%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET863-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 : Sat Jun 21 05:26:34 AM UTC 2025
% Result : Unsatisfiable 0.57s 0.73s
% Output : Proof 0.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET863-2 : TPTP v9.0.0. Released v3.2.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 05:49:05 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.57/0.73 % SZS status Unsatisfiable
% 0.57/0.73 % SZS output start Proof
% 0.57/0.73 tff(c_in_type, type, (
% 0.57/0.73 c_in: ( $i * $i * $i ) > $o)).
% 0.57/0.73 tff(tc_set_type, type, (
% 0.57/0.73 tc_set: $i > $i)).
% 0.57/0.73 tff(t_a_type, type, (
% 0.57/0.73 t_a: $i)).
% 0.57/0.73 tff(v_c_type, type, (
% 0.57/0.73 v_c: $i)).
% 0.57/0.73 tff(c_Zorn_Omaxchain__super__lemma__1_type, type, (
% 0.57/0.73 c_Zorn_Omaxchain__super__lemma__1: ( $i * $i * $i ) > $i)).
% 0.57/0.73 tff(v_y_type, type, (
% 0.57/0.73 v_y: $i)).
% 0.57/0.73 tff(c_lessequals_type, type, (
% 0.57/0.73 c_lessequals: ( $i * $i * $i ) > $o)).
% 0.57/0.73 tff(c_Zorn_Ochain_type, type, (
% 0.57/0.73 c_Zorn_Ochain: ( $i * $i ) > $i)).
% 0.57/0.73 tff(v_S_type, type, (
% 0.57/0.73 v_S: $i)).
% 0.57/0.73 tff(c_union_type, type, (
% 0.57/0.73 c_union: ( $i * $i * $i ) > $i)).
% 0.57/0.73 tff(c_insert_type, type, (
% 0.57/0.73 c_insert: ( $i * $i * $i ) > $i)).
% 0.57/0.73 tff(c_emptyset_type, type, (
% 0.57/0.73 c_emptyset: $i)).
% 0.57/0.73 tff(v_x_type, type, (
% 0.57/0.73 v_x: $i)).
% 0.57/0.73 tff(c_Main_OsubsetI__1_type, type, (
% 0.57/0.73 c_Main_OsubsetI__1: ( $i * $i * $i ) > $i)).
% 0.57/0.73 tff(c_Zorn_Ochain__extend__1_type, type, (
% 0.57/0.73 c_Zorn_Ochain__extend__1: ( $i * $i * $i ) > $i)).
% 0.57/0.73 tff(v_xa_type, type, (
% 0.57/0.73 v_xa: $i)).
% 0.57/0.73 tff(c_Zorn_Omaxchain_type, type, (
% 0.57/0.73 c_Zorn_Omaxchain: ( $i * $i ) > $i)).
% 0.57/0.73 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)).
% 0.57/0.73 tff(2,plain,
% 0.57/0.73 (c_in(v_x, v_S, tc_set(t_a)) <=> c_in(v_x, v_S, tc_set(t_a))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(3,axiom,(c_in(v_x, v_S, tc_set(t_a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_3')).
% 0.57/0.73 tff(4,plain,
% 0.57/0.73 (c_in(v_x, v_S, tc_set(t_a))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.57/0.73 tff(5,plain,
% 0.57/0.73 (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)))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(6,axiom,(c_in(v_c, c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_1')).
% 0.57/0.73 tff(7,plain,
% 0.57/0.73 (c_in(v_c, c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.57/0.73 tff(8,plain,
% 0.57/0.73 (^[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)))))),
% 0.57/0.73 inference(bind,[status(th)],[])).
% 0.57/0.73 tff(9,plain,
% 0.57/0.73 (![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))))),
% 0.57/0.73 inference(quant_intro,[status(thm)],[8])).
% 0.57/0.73 tff(10,plain,
% 0.57/0.73 (![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))))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(11,plain,
% 0.57/0.73 (^[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))))))),
% 0.57/0.73 inference(bind,[status(th)],[])).
% 0.57/0.73 tff(12,plain,
% 0.57/0.73 (![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))))),
% 0.57/0.73 inference(quant_intro,[status(thm)],[11])).
% 0.57/0.73 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/sandbox/benchmark/theBenchmark.p','cls_Zorn_Ochain__extend_1')).
% 0.57/0.73 tff(14,plain,
% 0.57/0.73 (![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))))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.57/0.73 tff(15,plain,
% 0.57/0.73 (![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))))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.57/0.73 tff(16,plain,(
% 0.57/0.73 ![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))))),
% 0.57/0.73 inference(skolemize,[status(sab)],[15])).
% 0.57/0.73 tff(17,plain,
% 0.57/0.73 (![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))))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.57/0.73 tff(18,plain,
% 0.57/0.73 (((~![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_in(v_c, 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_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_in(v_c, 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_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, tc_set(t_a))))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(19,plain,
% 0.57/0.73 ((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_in(v_c, 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_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, tc_set(t_a))))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(20,plain,
% 0.57/0.73 (((~![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_in(v_c, 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_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, tc_set(t_a)))))),
% 0.57/0.74 inference(monotonicity,[status(thm)],[19])).
% 0.57/0.74 tff(21,plain,
% 0.57/0.74 (((~![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_in(v_c, 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_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, tc_set(t_a))))),
% 0.57/0.74 inference(transitivity,[status(thm)],[20, 18])).
% 0.57/0.74 tff(22,plain,
% 0.57/0.74 ((~![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))))),
% 0.57/0.74 inference(quant_inst,[status(thm)],[])).
% 0.57/0.74 tff(23,plain,
% 0.57/0.74 ((~![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_in(v_c, 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_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, tc_set(t_a)))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.57/0.74 tff(24,plain,
% 0.57/0.74 (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_Ochain__extend__1(v_c, v_x, t_a), v_x, tc_set(t_a)))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[23, 17, 7, 4])).
% 0.57/0.74 tff(25,plain,
% 0.57/0.74 (~c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, tc_set(t_a))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[24, 1])).
% 0.57/0.74 tff(26,assumption,(~c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, tc_set(t_a))), introduced(assumption)).
% 0.57/0.74 tff(27,assumption,(~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)), introduced(assumption)).
% 0.57/0.74 tff(28,plain,
% 0.57/0.74 (^[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))))),
% 0.57/0.74 inference(bind,[status(th)],[])).
% 0.57/0.74 tff(29,plain,
% 0.57/0.74 (![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)))),
% 0.57/0.74 inference(quant_intro,[status(thm)],[28])).
% 0.57/0.74 tff(30,plain,
% 0.57/0.74 (![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)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(31,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/sandbox/benchmark/theBenchmark.p','cls_Set_OsubsetI_0')).
% 0.57/0.74 tff(32,plain,
% 0.57/0.74 (![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)))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.57/0.74 tff(33,plain,(
% 0.57/0.74 ![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)))),
% 0.57/0.74 inference(skolemize,[status(sab)],[32])).
% 0.57/0.74 tff(34,plain,
% 0.57/0.74 (![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)))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.57/0.74 tff(35,plain,
% 0.57/0.74 (((~![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))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(36,plain,
% 0.57/0.74 ((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))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(37,plain,
% 0.57/0.74 (((~![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)))),
% 0.57/0.74 inference(monotonicity,[status(thm)],[36])).
% 0.57/0.74 tff(38,plain,
% 0.57/0.74 (((~![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))),
% 0.57/0.74 inference(transitivity,[status(thm)],[37, 35])).
% 0.57/0.74 tff(39,plain,
% 0.57/0.74 ((~![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)))),
% 0.57/0.74 inference(quant_inst,[status(thm)],[])).
% 0.57/0.74 tff(40,plain,
% 0.57/0.74 ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), c_Zorn_Ochain__extend__1(v_c, v_x, t_a), t_a)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.57/0.74 tff(41,plain,
% 0.57/0.74 ($false),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[40, 34, 27, 26])).
% 0.57/0.74 tff(42,plain,(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))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.74 tff(43,plain,
% 0.57/0.74 (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)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[42, 25])).
% 0.57/0.74 tff(44,plain,
% 0.57/0.74 (^[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)))))),
% 0.57/0.74 inference(bind,[status(th)],[])).
% 0.57/0.74 tff(45,plain,
% 0.57/0.74 (![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))))),
% 0.57/0.74 inference(quant_intro,[status(thm)],[44])).
% 0.57/0.74 tff(46,plain,
% 0.57/0.74 (![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))))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(47,plain,
% 0.57/0.74 (^[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))))))),
% 0.57/0.74 inference(bind,[status(th)],[])).
% 0.57/0.74 tff(48,plain,
% 0.57/0.74 (![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))))),
% 0.57/0.74 inference(quant_intro,[status(thm)],[47])).
% 0.57/0.74 tff(49,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/sandbox/benchmark/theBenchmark.p','cls_Zorn_Ochain__extend_0')).
% 0.57/0.74 tff(50,plain,
% 0.57/0.74 (![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))))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.57/0.74 tff(51,plain,
% 0.57/0.74 (![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))))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.57/0.74 tff(52,plain,(
% 0.57/0.74 ![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))))),
% 0.57/0.74 inference(skolemize,[status(sab)],[51])).
% 0.57/0.74 tff(53,plain,
% 0.57/0.74 (![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))))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.57/0.74 tff(54,plain,
% 0.57/0.74 (((~![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(v_c, 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(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_c, 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(v_c, 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(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_c, tc_set(t_a)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(55,plain,
% 0.57/0.74 ((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(v_c, 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(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_c, tc_set(t_a)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(56,plain,
% 0.57/0.74 (((~![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(v_c, 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(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_c, tc_set(t_a))))),
% 0.57/0.74 inference(monotonicity,[status(thm)],[55])).
% 0.57/0.74 tff(57,plain,
% 0.57/0.74 (((~![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(v_c, 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(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_c, tc_set(t_a)))),
% 0.57/0.74 inference(transitivity,[status(thm)],[56, 54])).
% 0.57/0.74 tff(58,plain,
% 0.57/0.74 ((~![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))))),
% 0.57/0.74 inference(quant_inst,[status(thm)],[])).
% 0.57/0.74 tff(59,plain,
% 0.57/0.74 ((~![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(v_c, 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(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_c, tc_set(t_a))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.57/0.74 tff(60,plain,
% 0.57/0.74 (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))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[59, 53, 7, 4])).
% 0.57/0.74 tff(61,plain,
% 0.57/0.74 (c_in(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_c, tc_set(t_a))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[60, 1])).
% 0.57/0.74 tff(62,assumption,(c_in(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_c, tc_set(t_a))), introduced(assumption)).
% 0.57/0.74 tff(63,assumption,(~c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_y, tc_set(t_a))), introduced(assumption)).
% 0.57/0.74 tff(64,plain,
% 0.57/0.74 (^[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)))))),
% 0.57/0.74 inference(bind,[status(th)],[])).
% 0.57/0.74 tff(65,plain,
% 0.57/0.74 (![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))))),
% 0.57/0.74 inference(quant_intro,[status(thm)],[64])).
% 0.57/0.74 tff(66,plain,
% 0.57/0.74 (![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))))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(67,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/sandbox/benchmark/theBenchmark.p','cls_conjecture_7')).
% 0.57/0.74 tff(68,plain,
% 0.57/0.74 (![V_U: $i] : (c_lessequals(V_U, v_y, tc_set(t_a)) | (~c_in(V_U, v_c, tc_set(t_a))))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.57/0.74 tff(69,plain,(
% 0.57/0.74 ![V_U: $i] : (c_lessequals(V_U, v_y, tc_set(t_a)) | (~c_in(V_U, v_c, tc_set(t_a))))),
% 0.57/0.74 inference(skolemize,[status(sab)],[68])).
% 0.57/0.74 tff(70,plain,
% 0.57/0.74 (![V_U: $i] : (c_lessequals(V_U, v_y, tc_set(t_a)) | (~c_in(V_U, v_c, tc_set(t_a))))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.57/0.74 tff(71,plain,
% 0.57/0.74 (((~![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)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(72,plain,
% 0.57/0.75 ((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)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(73,plain,
% 0.57/0.75 (((~![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))))),
% 0.57/0.75 inference(monotonicity,[status(thm)],[72])).
% 0.57/0.75 tff(74,plain,
% 0.57/0.75 (((~![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)))),
% 0.57/0.75 inference(transitivity,[status(thm)],[73, 71])).
% 0.57/0.75 tff(75,plain,
% 0.57/0.75 ((~![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))))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(76,plain,
% 0.57/0.75 ((~![V_U: $i] : (c_lessequals(V_U, v_y, tc_set(t_a)) | (~c_in(V_U, v_c, tc_set(t_a))))) | (~c_in(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_c, tc_set(t_a))) | c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_y, tc_set(t_a))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.57/0.75 tff(77,plain,
% 0.57/0.75 ($false),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[76, 70, 63, 62])).
% 0.57/0.75 tff(78,plain,(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)))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.75 tff(79,plain,
% 0.57/0.75 (c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_y, tc_set(t_a))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[78, 61])).
% 0.57/0.75 tff(80,plain,
% 0.57/0.75 (^[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))))),
% 0.57/0.75 inference(bind,[status(th)],[])).
% 0.57/0.75 tff(81,plain,
% 0.57/0.75 (![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)))),
% 0.57/0.75 inference(quant_intro,[status(thm)],[80])).
% 0.57/0.75 tff(82,plain,
% 0.57/0.75 (![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)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(83,plain,
% 0.57/0.75 (^[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))))),
% 0.57/0.75 inference(bind,[status(th)],[])).
% 0.57/0.75 tff(84,plain,
% 0.57/0.75 (![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)))),
% 0.57/0.75 inference(quant_intro,[status(thm)],[83])).
% 0.57/0.75 tff(85,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/sandbox/benchmark/theBenchmark.p','cls_Set_OsubsetD_0')).
% 0.57/0.75 tff(86,plain,
% 0.57/0.75 (![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)))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.57/0.75 tff(87,plain,
% 0.57/0.75 (![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)))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.57/0.75 tff(88,plain,(
% 0.57/0.75 ![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)))),
% 0.57/0.75 inference(skolemize,[status(sab)],[87])).
% 0.57/0.75 tff(89,plain,
% 0.57/0.75 (![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)))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.57/0.75 tff(90,plain,
% 0.57/0.75 (((~![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))))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(91,plain,
% 0.57/0.75 ((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))))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(92,plain,
% 0.57/0.75 (((~![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)))))),
% 0.57/0.75 inference(monotonicity,[status(thm)],[91])).
% 0.57/0.75 tff(93,plain,
% 0.57/0.75 (((~![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))))),
% 0.57/0.75 inference(transitivity,[status(thm)],[92, 90])).
% 0.57/0.75 tff(94,plain,
% 0.57/0.75 ((~![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)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(95,plain,
% 0.57/0.75 ((~![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)))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.57/0.75 tff(96,plain,
% 0.57/0.75 ((~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)))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[95, 89])).
% 0.57/0.75 tff(97,plain,
% 0.57/0.75 (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)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[96, 79, 43])).
% 0.57/0.75 tff(98,assumption,(~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)), introduced(assumption)).
% 0.57/0.75 tff(99,assumption,(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)), introduced(assumption)).
% 0.57/0.75 tff(100,plain,
% 0.57/0.75 (c_lessequals(v_y, v_x, tc_set(t_a)) <=> c_lessequals(v_y, v_x, tc_set(t_a))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(101,axiom,(c_lessequals(v_y, v_x, tc_set(t_a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_4')).
% 0.57/0.75 tff(102,plain,
% 0.57/0.75 (c_lessequals(v_y, v_x, tc_set(t_a))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.57/0.75 tff(103,plain,
% 0.57/0.75 (((~![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_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)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(104,plain,
% 0.57/0.75 ((~![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)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(105,plain,
% 0.57/0.75 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))) | c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_x, t_a) | (~c_lessequals(v_y, v_x, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_y, t_a))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.57/0.75 tff(106,plain,
% 0.57/0.75 ($false),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[105, 89, 102, 99, 98])).
% 0.57/0.75 tff(107,plain,(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_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_y, t_a))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.75 tff(108,plain,
% 0.57/0.75 (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)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[107, 97])).
% 0.57/0.75 tff(109,plain,
% 0.57/0.75 (^[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))))),
% 0.57/0.75 inference(bind,[status(th)],[])).
% 0.57/0.75 tff(110,plain,
% 0.57/0.75 (![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)))),
% 0.57/0.75 inference(quant_intro,[status(thm)],[109])).
% 0.57/0.75 tff(111,plain,
% 0.57/0.75 (![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)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(112,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/sandbox/benchmark/theBenchmark.p','cls_Set_OsubsetI_1')).
% 0.57/0.75 tff(113,plain,
% 0.57/0.75 (![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)))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.57/0.75 tff(114,plain,(
% 0.57/0.75 ![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)))),
% 0.57/0.75 inference(skolemize,[status(sab)],[113])).
% 0.57/0.75 tff(115,plain,
% 0.57/0.75 (![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)))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.57/0.75 tff(116,plain,
% 0.57/0.75 (((~![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)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(117,plain,
% 0.57/0.75 ((~![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)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(118,plain,
% 0.57/0.75 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, t_a), v_x, t_a)) | c_lessequals(c_Zorn_Ochain__extend__1(v_c, v_x, t_a), v_x, tc_set(t_a))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.57/0.75 tff(119,plain,
% 0.57/0.75 ($false),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[118, 115, 25, 108])).
% 0.57/0.75 tff(120,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,[]))).
% 0.57/0.75 tff(121,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)).
% 0.57/0.75 tff(122,assumption,(c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_y, tc_set(t_a))), introduced(assumption)).
% 0.57/0.75 tff(123,plain,
% 0.57/0.75 ((~c_in(v_xa, v_y, t_a)) <=> (~c_in(v_xa, v_y, t_a))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(124,axiom,(~c_in(v_xa, v_y, t_a)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_6')).
% 0.57/0.75 tff(125,plain,
% 0.57/0.75 (~c_in(v_xa, v_y, t_a)),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.57/0.75 tff(126,plain,
% 0.57/0.75 (c_in(v_xa, v_x, t_a) <=> c_in(v_xa, v_x, t_a)),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(127,axiom,(c_in(v_xa, v_x, t_a)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_5')).
% 0.57/0.75 tff(128,plain,
% 0.57/0.75 (c_in(v_xa, v_x, t_a)),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.57/0.75 tff(129,plain,
% 0.57/0.75 (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)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(130,axiom,(c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.57/0.75 tff(131,plain,
% 0.57/0.75 (c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.57/0.75 tff(132,plain,
% 0.57/0.75 (^[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)))))),
% 0.57/0.75 inference(bind,[status(th)],[])).
% 0.57/0.75 tff(133,plain,
% 0.57/0.75 (![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))))),
% 0.57/0.75 inference(quant_intro,[status(thm)],[132])).
% 0.57/0.75 tff(134,plain,
% 0.57/0.75 (![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))))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(135,plain,
% 0.57/0.75 (^[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))))))),
% 0.57/0.75 inference(bind,[status(th)],[])).
% 0.57/0.75 tff(136,plain,
% 0.57/0.75 (![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))))),
% 0.57/0.75 inference(quant_intro,[status(thm)],[135])).
% 0.57/0.75 tff(137,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/sandbox/benchmark/theBenchmark.p','cls_Zorn_Omaxchain__super__lemma_1')).
% 0.57/0.75 tff(138,plain,
% 0.57/0.75 (![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))))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.57/0.75 tff(139,plain,
% 0.57/0.75 (![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))))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[138, 134])).
% 0.57/0.75 tff(140,plain,(
% 0.57/0.75 ![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))))),
% 0.57/0.75 inference(skolemize,[status(sab)],[139])).
% 0.57/0.75 tff(141,plain,
% 0.57/0.75 (![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))))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[140, 133])).
% 0.57/0.75 tff(142,plain,
% 0.57/0.75 (((~![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_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_y, tc_set(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)))))) <=> ((~![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_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_y, tc_set(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)))))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(143,plain,
% 0.57/0.76 ((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_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_y, tc_set(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)))))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(144,plain,
% 0.57/0.76 (((~![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_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_y, tc_set(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))))))),
% 0.57/0.76 inference(monotonicity,[status(thm)],[143])).
% 0.57/0.76 tff(145,plain,
% 0.57/0.76 (((~![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_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_y, tc_set(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)))))),
% 0.57/0.76 inference(transitivity,[status(thm)],[144, 142])).
% 0.57/0.76 tff(146,plain,
% 0.57/0.76 ((~![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))))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(147,plain,
% 0.57/0.76 ((~![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (c_in(V_z, V_y, T_a) | (~c_in(c_union(c_insert(V_x, c_emptyset, tc_set(T_a)), V_c, tc_set(T_a)), c_Zorn_Ochain(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_z, V_x, T_a)) | (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_y, tc_set(T_a))))) | c_in(v_xa, v_y, t_a) | (~c_in(v_xa, v_x, t_a)) | (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_y, tc_set(t_a))) | (~c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_in(c_union(c_insert(v_x, c_emptyset, tc_set(t_a)), v_c, tc_set(t_a)), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.57/0.76 tff(148,plain,
% 0.57/0.76 ($false),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[147, 141, 131, 128, 125, 122, 121])).
% 0.57/0.76 tff(149,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)))) | (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_y, tc_set(t_a)))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.76 tff(150,plain,
% 0.57/0.76 (~c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_y, tc_set(t_a))),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[149, 120])).
% 0.57/0.76 tff(151,plain,
% 0.57/0.76 (((~![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_Omaxchain__super__lemma__1(v_c, v_y, t_a), 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)))) <=> ((~![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_Omaxchain__super__lemma__1(v_c, v_y, t_a), 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)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(152,plain,
% 0.57/0.76 ((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)))) <=> ((~c_in(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), 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)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(153,plain,
% 0.57/0.76 (((~![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_in(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), 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))))),
% 0.57/0.76 inference(monotonicity,[status(thm)],[152])).
% 0.57/0.76 tff(154,plain,
% 0.57/0.76 (((~![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_in(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), 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)))),
% 0.57/0.76 inference(transitivity,[status(thm)],[153, 151])).
% 0.57/0.76 tff(155,plain,
% 0.57/0.76 ((~![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))))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(156,plain,
% 0.57/0.76 ((~![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_Omaxchain__super__lemma__1(v_c, v_y, t_a), 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))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.57/0.76 tff(157,plain,
% 0.57/0.76 (~c_in(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_c, tc_set(t_a))),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[156, 70, 150])).
% 0.57/0.76 tff(158,plain,
% 0.57/0.76 (^[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))))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(159,plain,
% 0.57/0.76 (![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)))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[158])).
% 0.57/0.76 tff(160,plain,
% 0.57/0.76 (![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)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(161,plain,
% 0.57/0.76 (^[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)))))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(162,plain,
% 0.57/0.76 (![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)))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[161])).
% 0.57/0.76 tff(163,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/sandbox/benchmark/theBenchmark.p','cls_Zorn_Omaxchain__super__lemma_0')).
% 0.57/0.76 tff(164,plain,
% 0.57/0.76 (![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)))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.57/0.76 tff(165,plain,
% 0.57/0.76 (![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)))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[164, 160])).
% 0.57/0.76 tff(166,plain,(
% 0.57/0.76 ![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)))),
% 0.57/0.76 inference(skolemize,[status(sab)],[165])).
% 0.57/0.76 tff(167,plain,
% 0.57/0.76 (![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)))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[166, 159])).
% 0.57/0.76 tff(168,plain,
% 0.57/0.76 (((~![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(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_c, tc_set(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)))))) <=> ((~![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(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_c, tc_set(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)))))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(169,plain,
% 0.57/0.76 ((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(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_c, tc_set(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)))))),
% 0.61/0.76 inference(rewrite,[status(thm)],[])).
% 0.61/0.76 tff(170,plain,
% 0.61/0.76 (((~![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(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_c, tc_set(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))))))),
% 0.61/0.76 inference(monotonicity,[status(thm)],[169])).
% 0.61/0.76 tff(171,plain,
% 0.61/0.76 (((~![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(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_c, tc_set(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)))))),
% 0.61/0.76 inference(transitivity,[status(thm)],[170, 168])).
% 0.61/0.76 tff(172,plain,
% 0.61/0.76 ((~![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)))),
% 0.61/0.76 inference(quant_inst,[status(thm)],[])).
% 0.61/0.76 tff(173,plain,
% 0.61/0.76 ((~![V_c: $i, V_x: $i, V_z: $i, V_S: $i, T_a: $i, V_y: $i] : (c_in(c_Zorn_Omaxchain__super__lemma__1(V_c, V_y, T_a), V_c, tc_set(T_a)) | c_in(V_z, V_y, T_a) | (~c_in(c_union(c_insert(V_x, c_emptyset, tc_set(T_a)), V_c, tc_set(T_a)), c_Zorn_Ochain(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_z, V_x, T_a)))) | c_in(v_xa, v_y, t_a) | (~c_in(v_xa, v_x, t_a)) | c_in(c_Zorn_Omaxchain__super__lemma__1(v_c, v_y, t_a), v_c, tc_set(t_a)) | (~c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_in(c_union(c_insert(v_x, c_emptyset, tc_set(t_a)), v_c, tc_set(t_a)), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.61/0.77 tff(174,plain,
% 0.61/0.77 ($false),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[173, 167, 131, 128, 125, 120, 157])).
% 0.61/0.77 % SZS output end Proof
% 0.61/0.77 % E exiting
%------------------------------------------------------------------------------