%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG222+2 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 11:49:01 AM UTC 2026
% Result : Theorem 100.40s 13.64s
% Output : CNFRefutation 100.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 39
% Syntax : Number of formulae : 176 ( 54 unt; 31 def)
% Number of atoms : 833 ( 7 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 1086 ( 429 ~; 466 |; 138 &)
% ( 31 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 52 ( 50 usr; 32 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-4 aty)
% Number of variables : 84 ( 80 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f57,axiom,
! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f86,axiom,
! [A,B] : r1_tarski(k3_xboole_0(A,B),A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f571,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(f574,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(f3273,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(f3442,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(f3459,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(f3462,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(f3463,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)],[f3462]) ).
fof(f3672,plain,
! [X0,X1] : k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f3723,plain,
! [X0,X1] : r1_tarski(k3_xboole_0(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f4684,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)],[f571]) ).
fof(f4685,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X1))
| m1_subset_1(k5_subset_1(X1,X2,X0),k1_zfmisc_1(X1))
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[status(thm)],[f4684]) ).
fof(f4691,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)],[f574]) ).
fof(f4692,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X0,k1_zfmisc_1(X2))
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| k3_xboole_0(X0,X1) = k5_subset_1(X2,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f4691]) ).
fof(f12668,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)],[f3273]) ).
fof(f12669,plain,
! [X0,X1,X2,X3,X4] :
( ~ v4_group_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X0)
| ~ v7_vectsp_1(X1)
| ~ v5_vectsp_2(X0,X1)
| v3_struct_0(X0)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X0)
| ~ m1_rmod_2(X2,X1,X0)
| ~ v6_vectsp_1(X1)
| ~ m1_rmod_2(X2,X1,X3)
| ~ m1_rmod_2(X4,X1,X0)
| ~ v3_rlvect_1(X0)
| ~ m1_rmod_2(X3,X1,X0)
| ~ l3_vectsp_1(X1)
| ~ v3_rlvect_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v6_rlvect_1(X0)
| ~ m1_rmod_2(X2,X1,X4)
| m1_rmod_2(X2,X1,k2_rmod_3(X1,X0,X3,X4))
| v3_struct_0(X1)
| ~ v4_rlvect_1(X1)
| ~ l1_vectsp_2(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f12668]) ).
fof(f13110,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)],[f3442]) ).
fof(f13112,plain,
! [X0,X1,X2] :
( ~ l1_vectsp_2(X2,X0)
| ~ l3_vectsp_1(X0)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v3_rlvect_1(X0)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X0)
| ~ v4_group_1(X0)
| ~ v5_vectsp_2(X2,X0)
| ~ v4_rlvect_1(X0)
| v3_struct_0(X2)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v2_vectsp_2(X0)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| v10_vectsp_1(X0)
| ~ v7_group_1(X0)
| m1_rmod_2(k1_rmod_5(X0,X2,X1),X0,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f13110]) ).
fof(f13154,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)],[f3459]) ).
fof(f13155,plain,
! [X0,X1,X2,X3] :
( ~ v5_vectsp_2(X2,X0)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
| ~ v8_vectsp_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| v3_struct_0(X0)
| ~ l3_vectsp_1(X0)
| ~ v2_vectsp_2(X0)
| ~ r1_tarski(X1,X3)
| ~ l1_vectsp_2(X2,X0)
| ~ v3_rlvect_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v3_rlvect_1(X2)
| v3_struct_0(X2)
| ~ v7_vectsp_1(X0)
| ~ v5_rlvect_1(X0)
| m1_rmod_2(k1_rmod_5(X0,X2,X1),X0,k1_rmod_5(X0,X2,X3))
| ~ v6_rlvect_1(X2)
| ~ v7_group_1(X0)
| ~ v4_group_1(X0)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))
| v10_vectsp_1(X0) ),
inference(cnf_transformation,[status(thm)],[f13154]) ).
fof(f13160,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)],[f3463]) ).
fof(f13161,plain,
( ~ m1_rmod_2(k1_rmod_5(sK845_skl,sK846_skl,k5_subset_1(u1_struct_0(sK846_skl),sK847_skl,sK848_skl)),sK845_skl,k2_rmod_3(sK845_skl,sK846_skl,k1_rmod_5(sK845_skl,sK846_skl,sK847_skl),k1_rmod_5(sK845_skl,sK846_skl,sK848_skl)))
& m1_subset_1(sK848_skl,k1_zfmisc_1(u1_struct_0(sK846_skl)))
& m1_subset_1(sK847_skl,k1_zfmisc_1(u1_struct_0(sK846_skl)))
& l1_vectsp_2(sK846_skl,sK845_skl)
& v5_vectsp_2(sK846_skl,sK845_skl)
& v6_rlvect_1(sK846_skl)
& v5_rlvect_1(sK846_skl)
& v4_rlvect_1(sK846_skl)
& v3_rlvect_1(sK846_skl)
& ~ v3_struct_0(sK846_skl)
& l3_vectsp_1(sK845_skl)
& v2_vectsp_2(sK845_skl)
& ~ v10_vectsp_1(sK845_skl)
& v8_vectsp_1(sK845_skl)
& v7_vectsp_1(sK845_skl)
& v6_vectsp_1(sK845_skl)
& v7_group_1(sK845_skl)
& v4_group_1(sK845_skl)
& v6_rlvect_1(sK845_skl)
& v5_rlvect_1(sK845_skl)
& v4_rlvect_1(sK845_skl)
& v3_rlvect_1(sK845_skl)
& ~ v3_struct_0(sK845_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK845_skl,sK846_skl,sK847_skl,sK848_skl]),skolemize(A,sK845_skl),skolemize(B,sK846_skl),skolemize(C,sK847_skl),skolemize(D,sK848_skl)],[f13160]) ).
fof(f13162,plain,
~ v3_struct_0(sK845_skl),
inference(cnf_transformation,[status(thm)],[f13161]) ).
fof(f13163,plain,
v3_rlvect_1(sK845_skl),
inference(cnf_transformation,[status(thm)],[f13161]) ).
fof(f13164,plain,
v4_rlvect_1(sK845_skl),
inference(cnf_transformation,[status(thm)],[f13161]) ).
fof(f13165,plain,
v5_rlvect_1(sK845_skl),
inference(cnf_transformation,[status(thm)],[f13161]) ).
fof(f13166,plain,
v6_rlvect_1(sK845_skl),
inference(cnf_transformation,[status(thm)],[f13161]) ).
fof(f13167,plain,
v4_group_1(sK845_skl),
inference(cnf_transformation,[status(thm)],[f13161]) ).
fof(f13168,plain,
v7_group_1(sK845_skl),
inference(cnf_transformation,[status(thm)],[f13161]) ).
fof(f13169,plain,
v6_vectsp_1(sK845_skl),
inference(cnf_transformation,[status(thm)],[f13161]) ).
fof(f13170,plain,
v7_vectsp_1(sK845_skl),
inference(cnf_transformation,[status(thm)],[f13161]) ).
fof(f13171,plain,
v8_vectsp_1(sK845_skl),
inference(cnf_transformation,[status(thm)],[f13161]) ).
fof(f13172,plain,
~ v10_vectsp_1(sK845_skl),
inference(cnf_transformation,[status(thm)],[f13161]) ).
fof(f13173,plain,
v2_vectsp_2(sK845_skl),
inference(cnf_transformation,[status(thm)],[f13161]) ).
fof(f13174,plain,
l3_vectsp_1(sK845_skl),
inference(cnf_transformation,[status(thm)],[f13161]) ).
fof(f13175,plain,
~ v3_struct_0(sK846_skl),
inference(cnf_transformation,[status(thm)],[f13161]) ).
fof(f13176,plain,
v3_rlvect_1(sK846_skl),
inference(cnf_transformation,[status(thm)],[f13161]) ).
fof(f13177,plain,
v4_rlvect_1(sK846_skl),
inference(cnf_transformation,[status(thm)],[f13161]) ).
fof(f13178,plain,
v5_rlvect_1(sK846_skl),
inference(cnf_transformation,[status(thm)],[f13161]) ).
fof(f13179,plain,
v6_rlvect_1(sK846_skl),
inference(cnf_transformation,[status(thm)],[f13161]) ).
fof(f13180,plain,
v5_vectsp_2(sK846_skl,sK845_skl),
inference(cnf_transformation,[status(thm)],[f13161]) ).
fof(f13181,plain,
l1_vectsp_2(sK846_skl,sK845_skl),
inference(cnf_transformation,[status(thm)],[f13161]) ).
fof(f13182,plain,
m1_subset_1(sK847_skl,k1_zfmisc_1(u1_struct_0(sK846_skl))),
inference(cnf_transformation,[status(thm)],[f13161]) ).
fof(f13183,plain,
m1_subset_1(sK848_skl,k1_zfmisc_1(u1_struct_0(sK846_skl))),
inference(cnf_transformation,[status(thm)],[f13161]) ).
fof(f13184,plain,
~ m1_rmod_2(k1_rmod_5(sK845_skl,sK846_skl,k5_subset_1(u1_struct_0(sK846_skl),sK847_skl,sK848_skl)),sK845_skl,k2_rmod_3(sK845_skl,sK846_skl,k1_rmod_5(sK845_skl,sK846_skl,sK847_skl),k1_rmod_5(sK845_skl,sK846_skl,sK848_skl))),
inference(cnf_transformation,[status(thm)],[f13161]) ).
fof(f16994,definition,
( sQ515_spl
<=> v7_vectsp_1(sK845_skl) ),
introduced(definition,[new_symbols(definition,[sQ515_spl])],[split_symbol_definition]) ).
fof(f16996,plain,
( sQ515_spl
| ~ v7_vectsp_1(sK845_skl) ),
inference(component_clause,[status(thm)],[f16994]) ).
fof(f16997,definition,
( sQ516_spl
<=> v7_group_1(sK845_skl) ),
introduced(definition,[new_symbols(definition,[sQ516_spl])],[split_symbol_definition]) ).
fof(f16999,plain,
( sQ516_spl
| ~ v7_group_1(sK845_skl) ),
inference(component_clause,[status(thm)],[f16997]) ).
fof(f17000,definition,
( sQ517_spl
<=> v6_rlvect_1(sK845_skl) ),
introduced(definition,[new_symbols(definition,[sQ517_spl])],[split_symbol_definition]) ).
fof(f17002,plain,
( sQ517_spl
| ~ v6_rlvect_1(sK845_skl) ),
inference(component_clause,[status(thm)],[f17000]) ).
fof(f17006,definition,
( sQ519_spl
<=> l3_vectsp_1(sK845_skl) ),
introduced(definition,[new_symbols(definition,[sQ519_spl])],[split_symbol_definition]) ).
fof(f17008,plain,
( sQ519_spl
| ~ l3_vectsp_1(sK845_skl) ),
inference(component_clause,[status(thm)],[f17006]) ).
fof(f17009,definition,
( sQ520_spl
<=> v10_vectsp_1(sK845_skl) ),
introduced(definition,[new_symbols(definition,[sQ520_spl])],[split_symbol_definition]) ).
fof(f17010,plain,
( ~ sQ520_spl
| v10_vectsp_1(sK845_skl) ),
inference(component_clause,[status(thm)],[f17009]) ).
fof(f17012,definition,
( sQ521_spl
<=> v5_rlvect_1(sK845_skl) ),
introduced(definition,[new_symbols(definition,[sQ521_spl])],[split_symbol_definition]) ).
fof(f17014,plain,
( sQ521_spl
| ~ v5_rlvect_1(sK845_skl) ),
inference(component_clause,[status(thm)],[f17012]) ).
fof(f17015,definition,
( sQ522_spl
<=> v4_group_1(sK845_skl) ),
introduced(definition,[new_symbols(definition,[sQ522_spl])],[split_symbol_definition]) ).
fof(f17017,plain,
( sQ522_spl
| ~ v4_group_1(sK845_skl) ),
inference(component_clause,[status(thm)],[f17015]) ).
fof(f17018,definition,
( sQ523_spl
<=> v3_struct_0(sK845_skl) ),
introduced(definition,[new_symbols(definition,[sQ523_spl])],[split_symbol_definition]) ).
fof(f17019,plain,
( ~ sQ523_spl
| v3_struct_0(sK845_skl) ),
inference(component_clause,[status(thm)],[f17018]) ).
fof(f17021,definition,
( sQ524_spl
<=> v3_rlvect_1(sK845_skl) ),
introduced(definition,[new_symbols(definition,[sQ524_spl])],[split_symbol_definition]) ).
fof(f17023,plain,
( sQ524_spl
| ~ v3_rlvect_1(sK845_skl) ),
inference(component_clause,[status(thm)],[f17021]) ).
fof(f17024,definition,
( sQ525_spl
<=> v2_vectsp_2(sK845_skl) ),
introduced(definition,[new_symbols(definition,[sQ525_spl])],[split_symbol_definition]) ).
fof(f17026,plain,
( sQ525_spl
| ~ v2_vectsp_2(sK845_skl) ),
inference(component_clause,[status(thm)],[f17024]) ).
fof(f17027,definition,
( sQ526_spl
<=> v4_rlvect_1(sK845_skl) ),
introduced(definition,[new_symbols(definition,[sQ526_spl])],[split_symbol_definition]) ).
fof(f17029,plain,
( sQ526_spl
| ~ v4_rlvect_1(sK845_skl) ),
inference(component_clause,[status(thm)],[f17027]) ).
fof(f17030,definition,
( sQ527_spl
<=> v8_vectsp_1(sK845_skl) ),
introduced(definition,[new_symbols(definition,[sQ527_spl])],[split_symbol_definition]) ).
fof(f17032,plain,
( sQ527_spl
| ~ v8_vectsp_1(sK845_skl) ),
inference(component_clause,[status(thm)],[f17030]) ).
fof(f17034,plain,
( sQ521_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f17014,f13165]) ).
fof(f17035,plain,
sQ521_spl,
inference(contradiction_clause,[status(thm)],[f17034]) ).
fof(f17036,plain,
( sQ526_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f17029,f13164]) ).
fof(f17037,plain,
sQ526_spl,
inference(contradiction_clause,[status(thm)],[f17036]) ).
fof(f17038,plain,
( sQ516_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f16999,f13168]) ).
fof(f17039,plain,
sQ516_spl,
inference(contradiction_clause,[status(thm)],[f17038]) ).
fof(f17040,plain,
( sQ524_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f17023,f13163]) ).
fof(f17041,plain,
sQ524_spl,
inference(contradiction_clause,[status(thm)],[f17040]) ).
fof(f17042,plain,
( ~ sQ523_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f17019,f13162]) ).
fof(f17043,plain,
~ sQ523_spl,
inference(contradiction_clause,[status(thm)],[f17042]) ).
fof(f17044,plain,
( sQ517_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f17002,f13166]) ).
fof(f17045,plain,
sQ517_spl,
inference(contradiction_clause,[status(thm)],[f17044]) ).
fof(f17046,plain,
( ~ sQ520_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f17010,f13172]) ).
fof(f17047,plain,
~ sQ520_spl,
inference(contradiction_clause,[status(thm)],[f17046]) ).
fof(f17048,plain,
( sQ519_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f17008,f13174]) ).
fof(f17049,plain,
sQ519_spl,
inference(contradiction_clause,[status(thm)],[f17048]) ).
fof(f17053,definition,
( sQ528_spl
<=> v6_vectsp_1(sK845_skl) ),
introduced(definition,[new_symbols(definition,[sQ528_spl])],[split_symbol_definition]) ).
fof(f17055,plain,
( sQ528_spl
| ~ v6_vectsp_1(sK845_skl) ),
inference(component_clause,[status(thm)],[f17053]) ).
fof(f17057,plain,
( sQ528_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f17055,f13169]) ).
fof(f17058,plain,
sQ528_spl,
inference(contradiction_clause,[status(thm)],[f17057]) ).
fof(f17083,plain,
! [X0,X1,X2] :
( ~ v7_group_1(sK845_skl)
| ~ v7_vectsp_1(sK845_skl)
| ~ v3_rlvect_1(sK845_skl)
| ~ v6_vectsp_1(sK845_skl)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
| ~ r1_tarski(X1,X2)
| ~ v4_rlvect_1(sK845_skl)
| ~ v4_rlvect_1(X0)
| ~ l1_vectsp_2(X0,sK845_skl)
| ~ v6_rlvect_1(sK845_skl)
| ~ v6_rlvect_1(X0)
| ~ v4_group_1(sK845_skl)
| ~ v3_rlvect_1(X0)
| m1_rmod_2(k1_rmod_5(sK845_skl,X0,X1),sK845_skl,k1_rmod_5(sK845_skl,X0,X2))
| v3_struct_0(sK845_skl)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ v5_rlvect_1(X0)
| v3_struct_0(X0)
| ~ v5_vectsp_2(X0,sK845_skl)
| v10_vectsp_1(sK845_skl)
| ~ l3_vectsp_1(sK845_skl)
| ~ v5_rlvect_1(sK845_skl)
| ~ v2_vectsp_2(sK845_skl) ),
inference(resolution,[status(thm)],[f13171,f13155]) ).
fof(f17093,definition,
! [X0,X1,X2] :
( sQ533_spl
<=> ( ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
| ~ r1_tarski(X1,X2)
| ~ v4_rlvect_1(X0)
| ~ l1_vectsp_2(X0,sK845_skl)
| ~ v6_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| m1_rmod_2(k1_rmod_5(sK845_skl,X0,X1),sK845_skl,k1_rmod_5(sK845_skl,X0,X2))
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ v5_rlvect_1(X0)
| v3_struct_0(X0)
| ~ v5_vectsp_2(X0,sK845_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ533_spl])],[split_symbol_definition]) ).
fof(f17094,plain,
! [X0,X1,X2] :
( ~ sQ533_spl
| ~ v5_rlvect_1(X0)
| v3_struct_0(X0)
| ~ l1_vectsp_2(X0,sK845_skl)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
| ~ r1_tarski(X1,X2)
| ~ v6_rlvect_1(X0)
| m1_rmod_2(k1_rmod_5(sK845_skl,X0,X1),sK845_skl,k1_rmod_5(sK845_skl,X0,X2))
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| ~ v5_vectsp_2(X0,sK845_skl) ),
inference(component_clause,[status(thm)],[f17093]) ).
fof(f17096,plain,
( ~ sQ516_spl
| ~ sQ515_spl
| ~ sQ524_spl
| ~ sQ528_spl
| ~ sQ526_spl
| ~ sQ517_spl
| ~ sQ522_spl
| sQ523_spl
| sQ533_spl
| sQ520_spl
| ~ sQ519_spl
| ~ sQ521_spl
| ~ sQ525_spl ),
inference(split_clause,[status(thm)],[f17083,f17024,f17012,f17006,f17009,f17093,f17018,f17015,f17000,f17027,f17053,f17021,f16994,f16997]) ).
fof(f17102,plain,
( sQ522_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f17017,f13167]) ).
fof(f17103,plain,
sQ522_spl,
inference(contradiction_clause,[status(thm)],[f17102]) ).
fof(f17106,plain,
( sQ525_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f17026,f13173]) ).
fof(f17107,plain,
sQ525_spl,
inference(contradiction_clause,[status(thm)],[f17106]) ).
fof(f17112,definition,
( sQ535_spl
<=> m1_subset_1(sK848_skl,k1_zfmisc_1(u1_struct_0(sK846_skl))) ),
introduced(definition,[new_symbols(definition,[sQ535_spl])],[split_symbol_definition]) ).
fof(f17114,plain,
( sQ535_spl
| ~ m1_subset_1(sK848_skl,k1_zfmisc_1(u1_struct_0(sK846_skl))) ),
inference(component_clause,[status(thm)],[f17112]) ).
fof(f17119,plain,
! [X0] :
( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK846_skl)))
| k5_subset_1(u1_struct_0(sK846_skl),X0,sK848_skl) = k3_xboole_0(X0,sK848_skl) ),
inference(resolution,[status(thm)],[f4692,f13183]) ).
fof(f17141,plain,
( sQ535_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f17114,f13183]) ).
fof(f17142,plain,
sQ535_spl,
inference(contradiction_clause,[status(thm)],[f17141]) ).
fof(f17160,plain,
( sQ527_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f17032,f13171]) ).
fof(f17161,plain,
sQ527_spl,
inference(contradiction_clause,[status(thm)],[f17160]) ).
fof(f17185,plain,
( sQ515_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f16996,f13170]) ).
fof(f17186,plain,
sQ515_spl,
inference(contradiction_clause,[status(thm)],[f17185]) ).
fof(f17214,definition,
( sQ542_spl
<=> m1_subset_1(sK847_skl,k1_zfmisc_1(u1_struct_0(sK846_skl))) ),
introduced(definition,[new_symbols(definition,[sQ542_spl])],[split_symbol_definition]) ).
fof(f17216,plain,
( sQ542_spl
| ~ m1_subset_1(sK847_skl,k1_zfmisc_1(u1_struct_0(sK846_skl))) ),
inference(component_clause,[status(thm)],[f17214]) ).
fof(f17222,plain,
( sQ542_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f17216,f13182]) ).
fof(f17223,plain,
sQ542_spl,
inference(contradiction_clause,[status(thm)],[f17222]) ).
fof(f17315,plain,
k3_xboole_0(sK847_skl,sK848_skl) = k5_subset_1(u1_struct_0(sK846_skl),sK847_skl,sK848_skl),
inference(resolution,[status(thm)],[f17119,f13182]) ).
fof(f17321,definition,
( sQ550_spl
<=> v5_rlvect_1(sK846_skl) ),
introduced(definition,[new_symbols(definition,[sQ550_spl])],[split_symbol_definition]) ).
fof(f17323,plain,
( sQ550_spl
| ~ v5_rlvect_1(sK846_skl) ),
inference(component_clause,[status(thm)],[f17321]) ).
fof(f17324,definition,
( sQ551_spl
<=> v6_rlvect_1(sK846_skl) ),
introduced(definition,[new_symbols(definition,[sQ551_spl])],[split_symbol_definition]) ).
fof(f17326,plain,
( sQ551_spl
| ~ v6_rlvect_1(sK846_skl) ),
inference(component_clause,[status(thm)],[f17324]) ).
fof(f17330,definition,
( sQ553_spl
<=> v3_rlvect_1(sK846_skl) ),
introduced(definition,[new_symbols(definition,[sQ553_spl])],[split_symbol_definition]) ).
fof(f17332,plain,
( sQ553_spl
| ~ v3_rlvect_1(sK846_skl) ),
inference(component_clause,[status(thm)],[f17330]) ).
fof(f17333,definition,
( sQ554_spl
<=> v4_rlvect_1(sK846_skl) ),
introduced(definition,[new_symbols(definition,[sQ554_spl])],[split_symbol_definition]) ).
fof(f17335,plain,
( sQ554_spl
| ~ v4_rlvect_1(sK846_skl) ),
inference(component_clause,[status(thm)],[f17333]) ).
fof(f17336,definition,
( sQ555_spl
<=> v3_struct_0(sK846_skl) ),
introduced(definition,[new_symbols(definition,[sQ555_spl])],[split_symbol_definition]) ).
fof(f17337,plain,
( ~ sQ555_spl
| v3_struct_0(sK846_skl) ),
inference(component_clause,[status(thm)],[f17336]) ).
fof(f17339,definition,
( sQ556_spl
<=> l1_vectsp_2(sK846_skl,sK845_skl) ),
introduced(definition,[new_symbols(definition,[sQ556_spl])],[split_symbol_definition]) ).
fof(f17341,plain,
( sQ556_spl
| ~ l1_vectsp_2(sK846_skl,sK845_skl) ),
inference(component_clause,[status(thm)],[f17339]) ).
fof(f17343,plain,
( sQ556_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f17341,f13181]) ).
fof(f17344,plain,
sQ556_spl,
inference(contradiction_clause,[status(thm)],[f17343]) ).
fof(f17345,plain,
( sQ551_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f17326,f13179]) ).
fof(f17346,plain,
sQ551_spl,
inference(contradiction_clause,[status(thm)],[f17345]) ).
fof(f17347,plain,
( sQ550_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f17323,f13178]) ).
fof(f17348,plain,
sQ550_spl,
inference(contradiction_clause,[status(thm)],[f17347]) ).
fof(f17349,plain,
( sQ554_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f17335,f13177]) ).
fof(f17350,plain,
sQ554_spl,
inference(contradiction_clause,[status(thm)],[f17349]) ).
fof(f17351,plain,
( sQ553_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f17332,f13176]) ).
fof(f17352,plain,
sQ553_spl,
inference(contradiction_clause,[status(thm)],[f17351]) ).
fof(f17353,plain,
( ~ sQ555_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f17337,f13175]) ).
fof(f17354,plain,
~ sQ555_spl,
inference(contradiction_clause,[status(thm)],[f17353]) ).
fof(f17367,plain,
~ m1_rmod_2(k1_rmod_5(sK845_skl,sK846_skl,k3_xboole_0(sK847_skl,sK848_skl)),sK845_skl,k2_rmod_3(sK845_skl,sK846_skl,k1_rmod_5(sK845_skl,sK846_skl,sK847_skl),k1_rmod_5(sK845_skl,sK846_skl,sK848_skl))),
inference(backward_demodulation,[status(thm)],[f17315,f13184]) ).
fof(f17369,plain,
( ~ m1_subset_1(sK847_skl,k1_zfmisc_1(u1_struct_0(sK846_skl)))
| ~ m1_subset_1(sK848_skl,k1_zfmisc_1(u1_struct_0(sK846_skl)))
| m1_subset_1(k3_xboole_0(sK847_skl,sK848_skl),k1_zfmisc_1(u1_struct_0(sK846_skl))) ),
inference(paramodulation,[status(thm)],[f17315,f4685]) ).
fof(f17380,definition,
( sQ560_spl
<=> m1_subset_1(k3_xboole_0(sK847_skl,sK848_skl),k1_zfmisc_1(u1_struct_0(sK846_skl))) ),
introduced(definition,[new_symbols(definition,[sQ560_spl])],[split_symbol_definition]) ).
fof(f17383,plain,
( ~ sQ542_spl
| ~ sQ535_spl
| sQ560_spl ),
inference(split_clause,[status(thm)],[f17369,f17380,f17112,f17214]) ).
fof(f17388,plain,
( ~ v4_group_1(sK845_skl)
| ~ v6_rlvect_1(sK845_skl)
| ~ v5_rlvect_1(sK846_skl)
| ~ v7_vectsp_1(sK845_skl)
| ~ v5_vectsp_2(sK846_skl,sK845_skl)
| v3_struct_0(sK846_skl)
| ~ v5_rlvect_1(sK845_skl)
| ~ v4_rlvect_1(sK846_skl)
| ~ m1_rmod_2(k1_rmod_5(sK845_skl,sK846_skl,k3_xboole_0(sK847_skl,sK848_skl)),sK845_skl,sK846_skl)
| ~ v6_vectsp_1(sK845_skl)
| ~ m1_rmod_2(k1_rmod_5(sK845_skl,sK846_skl,k3_xboole_0(sK847_skl,sK848_skl)),sK845_skl,k1_rmod_5(sK845_skl,sK846_skl,sK847_skl))
| ~ m1_rmod_2(k1_rmod_5(sK845_skl,sK846_skl,sK848_skl),sK845_skl,sK846_skl)
| ~ v3_rlvect_1(sK846_skl)
| ~ m1_rmod_2(k1_rmod_5(sK845_skl,sK846_skl,sK847_skl),sK845_skl,sK846_skl)
| ~ l3_vectsp_1(sK845_skl)
| ~ v3_rlvect_1(sK845_skl)
| ~ v8_vectsp_1(sK845_skl)
| ~ v6_rlvect_1(sK846_skl)
| ~ m1_rmod_2(k1_rmod_5(sK845_skl,sK846_skl,k3_xboole_0(sK847_skl,sK848_skl)),sK845_skl,k1_rmod_5(sK845_skl,sK846_skl,sK848_skl))
| v3_struct_0(sK845_skl)
| ~ v4_rlvect_1(sK845_skl)
| ~ l1_vectsp_2(sK846_skl,sK845_skl) ),
inference(resolution,[status(thm)],[f17367,f12669]) ).
fof(f17389,definition,
( sQ561_spl
<=> m1_rmod_2(k1_rmod_5(sK845_skl,sK846_skl,k3_xboole_0(sK847_skl,sK848_skl)),sK845_skl,k1_rmod_5(sK845_skl,sK846_skl,sK848_skl)) ),
introduced(definition,[new_symbols(definition,[sQ561_spl])],[split_symbol_definition]) ).
fof(f17391,plain,
( sQ561_spl
| ~ m1_rmod_2(k1_rmod_5(sK845_skl,sK846_skl,k3_xboole_0(sK847_skl,sK848_skl)),sK845_skl,k1_rmod_5(sK845_skl,sK846_skl,sK848_skl)) ),
inference(component_clause,[status(thm)],[f17389]) ).
fof(f17392,definition,
( sQ562_spl
<=> m1_rmod_2(k1_rmod_5(sK845_skl,sK846_skl,sK847_skl),sK845_skl,sK846_skl) ),
introduced(definition,[new_symbols(definition,[sQ562_spl])],[split_symbol_definition]) ).
fof(f17394,plain,
( sQ562_spl
| ~ m1_rmod_2(k1_rmod_5(sK845_skl,sK846_skl,sK847_skl),sK845_skl,sK846_skl) ),
inference(component_clause,[status(thm)],[f17392]) ).
fof(f17395,definition,
( sQ563_spl
<=> m1_rmod_2(k1_rmod_5(sK845_skl,sK846_skl,sK848_skl),sK845_skl,sK846_skl) ),
introduced(definition,[new_symbols(definition,[sQ563_spl])],[split_symbol_definition]) ).
fof(f17397,plain,
( sQ563_spl
| ~ m1_rmod_2(k1_rmod_5(sK845_skl,sK846_skl,sK848_skl),sK845_skl,sK846_skl) ),
inference(component_clause,[status(thm)],[f17395]) ).
fof(f17398,definition,
( sQ564_spl
<=> m1_rmod_2(k1_rmod_5(sK845_skl,sK846_skl,k3_xboole_0(sK847_skl,sK848_skl)),sK845_skl,k1_rmod_5(sK845_skl,sK846_skl,sK847_skl)) ),
introduced(definition,[new_symbols(definition,[sQ564_spl])],[split_symbol_definition]) ).
fof(f17400,plain,
( sQ564_spl
| ~ m1_rmod_2(k1_rmod_5(sK845_skl,sK846_skl,k3_xboole_0(sK847_skl,sK848_skl)),sK845_skl,k1_rmod_5(sK845_skl,sK846_skl,sK847_skl)) ),
inference(component_clause,[status(thm)],[f17398]) ).
fof(f17401,definition,
( sQ565_spl
<=> m1_rmod_2(k1_rmod_5(sK845_skl,sK846_skl,k3_xboole_0(sK847_skl,sK848_skl)),sK845_skl,sK846_skl) ),
introduced(definition,[new_symbols(definition,[sQ565_spl])],[split_symbol_definition]) ).
fof(f17403,plain,
( sQ565_spl
| ~ m1_rmod_2(k1_rmod_5(sK845_skl,sK846_skl,k3_xboole_0(sK847_skl,sK848_skl)),sK845_skl,sK846_skl) ),
inference(component_clause,[status(thm)],[f17401]) ).
fof(f17404,definition,
( sQ566_spl
<=> v5_vectsp_2(sK846_skl,sK845_skl) ),
introduced(definition,[new_symbols(definition,[sQ566_spl])],[split_symbol_definition]) ).
fof(f17406,plain,
( sQ566_spl
| ~ v5_vectsp_2(sK846_skl,sK845_skl) ),
inference(component_clause,[status(thm)],[f17404]) ).
fof(f17407,plain,
( ~ sQ522_spl
| ~ sQ517_spl
| ~ sQ550_spl
| ~ sQ515_spl
| ~ sQ566_spl
| sQ555_spl
| ~ sQ521_spl
| ~ sQ554_spl
| ~ sQ565_spl
| ~ sQ528_spl
| ~ sQ564_spl
| ~ sQ563_spl
| ~ sQ553_spl
| ~ sQ562_spl
| ~ sQ519_spl
| ~ sQ524_spl
| ~ sQ527_spl
| ~ sQ551_spl
| ~ sQ561_spl
| sQ523_spl
| ~ sQ526_spl
| ~ sQ556_spl ),
inference(split_clause,[status(thm)],[f17388,f17339,f17027,f17018,f17389,f17324,f17030,f17021,f17006,f17392,f17330,f17395,f17398,f17053,f17401,f17333,f17012,f17336,f17404,f16994,f17321,f17000,f17015]) ).
fof(f17408,plain,
( sQ566_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f17406,f13180]) ).
fof(f17409,plain,
sQ566_spl,
inference(contradiction_clause,[status(thm)],[f17408]) ).
fof(f17410,plain,
( sQ562_spl
| v10_vectsp_1(sK845_skl)
| ~ v6_vectsp_1(sK845_skl)
| ~ v7_vectsp_1(sK845_skl)
| v3_struct_0(sK846_skl)
| ~ v8_vectsp_1(sK845_skl)
| ~ l1_vectsp_2(sK846_skl,sK845_skl)
| ~ v6_rlvect_1(sK846_skl)
| ~ v7_group_1(sK845_skl)
| v3_struct_0(sK845_skl)
| ~ v3_rlvect_1(sK846_skl)
| ~ l3_vectsp_1(sK845_skl)
| ~ v5_rlvect_1(sK846_skl)
| ~ v5_rlvect_1(sK845_skl)
| ~ v4_group_1(sK845_skl)
| ~ v6_rlvect_1(sK845_skl)
| ~ m1_subset_1(sK847_skl,k1_zfmisc_1(u1_struct_0(sK846_skl)))
| ~ v3_rlvect_1(sK845_skl)
| ~ v4_rlvect_1(sK846_skl)
| ~ v5_vectsp_2(sK846_skl,sK845_skl)
| ~ v2_vectsp_2(sK845_skl)
| ~ v4_rlvect_1(sK845_skl) ),
inference(resolution,[status(thm)],[f17394,f13112]) ).
fof(f17411,plain,
( sQ562_spl
| sQ520_spl
| ~ sQ528_spl
| ~ sQ515_spl
| sQ555_spl
| ~ sQ527_spl
| ~ sQ556_spl
| ~ sQ551_spl
| ~ sQ516_spl
| sQ523_spl
| ~ sQ553_spl
| ~ sQ519_spl
| ~ sQ550_spl
| ~ sQ521_spl
| ~ sQ522_spl
| ~ sQ517_spl
| ~ sQ542_spl
| ~ sQ524_spl
| ~ sQ554_spl
| ~ sQ566_spl
| ~ sQ525_spl
| ~ sQ526_spl ),
inference(split_clause,[status(thm)],[f17410,f17027,f17024,f17404,f17333,f17021,f17214,f17000,f17015,f17012,f17321,f17006,f17330,f17018,f16997,f17324,f17339,f17030,f17336,f16994,f17053,f17009,f17392]) ).
fof(f17412,plain,
( sQ563_spl
| v10_vectsp_1(sK845_skl)
| ~ v6_vectsp_1(sK845_skl)
| ~ v7_vectsp_1(sK845_skl)
| v3_struct_0(sK846_skl)
| ~ v8_vectsp_1(sK845_skl)
| ~ l1_vectsp_2(sK846_skl,sK845_skl)
| ~ v6_rlvect_1(sK846_skl)
| ~ v7_group_1(sK845_skl)
| v3_struct_0(sK845_skl)
| ~ v3_rlvect_1(sK846_skl)
| ~ l3_vectsp_1(sK845_skl)
| ~ v5_rlvect_1(sK846_skl)
| ~ v5_rlvect_1(sK845_skl)
| ~ v4_group_1(sK845_skl)
| ~ v6_rlvect_1(sK845_skl)
| ~ m1_subset_1(sK848_skl,k1_zfmisc_1(u1_struct_0(sK846_skl)))
| ~ v3_rlvect_1(sK845_skl)
| ~ v4_rlvect_1(sK846_skl)
| ~ v5_vectsp_2(sK846_skl,sK845_skl)
| ~ v2_vectsp_2(sK845_skl)
| ~ v4_rlvect_1(sK845_skl) ),
inference(resolution,[status(thm)],[f17397,f13112]) ).
fof(f17413,plain,
( sQ563_spl
| sQ520_spl
| ~ sQ528_spl
| ~ sQ515_spl
| sQ555_spl
| ~ sQ527_spl
| ~ sQ556_spl
| ~ sQ551_spl
| ~ sQ516_spl
| sQ523_spl
| ~ sQ553_spl
| ~ sQ519_spl
| ~ sQ550_spl
| ~ sQ521_spl
| ~ sQ522_spl
| ~ sQ517_spl
| ~ sQ535_spl
| ~ sQ524_spl
| ~ sQ554_spl
| ~ sQ566_spl
| ~ sQ525_spl
| ~ sQ526_spl ),
inference(split_clause,[status(thm)],[f17412,f17027,f17024,f17404,f17333,f17021,f17112,f17000,f17015,f17012,f17321,f17006,f17330,f17018,f16997,f17324,f17339,f17030,f17336,f16994,f17053,f17009,f17395]) ).
fof(f17661,plain,
( ~ sQ533_spl
| sQ564_spl
| ~ r1_tarski(k3_xboole_0(sK847_skl,sK848_skl),sK847_skl)
| v3_struct_0(sK846_skl)
| ~ v5_vectsp_2(sK846_skl,sK845_skl)
| ~ m1_subset_1(k3_xboole_0(sK847_skl,sK848_skl),k1_zfmisc_1(u1_struct_0(sK846_skl)))
| ~ m1_subset_1(sK847_skl,k1_zfmisc_1(u1_struct_0(sK846_skl)))
| ~ v6_rlvect_1(sK846_skl)
| ~ v4_rlvect_1(sK846_skl)
| ~ v5_rlvect_1(sK846_skl)
| ~ v3_rlvect_1(sK846_skl)
| ~ l1_vectsp_2(sK846_skl,sK845_skl) ),
inference(resolution,[status(thm)],[f17400,f17094]) ).
fof(f17662,definition,
( sQ608_spl
<=> r1_tarski(k3_xboole_0(sK847_skl,sK848_skl),sK847_skl) ),
introduced(definition,[new_symbols(definition,[sQ608_spl])],[split_symbol_definition]) ).
fof(f17664,plain,
( sQ608_spl
| ~ r1_tarski(k3_xboole_0(sK847_skl,sK848_skl),sK847_skl) ),
inference(component_clause,[status(thm)],[f17662]) ).
fof(f17665,plain,
( ~ sQ533_spl
| sQ564_spl
| ~ sQ608_spl
| sQ555_spl
| ~ sQ566_spl
| ~ sQ560_spl
| ~ sQ542_spl
| ~ sQ551_spl
| ~ sQ554_spl
| ~ sQ550_spl
| ~ sQ553_spl
| ~ sQ556_spl ),
inference(split_clause,[status(thm)],[f17661,f17339,f17330,f17321,f17333,f17324,f17214,f17380,f17404,f17336,f17662,f17398,f17093]) ).
fof(f17678,plain,
( ~ sQ533_spl
| sQ561_spl
| ~ r1_tarski(k3_xboole_0(sK847_skl,sK848_skl),sK848_skl)
| v3_struct_0(sK846_skl)
| ~ v5_vectsp_2(sK846_skl,sK845_skl)
| ~ m1_subset_1(k3_xboole_0(sK847_skl,sK848_skl),k1_zfmisc_1(u1_struct_0(sK846_skl)))
| ~ m1_subset_1(sK848_skl,k1_zfmisc_1(u1_struct_0(sK846_skl)))
| ~ v6_rlvect_1(sK846_skl)
| ~ v4_rlvect_1(sK846_skl)
| ~ v5_rlvect_1(sK846_skl)
| ~ v3_rlvect_1(sK846_skl)
| ~ l1_vectsp_2(sK846_skl,sK845_skl) ),
inference(resolution,[status(thm)],[f17391,f17094]) ).
fof(f17679,definition,
( sQ610_spl
<=> r1_tarski(k3_xboole_0(sK847_skl,sK848_skl),sK848_skl) ),
introduced(definition,[new_symbols(definition,[sQ610_spl])],[split_symbol_definition]) ).
fof(f17681,plain,
( sQ610_spl
| ~ r1_tarski(k3_xboole_0(sK847_skl,sK848_skl),sK848_skl) ),
inference(component_clause,[status(thm)],[f17679]) ).
fof(f17682,plain,
( ~ sQ533_spl
| sQ561_spl
| ~ sQ610_spl
| sQ555_spl
| ~ sQ566_spl
| ~ sQ560_spl
| ~ sQ535_spl
| ~ sQ551_spl
| ~ sQ554_spl
| ~ sQ550_spl
| ~ sQ553_spl
| ~ sQ556_spl ),
inference(split_clause,[status(thm)],[f17678,f17339,f17330,f17321,f17333,f17324,f17112,f17380,f17404,f17336,f17679,f17389,f17093]) ).
fof(f17697,plain,
( sQ565_spl
| v10_vectsp_1(sK845_skl)
| ~ v6_vectsp_1(sK845_skl)
| ~ v7_vectsp_1(sK845_skl)
| v3_struct_0(sK846_skl)
| ~ v8_vectsp_1(sK845_skl)
| ~ l1_vectsp_2(sK846_skl,sK845_skl)
| ~ v6_rlvect_1(sK846_skl)
| ~ v7_group_1(sK845_skl)
| v3_struct_0(sK845_skl)
| ~ v3_rlvect_1(sK846_skl)
| ~ l3_vectsp_1(sK845_skl)
| ~ v5_rlvect_1(sK846_skl)
| ~ v5_rlvect_1(sK845_skl)
| ~ v4_group_1(sK845_skl)
| ~ v6_rlvect_1(sK845_skl)
| ~ m1_subset_1(k3_xboole_0(sK847_skl,sK848_skl),k1_zfmisc_1(u1_struct_0(sK846_skl)))
| ~ v3_rlvect_1(sK845_skl)
| ~ v4_rlvect_1(sK846_skl)
| ~ v5_vectsp_2(sK846_skl,sK845_skl)
| ~ v2_vectsp_2(sK845_skl)
| ~ v4_rlvect_1(sK845_skl) ),
inference(resolution,[status(thm)],[f17403,f13112]) ).
fof(f17698,plain,
( sQ565_spl
| sQ520_spl
| ~ sQ528_spl
| ~ sQ515_spl
| sQ555_spl
| ~ sQ527_spl
| ~ sQ556_spl
| ~ sQ551_spl
| ~ sQ516_spl
| sQ523_spl
| ~ sQ553_spl
| ~ sQ519_spl
| ~ sQ550_spl
| ~ sQ521_spl
| ~ sQ522_spl
| ~ sQ517_spl
| ~ sQ560_spl
| ~ sQ524_spl
| ~ sQ554_spl
| ~ sQ566_spl
| ~ sQ525_spl
| ~ sQ526_spl ),
inference(split_clause,[status(thm)],[f17697,f17027,f17024,f17404,f17333,f17021,f17380,f17000,f17015,f17012,f17321,f17006,f17330,f17018,f16997,f17324,f17339,f17030,f17336,f16994,f17053,f17009,f17401]) ).
fof(f18277,plain,
( sQ608_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f17664,f3723]) ).
fof(f18292,plain,
sQ608_spl,
inference(contradiction_clause,[status(thm)],[f18277]) ).
fof(f23985,plain,
( sQ610_spl
| ~ r1_tarski(k3_xboole_0(sK848_skl,sK847_skl),sK848_skl) ),
inference(paramodulation,[status(thm)],[f3672,f17681]) ).
fof(f24012,plain,
( sQ610_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f23985,f3723]) ).
fof(f24013,plain,
sQ610_spl,
inference(contradiction_clause,[status(thm)],[f24012]) ).
fof(f24014,plain,
$false,
inference(sat_refutation,[status(thm)],[f17035,f17037,f17039,f17041,f17043,f17045,f17047,f17049,f17058,f17096,f17103,f17107,f17142,f17161,f17186,f17223,f17344,f17346,f17348,f17350,f17352,f17354,f17383,f17407,f17409,f17411,f17413,f17665,f17682,f17698,f18292,f24013]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG222+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.43 % Computer : n004.cluster.edu
% 0.19/0.43 % Model : x86_64 x86_64
% 0.19/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.43 % Memory : 8046.5625MB
% 0.19/0.43 % OS : Linux 6.8.0-71-generic
% 0.19/0.43 % CPULimit : 300
% 0.19/0.43 % WCLimit : 300
% 0.19/0.43 % DateTime : Mon Sep 21 13:05:07 UTC 2026
% 0.19/0.43 % CPUTime :
% 0.66/0.98 % Drodi V4.1.1
% 100.40/13.64 % Refutation found
% 100.40/13.64 % SZS status Theorem for theBenchmark: Theorem is valid
% 100.40/13.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 100.40/13.74 % Elapsed time: 13.296179 seconds
% 100.40/13.74 % CPU time: 100.897676 seconds
% 100.40/13.74 % Total memory used: 1.011 GB
% 100.40/13.74 % Net memory used: 962.845 MB
%------------------------------------------------------------------------------