TSTP Solution File: SET863-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET863-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 Sep 20 05:08:27 EDT 2022
% Result : Unsatisfiable 12.50s 8.30s
% Output : Proof 12.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET863-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 08:32:45 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 12.50/8.30 % SZS status Unsatisfiable
% 12.50/8.30 % SZS output start Proof
% 12.50/8.30 tff(c_in_type, type, (
% 12.50/8.30 c_in: ( $i * $i * $i ) > $o)).
% 12.50/8.30 tff(tc_set_type, type, (
% 12.50/8.30 tc_set: $i > $i)).
% 12.50/8.30 tff(t_a_type, type, (
% 12.50/8.30 t_a: $i)).
% 12.50/8.30 tff(v_c_type, type, (
% 12.50/8.30 v_c: $i)).
% 12.50/8.30 tff(c_Zorn_Omaxchain__super__lemma__1_type, type, (
% 12.50/8.30 c_Zorn_Omaxchain__super__lemma__1: ( $i * $i * $i ) > $i)).
% 12.50/8.30 tff(v_y_type, type, (
% 12.50/8.30 v_y: $i)).
% 12.50/8.30 tff(c_lessequals_type, type, (
% 12.50/8.30 c_lessequals: ( $i * $i * $i ) > $o)).
% 12.50/8.30 tff(c_Zorn_Ochain_type, type, (
% 12.50/8.30 c_Zorn_Ochain: ( $i * $i ) > $i)).
% 12.50/8.30 tff(v_S_type, type, (
% 12.50/8.30 v_S: $i)).
% 12.50/8.30 tff(c_union_type, type, (
% 12.50/8.30 c_union: ( $i * $i * $i ) > $i)).
% 12.50/8.30 tff(c_insert_type, type, (
% 12.50/8.30 c_insert: ( $i * $i * $i ) > $i)).
% 12.50/8.30 tff(c_emptyset_type, type, (
% 12.50/8.30 c_emptyset: $i)).
% 12.50/8.30 tff(v_x_type, type, (
% 12.50/8.30 v_x: $i)).
% 12.50/8.30 tff(c_Main_OsubsetI__1_type, type, (
% 12.50/8.30 c_Main_OsubsetI__1: ( $i * $i * $i ) > $i)).
% 12.50/8.30 tff(c_Zorn_Ochain__extend__1_type, type, (
% 12.50/8.30 c_Zorn_Ochain__extend__1: ( $i * $i * $i ) > $i)).
% 12.50/8.30 tff(v_xa_type, type, (
% 12.50/8.30 v_xa: $i)).
% 12.50/8.30 tff(c_Zorn_Omaxchain_type, type, (
% 12.50/8.30 c_Zorn_Omaxchain: ( $i * $i ) > $i)).
% 12.50/8.30 tff(1,assumption,(~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)))), introduced(assumption)).
% 12.50/8.30 tff(2,plain,
% 12.50/8.30 (c_in(v_x, v_S, tc_set(t_a)) <=> c_in(v_x, v_S, tc_set(t_a))),
% 12.50/8.30 inference(rewrite,[status(thm)],[])).
% 12.50/8.30 tff(3,axiom,(c_in(v_x, v_S, tc_set(t_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_3')).
% 12.50/8.30 tff(4,plain,
% 12.50/8.30 (c_in(v_x, v_S, tc_set(t_a))),
% 12.50/8.30 inference(modus_ponens,[status(thm)],[3, 2])).
% 12.50/8.30 tff(5,plain,
% 12.50/8.30 (c_in(v_c, c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))) <=> c_in(v_c, c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))),
% 12.50/8.30 inference(rewrite,[status(thm)],[])).
% 12.50/8.30 tff(6,axiom,(c_in(v_c, c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_1')).
% 12.50/8.30 tff(7,plain,
% 12.50/8.30 (c_in(v_c, c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))),
% 12.50/8.30 inference(modus_ponens,[status(thm)],[6, 5])).
% 12.50/8.30 tff(8,plain,
% 12.50/8.30 (^[V_c: $i, V_z: $i, V_S: $i, T_a: $i] : refl((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(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))) | (~c_lessequals(c_Zorn_Ochain__extend__1(V_c, V_z, T_a), V_z, tc_set(T_a)))) <=> (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(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))) | (~c_lessequals(c_Zorn_Ochain__extend__1(V_c, V_z, T_a), V_z, tc_set(T_a)))))),
% 12.50/8.30 inference(bind,[status(th)],[])).
% 12.50/8.30 tff(9,plain,
% 12.50/8.30 (![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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(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))) | (~c_lessequals(c_Zorn_Ochain__extend__1(V_c, V_z, T_a), V_z, tc_set(T_a)))) <=> ![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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(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))) | (~c_lessequals(c_Zorn_Ochain__extend__1(V_c, V_z, T_a), V_z, tc_set(T_a))))),
% 12.50/8.30 inference(quant_intro,[status(thm)],[8])).
% 12.50/8.30 tff(10,plain,
% 12.50/8.30 (![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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(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))) | (~c_lessequals(c_Zorn_Ochain__extend__1(V_c, V_z, T_a), V_z, tc_set(T_a)))) <=> ![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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(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))) | (~c_lessequals(c_Zorn_Ochain__extend__1(V_c, V_z, T_a), V_z, tc_set(T_a))))),
% 12.50/8.30 inference(rewrite,[status(thm)],[])).
% 12.50/8.30 tff(11,plain,
% 12.50/8.30 (^[V_c: $i, V_z: $i, V_S: $i, T_a: $i] : trans(monotonicity(rewrite((((~c_in(V_z, V_S, tc_set(T_a))) | (~c_in(V_c, 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))) | (~c_lessequals(c_Zorn_Ochain__extend__1(V_c, V_z, T_a), V_z, tc_set(T_a))))), (((((~c_in(V_z, V_S, tc_set(T_a))) | (~c_in(V_c, 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(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(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))) | (~c_lessequals(c_Zorn_Ochain__extend__1(V_c, V_z, T_a), V_z, tc_set(T_a)))) | 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)))))), rewrite((((~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))) | (~c_lessequals(c_Zorn_Ochain__extend__1(V_c, V_z, T_a), V_z, tc_set(T_a)))) | 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_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(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))) | (~c_lessequals(c_Zorn_Ochain__extend__1(V_c, V_z, T_a), V_z, tc_set(T_a))))), (((((~c_in(V_z, V_S, tc_set(T_a))) | (~c_in(V_c, 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(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_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(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))) | (~c_lessequals(c_Zorn_Ochain__extend__1(V_c, V_z, T_a), V_z, tc_set(T_a))))))),
% 12.50/8.30 inference(bind,[status(th)],[])).
% 12.50/8.30 tff(12,plain,
% 12.50/8.30 (![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : ((((~c_in(V_z, V_S, tc_set(T_a))) | (~c_in(V_c, 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(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)))) <=> ![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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(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))) | (~c_lessequals(c_Zorn_Ochain__extend__1(V_c, V_z, T_a), V_z, tc_set(T_a))))),
% 12.50/8.30 inference(quant_intro,[status(thm)],[11])).
% 12.50/8.30 tff(13,axiom,(![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : ((((~c_in(V_z, V_S, tc_set(T_a))) | (~c_in(V_c, 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(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))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Zorn_Ochain__extend_1')).
% 12.50/8.30 tff(14,plain,
% 12.50/8.30 (![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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(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))) | (~c_lessequals(c_Zorn_Ochain__extend__1(V_c, V_z, T_a), V_z, tc_set(T_a))))),
% 12.50/8.30 inference(modus_ponens,[status(thm)],[13, 12])).
% 12.50/8.30 tff(15,plain,
% 12.50/8.30 (![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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(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))) | (~c_lessequals(c_Zorn_Ochain__extend__1(V_c, V_z, T_a), V_z, tc_set(T_a))))),
% 12.50/8.30 inference(modus_ponens,[status(thm)],[14, 10])).
% 12.50/8.30 tff(16,plain,(
% 12.50/8.30 ![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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(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))) | (~c_lessequals(c_Zorn_Ochain__extend__1(V_c, V_z, T_a), V_z, tc_set(T_a))))),
% 12.50/8.30 inference(skolemize,[status(sab)],[15])).
% 12.50/8.30 tff(17,plain,
% 12.50/8.30 (![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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(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))) | (~c_lessequals(c_Zorn_Ochain__extend__1(V_c, V_z, T_a), V_z, tc_set(T_a))))),
% 12.50/8.30 inference(modus_ponens,[status(thm)],[16, 9])).
% 12.50/8.30 tff(18,plain,
% 12.50/8.30 (((~![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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(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))) | (~c_lessequals(c_Zorn_Ochain__extend__1(V_c, V_z, T_a), V_z, tc_set(T_a))))) | ((~c_in(v_x, v_S, tc_set(t_a))) | (~c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, 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_Ochain(v_S, t_a), tc_set(tc_set(t_a)))))) <=> ((~![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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(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))) | (~c_lessequals(c_Zorn_Ochain__extend__1(V_c, V_z, T_a), V_z, tc_set(T_a))))) | (~c_in(v_x, v_S, tc_set(t_a))) | (~c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, 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_Ochain(v_S, t_a), tc_set(tc_set(t_a)))))),
% 12.50/8.30 inference(rewrite,[status(thm)],[])).
% 12.50/8.30 tff(19,plain,
% 12.50/8.30 ((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_Ochain(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_in(v_x, v_S, tc_set(t_a))) | (~c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, tc_set(t_a)))) <=> ((~c_in(v_x, v_S, tc_set(t_a))) | (~c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, 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_Ochain(v_S, t_a), tc_set(tc_set(t_a)))))),
% 12.50/8.30 inference(rewrite,[status(thm)],[])).
% 12.50/8.30 tff(20,plain,
% 12.50/8.30 (((~![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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(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))) | (~c_lessequals(c_Zorn_Ochain__extend__1(V_c, V_z, T_a), V_z, 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_Ochain(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_in(v_x, v_S, tc_set(t_a))) | (~c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, tc_set(t_a))))) <=> ((~![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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(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))) | (~c_lessequals(c_Zorn_Ochain__extend__1(V_c, V_z, T_a), V_z, tc_set(T_a))))) | ((~c_in(v_x, v_S, tc_set(t_a))) | (~c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, 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_Ochain(v_S, t_a), tc_set(tc_set(t_a))))))),
% 12.50/8.30 inference(monotonicity,[status(thm)],[19])).
% 12.50/8.30 tff(21,plain,
% 12.50/8.30 (((~![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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(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))) | (~c_lessequals(c_Zorn_Ochain__extend__1(V_c, V_z, T_a), V_z, 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_Ochain(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_in(v_x, v_S, tc_set(t_a))) | (~c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, tc_set(t_a))))) <=> ((~![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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(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))) | (~c_lessequals(c_Zorn_Ochain__extend__1(V_c, V_z, T_a), V_z, tc_set(T_a))))) | (~c_in(v_x, v_S, tc_set(t_a))) | (~c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, 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_Ochain(v_S, t_a), tc_set(tc_set(t_a)))))),
% 12.50/8.30 inference(transitivity,[status(thm)],[20, 18])).
% 12.50/8.30 tff(22,plain,
% 12.50/8.30 ((~![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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(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))) | (~c_lessequals(c_Zorn_Ochain__extend__1(V_c, V_z, T_a), V_z, 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_Ochain(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_in(v_x, v_S, tc_set(t_a))) | (~c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, tc_set(t_a))))),
% 12.50/8.30 inference(quant_inst,[status(thm)],[])).
% 12.50/8.30 tff(23,plain,
% 12.50/8.30 ((~![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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(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))) | (~c_lessequals(c_Zorn_Ochain__extend__1(V_c, V_z, T_a), V_z, tc_set(T_a))))) | (~c_in(v_x, v_S, tc_set(t_a))) | (~c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, 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_Ochain(v_S, t_a), tc_set(tc_set(t_a))))),
% 12.50/8.30 inference(modus_ponens,[status(thm)],[22, 21])).
% 12.50/8.30 tff(24,plain,
% 12.50/8.30 (~c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, tc_set(t_a))),
% 12.50/8.30 inference(unit_resolution,[status(thm)],[23, 17, 7, 4, 1])).
% 12.50/8.30 tff(25,plain,
% 12.50/8.30 (^[T_a: $i, V_B: $i, V_A: $i] : refl(((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_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)) | c_lessequals(V_A, V_B, tc_set(T_a))))),
% 12.50/8.30 inference(bind,[status(th)],[])).
% 12.50/8.30 tff(26,plain,
% 12.50/8.30 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 12.50/8.30 inference(quant_intro,[status(thm)],[25])).
% 12.50/8.30 tff(27,plain,
% 12.50/8.30 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 12.50/8.30 inference(rewrite,[status(thm)],[])).
% 12.50/8.30 tff(28,axiom,(![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OsubsetI_1')).
% 12.50/8.31 tff(29,plain,
% 12.50/8.31 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 12.50/8.31 inference(modus_ponens,[status(thm)],[28, 27])).
% 12.50/8.31 tff(30,plain,(
% 12.50/8.31 ![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 12.50/8.31 inference(skolemize,[status(sab)],[29])).
% 12.50/8.31 tff(31,plain,
% 12.50/8.31 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 12.50/8.31 inference(modus_ponens,[status(thm)],[30, 26])).
% 12.50/8.31 tff(32,plain,
% 12.50/8.31 (((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_x, t_a)) | c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, tc_set(t_a)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_x, t_a)) | c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, tc_set(t_a)))),
% 12.50/8.31 inference(rewrite,[status(thm)],[])).
% 12.50/8.31 tff(33,plain,
% 12.50/8.31 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_x, t_a)) | c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, tc_set(t_a)))),
% 12.50/8.31 inference(quant_inst,[status(thm)],[])).
% 12.50/8.31 tff(34,plain,
% 12.50/8.31 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_x, t_a)) | c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, tc_set(t_a))),
% 12.50/8.31 inference(modus_ponens,[status(thm)],[33, 32])).
% 12.50/8.31 tff(35,plain,
% 12.50/8.31 (~c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_x, t_a)),
% 12.50/8.31 inference(unit_resolution,[status(thm)],[34, 31, 24])).
% 12.50/8.31 tff(36,plain,
% 12.50/8.31 (^[V_c: $i, V_z: $i, V_S: $i, T_a: $i] : refl((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)))) <=> (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)))))),
% 12.50/8.31 inference(bind,[status(th)],[])).
% 12.50/8.31 tff(37,plain,
% 12.50/8.31 (![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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)))) <=> ![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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))))),
% 12.50/8.31 inference(quant_intro,[status(thm)],[36])).
% 12.50/8.31 tff(38,plain,
% 12.50/8.31 (![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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)))) <=> ![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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))))),
% 12.50/8.31 inference(rewrite,[status(thm)],[])).
% 12.50/8.31 tff(39,plain,
% 12.50/8.31 (^[V_c: $i, V_z: $i, V_S: $i, T_a: $i] : trans(monotonicity(rewrite((((~c_in(V_z, V_S, 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_Ochain__extend__1(V_c, V_z, T_a), V_c, 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))))), (((((~c_in(V_z, V_S, 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_Ochain__extend__1(V_c, V_z, T_a), V_c, tc_set(T_a))) | 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)))) | 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)))))), rewrite(((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)))) | 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_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))))), (((((~c_in(V_z, V_S, 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_Ochain__extend__1(V_c, V_z, T_a), V_c, tc_set(T_a))) | 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_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))))))),
% 12.50/8.31 inference(bind,[status(th)],[])).
% 12.50/8.31 tff(40,plain,
% 12.50/8.31 (![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : ((((~c_in(V_z, V_S, 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_Ochain__extend__1(V_c, V_z, T_a), V_c, tc_set(T_a))) | 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)))) <=> ![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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))))),
% 12.50/8.31 inference(quant_intro,[status(thm)],[39])).
% 12.50/8.31 tff(41,axiom,(![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : ((((~c_in(V_z, V_S, 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_Ochain__extend__1(V_c, V_z, T_a), V_c, tc_set(T_a))) | 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))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Zorn_Ochain__extend_0')).
% 12.50/8.31 tff(42,plain,
% 12.50/8.31 (![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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))))),
% 12.50/8.31 inference(modus_ponens,[status(thm)],[41, 40])).
% 12.50/8.31 tff(43,plain,
% 12.50/8.31 (![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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))))),
% 12.50/8.31 inference(modus_ponens,[status(thm)],[42, 38])).
% 12.50/8.31 tff(44,plain,(
% 12.50/8.31 ![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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))))),
% 12.50/8.31 inference(skolemize,[status(sab)],[43])).
% 12.50/8.31 tff(45,plain,
% 12.50/8.31 (![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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))))),
% 12.50/8.31 inference(modus_ponens,[status(thm)],[44, 37])).
% 12.50/8.31 tff(46,plain,
% 12.50/8.31 (((~![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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))))) | ((~c_in(v_x, v_S, tc_set(t_a))) | c_in(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_c, 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_Ochain(v_S, t_a), tc_set(tc_set(t_a)))))) <=> ((~![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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))))) | (~c_in(v_x, v_S, tc_set(t_a))) | c_in(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_c, 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_Ochain(v_S, t_a), tc_set(tc_set(t_a)))))),
% 12.50/8.31 inference(rewrite,[status(thm)],[])).
% 12.50/8.31 tff(47,plain,
% 12.50/8.31 ((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(c_Zorn_Ochain__extend__1(v_c, v_x, 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_S, tc_set(t_a)))) <=> ((~c_in(v_x, v_S, tc_set(t_a))) | c_in(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_c, 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_Ochain(v_S, t_a), tc_set(tc_set(t_a)))))),
% 12.50/8.31 inference(rewrite,[status(thm)],[])).
% 12.50/8.31 tff(48,plain,
% 12.50/8.31 (((~![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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))))) | (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(c_Zorn_Ochain__extend__1(v_c, v_x, 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_S, tc_set(t_a))))) <=> ((~![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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))))) | ((~c_in(v_x, v_S, tc_set(t_a))) | c_in(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_c, 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_Ochain(v_S, t_a), tc_set(tc_set(t_a))))))),
% 12.50/8.31 inference(monotonicity,[status(thm)],[47])).
% 12.50/8.31 tff(49,plain,
% 12.50/8.31 (((~![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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))))) | (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(c_Zorn_Ochain__extend__1(v_c, v_x, 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_S, tc_set(t_a))))) <=> ((~![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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))))) | (~c_in(v_x, v_S, tc_set(t_a))) | c_in(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_c, 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_Ochain(v_S, t_a), tc_set(tc_set(t_a)))))),
% 12.50/8.31 inference(transitivity,[status(thm)],[48, 46])).
% 12.50/8.31 tff(50,plain,
% 12.50/8.31 ((~![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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))))) | (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(c_Zorn_Ochain__extend__1(v_c, v_x, 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_S, tc_set(t_a))))),
% 12.50/8.31 inference(quant_inst,[status(thm)],[])).
% 12.50/8.31 tff(51,plain,
% 12.50/8.31 ((~![V_c: $i, V_z: $i, V_S: $i, T_a: $i] : (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))))) | (~c_in(v_x, v_S, tc_set(t_a))) | c_in(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_c, 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_Ochain(v_S, t_a), tc_set(tc_set(t_a))))),
% 12.50/8.31 inference(modus_ponens,[status(thm)],[50, 49])).
% 12.50/8.31 tff(52,plain,
% 12.50/8.31 (c_in(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_c, tc_set(t_a))),
% 12.50/8.31 inference(unit_resolution,[status(thm)],[51, 45, 7, 4, 1])).
% 12.50/8.31 tff(53,plain,
% 12.50/8.31 (^[V_U: $i] : refl((c_lessequals(V_U, v_y, tc_set(t_a)) | (~c_in(V_U, v_c, tc_set(t_a)))) <=> (c_lessequals(V_U, v_y, tc_set(t_a)) | (~c_in(V_U, v_c, tc_set(t_a)))))),
% 12.50/8.31 inference(bind,[status(th)],[])).
% 12.50/8.31 tff(54,plain,
% 12.50/8.31 (![V_U: $i] : (c_lessequals(V_U, v_y, tc_set(t_a)) | (~c_in(V_U, v_c, tc_set(t_a)))) <=> ![V_U: $i] : (c_lessequals(V_U, v_y, tc_set(t_a)) | (~c_in(V_U, v_c, tc_set(t_a))))),
% 12.50/8.31 inference(quant_intro,[status(thm)],[53])).
% 12.50/8.31 tff(55,plain,
% 12.50/8.31 (![V_U: $i] : (c_lessequals(V_U, v_y, tc_set(t_a)) | (~c_in(V_U, v_c, tc_set(t_a)))) <=> ![V_U: $i] : (c_lessequals(V_U, v_y, tc_set(t_a)) | (~c_in(V_U, v_c, tc_set(t_a))))),
% 12.50/8.31 inference(rewrite,[status(thm)],[])).
% 12.50/8.31 tff(56,axiom,(![V_U: $i] : (c_lessequals(V_U, v_y, tc_set(t_a)) | (~c_in(V_U, v_c, tc_set(t_a))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_7')).
% 12.50/8.31 tff(57,plain,
% 12.50/8.31 (![V_U: $i] : (c_lessequals(V_U, v_y, tc_set(t_a)) | (~c_in(V_U, v_c, tc_set(t_a))))),
% 12.50/8.31 inference(modus_ponens,[status(thm)],[56, 55])).
% 12.50/8.31 tff(58,plain,(
% 12.50/8.31 ![V_U: $i] : (c_lessequals(V_U, v_y, tc_set(t_a)) | (~c_in(V_U, v_c, tc_set(t_a))))),
% 12.50/8.31 inference(skolemize,[status(sab)],[57])).
% 12.50/8.31 tff(59,plain,
% 12.50/8.31 (![V_U: $i] : (c_lessequals(V_U, v_y, tc_set(t_a)) | (~c_in(V_U, v_c, tc_set(t_a))))),
% 12.50/8.31 inference(modus_ponens,[status(thm)],[58, 54])).
% 12.50/8.31 tff(60,plain,
% 12.50/8.31 (((~![V_U: $i] : (c_lessequals(V_U, v_y, tc_set(t_a)) | (~c_in(V_U, v_c, tc_set(t_a))))) | ((~c_in(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_c, tc_set(t_a))) | c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_y, tc_set(t_a)))) <=> ((~![V_U: $i] : (c_lessequals(V_U, v_y, tc_set(t_a)) | (~c_in(V_U, v_c, tc_set(t_a))))) | (~c_in(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_c, tc_set(t_a))) | c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_y, tc_set(t_a)))),
% 12.50/8.31 inference(rewrite,[status(thm)],[])).
% 12.50/8.31 tff(61,plain,
% 12.50/8.31 ((c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_y, tc_set(t_a)) | (~c_in(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_c, tc_set(t_a)))) <=> ((~c_in(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_c, tc_set(t_a))) | c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_y, tc_set(t_a)))),
% 12.50/8.31 inference(rewrite,[status(thm)],[])).
% 12.50/8.31 tff(62,plain,
% 12.50/8.31 (((~![V_U: $i] : (c_lessequals(V_U, v_y, tc_set(t_a)) | (~c_in(V_U, v_c, tc_set(t_a))))) | (c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_y, tc_set(t_a)) | (~c_in(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_c, tc_set(t_a))))) <=> ((~![V_U: $i] : (c_lessequals(V_U, v_y, tc_set(t_a)) | (~c_in(V_U, v_c, tc_set(t_a))))) | ((~c_in(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_c, tc_set(t_a))) | c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_y, tc_set(t_a))))),
% 12.50/8.31 inference(monotonicity,[status(thm)],[61])).
% 12.50/8.31 tff(63,plain,
% 12.50/8.31 (((~![V_U: $i] : (c_lessequals(V_U, v_y, tc_set(t_a)) | (~c_in(V_U, v_c, tc_set(t_a))))) | (c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_y, tc_set(t_a)) | (~c_in(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_c, tc_set(t_a))))) <=> ((~![V_U: $i] : (c_lessequals(V_U, v_y, tc_set(t_a)) | (~c_in(V_U, v_c, tc_set(t_a))))) | (~c_in(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_c, tc_set(t_a))) | c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_y, tc_set(t_a)))),
% 12.50/8.31 inference(transitivity,[status(thm)],[62, 60])).
% 12.50/8.31 tff(64,plain,
% 12.50/8.31 ((~![V_U: $i] : (c_lessequals(V_U, v_y, tc_set(t_a)) | (~c_in(V_U, v_c, tc_set(t_a))))) | (c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_y, tc_set(t_a)) | (~c_in(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_c, tc_set(t_a))))),
% 12.50/8.31 inference(quant_inst,[status(thm)],[])).
% 12.50/8.31 tff(65,plain,
% 12.50/8.31 ((~![V_U: $i] : (c_lessequals(V_U, v_y, tc_set(t_a)) | (~c_in(V_U, v_c, tc_set(t_a))))) | (~c_in(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_c, tc_set(t_a))) | c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_y, tc_set(t_a))),
% 12.50/8.31 inference(modus_ponens,[status(thm)],[64, 63])).
% 12.50/8.31 tff(66,plain,
% 12.50/8.31 (c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_y, tc_set(t_a))),
% 12.50/8.31 inference(unit_resolution,[status(thm)],[65, 59, 52])).
% 12.50/8.31 tff(67,plain,
% 12.50/8.31 (^[T_a: $i, V_B: $i, V_A: $i] : refl((c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, 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) | c_lessequals(V_A, V_B, tc_set(T_a))))),
% 12.50/8.31 inference(bind,[status(th)],[])).
% 12.50/8.31 tff(68,plain,
% 12.50/8.31 (![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 12.50/8.31 inference(quant_intro,[status(thm)],[67])).
% 12.50/8.31 tff(69,plain,
% 12.50/8.31 (![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 12.50/8.31 inference(rewrite,[status(thm)],[])).
% 12.50/8.31 tff(70,axiom,(![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OsubsetI_0')).
% 12.50/8.31 tff(71,plain,
% 12.50/8.31 (![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 12.50/8.31 inference(modus_ponens,[status(thm)],[70, 69])).
% 12.50/8.31 tff(72,plain,(
% 12.50/8.31 ![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 12.50/8.31 inference(skolemize,[status(sab)],[71])).
% 12.50/8.31 tff(73,plain,
% 12.50/8.31 (![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 12.50/8.31 inference(modus_ponens,[status(thm)],[72, 68])).
% 12.50/8.31 tff(74,plain,
% 12.50/8.31 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), c_Zorn_Ochain__extend__1(v_c, v_x, t_a), t_a))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), c_Zorn_Ochain__extend__1(v_c, v_x, t_a), t_a))),
% 12.50/8.31 inference(rewrite,[status(thm)],[])).
% 12.50/8.31 tff(75,plain,
% 12.50/8.31 ((c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), c_Zorn_Ochain__extend__1(v_c, v_x, t_a), t_a) | c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, tc_set(t_a))) <=> (c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), c_Zorn_Ochain__extend__1(v_c, v_x, t_a), t_a))),
% 12.50/8.31 inference(rewrite,[status(thm)],[])).
% 12.50/8.31 tff(76,plain,
% 12.50/8.31 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), c_Zorn_Ochain__extend__1(v_c, v_x, t_a), t_a) | c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, tc_set(t_a)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), c_Zorn_Ochain__extend__1(v_c, v_x, t_a), t_a)))),
% 12.50/8.31 inference(monotonicity,[status(thm)],[75])).
% 12.50/8.31 tff(77,plain,
% 12.50/8.31 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), c_Zorn_Ochain__extend__1(v_c, v_x, t_a), t_a) | c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, tc_set(t_a)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), c_Zorn_Ochain__extend__1(v_c, v_x, t_a), t_a))),
% 12.50/8.31 inference(transitivity,[status(thm)],[76, 74])).
% 12.50/8.31 tff(78,plain,
% 12.50/8.31 ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), c_Zorn_Ochain__extend__1(v_c, v_x, t_a), t_a) | c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, tc_set(t_a)))),
% 12.50/8.31 inference(quant_inst,[status(thm)],[])).
% 12.50/8.31 tff(79,plain,
% 12.50/8.31 ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), c_Zorn_Ochain__extend__1(v_c, v_x, t_a), t_a)),
% 12.50/8.31 inference(modus_ponens,[status(thm)],[78, 77])).
% 12.50/8.31 tff(80,plain,
% 12.50/8.31 (c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), c_Zorn_Ochain__extend__1(v_c, v_x, t_a), t_a)),
% 12.50/8.31 inference(unit_resolution,[status(thm)],[79, 73, 24])).
% 12.50/8.31 tff(81,plain,
% 12.50/8.31 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : refl((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))) <=> (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))))),
% 12.50/8.31 inference(bind,[status(th)],[])).
% 12.50/8.31 tff(82,plain,
% 12.50/8.31 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (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))) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (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)))),
% 12.50/8.31 inference(quant_intro,[status(thm)],[81])).
% 12.50/8.31 tff(83,plain,
% 12.50/8.31 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (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))) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (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)))),
% 12.50/8.31 inference(rewrite,[status(thm)],[])).
% 12.50/8.31 tff(84,plain,
% 12.50/8.31 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : rewrite((((~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | c_in(V_c, V_B, T_a)) <=> (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))))),
% 12.50/8.31 inference(bind,[status(th)],[])).
% 12.50/8.31 tff(85,plain,
% 12.50/8.31 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | c_in(V_c, V_B, T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (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)))),
% 12.50/8.31 inference(quant_intro,[status(thm)],[84])).
% 12.50/8.31 tff(86,axiom,(![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | c_in(V_c, V_B, T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OsubsetD_0')).
% 12.50/8.31 tff(87,plain,
% 12.50/8.31 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (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)))),
% 12.50/8.31 inference(modus_ponens,[status(thm)],[86, 85])).
% 12.50/8.31 tff(88,plain,
% 12.50/8.31 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (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)))),
% 12.50/8.31 inference(modus_ponens,[status(thm)],[87, 83])).
% 12.50/8.31 tff(89,plain,(
% 12.50/8.31 ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (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)))),
% 12.50/8.31 inference(skolemize,[status(sab)],[88])).
% 12.50/8.31 tff(90,plain,
% 12.50/8.31 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (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)))),
% 12.50/8.31 inference(modus_ponens,[status(thm)],[89, 82])).
% 12.50/8.31 tff(91,plain,
% 12.50/8.31 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (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)))) | ((~c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), c_Zorn_Ochain__extend__1(v_c, v_x, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_y, t_a) | (~c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_y, tc_set(t_a))))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (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)))) | (~c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), c_Zorn_Ochain__extend__1(v_c, v_x, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_y, t_a) | (~c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_y, tc_set(t_a))))),
% 12.50/8.31 inference(rewrite,[status(thm)],[])).
% 12.50/8.31 tff(92,plain,
% 12.50/8.31 ((c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_y, t_a) | (~c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_y, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), c_Zorn_Ochain__extend__1(v_c, v_x, t_a), t_a))) <=> ((~c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), c_Zorn_Ochain__extend__1(v_c, v_x, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_y, t_a) | (~c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_y, tc_set(t_a))))),
% 12.50/8.32 inference(rewrite,[status(thm)],[])).
% 12.50/8.32 tff(93,plain,
% 12.50/8.32 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (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)))) | (c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_y, t_a) | (~c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_y, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), c_Zorn_Ochain__extend__1(v_c, v_x, t_a), t_a)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (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)))) | ((~c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), c_Zorn_Ochain__extend__1(v_c, v_x, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_y, t_a) | (~c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_y, tc_set(t_a)))))),
% 12.50/8.32 inference(monotonicity,[status(thm)],[92])).
% 12.50/8.32 tff(94,plain,
% 12.50/8.32 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (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)))) | (c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_y, t_a) | (~c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_y, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), c_Zorn_Ochain__extend__1(v_c, v_x, t_a), t_a)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (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)))) | (~c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), c_Zorn_Ochain__extend__1(v_c, v_x, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_y, t_a) | (~c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_y, tc_set(t_a))))),
% 12.50/8.32 inference(transitivity,[status(thm)],[93, 91])).
% 12.50/8.32 tff(95,plain,
% 12.50/8.32 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (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)))) | (c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_y, t_a) | (~c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_y, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), c_Zorn_Ochain__extend__1(v_c, v_x, t_a), t_a)))),
% 12.50/8.32 inference(quant_inst,[status(thm)],[])).
% 12.50/8.32 tff(96,plain,
% 12.50/8.32 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (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)))) | (~c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), c_Zorn_Ochain__extend__1(v_c, v_x, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_y, t_a) | (~c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_y, tc_set(t_a)))),
% 12.50/8.32 inference(modus_ponens,[status(thm)],[95, 94])).
% 12.50/8.32 tff(97,plain,
% 12.50/8.32 ((~c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), c_Zorn_Ochain__extend__1(v_c, v_x, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_y, t_a) | (~c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_y, tc_set(t_a)))),
% 12.50/8.32 inference(unit_resolution,[status(thm)],[96, 90])).
% 12.50/8.32 tff(98,plain,
% 12.50/8.32 (c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_y, t_a)),
% 12.50/8.32 inference(unit_resolution,[status(thm)],[97, 80, 66])).
% 12.50/8.32 tff(99,plain,
% 12.50/8.32 (c_lessequals(v_y, v_x, tc_set(t_a)) <=> c_lessequals(v_y, v_x, tc_set(t_a))),
% 12.50/8.32 inference(rewrite,[status(thm)],[])).
% 12.50/8.32 tff(100,axiom,(c_lessequals(v_y, v_x, tc_set(t_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_4')).
% 12.50/8.32 tff(101,plain,
% 12.50/8.32 (c_lessequals(v_y, v_x, tc_set(t_a))),
% 12.50/8.32 inference(modus_ponens,[status(thm)],[100, 99])).
% 12.50/8.32 tff(102,plain,
% 12.50/8.32 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (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)))) | ((~c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_y, t_a)) | c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_x, t_a) | (~c_lessequals(v_y, v_x, tc_set(t_a))))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (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)))) | (~c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_y, t_a)) | c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_x, t_a) | (~c_lessequals(v_y, v_x, tc_set(t_a))))),
% 12.50/8.32 inference(rewrite,[status(thm)],[])).
% 12.50/8.32 tff(103,plain,
% 12.50/8.32 ((c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_x, t_a) | (~c_lessequals(v_y, v_x, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_y, t_a))) <=> ((~c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_y, t_a)) | c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_x, t_a) | (~c_lessequals(v_y, v_x, tc_set(t_a))))),
% 12.50/8.32 inference(rewrite,[status(thm)],[])).
% 12.50/8.32 tff(104,plain,
% 12.50/8.32 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (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)))) | (c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_x, t_a) | (~c_lessequals(v_y, v_x, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_y, t_a)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (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)))) | ((~c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_y, t_a)) | c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_x, t_a) | (~c_lessequals(v_y, v_x, tc_set(t_a)))))),
% 12.50/8.32 inference(monotonicity,[status(thm)],[103])).
% 12.50/8.32 tff(105,plain,
% 12.50/8.32 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (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)))) | (c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_x, t_a) | (~c_lessequals(v_y, v_x, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_y, t_a)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (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)))) | (~c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_y, t_a)) | c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_x, t_a) | (~c_lessequals(v_y, v_x, tc_set(t_a))))),
% 12.50/8.32 inference(transitivity,[status(thm)],[104, 102])).
% 12.50/8.32 tff(106,plain,
% 12.50/8.32 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (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)))) | (c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_x, t_a) | (~c_lessequals(v_y, v_x, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_y, t_a)))),
% 12.50/8.32 inference(quant_inst,[status(thm)],[])).
% 12.50/8.32 tff(107,plain,
% 12.50/8.32 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))) | (~c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_y, t_a)) | c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_x, t_a) | (~c_lessequals(v_y, v_x, tc_set(t_a)))),
% 12.50/8.32 inference(modus_ponens,[status(thm)],[106, 105])).
% 12.50/8.32 tff(108,plain,
% 12.50/8.32 ($false),
% 12.50/8.32 inference(unit_resolution,[status(thm)],[107, 90, 101, 98, 35])).
% 12.50/8.32 tff(109,plain,(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)))), inference(lemma,lemma(discharge,[]))).
% 12.50/8.32 tff(110,plain,
% 12.50/8.32 ((~c_in(v_xa, v_y, t_a)) <=> (~c_in(v_xa, v_y, t_a))),
% 12.50/8.32 inference(rewrite,[status(thm)],[])).
% 12.50/8.32 tff(111,axiom,(~c_in(v_xa, v_y, t_a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_6')).
% 12.50/8.32 tff(112,plain,
% 12.50/8.32 (~c_in(v_xa, v_y, t_a)),
% 12.50/8.32 inference(modus_ponens,[status(thm)],[111, 110])).
% 12.50/8.32 tff(113,plain,
% 12.50/8.32 (c_in(v_xa, v_x, t_a) <=> c_in(v_xa, v_x, t_a)),
% 12.50/8.32 inference(rewrite,[status(thm)],[])).
% 12.50/8.32 tff(114,axiom,(c_in(v_xa, v_x, t_a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_5')).
% 12.50/8.32 tff(115,plain,
% 12.50/8.32 (c_in(v_xa, v_x, t_a)),
% 12.50/8.32 inference(modus_ponens,[status(thm)],[114, 113])).
% 12.50/8.32 tff(116,plain,
% 12.50/8.32 (c_in(v_c, c_Zorn_Omaxchain(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)))),
% 12.50/8.32 inference(rewrite,[status(thm)],[])).
% 12.50/8.32 tff(117,axiom,(c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_0')).
% 12.50/8.32 tff(118,plain,
% 12.50/8.32 (c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))),
% 12.50/8.32 inference(modus_ponens,[status(thm)],[117, 116])).
% 12.50/8.32 tff(119,plain,
% 12.50/8.32 (^[V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : refl((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)) | (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_y, 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)) | (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_y, tc_set(T_a)))))),
% 12.50/8.32 inference(bind,[status(th)],[])).
% 12.50/8.32 tff(120,plain,
% 12.50/8.32 (![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (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)) | (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_y, tc_set(T_a)))) <=> ![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (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)) | (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_y, tc_set(T_a))))),
% 12.50/8.32 inference(quant_intro,[status(thm)],[119])).
% 12.50/8.32 tff(121,plain,
% 12.50/8.32 (![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (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)) | (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_y, tc_set(T_a)))) <=> ![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (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)) | (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_y, tc_set(T_a))))),
% 12.50/8.32 inference(rewrite,[status(thm)],[])).
% 12.50/8.32 tff(122,plain,
% 12.50/8.32 (^[V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c_in(V_z, V_x, T_a)) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(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(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)))), (((((~c_in(V_z, V_x, T_a)) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(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_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))) | (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_y, tc_set(T_a)))))), rewrite((((~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))) | (~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)) | (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_y, tc_set(T_a))))), (((((~c_in(V_z, V_x, T_a)) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(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_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)) | (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_y, tc_set(T_a)))))), ((((((~c_in(V_z, V_x, T_a)) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(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_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_y, 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)) | (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_y, tc_set(T_a)))) | c_in(V_z, V_y, T_a)))), rewrite((((~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)) | (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_y, tc_set(T_a)))) | c_in(V_z, V_y, 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)) | (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_y, tc_set(T_a))))), ((((((~c_in(V_z, V_x, T_a)) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(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_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_y, tc_set(T_a)))) | c_in(V_z, V_y, 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)) | (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_y, tc_set(T_a))))))),
% 12.50/8.32 inference(bind,[status(th)],[])).
% 12.50/8.32 tff(123,plain,
% 12.50/8.32 (![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (((((~c_in(V_z, V_x, T_a)) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(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_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_y, tc_set(T_a)))) | c_in(V_z, V_y, T_a)) <=> ![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (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)) | (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_y, tc_set(T_a))))),
% 12.50/8.32 inference(quant_intro,[status(thm)],[122])).
% 12.50/8.32 tff(124,axiom,(![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (((((~c_in(V_z, V_x, T_a)) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(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_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_y, tc_set(T_a)))) | c_in(V_z, V_y, T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Zorn_Omaxchain__super__lemma_1')).
% 12.50/8.32 tff(125,plain,
% 12.50/8.32 (![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (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)) | (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_y, tc_set(T_a))))),
% 12.50/8.32 inference(modus_ponens,[status(thm)],[124, 123])).
% 12.50/8.32 tff(126,plain,
% 12.50/8.32 (![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (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)) | (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_y, tc_set(T_a))))),
% 12.50/8.32 inference(modus_ponens,[status(thm)],[125, 121])).
% 12.50/8.32 tff(127,plain,(
% 12.50/8.32 ![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (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)) | (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_y, tc_set(T_a))))),
% 12.50/8.32 inference(skolemize,[status(sab)],[126])).
% 12.50/8.32 tff(128,plain,
% 12.50/8.32 (![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (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)) | (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_y, tc_set(T_a))))),
% 12.50/8.32 inference(modus_ponens,[status(thm)],[127, 120])).
% 12.50/8.32 tff(129,plain,
% 12.50/8.32 (((~![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (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)) | (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_y, tc_set(T_a))))) | (c_in(v_xa, v_y, t_a) | (~c_in(v_xa, v_x, t_a)) | (~c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(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_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_y, tc_set(t_a))))) <=> ((~![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (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)) | (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_y, tc_set(T_a))))) | c_in(v_xa, v_y, t_a) | (~c_in(v_xa, v_x, t_a)) | (~c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(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_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_y, tc_set(t_a))))),
% 12.50/8.32 inference(rewrite,[status(thm)],[])).
% 12.50/8.32 tff(130,plain,
% 12.50/8.32 ((c_in(v_xa, 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_xa, v_x, t_a)) | (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_y, tc_set(t_a)))) <=> (c_in(v_xa, v_y, t_a) | (~c_in(v_xa, v_x, t_a)) | (~c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(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_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_y, tc_set(t_a))))),
% 12.50/8.32 inference(rewrite,[status(thm)],[])).
% 12.50/8.32 tff(131,plain,
% 12.50/8.32 (((~![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (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)) | (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_y, tc_set(T_a))))) | (c_in(v_xa, 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_xa, v_x, t_a)) | (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_y, tc_set(t_a))))) <=> ((~![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (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)) | (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_y, tc_set(T_a))))) | (c_in(v_xa, v_y, t_a) | (~c_in(v_xa, v_x, t_a)) | (~c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(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_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_y, tc_set(t_a)))))),
% 12.50/8.32 inference(monotonicity,[status(thm)],[130])).
% 12.50/8.32 tff(132,plain,
% 12.50/8.32 (((~![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (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)) | (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_y, tc_set(T_a))))) | (c_in(v_xa, 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_xa, v_x, t_a)) | (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_y, tc_set(t_a))))) <=> ((~![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (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)) | (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_y, tc_set(T_a))))) | c_in(v_xa, v_y, t_a) | (~c_in(v_xa, v_x, t_a)) | (~c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(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_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_y, tc_set(t_a))))),
% 12.50/8.32 inference(transitivity,[status(thm)],[131, 129])).
% 12.50/8.32 tff(133,plain,
% 12.50/8.32 ((~![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (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)) | (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_y, tc_set(T_a))))) | (c_in(v_xa, 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_xa, v_x, t_a)) | (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_y, tc_set(t_a))))),
% 12.50/8.32 inference(quant_inst,[status(thm)],[])).
% 12.50/8.32 tff(134,plain,
% 12.50/8.32 ((~![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (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)) | (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_y, tc_set(T_a))))) | c_in(v_xa, v_y, t_a) | (~c_in(v_xa, v_x, t_a)) | (~c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(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_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_y, tc_set(t_a)))),
% 12.50/8.32 inference(modus_ponens,[status(thm)],[133, 132])).
% 12.50/8.32 tff(135,plain,
% 12.50/8.32 (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_y, tc_set(t_a))),
% 12.50/8.32 inference(unit_resolution,[status(thm)],[134, 128, 118, 115, 112, 109])).
% 12.50/8.32 tff(136,plain,
% 12.50/8.32 (((~![V_U: $i] : (c_lessequals(V_U, v_y, tc_set(t_a)) | (~c_in(V_U, v_c, tc_set(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_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_c, tc_set(t_a))))) <=> ((~![V_U: $i] : (c_lessequals(V_U, v_y, tc_set(t_a)) | (~c_in(V_U, v_c, tc_set(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_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_c, tc_set(t_a))))),
% 12.50/8.32 inference(rewrite,[status(thm)],[])).
% 12.50/8.32 tff(137,plain,
% 12.50/8.32 ((~![V_U: $i] : (c_lessequals(V_U, v_y, tc_set(t_a)) | (~c_in(V_U, v_c, tc_set(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_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_c, tc_set(t_a))))),
% 12.50/8.32 inference(quant_inst,[status(thm)],[])).
% 12.50/8.32 tff(138,plain,
% 12.50/8.32 ((~![V_U: $i] : (c_lessequals(V_U, v_y, tc_set(t_a)) | (~c_in(V_U, v_c, tc_set(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_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_c, tc_set(t_a)))),
% 12.50/8.32 inference(modus_ponens,[status(thm)],[137, 136])).
% 12.50/8.32 tff(139,plain,
% 12.50/8.32 (~c_in(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_c, tc_set(t_a))),
% 12.50/8.32 inference(unit_resolution,[status(thm)],[138, 59, 135])).
% 12.50/8.32 tff(140,plain,
% 12.50/8.32 (^[V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : refl((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))) <=> (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))))),
% 12.50/8.32 inference(bind,[status(th)],[])).
% 12.50/8.32 tff(141,plain,
% 12.50/8.32 (![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (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))) <=> ![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (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)))),
% 12.50/8.32 inference(quant_intro,[status(thm)],[140])).
% 12.50/8.32 tff(142,plain,
% 12.50/8.32 (![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (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))) <=> ![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (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)))),
% 12.50/8.32 inference(rewrite,[status(thm)],[])).
% 12.50/8.32 tff(143,plain,
% 12.50/8.32 (^[V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c_in(V_z, V_x, T_a)) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(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(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)))), (((((~c_in(V_z, V_x, T_a)) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(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_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))) | c_in(V_z, V_y, T_a)))), rewrite((((~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))) | c_in(V_z, V_y, 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)))), (((((~c_in(V_z, V_x, T_a)) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(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_z, V_y, 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))))), ((((((~c_in(V_z, V_x, T_a)) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(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_z, V_y, T_a)) | 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))) | c_in(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_c, tc_set(T_a))))), rewrite(((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))) | c_in(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_c, tc_set(T_a))) <=> (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)))), ((((((~c_in(V_z, V_x, T_a)) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(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_z, V_y, T_a)) | c_in(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_c, tc_set(T_a))) <=> (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)))))),
% 12.50/8.32 inference(bind,[status(th)],[])).
% 12.50/8.32 tff(144,plain,
% 12.50/8.32 (![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (((((~c_in(V_z, V_x, T_a)) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(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_z, V_y, T_a)) | c_in(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_c, tc_set(T_a))) <=> ![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (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)))),
% 12.50/8.32 inference(quant_intro,[status(thm)],[143])).
% 12.50/8.32 tff(145,axiom,(![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (((((~c_in(V_z, V_x, T_a)) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(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_z, V_y, T_a)) | c_in(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_c, tc_set(T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Zorn_Omaxchain__super__lemma_0')).
% 12.50/8.32 tff(146,plain,
% 12.50/8.32 (![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (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)))),
% 12.50/8.32 inference(modus_ponens,[status(thm)],[145, 144])).
% 12.50/8.32 tff(147,plain,
% 12.50/8.32 (![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (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)))),
% 12.50/8.32 inference(modus_ponens,[status(thm)],[146, 142])).
% 12.50/8.32 tff(148,plain,(
% 12.50/8.32 ![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (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)))),
% 12.50/8.32 inference(skolemize,[status(sab)],[147])).
% 12.50/8.32 tff(149,plain,
% 12.50/8.32 (![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (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)))),
% 12.50/8.32 inference(modus_ponens,[status(thm)],[148, 141])).
% 12.50/8.32 tff(150,plain,
% 12.50/8.32 (((~![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (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)))) | (c_in(v_xa, v_y, t_a) | (~c_in(v_xa, v_x, t_a)) | (~c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(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(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_c, tc_set(t_a)))) <=> ((~![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (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)))) | c_in(v_xa, v_y, t_a) | (~c_in(v_xa, v_x, t_a)) | (~c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(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(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_c, tc_set(t_a)))),
% 12.50/8.33 inference(rewrite,[status(thm)],[])).
% 12.50/8.33 tff(151,plain,
% 12.50/8.33 ((c_in(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_c, tc_set(t_a)) | c_in(v_xa, 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_xa, v_x, t_a))) <=> (c_in(v_xa, v_y, t_a) | (~c_in(v_xa, v_x, t_a)) | (~c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(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(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_c, tc_set(t_a)))),
% 12.50/8.33 inference(rewrite,[status(thm)],[])).
% 12.50/8.33 tff(152,plain,
% 12.50/8.33 (((~![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (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)))) | (c_in(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_c, tc_set(t_a)) | c_in(v_xa, 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_xa, v_x, t_a)))) <=> ((~![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (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)))) | (c_in(v_xa, v_y, t_a) | (~c_in(v_xa, v_x, t_a)) | (~c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(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(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_c, tc_set(t_a))))),
% 12.50/8.33 inference(monotonicity,[status(thm)],[151])).
% 12.50/8.33 tff(153,plain,
% 12.50/8.33 (((~![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (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)))) | (c_in(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_c, tc_set(t_a)) | c_in(v_xa, 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_xa, v_x, t_a)))) <=> ((~![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (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)))) | c_in(v_xa, v_y, t_a) | (~c_in(v_xa, v_x, t_a)) | (~c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(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(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_c, tc_set(t_a)))),
% 12.59/8.33 inference(transitivity,[status(thm)],[152, 150])).
% 12.59/8.33 tff(154,plain,
% 12.59/8.33 ((~![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (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)))) | (c_in(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_c, tc_set(t_a)) | c_in(v_xa, 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_xa, v_x, t_a)))),
% 12.59/8.33 inference(quant_inst,[status(thm)],[])).
% 12.59/8.33 tff(155,plain,
% 12.59/8.33 ((~![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (c_in(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_c, tc_set(T_a)) | c_in(V_z, V_y, T_a) | (~c_in(c_union(c_insert(V_x, c_emptyset, tc_set(T_a)), V_c, tc_set(T_a)), c_Zorn_Ochain(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_z, V_x, T_a)))) | c_in(v_xa, v_y, t_a) | (~c_in(v_xa, v_x, t_a)) | (~c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_in(c_union(c_insert(v_x, c_emptyset, tc_set(t_a)), v_c, tc_set(t_a)), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_c, tc_set(t_a))),
% 12.59/8.33 inference(modus_ponens,[status(thm)],[154, 153])).
% 12.59/8.33 tff(156,plain,
% 12.59/8.33 ($false),
% 12.59/8.33 inference(unit_resolution,[status(thm)],[155, 149, 118, 115, 112, 109, 139])).
% 12.59/8.33 % SZS output end Proof
%------------------------------------------------------------------------------