%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG222+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 : 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 11:49:00 AM UTC 2026
% Result : Theorem 0.11s 0.47s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 43
% Syntax : Number of formulae : 198 ( 68 unt; 32 def)
% Number of atoms : 891 ( 13 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 1152 ( 459 ~; 498 |; 140 &)
% ( 32 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 54 ( 52 usr; 33 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 104 ( 98 !; 6 ?)
% 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)
& 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)))
=> m1_rmod_2(k1_rmod_5(A,B,k5_subset_1(u1_struct_0(B),C,D)),A,k2_rmod_3(A,B,k1_rmod_5(A,B,C),k1_rmod_5(A,B,D))) ) ) ) ),
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)
& 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)))
=> m1_rmod_2(k1_rmod_5(A,B,k5_subset_1(u1_struct_0(B),C,D)),A,k2_rmod_3(A,B,k1_rmod_5(A,B,C),k1_rmod_5(A,B,D))) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f8,axiom,
! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,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(f17,axiom,
! [A,B,C] :
( ( m1_subset_1(C,k1_zfmisc_1(A))
& m1_subset_1(B,k1_zfmisc_1(A)) )
=> m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,axiom,
? [A] : v1_xboole_0(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f59,axiom,
! [A] :
? [B] :
( v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,axiom,
! [A,B,C] :
( ( m1_subset_1(C,k1_zfmisc_1(A))
& m1_subset_1(B,k1_zfmisc_1(A)) )
=> k5_subset_1(A,B,C) = k3_xboole_0(B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f69,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(f70,axiom,
! [A,B] : r1_tarski(k3_xboole_0(A,B),A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f72,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_rmod_2(C,A,B)
=> ! [D] :
( m1_rmod_2(D,A,B)
=> ! [E] :
( m1_rmod_2(E,A,B)
=> ( ( m1_rmod_2(C,A,E)
& m1_rmod_2(C,A,D) )
=> m1_rmod_2(C,A,k2_rmod_3(A,B,D,E)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f78,axiom,
! [A] :
( v1_xboole_0(A)
=> A = k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f81,plain,
? [A] :
( ? [B] :
( ? [C] :
( ? [D] :
( ~ m1_rmod_2(k1_rmod_5(A,B,k5_subset_1(u1_struct_0(B),C,D)),A,k2_rmod_3(A,B,k1_rmod_5(A,B,C),k1_rmod_5(A,B,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)],[f2]) ).
fof(f82,plain,
( ~ m1_rmod_2(k1_rmod_5(sK0_skl,sK1_skl,k5_subset_1(u1_struct_0(sK1_skl),sK2_skl,sK3_skl)),sK0_skl,k2_rmod_3(sK0_skl,sK1_skl,k1_rmod_5(sK0_skl,sK1_skl,sK2_skl),k1_rmod_5(sK0_skl,sK1_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)
& 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)],[f81]) ).
fof(f83,plain,
~ v3_struct_0(sK0_skl),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f84,plain,
v3_rlvect_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f85,plain,
v4_rlvect_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f86,plain,
v5_rlvect_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f87,plain,
v6_rlvect_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f88,plain,
v4_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f89,plain,
v7_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f90,plain,
v6_vectsp_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f91,plain,
v7_vectsp_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f92,plain,
v8_vectsp_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f93,plain,
~ v10_vectsp_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f94,plain,
v2_vectsp_2(sK0_skl),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f95,plain,
l3_vectsp_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f96,plain,
~ v3_struct_0(sK1_skl),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f97,plain,
v3_rlvect_1(sK1_skl),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f98,plain,
v4_rlvect_1(sK1_skl),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f99,plain,
v5_rlvect_1(sK1_skl),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f100,plain,
v6_rlvect_1(sK1_skl),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f101,plain,
v5_vectsp_2(sK1_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f102,plain,
l1_vectsp_2(sK1_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f103,plain,
m1_subset_1(sK2_skl,k1_zfmisc_1(u1_struct_0(sK1_skl))),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f104,plain,
m1_subset_1(sK3_skl,k1_zfmisc_1(u1_struct_0(sK1_skl))),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f105,plain,
~ m1_rmod_2(k1_rmod_5(sK0_skl,sK1_skl,k5_subset_1(u1_struct_0(sK1_skl),sK2_skl,sK3_skl)),sK0_skl,k2_rmod_3(sK0_skl,sK1_skl,k1_rmod_5(sK0_skl,sK1_skl,sK2_skl),k1_rmod_5(sK0_skl,sK1_skl,sK3_skl))),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f123,plain,
! [X0,X1] : k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f129,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)],[f11]) ).
fof(f131,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)],[f129]) ).
fof(f135,plain,
! [A,B,C] :
( m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A))
| ~ m1_subset_1(C,k1_zfmisc_1(A))
| ~ m1_subset_1(B,k1_zfmisc_1(A)) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f136,plain,
! [X0,X1,X2] :
( m1_subset_1(k5_subset_1(X1,X0,X2),k1_zfmisc_1(X1))
| ~ m1_subset_1(X2,k1_zfmisc_1(X1))
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f252,plain,
v1_xboole_0(sK20_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl]),skolemize(A,sK20_skl)],[f58]) ).
fof(f253,plain,
v1_xboole_0(sK20_skl),
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f254,plain,
! [A] :
( v1_xboole_0(sK21_skl(A))
& m1_subset_1(sK21_skl(A),k1_zfmisc_1(A)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21_skl]),skolemize(B,sK21_skl(A))],[f59]) ).
fof(f255,plain,
! [X0] : m1_subset_1(sK21_skl(X0),k1_zfmisc_1(X0)),
inference(cnf_transformation,[status(thm)],[f254]) ).
fof(f256,plain,
! [X0] : v1_xboole_0(sK21_skl(X0)),
inference(cnf_transformation,[status(thm)],[f254]) ).
fof(f277,plain,
! [A,B,C] :
( k5_subset_1(A,B,C) = k3_xboole_0(B,C)
| ~ m1_subset_1(C,k1_zfmisc_1(A))
| ~ m1_subset_1(B,k1_zfmisc_1(A)) ),
inference(pre_NNF_transformation,[status(thm)],[f66]) ).
fof(f278,plain,
! [X0,X1,X2] :
( k5_subset_1(X1,X0,X2) = k3_xboole_0(X0,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X1))
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[status(thm)],[f277]) ).
fof(f285,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)],[f69]) ).
fof(f286,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)],[f285]) ).
fof(f287,plain,
! [X0,X1] : r1_tarski(k3_xboole_0(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f290,plain,
! [A] :
( ! [B] :
( ! [C] :
( ! [D] :
( ! [E] :
( m1_rmod_2(C,A,k2_rmod_3(A,B,D,E))
| ~ m1_rmod_2(C,A,E)
| ~ m1_rmod_2(C,A,D)
| ~ m1_rmod_2(E,A,B) )
| ~ m1_rmod_2(D,A,B) )
| ~ 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)],[f72]) ).
fof(f291,plain,
! [X0,X1,X2,X3,X4] :
( m1_rmod_2(X2,X0,k2_rmod_3(X0,X1,X3,X4))
| ~ m1_rmod_2(X2,X0,X4)
| ~ m1_rmod_2(X2,X0,X3)
| ~ m1_rmod_2(X4,X0,X1)
| ~ m1_rmod_2(X3,X0,X1)
| ~ 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)],[f290]) ).
fof(f305,plain,
! [A] :
( A = k1_xboole_0
| ~ v1_xboole_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f78]) ).
fof(f306,plain,
! [X0] :
( X0 = k1_xboole_0
| ~ v1_xboole_0(X0) ),
inference(cnf_transformation,[status(thm)],[f305]) ).
fof(f320,plain,
! [X0] :
( k5_subset_1(u1_struct_0(sK1_skl),X0,sK3_skl) = k3_xboole_0(X0,sK3_skl)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
inference(resolution,[status(thm)],[f278,f104]) ).
fof(f323,plain,
k5_subset_1(u1_struct_0(sK1_skl),sK2_skl,sK3_skl) = k3_xboole_0(sK2_skl,sK3_skl),
inference(resolution,[status(thm)],[f320,f103]) ).
fof(f327,plain,
~ m1_rmod_2(k1_rmod_5(sK0_skl,sK1_skl,k3_xboole_0(sK2_skl,sK3_skl)),sK0_skl,k2_rmod_3(sK0_skl,sK1_skl,k1_rmod_5(sK0_skl,sK1_skl,sK2_skl),k1_rmod_5(sK0_skl,sK1_skl,sK3_skl))),
inference(backward_demodulation,[status(thm)],[f323,f105]) ).
fof(f328,plain,
! [X0] :
( m1_subset_1(k5_subset_1(u1_struct_0(sK1_skl),X0,sK3_skl),k1_zfmisc_1(u1_struct_0(sK1_skl)))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
inference(resolution,[status(thm)],[f136,f104]) ).
fof(f342,plain,
m1_subset_1(k5_subset_1(u1_struct_0(sK1_skl),sK2_skl,sK3_skl),k1_zfmisc_1(u1_struct_0(sK1_skl))),
inference(resolution,[status(thm)],[f328,f103]) ).
fof(f344,plain,
m1_subset_1(k3_xboole_0(sK2_skl,sK3_skl),k1_zfmisc_1(u1_struct_0(sK1_skl))),
inference(forward_demodulation,[status(thm)],[f323,f342]) ).
fof(f419,plain,
! [X0,X1,X2,X3] :
( m1_rmod_2(X1,sK0_skl,k2_rmod_3(sK0_skl,X0,X2,X3))
| ~ m1_rmod_2(X1,sK0_skl,X3)
| ~ m1_rmod_2(X1,sK0_skl,X2)
| ~ m1_rmod_2(X3,sK0_skl,X0)
| ~ m1_rmod_2(X2,sK0_skl,X0)
| ~ m1_rmod_2(X1,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)
| ~ 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)],[f291,f91]) ).
fof(f420,definition,
( sQ0_spl
<=> v3_struct_0(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f421,plain,
( ~ sQ0_spl
| v3_struct_0(sK0_skl) ),
inference(component_clause,[status(thm)],[f420]) ).
fof(f423,definition,
( sQ1_spl
<=> v3_rlvect_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f425,plain,
( sQ1_spl
| ~ v3_rlvect_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f423]) ).
fof(f426,definition,
( sQ2_spl
<=> v4_rlvect_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f428,plain,
( sQ2_spl
| ~ v4_rlvect_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f426]) ).
fof(f429,definition,
( sQ3_spl
<=> v5_rlvect_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f431,plain,
( sQ3_spl
| ~ v5_rlvect_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f429]) ).
fof(f432,definition,
( sQ4_spl
<=> v6_rlvect_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f434,plain,
( sQ4_spl
| ~ v6_rlvect_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f432]) ).
fof(f435,definition,
( sQ5_spl
<=> v4_group_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f437,plain,
( sQ5_spl
| ~ v4_group_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f435]) ).
fof(f438,definition,
( sQ6_spl
<=> v6_vectsp_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f440,plain,
( sQ6_spl
| ~ v6_vectsp_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f438]) ).
fof(f441,definition,
( sQ7_spl
<=> v8_vectsp_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f443,plain,
( sQ7_spl
| ~ v8_vectsp_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f441]) ).
fof(f444,definition,
( sQ8_spl
<=> l3_vectsp_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f446,plain,
( sQ8_spl
| ~ l3_vectsp_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f444]) ).
fof(f447,definition,
! [X0,X1,X2,X3] :
( sQ9_spl
<=> ( m1_rmod_2(X1,sK0_skl,k2_rmod_3(sK0_skl,X0,X2,X3))
| ~ m1_rmod_2(X1,sK0_skl,X3)
| ~ m1_rmod_2(X1,sK0_skl,X2)
| ~ m1_rmod_2(X3,sK0_skl,X0)
| ~ m1_rmod_2(X2,sK0_skl,X0)
| ~ m1_rmod_2(X1,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,[sQ9_spl])],[split_symbol_definition]) ).
fof(f448,plain,
! [X0,X1,X2,X3] :
( ~ sQ9_spl
| m1_rmod_2(X1,sK0_skl,k2_rmod_3(sK0_skl,X0,X2,X3))
| ~ m1_rmod_2(X1,sK0_skl,X3)
| ~ m1_rmod_2(X1,sK0_skl,X2)
| ~ m1_rmod_2(X3,sK0_skl,X0)
| ~ m1_rmod_2(X2,sK0_skl,X0)
| ~ m1_rmod_2(X1,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)],[f447]) ).
fof(f450,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)],[f419,f420,f423,f426,f429,f432,f435,f438,f441,f444,f447]) ).
fof(f462,plain,
! [X0] : sK21_skl(X0) = k1_xboole_0,
inference(resolution,[status(thm)],[f306,f256]) ).
fof(f463,plain,
sK20_skl = k1_xboole_0,
inference(resolution,[status(thm)],[f306,f253]) ).
fof(f480,plain,
( ~ sQ9_spl
| ~ m1_rmod_2(k1_rmod_5(sK0_skl,sK1_skl,k3_xboole_0(sK2_skl,sK3_skl)),sK0_skl,k1_rmod_5(sK0_skl,sK1_skl,sK3_skl))
| ~ m1_rmod_2(k1_rmod_5(sK0_skl,sK1_skl,k3_xboole_0(sK2_skl,sK3_skl)),sK0_skl,k1_rmod_5(sK0_skl,sK1_skl,sK2_skl))
| ~ m1_rmod_2(k1_rmod_5(sK0_skl,sK1_skl,sK3_skl),sK0_skl,sK1_skl)
| ~ m1_rmod_2(k1_rmod_5(sK0_skl,sK1_skl,sK2_skl),sK0_skl,sK1_skl)
| ~ m1_rmod_2(k1_rmod_5(sK0_skl,sK1_skl,k3_xboole_0(sK2_skl,sK3_skl)),sK0_skl,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) ),
inference(resolution,[status(thm)],[f448,f327]) ).
fof(f481,definition,
( sQ10_spl
<=> v3_struct_0(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f482,plain,
( ~ sQ10_spl
| v3_struct_0(sK1_skl) ),
inference(component_clause,[status(thm)],[f481]) ).
fof(f484,definition,
( sQ11_spl
<=> v3_rlvect_1(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f486,plain,
( sQ11_spl
| ~ v3_rlvect_1(sK1_skl) ),
inference(component_clause,[status(thm)],[f484]) ).
fof(f487,definition,
( sQ12_spl
<=> v4_rlvect_1(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f489,plain,
( sQ12_spl
| ~ v4_rlvect_1(sK1_skl) ),
inference(component_clause,[status(thm)],[f487]) ).
fof(f490,definition,
( sQ13_spl
<=> v5_rlvect_1(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f492,plain,
( sQ13_spl
| ~ v5_rlvect_1(sK1_skl) ),
inference(component_clause,[status(thm)],[f490]) ).
fof(f493,definition,
( sQ14_spl
<=> v6_rlvect_1(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f495,plain,
( sQ14_spl
| ~ v6_rlvect_1(sK1_skl) ),
inference(component_clause,[status(thm)],[f493]) ).
fof(f496,definition,
( sQ15_spl
<=> v5_vectsp_2(sK1_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f498,plain,
( sQ15_spl
| ~ v5_vectsp_2(sK1_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f496]) ).
fof(f499,definition,
( sQ16_spl
<=> l1_vectsp_2(sK1_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f501,plain,
( sQ16_spl
| ~ l1_vectsp_2(sK1_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f499]) ).
fof(f502,definition,
( sQ17_spl
<=> m1_rmod_2(k1_rmod_5(sK0_skl,sK1_skl,k3_xboole_0(sK2_skl,sK3_skl)),sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f504,plain,
( sQ17_spl
| ~ m1_rmod_2(k1_rmod_5(sK0_skl,sK1_skl,k3_xboole_0(sK2_skl,sK3_skl)),sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f502]) ).
fof(f505,definition,
( sQ18_spl
<=> m1_rmod_2(k1_rmod_5(sK0_skl,sK1_skl,sK2_skl),sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f507,plain,
( sQ18_spl
| ~ m1_rmod_2(k1_rmod_5(sK0_skl,sK1_skl,sK2_skl),sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f505]) ).
fof(f508,definition,
( sQ19_spl
<=> m1_rmod_2(k1_rmod_5(sK0_skl,sK1_skl,sK3_skl),sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f510,plain,
( sQ19_spl
| ~ m1_rmod_2(k1_rmod_5(sK0_skl,sK1_skl,sK3_skl),sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f508]) ).
fof(f511,definition,
( sQ20_spl
<=> m1_rmod_2(k1_rmod_5(sK0_skl,sK1_skl,k3_xboole_0(sK2_skl,sK3_skl)),sK0_skl,k1_rmod_5(sK0_skl,sK1_skl,sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f513,plain,
( sQ20_spl
| ~ m1_rmod_2(k1_rmod_5(sK0_skl,sK1_skl,k3_xboole_0(sK2_skl,sK3_skl)),sK0_skl,k1_rmod_5(sK0_skl,sK1_skl,sK2_skl)) ),
inference(component_clause,[status(thm)],[f511]) ).
fof(f514,definition,
( sQ21_spl
<=> m1_rmod_2(k1_rmod_5(sK0_skl,sK1_skl,k3_xboole_0(sK2_skl,sK3_skl)),sK0_skl,k1_rmod_5(sK0_skl,sK1_skl,sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f516,plain,
( sQ21_spl
| ~ m1_rmod_2(k1_rmod_5(sK0_skl,sK1_skl,k3_xboole_0(sK2_skl,sK3_skl)),sK0_skl,k1_rmod_5(sK0_skl,sK1_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f514]) ).
fof(f517,plain,
( ~ sQ9_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 ),
inference(split_clause,[status(thm)],[f480,f481,f484,f487,f490,f493,f496,f499,f502,f505,f508,f511,f514,f447]) ).
fof(f518,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f501,f102]) ).
fof(f519,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f518]) ).
fof(f520,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f498,f101]) ).
fof(f521,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f520]) ).
fof(f522,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f495,f100]) ).
fof(f523,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f522]) ).
fof(f524,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f492,f99]) ).
fof(f525,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f524]) ).
fof(f526,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f489,f98]) ).
fof(f527,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f526]) ).
fof(f528,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f486,f97]) ).
fof(f529,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f528]) ).
fof(f530,plain,
( ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f482,f96]) ).
fof(f531,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f530]) ).
fof(f532,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f446,f95]) ).
fof(f533,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f532]) ).
fof(f534,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f443,f92]) ).
fof(f535,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f534]) ).
fof(f536,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f440,f90]) ).
fof(f537,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f536]) ).
fof(f538,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f437,f88]) ).
fof(f539,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f538]) ).
fof(f540,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f434,f87]) ).
fof(f541,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f540]) ).
fof(f542,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f431,f86]) ).
fof(f543,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f542]) ).
fof(f544,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f428,f85]) ).
fof(f545,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f544]) ).
fof(f546,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f425,f84]) ).
fof(f547,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f546]) ).
fof(f548,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f421,f83]) ).
fof(f549,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f548]) ).
fof(f567,plain,
! [X0] : sK21_skl(X0) = sK20_skl,
inference(forward_demodulation,[status(thm)],[f463,f462]) ).
fof(f598,plain,
! [X0,X1] : r1_tarski(k3_xboole_0(X0,X1),X1),
inference(paramodulation,[status(thm)],[f123,f287]) ).
fof(f623,plain,
( sQ21_spl
| ~ r1_tarski(k3_xboole_0(sK2_skl,sK3_skl),sK3_skl)
| ~ m1_subset_1(sK3_skl,k1_zfmisc_1(u1_struct_0(sK1_skl)))
| ~ m1_subset_1(k3_xboole_0(sK2_skl,sK3_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)
| ~ 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)],[f516,f286]) ).
fof(f624,definition,
( sQ22_spl
<=> v7_group_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f626,plain,
( sQ22_spl
| ~ v7_group_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f624]) ).
fof(f627,definition,
( sQ23_spl
<=> v7_vectsp_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f629,plain,
( sQ23_spl
| ~ v7_vectsp_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f627]) ).
fof(f630,definition,
( sQ24_spl
<=> v10_vectsp_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f631,plain,
( ~ sQ24_spl
| v10_vectsp_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f630]) ).
fof(f633,definition,
( sQ25_spl
<=> v2_vectsp_2(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f635,plain,
( sQ25_spl
| ~ v2_vectsp_2(sK0_skl) ),
inference(component_clause,[status(thm)],[f633]) ).
fof(f636,definition,
( sQ26_spl
<=> m1_subset_1(k3_xboole_0(sK2_skl,sK3_skl),k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f638,plain,
( sQ26_spl
| ~ m1_subset_1(k3_xboole_0(sK2_skl,sK3_skl),k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
inference(component_clause,[status(thm)],[f636]) ).
fof(f639,definition,
( sQ27_spl
<=> m1_subset_1(sK3_skl,k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f641,plain,
( sQ27_spl
| ~ m1_subset_1(sK3_skl,k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
inference(component_clause,[status(thm)],[f639]) ).
fof(f642,definition,
( sQ28_spl
<=> r1_tarski(k3_xboole_0(sK2_skl,sK3_skl),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f644,plain,
( sQ28_spl
| ~ r1_tarski(k3_xboole_0(sK2_skl,sK3_skl),sK3_skl) ),
inference(component_clause,[status(thm)],[f642]) ).
fof(f645,plain,
( sQ21_spl
| ~ sQ28_spl
| ~ sQ27_spl
| ~ sQ26_spl
| ~ sQ16_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sQ10_spl
| ~ sQ8_spl
| ~ sQ25_spl
| sQ24_spl
| ~ sQ7_spl
| ~ sQ23_spl
| ~ sQ6_spl
| ~ sQ22_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f623,f420,f423,f426,f429,f432,f435,f624,f438,f627,f441,f630,f633,f444,f481,f484,f487,f490,f493,f496,f499,f636,f639,f642,f514]) ).
fof(f646,plain,
( sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f641,f104]) ).
fof(f647,plain,
sQ27_spl,
inference(contradiction_clause,[status(thm)],[f646]) ).
fof(f648,plain,
( sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f638,f344]) ).
fof(f649,plain,
sQ26_spl,
inference(contradiction_clause,[status(thm)],[f648]) ).
fof(f650,plain,
( sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f635,f94]) ).
fof(f651,plain,
sQ25_spl,
inference(contradiction_clause,[status(thm)],[f650]) ).
fof(f652,plain,
( ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f631,f93]) ).
fof(f653,plain,
~ sQ24_spl,
inference(contradiction_clause,[status(thm)],[f652]) ).
fof(f654,plain,
( sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f629,f91]) ).
fof(f655,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f654]) ).
fof(f656,plain,
( sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f626,f89]) ).
fof(f657,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f656]) ).
fof(f660,plain,
( sQ28_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f644,f598]) ).
fof(f665,plain,
sQ28_spl,
inference(contradiction_clause,[status(thm)],[f660]) ).
fof(f726,definition,
( sQ30_spl
<=> m1_subset_1(sK2_skl,k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f728,plain,
( sQ30_spl
| ~ m1_subset_1(sK2_skl,k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
inference(component_clause,[status(thm)],[f726]) ).
fof(f733,plain,
( sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f728,f103]) ).
fof(f734,plain,
sQ30_spl,
inference(contradiction_clause,[status(thm)],[f733]) ).
fof(f762,plain,
( sQ20_spl
| ~ r1_tarski(k3_xboole_0(sK2_skl,sK3_skl),sK2_skl)
| ~ m1_subset_1(sK2_skl,k1_zfmisc_1(u1_struct_0(sK1_skl)))
| ~ m1_subset_1(k3_xboole_0(sK2_skl,sK3_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)
| ~ 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)],[f513,f286]) ).
fof(f763,definition,
( sQ32_spl
<=> r1_tarski(k3_xboole_0(sK2_skl,sK3_skl),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f765,plain,
( sQ32_spl
| ~ r1_tarski(k3_xboole_0(sK2_skl,sK3_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f763]) ).
fof(f766,plain,
( sQ20_spl
| ~ sQ32_spl
| ~ sQ30_spl
| ~ sQ26_spl
| ~ sQ16_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sQ10_spl
| ~ sQ8_spl
| ~ sQ25_spl
| sQ24_spl
| ~ sQ7_spl
| ~ sQ23_spl
| ~ sQ6_spl
| ~ sQ22_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f762,f420,f423,f426,f429,f432,f435,f624,f438,f627,f441,f630,f633,f444,f481,f484,f487,f490,f493,f496,f499,f636,f726,f763,f511]) ).
fof(f767,plain,
( sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f765,f287]) ).
fof(f768,plain,
sQ32_spl,
inference(contradiction_clause,[status(thm)],[f767]) ).
fof(f769,plain,
! [X0] : m1_subset_1(sK20_skl,k1_zfmisc_1(X0)),
inference(forward_demodulation,[status(thm)],[f567,f255]) ).
fof(f801,definition,
! [X0] :
( sQ33_spl
<=> ~ m1_subset_1(sK20_skl,k1_zfmisc_1(X0)) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f802,plain,
! [X0] :
( ~ sQ33_spl
| ~ m1_subset_1(sK20_skl,k1_zfmisc_1(X0)) ),
inference(component_clause,[status(thm)],[f801]) ).
fof(f808,plain,
( ~ sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f802,f769]) ).
fof(f809,plain,
~ sQ33_spl,
inference(contradiction_clause,[status(thm)],[f808]) ).
fof(f814,plain,
( sQ19_spl
| ~ m1_subset_1(sK3_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)
| ~ 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)],[f510,f131]) ).
fof(f815,plain,
( sQ19_spl
| ~ sQ27_spl
| ~ sQ16_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sQ10_spl
| ~ sQ8_spl
| ~ sQ25_spl
| sQ24_spl
| ~ sQ7_spl
| ~ sQ23_spl
| ~ sQ6_spl
| ~ sQ22_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f814,f420,f423,f426,f429,f432,f435,f624,f438,f627,f441,f630,f633,f444,f481,f484,f487,f490,f493,f496,f499,f639,f508]) ).
fof(f902,plain,
( sQ17_spl
| ~ m1_subset_1(k3_xboole_0(sK2_skl,sK3_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)
| ~ 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)],[f504,f131]) ).
fof(f903,plain,
( sQ17_spl
| ~ sQ26_spl
| ~ sQ16_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sQ10_spl
| ~ sQ8_spl
| ~ sQ25_spl
| sQ24_spl
| ~ sQ7_spl
| ~ sQ23_spl
| ~ sQ6_spl
| ~ sQ22_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f902,f420,f423,f426,f429,f432,f435,f624,f438,f627,f441,f630,f633,f444,f481,f484,f487,f490,f493,f496,f499,f636,f502]) ).
fof(f979,plain,
( sQ18_spl
| ~ 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)
| ~ 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)],[f507,f131]) ).
fof(f980,plain,
( sQ18_spl
| ~ sQ30_spl
| ~ sQ16_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sQ10_spl
| ~ sQ8_spl
| ~ sQ25_spl
| sQ24_spl
| ~ sQ7_spl
| ~ sQ23_spl
| ~ sQ6_spl
| ~ sQ22_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f979,f420,f423,f426,f429,f432,f435,f624,f438,f627,f441,f630,f633,f444,f481,f484,f487,f490,f493,f496,f499,f726,f505]) ).
fof(f981,plain,
$false,
inference(sat_refutation,[status(thm)],[f450,f517,f519,f521,f523,f525,f527,f529,f531,f533,f535,f537,f539,f541,f543,f545,f547,f549,f645,f647,f649,f651,f653,f655,f657,f665,f734,f766,f768,f809,f815,f903,f980]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG222+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 13:05:50 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 0.11/0.47 % Refutation found
% 0.11/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.49 % Elapsed time: 0.114619 seconds
% 0.11/0.49 % CPU time: 0.573891 seconds
% 0.11/0.49 % Total memory used: 118.604 MB
% 0.11/0.49 % Net memory used: 117.879 MB
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