%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM401+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 01:40:26 PM UTC 2026
% Result : Theorem 0.10s 0.62s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 45
% Syntax : Number of formulae : 213 ( 23 unt; 25 def)
% Number of atoms : 648 ( 71 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 731 ( 296 ~; 316 |; 68 &)
% ( 36 <=>; 14 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 38 ( 36 usr; 26 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 199 ( 189 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
=> ordinal(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(B,A)
| ordinal_subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A] : succ(A) = set_union2(A,singleton(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(set_union2(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [A] :
( ordinal(A)
=> ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [A] : in(A,succ(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [A] : set_union2(A,empty_set) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ in(B,A)
& A != B
& ~ in(A,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,conjecture,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( in(A,succ(B))
<=> ordinal_subset(A,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( in(A,succ(B))
<=> ordinal_subset(A,B) ) ) ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f54,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f57,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f60,plain,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f61,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f62,plain,
! [X0] :
( epsilon_connected(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f69,plain,
! [A] :
( ordinal(A)
| ~ epsilon_connected(A)
| ~ epsilon_transitive(A) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f70,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f75,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f76,plain,
! [A,B] :
( ordinal_subset(B,A)
| ordinal_subset(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f77,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f78,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(NNF_transformation,[status(thm)],[f10]) ).
fof(f79,plain,
( ! [A,B] :
( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(miniscoping,[status(thm)],[f78]) ).
fof(f80,plain,
! [X0,X1] :
( subset(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f82,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f83,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f84,plain,
! [A,B] :
( ( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ( ! [C] :
( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f85,plain,
( ! [A,B] :
( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(miniscoping,[status(thm)],[f84]) ).
fof(f86,plain,
( ! [A,B] :
( ( ( sK0_skl(B,A) = A
| in(sK0_skl(B,A),B) )
& ( sK0_skl(B,A) != A
| ~ in(sK0_skl(B,A),B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f85]) ).
fof(f87,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f91,plain,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( subset(B,A)
| ~ in(B,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f92,plain,
! [A] :
( ( ? [B] :
( ~ subset(B,A)
& in(B,A) )
| epsilon_transitive(A) )
& ( ! [B] :
( subset(B,A)
| ~ in(B,A) )
| ~ epsilon_transitive(A) ) ),
inference(NNF_transformation,[status(thm)],[f91]) ).
fof(f93,plain,
( ! [A] :
( ? [B] :
( ~ subset(B,A)
& in(B,A) )
| epsilon_transitive(A) )
& ! [A] :
( ! [B] :
( subset(B,A)
| ~ in(B,A) )
| ~ epsilon_transitive(A) ) ),
inference(miniscoping,[status(thm)],[f92]) ).
fof(f94,plain,
( ! [A] :
( ( ~ subset(sK1_skl(A),A)
& in(sK1_skl(A),A) )
| epsilon_transitive(A) )
& ! [A] :
( ! [B] :
( subset(B,A)
| ~ in(B,A) )
| ~ epsilon_transitive(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(B,sK1_skl(A))],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ in(X1,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f98,plain,
! [A,B,C] :
( ( ? [D] :
( ( in(D,B)
| in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& ~ in(D,A) )
| ~ in(D,C) ) )
| C = set_union2(A,B) )
& ( ! [D] :
( ( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f14]) ).
fof(f99,plain,
( ! [A,B,C] :
( ? [D] :
( ( in(D,B)
| in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& ~ in(D,A) )
| ~ in(D,C) ) )
| C = set_union2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ! [D] :
( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(miniscoping,[status(thm)],[f98]) ).
fof(f100,plain,
( ! [A,B,C] :
( ( ( in(sK2_skl(C,B,A),B)
| in(sK2_skl(C,B,A),A)
| in(sK2_skl(C,B,A),C) )
& ( ( ~ in(sK2_skl(C,B,A),B)
& ~ in(sK2_skl(C,B,A),A) )
| ~ in(sK2_skl(C,B,A),C) ) )
| C = set_union2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ! [D] :
( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(D,sK2_skl(C,B,A))],[f99]) ).
fof(f101,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f102,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X1)
| in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f103,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f109,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f110,plain,
relation(empty_set),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f121,plain,
ordinal(empty_set),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f122,plain,
! [A,B] :
( relation(set_union2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f123,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f127,plain,
! [A] :
( ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f129,plain,
! [X0] :
( epsilon_transitive(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f130,plain,
! [X0] :
( epsilon_connected(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f131,plain,
! [X0] :
( ordinal(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f188,plain,
! [A,B] :
( ( ordinal_subset(A,B)
<=> subset(A,B) )
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f189,plain,
! [A,B] :
( ( ( ~ subset(A,B)
| ordinal_subset(A,B) )
& ( subset(A,B)
| ~ ordinal_subset(A,B) ) )
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(NNF_transformation,[status(thm)],[f188]) ).
fof(f190,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f189]) ).
fof(f191,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f189]) ).
fof(f197,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f199,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f202,plain,
! [A] :
( ! [B] :
( in(B,A)
| A = B
| in(A,B)
| ~ ordinal(B) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f203,plain,
! [X0,X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f206,plain,
? [A] :
( ? [B] :
( ( in(A,succ(B))
<~> ordinal_subset(A,B) )
& ordinal(B) )
& ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f49]) ).
fof(f207,plain,
? [A] :
( ? [B] :
( ( ~ ordinal_subset(A,B)
| ~ in(A,succ(B)) )
& ( ordinal_subset(A,B)
| in(A,succ(B)) )
& ordinal(B) )
& ordinal(A) ),
inference(NNF_transformation,[status(thm)],[f206]) ).
fof(f208,plain,
( ( ~ ordinal_subset(sK17_skl,sK18_skl)
| ~ in(sK17_skl,succ(sK18_skl)) )
& ( ordinal_subset(sK17_skl,sK18_skl)
| in(sK17_skl,succ(sK18_skl)) )
& ordinal(sK18_skl)
& ordinal(sK17_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl]),skolemize(A,sK17_skl),skolemize(B,sK18_skl)],[f207]) ).
fof(f209,plain,
ordinal(sK17_skl),
inference(cnf_transformation,[status(thm)],[f208]) ).
fof(f210,plain,
ordinal(sK18_skl),
inference(cnf_transformation,[status(thm)],[f208]) ).
fof(f211,plain,
( ordinal_subset(sK17_skl,sK18_skl)
| in(sK17_skl,succ(sK18_skl)) ),
inference(cnf_transformation,[status(thm)],[f208]) ).
fof(f212,plain,
( ~ ordinal_subset(sK17_skl,sK18_skl)
| ~ in(sK17_skl,succ(sK18_skl)) ),
inference(cnf_transformation,[status(thm)],[f208]) ).
fof(f225,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f226,plain,
! [B] :
( ~ empty(B)
| ! [A] : ~ in(A,B) ),
inference(miniscoping,[status(thm)],[f225]) ).
fof(f227,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f226]) ).
fof(f238,definition,
( sQ2_spl
<=> in(sK17_skl,succ(sK18_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f239,plain,
( ~ sQ2_spl
| in(sK17_skl,succ(sK18_skl)) ),
inference(component_clause,[status(thm)],[f238]) ).
fof(f240,plain,
( sQ2_spl
| ~ in(sK17_skl,succ(sK18_skl)) ),
inference(component_clause,[status(thm)],[f238]) ).
fof(f241,definition,
( sQ3_spl
<=> ordinal_subset(sK17_skl,sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f243,plain,
( sQ3_spl
| ~ ordinal_subset(sK17_skl,sK18_skl) ),
inference(component_clause,[status(thm)],[f241]) ).
fof(f244,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f211,f238,f241]) ).
fof(f245,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f212,f238,f241]) ).
fof(f246,plain,
! [X0] : subset(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f80]) ).
fof(f248,plain,
! [X0,X1] :
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f87]) ).
fof(f250,plain,
! [X0,X1,X2] :
( in(X0,X2)
| in(X0,X1)
| ~ in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f101]) ).
fof(f251,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f102]) ).
fof(f252,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f103]) ).
fof(f253,plain,
! [X0] : ~ in(succ(X0),X0),
inference(resolution,[status(thm)],[f57,f197]) ).
fof(f257,definition,
( sQ4_spl
<=> ordinal(succ(sK18_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f259,plain,
( sQ4_spl
| ~ ordinal(succ(sK18_skl)) ),
inference(component_clause,[status(thm)],[f257]) ).
fof(f260,definition,
( sQ5_spl
<=> ordinal(sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f262,plain,
( sQ5_spl
| ~ ordinal(sK17_skl) ),
inference(component_clause,[status(thm)],[f260]) ).
fof(f270,plain,
( sQ3_spl
| ~ subset(sK17_skl,sK18_skl)
| ~ ordinal(sK18_skl)
| ~ ordinal(sK17_skl) ),
inference(resolution,[status(thm)],[f243,f191]) ).
fof(f272,definition,
( sQ8_spl
<=> ordinal(sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f274,plain,
( sQ8_spl
| ~ ordinal(sK18_skl) ),
inference(component_clause,[status(thm)],[f272]) ).
fof(f275,definition,
( sQ9_spl
<=> subset(sK17_skl,sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f276,plain,
( ~ sQ9_spl
| subset(sK17_skl,sK18_skl) ),
inference(component_clause,[status(thm)],[f275]) ).
fof(f277,plain,
( sQ9_spl
| ~ subset(sK17_skl,sK18_skl) ),
inference(component_clause,[status(thm)],[f275]) ).
fof(f278,plain,
( sQ3_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f270,f260,f272,f275,f241]) ).
fof(f279,definition,
( sQ10_spl
<=> ordinal_subset(sK18_skl,sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f280,plain,
( ~ sQ10_spl
| ordinal_subset(sK18_skl,sK17_skl) ),
inference(component_clause,[status(thm)],[f279]) ).
fof(f281,plain,
( sQ10_spl
| ~ ordinal_subset(sK18_skl,sK17_skl) ),
inference(component_clause,[status(thm)],[f279]) ).
fof(f283,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f262,f209]) ).
fof(f284,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f283]) ).
fof(f285,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f274,f210]) ).
fof(f286,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f285]) ).
fof(f287,plain,
( sQ9_spl
| ~ ordinal_subset(sK17_skl,sK18_skl)
| ~ ordinal(sK18_skl)
| ~ ordinal(sK17_skl) ),
inference(resolution,[status(thm)],[f277,f190]) ).
fof(f288,plain,
( sQ9_spl
| ~ sQ3_spl
| ~ sQ8_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f287,f260,f272,f241,f275]) ).
fof(f299,definition,
( sQ11_spl
<=> epsilon_transitive(sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f311,plain,
( ~ sQ9_spl
| ~ subset(sK18_skl,sK17_skl)
| sK18_skl = sK17_skl ),
inference(resolution,[status(thm)],[f82,f276]) ).
fof(f312,plain,
! [X0,X1] :
( ~ ordinal_subset(X1,X0)
| ~ ordinal(X0)
| ~ ordinal(X1)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f82,f190]) ).
fof(f314,definition,
( sQ12_spl
<=> sK18_skl = sK17_skl ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f315,plain,
( ~ sQ12_spl
| sK18_skl = sK17_skl ),
inference(component_clause,[status(thm)],[f314]) ).
fof(f317,definition,
( sQ13_spl
<=> subset(sK18_skl,sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f319,plain,
( sQ13_spl
| ~ subset(sK18_skl,sK17_skl) ),
inference(component_clause,[status(thm)],[f317]) ).
fof(f320,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f311,f314,f317,f275]) ).
fof(f321,plain,
! [X0] : succ(X0) = set_union2(singleton(X0),X0),
inference(paramodulation,[status(thm)],[f75,f83]) ).
fof(f334,plain,
! [X0,X1] :
( ~ ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ ordinal_subset(X1,X0)
| ~ ordinal(X0)
| ~ ordinal(X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f312,f190]) ).
fof(f336,plain,
! [X0,X1] :
( ~ ordinal_subset(X0,X1)
| ~ ordinal_subset(X1,X0)
| ~ ordinal(X0)
| ~ ordinal(X1)
| X0 = X1 ),
inference(duplicate_literals_removal,[status(thm)],[f334]) ).
fof(f337,plain,
( ~ sQ10_spl
| ~ ordinal_subset(sK17_skl,sK18_skl)
| ~ ordinal(sK17_skl)
| ~ ordinal(sK18_skl)
| sK17_skl = sK18_skl ),
inference(resolution,[status(thm)],[f336,f280]) ).
fof(f341,plain,
( ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ8_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f337,f314,f272,f260,f241,f279]) ).
fof(f361,plain,
! [X0,X1] :
( ~ ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0)
| X1 = X0
| ~ in(X1,X0)
| ~ epsilon_transitive(X0) ),
inference(resolution,[status(thm)],[f95,f312]) ).
fof(f366,definition,
( sQ15_spl
<=> in(sK17_skl,sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f367,plain,
( ~ sQ15_spl
| in(sK17_skl,sK18_skl) ),
inference(component_clause,[status(thm)],[f366]) ).
fof(f368,plain,
( sQ15_spl
| ~ in(sK17_skl,sK18_skl) ),
inference(component_clause,[status(thm)],[f366]) ).
fof(f370,plain,
! [X0,X1] :
( ~ ordinal_subset(X1,X0)
| ~ ordinal(X0)
| ~ ordinal(X1)
| X0 = X1
| ~ in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f361,f61]) ).
fof(f373,plain,
! [X0,X1] :
( ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ ordinal(X0)
| ~ ordinal(X1)
| X0 = X1
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f370,f77]) ).
fof(f377,plain,
! [X0,X1] :
( ordinal_subset(X0,X1)
| ~ ordinal(X0)
| ~ ordinal(X1)
| X0 = X1
| ~ in(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f373]) ).
fof(f381,plain,
( sQ9_spl
| ~ sQ12_spl
| ~ subset(sK17_skl,sK17_skl) ),
inference(backward_demodulation,[status(thm)],[f315,f277]) ).
fof(f384,plain,
( sQ9_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f381,f246]) ).
fof(f385,plain,
( sQ9_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f384]) ).
fof(f388,plain,
! [X0,X1] :
( in(X0,singleton(X1))
| in(X0,X1)
| ~ in(X0,succ(X1)) ),
inference(paramodulation,[status(thm)],[f83,f250]) ).
fof(f392,plain,
( sQ15_spl
| sK18_skl = sK17_skl
| in(sK18_skl,sK17_skl)
| ~ ordinal(sK17_skl)
| ~ ordinal(sK18_skl) ),
inference(resolution,[status(thm)],[f368,f203]) ).
fof(f393,definition,
( sQ16_spl
<=> in(sK18_skl,sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f396,plain,
( sQ15_spl
| sQ12_spl
| sQ16_spl
| ~ sQ5_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f392,f272,f260,f393,f314,f366]) ).
fof(f417,plain,
( sQ3_spl
| ~ ordinal(sK17_skl)
| ~ ordinal(sK18_skl)
| sK17_skl = sK18_skl
| ~ in(sK17_skl,sK18_skl) ),
inference(resolution,[status(thm)],[f377,f243]) ).
fof(f420,plain,
( sQ3_spl
| ~ sQ5_spl
| ~ sQ8_spl
| sQ12_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f417,f366,f314,f272,f260,f241]) ).
fof(f449,plain,
! [X0] : set_union2(empty_set,X0) = X0,
inference(paramodulation,[status(thm)],[f75,f199]) ).
fof(f499,plain,
! [X0] :
( ~ sQ2_spl
| in(sK17_skl,set_union2(succ(sK18_skl),X0)) ),
inference(resolution,[status(thm)],[f251,f239]) ).
fof(f528,definition,
( sQ18_spl
<=> ordinal(succ(sK17_skl)) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f530,plain,
( sQ18_spl
| ~ ordinal(succ(sK17_skl)) ),
inference(component_clause,[status(thm)],[f528]) ).
fof(f543,plain,
( ~ sQ2_spl
| in(sK17_skl,succ(succ(sK18_skl))) ),
inference(paramodulation,[status(thm)],[f83,f499]) ).
fof(f563,plain,
( sQ18_spl
| ~ ordinal(sK17_skl) ),
inference(resolution,[status(thm)],[f530,f131]) ).
fof(f566,plain,
( sQ18_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f563,f260,f528]) ).
fof(f599,plain,
! [X0] : ~ in(X0,empty_set),
inference(resolution,[status(thm)],[f227,f109]) ).
fof(f601,plain,
! [X0] :
( empty_set = X0
| in(empty_set,X0)
| ~ ordinal(X0)
| ~ ordinal(empty_set) ),
inference(resolution,[status(thm)],[f599,f203]) ).
fof(f602,definition,
( sQ24_spl
<=> ordinal(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f604,plain,
( sQ24_spl
| ~ ordinal(empty_set) ),
inference(component_clause,[status(thm)],[f602]) ).
fof(f605,definition,
! [X0] :
( sQ25_spl
<=> ( empty_set = X0
| in(empty_set,X0)
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f608,plain,
( sQ25_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f601,f602,f605]) ).
fof(f609,plain,
( sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f604,f121]) ).
fof(f610,plain,
sQ24_spl,
inference(contradiction_clause,[status(thm)],[f609]) ).
fof(f672,plain,
! [X0] :
( relation(X0)
| ~ relation(X0)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f449,f123]) ).
fof(f678,definition,
( sQ31_spl
<=> relation(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f680,plain,
( sQ31_spl
| ~ relation(empty_set) ),
inference(component_clause,[status(thm)],[f678]) ).
fof(f681,definition,
! [X0] :
( sQ32_spl
<=> ( relation(X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f684,plain,
( sQ32_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f672,f678,f681]) ).
fof(f686,plain,
( sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f680,f110]) ).
fof(f687,plain,
sQ31_spl,
inference(contradiction_clause,[status(thm)],[f686]) ).
fof(f928,plain,
( ~ sQ2_spl
| ~ in(succ(succ(sK18_skl)),sK17_skl) ),
inference(resolution,[status(thm)],[f543,f57]) ).
fof(f929,plain,
( ~ sQ2_spl
| sK17_skl = succ(succ(sK18_skl))
| in(sK17_skl,succ(succ(sK18_skl)))
| ~ ordinal(succ(succ(sK18_skl)))
| ~ ordinal(sK17_skl) ),
inference(resolution,[status(thm)],[f928,f203]) ).
fof(f930,definition,
( sQ38_spl
<=> ordinal(succ(succ(sK18_skl))) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f932,plain,
( sQ38_spl
| ~ ordinal(succ(succ(sK18_skl))) ),
inference(component_clause,[status(thm)],[f930]) ).
fof(f933,definition,
( sQ39_spl
<=> in(sK17_skl,succ(succ(sK18_skl))) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f936,definition,
( sQ40_spl
<=> sK17_skl = succ(succ(sK18_skl)) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f937,plain,
( ~ sQ40_spl
| sK17_skl = succ(succ(sK18_skl)) ),
inference(component_clause,[status(thm)],[f936]) ).
fof(f939,plain,
( ~ sQ2_spl
| sQ40_spl
| sQ39_spl
| ~ sQ38_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f929,f260,f930,f933,f936,f238]) ).
fof(f962,plain,
( ~ sQ40_spl
| epsilon_transitive(sK17_skl)
| ~ ordinal(succ(sK18_skl)) ),
inference(paramodulation,[status(thm)],[f937,f129]) ).
fof(f963,plain,
( ~ sQ40_spl
| ~ in(sK17_skl,succ(sK18_skl)) ),
inference(paramodulation,[status(thm)],[f937,f253]) ).
fof(f972,plain,
( ~ sQ40_spl
| sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f962,f257,f299,f936]) ).
fof(f973,plain,
( ~ sQ40_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f963,f238,f936]) ).
fof(f977,plain,
( sQ38_spl
| ~ epsilon_connected(succ(succ(sK18_skl)))
| ~ epsilon_transitive(succ(succ(sK18_skl))) ),
inference(resolution,[status(thm)],[f932,f70]) ).
fof(f979,definition,
( sQ42_spl
<=> epsilon_transitive(succ(succ(sK18_skl))) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f981,plain,
( sQ42_spl
| ~ epsilon_transitive(succ(succ(sK18_skl))) ),
inference(component_clause,[status(thm)],[f979]) ).
fof(f982,definition,
( sQ43_spl
<=> epsilon_connected(succ(succ(sK18_skl))) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f984,plain,
( sQ43_spl
| ~ epsilon_connected(succ(succ(sK18_skl))) ),
inference(component_clause,[status(thm)],[f982]) ).
fof(f985,plain,
( sQ38_spl
| ~ sQ43_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f977,f979,f982,f930]) ).
fof(f986,plain,
( sQ4_spl
| ~ ordinal(sK18_skl) ),
inference(resolution,[status(thm)],[f259,f131]) ).
fof(f989,plain,
( sQ4_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f986,f272,f257]) ).
fof(f990,definition,
( sQ44_spl
<=> epsilon_transitive(succ(sK18_skl)) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f992,plain,
( sQ44_spl
| ~ epsilon_transitive(succ(sK18_skl)) ),
inference(component_clause,[status(thm)],[f990]) ).
fof(f993,definition,
( sQ45_spl
<=> epsilon_connected(succ(sK18_skl)) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f995,plain,
( sQ45_spl
| ~ epsilon_connected(succ(sK18_skl)) ),
inference(component_clause,[status(thm)],[f993]) ).
fof(f999,plain,
( sQ45_spl
| ~ ordinal(succ(sK18_skl)) ),
inference(resolution,[status(thm)],[f995,f62]) ).
fof(f1001,plain,
( sQ45_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f999,f257,f993]) ).
fof(f1006,plain,
( sQ44_spl
| ~ ordinal(succ(sK18_skl)) ),
inference(resolution,[status(thm)],[f992,f61]) ).
fof(f1008,plain,
( sQ44_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1006,f257,f990]) ).
fof(f1013,plain,
( sQ43_spl
| ~ ordinal(succ(sK18_skl)) ),
inference(resolution,[status(thm)],[f984,f130]) ).
fof(f1016,plain,
( sQ43_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1013,f257,f982]) ).
fof(f1017,plain,
( sQ42_spl
| ~ ordinal(succ(sK18_skl)) ),
inference(resolution,[status(thm)],[f981,f129]) ).
fof(f1022,plain,
( sQ42_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1017,f257,f979]) ).
fof(f1087,plain,
( sQ2_spl
| ~ sQ12_spl
| ~ in(sK17_skl,succ(sK17_skl)) ),
inference(backward_demodulation,[status(thm)],[f315,f240]) ).
fof(f1089,plain,
( sQ2_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1087,f197]) ).
fof(f1090,plain,
( sQ2_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f1089]) ).
fof(f1105,plain,
( sQ13_spl
| ~ in(sK18_skl,sK17_skl)
| ~ epsilon_transitive(sK17_skl) ),
inference(resolution,[status(thm)],[f319,f95]) ).
fof(f1106,plain,
( sQ13_spl
| ~ ordinal_subset(sK18_skl,sK17_skl)
| ~ ordinal(sK17_skl)
| ~ ordinal(sK18_skl) ),
inference(resolution,[status(thm)],[f319,f190]) ).
fof(f1107,plain,
( sQ13_spl
| ~ sQ16_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1105,f299,f393,f317]) ).
fof(f1108,plain,
( sQ13_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1106,f272,f260,f279,f317]) ).
fof(f1116,plain,
! [X0] :
( ~ sQ15_spl
| in(sK17_skl,set_union2(X0,sK18_skl)) ),
inference(resolution,[status(thm)],[f367,f252]) ).
fof(f1119,plain,
( sQ10_spl
| ~ ordinal(sK18_skl)
| ~ ordinal(sK17_skl)
| sK18_skl = sK17_skl
| ~ in(sK18_skl,sK17_skl) ),
inference(resolution,[status(thm)],[f281,f377]) ).
fof(f1122,plain,
( sQ10_spl
| ~ sQ8_spl
| ~ sQ5_spl
| sQ12_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1119,f393,f314,f260,f272,f279]) ).
fof(f1274,plain,
( ~ sQ15_spl
| in(sK17_skl,succ(sK18_skl)) ),
inference(paramodulation,[status(thm)],[f321,f1116]) ).
fof(f1280,plain,
( ~ sQ15_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1274,f238,f366]) ).
fof(f1316,plain,
( ~ sQ2_spl
| in(sK17_skl,singleton(sK18_skl))
| in(sK17_skl,sK18_skl) ),
inference(resolution,[status(thm)],[f239,f388]) ).
fof(f1320,definition,
( sQ50_spl
<=> in(sK17_skl,singleton(sK18_skl)) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f1321,plain,
( ~ sQ50_spl
| in(sK17_skl,singleton(sK18_skl)) ),
inference(component_clause,[status(thm)],[f1320]) ).
fof(f1323,plain,
( ~ sQ2_spl
| sQ50_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f1316,f366,f1320,f238]) ).
fof(f1338,plain,
( ~ sQ50_spl
| sK17_skl = sK18_skl ),
inference(resolution,[status(thm)],[f1321,f248]) ).
fof(f1344,plain,
( ~ sQ50_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f1338,f314,f1320]) ).
fof(f1345,plain,
$false,
inference(sat_refutation,[status(thm)],[f244,f245,f278,f284,f286,f288,f320,f341,f385,f396,f420,f566,f608,f610,f684,f687,f939,f972,f973,f985,f989,f1001,f1008,f1016,f1022,f1090,f1107,f1108,f1122,f1280,f1323,f1344]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM401+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n010.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 02:27:24 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 0.10/0.62 % Refutation found
% 0.10/0.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.64 % Elapsed time: 0.259087 seconds
% 0.10/0.64 % CPU time: 1.658798 seconds
% 0.10/0.64 % Total memory used: 125.495 MB
% 0.10/0.64 % Net memory used: 123.014 MB
%------------------------------------------------------------------------------