%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LAT379+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 01:03:02 PM UTC 2026
% Result : Theorem 0.21s 0.68s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 36
% Syntax : Number of formulae : 159 ( 28 unt; 22 def)
% Number of atoms : 698 ( 12 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 882 ( 343 ~; 401 |; 84 &)
% ( 28 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 47 ( 45 usr; 23 prp; 0-4 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-3 aty)
% Number of variables : 160 ( 151 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [A] :
( ( l1_orders_2(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_orders_2(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(C) )
=> ( v4_waybel34(C,A,B)
=> ( v5_waybel34(C,A,B)
& v20_waybel_0(C,A,B) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [A] :
( ( l1_orders_2(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_orders_2(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(C) )
=> ( v4_waybel34(C,A,B)
=> ( v5_waybel34(C,A,B)
& v20_waybel_0(C,A,B) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f27,axiom,
! [A] :
( ( l1_orders_2(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_orders_2(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(C) )
=> ( v4_waybel34(C,A,B)
<=> ! [D] :
( ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
& v1_finset_1(D) )
=> r4_waybel_0(A,B,C,D) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A] :
( ( l1_orders_2(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_orders_2(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(C) )
=> ( v5_waybel34(C,A,B)
<=> r4_waybel_0(A,B,C,k1_pre_topc(A)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [A] :
( l1_struct_0(A)
=> k1_pre_topc(A) = k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [A] :
( ( l1_orders_2(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_orders_2(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(C) )
=> ( v20_waybel_0(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> r4_waybel_0(A,B,C,k2_struct_0(A,D,E)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [A] :
( l1_struct_0(A)
=> m1_subset_1(k1_pre_topc(A),k1_zfmisc_1(u1_struct_0(A))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [A,B,C] :
( ( m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(B,u1_struct_0(A))
& l1_struct_0(A)
& ~ v3_struct_0(A) )
=> m1_subset_1(k2_struct_0(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [A] :
( l1_orders_2(A)
=> l1_struct_0(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,axiom,
? [A] : l1_struct_0(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [A] :
? [B] : m1_subset_1(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [A] :
( l1_orders_2(A)
=> ( v13_waybel_0(k1_pre_topc(A),A)
& v12_waybel_0(k1_pre_topc(A),A)
& v2_waybel_0(k1_pre_topc(A),A)
& v1_waybel_0(k1_pre_topc(A),A)
& v5_membered(k1_pre_topc(A))
& v4_membered(k1_pre_topc(A))
& v3_membered(k1_pre_topc(A))
& v2_membered(k1_pre_topc(A))
& v1_membered(k1_pre_topc(A))
& v5_orders_2(k1_pre_topc(A),A)
& v1_finset_1(k1_pre_topc(A))
& v1_xboole_0(k1_pre_topc(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [A,B] :
( v1_finset_1(k2_tarski(A,B))
& ~ v1_xboole_0(k2_tarski(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f69,axiom,
? [A] :
( ~ v3_struct_0(A)
& l1_struct_0(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f74,axiom,
! [A,B,C] :
( ( m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(B,u1_struct_0(A))
& l1_struct_0(A)
& ~ v3_struct_0(A) )
=> k2_struct_0(A,B,C) = k2_tarski(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f85,plain,
? [A] :
( ? [B] :
( ? [C] :
( ( ~ v5_waybel34(C,A,B)
| ~ v20_waybel_0(C,A,B) )
& v4_waybel34(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(C) )
& l1_orders_2(B)
& ~ v3_struct_0(B) )
& l1_orders_2(A)
& ~ v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f86,plain,
( ( ~ v5_waybel34(sK2_skl,sK0_skl,sK1_skl)
| ~ v20_waybel_0(sK2_skl,sK0_skl,sK1_skl) )
& v4_waybel34(sK2_skl,sK0_skl,sK1_skl)
& m2_relset_1(sK2_skl,u1_struct_0(sK0_skl),u1_struct_0(sK1_skl))
& v1_funct_2(sK2_skl,u1_struct_0(sK0_skl),u1_struct_0(sK1_skl))
& v1_funct_1(sK2_skl)
& l1_orders_2(sK1_skl)
& ~ v3_struct_0(sK1_skl)
& l1_orders_2(sK0_skl)
& ~ v3_struct_0(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl),skolemize(C,sK2_skl)],[f85]) ).
fof(f87,plain,
~ v3_struct_0(sK0_skl),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f88,plain,
l1_orders_2(sK0_skl),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f89,plain,
~ v3_struct_0(sK1_skl),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f90,plain,
l1_orders_2(sK1_skl),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f91,plain,
v1_funct_1(sK2_skl),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f92,plain,
v1_funct_2(sK2_skl,u1_struct_0(sK0_skl),u1_struct_0(sK1_skl)),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f93,plain,
m2_relset_1(sK2_skl,u1_struct_0(sK0_skl),u1_struct_0(sK1_skl)),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f94,plain,
v4_waybel34(sK2_skl,sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f95,plain,
( ~ v5_waybel34(sK2_skl,sK0_skl,sK1_skl)
| ~ v20_waybel_0(sK2_skl,sK0_skl,sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f170,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( v4_waybel34(C,A,B)
<=> ! [D] :
( r4_waybel_0(A,B,C,D)
| ~ m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
| ~ v1_finset_1(D) ) )
| ~ m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
| ~ v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
| ~ v1_funct_1(C) )
| ~ l1_orders_2(B)
| v3_struct_0(B) )
| ~ l1_orders_2(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f171,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ? [D] :
( ~ r4_waybel_0(A,B,C,D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
& v1_finset_1(D) )
| v4_waybel34(C,A,B) )
& ( ! [D] :
( r4_waybel_0(A,B,C,D)
| ~ m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
| ~ v1_finset_1(D) )
| ~ v4_waybel34(C,A,B) ) )
| ~ m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
| ~ v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
| ~ v1_funct_1(C) )
| ~ l1_orders_2(B)
| v3_struct_0(B) )
| ~ l1_orders_2(A)
| v3_struct_0(A) ),
inference(NNF_transformation,[status(thm)],[f170]) ).
fof(f172,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ( ~ r4_waybel_0(A,B,C,sK3_skl(C,B,A))
& m1_subset_1(sK3_skl(C,B,A),k1_zfmisc_1(u1_struct_0(A)))
& v1_finset_1(sK3_skl(C,B,A)) )
| v4_waybel34(C,A,B) )
& ( ! [D] :
( r4_waybel_0(A,B,C,D)
| ~ m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
| ~ v1_finset_1(D) )
| ~ v4_waybel34(C,A,B) ) )
| ~ m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
| ~ v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
| ~ v1_funct_1(C) )
| ~ l1_orders_2(B)
| v3_struct_0(B) )
| ~ l1_orders_2(A)
| v3_struct_0(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(D,sK3_skl(C,B,A))],[f171]) ).
fof(f173,plain,
! [X0,X1,X2,X3] :
( r4_waybel_0(X0,X1,X2,X3)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_finset_1(X3)
| ~ v4_waybel34(X2,X0,X1)
| ~ m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_1(X2)
| ~ l1_orders_2(X1)
| v3_struct_0(X1)
| ~ l1_orders_2(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f172]) ).
fof(f177,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( v5_waybel34(C,A,B)
<=> r4_waybel_0(A,B,C,k1_pre_topc(A)) )
| ~ m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
| ~ v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
| ~ v1_funct_1(C) )
| ~ l1_orders_2(B)
| v3_struct_0(B) )
| ~ l1_orders_2(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f178,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ~ r4_waybel_0(A,B,C,k1_pre_topc(A))
| v5_waybel34(C,A,B) )
& ( r4_waybel_0(A,B,C,k1_pre_topc(A))
| ~ v5_waybel34(C,A,B) ) )
| ~ m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
| ~ v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
| ~ v1_funct_1(C) )
| ~ l1_orders_2(B)
| v3_struct_0(B) )
| ~ l1_orders_2(A)
| v3_struct_0(A) ),
inference(NNF_transformation,[status(thm)],[f177]) ).
fof(f180,plain,
! [X0,X1,X2] :
( ~ r4_waybel_0(X0,X1,X2,k1_pre_topc(X0))
| v5_waybel34(X2,X0,X1)
| ~ m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_1(X2)
| ~ l1_orders_2(X1)
| v3_struct_0(X1)
| ~ l1_orders_2(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f178]) ).
fof(f181,plain,
! [A] :
( k1_pre_topc(A) = k1_xboole_0
| ~ l1_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f182,plain,
! [X0] :
( k1_pre_topc(X0) = k1_xboole_0
| ~ l1_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f181]) ).
fof(f183,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( v20_waybel_0(C,A,B)
<=> ! [D] :
( ! [E] :
( r4_waybel_0(A,B,C,k2_struct_0(A,D,E))
| ~ m1_subset_1(E,u1_struct_0(A)) )
| ~ m1_subset_1(D,u1_struct_0(A)) ) )
| ~ m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
| ~ v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
| ~ v1_funct_1(C) )
| ~ l1_orders_2(B)
| v3_struct_0(B) )
| ~ l1_orders_2(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f184,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ? [D] :
( ? [E] :
( ~ r4_waybel_0(A,B,C,k2_struct_0(A,D,E))
& m1_subset_1(E,u1_struct_0(A)) )
& m1_subset_1(D,u1_struct_0(A)) )
| v20_waybel_0(C,A,B) )
& ( ! [D] :
( ! [E] :
( r4_waybel_0(A,B,C,k2_struct_0(A,D,E))
| ~ m1_subset_1(E,u1_struct_0(A)) )
| ~ m1_subset_1(D,u1_struct_0(A)) )
| ~ v20_waybel_0(C,A,B) ) )
| ~ m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
| ~ v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
| ~ v1_funct_1(C) )
| ~ l1_orders_2(B)
| v3_struct_0(B) )
| ~ l1_orders_2(A)
| v3_struct_0(A) ),
inference(NNF_transformation,[status(thm)],[f183]) ).
fof(f185,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ( ~ r4_waybel_0(A,B,C,k2_struct_0(A,sK4_skl(C,B,A),sK5_skl(C,B,A)))
& m1_subset_1(sK5_skl(C,B,A),u1_struct_0(A))
& m1_subset_1(sK4_skl(C,B,A),u1_struct_0(A)) )
| v20_waybel_0(C,A,B) )
& ( ! [D] :
( ! [E] :
( r4_waybel_0(A,B,C,k2_struct_0(A,D,E))
| ~ m1_subset_1(E,u1_struct_0(A)) )
| ~ m1_subset_1(D,u1_struct_0(A)) )
| ~ v20_waybel_0(C,A,B) ) )
| ~ m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
| ~ v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
| ~ v1_funct_1(C) )
| ~ l1_orders_2(B)
| v3_struct_0(B) )
| ~ l1_orders_2(A)
| v3_struct_0(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl]),skolemize(D,sK4_skl(C,B,A)),skolemize(E,sK5_skl(C,B,A))],[f184]) ).
fof(f187,plain,
! [X0,X1,X2] :
( m1_subset_1(sK4_skl(X2,X1,X0),u1_struct_0(X0))
| v20_waybel_0(X2,X0,X1)
| ~ m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_1(X2)
| ~ l1_orders_2(X1)
| v3_struct_0(X1)
| ~ l1_orders_2(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f185]) ).
fof(f188,plain,
! [X0,X1,X2] :
( m1_subset_1(sK5_skl(X2,X1,X0),u1_struct_0(X0))
| v20_waybel_0(X2,X0,X1)
| ~ m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_1(X2)
| ~ l1_orders_2(X1)
| v3_struct_0(X1)
| ~ l1_orders_2(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f185]) ).
fof(f189,plain,
! [X0,X1,X2] :
( ~ r4_waybel_0(X0,X1,X2,k2_struct_0(X0,sK4_skl(X2,X1,X0),sK5_skl(X2,X1,X0)))
| v20_waybel_0(X2,X0,X1)
| ~ m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_1(X2)
| ~ l1_orders_2(X1)
| v3_struct_0(X1)
| ~ l1_orders_2(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f185]) ).
fof(f190,plain,
! [A] :
( m1_subset_1(k1_pre_topc(A),k1_zfmisc_1(u1_struct_0(A)))
| ~ l1_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f191,plain,
! [X0] :
( m1_subset_1(k1_pre_topc(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f192,plain,
! [A,B,C] :
( m1_subset_1(k2_struct_0(A,B,C),k1_zfmisc_1(u1_struct_0(A)))
| ~ m1_subset_1(C,u1_struct_0(A))
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l1_struct_0(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f193,plain,
! [X0,X1,X2] :
( m1_subset_1(k2_struct_0(X0,X1,X2),k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f194,plain,
! [A] :
( l1_struct_0(A)
| ~ l1_orders_2(A) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f195,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f200,plain,
l1_struct_0(sK7_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(A,sK7_skl)],[f44]) ).
fof(f201,plain,
l1_struct_0(sK7_skl),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f204,plain,
! [A] : m1_subset_1(sK9_skl(A),A),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(B,sK9_skl(A))],[f46]) ).
fof(f205,plain,
! [X0] : m1_subset_1(sK9_skl(X0),X0),
inference(cnf_transformation,[status(thm)],[f204]) ).
fof(f239,plain,
! [A] :
( ( v13_waybel_0(k1_pre_topc(A),A)
& v12_waybel_0(k1_pre_topc(A),A)
& v2_waybel_0(k1_pre_topc(A),A)
& v1_waybel_0(k1_pre_topc(A),A)
& v5_membered(k1_pre_topc(A))
& v4_membered(k1_pre_topc(A))
& v3_membered(k1_pre_topc(A))
& v2_membered(k1_pre_topc(A))
& v1_membered(k1_pre_topc(A))
& v5_orders_2(k1_pre_topc(A),A)
& v1_finset_1(k1_pre_topc(A))
& v1_xboole_0(k1_pre_topc(A)) )
| ~ l1_orders_2(A) ),
inference(pre_NNF_transformation,[status(thm)],[f56]) ).
fof(f241,plain,
! [X0] :
( v1_finset_1(k1_pre_topc(X0))
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[status(thm)],[f239]) ).
fof(f263,plain,
( ! [A,B] : v1_finset_1(k2_tarski(A,B))
& ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
inference(miniscoping,[status(thm)],[f58]) ).
fof(f265,plain,
! [X0,X1] : v1_finset_1(k2_tarski(X0,X1)),
inference(cnf_transformation,[status(thm)],[f263]) ).
fof(f309,plain,
( ~ v3_struct_0(sK19_skl)
& l1_struct_0(sK19_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl]),skolemize(A,sK19_skl)],[f69]) ).
fof(f310,plain,
l1_struct_0(sK19_skl),
inference(cnf_transformation,[status(thm)],[f309]) ).
fof(f332,plain,
! [A,B,C] :
( k2_struct_0(A,B,C) = k2_tarski(B,C)
| ~ m1_subset_1(C,u1_struct_0(A))
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l1_struct_0(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f74]) ).
fof(f333,plain,
! [X0,X1,X2] :
( k2_struct_0(X0,X1,X2) = k2_tarski(X1,X2)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f332]) ).
fof(f362,definition,
( sQ0_spl
<=> v20_waybel_0(sK2_skl,sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f365,definition,
( sQ1_spl
<=> v5_waybel34(sK2_skl,sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f368,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f95,f362,f365]) ).
fof(f375,plain,
( m1_subset_1(sK4_skl(sK2_skl,sK1_skl,sK0_skl),u1_struct_0(sK0_skl))
| v20_waybel_0(sK2_skl,sK0_skl,sK1_skl)
| ~ m2_relset_1(sK2_skl,u1_struct_0(sK0_skl),u1_struct_0(sK1_skl))
| ~ v1_funct_1(sK2_skl)
| ~ l1_orders_2(sK1_skl)
| v3_struct_0(sK1_skl)
| ~ l1_orders_2(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f187,f92]) ).
fof(f376,definition,
( sQ2_spl
<=> v3_struct_0(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f377,plain,
( ~ sQ2_spl
| v3_struct_0(sK0_skl) ),
inference(component_clause,[status(thm)],[f376]) ).
fof(f379,definition,
( sQ3_spl
<=> l1_orders_2(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f381,plain,
( sQ3_spl
| ~ l1_orders_2(sK0_skl) ),
inference(component_clause,[status(thm)],[f379]) ).
fof(f382,definition,
( sQ4_spl
<=> v3_struct_0(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f383,plain,
( ~ sQ4_spl
| v3_struct_0(sK1_skl) ),
inference(component_clause,[status(thm)],[f382]) ).
fof(f385,definition,
( sQ5_spl
<=> l1_orders_2(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f387,plain,
( sQ5_spl
| ~ l1_orders_2(sK1_skl) ),
inference(component_clause,[status(thm)],[f385]) ).
fof(f388,definition,
( sQ6_spl
<=> v1_funct_1(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f390,plain,
( sQ6_spl
| ~ v1_funct_1(sK2_skl) ),
inference(component_clause,[status(thm)],[f388]) ).
fof(f391,definition,
( sQ7_spl
<=> m2_relset_1(sK2_skl,u1_struct_0(sK0_skl),u1_struct_0(sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f393,plain,
( sQ7_spl
| ~ m2_relset_1(sK2_skl,u1_struct_0(sK0_skl),u1_struct_0(sK1_skl)) ),
inference(component_clause,[status(thm)],[f391]) ).
fof(f394,definition,
( sQ8_spl
<=> m1_subset_1(sK4_skl(sK2_skl,sK1_skl,sK0_skl),u1_struct_0(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f395,plain,
( ~ sQ8_spl
| m1_subset_1(sK4_skl(sK2_skl,sK1_skl,sK0_skl),u1_struct_0(sK0_skl)) ),
inference(component_clause,[status(thm)],[f394]) ).
fof(f397,plain,
( sQ8_spl
| sQ0_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ4_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f375,f376,f379,f382,f385,f388,f391,f362,f394]) ).
fof(f400,definition,
( sQ9_spl
<=> l1_struct_0(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f401,plain,
( ~ sQ9_spl
| l1_struct_0(sK0_skl) ),
inference(component_clause,[status(thm)],[f400]) ).
fof(f402,plain,
( sQ9_spl
| ~ l1_struct_0(sK0_skl) ),
inference(component_clause,[status(thm)],[f400]) ).
fof(f411,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f377,f87]) ).
fof(f412,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f411]) ).
fof(f413,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f381,f88]) ).
fof(f414,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f413]) ).
fof(f415,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f393,f93]) ).
fof(f416,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f415]) ).
fof(f417,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f390,f91]) ).
fof(f418,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f417]) ).
fof(f419,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f387,f90]) ).
fof(f420,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f419]) ).
fof(f421,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f383,f89]) ).
fof(f422,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f421]) ).
fof(f427,plain,
( m1_subset_1(sK5_skl(sK2_skl,sK1_skl,sK0_skl),u1_struct_0(sK0_skl))
| v20_waybel_0(sK2_skl,sK0_skl,sK1_skl)
| ~ m2_relset_1(sK2_skl,u1_struct_0(sK0_skl),u1_struct_0(sK1_skl))
| ~ v1_funct_1(sK2_skl)
| ~ l1_orders_2(sK1_skl)
| v3_struct_0(sK1_skl)
| ~ l1_orders_2(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f188,f92]) ).
fof(f428,definition,
( sQ12_spl
<=> m1_subset_1(sK5_skl(sK2_skl,sK1_skl,sK0_skl),u1_struct_0(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f429,plain,
( ~ sQ12_spl
| m1_subset_1(sK5_skl(sK2_skl,sK1_skl,sK0_skl),u1_struct_0(sK0_skl)) ),
inference(component_clause,[status(thm)],[f428]) ).
fof(f431,plain,
( sQ12_spl
| sQ0_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ4_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f427,f376,f379,f382,f385,f388,f391,f362,f428]) ).
fof(f433,definition,
( sQ13_spl
<=> v1_funct_2(sK2_skl,u1_struct_0(sK0_skl),u1_struct_0(sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f435,plain,
( sQ13_spl
| ~ v1_funct_2(sK2_skl,u1_struct_0(sK0_skl),u1_struct_0(sK1_skl)) ),
inference(component_clause,[status(thm)],[f433]) ).
fof(f464,plain,
! [X0,X1,X2] :
( r4_waybel_0(X0,X1,X2,k1_pre_topc(X0))
| ~ v1_finset_1(k1_pre_topc(X0))
| ~ v4_waybel34(X2,X0,X1)
| ~ m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_1(X2)
| ~ l1_orders_2(X1)
| v3_struct_0(X1)
| ~ l1_orders_2(X0)
| v3_struct_0(X0)
| ~ l1_struct_0(X0) ),
inference(resolution,[status(thm)],[f191,f173]) ).
fof(f465,plain,
! [X0,X1,X2,X3,X4] :
( r4_waybel_0(X0,X3,X4,k2_struct_0(X0,X1,X2))
| ~ v1_finset_1(k2_struct_0(X0,X1,X2))
| ~ v4_waybel34(X4,X0,X3)
| ~ m2_relset_1(X4,u1_struct_0(X0),u1_struct_0(X3))
| ~ v1_funct_2(X4,u1_struct_0(X0),u1_struct_0(X3))
| ~ v1_funct_1(X4)
| ~ l1_orders_2(X3)
| v3_struct_0(X3)
| ~ l1_orders_2(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(resolution,[status(thm)],[f193,f173]) ).
fof(f466,plain,
! [X0,X1,X2,X3,X4] :
( r4_waybel_0(X0,X3,X4,k2_struct_0(X0,X1,X2))
| ~ v1_finset_1(k2_struct_0(X0,X1,X2))
| ~ v4_waybel34(X4,X0,X3)
| ~ m2_relset_1(X4,u1_struct_0(X0),u1_struct_0(X3))
| ~ v1_funct_2(X4,u1_struct_0(X0),u1_struct_0(X3))
| ~ v1_funct_1(X4)
| ~ l1_orders_2(X3)
| v3_struct_0(X3)
| ~ l1_orders_2(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f465]) ).
fof(f467,plain,
( sQ9_spl
| ~ l1_orders_2(sK0_skl) ),
inference(resolution,[status(thm)],[f195,f402]) ).
fof(f469,plain,
( sQ9_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f467,f379,f400]) ).
fof(f471,plain,
( ~ sQ9_spl
| k1_pre_topc(sK0_skl) = k1_xboole_0 ),
inference(resolution,[status(thm)],[f401,f182]) ).
fof(f475,plain,
! [X0,X1] :
( ~ sQ9_spl
| ~ r4_waybel_0(sK0_skl,X0,X1,k1_xboole_0)
| v5_waybel34(X1,sK0_skl,X0)
| ~ m2_relset_1(X1,u1_struct_0(sK0_skl),u1_struct_0(X0))
| ~ v1_funct_2(X1,u1_struct_0(sK0_skl),u1_struct_0(X0))
| ~ v1_funct_1(X1)
| ~ l1_orders_2(X0)
| v3_struct_0(X0)
| ~ l1_orders_2(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(paramodulation,[status(thm)],[f471,f180]) ).
fof(f480,definition,
! [X0,X1] :
( sQ20_spl
<=> ( ~ r4_waybel_0(sK0_skl,X0,X1,k1_xboole_0)
| v5_waybel34(X1,sK0_skl,X0)
| ~ m2_relset_1(X1,u1_struct_0(sK0_skl),u1_struct_0(X0))
| ~ v1_funct_2(X1,u1_struct_0(sK0_skl),u1_struct_0(X0))
| ~ v1_funct_1(X1)
| ~ l1_orders_2(X0)
| v3_struct_0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f481,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ r4_waybel_0(sK0_skl,X0,X1,k1_xboole_0)
| v5_waybel34(X1,sK0_skl,X0)
| ~ m2_relset_1(X1,u1_struct_0(sK0_skl),u1_struct_0(X0))
| ~ v1_funct_2(X1,u1_struct_0(sK0_skl),u1_struct_0(X0))
| ~ v1_funct_1(X1)
| ~ l1_orders_2(X0)
| v3_struct_0(X0) ),
inference(component_clause,[status(thm)],[f480]) ).
fof(f483,plain,
( ~ sQ9_spl
| sQ20_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f475,f376,f379,f480,f400]) ).
fof(f492,plain,
! [X0,X1,X2] :
( r4_waybel_0(X0,X1,X2,k1_pre_topc(X0))
| ~ v1_finset_1(k1_pre_topc(X0))
| ~ v4_waybel34(X2,X0,X1)
| ~ m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_1(X2)
| ~ l1_orders_2(X1)
| v3_struct_0(X1)
| ~ l1_orders_2(X0)
| v3_struct_0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f464,f195]) ).
fof(f494,definition,
( sQ23_spl
<=> v4_waybel34(sK2_skl,sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f496,plain,
( sQ23_spl
| ~ v4_waybel34(sK2_skl,sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f494]) ).
fof(f500,definition,
( sQ25_spl
<=> r4_waybel_0(sK0_skl,sK1_skl,sK2_skl,k1_pre_topc(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f501,plain,
( ~ sQ25_spl
| r4_waybel_0(sK0_skl,sK1_skl,sK2_skl,k1_pre_topc(sK0_skl)) ),
inference(component_clause,[status(thm)],[f500]) ).
fof(f504,plain,
( ~ sQ25_spl
| ~ sQ9_spl
| r4_waybel_0(sK0_skl,sK1_skl,sK2_skl,k1_xboole_0) ),
inference(forward_demodulation,[status(thm)],[f471,f501]) ).
fof(f506,plain,
( sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f496,f94]) ).
fof(f507,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f506]) ).
fof(f508,plain,
! [X0,X1,X2,X3,X4] :
( r4_waybel_0(X0,X3,X4,k2_struct_0(X0,X1,X2))
| ~ v1_finset_1(k2_struct_0(X0,X1,X2))
| ~ v4_waybel34(X4,X0,X3)
| ~ m2_relset_1(X4,u1_struct_0(X0),u1_struct_0(X3))
| ~ v1_funct_2(X4,u1_struct_0(X0),u1_struct_0(X3))
| ~ v1_funct_1(X4)
| ~ l1_orders_2(X3)
| v3_struct_0(X3)
| ~ l1_orders_2(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| v3_struct_0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f466,f195]) ).
fof(f509,plain,
! [X0,X1] :
( r4_waybel_0(sK0_skl,sK1_skl,sK2_skl,k2_struct_0(sK0_skl,X0,X1))
| ~ v1_finset_1(k2_struct_0(sK0_skl,X0,X1))
| ~ v4_waybel34(sK2_skl,sK0_skl,sK1_skl)
| ~ m2_relset_1(sK2_skl,u1_struct_0(sK0_skl),u1_struct_0(sK1_skl))
| ~ v1_funct_1(sK2_skl)
| ~ l1_orders_2(sK1_skl)
| v3_struct_0(sK1_skl)
| ~ l1_orders_2(sK0_skl)
| ~ m1_subset_1(X1,u1_struct_0(sK0_skl))
| ~ m1_subset_1(X0,u1_struct_0(sK0_skl))
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f508,f92]) ).
fof(f510,definition,
! [X0,X1] :
( sQ26_spl
<=> ( r4_waybel_0(sK0_skl,sK1_skl,sK2_skl,k2_struct_0(sK0_skl,X0,X1))
| ~ v1_finset_1(k2_struct_0(sK0_skl,X0,X1))
| ~ m1_subset_1(X1,u1_struct_0(sK0_skl))
| ~ m1_subset_1(X0,u1_struct_0(sK0_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f511,plain,
! [X0,X1] :
( ~ sQ26_spl
| r4_waybel_0(sK0_skl,sK1_skl,sK2_skl,k2_struct_0(sK0_skl,X0,X1))
| ~ v1_finset_1(k2_struct_0(sK0_skl,X0,X1))
| ~ m1_subset_1(X1,u1_struct_0(sK0_skl))
| ~ m1_subset_1(X0,u1_struct_0(sK0_skl)) ),
inference(component_clause,[status(thm)],[f510]) ).
fof(f513,plain,
( ~ sQ23_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ4_spl
| ~ sQ3_spl
| sQ26_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f509,f376,f510,f379,f382,f385,f388,f391,f494]) ).
fof(f537,plain,
( ~ sQ26_spl
| v20_waybel_0(sK2_skl,sK0_skl,sK1_skl)
| ~ m2_relset_1(sK2_skl,u1_struct_0(sK0_skl),u1_struct_0(sK1_skl))
| ~ v1_funct_2(sK2_skl,u1_struct_0(sK0_skl),u1_struct_0(sK1_skl))
| ~ v1_funct_1(sK2_skl)
| ~ l1_orders_2(sK1_skl)
| v3_struct_0(sK1_skl)
| ~ l1_orders_2(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ v1_finset_1(k2_struct_0(sK0_skl,sK4_skl(sK2_skl,sK1_skl,sK0_skl),sK5_skl(sK2_skl,sK1_skl,sK0_skl)))
| ~ m1_subset_1(sK5_skl(sK2_skl,sK1_skl,sK0_skl),u1_struct_0(sK0_skl))
| ~ m1_subset_1(sK4_skl(sK2_skl,sK1_skl,sK0_skl),u1_struct_0(sK0_skl)) ),
inference(resolution,[status(thm)],[f511,f189]) ).
fof(f538,definition,
( sQ27_spl
<=> v1_finset_1(k2_struct_0(sK0_skl,sK4_skl(sK2_skl,sK1_skl,sK0_skl),sK5_skl(sK2_skl,sK1_skl,sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f540,plain,
( sQ27_spl
| ~ v1_finset_1(k2_struct_0(sK0_skl,sK4_skl(sK2_skl,sK1_skl,sK0_skl),sK5_skl(sK2_skl,sK1_skl,sK0_skl))) ),
inference(component_clause,[status(thm)],[f538]) ).
fof(f541,plain,
( ~ sQ26_spl
| sQ0_spl
| ~ sQ7_spl
| ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ4_spl
| ~ sQ3_spl
| sQ2_spl
| ~ sQ27_spl
| ~ sQ12_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f537,f394,f428,f538,f376,f379,f382,f385,f388,f433,f391,f362,f510]) ).
fof(f542,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f435,f92]) ).
fof(f543,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f542]) ).
fof(f560,plain,
( ~ sQ20_spl
| ~ r4_waybel_0(sK0_skl,sK1_skl,sK2_skl,k1_xboole_0)
| v5_waybel34(sK2_skl,sK0_skl,sK1_skl)
| ~ m2_relset_1(sK2_skl,u1_struct_0(sK0_skl),u1_struct_0(sK1_skl))
| ~ v1_funct_1(sK2_skl)
| ~ l1_orders_2(sK1_skl)
| v3_struct_0(sK1_skl) ),
inference(resolution,[status(thm)],[f481,f92]) ).
fof(f561,definition,
( sQ28_spl
<=> r4_waybel_0(sK0_skl,sK1_skl,sK2_skl,k1_xboole_0) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f563,plain,
( sQ28_spl
| ~ r4_waybel_0(sK0_skl,sK1_skl,sK2_skl,k1_xboole_0) ),
inference(component_clause,[status(thm)],[f561]) ).
fof(f564,plain,
( ~ sQ20_spl
| ~ sQ28_spl
| sQ1_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f560,f382,f385,f388,f391,f365,f561,f480]) ).
fof(f565,plain,
( sQ28_spl
| ~ sQ25_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f563,f504]) ).
fof(f566,plain,
( sQ28_spl
| ~ sQ25_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f565]) ).
fof(f642,definition,
( sQ36_spl
<=> m1_subset_1(sK9_skl(u1_struct_0(sK0_skl)),u1_struct_0(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f644,plain,
( sQ36_spl
| ~ m1_subset_1(sK9_skl(u1_struct_0(sK0_skl)),u1_struct_0(sK0_skl)) ),
inference(component_clause,[status(thm)],[f642]) ).
fof(f660,plain,
( sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f644,f205]) ).
fof(f661,plain,
sQ36_spl,
inference(contradiction_clause,[status(thm)],[f660]) ).
fof(f724,plain,
! [X0,X1,X2] :
( r4_waybel_0(X0,X1,X2,k1_pre_topc(X0))
| ~ v4_waybel34(X2,X0,X1)
| ~ m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v1_funct_1(X2)
| ~ l1_orders_2(X1)
| v3_struct_0(X1)
| ~ l1_orders_2(X0)
| v3_struct_0(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f492,f241]) ).
fof(f741,plain,
( r4_waybel_0(sK0_skl,sK1_skl,sK2_skl,k1_pre_topc(sK0_skl))
| ~ v4_waybel34(sK2_skl,sK0_skl,sK1_skl)
| ~ m2_relset_1(sK2_skl,u1_struct_0(sK0_skl),u1_struct_0(sK1_skl))
| ~ v1_funct_1(sK2_skl)
| ~ l1_orders_2(sK1_skl)
| v3_struct_0(sK1_skl)
| ~ l1_orders_2(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f724,f92]) ).
fof(f742,plain,
( sQ25_spl
| ~ sQ23_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ4_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f741,f376,f379,f382,f385,f388,f391,f494,f500]) ).
fof(f774,definition,
( sQ57_spl
<=> l1_struct_0(sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f776,plain,
( sQ57_spl
| ~ l1_struct_0(sK7_skl) ),
inference(component_clause,[status(thm)],[f774]) ).
fof(f794,plain,
( sQ57_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f776,f201]) ).
fof(f795,plain,
sQ57_spl,
inference(contradiction_clause,[status(thm)],[f794]) ).
fof(f905,definition,
( sQ76_spl
<=> l1_struct_0(sK19_skl) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f907,plain,
( sQ76_spl
| ~ l1_struct_0(sK19_skl) ),
inference(component_clause,[status(thm)],[f905]) ).
fof(f925,plain,
( sQ76_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f907,f310]) ).
fof(f926,plain,
sQ76_spl,
inference(contradiction_clause,[status(thm)],[f925]) ).
fof(f979,plain,
! [X0,X1] :
( k2_struct_0(sK0_skl,X0,X1) = k2_tarski(X0,X1)
| ~ m1_subset_1(X1,u1_struct_0(sK0_skl))
| ~ m1_subset_1(X0,u1_struct_0(sK0_skl))
| ~ l1_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f333,f87]) ).
fof(f991,definition,
! [X0,X1] :
( sQ86_spl
<=> ( k2_struct_0(sK0_skl,X0,X1) = k2_tarski(X0,X1)
| ~ m1_subset_1(X1,u1_struct_0(sK0_skl))
| ~ m1_subset_1(X0,u1_struct_0(sK0_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f992,plain,
! [X0,X1] :
( ~ sQ86_spl
| k2_struct_0(sK0_skl,X0,X1) = k2_tarski(X0,X1)
| ~ m1_subset_1(X1,u1_struct_0(sK0_skl))
| ~ m1_subset_1(X0,u1_struct_0(sK0_skl)) ),
inference(component_clause,[status(thm)],[f991]) ).
fof(f994,plain,
( sQ86_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f979,f400,f991]) ).
fof(f1001,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ86_spl
| k2_struct_0(sK0_skl,X0,sK5_skl(sK2_skl,sK1_skl,sK0_skl)) = k2_tarski(X0,sK5_skl(sK2_skl,sK1_skl,sK0_skl))
| ~ m1_subset_1(X0,u1_struct_0(sK0_skl)) ),
inference(resolution,[status(thm)],[f992,f429]) ).
fof(f1067,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ86_spl
| k2_struct_0(sK0_skl,sK4_skl(sK2_skl,sK1_skl,sK0_skl),sK5_skl(sK2_skl,sK1_skl,sK0_skl)) = k2_tarski(sK4_skl(sK2_skl,sK1_skl,sK0_skl),sK5_skl(sK2_skl,sK1_skl,sK0_skl)) ),
inference(resolution,[status(thm)],[f1001,f395]) ).
fof(f1131,plain,
( sQ27_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ86_spl
| ~ v1_finset_1(k2_tarski(sK4_skl(sK2_skl,sK1_skl,sK0_skl),sK5_skl(sK2_skl,sK1_skl,sK0_skl))) ),
inference(backward_demodulation,[status(thm)],[f1067,f540]) ).
fof(f1135,plain,
( sQ27_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ86_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1131,f265]) ).
fof(f1136,plain,
( sQ27_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ86_spl ),
inference(contradiction_clause,[status(thm)],[f1135]) ).
fof(f1137,plain,
$false,
inference(sat_refutation,[status(thm)],[f368,f397,f412,f414,f416,f418,f420,f422,f431,f469,f483,f507,f513,f541,f543,f564,f566,f661,f742,f795,f926,f994,f1136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LAT379+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.47 % Computer : n017.cluster.edu
% 0.16/0.47 % Model : x86_64 x86_64
% 0.16/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.47 % Memory : 8046.5625MB
% 0.16/0.47 % OS : Linux 6.8.0-71-generic
% 0.16/0.47 % CPULimit : 300
% 0.16/0.47 % WCLimit : 300
% 0.16/0.47 % DateTime : Sun Sep 20 23:51:27 UTC 2026
% 0.16/0.48 % CPUTime :
% 0.16/0.52 % Drodi V4.1.1
% 0.21/0.68 % Refutation found
% 0.21/0.68 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/0.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.72 % Elapsed time: 0.221700 seconds
% 0.21/0.72 % CPU time: 1.107015 seconds
% 0.21/0.72 % Total memory used: 125.339 MB
% 0.21/0.72 % Net memory used: 124.814 MB
%------------------------------------------------------------------------------