%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET861-2 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:08:50 PM UTC 2026
% Result : Unsatisfiable 21.76s 13.34s
% Output : CNFRefutation 21.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 67
% Number of leaves : 15
% Syntax : Number of clauses : 109 ( 11 unt; 50 nHn; 79 RR)
% Number of literals : 301 ( 5 equ; 135 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 3 con; 0-3 aty)
% Number of variables : 169 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Set_OsubsetD_0,axiom,
( c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X2,X4,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
cnf(cls_Zorn_Omaxchain__subset__chain_0,axiom,
c_lessequals(c_Zorn_Omaxchain(X1,X2),c_Zorn_Ochain(X1,X2),tc_set(tc_set(tc_set(X2)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__subset__chain_0) ).
cnf(cls_Zorn_OHausdorff_0,axiom,
c_in(c_Zorn_OHausdorff__1(X1,X2),c_Zorn_Omaxchain(X1,X2),tc_set(tc_set(X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OHausdorff_0) ).
cnf(cls_Zorn_Ochain__extend_0,axiom,
( c_in(c_Zorn_Ochain__extend__1(X4,X1,X3),X4,tc_set(X3))
| c_in(c_union(c_insert(X1,c_emptyset,tc_set(X3)),X4,tc_set(X3)),c_Zorn_Ochain(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,X2,tc_set(X3))
| ~ c_in(X4,c_Zorn_Ochain(X2,X3),tc_set(tc_set(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Ochain__extend_0) ).
cnf(cls_conjecture_1,negated_conjecture,
( c_in(v_xa(X1),v_S,tc_set(t_a))
| ~ c_in(X1,v_S,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_0,negated_conjecture,
( c_in(v_x(X1),v_S,tc_set(t_a))
| ~ c_in(X1,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_Zorn_Omaxchain__super__lemma_0,axiom,
( c_in(X1,X6,X3)
| c_in(c_Zorn_Omaxchain__super__lemma__1(X4,X6,X3),X4,tc_set(X3))
| ~ c_in(X1,X2,X3)
| ~ c_in(X4,c_Zorn_Omaxchain(X5,X3),tc_set(tc_set(X3)))
| ~ c_in(c_union(c_insert(X2,c_emptyset,tc_set(X3)),X4,tc_set(X3)),c_Zorn_Ochain(X5,X3),tc_set(tc_set(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__super__lemma_0) ).
cnf(cls_Set_OsubsetI_0,axiom,
( c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3)
| c_lessequals(X1,X2,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
cnf(cls_Set_OsubsetI_1,axiom,
( c_lessequals(X1,X2,tc_set(X3))
| ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
cnf(cls_Set_Osubset__antisym_0,axiom,
( X2 = X1
| ~ c_lessequals(X1,X2,tc_set(X3))
| ~ c_lessequals(X2,X1,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
cnf(cls_conjecture_2,negated_conjecture,
( c_lessequals(X1,v_xa(X1),tc_set(t_a))
| ~ c_in(X1,v_S,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_conjecture_3,negated_conjecture,
( X1 != v_xa(X1)
| ~ c_in(X1,v_S,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_conjecture_4,negated_conjecture,
( c_lessequals(X1,v_x(X2),tc_set(t_a))
| ~ c_in(X1,X2,tc_set(t_a))
| ~ c_in(X2,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
cnf(cls_Zorn_Ochain__extend_1,axiom,
( c_in(c_union(c_insert(X1,c_emptyset,tc_set(X3)),X4,tc_set(X3)),c_Zorn_Ochain(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,X2,tc_set(X3))
| ~ c_in(X4,c_Zorn_Ochain(X2,X3),tc_set(tc_set(X3)))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(X4,X1,X3),X1,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Ochain__extend_1) ).
cnf(cls_Zorn_Omaxchain__super__lemma_1,axiom,
( c_in(X1,X6,X3)
| ~ c_in(X1,X2,X3)
| ~ c_in(X4,c_Zorn_Omaxchain(X5,X3),tc_set(tc_set(X3)))
| ~ c_in(c_union(c_insert(X2,c_emptyset,tc_set(X3)),X4,tc_set(X3)),c_Zorn_Ochain(X5,X3),tc_set(tc_set(X3)))
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(X4,X6,X3),X6,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__super__lemma_1) ).
cnf(c_0_15,axiom,
( c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X2,X4,tc_set(X3)) ),
cls_Set_OsubsetD_0 ).
cnf(c_0_16,axiom,
c_lessequals(c_Zorn_Omaxchain(X1,X2),c_Zorn_Ochain(X1,X2),tc_set(tc_set(tc_set(X2)))),
cls_Zorn_Omaxchain__subset__chain_0 ).
cnf(c_0_17,plain,
( c_in(X1,c_Zorn_Ochain(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_Omaxchain(X2,X3),tc_set(tc_set(X3))) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,axiom,
c_in(c_Zorn_OHausdorff__1(X1,X2),c_Zorn_Omaxchain(X1,X2),tc_set(tc_set(X2))),
cls_Zorn_OHausdorff_0 ).
cnf(c_0_19,axiom,
( c_in(c_Zorn_Ochain__extend__1(X4,X1,X3),X4,tc_set(X3))
| c_in(c_union(c_insert(X1,c_emptyset,tc_set(X3)),X4,tc_set(X3)),c_Zorn_Ochain(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,X2,tc_set(X3))
| ~ c_in(X4,c_Zorn_Ochain(X2,X3),tc_set(tc_set(X3))) ),
cls_Zorn_Ochain__extend_0 ).
cnf(c_0_20,plain,
c_in(c_Zorn_OHausdorff__1(X1,X2),c_Zorn_Ochain(X1,X2),tc_set(tc_set(X2))),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
( c_in(c_union(c_insert(X1,c_emptyset,tc_set(X2)),c_Zorn_OHausdorff__1(X3,X2),tc_set(X2)),c_Zorn_Ochain(X3,X2),tc_set(tc_set(X2)))
| c_in(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(X3,X2),X1,X2),c_Zorn_OHausdorff__1(X3,X2),tc_set(X2))
| ~ c_in(X1,X3,tc_set(X2)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,negated_conjecture,
( c_in(v_xa(X1),v_S,tc_set(t_a))
| ~ c_in(X1,v_S,tc_set(t_a)) ),
cls_conjecture_1 ).
cnf(c_0_23,negated_conjecture,
( c_in(c_union(c_insert(v_xa(X1),c_emptyset,tc_set(t_a)),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(X1),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| ~ c_in(X1,v_S,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_24,negated_conjecture,
( c_in(c_union(c_insert(v_xa(v_xa(X1)),c_emptyset,tc_set(t_a)),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(X1)),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| ~ c_in(X1,v_S,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
( c_in(v_x(X1),v_S,tc_set(t_a))
| ~ c_in(X1,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
cls_conjecture_0 ).
cnf(c_0_26,negated_conjecture,
( c_in(c_union(c_insert(v_xa(v_xa(v_x(X1))),c_emptyset,tc_set(t_a)),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_x(X1))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| ~ c_in(X1,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,axiom,
( c_in(X1,X6,X3)
| c_in(c_Zorn_Omaxchain__super__lemma__1(X4,X6,X3),X4,tc_set(X3))
| ~ c_in(X1,X2,X3)
| ~ c_in(X4,c_Zorn_Omaxchain(X5,X3),tc_set(tc_set(X3)))
| ~ c_in(c_union(c_insert(X2,c_emptyset,tc_set(X3)),X4,tc_set(X3)),c_Zorn_Ochain(X5,X3),tc_set(tc_set(X3))) ),
cls_Zorn_Omaxchain__super__lemma_0 ).
cnf(c_0_28,negated_conjecture,
( c_in(c_union(c_insert(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),c_emptyset,tc_set(t_a)),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_26,c_0_20]) ).
cnf(c_0_29,negated_conjecture,
( c_in(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),X1,t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| c_in(X2,X1,t_a)
| ~ c_in(X2,v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),t_a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_18])]) ).
cnf(c_0_30,axiom,
( c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3)
| c_lessequals(X1,X2,tc_set(X3)) ),
cls_Set_OsubsetI_0 ).
cnf(c_0_31,axiom,
( c_lessequals(X1,X2,tc_set(X3))
| ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3) ),
cls_Set_OsubsetI_1 ).
cnf(c_0_32,negated_conjecture,
( c_in(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),X1,t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),X2,t_a),X1,t_a)
| c_lessequals(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),X2,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,axiom,
( X2 = X1
| ~ c_lessequals(X1,X2,tc_set(X3))
| ~ c_lessequals(X2,X1,tc_set(X3)) ),
cls_Set_Osubset__antisym_0 ).
cnf(c_0_34,negated_conjecture,
( c_in(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),X1,t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| c_lessequals(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),X1,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,negated_conjecture,
( X1 = v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))
| c_in(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),X1,t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| ~ c_lessequals(X1,v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_36,negated_conjecture,
( c_lessequals(X1,v_xa(X1),tc_set(t_a))
| ~ c_in(X1,v_S,tc_set(t_a)) ),
cls_conjecture_2 ).
cnf(c_0_37,negated_conjecture,
( X1 != v_xa(X1)
| ~ c_in(X1,v_S,tc_set(t_a)) ),
cls_conjecture_3 ).
cnf(c_0_38,negated_conjecture,
( c_lessequals(X1,v_x(X2),tc_set(t_a))
| ~ c_in(X1,X2,tc_set(t_a))
| ~ c_in(X2,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
cls_conjecture_4 ).
cnf(c_0_39,negated_conjecture,
( c_in(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| ~ c_in(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),v_S,tc_set(t_a)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
cnf(c_0_40,negated_conjecture,
( c_in(X1,v_x(X2),t_a)
| ~ c_in(X2,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X3,X2,tc_set(t_a))
| ~ c_in(X1,X3,t_a) ),
inference(spm,[status(thm)],[c_0_15,c_0_38]) ).
cnf(c_0_41,negated_conjecture,
( c_in(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| ~ c_in(v_x(c_Zorn_OHausdorff__1(v_S,t_a)),v_S,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_39,c_0_22]) ).
cnf(c_0_42,negated_conjecture,
( c_in(X1,v_xa(X2),t_a)
| ~ c_in(X2,v_S,tc_set(t_a))
| ~ c_in(X1,X2,t_a) ),
inference(spm,[status(thm)],[c_0_15,c_0_36]) ).
cnf(c_0_43,negated_conjecture,
( c_in(X1,v_x(c_Zorn_OHausdorff__1(v_S,t_a)),t_a)
| ~ c_in(X2,c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| ~ c_in(X1,X2,t_a) ),
inference(spm,[status(thm)],[c_0_40,c_0_20]) ).
cnf(c_0_44,negated_conjecture,
( c_in(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_25]),c_0_20])]) ).
cnf(c_0_45,negated_conjecture,
( c_lessequals(X1,v_xa(X2),tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(X1,v_xa(X2),t_a),X2,t_a)
| ~ c_in(X2,v_S,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_31,c_0_42]) ).
cnf(c_0_46,negated_conjecture,
( c_in(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| c_in(X1,v_x(c_Zorn_OHausdorff__1(v_S,t_a)),t_a)
| ~ c_in(X1,c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),t_a),t_a) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_47,negated_conjecture,
( c_lessequals(X1,v_xa(v_xa(X2)),tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(X1,v_xa(v_xa(X2)),t_a),X2,t_a)
| ~ c_in(X2,v_S,tc_set(t_a)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_42]),c_0_22]) ).
cnf(c_0_48,negated_conjecture,
( c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),t_a),X1,t_a),v_x(c_Zorn_OHausdorff__1(v_S,t_a)),t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| c_lessequals(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),t_a),X1,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_46,c_0_30]) ).
cnf(c_0_49,axiom,
( c_in(c_union(c_insert(X1,c_emptyset,tc_set(X3)),X4,tc_set(X3)),c_Zorn_Ochain(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,X2,tc_set(X3))
| ~ c_in(X4,c_Zorn_Ochain(X2,X3),tc_set(tc_set(X3)))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(X4,X1,X3),X1,tc_set(X3)) ),
cls_Zorn_Ochain__extend_1 ).
cnf(c_0_50,negated_conjecture,
( c_in(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| c_lessequals(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),t_a),v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),tc_set(t_a))
| ~ c_in(v_x(c_Zorn_OHausdorff__1(v_S,t_a)),v_S,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_51,plain,
( c_in(c_union(c_insert(X1,c_emptyset,tc_set(X2)),c_Zorn_OHausdorff__1(X3,X2),tc_set(X2)),c_Zorn_Ochain(X3,X2),tc_set(tc_set(X2)))
| ~ c_in(X1,X3,tc_set(X2))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(X3,X2),X1,X2),X1,tc_set(X2)) ),
inference(spm,[status(thm)],[c_0_49,c_0_20]) ).
cnf(c_0_52,negated_conjecture,
( c_in(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| c_lessequals(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),t_a),v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),tc_set(t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_25]),c_0_20])]) ).
cnf(c_0_53,negated_conjecture,
( c_in(c_union(c_insert(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),c_emptyset,tc_set(t_a)),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| ~ c_in(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),v_S,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_54,negated_conjecture,
( c_in(c_union(c_insert(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),c_emptyset,tc_set(t_a)),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| ~ c_in(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),v_S,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_53,c_0_22]) ).
cnf(c_0_55,negated_conjecture,
( c_in(c_union(c_insert(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),c_emptyset,tc_set(t_a)),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| ~ c_in(v_x(c_Zorn_OHausdorff__1(v_S,t_a)),v_S,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_54,c_0_22]) ).
cnf(c_0_56,negated_conjecture,
( c_in(c_union(c_insert(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),c_emptyset,tc_set(t_a)),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_25]),c_0_20])]) ).
cnf(c_0_57,negated_conjecture,
( c_in(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),X1,t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| c_in(X2,X1,t_a)
| ~ c_in(X2,v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),t_a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_56]),c_0_18])]) ).
cnf(c_0_58,negated_conjecture,
( c_in(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),X1,t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),X2,t_a),X1,t_a)
| c_lessequals(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),X2,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_57,c_0_30]) ).
cnf(c_0_59,negated_conjecture,
( ~ c_in(X1,v_S,tc_set(t_a))
| ~ c_lessequals(v_xa(X1),X1,tc_set(t_a)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_36]),c_0_37]) ).
cnf(c_0_60,negated_conjecture,
( c_in(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),X1,t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| c_lessequals(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),X1,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_31,c_0_58]) ).
cnf(c_0_61,negated_conjecture,
( c_in(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| ~ c_in(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),v_S,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_62,negated_conjecture,
( c_in(X1,v_x(c_Zorn_OHausdorff__1(v_S,t_a)),t_a)
| ~ c_in(X1,c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a),t_a)
| ~ c_in(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),v_S,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_43,c_0_61]) ).
cnf(c_0_63,negated_conjecture,
( c_in(c_Main_OsubsetI__1(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a),X1,t_a),v_x(c_Zorn_OHausdorff__1(v_S,t_a)),t_a)
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a),X1,tc_set(t_a))
| ~ c_in(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),v_S,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_62,c_0_30]) ).
cnf(c_0_64,negated_conjecture,
( c_in(c_Main_OsubsetI__1(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a),X1,t_a),v_x(c_Zorn_OHausdorff__1(v_S,t_a)),t_a)
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a),X1,tc_set(t_a))
| ~ c_in(v_x(c_Zorn_OHausdorff__1(v_S,t_a)),v_S,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_63,c_0_22]) ).
cnf(c_0_65,negated_conjecture,
( c_in(c_Main_OsubsetI__1(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a),X1,t_a),v_x(c_Zorn_OHausdorff__1(v_S,t_a)),t_a)
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a),X1,tc_set(t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_25]),c_0_20])]) ).
cnf(c_0_66,negated_conjecture,
( c_in(c_union(c_insert(v_xa(v_xa(v_xa(X1))),c_emptyset,tc_set(t_a)),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_xa(X1))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| ~ c_in(X1,v_S,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_24,c_0_22]) ).
cnf(c_0_67,negated_conjecture,
( c_lessequals(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),tc_set(t_a))
| ~ c_in(v_x(c_Zorn_OHausdorff__1(v_S,t_a)),v_S,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_45,c_0_65]) ).
cnf(c_0_68,negated_conjecture,
( c_in(c_union(c_insert(v_xa(v_xa(v_xa(v_x(X1)))),c_emptyset,tc_set(t_a)),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_xa(v_x(X1)))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| ~ c_in(X1,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_66,c_0_25]) ).
cnf(c_0_69,negated_conjecture,
( c_in(X1,v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a)
| ~ c_in(X1,c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a),t_a)
| ~ c_in(v_x(c_Zorn_OHausdorff__1(v_S,t_a)),v_S,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_15,c_0_67]) ).
cnf(c_0_70,axiom,
( c_in(X1,X6,X3)
| ~ c_in(X1,X2,X3)
| ~ c_in(X4,c_Zorn_Omaxchain(X5,X3),tc_set(tc_set(X3)))
| ~ c_in(c_union(c_insert(X2,c_emptyset,tc_set(X3)),X4,tc_set(X3)),c_Zorn_Ochain(X5,X3),tc_set(tc_set(X3)))
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(X4,X6,X3),X6,tc_set(X3)) ),
cls_Zorn_Omaxchain__super__lemma_1 ).
cnf(c_0_71,negated_conjecture,
( c_in(c_union(c_insert(v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),c_emptyset,tc_set(t_a)),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_68,c_0_20]) ).
cnf(c_0_72,negated_conjecture,
( c_in(c_Main_OsubsetI__1(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a),X1,t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a)
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a),X1,tc_set(t_a))
| ~ c_in(v_x(c_Zorn_OHausdorff__1(v_S,t_a)),v_S,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_69,c_0_30]) ).
cnf(c_0_73,negated_conjecture,
( c_in(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| c_in(X1,X2,t_a)
| ~ c_in(X1,v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),X2,t_a),X2,tc_set(t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_18])]) ).
cnf(c_0_74,negated_conjecture,
( c_in(c_Main_OsubsetI__1(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a),X1,t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a)
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a),X1,tc_set(t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_25]),c_0_20])]) ).
cnf(c_0_75,negated_conjecture,
( c_in(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),X1,t_a),X2,t_a)
| c_lessequals(v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),X1,tc_set(t_a))
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),X2,t_a),X2,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_73,c_0_30]) ).
cnf(c_0_76,negated_conjecture,
c_lessequals(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),tc_set(t_a)),
inference(spm,[status(thm)],[c_0_31,c_0_74]) ).
cnf(c_0_77,negated_conjecture,
( c_in(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),X1,t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a)
| c_lessequals(v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),X1,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_78,negated_conjecture,
( c_in(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| c_lessequals(v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),tc_set(t_a))
| ~ c_in(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),v_S,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_45,c_0_77]) ).
cnf(c_0_79,negated_conjecture,
( c_in(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| c_lessequals(v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),tc_set(t_a))
| ~ c_in(v_x(c_Zorn_OHausdorff__1(v_S,t_a)),v_S,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_78,c_0_22]) ).
cnf(c_0_80,negated_conjecture,
( c_in(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| c_lessequals(v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),tc_set(t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_25]),c_0_20])]) ).
cnf(c_0_81,negated_conjecture,
( c_in(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),t_a),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a))
| ~ c_in(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),v_S,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_59,c_0_80]) ).
cnf(c_0_82,negated_conjecture,
( c_in(X1,v_x(c_Zorn_OHausdorff__1(v_S,t_a)),t_a)
| ~ c_in(X1,c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),t_a),t_a)
| ~ c_in(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),v_S,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_43,c_0_81]) ).
cnf(c_0_83,negated_conjecture,
( c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),t_a),X1,t_a),v_x(c_Zorn_OHausdorff__1(v_S,t_a)),t_a)
| c_lessequals(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),t_a),X1,tc_set(t_a))
| ~ c_in(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),v_S,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_82,c_0_30]) ).
cnf(c_0_84,negated_conjecture,
( c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),t_a),X1,t_a),v_x(c_Zorn_OHausdorff__1(v_S,t_a)),t_a)
| c_lessequals(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),t_a),X1,tc_set(t_a))
| ~ c_in(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),v_S,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_83,c_0_22]) ).
cnf(c_0_85,negated_conjecture,
( c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),t_a),X1,t_a),v_x(c_Zorn_OHausdorff__1(v_S,t_a)),t_a)
| c_lessequals(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),t_a),X1,tc_set(t_a))
| ~ c_in(v_x(c_Zorn_OHausdorff__1(v_S,t_a)),v_S,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_84,c_0_22]) ).
cnf(c_0_86,negated_conjecture,
( c_lessequals(X1,v_xa(v_xa(v_xa(X2))),tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(X1,v_xa(v_xa(v_xa(X2))),t_a),X2,t_a)
| ~ c_in(X2,v_S,tc_set(t_a)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_42]),c_0_22]) ).
cnf(c_0_87,negated_conjecture,
( c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),t_a),X1,t_a),v_x(c_Zorn_OHausdorff__1(v_S,t_a)),t_a)
| c_lessequals(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),t_a),X1,tc_set(t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_25]),c_0_20])]) ).
cnf(c_0_88,negated_conjecture,
( c_lessequals(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),t_a),v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),tc_set(t_a))
| ~ c_in(v_x(c_Zorn_OHausdorff__1(v_S,t_a)),v_S,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_89,negated_conjecture,
( c_in(X1,v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),t_a)
| ~ c_in(X1,c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),t_a),t_a)
| ~ c_in(v_x(c_Zorn_OHausdorff__1(v_S,t_a)),v_S,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_15,c_0_88]) ).
cnf(c_0_90,negated_conjecture,
( c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),t_a),X1,t_a),v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),t_a)
| c_lessequals(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),t_a),X1,tc_set(t_a))
| ~ c_in(v_x(c_Zorn_OHausdorff__1(v_S,t_a)),v_S,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_89,c_0_30]) ).
cnf(c_0_91,negated_conjecture,
( c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),t_a),X1,t_a),v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),t_a)
| c_lessequals(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),t_a),X1,tc_set(t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_25]),c_0_20])]) ).
cnf(c_0_92,negated_conjecture,
c_lessequals(c_Zorn_Ochain__extend__1(c_Zorn_OHausdorff__1(v_S,t_a),v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),t_a),v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),tc_set(t_a)),
inference(spm,[status(thm)],[c_0_31,c_0_91]) ).
cnf(c_0_93,negated_conjecture,
( c_in(c_union(c_insert(v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),c_emptyset,tc_set(t_a)),c_Zorn_OHausdorff__1(v_S,t_a),tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),v_S,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_51,c_0_92]) ).
cnf(c_0_94,negated_conjecture,
( c_in(X1,X2,t_a)
| ~ c_in(v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),v_S,tc_set(t_a))
| ~ c_in(X1,v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),X2,t_a),X2,tc_set(t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_93]),c_0_18])]) ).
cnf(c_0_95,negated_conjecture,
( c_in(X1,X2,t_a)
| ~ c_in(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),v_S,tc_set(t_a))
| ~ c_in(X1,v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),X2,t_a),X2,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_94,c_0_22]) ).
cnf(c_0_96,negated_conjecture,
( c_in(X1,X2,t_a)
| ~ c_in(X1,v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),t_a)
| ~ c_in(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),v_S,tc_set(t_a))
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),X2,t_a),X2,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_95,c_0_22]) ).
cnf(c_0_97,negated_conjecture,
( c_in(X1,X2,t_a)
| ~ c_in(X1,v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),t_a)
| ~ c_in(v_x(c_Zorn_OHausdorff__1(v_S,t_a)),v_S,tc_set(t_a))
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),X2,t_a),X2,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_96,c_0_22]) ).
cnf(c_0_98,negated_conjecture,
( c_in(X1,X2,t_a)
| ~ c_in(X1,v_xa(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))))),t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),X2,t_a),X2,tc_set(t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_25]),c_0_20])]) ).
cnf(c_0_99,negated_conjecture,
( c_in(X1,X2,t_a)
| ~ c_in(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),v_S,tc_set(t_a))
| ~ c_in(X1,v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),X2,t_a),X2,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_98,c_0_42]) ).
cnf(c_0_100,negated_conjecture,
( c_in(X1,X2,t_a)
| ~ c_in(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),v_S,tc_set(t_a))
| ~ c_in(X1,v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),X2,t_a),X2,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_99,c_0_22]) ).
cnf(c_0_101,negated_conjecture,
( c_in(X1,X2,t_a)
| ~ c_in(X1,v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),t_a)
| ~ c_in(v_x(c_Zorn_OHausdorff__1(v_S,t_a)),v_S,tc_set(t_a))
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),X2,t_a),X2,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_100,c_0_22]) ).
cnf(c_0_102,negated_conjecture,
( c_in(X1,X2,t_a)
| ~ c_in(X1,v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(c_Zorn_OHausdorff__1(v_S,t_a),X2,t_a),X2,tc_set(t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_25]),c_0_20])]) ).
cnf(c_0_103,negated_conjecture,
( c_in(X1,v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a)
| ~ c_in(X1,v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),t_a) ),
inference(spm,[status(thm)],[c_0_102,c_0_76]) ).
cnf(c_0_104,negated_conjecture,
( c_in(c_Main_OsubsetI__1(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),X1,t_a),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),t_a)
| c_lessequals(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),X1,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_103,c_0_30]) ).
cnf(c_0_105,negated_conjecture,
c_lessequals(v_xa(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a)))),v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),tc_set(t_a)),
inference(spm,[status(thm)],[c_0_31,c_0_104]) ).
cnf(c_0_106,negated_conjecture,
~ c_in(v_xa(v_x(c_Zorn_OHausdorff__1(v_S,t_a))),v_S,tc_set(t_a)),
inference(spm,[status(thm)],[c_0_59,c_0_105]) ).
cnf(c_0_107,negated_conjecture,
~ c_in(v_x(c_Zorn_OHausdorff__1(v_S,t_a)),v_S,tc_set(t_a)),
inference(spm,[status(thm)],[c_0_106,c_0_22]) ).
cnf(c_0_108,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_25]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET861-2 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.33 % Computer : n027.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 02:38:20 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 21.76/13.34 % Version : CSE_E---1.7
% 21.76/13.34 % Problem : theBenchmark.p
% 21.76/13.34 % SZS status Unsatisfiable for theBenchmark.p
% 21.76/13.34 % SZS output start CNFRefutation
% See solution above
% 21.86/13.42 % Total time : 9.380s
%------------------------------------------------------------------------------