%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET865-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 7.36s 7.54s
% Output : Proof 7.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET865-2 : TPTP v9.0.0. Released v3.2.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 05:48:35 EDT 2025
% 0.12/0.34 % CPUTime :
% 7.36/7.54 % SZS status Unsatisfiable
% 7.36/7.54 % SZS output start Proof
% 7.36/7.54 tff(c_lessequals_type, type, (
% 7.36/7.54 c_lessequals: ( $i * $i * $i ) > $o)).
% 7.36/7.54 tff(tc_set_type, type, (
% 7.36/7.54 tc_set: $i > $i)).
% 7.36/7.54 tff(t_a_type, type, (
% 7.36/7.54 t_a: $i)).
% 7.36/7.54 tff(c_Zorn_Ochain_type, type, (
% 7.36/7.54 c_Zorn_Ochain: ( $i * $i ) > $i)).
% 7.36/7.54 tff(v_S_type, type, (
% 7.36/7.54 v_S: $i)).
% 7.36/7.54 tff(c_Zorn_Omaxchain_type, type, (
% 7.36/7.54 c_Zorn_Omaxchain: ( $i * $i ) > $i)).
% 7.36/7.54 tff(c_in_type, type, (
% 7.36/7.54 c_in: ( $i * $i * $i ) > $o)).
% 7.36/7.54 tff(v_x_type, type, (
% 7.36/7.54 v_x: $i > $i)).
% 7.36/7.54 tff(c_Union_type, type, (
% 7.36/7.54 c_Union: ( $i * $i ) > $i)).
% 7.36/7.54 tff(c_Zorn_OHausdorff__1_type, type, (
% 7.36/7.54 c_Zorn_OHausdorff__1: ( $i * $i ) > $i)).
% 7.36/7.54 tff(1,assumption,(c_lessequals(c_Zorn_Omaxchain(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(tc_set(t_a))))), introduced(assumption)).
% 7.36/7.54 tff(2,plain,
% 7.36/7.54 (^[V_S: $i, T_a: $i] : refl(c_in(c_Zorn_OHausdorff__1(V_S, T_a), c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a))) <=> c_in(c_Zorn_OHausdorff__1(V_S, T_a), c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a))))),
% 7.36/7.54 inference(bind,[status(th)],[])).
% 7.36/7.54 tff(3,plain,
% 7.36/7.54 (![V_S: $i, T_a: $i] : c_in(c_Zorn_OHausdorff__1(V_S, T_a), c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a))) <=> ![V_S: $i, T_a: $i] : c_in(c_Zorn_OHausdorff__1(V_S, T_a), c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))),
% 7.36/7.54 inference(quant_intro,[status(thm)],[2])).
% 7.36/7.54 tff(4,plain,
% 7.36/7.54 (![V_S: $i, T_a: $i] : c_in(c_Zorn_OHausdorff__1(V_S, T_a), c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a))) <=> ![V_S: $i, T_a: $i] : c_in(c_Zorn_OHausdorff__1(V_S, T_a), c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))),
% 7.36/7.54 inference(rewrite,[status(thm)],[])).
% 7.36/7.54 tff(5,axiom,(![V_S: $i, T_a: $i] : c_in(c_Zorn_OHausdorff__1(V_S, T_a), c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Zorn_OHausdorff_0')).
% 7.36/7.54 tff(6,plain,
% 7.36/7.54 (![V_S: $i, T_a: $i] : c_in(c_Zorn_OHausdorff__1(V_S, T_a), c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))),
% 7.36/7.54 inference(modus_ponens,[status(thm)],[5, 4])).
% 7.36/7.54 tff(7,plain,(
% 7.36/7.54 ![V_S: $i, T_a: $i] : c_in(c_Zorn_OHausdorff__1(V_S, T_a), c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))),
% 7.36/7.54 inference(skolemize,[status(sab)],[6])).
% 7.36/7.54 tff(8,plain,
% 7.36/7.54 (![V_S: $i, T_a: $i] : c_in(c_Zorn_OHausdorff__1(V_S, T_a), c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))),
% 7.36/7.54 inference(modus_ponens,[status(thm)],[7, 3])).
% 7.36/7.54 tff(9,plain,
% 7.36/7.54 ((~![V_S: $i, T_a: $i] : c_in(c_Zorn_OHausdorff__1(V_S, T_a), c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))) | c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))),
% 7.36/7.54 inference(quant_inst,[status(thm)],[])).
% 7.36/7.54 tff(10,plain,
% 7.36/7.54 (c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))),
% 7.36/7.54 inference(unit_resolution,[status(thm)],[9, 8])).
% 7.36/7.54 tff(11,plain,
% 7.36/7.54 (^[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))))),
% 7.36/7.54 inference(bind,[status(th)],[])).
% 7.36/7.54 tff(12,plain,
% 7.36/7.54 (![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)))),
% 7.36/7.54 inference(quant_intro,[status(thm)],[11])).
% 7.36/7.54 tff(13,plain,
% 7.36/7.54 (![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)))),
% 7.36/7.54 inference(rewrite,[status(thm)],[])).
% 7.36/7.54 tff(14,plain,
% 7.36/7.54 (^[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))))),
% 7.36/7.54 inference(bind,[status(th)],[])).
% 7.36/7.54 tff(15,plain,
% 7.36/7.54 (![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)))),
% 7.36/7.54 inference(quant_intro,[status(thm)],[14])).
% 7.36/7.54 tff(16,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')).
% 7.36/7.54 tff(17,plain,
% 7.36/7.54 (![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)))),
% 7.36/7.54 inference(modus_ponens,[status(thm)],[16, 15])).
% 7.36/7.54 tff(18,plain,
% 7.36/7.54 (![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)))),
% 7.36/7.54 inference(modus_ponens,[status(thm)],[17, 13])).
% 7.36/7.54 tff(19,plain,(
% 7.36/7.54 ![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)))),
% 7.36/7.54 inference(skolemize,[status(sab)],[18])).
% 7.36/7.54 tff(20,plain,
% 7.36/7.54 (![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)))),
% 7.36/7.54 inference(modus_ponens,[status(thm)],[19, 12])).
% 7.36/7.54 tff(21,plain,
% 7.36/7.54 (((~![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_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))) | (~c_lessequals(c_Zorn_Omaxchain(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(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_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))) | (~c_lessequals(c_Zorn_Omaxchain(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(tc_set(t_a))))))),
% 7.36/7.54 inference(rewrite,[status(thm)],[])).
% 7.36/7.54 tff(22,plain,
% 7.36/7.54 ((c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))) | (~c_lessequals(c_Zorn_Omaxchain(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(tc_set(t_a))))) | (~c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))))) <=> ((~c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))) | (~c_lessequals(c_Zorn_Omaxchain(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(tc_set(t_a))))))),
% 7.36/7.54 inference(rewrite,[status(thm)],[])).
% 7.36/7.54 tff(23,plain,
% 7.36/7.54 (((~![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_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))) | (~c_lessequals(c_Zorn_Omaxchain(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(tc_set(t_a))))) | (~c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(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_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))) | (~c_lessequals(c_Zorn_Omaxchain(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(tc_set(t_a)))))))),
% 7.36/7.54 inference(monotonicity,[status(thm)],[22])).
% 7.36/7.54 tff(24,plain,
% 7.36/7.54 (((~![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_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))) | (~c_lessequals(c_Zorn_Omaxchain(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(tc_set(t_a))))) | (~c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(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_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))) | (~c_lessequals(c_Zorn_Omaxchain(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(tc_set(t_a))))))),
% 7.36/7.54 inference(transitivity,[status(thm)],[23, 21])).
% 7.36/7.54 tff(25,plain,
% 7.36/7.54 ((~![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_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))) | (~c_lessequals(c_Zorn_Omaxchain(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(tc_set(t_a))))) | (~c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))))),
% 7.36/7.54 inference(quant_inst,[status(thm)],[])).
% 7.36/7.54 tff(26,plain,
% 7.36/7.54 ((~![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_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))) | (~c_lessequals(c_Zorn_Omaxchain(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(tc_set(t_a)))))),
% 7.36/7.54 inference(modus_ponens,[status(thm)],[25, 24])).
% 7.36/7.54 tff(27,plain,
% 7.36/7.54 ((~c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))) | (~c_lessequals(c_Zorn_Omaxchain(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(tc_set(t_a)))))),
% 7.36/7.54 inference(unit_resolution,[status(thm)],[26, 20])).
% 7.36/7.54 tff(28,plain,
% 7.36/7.54 (c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))),
% 7.36/7.54 inference(unit_resolution,[status(thm)],[27, 10, 1])).
% 7.36/7.54 tff(29,plain,
% 7.36/7.54 (^[V_U: $i] : refl(((~c_in(V_U, c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Union(V_U, t_a), v_S, tc_set(t_a))) <=> ((~c_in(V_U, c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Union(V_U, t_a), v_S, tc_set(t_a))))),
% 7.36/7.54 inference(bind,[status(th)],[])).
% 7.36/7.54 tff(30,plain,
% 7.36/7.54 (![V_U: $i] : ((~c_in(V_U, c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Union(V_U, t_a), v_S, tc_set(t_a))) <=> ![V_U: $i] : ((~c_in(V_U, c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Union(V_U, t_a), v_S, tc_set(t_a)))),
% 7.36/7.54 inference(quant_intro,[status(thm)],[29])).
% 7.36/7.54 tff(31,plain,
% 7.36/7.54 (![V_U: $i] : ((~c_in(V_U, c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Union(V_U, t_a), v_S, tc_set(t_a))) <=> ![V_U: $i] : ((~c_in(V_U, c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Union(V_U, t_a), v_S, tc_set(t_a)))),
% 7.36/7.54 inference(rewrite,[status(thm)],[])).
% 7.36/7.54 tff(32,plain,
% 7.36/7.54 (^[V_U: $i] : rewrite((c_in(c_Union(V_U, t_a), v_S, tc_set(t_a)) | (~c_in(V_U, c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))))) <=> ((~c_in(V_U, c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Union(V_U, t_a), v_S, tc_set(t_a))))),
% 7.36/7.54 inference(bind,[status(th)],[])).
% 7.36/7.54 tff(33,plain,
% 7.36/7.54 (![V_U: $i] : (c_in(c_Union(V_U, t_a), v_S, tc_set(t_a)) | (~c_in(V_U, c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))))) <=> ![V_U: $i] : ((~c_in(V_U, c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Union(V_U, t_a), v_S, tc_set(t_a)))),
% 7.36/7.54 inference(quant_intro,[status(thm)],[32])).
% 7.36/7.54 tff(34,axiom,(![V_U: $i] : (c_in(c_Union(V_U, t_a), v_S, tc_set(t_a)) | (~c_in(V_U, c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_0')).
% 7.36/7.54 tff(35,plain,
% 7.36/7.54 (![V_U: $i] : ((~c_in(V_U, c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Union(V_U, t_a), v_S, tc_set(t_a)))),
% 7.36/7.54 inference(modus_ponens,[status(thm)],[34, 33])).
% 7.36/7.54 tff(36,plain,
% 7.36/7.54 (![V_U: $i] : ((~c_in(V_U, c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Union(V_U, t_a), v_S, tc_set(t_a)))),
% 7.36/7.54 inference(modus_ponens,[status(thm)],[35, 31])).
% 7.36/7.54 tff(37,plain,(
% 7.36/7.54 ![V_U: $i] : ((~c_in(V_U, c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Union(V_U, t_a), v_S, tc_set(t_a)))),
% 7.36/7.54 inference(skolemize,[status(sab)],[36])).
% 7.36/7.54 tff(38,plain,
% 7.36/7.54 (![V_U: $i] : ((~c_in(V_U, c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Union(V_U, t_a), v_S, tc_set(t_a)))),
% 7.36/7.54 inference(modus_ponens,[status(thm)],[37, 30])).
% 7.36/7.54 tff(39,plain,
% 7.36/7.54 (((~![V_U: $i] : ((~c_in(V_U, c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Union(V_U, t_a), v_S, tc_set(t_a)))) | ((~c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a)))) <=> ((~![V_U: $i] : ((~c_in(V_U, c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Union(V_U, t_a), v_S, tc_set(t_a)))) | (~c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a)))),
% 7.36/7.54 inference(rewrite,[status(thm)],[])).
% 7.36/7.54 tff(40,plain,
% 7.36/7.54 ((~![V_U: $i] : ((~c_in(V_U, c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Union(V_U, t_a), v_S, tc_set(t_a)))) | ((~c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a)))),
% 7.36/7.54 inference(quant_inst,[status(thm)],[])).
% 7.36/7.54 tff(41,plain,
% 7.36/7.54 ((~![V_U: $i] : ((~c_in(V_U, c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Union(V_U, t_a), v_S, tc_set(t_a)))) | (~c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a))),
% 7.36/7.54 inference(modus_ponens,[status(thm)],[40, 39])).
% 7.36/7.54 tff(42,plain,
% 7.36/7.54 (c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a))),
% 7.36/7.54 inference(unit_resolution,[status(thm)],[41, 38, 28])).
% 7.36/7.54 tff(43,plain,
% 7.36/7.54 (^[V_U: $i] : refl(((~c_in(V_U, v_S, tc_set(t_a))) | c_in(v_x(V_U), v_S, tc_set(t_a))) <=> ((~c_in(V_U, v_S, tc_set(t_a))) | c_in(v_x(V_U), v_S, tc_set(t_a))))),
% 7.36/7.54 inference(bind,[status(th)],[])).
% 7.36/7.54 tff(44,plain,
% 7.36/7.54 (![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | c_in(v_x(V_U), v_S, tc_set(t_a))) <=> ![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | c_in(v_x(V_U), v_S, tc_set(t_a)))),
% 7.36/7.54 inference(quant_intro,[status(thm)],[43])).
% 7.36/7.54 tff(45,plain,
% 7.36/7.54 (![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | c_in(v_x(V_U), v_S, tc_set(t_a))) <=> ![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | c_in(v_x(V_U), v_S, tc_set(t_a)))),
% 7.36/7.54 inference(rewrite,[status(thm)],[])).
% 7.36/7.54 tff(46,plain,
% 7.36/7.54 (^[V_U: $i] : rewrite((c_in(v_x(V_U), v_S, tc_set(t_a)) | (~c_in(V_U, v_S, tc_set(t_a)))) <=> ((~c_in(V_U, v_S, tc_set(t_a))) | c_in(v_x(V_U), v_S, tc_set(t_a))))),
% 7.36/7.54 inference(bind,[status(th)],[])).
% 7.36/7.54 tff(47,plain,
% 7.36/7.54 (![V_U: $i] : (c_in(v_x(V_U), v_S, tc_set(t_a)) | (~c_in(V_U, v_S, tc_set(t_a)))) <=> ![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | c_in(v_x(V_U), v_S, tc_set(t_a)))),
% 7.36/7.54 inference(quant_intro,[status(thm)],[46])).
% 7.36/7.54 tff(48,axiom,(![V_U: $i] : (c_in(v_x(V_U), v_S, tc_set(t_a)) | (~c_in(V_U, v_S, tc_set(t_a))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_1')).
% 7.36/7.54 tff(49,plain,
% 7.36/7.54 (![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | c_in(v_x(V_U), v_S, tc_set(t_a)))),
% 7.36/7.54 inference(modus_ponens,[status(thm)],[48, 47])).
% 7.36/7.54 tff(50,plain,
% 7.36/7.54 (![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | c_in(v_x(V_U), v_S, tc_set(t_a)))),
% 7.36/7.54 inference(modus_ponens,[status(thm)],[49, 45])).
% 7.36/7.54 tff(51,plain,(
% 7.36/7.54 ![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | c_in(v_x(V_U), v_S, tc_set(t_a)))),
% 7.36/7.54 inference(skolemize,[status(sab)],[50])).
% 7.36/7.54 tff(52,plain,
% 7.36/7.54 (![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | c_in(v_x(V_U), v_S, tc_set(t_a)))),
% 7.36/7.54 inference(modus_ponens,[status(thm)],[51, 44])).
% 7.36/7.54 tff(53,plain,
% 7.36/7.54 (((~![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | c_in(v_x(V_U), v_S, tc_set(t_a)))) | ((~c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a))) | c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, tc_set(t_a)))) <=> ((~![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | c_in(v_x(V_U), v_S, tc_set(t_a)))) | (~c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a))) | c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, tc_set(t_a)))),
% 7.36/7.54 inference(rewrite,[status(thm)],[])).
% 7.36/7.54 tff(54,plain,
% 7.36/7.54 ((~![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | c_in(v_x(V_U), v_S, tc_set(t_a)))) | ((~c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a))) | c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, tc_set(t_a)))),
% 7.36/7.54 inference(quant_inst,[status(thm)],[])).
% 7.36/7.54 tff(55,plain,
% 7.36/7.54 ((~![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | c_in(v_x(V_U), v_S, tc_set(t_a)))) | (~c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a))) | c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, tc_set(t_a))),
% 7.36/7.54 inference(modus_ponens,[status(thm)],[54, 53])).
% 7.36/7.54 tff(56,plain,
% 7.36/7.54 (c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, tc_set(t_a))),
% 7.36/7.54 inference(unit_resolution,[status(thm)],[55, 52, 42])).
% 7.36/7.54 tff(57,plain,
% 7.36/7.54 (^[V_U: $i] : refl(((~(V_U = v_x(V_U))) | (~c_in(V_U, v_S, tc_set(t_a)))) <=> ((~(V_U = v_x(V_U))) | (~c_in(V_U, v_S, tc_set(t_a)))))),
% 7.36/7.54 inference(bind,[status(th)],[])).
% 7.36/7.54 tff(58,plain,
% 7.36/7.54 (![V_U: $i] : ((~(V_U = v_x(V_U))) | (~c_in(V_U, v_S, tc_set(t_a)))) <=> ![V_U: $i] : ((~(V_U = v_x(V_U))) | (~c_in(V_U, v_S, tc_set(t_a))))),
% 7.36/7.54 inference(quant_intro,[status(thm)],[57])).
% 7.36/7.54 tff(59,plain,
% 7.36/7.54 (![V_U: $i] : ((~(V_U = v_x(V_U))) | (~c_in(V_U, v_S, tc_set(t_a)))) <=> ![V_U: $i] : ((~(V_U = v_x(V_U))) | (~c_in(V_U, v_S, tc_set(t_a))))),
% 7.36/7.54 inference(rewrite,[status(thm)],[])).
% 7.36/7.54 tff(60,axiom,(![V_U: $i] : ((~(V_U = v_x(V_U))) | (~c_in(V_U, v_S, tc_set(t_a))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_3')).
% 7.36/7.54 tff(61,plain,
% 7.36/7.54 (![V_U: $i] : ((~(V_U = v_x(V_U))) | (~c_in(V_U, v_S, tc_set(t_a))))),
% 7.36/7.54 inference(modus_ponens,[status(thm)],[60, 59])).
% 7.36/7.54 tff(62,plain,(
% 7.36/7.54 ![V_U: $i] : ((~(V_U = v_x(V_U))) | (~c_in(V_U, v_S, tc_set(t_a))))),
% 7.36/7.54 inference(skolemize,[status(sab)],[61])).
% 7.36/7.54 tff(63,plain,
% 7.36/7.54 (![V_U: $i] : ((~(V_U = v_x(V_U))) | (~c_in(V_U, v_S, tc_set(t_a))))),
% 7.36/7.54 inference(modus_ponens,[status(thm)],[62, 58])).
% 7.36/7.54 tff(64,plain,
% 7.36/7.54 (((~![V_U: $i] : ((~(V_U = v_x(V_U))) | (~c_in(V_U, v_S, tc_set(t_a))))) | ((~c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a))) | (~(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a) = v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)))))) <=> ((~![V_U: $i] : ((~(V_U = v_x(V_U))) | (~c_in(V_U, v_S, tc_set(t_a))))) | (~c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a))) | (~(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a) = v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)))))),
% 7.36/7.54 inference(rewrite,[status(thm)],[])).
% 7.36/7.54 tff(65,plain,
% 7.36/7.54 (((~(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a) = v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)))) | (~c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a)))) <=> ((~c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a))) | (~(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a) = v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)))))),
% 7.36/7.54 inference(rewrite,[status(thm)],[])).
% 7.36/7.54 tff(66,plain,
% 7.36/7.54 (((~![V_U: $i] : ((~(V_U = v_x(V_U))) | (~c_in(V_U, v_S, tc_set(t_a))))) | ((~(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a) = v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)))) | (~c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a))))) <=> ((~![V_U: $i] : ((~(V_U = v_x(V_U))) | (~c_in(V_U, v_S, tc_set(t_a))))) | ((~c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a))) | (~(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a) = v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))))))),
% 7.36/7.54 inference(monotonicity,[status(thm)],[65])).
% 7.36/7.54 tff(67,plain,
% 7.36/7.54 (((~![V_U: $i] : ((~(V_U = v_x(V_U))) | (~c_in(V_U, v_S, tc_set(t_a))))) | ((~(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a) = v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)))) | (~c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a))))) <=> ((~![V_U: $i] : ((~(V_U = v_x(V_U))) | (~c_in(V_U, v_S, tc_set(t_a))))) | (~c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a))) | (~(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a) = v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)))))),
% 7.36/7.54 inference(transitivity,[status(thm)],[66, 64])).
% 7.36/7.54 tff(68,plain,
% 7.36/7.54 ((~![V_U: $i] : ((~(V_U = v_x(V_U))) | (~c_in(V_U, v_S, tc_set(t_a))))) | ((~(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a) = v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)))) | (~c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a))))),
% 7.36/7.54 inference(quant_inst,[status(thm)],[])).
% 7.36/7.54 tff(69,plain,
% 7.36/7.54 ((~![V_U: $i] : ((~(V_U = v_x(V_U))) | (~c_in(V_U, v_S, tc_set(t_a))))) | (~c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a))) | (~(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a) = v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))))),
% 7.36/7.54 inference(modus_ponens,[status(thm)],[68, 67])).
% 7.36/7.54 tff(70,plain,
% 7.36/7.54 (~(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a) = v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)))),
% 7.36/7.54 inference(unit_resolution,[status(thm)],[69, 63, 42])).
% 7.36/7.54 tff(71,plain,
% 7.36/7.54 (^[V_U: $i] : refl(((~c_in(V_U, v_S, tc_set(t_a))) | c_lessequals(V_U, v_x(V_U), tc_set(t_a))) <=> ((~c_in(V_U, v_S, tc_set(t_a))) | c_lessequals(V_U, v_x(V_U), tc_set(t_a))))),
% 7.36/7.54 inference(bind,[status(th)],[])).
% 7.36/7.54 tff(72,plain,
% 7.36/7.54 (![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | c_lessequals(V_U, v_x(V_U), tc_set(t_a))) <=> ![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | c_lessequals(V_U, v_x(V_U), tc_set(t_a)))),
% 7.36/7.54 inference(quant_intro,[status(thm)],[71])).
% 7.36/7.54 tff(73,plain,
% 7.36/7.54 (![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | c_lessequals(V_U, v_x(V_U), tc_set(t_a))) <=> ![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | c_lessequals(V_U, v_x(V_U), tc_set(t_a)))),
% 7.36/7.54 inference(rewrite,[status(thm)],[])).
% 7.36/7.54 tff(74,plain,
% 7.36/7.54 (^[V_U: $i] : rewrite((c_lessequals(V_U, v_x(V_U), tc_set(t_a)) | (~c_in(V_U, v_S, tc_set(t_a)))) <=> ((~c_in(V_U, v_S, tc_set(t_a))) | c_lessequals(V_U, v_x(V_U), tc_set(t_a))))),
% 7.36/7.54 inference(bind,[status(th)],[])).
% 7.36/7.54 tff(75,plain,
% 7.36/7.54 (![V_U: $i] : (c_lessequals(V_U, v_x(V_U), tc_set(t_a)) | (~c_in(V_U, v_S, tc_set(t_a)))) <=> ![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | c_lessequals(V_U, v_x(V_U), tc_set(t_a)))),
% 7.36/7.54 inference(quant_intro,[status(thm)],[74])).
% 7.36/7.54 tff(76,axiom,(![V_U: $i] : (c_lessequals(V_U, v_x(V_U), tc_set(t_a)) | (~c_in(V_U, v_S, tc_set(t_a))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_2')).
% 7.36/7.54 tff(77,plain,
% 7.36/7.54 (![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | c_lessequals(V_U, v_x(V_U), tc_set(t_a)))),
% 7.36/7.54 inference(modus_ponens,[status(thm)],[76, 75])).
% 7.36/7.54 tff(78,plain,
% 7.36/7.54 (![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | c_lessequals(V_U, v_x(V_U), tc_set(t_a)))),
% 7.36/7.54 inference(modus_ponens,[status(thm)],[77, 73])).
% 7.36/7.54 tff(79,plain,(
% 7.36/7.54 ![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | c_lessequals(V_U, v_x(V_U), tc_set(t_a)))),
% 7.36/7.54 inference(skolemize,[status(sab)],[78])).
% 7.36/7.54 tff(80,plain,
% 7.36/7.54 (![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | c_lessequals(V_U, v_x(V_U), tc_set(t_a)))),
% 7.36/7.54 inference(modus_ponens,[status(thm)],[79, 72])).
% 7.36/7.54 tff(81,plain,
% 7.36/7.54 (((~![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | c_lessequals(V_U, v_x(V_U), tc_set(t_a)))) | ((~c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a))) | c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a)))) <=> ((~![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | c_lessequals(V_U, v_x(V_U), tc_set(t_a)))) | (~c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a))) | c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a)))),
% 7.36/7.54 inference(rewrite,[status(thm)],[])).
% 7.36/7.54 tff(82,plain,
% 7.36/7.54 ((~![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | c_lessequals(V_U, v_x(V_U), tc_set(t_a)))) | ((~c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a))) | c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a)))),
% 7.36/7.54 inference(quant_inst,[status(thm)],[])).
% 7.36/7.54 tff(83,plain,
% 7.36/7.54 ((~![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | c_lessequals(V_U, v_x(V_U), tc_set(t_a)))) | (~c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a))) | c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a))),
% 7.36/7.54 inference(modus_ponens,[status(thm)],[82, 81])).
% 7.36/7.54 tff(84,plain,
% 7.36/7.54 (c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a))),
% 7.36/7.54 inference(unit_resolution,[status(thm)],[83, 80, 42])).
% 7.36/7.54 tff(85,plain,
% 7.36/7.54 (^[V_c: $i, V_u: $i, V_S: $i, T_a: $i] : refl(((c_Union(V_c, T_a) = V_u) | (~c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a))) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_u, V_S, tc_set(T_a)))) <=> ((c_Union(V_c, T_a) = V_u) | (~c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a))) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_u, V_S, tc_set(T_a)))))),
% 7.36/7.54 inference(bind,[status(th)],[])).
% 7.36/7.54 tff(86,plain,
% 7.36/7.54 (![V_c: $i, V_u: $i, V_S: $i, T_a: $i] : ((c_Union(V_c, T_a) = V_u) | (~c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a))) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_u, V_S, tc_set(T_a)))) <=> ![V_c: $i, V_u: $i, V_S: $i, T_a: $i] : ((c_Union(V_c, T_a) = V_u) | (~c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a))) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_u, V_S, tc_set(T_a))))),
% 7.36/7.54 inference(quant_intro,[status(thm)],[85])).
% 7.36/7.54 tff(87,plain,
% 7.36/7.54 (![V_c: $i, V_u: $i, V_S: $i, T_a: $i] : ((c_Union(V_c, T_a) = V_u) | (~c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a))) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_u, V_S, tc_set(T_a)))) <=> ![V_c: $i, V_u: $i, V_S: $i, T_a: $i] : ((c_Union(V_c, T_a) = V_u) | (~c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a))) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_u, V_S, tc_set(T_a))))),
% 7.36/7.54 inference(rewrite,[status(thm)],[])).
% 7.36/7.54 tff(88,plain,
% 7.36/7.54 (^[V_c: $i, V_u: $i, V_S: $i, T_a: $i] : trans(monotonicity(rewrite((((~c_in(V_u, V_S, tc_set(T_a))) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a))))) | (~c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a)))) <=> ((~c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a))) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_u, V_S, tc_set(T_a))))), (((((~c_in(V_u, V_S, tc_set(T_a))) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a))))) | (~c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a)))) | (c_Union(V_c, T_a) = V_u)) <=> (((~c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a))) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_u, V_S, tc_set(T_a)))) | (c_Union(V_c, T_a) = V_u)))), rewrite((((~c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a))) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_u, V_S, tc_set(T_a)))) | (c_Union(V_c, T_a) = V_u)) <=> ((c_Union(V_c, T_a) = V_u) | (~c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a))) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_u, V_S, tc_set(T_a))))), (((((~c_in(V_u, V_S, tc_set(T_a))) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a))))) | (~c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a)))) | (c_Union(V_c, T_a) = V_u)) <=> ((c_Union(V_c, T_a) = V_u) | (~c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a))) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_u, V_S, tc_set(T_a))))))),
% 7.36/7.54 inference(bind,[status(th)],[])).
% 7.36/7.54 tff(89,plain,
% 7.36/7.54 (![V_c: $i, V_u: $i, V_S: $i, T_a: $i] : ((((~c_in(V_u, V_S, tc_set(T_a))) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a))))) | (~c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a)))) | (c_Union(V_c, T_a) = V_u)) <=> ![V_c: $i, V_u: $i, V_S: $i, T_a: $i] : ((c_Union(V_c, T_a) = V_u) | (~c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a))) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_u, V_S, tc_set(T_a))))),
% 7.36/7.54 inference(quant_intro,[status(thm)],[88])).
% 7.36/7.55 tff(90,axiom,(![V_c: $i, V_u: $i, V_S: $i, T_a: $i] : ((((~c_in(V_u, V_S, tc_set(T_a))) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a))))) | (~c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a)))) | (c_Union(V_c, T_a) = V_u))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Zorn_Omaxchain__Zorn_0')).
% 7.36/7.55 tff(91,plain,
% 7.36/7.55 (![V_c: $i, V_u: $i, V_S: $i, T_a: $i] : ((c_Union(V_c, T_a) = V_u) | (~c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a))) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_u, V_S, tc_set(T_a))))),
% 7.36/7.55 inference(modus_ponens,[status(thm)],[90, 89])).
% 7.36/7.55 tff(92,plain,
% 7.36/7.55 (![V_c: $i, V_u: $i, V_S: $i, T_a: $i] : ((c_Union(V_c, T_a) = V_u) | (~c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a))) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_u, V_S, tc_set(T_a))))),
% 7.36/7.55 inference(modus_ponens,[status(thm)],[91, 87])).
% 7.36/7.55 tff(93,plain,(
% 7.36/7.55 ![V_c: $i, V_u: $i, V_S: $i, T_a: $i] : ((c_Union(V_c, T_a) = V_u) | (~c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a))) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_u, V_S, tc_set(T_a))))),
% 7.36/7.55 inference(skolemize,[status(sab)],[92])).
% 7.36/7.55 tff(94,plain,
% 7.36/7.55 (![V_c: $i, V_u: $i, V_S: $i, T_a: $i] : ((c_Union(V_c, T_a) = V_u) | (~c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a))) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_u, V_S, tc_set(T_a))))),
% 7.36/7.55 inference(modus_ponens,[status(thm)],[93, 86])).
% 7.36/7.55 tff(95,plain,
% 7.36/7.55 (((~![V_c: $i, V_u: $i, V_S: $i, T_a: $i] : ((c_Union(V_c, T_a) = V_u) | (~c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a))) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_u, V_S, tc_set(T_a))))) | ((~c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))) | (c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a) = v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))) | (~c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, tc_set(t_a))) | (~c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a))))) <=> ((~![V_c: $i, V_u: $i, V_S: $i, T_a: $i] : ((c_Union(V_c, T_a) = V_u) | (~c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a))) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_u, V_S, tc_set(T_a))))) | (~c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))) | (c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a) = v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))) | (~c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, tc_set(t_a))) | (~c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a))))),
% 7.36/7.55 inference(rewrite,[status(thm)],[])).
% 7.36/7.55 tff(96,plain,
% 7.36/7.55 (((c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a) = v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))) | (~c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a))) | (~c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, tc_set(t_a)))) <=> ((~c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))) | (c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a) = v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))) | (~c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, tc_set(t_a))) | (~c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a))))),
% 7.36/7.55 inference(rewrite,[status(thm)],[])).
% 7.36/7.55 tff(97,plain,
% 7.36/7.55 (((~![V_c: $i, V_u: $i, V_S: $i, T_a: $i] : ((c_Union(V_c, T_a) = V_u) | (~c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a))) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_u, V_S, tc_set(T_a))))) | ((c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a) = v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))) | (~c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a))) | (~c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, tc_set(t_a))))) <=> ((~![V_c: $i, V_u: $i, V_S: $i, T_a: $i] : ((c_Union(V_c, T_a) = V_u) | (~c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a))) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_u, V_S, tc_set(T_a))))) | ((~c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))) | (c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a) = v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))) | (~c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, tc_set(t_a))) | (~c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a)))))),
% 7.36/7.55 inference(monotonicity,[status(thm)],[96])).
% 7.36/7.55 tff(98,plain,
% 7.36/7.55 (((~![V_c: $i, V_u: $i, V_S: $i, T_a: $i] : ((c_Union(V_c, T_a) = V_u) | (~c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a))) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_u, V_S, tc_set(T_a))))) | ((c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a) = v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))) | (~c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a))) | (~c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, tc_set(t_a))))) <=> ((~![V_c: $i, V_u: $i, V_S: $i, T_a: $i] : ((c_Union(V_c, T_a) = V_u) | (~c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a))) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_u, V_S, tc_set(T_a))))) | (~c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))) | (c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a) = v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))) | (~c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, tc_set(t_a))) | (~c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a))))),
% 7.36/7.55 inference(transitivity,[status(thm)],[97, 95])).
% 7.36/7.55 tff(99,plain,
% 7.36/7.55 ((~![V_c: $i, V_u: $i, V_S: $i, T_a: $i] : ((c_Union(V_c, T_a) = V_u) | (~c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a))) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_u, V_S, tc_set(T_a))))) | ((c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a) = v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))) | (~c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a))) | (~c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, tc_set(t_a))))),
% 7.36/7.55 inference(quant_inst,[status(thm)],[])).
% 7.36/7.55 tff(100,plain,
% 7.36/7.55 ((~![V_c: $i, V_u: $i, V_S: $i, T_a: $i] : ((c_Union(V_c, T_a) = V_u) | (~c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a))) | (~c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_u, V_S, tc_set(T_a))))) | (~c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))) | (c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a) = v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))) | (~c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, tc_set(t_a))) | (~c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a)))),
% 7.36/7.55 inference(modus_ponens,[status(thm)],[99, 98])).
% 7.36/7.55 tff(101,plain,
% 7.36/7.55 ($false),
% 7.36/7.55 inference(unit_resolution,[status(thm)],[100, 94, 10, 84, 70, 56])).
% 7.36/7.55 tff(102,plain,(~c_lessequals(c_Zorn_Omaxchain(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(tc_set(t_a))))), inference(lemma,lemma(discharge,[]))).
% 7.36/7.55 tff(103,plain,
% 7.36/7.55 (^[V_S: $i, T_a: $i] : refl(c_lessequals(c_Zorn_Omaxchain(V_S, T_a), c_Zorn_Ochain(V_S, T_a), tc_set(tc_set(tc_set(T_a)))) <=> c_lessequals(c_Zorn_Omaxchain(V_S, T_a), c_Zorn_Ochain(V_S, T_a), tc_set(tc_set(tc_set(T_a)))))),
% 7.36/7.55 inference(bind,[status(th)],[])).
% 7.36/7.55 tff(104,plain,
% 7.36/7.55 (![V_S: $i, T_a: $i] : c_lessequals(c_Zorn_Omaxchain(V_S, T_a), c_Zorn_Ochain(V_S, T_a), tc_set(tc_set(tc_set(T_a)))) <=> ![V_S: $i, T_a: $i] : c_lessequals(c_Zorn_Omaxchain(V_S, T_a), c_Zorn_Ochain(V_S, T_a), tc_set(tc_set(tc_set(T_a))))),
% 7.36/7.55 inference(quant_intro,[status(thm)],[103])).
% 7.36/7.55 tff(105,plain,
% 7.36/7.55 (![V_S: $i, T_a: $i] : c_lessequals(c_Zorn_Omaxchain(V_S, T_a), c_Zorn_Ochain(V_S, T_a), tc_set(tc_set(tc_set(T_a)))) <=> ![V_S: $i, T_a: $i] : c_lessequals(c_Zorn_Omaxchain(V_S, T_a), c_Zorn_Ochain(V_S, T_a), tc_set(tc_set(tc_set(T_a))))),
% 7.36/7.55 inference(rewrite,[status(thm)],[])).
% 7.36/7.55 tff(106,axiom,(![V_S: $i, T_a: $i] : c_lessequals(c_Zorn_Omaxchain(V_S, T_a), c_Zorn_Ochain(V_S, T_a), tc_set(tc_set(tc_set(T_a))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Zorn_Omaxchain__subset__chain_0')).
% 7.36/7.55 tff(107,plain,
% 7.36/7.55 (![V_S: $i, T_a: $i] : c_lessequals(c_Zorn_Omaxchain(V_S, T_a), c_Zorn_Ochain(V_S, T_a), tc_set(tc_set(tc_set(T_a))))),
% 7.36/7.55 inference(modus_ponens,[status(thm)],[106, 105])).
% 7.36/7.55 tff(108,plain,(
% 7.36/7.55 ![V_S: $i, T_a: $i] : c_lessequals(c_Zorn_Omaxchain(V_S, T_a), c_Zorn_Ochain(V_S, T_a), tc_set(tc_set(tc_set(T_a))))),
% 7.36/7.55 inference(skolemize,[status(sab)],[107])).
% 7.36/7.55 tff(109,plain,
% 7.36/7.55 (![V_S: $i, T_a: $i] : c_lessequals(c_Zorn_Omaxchain(V_S, T_a), c_Zorn_Ochain(V_S, T_a), tc_set(tc_set(tc_set(T_a))))),
% 7.36/7.55 inference(modus_ponens,[status(thm)],[108, 104])).
% 7.36/7.55 tff(110,plain,
% 7.36/7.55 ((~![V_S: $i, T_a: $i] : c_lessequals(c_Zorn_Omaxchain(V_S, T_a), c_Zorn_Ochain(V_S, T_a), tc_set(tc_set(tc_set(T_a))))) | c_lessequals(c_Zorn_Omaxchain(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(tc_set(t_a))))),
% 7.36/7.55 inference(quant_inst,[status(thm)],[])).
% 7.36/7.55 tff(111,plain,
% 7.36/7.55 ($false),
% 7.36/7.55 inference(unit_resolution,[status(thm)],[110, 109, 102])).
% 7.36/7.55 % SZS output end Proof
% 7.36/7.55 % E exiting
%------------------------------------------------------------------------------