%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET854-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n015.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 : Fri Sep 25 02:48:48 PM UTC 2026
% Result : Unsatisfiable 88.53s 20.87s
% Output : CNFRefutation 88.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 20
% Syntax : Number of formulae : 92 ( 19 unt; 0 def)
% Number of atoms : 305 ( 39 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 365 ( 152 ~; 213 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 153 ( 0 sgn 153 !; 0 ?; 104 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( X1 = X0
| ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
fof(f2,plain,
! [X2,X0,X1] :
( X0 = X1
| ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(reorient_equations,[],[f1]) ).
fof(f3,axiom,
! [X2,X3,X0,X1] :
( c_in(X0,X3,X2)
| ~ c_lessequals(X1,X3,tc_set(X2))
| ~ c_in(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
fof(f4,axiom,
! [X2,X0,X1] :
( c_lessequals(X0,X1,tc_set(X2))
| c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f5,axiom,
! [X2,X0,X1] :
( c_lessequals(X0,X1,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f6,axiom,
! [X2,X0,X1] : c_lessequals(X0,c_Zorn_Osucc(X1,X0,X2),tc_set(tc_set(X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OAbrial__axiom1_0) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| c_lessequals(X3,X0,tc_set(tc_set(X2)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_0) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),X0,tc_set(tc_set(X2)))
| c_lessequals(X3,X0,tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_1) ).
fof(f9,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| c_lessequals(X3,X0,tc_set(tc_set(X2)))
| c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2) != X0
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_2) ).
fof(f10,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| c_lessequals(X3,X0,tc_set(tc_set(X2)))
| ~ c_lessequals(c_Zorn_Osucc(X1,c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),X2),X0,tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_3) ).
fof(f11,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_Union(X2,X3),X0,tc_set(X3))
| c_lessequals(X1,c_Union(X2,X3),tc_set(X3))
| c_in(c_Zorn_OUnion__lemma0__1(X0,X1,X2,X3),X2,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OUnion__lemma0_0) ).
fof(f12,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_Union(X2,X3),X0,tc_set(X3))
| c_lessequals(X1,c_Union(X2,X3),tc_set(X3))
| ~ c_lessequals(c_Zorn_OUnion__lemma0__1(X0,X1,X2,X3),X0,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OUnion__lemma0_1) ).
fof(f13,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_Union(X2,X3),X1,tc_set(X3))
| c_lessequals(X0,c_Union(X2,X3),tc_set(X3))
| ~ c_lessequals(X0,c_Zorn_OUnion__lemma0__1(X1,X0,X2,X3),tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OUnion__lemma0_2) ).
fof(f14,negated_conjecture,
c_lessequals(v_Y,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f15,negated_conjecture,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f16,negated_conjecture,
c_lessequals(v_x,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f17,negated_conjecture,
v_x != c_Union(v_Y,tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f18,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f19,negated_conjecture,
! [X0,X1] :
( ~ c_in(X1,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(X0,X1,tc_set(tc_set(t_a)))
| X0 = X1
| c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),X1,tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X3,X1,X2)
| ~ c_in(X3,X0,X2)
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,X1,tc_set(X2))
| c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,X1,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] : c_lessequals(X0,c_Zorn_Osucc(X1,X0,X2),tc_set(tc_set(X2))),
inference(cnf_transformation,[],[f6]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X3,X0,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X3,X0,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),X0,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X3,X1,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X0,X1,X2),X3,tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X0,X2),tc_set(tc_set(X2)))
| ~ c_in(X1,c_Zorn_OTFin(X0,X2),tc_set(tc_set(X2)))
| ( c_Zorn_OTFin__linear__lemma1__1(X0,X1,X2) != X1 ) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X3,X1,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X0,X1,X2),X3,tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X0,X2),tc_set(tc_set(X2)))
| ~ c_in(X1,c_Zorn_OTFin(X0,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(c_Zorn_Osucc(X0,c_Zorn_OTFin__linear__lemma1__1(X0,X1,X2),X2),X1,tc_set(tc_set(X2))) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X1,c_Union(X2,X3),tc_set(X3))
| c_lessequals(c_Union(X2,X3),X0,tc_set(X3))
| c_in(c_Zorn_OUnion__lemma0__1(X0,X1,X2,X3),X2,tc_set(X3)) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X1,c_Union(X2,X3),tc_set(X3))
| c_lessequals(c_Union(X2,X3),X0,tc_set(X3))
| ~ c_lessequals(c_Zorn_OUnion__lemma0__1(X0,X1,X2,X3),X0,tc_set(X3)) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X0,c_Union(X2,X3),tc_set(X3))
| c_lessequals(c_Union(X2,X3),X1,tc_set(X3))
| ~ c_lessequals(X0,c_Zorn_OUnion__lemma0__1(X1,X0,X2,X3),tc_set(X3)) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_79,negated_conjecture,
c_lessequals(v_Y,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))),
inference(cnf_transformation,[],[f14]) ).
tcf(c_80,negated_conjecture,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[],[f15]) ).
tcf(c_81,negated_conjecture,
c_lessequals(v_x,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
inference(cnf_transformation,[],[f16]) ).
tcf(c_82,negated_conjecture,
c_Union(v_Y,tc_set(t_a)) != v_x,
inference(cnf_transformation,[],[f17]) ).
tcf(c_83,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
inference(cnf_transformation,[],[f18]) ).
tcf(c_84,negated_conjecture,
! [X0: $i,X1: $i] :
( c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),X1,tc_set(tc_set(t_a)))
| ( X0 = X1 )
| ~ c_in(X1,v_Y,tc_set(tc_set(t_a)))
| ~ c_lessequals(X0,X1,tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_206,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_211,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_in(X0,X2,X4)
| ~ c_in(X1,X3,X5)
| ( X4 != X5 )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_594,plain,
! [X0: $i] :
( ( c_Union(v_Y,tc_set(t_a)) = v_x )
| ~ c_lessequals(v_x,c_Union(v_Y,tc_set(t_a)),tc_set(X0))
| ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_x,tc_set(X0)) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_635,plain,
! [X0: $i] :
( ( c_Union(v_Y,tc_set(t_a)) = v_x )
| ~ c_lessequals(v_x,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(X0)))
| ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_x,tc_set(tc_set(X0))) ),
inference(instantiation,[status(thm)],[c_594]) ).
tcf(c_638,plain,
( ( c_Union(v_Y,tc_set(t_a)) = v_x )
| ~ c_lessequals(v_x,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_x,tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_635]) ).
tcf(c_652,plain,
! [X0: $i] : tc_set(X0) = tc_set(X0),
inference(instantiation,[status(thm)],[c_206]) ).
tcf(c_752,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_Union(X1,X2),v_x,tc_set(X2))
| c_lessequals(X0,c_Union(X1,X2),tc_set(X2))
| ~ c_lessequals(c_Zorn_OUnion__lemma0__1(v_x,X0,X1,X2),v_x,tc_set(X2)) ),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_753,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_Union(X1,X2),v_x,tc_set(X2))
| c_lessequals(X0,c_Union(X1,X2),tc_set(X2))
| c_in(c_Zorn_OUnion__lemma0__1(v_x,X0,X1,X2),X1,tc_set(X2)) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_881,plain,
tc_set(tc_set(t_a)) = tc_set(tc_set(t_a)),
inference(instantiation,[status(thm)],[c_652]) ).
tcf(c_1204,plain,
( c_lessequals(c_Union(v_Y,tc_set(t_a)),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_x,tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_752]) ).
tcf(c_1214,plain,
( c_lessequals(c_Union(v_Y,tc_set(t_a)),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_in(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_753]) ).
tcf(c_1533,plain,
v_Y = v_Y,
inference(instantiation,[status(thm)],[c_206]) ).
tcf(c_2622,plain,
! [X0: $i] :
( c_lessequals(c_Union(v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_OUnion__lemma0__1(X0,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_2636,plain,
! [X0: $i] :
( c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),v_x,tc_set(tc_set(t_a)))
| ( X0 = v_x )
| ~ c_in(v_x,v_Y,tc_set(tc_set(t_a)))
| ~ c_lessequals(X0,v_x,tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_2648,plain,
! [X0: $i] :
( c_lessequals(c_Zorn_OUnion__lemma0__1(X0,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a)))
| c_in(c_Main_OsubsetI__1(c_Zorn_OUnion__lemma0__1(X0,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),X0,tc_set(t_a)),c_Zorn_OUnion__lemma0__1(X0,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(t_a)) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_2651,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X1,X0,t_a),X0,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OUnion__lemma0__1(X0,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(X1,X0,t_a),c_Zorn_OUnion__lemma0__1(X0,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(X1,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OUnion__lemma0__1(X0,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),c_Zorn_OTFin(X1,t_a),tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_73]) ).
tcf(c_2652,plain,
! [X0: $i,X1: $i] :
( c_in(c_Zorn_OTFin__linear__lemma1__1(X1,X0,t_a),c_Zorn_OTFin(X1,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OUnion__lemma0__1(X0,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(X1,X0,t_a),c_Zorn_OUnion__lemma0__1(X0,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(X1,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OUnion__lemma0__1(X0,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),c_Zorn_OTFin(X1,t_a),tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_2655,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_Zorn_OUnion__lemma0__1(X0,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(X1,X0,t_a),c_Zorn_OUnion__lemma0__1(X0,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(X1,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Osucc(X1,c_Zorn_OTFin__linear__lemma1__1(X1,X0,t_a),t_a),X0,tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OUnion__lemma0__1(X0,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),c_Zorn_OTFin(X1,t_a),tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_2656,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(X0,X1,t_a),c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_in(X1,c_Zorn_OTFin(X0,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),c_Zorn_OTFin(X0,t_a),tc_set(tc_set(t_a)))
| ( c_Zorn_OTFin__linear__lemma1__1(X0,X1,t_a) != X1 ) ),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_2666,plain,
! [X0: $i,X1: $i] :
( c_in(c_Zorn_OUnion__lemma0__1(X0,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),X1,tc_set(tc_set(t_a)))
| ~ c_lessequals(v_Y,X1,tc_set(tc_set(tc_set(t_a))))
| ~ c_in(c_Zorn_OUnion__lemma0__1(X0,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_2668,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ( X0 = c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)) )
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
| ~ c_lessequals(X0,c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_2704,plain,
( c_lessequals(c_Union(v_Y,tc_set(t_a)),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_2622]) ).
tcf(c_2744,plain,
! [X0: $i] :
( c_in(c_Zorn_OUnion__lemma0__1(X0,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(v_Y,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a))))
| ~ c_in(c_Zorn_OUnion__lemma0__1(X0,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_2666]) ).
tcf(c_2787,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(v_x,X0,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X1,X0,X2),v_x,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),X0,tc_set(tc_set(X2)))
| ~ c_in(v_x,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
inference(instantiation,[status(thm)],[c_73]) ).
tcf(c_2788,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(v_x,X0,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X1,X0,X2),v_x,tc_set(tc_set(X2)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(v_x,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_2810,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(v_x,X1,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X0,X1,X2),v_x,tc_set(tc_set(X2)))
| ~ c_in(v_x,c_Zorn_OTFin(X0,X2),tc_set(tc_set(X2)))
| ~ c_in(X1,c_Zorn_OTFin(X0,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(c_Zorn_Osucc(X0,c_Zorn_OTFin__linear__lemma1__1(X0,X1,X2),X2),X1,tc_set(tc_set(X2))) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_2811,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(v_x,X1,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X0,X1,X2),v_x,tc_set(tc_set(X2)))
| ~ c_in(v_x,c_Zorn_OTFin(X0,X2),tc_set(tc_set(X2)))
| ~ c_in(X1,c_Zorn_OTFin(X0,X2),tc_set(tc_set(X2)))
| ( c_Zorn_OTFin__linear__lemma1__1(X0,X1,X2) != X1 ) ),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_3341,plain,
( c_lessequals(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_x,tc_set(tc_set(t_a)))
| c_in(c_Main_OsubsetI__1(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_x,tc_set(t_a)),c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(t_a)) ),
inference(instantiation,[status(thm)],[c_2648]) ).
tcf(c_3347,plain,
( c_in(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(v_Y,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a))))
| ~ c_in(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_2744]) ).
tcf(c_3352,plain,
! [X0: $i] :
( c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ( X0 = c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)) )
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
| ~ c_lessequals(X0,c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_2668]) ).
tcf(c_4588,plain,
( c_lessequals(v_x,c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),t_a),v_x,tc_set(tc_set(t_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_2788]) ).
tcf(c_4589,plain,
( c_lessequals(v_x,c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),t_a),c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_2787]) ).
tcf(c_4590,plain,
( c_lessequals(v_x,c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),t_a),v_x,tc_set(tc_set(t_a)))
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ( c_Zorn_OTFin__linear__lemma1__1(v_S,c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),t_a) != c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)) ) ),
inference(instantiation,[status(thm)],[c_2811]) ).
tcf(c_4591,plain,
( c_lessequals(v_x,c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),t_a),v_x,tc_set(tc_set(t_a)))
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),t_a),t_a),c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_2810]) ).
tcf(c_4595,plain,
( c_lessequals(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),t_a),v_x,tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_2655]) ).
tcf(c_4596,plain,
( c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_2652]) ).
tcf(c_4597,plain,
( c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_2651]) ).
tcf(c_4598,plain,
( c_lessequals(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) != v_x ) ),
inference(instantiation,[status(thm)],[c_2656]) ).
tcf(c_4651,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ( v_x = c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)) )
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
| ~ c_lessequals(v_x,c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_3352]) ).
tcf(c_10022,plain,
( c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),t_a),v_x,tc_set(tc_set(t_a)))
| ( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x )
| ~ c_in(v_x,v_Y,tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x,tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_2636]) ).
tcf(c_30974,plain,
( c_lessequals(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_x,tc_set(tc_set(t_a)))
| ~ c_in(c_Main_OsubsetI__1(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_x,tc_set(t_a)),v_x,tc_set(t_a)) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_30983,plain,
! [X0: $i] :
( c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ( X0 = c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)) )
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
| ~ c_lessequals(X0,c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_31289,plain,
! [X0: $i] :
( c_in(c_Main_OsubsetI__1(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_x,tc_set(t_a)),X0,tc_set(t_a))
| ~ c_lessequals(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a)))
| ~ c_in(c_Main_OsubsetI__1(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_x,tc_set(t_a)),c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(t_a)) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_32914,plain,
! [X0: $i] : c_lessequals(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),c_Zorn_Osucc(X0,c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),t_a),tc_set(tc_set(t_a))),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_34561,plain,
! [X0: $i,X1: $i] :
( c_in(c_Main_OsubsetI__1(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_x,tc_set(t_a)),X1,tc_set(t_a))
| ~ c_lessequals(X0,X1,tc_set(tc_set(t_a)))
| ~ c_in(c_Main_OsubsetI__1(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_x,tc_set(t_a)),X0,tc_set(t_a)) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_37476,plain,
! [X0: $i] :
( c_in(c_Main_OsubsetI__1(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_x,tc_set(t_a)),c_Zorn_Osucc(v_S,c_Zorn_OUnion__lemma0__1(v_x,X0,v_Y,tc_set(t_a)),t_a),tc_set(t_a))
| ~ c_lessequals(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),c_Zorn_Osucc(v_S,c_Zorn_OUnion__lemma0__1(v_x,X0,v_Y,tc_set(t_a)),t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_Main_OsubsetI__1(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_x,tc_set(t_a)),c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(t_a)) ),
inference(instantiation,[status(thm)],[c_31289]) ).
tcf(c_37870,plain,
( c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),t_a),t_a),c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ( c_Zorn_OTFin__linear__lemma1__1(v_S,c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),t_a) = c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)) )
| ~ c_in(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),t_a),c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_30983]) ).
tcf(c_40084,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X1,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(X2,X3,X0)
| ( v_Y != X3 )
| ( X1 != X2 )
| ( tc_set(tc_set(t_a)) != X0 ) ),
inference(instantiation,[status(thm)],[c_211]) ).
tcf(c_43005,plain,
! [X0: $i,X1: $i] :
( c_in(X0,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
| ( v_Y != v_Y )
| ( X0 != c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)) )
| ( tc_set(tc_set(t_a)) != tc_set(tc_set(t_a)) ) ),
inference(instantiation,[status(thm)],[c_40084]) ).
tcf(c_47475,plain,
! [X0: $i] :
( c_in(c_Main_OsubsetI__1(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_x,tc_set(t_a)),v_x,tc_set(t_a))
| ~ c_lessequals(X0,v_x,tc_set(tc_set(t_a)))
| ~ c_in(c_Main_OsubsetI__1(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_x,tc_set(t_a)),X0,tc_set(t_a)) ),
inference(instantiation,[status(thm)],[c_34561]) ).
tcf(c_64764,plain,
( c_in(c_Main_OsubsetI__1(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_x,tc_set(t_a)),c_Zorn_Osucc(v_S,c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),t_a),tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_x,tc_set(t_a)),c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(t_a))
| ~ c_lessequals(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),c_Zorn_Osucc(v_S,c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),t_a),tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_37476]) ).
tcf(c_64765,plain,
c_lessequals(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),c_Zorn_Osucc(v_S,c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),t_a),tc_set(tc_set(t_a))),
inference(instantiation,[status(thm)],[c_32914]) ).
tcf(c_103811,plain,
( c_in(c_Main_OsubsetI__1(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_x,tc_set(t_a)),v_x,tc_set(t_a))
| ~ c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),t_a),v_x,tc_set(tc_set(t_a)))
| ~ c_in(c_Main_OsubsetI__1(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_x,tc_set(t_a)),c_Zorn_Osucc(v_S,c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),t_a),tc_set(t_a)) ),
inference(instantiation,[status(thm)],[c_47475]) ).
tcf(c_109748,plain,
( c_in(v_x,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
| ( v_x != c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)) )
| ( v_Y != v_Y )
| ( tc_set(tc_set(t_a)) != tc_set(tc_set(t_a)) ) ),
inference(instantiation,[status(thm)],[c_43005]) ).
tcf(c_109749,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_109748,c_103811,c_64765,c_64764,c_37870,c_30974,c_10022,c_4651,c_4598,c_4595,c_4596,c_4597,c_4590,c_4591,c_4588,c_4589,c_3347,c_3341,c_2704,c_1533,c_1214,c_1204,c_881,c_638,c_83,c_79,c_81,c_80,c_82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET854-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 12:17:41 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.42 % Proving...
% 88.53/20.87 % SZS status Started for theBenchmark.p
% 88.53/20.87 % SZS status Unsatisfiable for theBenchmark.p
% 88.53/20.87
% 88.53/20.87 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 88.53/20.87
% 88.53/20.87 % ------ iProver source info
% 88.53/20.87
% 88.53/20.87 % git: date: 2026-07-19 20:42:38 +0200
% 88.53/20.87 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 88.53/20.87 % git: non_committed_changes: false
% 88.53/20.87
% 88.53/20.87 % ------ Parsing...% successful
% 88.53/20.87
% 88.53/20.87
% 88.53/20.87 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 88.53/20.87
% 88.53/20.87 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 88.53/20.87
% 88.53/20.87 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 88.53/20.87
% 88.53/20.87 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 88.53/20.87 % ------ Proving...
% 88.53/20.87 % ------ Problem Properties
% 88.53/20.87
% 88.53/20.87 %
% 88.53/20.87 % clauses 18
% 88.53/20.87 % conjectures 6
% 88.53/20.87 % EPR 0
% 88.53/20.87 % Horn 9
% 88.53/20.87 % unary 6
% 88.53/20.87 % binary 2
% 88.53/20.87 % lits 50
% 88.53/20.87 % lits eq 4
% 88.53/20.87 % fd_pure 0
% 88.53/20.87 % fd_pseudo 0
% 88.53/20.87 % fd_cond 0
% 88.53/20.87 % fd_pseudo_cond 2
% 88.53/20.87 % AC symbols 0
% 88.53/20.87
% 88.53/20.87 % ------ Input Options Time Limit: Unbounded
% 88.53/20.87
% 88.53/20.87
% 88.53/20.87 % ------
% 88.53/20.87 % Current options:
% 88.53/20.87 % ------
% 88.53/20.87
% 88.53/20.87
% 88.53/20.87 %
% 88.53/20.87
% 88.53/20.87 % ------ Proving...
% 88.53/20.87 %
% 88.53/20.87
% 88.53/20.87 % SZS status Unsatisfiable for theBenchmark.p
% 88.53/20.87
% 88.53/20.87 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 88.53/20.88
% 88.53/20.88
%------------------------------------------------------------------------------