%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET862-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 02:10:51 PM UTC 2026
% Result : Unsatisfiable 2.86s 1.00s
% Output : CNFRefutation 2.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 83
% Syntax : Number of formulae : 342 ( 39 unt; 68 def)
% Number of atoms : 957 ( 71 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 1020 ( 405 ~; 547 |; 0 &)
% ( 68 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 72 ( 70 usr; 69 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 270 ( 270 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [V_B,V_A,T_a] :
( V_A = V_B
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [V_c,V_A,T_a,V_B] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [V_A,V_B,T_a] :
( c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [V_A,V_B,T_a] :
( c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [V_z,V_S,T_a,V_c] :
( c_in(c_union(c_insert(V_z,c_emptyset,tc_set(T_a)),V_c,tc_set(T_a)),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))
| c_in(c_Zorn_Ochain__extend__1(V_c,V_z,T_a),V_c,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_z,V_S,tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [V_z,V_S,T_a,V_c] :
( c_in(c_union(c_insert(V_z,c_emptyset,tc_set(T_a)),V_c,tc_set(T_a)),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(V_c,V_z,T_a),V_z,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_z,V_S,tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [V_z,V_x,T_a,V_c,V_S,V_y] :
( c_in(c_Zorn_Omaxchain__super__lemma__1(V_c,V_y,T_a),V_c,tc_set(T_a))
| c_in(V_z,V_y,T_a)
| ~ c_in(c_union(c_insert(V_x,c_emptyset,tc_set(T_a)),V_c,tc_set(T_a)),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_z,V_x,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [V_z,V_x,T_a,V_c,V_S,V_y] :
( c_in(V_z,V_y,T_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c,V_y,T_a),V_y,tc_set(T_a))
| ~ c_in(c_union(c_insert(V_x,c_emptyset,tc_set(T_a)),V_c,tc_set(T_a)),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_z,V_x,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
c_in(v_y,v_S,tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
! [V_U] :
( ~ c_in(V_U,v_c,tc_set(t_a))
| c_lessequals(V_U,v_y,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
! [V_U] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_in(v_x(V_U),v_S,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
! [V_U] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_lessequals(V_U,v_x(V_U),tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
! [V_U] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| V_U != v_x(V_U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,plain,
! [V_B,V_A] :
( V_A = V_B
| ! [T_a] :
( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f17,plain,
! [X0,X1,X2] :
( X1 = X0
| ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f18,plain,
! [V_c,T_a,V_B] :
( c_in(V_c,V_B,T_a)
| ! [V_A] :
( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f19,plain,
! [X0,X1,X2,X3] :
( c_in(X0,X3,X2)
| ~ c_lessequals(X1,X3,tc_set(X2))
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( c_lessequals(X0,X1,tc_set(X2))
| c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f21,plain,
! [X0,X1,X2] :
( c_lessequals(X0,X1,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( c_in(c_union(c_insert(X0,c_emptyset,tc_set(X2)),X3,tc_set(X2)),c_Zorn_Ochain(X1,X2),tc_set(tc_set(X2)))
| c_in(c_Zorn_Ochain__extend__1(X3,X0,X2),X3,tc_set(X2))
| ~ c_in(X3,c_Zorn_Ochain(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( c_in(c_union(c_insert(X0,c_emptyset,tc_set(X2)),X3,tc_set(X2)),c_Zorn_Ochain(X1,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(X3,X0,X2),X0,tc_set(X2))
| ~ c_in(X3,c_Zorn_Ochain(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f24,plain,
! [T_a,V_c,V_y] :
( c_in(c_Zorn_Omaxchain__super__lemma__1(V_c,V_y,T_a),V_c,tc_set(T_a))
| ! [V_z] :
( c_in(V_z,V_y,T_a)
| ! [V_x,V_S] :
( ~ c_in(c_union(c_insert(V_x,c_emptyset,tc_set(T_a)),V_c,tc_set(T_a)),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_z,V_x,T_a) ) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f25,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_in(c_Zorn_Omaxchain__super__lemma__1(X3,X5,X2),X3,tc_set(X2))
| c_in(X0,X5,X2)
| ~ c_in(c_union(c_insert(X1,c_emptyset,tc_set(X2)),X3,tc_set(X2)),c_Zorn_Ochain(X4,X2),tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_Omaxchain(X4,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
! [V_z,T_a,V_y] :
( c_in(V_z,V_y,T_a)
| ! [V_c] :
( ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c,V_y,T_a),V_y,tc_set(T_a))
| ! [V_x,V_S] :
( ~ c_in(c_union(c_insert(V_x,c_emptyset,tc_set(T_a)),V_c,tc_set(T_a)),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_z,V_x,T_a) ) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f27,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_in(X0,X5,X2)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(X3,X5,X2),X5,tc_set(X2))
| ~ c_in(c_union(c_insert(X1,c_emptyset,tc_set(X2)),X3,tc_set(X2)),c_Zorn_Ochain(X4,X2),tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_Omaxchain(X4,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f29,plain,
c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f30,plain,
c_in(v_y,v_S,tc_set(t_a)),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f31,plain,
! [X0] :
( ~ c_in(X0,v_c,tc_set(t_a))
| c_lessequals(X0,v_y,tc_set(t_a)) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f32,plain,
! [X0] :
( ~ c_in(X0,v_S,tc_set(t_a))
| c_in(v_x(X0),v_S,tc_set(t_a)) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f33,plain,
! [X0] :
( ~ c_in(X0,v_S,tc_set(t_a))
| c_lessequals(X0,v_x(X0),tc_set(t_a)) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f34,plain,
! [X0] :
( ~ c_in(X0,v_S,tc_set(t_a))
| X0 != v_x(X0) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f35,plain,
v_y != v_x(v_y),
inference(resolution,[status(thm)],[f34,f30]) ).
fof(f36,plain,
! [X0] :
( ~ c_in(X0,v_c,tc_set(t_a))
| X0 = v_y
| ~ c_lessequals(v_y,X0,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f17,f31]) ).
fof(f37,plain,
! [X0,X1] :
( ~ c_in(X1,v_c,tc_set(t_a))
| c_in(X0,v_y,t_a)
| ~ c_in(X0,X1,t_a) ),
inference(resolution,[status(thm)],[f19,f31]) ).
fof(f38,plain,
c_lessequals(v_y,v_x(v_y),tc_set(t_a)),
inference(resolution,[status(thm)],[f33,f30]) ).
fof(f39,plain,
! [X0] :
( c_in(X0,v_x(v_y),t_a)
| ~ c_in(X0,v_y,t_a) ),
inference(resolution,[status(thm)],[f38,f19]) ).
fof(f40,plain,
( v_y = v_x(v_y)
| ~ c_lessequals(v_x(v_y),v_y,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f38,f17]) ).
fof(f41,definition,
( sQ0_spl
<=> c_lessequals(v_x(v_y),v_y,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f43,plain,
( sQ0_spl
| ~ c_lessequals(v_x(v_y),v_y,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f41]) ).
fof(f44,definition,
( sQ1_spl
<=> v_y = v_x(v_y) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f45,plain,
( ~ sQ1_spl
| v_y = v_x(v_y) ),
inference(component_clause,[status(thm)],[f44]) ).
fof(f47,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f40,f41,f44]) ).
fof(f49,plain,
c_in(v_x(v_y),v_S,tc_set(t_a)),
inference(resolution,[status(thm)],[f32,f30]) ).
fof(f50,plain,
c_in(v_x(v_x(v_y)),v_S,tc_set(t_a)),
inference(resolution,[status(thm)],[f49,f32]) ).
fof(f51,plain,
c_lessequals(v_x(v_y),v_x(v_x(v_y)),tc_set(t_a)),
inference(resolution,[status(thm)],[f49,f33]) ).
fof(f52,plain,
v_x(v_y) != v_x(v_x(v_y)),
inference(resolution,[status(thm)],[f49,f34]) ).
fof(f53,plain,
c_in(v_x(v_x(v_x(v_y))),v_S,tc_set(t_a)),
inference(resolution,[status(thm)],[f50,f32]) ).
fof(f54,plain,
c_lessequals(v_x(v_x(v_y)),v_x(v_x(v_x(v_y))),tc_set(t_a)),
inference(resolution,[status(thm)],[f50,f33]) ).
fof(f55,plain,
v_x(v_x(v_y)) != v_x(v_x(v_x(v_y))),
inference(resolution,[status(thm)],[f50,f34]) ).
fof(f56,plain,
( sQ0_spl
| c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),v_x(v_y),t_a) ),
inference(resolution,[status(thm)],[f20,f43]) ).
fof(f57,plain,
! [X0,X1,X2,X3] :
( c_in(X3,X1,X2)
| ~ c_in(X3,X0,X2)
| c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2) ),
inference(resolution,[status(thm)],[f20,f19]) ).
fof(f58,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ c_lessequals(X1,X0,tc_set(X2))
| c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2) ),
inference(resolution,[status(thm)],[f20,f17]) ).
fof(f59,plain,
! [X0] :
( c_in(X0,v_x(v_x(v_y)),t_a)
| ~ c_in(X0,v_x(v_y),t_a) ),
inference(resolution,[status(thm)],[f51,f19]) ).
fof(f60,plain,
( v_x(v_y) = v_x(v_x(v_y))
| ~ c_lessequals(v_x(v_x(v_y)),v_x(v_y),tc_set(t_a)) ),
inference(resolution,[status(thm)],[f51,f17]) ).
fof(f61,definition,
( sQ2_spl
<=> c_lessequals(v_x(v_x(v_y)),v_x(v_y),tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f64,definition,
( sQ3_spl
<=> v_x(v_y) = v_x(v_x(v_y)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f65,plain,
( ~ sQ3_spl
| v_x(v_y) = v_x(v_x(v_y)) ),
inference(component_clause,[status(thm)],[f64]) ).
fof(f67,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f60,f61,f64]) ).
fof(f68,plain,
c_in(v_x(v_x(v_x(v_x(v_y)))),v_S,tc_set(t_a)),
inference(resolution,[status(thm)],[f53,f32]) ).
fof(f69,plain,
c_lessequals(v_x(v_x(v_x(v_y))),v_x(v_x(v_x(v_x(v_y)))),tc_set(t_a)),
inference(resolution,[status(thm)],[f53,f33]) ).
fof(f70,plain,
v_x(v_x(v_x(v_y))) != v_x(v_x(v_x(v_x(v_y)))),
inference(resolution,[status(thm)],[f53,f34]) ).
fof(f72,plain,
( v_x(v_x(v_y)) = v_x(v_y)
| c_in(c_Main_OsubsetI__1(v_x(v_x(v_y)),v_x(v_y),t_a),v_x(v_x(v_y)),t_a) ),
inference(resolution,[status(thm)],[f58,f51]) ).
fof(f73,plain,
( v_x(v_y) = v_y
| c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),v_x(v_y),t_a) ),
inference(resolution,[status(thm)],[f58,f38]) ).
fof(f74,plain,
! [X0] :
( ~ c_in(X0,v_c,tc_set(t_a))
| v_y = X0
| c_in(c_Main_OsubsetI__1(v_y,X0,t_a),v_y,t_a) ),
inference(resolution,[status(thm)],[f58,f31]) ).
fof(f75,plain,
! [X0,X1,X2] :
( c_in(c_Main_OsubsetI__1(X1,X0,X2),X1,X2)
| X0 = X1
| c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2) ),
inference(resolution,[status(thm)],[f58,f20]) ).
fof(f76,definition,
( sQ4_spl
<=> c_in(c_Main_OsubsetI__1(v_x(v_x(v_y)),v_x(v_y),t_a),v_x(v_x(v_y)),t_a) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f79,plain,
( sQ3_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f72,f76,f64]) ).
fof(f80,definition,
( sQ5_spl
<=> c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),v_x(v_y),t_a) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f83,plain,
( sQ1_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f73,f80,f44]) ).
fof(f84,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f45,f35]) ).
fof(f85,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f84]) ).
fof(f86,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f65,f52]) ).
fof(f87,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f86]) ).
fof(f91,plain,
c_in(v_x(v_x(v_x(v_x(v_x(v_y))))),v_S,tc_set(t_a)),
inference(resolution,[status(thm)],[f68,f32]) ).
fof(f92,plain,
c_lessequals(v_x(v_x(v_x(v_x(v_y)))),v_x(v_x(v_x(v_x(v_x(v_y))))),tc_set(t_a)),
inference(resolution,[status(thm)],[f68,f33]) ).
fof(f93,plain,
v_x(v_x(v_x(v_x(v_y)))) != v_x(v_x(v_x(v_x(v_x(v_y))))),
inference(resolution,[status(thm)],[f68,f34]) ).
fof(f94,plain,
! [X0,X1,X2] :
( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_c,tc_set(t_a))
| c_in(X0,X2,t_a)
| ~ c_in(c_union(c_insert(X1,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X0,X1,t_a) ),
inference(resolution,[status(thm)],[f25,f28]) ).
fof(f95,plain,
( v_x(v_x(v_x(v_y))) = v_x(v_x(v_y))
| c_in(c_Main_OsubsetI__1(v_x(v_x(v_x(v_y))),v_x(v_x(v_y)),t_a),v_x(v_x(v_x(v_y))),t_a) ),
inference(resolution,[status(thm)],[f54,f58]) ).
fof(f97,plain,
( v_x(v_x(v_y)) = v_x(v_x(v_x(v_y)))
| ~ c_lessequals(v_x(v_x(v_x(v_y))),v_x(v_x(v_y)),tc_set(t_a)) ),
inference(resolution,[status(thm)],[f54,f17]) ).
fof(f98,definition,
( sQ6_spl
<=> c_in(c_Main_OsubsetI__1(v_x(v_x(v_x(v_y))),v_x(v_x(v_y)),t_a),v_x(v_x(v_x(v_y))),t_a) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f101,definition,
( sQ7_spl
<=> v_x(v_x(v_x(v_y))) = v_x(v_x(v_y)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ7_spl
| v_x(v_x(v_x(v_y))) = v_x(v_x(v_y)) ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f104,plain,
( sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f95,f98,f101]) ).
fof(f105,definition,
( sQ8_spl
<=> c_lessequals(v_x(v_x(v_x(v_y))),v_x(v_x(v_y)),tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( sQ7_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f97,f105,f101]) ).
fof(f109,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f102,f55]) ).
fof(f110,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f109]) ).
fof(f112,plain,
! [X0] :
( sQ0_spl
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),X0,t_a)
| ~ c_in(c_union(c_insert(v_x(v_y),c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f94,f56]) ).
fof(f113,definition,
( sQ9_spl
<=> c_in(c_union(c_insert(v_x(v_y),c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f114,plain,
( ~ sQ9_spl
| c_in(c_union(c_insert(v_x(v_y),c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f115,plain,
( sQ9_spl
| ~ c_in(c_union(c_insert(v_x(v_y),c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f116,definition,
! [X0] :
( sQ10_spl
<=> ( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),X0,t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f117,plain,
! [X0] :
( ~ sQ10_spl
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),X0,t_a) ),
inference(component_clause,[status(thm)],[f116]) ).
fof(f119,plain,
( sQ0_spl
| sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f112,f113,f116,f41]) ).
fof(f126,plain,
! [X0,X1] :
( c_in(v_x(c_Main_OsubsetI__1(v_S,X1,tc_set(t_a))),v_S,tc_set(t_a))
| c_in(X0,X1,tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f57,f32]) ).
fof(f129,plain,
! [X0,X1,X2,X3] :
( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X3,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(X1,X2,t_a),X3,t_a)
| ~ c_in(c_union(c_insert(X1,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(X0,X2,t_a)
| ~ c_in(X0,X1,t_a) ),
inference(resolution,[status(thm)],[f57,f94]) ).
fof(f139,plain,
! [X0,X1,X2] :
( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(X1,X0,t_a),X2,t_a)
| ~ c_in(c_union(c_insert(X1,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| X0 = X1
| c_in(c_Main_OsubsetI__1(X0,X1,t_a),X0,t_a) ),
inference(resolution,[status(thm)],[f75,f94]) ).
fof(f141,plain,
c_lessequals(v_x(v_x(v_x(v_x(v_x(v_y))))),v_x(v_x(v_x(v_x(v_x(v_x(v_y)))))),tc_set(t_a)),
inference(resolution,[status(thm)],[f91,f33]) ).
fof(f142,plain,
v_x(v_x(v_x(v_x(v_x(v_y))))) != v_x(v_x(v_x(v_x(v_x(v_x(v_y)))))),
inference(resolution,[status(thm)],[f91,f34]) ).
fof(f152,plain,
( v_x(v_x(v_x(v_x(v_y)))) = v_x(v_x(v_x(v_y)))
| c_in(c_Main_OsubsetI__1(v_x(v_x(v_x(v_x(v_y)))),v_x(v_x(v_x(v_y))),t_a),v_x(v_x(v_x(v_x(v_y)))),t_a) ),
inference(resolution,[status(thm)],[f69,f58]) ).
fof(f154,plain,
( v_x(v_x(v_x(v_y))) = v_x(v_x(v_x(v_x(v_y))))
| ~ c_lessequals(v_x(v_x(v_x(v_x(v_y)))),v_x(v_x(v_x(v_y))),tc_set(t_a)) ),
inference(resolution,[status(thm)],[f69,f17]) ).
fof(f155,definition,
( sQ12_spl
<=> c_in(c_Main_OsubsetI__1(v_x(v_x(v_x(v_x(v_y)))),v_x(v_x(v_x(v_y))),t_a),v_x(v_x(v_x(v_x(v_y)))),t_a) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f158,definition,
( sQ13_spl
<=> v_x(v_x(v_x(v_x(v_y)))) = v_x(v_x(v_x(v_y))) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f159,plain,
( ~ sQ13_spl
| v_x(v_x(v_x(v_x(v_y)))) = v_x(v_x(v_x(v_y))) ),
inference(component_clause,[status(thm)],[f158]) ).
fof(f161,plain,
( sQ13_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f152,f155,f158]) ).
fof(f162,definition,
( sQ14_spl
<=> c_lessequals(v_x(v_x(v_x(v_x(v_y)))),v_x(v_x(v_x(v_y))),tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f165,plain,
( sQ13_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f154,f162,f158]) ).
fof(f166,plain,
( ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f159,f70]) ).
fof(f167,plain,
~ sQ13_spl,
inference(contradiction_clause,[status(thm)],[f166]) ).
fof(f173,plain,
! [X0] :
( X0 = v_c
| c_in(c_Main_OsubsetI__1(X0,v_c,tc_set(t_a)),X0,tc_set(t_a))
| v_y = c_Main_OsubsetI__1(v_c,X0,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_y,c_Main_OsubsetI__1(v_c,X0,tc_set(t_a)),t_a),v_y,t_a) ),
inference(resolution,[status(thm)],[f74,f75]) ).
fof(f174,plain,
! [X0,X1] :
( c_in(X1,X0,tc_set(t_a))
| ~ c_in(X1,v_c,tc_set(t_a))
| v_y = c_Main_OsubsetI__1(v_c,X0,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_y,c_Main_OsubsetI__1(v_c,X0,tc_set(t_a)),t_a),v_y,t_a) ),
inference(resolution,[status(thm)],[f74,f57]) ).
fof(f191,plain,
( v_x(v_x(v_x(v_x(v_x(v_y))))) = v_x(v_x(v_x(v_x(v_y))))
| c_in(c_Main_OsubsetI__1(v_x(v_x(v_x(v_x(v_x(v_y))))),v_x(v_x(v_x(v_x(v_y)))),t_a),v_x(v_x(v_x(v_x(v_x(v_y))))),t_a) ),
inference(resolution,[status(thm)],[f92,f58]) ).
fof(f193,plain,
( v_x(v_x(v_x(v_x(v_y)))) = v_x(v_x(v_x(v_x(v_x(v_y)))))
| ~ c_lessequals(v_x(v_x(v_x(v_x(v_x(v_y))))),v_x(v_x(v_x(v_x(v_y)))),tc_set(t_a)) ),
inference(resolution,[status(thm)],[f92,f17]) ).
fof(f194,definition,
( sQ18_spl
<=> c_in(c_Main_OsubsetI__1(v_x(v_x(v_x(v_x(v_x(v_y))))),v_x(v_x(v_x(v_x(v_y)))),t_a),v_x(v_x(v_x(v_x(v_x(v_y))))),t_a) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f197,definition,
( sQ19_spl
<=> v_x(v_x(v_x(v_x(v_x(v_y))))) = v_x(v_x(v_x(v_x(v_y)))) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f198,plain,
( ~ sQ19_spl
| v_x(v_x(v_x(v_x(v_x(v_y))))) = v_x(v_x(v_x(v_x(v_y)))) ),
inference(component_clause,[status(thm)],[f197]) ).
fof(f200,plain,
( sQ19_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f191,f194,f197]) ).
fof(f201,definition,
( sQ20_spl
<=> c_lessequals(v_x(v_x(v_x(v_x(v_x(v_y))))),v_x(v_x(v_x(v_x(v_y)))),tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f204,plain,
( sQ19_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f193,f201,f197]) ).
fof(f205,plain,
( ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f198,f93]) ).
fof(f206,plain,
~ sQ19_spl,
inference(contradiction_clause,[status(thm)],[f205]) ).
fof(f239,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_in(c_Zorn_Ochain__extend__1(X3,X1,X2),X3,tc_set(X2))
| ~ c_in(X3,c_Zorn_Ochain(X4,X2),tc_set(tc_set(X2)))
| ~ c_in(X1,X4,tc_set(X2))
| c_in(X0,X5,X2)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(X3,X5,X2),X5,tc_set(X2))
| ~ c_in(X3,c_Zorn_Omaxchain(X4,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,X1,X2) ),
inference(resolution,[status(thm)],[f27,f22]) ).
fof(f242,plain,
! [X0,X1,X2,X3] :
( ~ c_in(c_Zorn_Omaxchain__super__lemma__1(X2,v_y,t_a),v_c,tc_set(t_a))
| c_in(c_Zorn_Ochain__extend__1(X2,X1,t_a),X2,tc_set(t_a))
| ~ c_in(X2,c_Zorn_Ochain(X3,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X1,X3,tc_set(t_a))
| c_in(X0,v_y,t_a)
| ~ c_in(X2,c_Zorn_Omaxchain(X3,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X0,X1,t_a) ),
inference(resolution,[status(thm)],[f239,f31]) ).
fof(f243,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_in(c_Main_OsubsetI__1(c_Zorn_Omaxchain__super__lemma__1(X3,X5,X2),X5,X2),c_Zorn_Omaxchain__super__lemma__1(X3,X5,X2),X2)
| c_in(c_Zorn_Ochain__extend__1(X3,X1,X2),X3,tc_set(X2))
| ~ c_in(X3,c_Zorn_Ochain(X4,X2),tc_set(tc_set(X2)))
| ~ c_in(X1,X4,tc_set(X2))
| c_in(X0,X5,X2)
| ~ c_in(X3,c_Zorn_Omaxchain(X4,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,X1,X2) ),
inference(resolution,[status(thm)],[f239,f20]) ).
fof(f247,plain,
( v_x(v_x(v_x(v_x(v_x(v_x(v_y)))))) = v_x(v_x(v_x(v_x(v_x(v_y)))))
| c_in(c_Main_OsubsetI__1(v_x(v_x(v_x(v_x(v_x(v_x(v_y)))))),v_x(v_x(v_x(v_x(v_x(v_y))))),t_a),v_x(v_x(v_x(v_x(v_x(v_x(v_y)))))),t_a) ),
inference(resolution,[status(thm)],[f141,f58]) ).
fof(f249,plain,
( v_x(v_x(v_x(v_x(v_x(v_y))))) = v_x(v_x(v_x(v_x(v_x(v_x(v_y))))))
| ~ c_lessequals(v_x(v_x(v_x(v_x(v_x(v_x(v_y)))))),v_x(v_x(v_x(v_x(v_x(v_y))))),tc_set(t_a)) ),
inference(resolution,[status(thm)],[f141,f17]) ).
fof(f250,definition,
( sQ26_spl
<=> c_in(c_Main_OsubsetI__1(v_x(v_x(v_x(v_x(v_x(v_x(v_y)))))),v_x(v_x(v_x(v_x(v_x(v_y))))),t_a),v_x(v_x(v_x(v_x(v_x(v_x(v_y)))))),t_a) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f253,definition,
( sQ27_spl
<=> v_x(v_x(v_x(v_x(v_x(v_x(v_y)))))) = v_x(v_x(v_x(v_x(v_x(v_y))))) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f254,plain,
( ~ sQ27_spl
| v_x(v_x(v_x(v_x(v_x(v_x(v_y)))))) = v_x(v_x(v_x(v_x(v_x(v_y))))) ),
inference(component_clause,[status(thm)],[f253]) ).
fof(f256,plain,
( sQ27_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f247,f250,f253]) ).
fof(f257,definition,
( sQ28_spl
<=> c_lessequals(v_x(v_x(v_x(v_x(v_x(v_x(v_y)))))),v_x(v_x(v_x(v_x(v_x(v_y))))),tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f260,plain,
( sQ27_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f249,f257,f253]) ).
fof(f261,plain,
( ~ sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f254,f142]) ).
fof(f262,plain,
~ sQ27_spl,
inference(contradiction_clause,[status(thm)],[f261]) ).
fof(f274,definition,
( sQ31_spl
<=> c_in(c_Main_OsubsetI__1(v_x(v_x(v_y)),v_y,t_a),v_x(v_x(v_y)),t_a) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f277,definition,
( sQ32_spl
<=> v_x(v_x(v_y)) = v_y ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f278,plain,
( ~ sQ32_spl
| v_x(v_x(v_y)) = v_y ),
inference(component_clause,[status(thm)],[f277]) ).
fof(f280,definition,
( sQ33_spl
<=> c_lessequals(v_y,v_x(v_x(v_y)),tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f281,plain,
( ~ sQ33_spl
| c_lessequals(v_y,v_x(v_x(v_y)),tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f280]) ).
fof(f282,plain,
( sQ33_spl
| ~ c_lessequals(v_y,v_x(v_x(v_y)),tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f280]) ).
fof(f285,plain,
( ~ sQ33_spl
| v_x(v_x(v_y)) = v_y
| c_in(c_Main_OsubsetI__1(v_x(v_x(v_y)),v_y,t_a),v_x(v_x(v_y)),t_a) ),
inference(resolution,[status(thm)],[f281,f58]) ).
fof(f287,plain,
( ~ sQ33_spl
| v_y = v_x(v_x(v_y))
| ~ c_lessequals(v_x(v_x(v_y)),v_y,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f281,f17]) ).
fof(f288,plain,
( ~ sQ33_spl
| sQ32_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f285,f274,f277,f280]) ).
fof(f289,definition,
( sQ34_spl
<=> c_lessequals(v_x(v_x(v_y)),v_y,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f291,plain,
( sQ34_spl
| ~ c_lessequals(v_x(v_x(v_y)),v_y,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f289]) ).
fof(f292,plain,
( ~ sQ33_spl
| sQ32_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f287,f289,f277,f280]) ).
fof(f297,plain,
( ~ sQ32_spl
| c_lessequals(v_x(v_x(v_x(v_x(v_x(v_y))))),v_x(v_x(v_x(v_x(v_y)))),tc_set(t_a)) ),
inference(backward_demodulation,[status(thm)],[f278,f141]) ).
fof(f330,plain,
( ~ sQ32_spl
| c_lessequals(v_x(v_x(v_x(v_y))),v_x(v_x(v_x(v_x(v_y)))),tc_set(t_a)) ),
inference(forward_demodulation,[status(thm)],[f278,f297]) ).
fof(f331,plain,
( ~ sQ32_spl
| c_lessequals(v_x(v_y),v_x(v_x(v_x(v_x(v_y)))),tc_set(t_a)) ),
inference(forward_demodulation,[status(thm)],[f278,f330]) ).
fof(f332,plain,
( ~ sQ32_spl
| c_lessequals(v_x(v_y),v_x(v_x(v_y)),tc_set(t_a)) ),
inference(forward_demodulation,[status(thm)],[f278,f331]) ).
fof(f333,plain,
( ~ sQ32_spl
| c_lessequals(v_x(v_y),v_y,tc_set(t_a)) ),
inference(forward_demodulation,[status(thm)],[f278,f332]) ).
fof(f334,plain,
( ~ sQ32_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f333,f43]) ).
fof(f335,plain,
( ~ sQ32_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f334]) ).
fof(f336,plain,
( sQ34_spl
| ~ c_in(v_x(v_x(v_y)),v_c,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f291,f31]) ).
fof(f353,plain,
! [X0,X1] :
( v_x(c_Main_OsubsetI__1(v_S,X1,tc_set(t_a))) != v_x(v_x(c_Main_OsubsetI__1(v_S,X1,tc_set(t_a))))
| c_in(X0,X1,tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f126,f34]) ).
fof(f363,plain,
! [X0] :
( c_lessequals(X0,v_x(v_x(v_y)),tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(X0,v_x(v_x(v_y)),t_a),v_x(v_y),t_a) ),
inference(resolution,[status(thm)],[f59,f21]) ).
fof(f385,plain,
! [X0,X1,X2,X3] :
( ~ c_lessequals(c_Zorn_Ochain__extend__1(v_c,X1,t_a),X1,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X1,v_S,tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X3,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(X1,X2,t_a),X3,t_a)
| c_in(X0,X2,t_a)
| ~ c_in(X0,X1,t_a) ),
inference(resolution,[status(thm)],[f129,f23]) ).
fof(f386,plain,
! [X0,X1,X2,X3] :
( c_in(c_Zorn_Ochain__extend__1(v_c,X1,t_a),v_c,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X1,v_S,tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X3,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(X1,X2,t_a),X3,t_a)
| c_in(X0,X2,t_a)
| ~ c_in(X0,X1,t_a) ),
inference(resolution,[status(thm)],[f129,f22]) ).
fof(f387,definition,
! [X0,X1,X2,X3] :
( sQ37_spl
<=> ( ~ c_lessequals(c_Zorn_Ochain__extend__1(v_c,X1,t_a),X1,tc_set(t_a))
| ~ c_in(X1,v_S,tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X3,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(X1,X2,t_a),X3,t_a)
| c_in(X0,X2,t_a)
| ~ c_in(X0,X1,t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f388,plain,
! [X0,X1,X2,X3] :
( ~ sQ37_spl
| ~ c_lessequals(c_Zorn_Ochain__extend__1(v_c,X1,t_a),X1,tc_set(t_a))
| ~ c_in(X1,v_S,tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X3,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(X1,X2,t_a),X3,t_a)
| c_in(X0,X2,t_a)
| ~ c_in(X0,X1,t_a) ),
inference(component_clause,[status(thm)],[f387]) ).
fof(f390,definition,
( sQ38_spl
<=> c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f392,plain,
( sQ38_spl
| ~ c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f390]) ).
fof(f393,plain,
( ~ sQ38_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f385,f387,f390]) ).
fof(f394,definition,
! [X0,X1,X2,X3] :
( sQ39_spl
<=> ( c_in(c_Zorn_Ochain__extend__1(v_c,X1,t_a),v_c,tc_set(t_a))
| ~ c_in(X1,v_S,tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X3,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(X1,X2,t_a),X3,t_a)
| c_in(X0,X2,t_a)
| ~ c_in(X0,X1,t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f397,plain,
( ~ sQ38_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f386,f394,f390]) ).
fof(f398,plain,
( sQ38_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f392,f29]) ).
fof(f399,plain,
sQ38_spl,
inference(contradiction_clause,[status(thm)],[f398]) ).
fof(f435,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X5,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(c_Zorn_Omaxchain__super__lemma__1(X2,X4,t_a),X4,t_a),X5,t_a)
| ~ c_in(c_union(c_insert(c_Zorn_Omaxchain__super__lemma__1(X2,X4,t_a),c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Ochain__extend__1(X2,X1,t_a),X2,tc_set(t_a))
| ~ c_in(X2,c_Zorn_Ochain(X3,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X1,X3,tc_set(t_a))
| c_in(X0,X4,t_a)
| ~ c_in(X2,c_Zorn_Omaxchain(X3,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X0,X1,t_a) ),
inference(resolution,[status(thm)],[f243,f94]) ).
fof(f486,definition,
! [X1,X2,X3] :
( sQ44_spl
<=> ( c_in(c_Zorn_Ochain__extend__1(v_c,X2,t_a),v_c,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Ochain(X3,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X2,X3,tc_set(t_a))
| c_in(X1,v_y,t_a)
| ~ c_in(v_c,c_Zorn_Omaxchain(X3,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X1,X2,t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f490,plain,
! [X0,X1,X2] :
( ~ sQ10_spl
| c_in(c_Zorn_Ochain__extend__1(v_c,X1,t_a),v_c,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Ochain(X2,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X1,X2,tc_set(t_a))
| c_in(X0,v_y,t_a)
| ~ c_in(v_c,c_Zorn_Omaxchain(X2,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X0,X1,t_a)
| c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),v_y,t_a) ),
inference(resolution,[status(thm)],[f117,f242]) ).
fof(f495,definition,
( sQ45_spl
<=> c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),v_y,t_a) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f496,plain,
( ~ sQ45_spl
| c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),v_y,t_a) ),
inference(component_clause,[status(thm)],[f495]) ).
fof(f497,plain,
( sQ45_spl
| ~ c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),v_y,t_a) ),
inference(component_clause,[status(thm)],[f495]) ).
fof(f498,plain,
( ~ sQ10_spl
| sQ44_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f490,f495,f486,f116]) ).
fof(f499,plain,
( sQ9_spl
| ~ c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_x(v_y),tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x(v_y),v_S,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f115,f23]) ).
fof(f500,plain,
( sQ9_spl
| c_in(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_c,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x(v_y),v_S,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f115,f22]) ).
fof(f501,definition,
( sQ46_spl
<=> c_in(v_x(v_y),v_S,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f503,plain,
( sQ46_spl
| ~ c_in(v_x(v_y),v_S,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f501]) ).
fof(f504,definition,
( sQ47_spl
<=> c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_x(v_y),tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f506,plain,
( sQ47_spl
| ~ c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_x(v_y),tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f504]) ).
fof(f507,plain,
( sQ9_spl
| ~ sQ47_spl
| ~ sQ38_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f499,f501,f390,f504,f113]) ).
fof(f508,definition,
( sQ48_spl
<=> c_in(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_c,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f509,plain,
( ~ sQ48_spl
| c_in(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_c,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f508]) ).
fof(f511,plain,
( sQ9_spl
| sQ48_spl
| ~ sQ38_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f500,f501,f390,f508,f113]) ).
fof(f512,plain,
( sQ46_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f503,f49]) ).
fof(f513,plain,
sQ46_spl,
inference(contradiction_clause,[status(thm)],[f512]) ).
fof(f521,plain,
( ~ sQ48_spl
| v_y = c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a)
| c_in(c_Main_OsubsetI__1(v_y,c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),t_a),v_y,t_a) ),
inference(resolution,[status(thm)],[f509,f74]) ).
fof(f524,definition,
( sQ49_spl
<=> c_in(c_Main_OsubsetI__1(v_y,c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),t_a),v_y,t_a) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f525,plain,
( ~ sQ49_spl
| c_in(c_Main_OsubsetI__1(v_y,c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),t_a),v_y,t_a) ),
inference(component_clause,[status(thm)],[f524]) ).
fof(f527,definition,
( sQ50_spl
<=> v_y = c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f528,plain,
( ~ sQ50_spl
| v_y = c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a) ),
inference(component_clause,[status(thm)],[f527]) ).
fof(f530,plain,
( ~ sQ48_spl
| sQ50_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f521,f524,f527,f508]) ).
fof(f535,plain,
( ~ sQ48_spl
| ~ sQ50_spl
| c_in(v_y,v_c,tc_set(t_a)) ),
inference(backward_demodulation,[status(thm)],[f528,f509]) ).
fof(f539,definition,
! [X0,X2] :
( sQ52_spl
<=> ( c_in(X0,X2,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),X2,tc_set(t_a))
| ~ c_in(X0,v_x(v_y),t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f540,plain,
! [X0,X1] :
( ~ sQ52_spl
| c_in(X0,X1,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),X1,tc_set(t_a))
| ~ c_in(X0,v_x(v_y),t_a) ),
inference(component_clause,[status(thm)],[f539]) ).
fof(f557,plain,
! [X0] :
( ~ sQ48_spl
| c_in(X0,v_y,t_a)
| ~ c_in(X0,c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),t_a) ),
inference(resolution,[status(thm)],[f509,f37]) ).
fof(f561,plain,
( sQ47_spl
| c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_x(v_y),t_a),c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),t_a) ),
inference(resolution,[status(thm)],[f506,f20]) ).
fof(f568,plain,
! [X0] :
( ~ sQ49_spl
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_y,c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),t_a),X0,t_a)
| ~ c_in(c_union(c_insert(v_y,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f525,f94]) ).
fof(f569,definition,
( sQ56_spl
<=> c_in(c_union(c_insert(v_y,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f570,plain,
( ~ sQ56_spl
| c_in(c_union(c_insert(v_y,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f569]) ).
fof(f571,plain,
( sQ56_spl
| ~ c_in(c_union(c_insert(v_y,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f569]) ).
fof(f572,definition,
! [X0] :
( sQ57_spl
<=> ( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_y,c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),t_a),X0,t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f575,plain,
( ~ sQ49_spl
| sQ57_spl
| ~ sQ56_spl ),
inference(split_clause,[status(thm)],[f568,f569,f572,f524]) ).
fof(f587,definition,
( sQ60_spl
<=> c_lessequals(v_y,v_y,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f589,plain,
( sQ60_spl
| ~ c_lessequals(v_y,v_y,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f587]) ).
fof(f591,plain,
( sQ60_spl
| ~ c_in(v_y,v_c,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f589,f31]) ).
fof(f593,plain,
( sQ60_spl
| ~ sQ48_spl
| ~ sQ50_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f591,f535]) ).
fof(f594,plain,
( sQ60_spl
| ~ sQ48_spl
| ~ sQ50_spl ),
inference(contradiction_clause,[status(thm)],[f593]) ).
fof(f601,plain,
( sQ47_spl
| ~ sQ50_spl
| ~ c_lessequals(v_y,v_x(v_y),tc_set(t_a)) ),
inference(backward_demodulation,[status(thm)],[f528,f506]) ).
fof(f606,plain,
( sQ47_spl
| ~ sQ50_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f601,f38]) ).
fof(f607,plain,
( sQ47_spl
| ~ sQ50_spl ),
inference(contradiction_clause,[status(thm)],[f606]) ).
fof(f635,definition,
( sQ65_spl
<=> v_c = v_S ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f636,plain,
( ~ sQ65_spl
| v_c = v_S ),
inference(component_clause,[status(thm)],[f635]) ).
fof(f669,plain,
! [X0,X1,X2] :
( ~ c_lessequals(c_Zorn_Ochain__extend__1(v_c,X1,t_a),X1,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X1,v_S,tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(X1,X0,t_a),X2,t_a)
| X0 = X1
| c_in(c_Main_OsubsetI__1(X0,X1,t_a),X0,t_a) ),
inference(resolution,[status(thm)],[f139,f23]) ).
fof(f670,plain,
! [X0,X1,X2] :
( c_in(c_Zorn_Ochain__extend__1(v_c,X1,t_a),v_c,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X1,v_S,tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(X1,X0,t_a),X2,t_a)
| X0 = X1
| c_in(c_Main_OsubsetI__1(X0,X1,t_a),X0,t_a) ),
inference(resolution,[status(thm)],[f139,f22]) ).
fof(f671,definition,
! [X0,X1,X2] :
( sQ74_spl
<=> ( ~ c_lessequals(c_Zorn_Ochain__extend__1(v_c,X1,t_a),X1,tc_set(t_a))
| ~ c_in(X1,v_S,tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(X1,X0,t_a),X2,t_a)
| X0 = X1
| c_in(c_Main_OsubsetI__1(X0,X1,t_a),X0,t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f674,plain,
( ~ sQ38_spl
| sQ74_spl ),
inference(split_clause,[status(thm)],[f669,f671,f390]) ).
fof(f675,definition,
! [X0,X1,X2] :
( sQ75_spl
<=> ( c_in(c_Zorn_Ochain__extend__1(v_c,X1,t_a),v_c,tc_set(t_a))
| ~ c_in(X1,v_S,tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(X1,X0,t_a),X2,t_a)
| X0 = X1
| c_in(c_Main_OsubsetI__1(X0,X1,t_a),X0,t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f678,plain,
( ~ sQ38_spl
| sQ75_spl ),
inference(split_clause,[status(thm)],[f670,f675,f390]) ).
fof(f681,plain,
! [X0,X1] :
( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_y,c_Main_OsubsetI__1(v_c,X0,tc_set(t_a)),t_a),X1,t_a)
| ~ c_in(c_union(c_insert(v_y,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| X0 = v_c
| c_in(c_Main_OsubsetI__1(X0,v_c,tc_set(t_a)),X0,tc_set(t_a))
| v_y = c_Main_OsubsetI__1(v_c,X0,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f173,f94]) ).
fof(f682,definition,
! [X0,X1] :
( sQ76_spl
<=> ( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_y,c_Main_OsubsetI__1(v_c,X0,tc_set(t_a)),t_a),X1,t_a)
| X0 = v_c
| c_in(c_Main_OsubsetI__1(X0,v_c,tc_set(t_a)),X0,tc_set(t_a))
| v_y = c_Main_OsubsetI__1(v_c,X0,tc_set(t_a)) ) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f685,plain,
( ~ sQ56_spl
| sQ76_spl ),
inference(split_clause,[status(thm)],[f681,f682,f569]) ).
fof(f700,plain,
( sQ56_spl
| ~ c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_y,t_a),v_y,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_y,v_S,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f571,f23]) ).
fof(f701,plain,
( sQ56_spl
| c_in(c_Zorn_Ochain__extend__1(v_c,v_y,t_a),v_c,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_y,v_S,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f571,f22]) ).
fof(f702,definition,
( sQ79_spl
<=> c_in(v_y,v_S,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f704,plain,
( sQ79_spl
| ~ c_in(v_y,v_S,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f702]) ).
fof(f705,definition,
( sQ80_spl
<=> c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_y,t_a),v_y,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f706,plain,
( ~ sQ80_spl
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_y,t_a),v_y,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f705]) ).
fof(f707,plain,
( sQ80_spl
| ~ c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_y,t_a),v_y,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f705]) ).
fof(f708,plain,
( sQ56_spl
| ~ sQ80_spl
| ~ sQ38_spl
| ~ sQ79_spl ),
inference(split_clause,[status(thm)],[f700,f702,f390,f705,f569]) ).
fof(f709,definition,
( sQ81_spl
<=> c_in(c_Zorn_Ochain__extend__1(v_c,v_y,t_a),v_c,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f710,plain,
( ~ sQ81_spl
| c_in(c_Zorn_Ochain__extend__1(v_c,v_y,t_a),v_c,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f709]) ).
fof(f712,plain,
( sQ56_spl
| sQ81_spl
| ~ sQ38_spl
| ~ sQ79_spl ),
inference(split_clause,[status(thm)],[f701,f702,f390,f709,f569]) ).
fof(f713,plain,
( sQ79_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f704,f30]) ).
fof(f714,plain,
sQ79_spl,
inference(contradiction_clause,[status(thm)],[f713]) ).
fof(f717,plain,
! [X0,X1,X2] :
( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_y,c_Main_OsubsetI__1(v_c,X0,tc_set(t_a)),t_a),X2,t_a)
| ~ c_in(c_union(c_insert(v_y,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(X1,X0,tc_set(t_a))
| ~ c_in(X1,v_c,tc_set(t_a))
| v_y = c_Main_OsubsetI__1(v_c,X0,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f174,f94]) ).
fof(f718,definition,
! [X0,X1,X2] :
( sQ82_spl
<=> ( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_y,c_Main_OsubsetI__1(v_c,X0,tc_set(t_a)),t_a),X2,t_a)
| c_in(X1,X0,tc_set(t_a))
| ~ c_in(X1,v_c,tc_set(t_a))
| v_y = c_Main_OsubsetI__1(v_c,X0,tc_set(t_a)) ) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f721,plain,
( ~ sQ56_spl
| sQ82_spl ),
inference(split_clause,[status(thm)],[f717,f718,f569]) ).
fof(f733,plain,
! [X0,X1] :
( ~ sQ56_spl
| c_in(X0,X1,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),X1,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X0,v_y,t_a) ),
inference(resolution,[status(thm)],[f570,f27]) ).
fof(f734,definition,
! [X0,X1] :
( sQ83_spl
<=> ( c_in(X0,X1,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),X1,tc_set(t_a))
| ~ c_in(X0,v_y,t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f735,plain,
! [X0,X1] :
( ~ sQ83_spl
| c_in(X0,X1,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),X1,tc_set(t_a))
| ~ c_in(X0,v_y,t_a) ),
inference(component_clause,[status(thm)],[f734]) ).
fof(f737,definition,
( sQ84_spl
<=> c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f739,plain,
( sQ84_spl
| ~ c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f737]) ).
fof(f740,plain,
( ~ sQ56_spl
| ~ sQ84_spl
| sQ83_spl ),
inference(split_clause,[status(thm)],[f733,f734,f737,f569]) ).
fof(f741,plain,
! [X0] :
( ~ sQ83_spl
| ~ c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_c,tc_set(t_a))
| c_in(X0,v_y,t_a)
| ~ c_in(X0,v_y,t_a) ),
inference(resolution,[status(thm)],[f735,f31]) ).
fof(f743,definition,
! [X0] :
( sQ85_spl
<=> ( c_in(X0,v_y,t_a)
| ~ c_in(X0,v_y,t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f746,definition,
( sQ86_spl
<=> c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_c,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f749,plain,
( ~ sQ83_spl
| ~ sQ86_spl
| sQ85_spl ),
inference(split_clause,[status(thm)],[f741,f743,f746,f734]) ).
fof(f750,plain,
( sQ84_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f739,f28]) ).
fof(f751,plain,
sQ84_spl,
inference(contradiction_clause,[status(thm)],[f750]) ).
fof(f763,plain,
! [X0,X1] :
( ~ sQ9_spl
| c_in(X0,X1,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),X1,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X0,v_x(v_y),t_a) ),
inference(resolution,[status(thm)],[f114,f27]) ).
fof(f764,plain,
( ~ sQ9_spl
| ~ sQ84_spl
| sQ52_spl ),
inference(split_clause,[status(thm)],[f763,f539,f737,f113]) ).
fof(f784,plain,
( sQ34_spl
| ~ sQ65_spl
| ~ c_in(v_x(v_x(v_y)),v_S,tc_set(t_a)) ),
inference(backward_demodulation,[status(thm)],[f636,f336]) ).
fof(f817,plain,
( sQ34_spl
| ~ sQ65_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f784,f50]) ).
fof(f818,plain,
( sQ34_spl
| ~ sQ65_spl ),
inference(contradiction_clause,[status(thm)],[f817]) ).
fof(f848,plain,
( sQ33_spl
| c_in(c_Main_OsubsetI__1(v_y,v_x(v_x(v_y)),t_a),v_y,t_a) ),
inference(resolution,[status(thm)],[f282,f20]) ).
fof(f852,plain,
( ~ sQ81_spl
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_y,t_a),v_y,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f31,f710]) ).
fof(f857,plain,
( ~ sQ81_spl
| sQ80_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f852,f707]) ).
fof(f858,plain,
( ~ sQ81_spl
| sQ80_spl ),
inference(contradiction_clause,[status(thm)],[f857]) ).
fof(f863,plain,
! [X0,X1,X2] :
( c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_y,tc_set(t_a))
| c_in(X0,X2,t_a)
| ~ c_in(c_union(c_insert(X1,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X0,X1,t_a) ),
inference(resolution,[status(thm)],[f94,f31]) ).
fof(f911,plain,
( ~ c_in(v_x(v_y),v_c,tc_set(t_a))
| v_x(v_y) = v_y ),
inference(resolution,[status(thm)],[f36,f38]) ).
fof(f913,definition,
( sQ99_spl
<=> c_in(v_x(v_y),v_c,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f916,plain,
( ~ sQ99_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f911,f44,f913]) ).
fof(f922,plain,
( sQ33_spl
| c_in(c_Main_OsubsetI__1(v_y,v_x(v_x(v_y)),t_a),v_x(v_y),t_a) ),
inference(resolution,[status(thm)],[f848,f39]) ).
fof(f943,plain,
( sQ33_spl
| c_lessequals(v_y,v_x(v_x(v_y)),tc_set(t_a)) ),
inference(resolution,[status(thm)],[f922,f363]) ).
fof(f944,plain,
sQ33_spl,
inference(split_clause,[status(thm)],[f943,f280]) ).
fof(f945,plain,
( ~ sQ33_spl
| ~ c_in(v_x(v_x(v_y)),v_c,tc_set(t_a))
| v_x(v_x(v_y)) = v_y ),
inference(resolution,[status(thm)],[f281,f36]) ).
fof(f949,definition,
( sQ101_spl
<=> c_in(v_x(v_x(v_y)),v_c,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f952,plain,
( ~ sQ33_spl
| ~ sQ101_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f945,f277,f949,f280]) ).
fof(f1004,plain,
! [X0,X1,X2] :
( ~ c_lessequals(c_Zorn_Ochain__extend__1(v_c,X1,t_a),X1,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X1,v_S,tc_set(t_a))
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_y,tc_set(t_a))
| c_in(X0,X2,t_a)
| ~ c_in(X0,X1,t_a) ),
inference(resolution,[status(thm)],[f863,f23]) ).
fof(f1005,plain,
! [X0,X1,X2] :
( c_in(c_Zorn_Ochain__extend__1(v_c,X1,t_a),v_c,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X1,v_S,tc_set(t_a))
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_y,tc_set(t_a))
| c_in(X0,X2,t_a)
| ~ c_in(X0,X1,t_a) ),
inference(resolution,[status(thm)],[f863,f22]) ).
fof(f1006,definition,
! [X0,X1,X2] :
( sQ103_spl
<=> ( ~ c_lessequals(c_Zorn_Ochain__extend__1(v_c,X1,t_a),X1,tc_set(t_a))
| ~ c_in(X1,v_S,tc_set(t_a))
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_y,tc_set(t_a))
| c_in(X0,X2,t_a)
| ~ c_in(X0,X1,t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f1009,plain,
( ~ sQ38_spl
| sQ103_spl ),
inference(split_clause,[status(thm)],[f1004,f1006,f390]) ).
fof(f1010,definition,
! [X0,X1,X2] :
( sQ104_spl
<=> ( c_in(c_Zorn_Ochain__extend__1(v_c,X1,t_a),v_c,tc_set(t_a))
| ~ c_in(X1,v_S,tc_set(t_a))
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_y,tc_set(t_a))
| c_in(X0,X2,t_a)
| ~ c_in(X0,X1,t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f1013,plain,
( ~ sQ38_spl
| sQ104_spl ),
inference(split_clause,[status(thm)],[f1005,f1010,f390]) ).
fof(f1082,plain,
( ~ sQ48_spl
| sQ47_spl
| c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_x(v_y),t_a),v_y,t_a) ),
inference(resolution,[status(thm)],[f561,f557]) ).
fof(f1084,plain,
( ~ sQ48_spl
| sQ47_spl
| c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_x(v_y),t_a),v_x(v_y),t_a) ),
inference(resolution,[status(thm)],[f1082,f39]) ).
fof(f1085,plain,
( ~ sQ48_spl
| sQ47_spl
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_x(v_y),tc_set(t_a)) ),
inference(resolution,[status(thm)],[f1084,f21]) ).
fof(f1086,plain,
( ~ sQ48_spl
| sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1085,f506]) ).
fof(f1087,plain,
( ~ sQ48_spl
| sQ47_spl ),
inference(contradiction_clause,[status(thm)],[f1086]) ).
fof(f1091,plain,
( sQ34_spl
| v_x(c_Main_OsubsetI__1(v_S,v_c,tc_set(t_a))) != v_x(v_x(c_Main_OsubsetI__1(v_S,v_c,tc_set(t_a))))
| ~ c_in(v_x(v_x(v_y)),v_S,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f353,f336]) ).
fof(f1103,definition,
( sQ112_spl
<=> v_x(c_Main_OsubsetI__1(v_S,v_c,tc_set(t_a))) = v_x(v_x(c_Main_OsubsetI__1(v_S,v_c,tc_set(t_a)))) ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f1111,definition,
( sQ114_spl
<=> c_in(v_x(v_x(v_y)),v_S,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition]) ).
fof(f1113,plain,
( sQ114_spl
| ~ c_in(v_x(v_x(v_y)),v_S,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f1111]) ).
fof(f1114,plain,
( sQ34_spl
| ~ sQ112_spl
| ~ sQ114_spl ),
inference(split_clause,[status(thm)],[f1091,f1111,f1103,f289]) ).
fof(f1120,definition,
! [X0] :
( sQ116_spl
<=> ( ~ c_in(c_Main_OsubsetI__1(v_y,v_y,t_a),X0,t_a)
| ~ c_in(X0,v_S,tc_set(t_a)) ) ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f1121,plain,
! [X0] :
( ~ sQ116_spl
| ~ c_in(c_Main_OsubsetI__1(v_y,v_y,t_a),X0,t_a)
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f1120]) ).
fof(f1124,definition,
! [X0] :
( sQ117_spl
<=> ( c_lessequals(X0,v_y,tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ) ),
introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition]) ).
fof(f1125,plain,
! [X0] :
( ~ sQ117_spl
| c_lessequals(X0,v_y,tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f1124]) ).
fof(f1143,plain,
( sQ114_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1113,f50]) ).
fof(f1144,plain,
sQ114_spl,
inference(contradiction_clause,[status(thm)],[f1143]) ).
fof(f1174,plain,
( sQ34_spl
| ~ sQ117_spl
| ~ c_in(v_x(v_x(v_y)),v_S,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f1125,f291]) ).
fof(f1188,plain,
( sQ34_spl
| ~ sQ117_spl
| ~ sQ114_spl ),
inference(split_clause,[status(thm)],[f1174,f1111,f1124,f289]) ).
fof(f1218,plain,
! [X0] :
( ~ sQ116_spl
| c_in(X0,v_y,t_a)
| ~ c_in(X0,v_y,t_a)
| ~ c_in(v_y,v_S,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f1121,f57]) ).
fof(f1233,plain,
( ~ sQ116_spl
| sQ85_spl
| ~ sQ79_spl ),
inference(split_clause,[status(thm)],[f1218,f702,f743,f1120]) ).
fof(f1244,definition,
( sQ128_spl
<=> c_in(v_x(v_x(v_x(v_x(v_x(v_y))))),v_S,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f1246,plain,
( sQ128_spl
| ~ c_in(v_x(v_x(v_x(v_x(v_x(v_y))))),v_S,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f1244]) ).
fof(f1251,definition,
( sQ130_spl
<=> c_in(v_x(v_x(v_x(v_x(v_y)))),v_S,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ130_spl])],[split_symbol_definition]) ).
fof(f1253,plain,
( sQ130_spl
| ~ c_in(v_x(v_x(v_x(v_x(v_y)))),v_S,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f1251]) ).
fof(f1258,definition,
( sQ132_spl
<=> c_in(v_x(v_x(v_x(v_y))),v_S,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition]) ).
fof(f1260,plain,
( sQ132_spl
| ~ c_in(v_x(v_x(v_x(v_y))),v_S,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f1258]) ).
fof(f1267,plain,
( sQ132_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1260,f53]) ).
fof(f1268,plain,
sQ132_spl,
inference(contradiction_clause,[status(thm)],[f1267]) ).
fof(f1269,plain,
( sQ130_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1253,f68]) ).
fof(f1270,plain,
sQ130_spl,
inference(contradiction_clause,[status(thm)],[f1269]) ).
fof(f1271,plain,
( sQ128_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1246,f91]) ).
fof(f1272,plain,
sQ128_spl,
inference(contradiction_clause,[status(thm)],[f1271]) ).
fof(f1305,plain,
! [X0,X1,X2] :
( ~ sQ80_spl
| ~ sQ37_spl
| ~ c_in(v_y,v_S,tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_y,X1,t_a),X2,t_a)
| c_in(X0,X1,t_a)
| ~ c_in(X0,v_y,t_a) ),
inference(resolution,[status(thm)],[f388,f706]) ).
fof(f1307,definition,
! [X0,X1,X2] :
( sQ134_spl
<=> ( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_y,X1,t_a),X2,t_a)
| c_in(X0,X1,t_a)
| ~ c_in(X0,v_y,t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition]) ).
fof(f1310,plain,
( ~ sQ80_spl
| ~ sQ37_spl
| ~ sQ79_spl
| sQ134_spl ),
inference(split_clause,[status(thm)],[f1305,f1307,f702,f387,f705]) ).
fof(f1342,plain,
! [X0] :
( ~ sQ10_spl
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),v_y,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),X0,t_a) ),
inference(resolution,[status(thm)],[f117,f31]) ).
fof(f1345,plain,
( ~ sQ10_spl
| c_lessequals(v_x(v_y),v_y,tc_set(t_a))
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_y,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f1342,f21]) ).
fof(f1354,definition,
( sQ137_spl
<=> c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_y,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition]) ).
fof(f1355,plain,
( ~ sQ137_spl
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_y,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f1354]) ).
fof(f1357,plain,
( ~ sQ10_spl
| sQ0_spl
| sQ137_spl ),
inference(split_clause,[status(thm)],[f1345,f1354,f41,f116]) ).
fof(f1378,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ c_lessequals(c_Zorn_Ochain__extend__1(v_c,c_Zorn_Omaxchain__super__lemma__1(X2,X4,t_a),t_a),c_Zorn_Omaxchain__super__lemma__1(X2,X4,t_a),tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_Omaxchain__super__lemma__1(X2,X4,t_a),v_S,tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X5,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(c_Zorn_Omaxchain__super__lemma__1(X2,X4,t_a),X4,t_a),X5,t_a)
| c_in(c_Zorn_Ochain__extend__1(X2,X1,t_a),X2,tc_set(t_a))
| ~ c_in(X2,c_Zorn_Ochain(X3,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X1,X3,tc_set(t_a))
| c_in(X0,X4,t_a)
| ~ c_in(X2,c_Zorn_Omaxchain(X3,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X0,X1,t_a) ),
inference(resolution,[status(thm)],[f435,f23]) ).
fof(f1379,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_in(c_Zorn_Ochain__extend__1(v_c,c_Zorn_Omaxchain__super__lemma__1(X2,X4,t_a),t_a),v_c,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_Omaxchain__super__lemma__1(X2,X4,t_a),v_S,tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X5,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(c_Zorn_Omaxchain__super__lemma__1(X2,X4,t_a),X4,t_a),X5,t_a)
| c_in(c_Zorn_Ochain__extend__1(X2,X1,t_a),X2,tc_set(t_a))
| ~ c_in(X2,c_Zorn_Ochain(X3,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X1,X3,tc_set(t_a))
| c_in(X0,X4,t_a)
| ~ c_in(X2,c_Zorn_Omaxchain(X3,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X0,X1,t_a) ),
inference(resolution,[status(thm)],[f435,f22]) ).
fof(f1380,definition,
! [X0,X1,X2,X3,X4,X5] :
( sQ140_spl
<=> ( ~ c_lessequals(c_Zorn_Ochain__extend__1(v_c,c_Zorn_Omaxchain__super__lemma__1(X2,X4,t_a),t_a),c_Zorn_Omaxchain__super__lemma__1(X2,X4,t_a),tc_set(t_a))
| ~ c_in(c_Zorn_Omaxchain__super__lemma__1(X2,X4,t_a),v_S,tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X5,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(c_Zorn_Omaxchain__super__lemma__1(X2,X4,t_a),X4,t_a),X5,t_a)
| c_in(c_Zorn_Ochain__extend__1(X2,X1,t_a),X2,tc_set(t_a))
| ~ c_in(X2,c_Zorn_Ochain(X3,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X1,X3,tc_set(t_a))
| c_in(X0,X4,t_a)
| ~ c_in(X2,c_Zorn_Omaxchain(X3,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X0,X1,t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ140_spl])],[split_symbol_definition]) ).
fof(f1383,plain,
( ~ sQ38_spl
| sQ140_spl ),
inference(split_clause,[status(thm)],[f1378,f1380,f390]) ).
fof(f1384,definition,
! [X0,X1,X2,X3,X4,X5] :
( sQ141_spl
<=> ( c_in(c_Zorn_Ochain__extend__1(v_c,c_Zorn_Omaxchain__super__lemma__1(X2,X4,t_a),t_a),v_c,tc_set(t_a))
| ~ c_in(c_Zorn_Omaxchain__super__lemma__1(X2,X4,t_a),v_S,tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X5,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(c_Zorn_Omaxchain__super__lemma__1(X2,X4,t_a),X4,t_a),X5,t_a)
| c_in(c_Zorn_Ochain__extend__1(X2,X1,t_a),X2,tc_set(t_a))
| ~ c_in(X2,c_Zorn_Ochain(X3,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X1,X3,tc_set(t_a))
| c_in(X0,X4,t_a)
| ~ c_in(X2,c_Zorn_Omaxchain(X3,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X0,X1,t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ141_spl])],[split_symbol_definition]) ).
fof(f1387,plain,
( ~ sQ38_spl
| sQ141_spl ),
inference(split_clause,[status(thm)],[f1379,f1384,f390]) ).
fof(f1401,plain,
! [X0] :
( ~ sQ52_spl
| ~ sQ137_spl
| c_in(X0,v_y,t_a)
| ~ c_in(X0,v_x(v_y),t_a) ),
inference(resolution,[status(thm)],[f1355,f540]) ).
fof(f1405,plain,
( ~ sQ137_spl
| v_y = c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a)
| c_in(c_Main_OsubsetI__1(v_y,c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),t_a),v_y,t_a) ),
inference(resolution,[status(thm)],[f1355,f58]) ).
fof(f1407,plain,
( ~ sQ137_spl
| c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a) = v_y
| ~ c_lessequals(v_y,c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),tc_set(t_a)) ),
inference(resolution,[status(thm)],[f1355,f17]) ).
fof(f1408,definition,
( sQ143_spl
<=> c_in(c_Main_OsubsetI__1(v_y,c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),t_a),v_y,t_a) ),
introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition]) ).
fof(f1411,definition,
( sQ144_spl
<=> v_y = c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a) ),
introduced(definition,[new_symbols(definition,[sQ144_spl])],[split_symbol_definition]) ).
fof(f1412,plain,
( ~ sQ144_spl
| v_y = c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a) ),
inference(component_clause,[status(thm)],[f1411]) ).
fof(f1414,plain,
( ~ sQ137_spl
| sQ144_spl
| sQ143_spl ),
inference(split_clause,[status(thm)],[f1405,f1408,f1411,f1354]) ).
fof(f1415,definition,
( sQ145_spl
<=> c_lessequals(v_y,c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f1418,plain,
( ~ sQ137_spl
| sQ144_spl
| ~ sQ145_spl ),
inference(split_clause,[status(thm)],[f1407,f1415,f1411,f1354]) ).
fof(f1423,plain,
! [X0] :
( ~ sQ144_spl
| ~ sQ83_spl
| c_in(X0,v_y,t_a)
| ~ c_lessequals(v_y,v_y,tc_set(t_a))
| ~ c_in(X0,v_y,t_a) ),
inference(paramodulation,[status(thm)],[f1412,f735]) ).
fof(f1434,plain,
( ~ sQ144_spl
| ~ sQ83_spl
| ~ sQ60_spl
| sQ85_spl ),
inference(split_clause,[status(thm)],[f1423,f743,f587,f734,f1411]) ).
fof(f1479,plain,
( ~ sQ45_spl
| c_lessequals(v_x(v_y),v_y,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f496,f21]) ).
fof(f1482,plain,
( ~ sQ45_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1479,f43]) ).
fof(f1483,plain,
( ~ sQ45_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1482]) ).
fof(f1504,plain,
( ~ sQ52_spl
| ~ sQ137_spl
| sQ45_spl
| ~ c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),v_x(v_y),t_a) ),
inference(resolution,[status(thm)],[f497,f1401]) ).
fof(f1507,plain,
( ~ sQ52_spl
| ~ sQ137_spl
| sQ45_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1504,f56]) ).
fof(f1508,plain,
( ~ sQ52_spl
| ~ sQ137_spl
| sQ45_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1507]) ).
fof(f1509,plain,
$false,
inference(sat_refutation,[status(thm)],[f47,f67,f79,f83,f85,f87,f104,f108,f110,f119,f161,f165,f167,f200,f204,f206,f256,f260,f262,f288,f292,f335,f393,f397,f399,f498,f507,f511,f513,f530,f575,f594,f607,f674,f678,f685,f708,f712,f714,f721,f740,f749,f751,f764,f818,f858,f916,f944,f952,f1009,f1013,f1087,f1114,f1144,f1188,f1233,f1268,f1270,f1272,f1310,f1357,f1383,f1387,f1414,f1418,f1434,f1483,f1508]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET862-2 : 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 : n018.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 05:44:13 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.15/0.39 % Drodi V4.1.1
% 2.86/1.00 % Refutation found
% 2.86/1.00 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.86/1.00 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.86/1.03 % Elapsed time: 0.639858 seconds
% 2.86/1.03 % CPU time: 4.733724 seconds
% 2.86/1.03 % Total memory used: 146.808 MB
% 2.86/1.03 % Net memory used: 139.865 MB
%------------------------------------------------------------------------------