK2_skl,sK3_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)
& 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(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)],[f77]) ).
fof(f79,plain,
~ v3_struct_0(sK0_skl),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f80,plain,
v3_rlvect_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f81,plain,
v4_rlvect_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f82,plain,
v5_rlvect_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f83,plain,
v6_rlvect_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f84,plain,
v4_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f85,plain,
v6_vectsp_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f86,plain,
v7_vectsp_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f87,plain,
v8_vectsp_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f88,plain,
l3_vectsp_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f89,plain,
~ v3_struct_0(sK1_skl),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f90,plain,
v3_rlvect_1(sK1_skl),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f91,plain,
v4_rlvect_1(sK1_skl),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f92,plain,
v5_rlvect_1(sK1_skl),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f93,plain,
v6_rlvect_1(sK1_skl),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f94,plain,
v5_vectsp_2(sK1_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f95,plain,
l1_vectsp_2(sK1_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f96,plain,
m1_subset_1(sK2_skl,k1_zfmisc_1(u1_struct_0(sK1_skl))),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f97,plain,
m1_subset_1(sK3_skl,k1_zfmisc_1(u1_struct_0(sK1_skl))),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f98,plain,
r1_tarski(sK2_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f99,plain,
v1_rmod_5(sK3_skl,sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f100,plain,
~ v1_rmod_5(sK2_skl,sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f106,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( v1_rmod_5(C,A,B)
<=> ! [D] :
( k2_rmod_4(A,B,D) = k1_xboole_0
| k5_rmod_4(A,B,D) != k1_rlvect_1(B)
| ~ m2_rmod_4(D,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)
| ~ 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)],[f5]) ).
fof(f107,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ? [D] :
( k2_rmod_4(A,B,D) != k1_xboole_0
& k5_rmod_4(A,B,D) = k1_rlvect_1(B)
& m2_rmod_4(D,A,B,C) )
| v1_rmod_5(C,A,B) )
& ( ! [D] :
( k2_rmod_4(A,B,D) = k1_xboole_0
| k5_rmod_4(A,B,D) != k1_rlvect_1(B)
| ~ m2_rmod_4(D,A,B,C) )
| ~ v1_rmod_5(C,A,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)
| ~ 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(NNF_transformation,[status(thm)],[f106]) ).
fof(f108,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ( k2_rmod_4(A,B,sK4_skl(C,B,A)) != k1_xboole_0
& k5_rmod_4(A,B,sK4_skl(C,B,A)) = k1_rlvect_1(B)
& m2_rmod_4(sK4_skl(C,B,A),A,B,C) )
| v1_rmod_5(C,A,B) )
& ( ! [D] :
( k2_rmod_4(A,B,D) = k1_xboole_0
| k5_rmod_4(A,B,D) != k1_rlvect_1(B)
| ~ m2_rmod_4(D,A,B,C) )
| ~ v1_rmod_5(C,A,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)
| ~ 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(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(D,sK4_skl(C,B,A))],[f107]) ).
fof(f109,plain,
! [X0,X1,X2,X3] :
( k2_rmod_4(X0,X1,X3) = k1_xboole_0
| k5_rmod_4(X0,X1,X3) != k1_rlvect_1(X1)
| ~ m2_rmod_4(X3,X0,X1,X2)
| ~ v1_rmod_5(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)
| ~ 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)],[f108]) ).
fof(f110,plain,
! [X0,X1,X2] :
( m2_rmod_4(sK4_skl(X2,X1,X0),X0,X1,X2)
| v1_rmod_5(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)
| ~ 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)],[f108]) ).
fof(f111,plain,
! [X0,X1,X2] :
( k5_rmod_4(X0,X1,sK4_skl(X2,X1,X0)) = k1_rlvect_1(X1)
| v1_rmod_5(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)
| ~ 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)],[f108]) ).
fof(f112,plain,
! [X0,X1,X2] :
( k2_rmod_4(X0,X1,sK4_skl(X2,X1,X0)) != k1_xboole_0
| v1_rmod_5(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)
| ~ 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)],[f108]) ).
fof(f253,plain,
! [A] :
( ! [B] :
( ! [C] :
( ! [D] :
( ! [E] :
( m2_rmod_4(E,A,B,D)
| ~ r1_tarski(C,D)
| ~ m2_rmod_4(E,A,B,C) )
| ~ 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)
| ~ 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)],[f68]) ).
fof(f254,plain,
! [X0,X1,X2,X3,X4] :
( m2_rmod_4(X4,X0,X1,X3)
| ~ r1_tarski(X2,X3)
| ~ m2_rmod_4(X4,X0,X1,X2)
| ~ 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)
| ~ 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)],[f253]) ).
fof(f281,plain,
! [X0,X1] :
( k5_rmod_4(sK0_skl,X0,sK4_skl(X1,X0,sK0_skl)) = k1_rlvect_1(X0)
| v1_rmod_5(X1,sK0_skl,X0)
| ~ m1_subset_1(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)
| ~ v8_vectsp_1(sK0_skl)
| ~ v7_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)],[f111,f85]) ).
fof(f284,definition,
( sQ0_spl
<=> v3_struct_0(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f285,plain,
( ~ sQ0_spl
| v3_struct_0(sK0_skl) ),
inference(component_clause,[status(thm)],[f284]) ).
fof(f287,definition,
( sQ1_spl
<=> v3_rlvect_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f289,plain,
( sQ1_spl
| ~ v3_rlvect_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f287]) ).
fof(f290,definition,
( sQ2_spl
<=> v4_rlvect_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f292,plain,
( sQ2_spl
| ~ v4_rlvect_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f290]) ).
fof(f293,definition,
( sQ3_spl
<=> v5_rlvect_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f295,plain,
( sQ3_spl
| ~ v5_rlvect_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f293]) ).
fof(f296,definition,
( sQ4_spl
<=> v6_rlvect_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f298,plain,
( sQ4_spl
| ~ v6_rlvect_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f296]) ).
fof(f299,definition,
( sQ5_spl
<=> v4_group_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f301,plain,
( sQ5_spl
| ~ v4_group_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f299]) ).
fof(f302,definition,
( sQ6_spl
<=> v7_vectsp_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f304,plain,
( sQ6_spl
| ~ v7_vectsp_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f302]) ).
fof(f305,definition,
( sQ7_spl
<=> v8_vectsp_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f307,plain,
( sQ7_spl
| ~ v8_vectsp_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f305]) ).
fof(f308,definition,
( sQ8_spl
<=> l3_vectsp_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f310,plain,
( sQ8_spl
| ~ l3_vectsp_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f308]) ).
fof(f311,definition,
! [X0,X1] :
( sQ9_spl
<=> ( k5_rmod_4(sK0_skl,X0,sK4_skl(X1,X0,sK0_skl)) = k1_rlvect_1(X0)
| v1_rmod_5(X1,sK0_skl,X0)
| ~ m1_subset_1(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,[sQ9_spl])],[split_symbol_definition]) ).
fof(f312,plain,
! [X0,X1] :
( ~ sQ9_spl
| k5_rmod_4(sK0_skl,X0,sK4_skl(X1,X0,sK0_skl)) = k1_rlvect_1(X0)
| v1_rmod_5(X1,sK0_skl,X0)
| ~ m1_subset_1(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)],[f311]) ).
fof(f314,plain,
( sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f281,f284,f287,f290,f293,f296,f299,f302,f305,f308,f311]) ).
fof(f315,definition,
( sQ10_spl
<=> v6_vectsp_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f317,plain,
( sQ10_spl
| ~ v6_vectsp_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f315]) ).
fof(f320,plain,
! [X0] :
( ~ sQ9_spl
| k5_rmod_4(sK0_skl,sK1_skl,sK4_skl(X0,sK1_skl,sK0_skl)) = k1_rlvect_1(sK1_skl)
| v1_rmod_5(X0,sK0_skl,sK1_skl)
| ~ m1_subset_1(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)],[f312,f94]) ).
fof(f321,definition,
( sQ11_spl
<=> v3_struct_0(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f322,plain,
( ~ sQ11_spl
| v3_struct_0(sK1_skl) ),
inference(component_clause,[status(thm)],[f321]) ).
fof(f324,definition,
( sQ12_spl
<=> v3_rlvect_1(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f326,plain,
( sQ12_spl
| ~ v3_rlvect_1(sK1_skl) ),
inference(component_clause,[status(thm)],[f324]) ).
fof(f327,definition,
( sQ13_spl
<=> v4_rlvect_1(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f329,plain,
( sQ13_spl
| ~ v4_rlvect_1(sK1_skl) ),
inference(component_clause,[status(thm)],[f327]) ).
fof(f330,definition,
( sQ14_spl
<=> v5_rlvect_1(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f332,plain,
( sQ14_spl
| ~ v5_rlvect_1(sK1_skl) ),
inference(component_clause,[status(thm)],[f330]) ).
fof(f333,definition,
( sQ15_spl
<=> v6_rlvect_1(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f335,plain,
( sQ15_spl
| ~ v6_rlvect_1(sK1_skl) ),
inference(component_clause,[status(thm)],[f333]) ).
fof(f336,definition,
( sQ16_spl
<=> l1_vectsp_2(sK1_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f338,plain,
( sQ16_spl
| ~ l1_vectsp_2(sK1_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f336]) ).
fof(f339,definition,
! [X0] :
( sQ17_spl
<=> ( k5_rmod_4(sK0_skl,sK1_skl,sK4_skl(X0,sK1_skl,sK0_skl)) = k1_rlvect_1(sK1_skl)
| v1_rmod_5(X0,sK0_skl,sK1_skl)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f340,plain,
! [X0] :
( ~ sQ17_spl
| k5_rmod_4(sK0_skl,sK1_skl,sK4_skl(X0,sK1_skl,sK0_skl)) = k1_rlvect_1(sK1_skl)
| v1_rmod_5(X0,sK0_skl,sK1_skl)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
inference(component_clause,[status(thm)],[f339]) ).
fof(f342,plain,
( ~ sQ9_spl
| sQ17_spl
| ~ sQ16_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f320,f321,f324,f327,f330,f333,f336,f339,f311]) ).
fof(f343,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f310,f88]) ).
fof(f344,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f343]) ).
fof(f345,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f301,f84]) ).
fof(f346,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f345]) ).
fof(f347,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f298,f83]) ).
fof(f348,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f347]) ).
fof(f349,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f295,f82]) ).
fof(f350,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f349]) ).
fof(f351,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f292,f81]) ).
fof(f352,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f351]) ).
fof(f353,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f289,f80]) ).
fof(f354,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f353]) ).
fof(f355,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f285,f79]) ).
fof(f356,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f355]) ).
fof(f357,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f304,f86]) ).
fof(f358,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f357]) ).
fof(f359,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f317,f85]) ).
fof(f360,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f359]) ).
fof(f361,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f307,f87]) ).
fof(f362,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f361]) ).
fof(f365,plain,
( ~ sQ17_spl
| k5_rmod_4(sK0_skl,sK1_skl,sK4_skl(sK2_skl,sK1_skl,sK0_skl)) = k1_rlvect_1(sK1_skl)
| ~ m1_subset_1(sK2_skl,k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
inference(resolution,[status(thm)],[f340,f100]) ).
fof(f366,definition,
( sQ18_spl
<=> m1_subset_1(sK2_skl,k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f368,plain,
( sQ18_spl
| ~ m1_subset_1(sK2_skl,k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
inference(component_clause,[status(thm)],[f366]) ).
fof(f369,definition,
( sQ19_spl
<=> k5_rmod_4(sK0_skl,sK1_skl,sK4_skl(sK2_skl,sK1_skl,sK0_skl)) = k1_rlvect_1(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f370,plain,
( ~ sQ19_spl
| k5_rmod_4(sK0_skl,sK1_skl,sK4_skl(sK2_skl,sK1_skl,sK0_skl)) = k1_rlvect_1(sK1_skl) ),
inference(component_clause,[status(thm)],[f369]) ).
fof(f372,plain,
( ~ sQ17_spl
| sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f365,f366,f369,f339]) ).
fof(f373,plain,
( sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f368,f96]) ).
fof(f374,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f373]) ).
fof(f375,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f338,f95]) ).
fof(f376,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f375]) ).
fof(f377,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f335,f93]) ).
fof(f378,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f377]) ).
fof(f379,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f332,f92]) ).
fof(f380,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f379]) ).
fof(f381,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f329,f91]) ).
fof(f382,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f381]) ).
fof(f383,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f326,f90]) ).
fof(f384,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f383]) ).
fof(f385,plain,
( ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f322,f89]) ).
fof(f386,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f385]) ).
fof(f387,plain,
! [X0] :
( ~ sQ19_spl
| k2_rmod_4(sK0_skl,sK1_skl,sK4_skl(sK2_skl,sK1_skl,sK0_skl)) = k1_xboole_0
| ~ m2_rmod_4(sK4_skl(sK2_skl,sK1_skl,sK0_skl),sK0_skl,sK1_skl,X0)
| ~ v1_rmod_5(X0,sK0_skl,sK1_skl)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_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)],[f370,f109]) ).
fof(f389,definition,
( sQ20_spl
<=> v5_vectsp_2(sK1_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f391,plain,
( sQ20_spl
| ~ v5_vectsp_2(sK1_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f389]) ).
fof(f392,definition,
! [X0] :
( sQ21_spl
<=> ( ~ m2_rmod_4(sK4_skl(sK2_skl,sK1_skl,sK0_skl),sK0_skl,sK1_skl,X0)
| ~ v1_rmod_5(X0,sK0_skl,sK1_skl)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f393,plain,
! [X0] :
( ~ sQ21_spl
| ~ m2_rmod_4(sK4_skl(sK2_skl,sK1_skl,sK0_skl),sK0_skl,sK1_skl,X0)
| ~ v1_rmod_5(X0,sK0_skl,sK1_skl)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
inference(component_clause,[status(thm)],[f392]) ).
fof(f395,definition,
( sQ22_spl
<=> k2_rmod_4(sK0_skl,sK1_skl,sK4_skl(sK2_skl,sK1_skl,sK0_skl)) = k1_xboole_0 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f396,plain,
( ~ sQ22_spl
| k2_rmod_4(sK0_skl,sK1_skl,sK4_skl(sK2_skl,sK1_skl,sK0_skl)) = k1_xboole_0 ),
inference(component_clause,[status(thm)],[f395]) ).
fof(f398,plain,
( ~ sQ19_spl
| sQ22_spl
| sQ21_spl
| ~ sQ16_spl
| ~ sQ20_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| sQ11_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f387,f284,f287,f290,f293,f296,f299,f315,f302,f305,f308,f321,f324,f327,f330,f333,f389,f336,f392,f395,f369]) ).
fof(f403,plain,
( ~ sQ22_spl
| v1_rmod_5(sK2_skl,sK0_skl,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)
| ~ 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)],[f396,f112]) ).
fof(f405,definition,
( sQ24_spl
<=> v1_rmod_5(sK2_skl,sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f406,plain,
( ~ sQ24_spl
| v1_rmod_5(sK2_skl,sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f405]) ).
fof(f408,plain,
( ~ sQ22_spl
| sQ24_spl
| ~ sQ18_spl
| ~ sQ16_spl
| ~ sQ20_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| sQ11_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f403,f284,f287,f290,f293,f296,f299,f315,f302,f305,f308,f321,f324,f327,f330,f333,f389,f336,f366,f405,f395]) ).
fof(f413,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f391,f94]) ).
fof(f414,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f413]) ).
fof(f415,plain,
( ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f406,f100]) ).
fof(f416,plain,
~ sQ24_spl,
inference(contradiction_clause,[status(thm)],[f415]) ).
fof(f420,plain,
! [X0,X1] :
( ~ sQ21_spl
| ~ r1_tarski(X1,X0)
| ~ m2_rmod_4(sK4_skl(sK2_skl,sK1_skl,sK0_skl),sK0_skl,sK1_skl,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl)))
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(sK1_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)
| ~ v1_rmod_5(X0,sK0_skl,sK1_skl)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
inference(resolution,[status(thm)],[f393,f254]) ).
fof(f422,definition,
! [X0,X1] :
( sQ26_spl
<=> ( ~ r1_tarski(X1,X0)
| ~ m2_rmod_4(sK4_skl(sK2_skl,sK1_skl,sK0_skl),sK0_skl,sK1_skl,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl)))
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(sK1_skl)))
| ~ v1_rmod_5(X0,sK0_skl,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
| ~ r1_tarski(X1,X0)
| ~ m2_rmod_4(sK4_skl(sK2_skl,sK1_skl,sK0_skl),sK0_skl,sK1_skl,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl)))
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(sK1_skl)))
| ~ v1_rmod_5(X0,sK0_skl,sK1_skl)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
inference(component_clause,[status(thm)],[f422]) ).
fof(f425,plain,
( ~ sQ21_spl
| ~ sQ16_spl
| ~ sQ20_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| sQ11_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f420,f422,f284,f287,f290,f293,f296,f299,f315,f302,f305,f308,f321,f324,f327,f330,f333,f389,f336,f392]) ).
fof(f426,plain,
! [X0,X1] :
( ~ sQ26_spl
| ~ r1_tarski(X1,X0)
| ~ m2_rmod_4(sK4_skl(sK2_skl,sK1_skl,sK0_skl),sK0_skl,sK1_skl,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(sK1_skl)))
| ~ v1_rmod_5(X0,sK0_skl,sK1_skl)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
inference(duplicate_literals_removal,[status(thm)],[f423]) ).
fof(f427,plain,
! [X0] :
( ~ sQ26_spl
| v1_rmod_5(sK2_skl,sK0_skl,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)
| ~ 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)
| ~ r1_tarski(sK2_skl,X0)
| ~ m1_subset_1(sK2_skl,k1_zfmisc_1(u1_struct_0(sK1_skl)))
| ~ v1_rmod_5(X0,sK0_skl,sK1_skl)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
inference(resolution,[status(thm)],[f426,f110]) ).
fof(f429,definition,
! [X0] :
( sQ27_spl
<=> ( ~ r1_tarski(sK2_skl,X0)
| ~ v1_rmod_5(X0,sK0_skl,sK1_skl)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f430,plain,
! [X0] :
( ~ sQ27_spl
| ~ r1_tarski(sK2_skl,X0)
| ~ v1_rmod_5(X0,sK0_skl,sK1_skl)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
inference(component_clause,[status(thm)],[f429]) ).
fof(f432,plain,
( ~ sQ26_spl
| sQ24_spl
| ~ sQ16_spl
| ~ sQ20_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| sQ11_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl
| ~ sQ18_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f427,f429,f366,f284,f287,f290,f293,f296,f299,f315,f302,f305,f308,f321,f324,f327,f330,f333,f389,f336,f405,f422]) ).
fof(f438,plain,
( ~ sQ27_spl
| ~ r1_tarski(sK2_skl,sK3_skl)
| ~ m1_subset_1(sK3_skl,k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
inference(resolution,[status(thm)],[f430,f99]) ).
fof(f440,definition,
( sQ29_spl
<=> m1_subset_1(sK3_skl,k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f442,plain,
( sQ29_spl
| ~ m1_subset_1(sK3_skl,k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
inference(component_clause,[status(thm)],[f440]) ).
fof(f443,definition,
( sQ30_spl
<=> r1_tarski(sK2_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f445,plain,
( sQ30_spl
| ~ r1_tarski(sK2_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f443]) ).
fof(f446,plain,
( ~ sQ27_spl
| ~ sQ30_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f438,f440,f443,f429]) ).
fof(f448,plain,
( sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f442,f97]) ).
fof(f449,plain,
sQ29_spl,
inference(contradiction_clause,[status(thm)],[f448]) ).
fof(f450,plain,
( sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f445,f98]) ).
fof(f451,plain,
sQ30_spl,
inference(contradiction_clause,[status(thm)],[f450]) ).
fof(f452,plain,
$false,
inference(sat_refutation,[status(thm)],[f314,f342,f344,f346,f348,f350,f352,f354,f356,f358,f360,f362,f372,f374,f376,f378,f380,f382,f384,f386,f398,f408,f414,f416,f425,f432,f446,f449,f451]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG214+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.58 % Computer : n009.cluster.edu
% 0.10/5.58 % Model : x86_64 x86_64
% 0.10/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.58 % Memory : 8046.5625MB
% 0.10/5.58 % OS : Linux 6.8.0-71-generic
% 0.10/5.58 % CPULimit : 300
% 0.10/5.58 % WCLimit : 300
% 0.10/5.58 % DateTime : Mon Sep 21 13:02:02 UTC 2026
% 0.10/5.58 % CPUTime :
% 0.14/5.60 % Drodi V4.1.1
% 0.14/5.61 % Refutation found
% 0.14/5.61 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/5.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.64 % Elapsed time: 0.048631 seconds
% 0.14/5.64 % CPU time: 0.130928 seconds
% 0.14/5.64 % Total memory used: 51.956 MB
% 0.14/5.64 % Net memory used: 51.858 MB
%------------------------------------------------------------------------------