%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET847-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:26:30 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.50s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET847-2 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 05:46:24 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.50 % SZS status Unsatisfiable
% 0.19/0.50 % SZS output start Proof
% 0.19/0.50 tff(c_in_type, type, (
% 0.19/0.50 c_in: ( $i * $i * $i ) > $o)).
% 0.19/0.50 tff(tc_set_type, type, (
% 0.19/0.50 tc_set: $i > $i)).
% 0.19/0.50 tff(t_a_type, type, (
% 0.19/0.50 t_a: $i)).
% 0.19/0.50 tff(c_Zorn_Omaxchain_type, type, (
% 0.19/0.50 c_Zorn_Omaxchain: ( $i * $i ) > $i)).
% 0.19/0.50 tff(v_S_type, type, (
% 0.19/0.50 v_S: $i)).
% 0.19/0.50 tff(c_Zorn_Osucc_type, type, (
% 0.19/0.50 c_Zorn_Osucc: ( $i * $i * $i ) > $i)).
% 0.19/0.50 tff(c_Union_type, type, (
% 0.19/0.50 c_Union: ( $i * $i ) > $i)).
% 0.19/0.50 tff(c_Zorn_OTFin_type, type, (
% 0.19/0.50 c_Zorn_OTFin: ( $i * $i ) > $i)).
% 0.19/0.50 tff(c_minus_type, type, (
% 0.19/0.50 c_minus: ( $i * $i * $i ) > $i)).
% 0.19/0.50 tff(c_Zorn_Ochain_type, type, (
% 0.19/0.50 c_Zorn_Ochain: ( $i * $i ) > $i)).
% 0.19/0.50 tff(c_lessequals_type, type, (
% 0.19/0.50 c_lessequals: ( $i * $i * $i ) > $o)).
% 0.19/0.50 tff(1,assumption,(~c_lessequals(c_Zorn_OTFin(v_S, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(tc_set(t_a))))), introduced(assumption)).
% 0.19/0.50 tff(2,plain,
% 0.19/0.50 (^[T_a: $i, V_A: $i] : refl(c_lessequals(V_A, V_A, tc_set(T_a)) <=> c_lessequals(V_A, V_A, tc_set(T_a)))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(3,plain,
% 0.19/0.50 (![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a)) <=> ![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.50 tff(4,plain,
% 0.19/0.50 (![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a)) <=> ![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(5,axiom,(![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_Osubset__refl_0')).
% 0.19/0.50 tff(6,plain,
% 0.19/0.50 (![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.50 tff(7,plain,(
% 0.19/0.50 ![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))),
% 0.19/0.50 inference(skolemize,[status(sab)],[6])).
% 0.19/0.50 tff(8,plain,
% 0.19/0.50 (![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.50 tff(9,plain,
% 0.19/0.50 ((~![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))) | c_lessequals(c_Zorn_OTFin(v_S, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(tc_set(t_a))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(10,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.19/0.50 tff(11,plain,(c_lessequals(c_Zorn_OTFin(v_S, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(tc_set(t_a))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(12,plain,
% 0.19/0.50 (^[V_Y: $i, V_S: $i, T_a: $i] : refl(((~c_lessequals(V_Y, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(tc_set(T_a))))) | c_in(c_Union(V_Y, tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) <=> ((~c_lessequals(V_Y, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(tc_set(T_a))))) | c_in(c_Union(V_Y, tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(13,plain,
% 0.19/0.50 (![V_Y: $i, V_S: $i, T_a: $i] : ((~c_lessequals(V_Y, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(tc_set(T_a))))) | c_in(c_Union(V_Y, tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) <=> ![V_Y: $i, V_S: $i, T_a: $i] : ((~c_lessequals(V_Y, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(tc_set(T_a))))) | c_in(c_Union(V_Y, tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.50 tff(14,plain,
% 0.19/0.50 (![V_Y: $i, V_S: $i, T_a: $i] : ((~c_lessequals(V_Y, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(tc_set(T_a))))) | c_in(c_Union(V_Y, tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) <=> ![V_Y: $i, V_S: $i, T_a: $i] : ((~c_lessequals(V_Y, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(tc_set(T_a))))) | c_in(c_Union(V_Y, tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(15,axiom,(![V_Y: $i, V_S: $i, T_a: $i] : ((~c_lessequals(V_Y, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(tc_set(T_a))))) | c_in(c_Union(V_Y, tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Zorn_OTFin__UnionI_0')).
% 0.19/0.50 tff(16,plain,
% 0.19/0.50 (![V_Y: $i, V_S: $i, T_a: $i] : ((~c_lessequals(V_Y, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(tc_set(T_a))))) | c_in(c_Union(V_Y, tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.50 tff(17,plain,(
% 0.19/0.50 ![V_Y: $i, V_S: $i, T_a: $i] : ((~c_lessequals(V_Y, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(tc_set(T_a))))) | c_in(c_Union(V_Y, tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))))),
% 0.19/0.50 inference(skolemize,[status(sab)],[16])).
% 0.19/0.50 tff(18,plain,
% 0.19/0.50 (![V_Y: $i, V_S: $i, T_a: $i] : ((~c_lessequals(V_Y, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(tc_set(T_a))))) | c_in(c_Union(V_Y, tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.19/0.50 tff(19,plain,
% 0.19/0.50 (((~![V_Y: $i, V_S: $i, T_a: $i] : ((~c_lessequals(V_Y, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(tc_set(T_a))))) | c_in(c_Union(V_Y, tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))))) | ((~c_lessequals(c_Zorn_OTFin(v_S, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(tc_set(t_a))))) | c_in(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))))) <=> ((~![V_Y: $i, V_S: $i, T_a: $i] : ((~c_lessequals(V_Y, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(tc_set(T_a))))) | c_in(c_Union(V_Y, tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))))) | (~c_lessequals(c_Zorn_OTFin(v_S, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(tc_set(t_a))))) | c_in(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(20,plain,
% 0.19/0.50 ((~![V_Y: $i, V_S: $i, T_a: $i] : ((~c_lessequals(V_Y, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(tc_set(T_a))))) | c_in(c_Union(V_Y, tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))))) | ((~c_lessequals(c_Zorn_OTFin(v_S, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(tc_set(t_a))))) | c_in(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(21,plain,
% 0.19/0.50 ((~![V_Y: $i, V_S: $i, T_a: $i] : ((~c_lessequals(V_Y, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(tc_set(T_a))))) | c_in(c_Union(V_Y, tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))))) | (~c_lessequals(c_Zorn_OTFin(v_S, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(tc_set(t_a))))) | c_in(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.19/0.50 tff(22,plain,
% 0.19/0.50 (c_in(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[21, 18, 11])).
% 0.19/0.50 tff(23,plain,
% 0.19/0.50 (^[V_S: $i, T_a: $i] : refl(((~c_in(c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)) = c_Zorn_Osucc(V_S, c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), T_a))) <=> ((~c_in(c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)) = c_Zorn_Osucc(V_S, c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), T_a))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(24,plain,
% 0.19/0.50 (![V_S: $i, T_a: $i] : ((~c_in(c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)) = c_Zorn_Osucc(V_S, c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), T_a))) <=> ![V_S: $i, T_a: $i] : ((~c_in(c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)) = c_Zorn_Osucc(V_S, c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), T_a)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.50 tff(25,plain,
% 0.19/0.50 (![V_S: $i, T_a: $i] : ((~c_in(c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)) = c_Zorn_Osucc(V_S, c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), T_a))) <=> ![V_S: $i, T_a: $i] : ((~c_in(c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)) = c_Zorn_Osucc(V_S, c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), T_a)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(26,axiom,(![V_S: $i, T_a: $i] : ((~c_in(c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)) = c_Zorn_Osucc(V_S, c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), T_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Zorn_Oequal__succ__Union_1')).
% 0.19/0.50 tff(27,plain,
% 0.19/0.50 (![V_S: $i, T_a: $i] : ((~c_in(c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)) = c_Zorn_Osucc(V_S, c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), T_a)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.50 tff(28,plain,(
% 0.19/0.50 ![V_S: $i, T_a: $i] : ((~c_in(c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)) = c_Zorn_Osucc(V_S, c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), T_a)))),
% 0.19/0.50 inference(skolemize,[status(sab)],[27])).
% 0.19/0.50 tff(29,plain,
% 0.19/0.50 (![V_S: $i, T_a: $i] : ((~c_in(c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)) = c_Zorn_Osucc(V_S, c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), T_a)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.19/0.50 tff(30,plain,
% 0.19/0.50 (((~![V_S: $i, T_a: $i] : ((~c_in(c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)) = c_Zorn_Osucc(V_S, c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), T_a)))) | ((~c_in(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)) = c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a)))) <=> ((~![V_S: $i, T_a: $i] : ((~c_in(c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)) = c_Zorn_Osucc(V_S, c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), T_a)))) | (~c_in(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)) = c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(31,plain,
% 0.19/0.50 ((~![V_S: $i, T_a: $i] : ((~c_in(c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)) = c_Zorn_Osucc(V_S, c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), T_a)))) | ((~c_in(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)) = c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(32,plain,
% 0.19/0.50 ((~![V_S: $i, T_a: $i] : ((~c_in(c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)) = c_Zorn_Osucc(V_S, c_Union(c_Zorn_OTFin(V_S, T_a), tc_set(T_a)), T_a)))) | (~c_in(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)) = c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.19/0.50 tff(33,plain,
% 0.19/0.50 (c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)) = c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[32, 29, 22])).
% 0.19/0.50 tff(34,plain,
% 0.19/0.50 (c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a) = c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a))),
% 0.19/0.50 inference(symmetry,[status(thm)],[33])).
% 0.19/0.50 tff(35,plain,
% 0.19/0.50 (c_Zorn_Osucc(v_S, c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), t_a) = c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a)),
% 0.19/0.50 inference(monotonicity,[status(thm)],[34])).
% 0.19/0.50 tff(36,plain,
% 0.19/0.50 (^[V_c: $i, V_S: $i, T_a: $i] : refl(((~(c_Zorn_Osucc(V_S, V_c, T_a) = V_c)) | (~c_in(V_c, c_minus(c_Zorn_Ochain(V_S, T_a), c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(tc_set(T_a)))), tc_set(tc_set(T_a))))) <=> ((~(c_Zorn_Osucc(V_S, V_c, T_a) = V_c)) | (~c_in(V_c, c_minus(c_Zorn_Ochain(V_S, T_a), c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(tc_set(T_a)))), tc_set(tc_set(T_a))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(37,plain,
% 0.19/0.50 (![V_c: $i, V_S: $i, T_a: $i] : ((~(c_Zorn_Osucc(V_S, V_c, T_a) = V_c)) | (~c_in(V_c, c_minus(c_Zorn_Ochain(V_S, T_a), c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(tc_set(T_a)))), tc_set(tc_set(T_a))))) <=> ![V_c: $i, V_S: $i, T_a: $i] : ((~(c_Zorn_Osucc(V_S, V_c, T_a) = V_c)) | (~c_in(V_c, c_minus(c_Zorn_Ochain(V_S, T_a), c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(tc_set(T_a)))), tc_set(tc_set(T_a)))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[36])).
% 0.19/0.50 tff(38,plain,
% 0.19/0.50 (![V_c: $i, V_S: $i, T_a: $i] : ((~(c_Zorn_Osucc(V_S, V_c, T_a) = V_c)) | (~c_in(V_c, c_minus(c_Zorn_Ochain(V_S, T_a), c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(tc_set(T_a)))), tc_set(tc_set(T_a))))) <=> ![V_c: $i, V_S: $i, T_a: $i] : ((~(c_Zorn_Osucc(V_S, V_c, T_a) = V_c)) | (~c_in(V_c, c_minus(c_Zorn_Ochain(V_S, T_a), c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(tc_set(T_a)))), tc_set(tc_set(T_a)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(39,plain,
% 0.19/0.50 (^[V_c: $i, V_S: $i, T_a: $i] : rewrite(((~c_in(V_c, c_minus(c_Zorn_Ochain(V_S, T_a), c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(tc_set(T_a)))), tc_set(tc_set(T_a)))) | (~(c_Zorn_Osucc(V_S, V_c, T_a) = V_c))) <=> ((~(c_Zorn_Osucc(V_S, V_c, T_a) = V_c)) | (~c_in(V_c, c_minus(c_Zorn_Ochain(V_S, T_a), c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(tc_set(T_a)))), tc_set(tc_set(T_a))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(40,plain,
% 0.19/0.50 (![V_c: $i, V_S: $i, T_a: $i] : ((~c_in(V_c, c_minus(c_Zorn_Ochain(V_S, T_a), c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(tc_set(T_a)))), tc_set(tc_set(T_a)))) | (~(c_Zorn_Osucc(V_S, V_c, T_a) = V_c))) <=> ![V_c: $i, V_S: $i, T_a: $i] : ((~(c_Zorn_Osucc(V_S, V_c, T_a) = V_c)) | (~c_in(V_c, c_minus(c_Zorn_Ochain(V_S, T_a), c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(tc_set(T_a)))), tc_set(tc_set(T_a)))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[39])).
% 0.19/0.50 tff(41,axiom,(![V_c: $i, V_S: $i, T_a: $i] : ((~c_in(V_c, c_minus(c_Zorn_Ochain(V_S, T_a), c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(tc_set(T_a)))), tc_set(tc_set(T_a)))) | (~(c_Zorn_Osucc(V_S, V_c, T_a) = V_c)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Zorn_Osucc__not__equals_0')).
% 0.19/0.50 tff(42,plain,
% 0.19/0.50 (![V_c: $i, V_S: $i, T_a: $i] : ((~(c_Zorn_Osucc(V_S, V_c, T_a) = V_c)) | (~c_in(V_c, c_minus(c_Zorn_Ochain(V_S, T_a), c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(tc_set(T_a)))), tc_set(tc_set(T_a)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.19/0.50 tff(43,plain,
% 0.19/0.50 (![V_c: $i, V_S: $i, T_a: $i] : ((~(c_Zorn_Osucc(V_S, V_c, T_a) = V_c)) | (~c_in(V_c, c_minus(c_Zorn_Ochain(V_S, T_a), c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(tc_set(T_a)))), tc_set(tc_set(T_a)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.19/0.50 tff(44,plain,(
% 0.19/0.50 ![V_c: $i, V_S: $i, T_a: $i] : ((~(c_Zorn_Osucc(V_S, V_c, T_a) = V_c)) | (~c_in(V_c, c_minus(c_Zorn_Ochain(V_S, T_a), c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(tc_set(T_a)))), tc_set(tc_set(T_a)))))),
% 0.19/0.50 inference(skolemize,[status(sab)],[43])).
% 0.19/0.50 tff(45,plain,
% 0.19/0.50 (![V_c: $i, V_S: $i, T_a: $i] : ((~(c_Zorn_Osucc(V_S, V_c, T_a) = V_c)) | (~c_in(V_c, c_minus(c_Zorn_Ochain(V_S, T_a), c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(tc_set(T_a)))), tc_set(tc_set(T_a)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.19/0.50 tff(46,plain,
% 0.19/0.50 (((~![V_c: $i, V_S: $i, T_a: $i] : ((~(c_Zorn_Osucc(V_S, V_c, T_a) = V_c)) | (~c_in(V_c, c_minus(c_Zorn_Ochain(V_S, T_a), c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(tc_set(T_a)))), tc_set(tc_set(T_a)))))) | ((~(c_Zorn_Osucc(v_S, c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), t_a) = c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a))) | (~c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_minus(c_Zorn_Ochain(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(tc_set(t_a)))), tc_set(tc_set(t_a)))))) <=> ((~![V_c: $i, V_S: $i, T_a: $i] : ((~(c_Zorn_Osucc(V_S, V_c, T_a) = V_c)) | (~c_in(V_c, c_minus(c_Zorn_Ochain(V_S, T_a), c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(tc_set(T_a)))), tc_set(tc_set(T_a)))))) | (~(c_Zorn_Osucc(v_S, c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), t_a) = c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a))) | (~c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_minus(c_Zorn_Ochain(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(tc_set(t_a)))), tc_set(tc_set(t_a)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(47,plain,
% 0.19/0.50 ((~![V_c: $i, V_S: $i, T_a: $i] : ((~(c_Zorn_Osucc(V_S, V_c, T_a) = V_c)) | (~c_in(V_c, c_minus(c_Zorn_Ochain(V_S, T_a), c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(tc_set(T_a)))), tc_set(tc_set(T_a)))))) | ((~(c_Zorn_Osucc(v_S, c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), t_a) = c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a))) | (~c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_minus(c_Zorn_Ochain(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(tc_set(t_a)))), tc_set(tc_set(t_a)))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(48,plain,
% 0.19/0.50 ((~![V_c: $i, V_S: $i, T_a: $i] : ((~(c_Zorn_Osucc(V_S, V_c, T_a) = V_c)) | (~c_in(V_c, c_minus(c_Zorn_Ochain(V_S, T_a), c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(tc_set(T_a)))), tc_set(tc_set(T_a)))))) | (~(c_Zorn_Osucc(v_S, c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), t_a) = c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a))) | (~c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_minus(c_Zorn_Ochain(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(tc_set(t_a)))), tc_set(tc_set(t_a))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.19/0.50 tff(49,plain,
% 0.19/0.50 ((~(c_Zorn_Osucc(v_S, c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), t_a) = c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a))) | (~c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_minus(c_Zorn_Ochain(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(tc_set(t_a)))), tc_set(tc_set(t_a))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[48, 45])).
% 0.19/0.50 tff(50,plain,
% 0.19/0.50 (~c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_minus(c_Zorn_Ochain(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(tc_set(t_a)))), tc_set(tc_set(t_a)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[49, 35])).
% 0.19/0.50 tff(51,plain,
% 0.19/0.50 (c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))) <=> c_in(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[34])).
% 0.19/0.50 tff(52,plain,
% 0.19/0.50 (c_in(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))) <=> c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))),
% 0.19/0.50 inference(symmetry,[status(thm)],[51])).
% 0.19/0.50 tff(53,plain,
% 0.19/0.50 (c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[22, 52])).
% 0.19/0.50 tff(54,plain,
% 0.19/0.50 (^[V_c: $i, V_S: $i, T_a: $i] : refl(((~c_in(V_c, c_Zorn_OTFin(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_c, c_Zorn_OTFin(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)))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(55,plain,
% 0.19/0.50 (![V_c: $i, V_S: $i, T_a: $i] : ((~c_in(V_c, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | c_in(V_c, c_Zorn_Ochain(V_S, T_a), tc_set(tc_set(T_a)))) <=> ![V_c: $i, V_S: $i, T_a: $i] : ((~c_in(V_c, c_Zorn_OTFin(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))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.50 tff(56,plain,
% 0.19/0.50 (![V_c: $i, V_S: $i, T_a: $i] : ((~c_in(V_c, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | c_in(V_c, c_Zorn_Ochain(V_S, T_a), tc_set(tc_set(T_a)))) <=> ![V_c: $i, V_S: $i, T_a: $i] : ((~c_in(V_c, c_Zorn_OTFin(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))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(57,axiom,(![V_c: $i, V_S: $i, T_a: $i] : ((~c_in(V_c, c_Zorn_OTFin(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))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Zorn_OTFin__chain__lemma4_0')).
% 0.19/0.50 tff(58,plain,
% 0.19/0.50 (![V_c: $i, V_S: $i, T_a: $i] : ((~c_in(V_c, c_Zorn_OTFin(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))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.19/0.50 tff(59,plain,(
% 0.19/0.50 ![V_c: $i, V_S: $i, T_a: $i] : ((~c_in(V_c, c_Zorn_OTFin(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))))),
% 0.19/0.50 inference(skolemize,[status(sab)],[58])).
% 0.19/0.50 tff(60,plain,
% 0.19/0.50 (![V_c: $i, V_S: $i, T_a: $i] : ((~c_in(V_c, c_Zorn_OTFin(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))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.19/0.50 tff(61,plain,
% 0.19/0.50 (((~![V_c: $i, V_S: $i, T_a: $i] : ((~c_in(V_c, c_Zorn_OTFin(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(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))))) <=> ((~![V_c: $i, V_S: $i, T_a: $i] : ((~c_in(V_c, c_Zorn_OTFin(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(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(62,plain,
% 0.19/0.50 ((~![V_c: $i, V_S: $i, T_a: $i] : ((~c_in(V_c, c_Zorn_OTFin(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(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(63,plain,
% 0.19/0.50 ((~![V_c: $i, V_S: $i, T_a: $i] : ((~c_in(V_c, c_Zorn_OTFin(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(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.50 tff(64,plain,
% 0.19/0.50 ((~c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[63, 60])).
% 0.19/0.50 tff(65,plain,
% 0.19/0.50 (c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[64, 53])).
% 0.19/0.50 tff(66,plain,
% 0.19/0.50 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : refl((c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a))) <=> (c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(67,plain,
% 0.19/0.50 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a) | c_in(V_c, V_B, 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, c_minus(V_A, V_B, tc_set(T_a)), T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[66])).
% 0.19/0.50 tff(68,plain,
% 0.19/0.50 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a) | c_in(V_c, V_B, 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, c_minus(V_A, V_B, tc_set(T_a)), T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(69,plain,
% 0.19/0.50 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : rewrite((((~c_in(V_c, V_A, T_a)) | c_in(V_c, V_B, T_a)) | c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a)) <=> (c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(70,plain,
% 0.19/0.50 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_c, V_A, T_a)) | c_in(V_c, V_B, T_a)) | c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[69])).
% 0.19/0.50 tff(71,axiom,(![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_c, V_A, T_a)) | c_in(V_c, V_B, T_a)) | c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_ODiffI_0')).
% 0.19/0.50 tff(72,plain,
% 0.19/0.50 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.19/0.50 tff(73,plain,
% 0.19/0.50 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.19/0.50 tff(74,plain,(
% 0.19/0.50 ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)))),
% 0.19/0.50 inference(skolemize,[status(sab)],[73])).
% 0.19/0.50 tff(75,plain,
% 0.19/0.50 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.19/0.50 tff(76,plain,
% 0.19/0.50 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)))) | (c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_minus(c_Zorn_Ochain(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(tc_set(t_a)))), tc_set(tc_set(t_a))) | (~c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), 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, c_minus(V_A, V_B, tc_set(T_a)), T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)))) | c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_minus(c_Zorn_Ochain(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(tc_set(t_a)))), tc_set(tc_set(t_a))) | (~c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(77,plain,
% 0.19/0.50 ((c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_minus(c_Zorn_Ochain(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(tc_set(t_a)))), tc_set(tc_set(t_a))) | c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))) | (~c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))))) <=> (c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_minus(c_Zorn_Ochain(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(tc_set(t_a)))), tc_set(tc_set(t_a))) | (~c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(78,plain,
% 0.19/0.51 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)))) | (c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_minus(c_Zorn_Ochain(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(tc_set(t_a)))), tc_set(tc_set(t_a))) | c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))) | (~c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_Ochain(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, c_minus(V_A, V_B, tc_set(T_a)), T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)))) | (c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_minus(c_Zorn_Ochain(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(tc_set(t_a)))), tc_set(tc_set(t_a))) | (~c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[77])).
% 0.19/0.51 tff(79,plain,
% 0.19/0.51 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)))) | (c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_minus(c_Zorn_Ochain(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(tc_set(t_a)))), tc_set(tc_set(t_a))) | c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))) | (~c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_Ochain(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, c_minus(V_A, V_B, tc_set(T_a)), T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)))) | c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_minus(c_Zorn_Ochain(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(tc_set(t_a)))), tc_set(tc_set(t_a))) | (~c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[78, 76])).
% 0.19/0.51 tff(80,plain,
% 0.19/0.51 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)))) | (c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_minus(c_Zorn_Ochain(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(tc_set(t_a)))), tc_set(tc_set(t_a))) | c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))) | (~c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(81,plain,
% 0.19/0.51 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)))) | c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_minus(c_Zorn_Ochain(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(tc_set(t_a)))), tc_set(tc_set(t_a))) | (~c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.19/0.51 tff(82,plain,
% 0.19/0.51 (c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[81, 75, 65, 50])).
% 0.19/0.51 tff(83,plain,
% 0.19/0.51 (^[V_U: $i] : refl((~c_in(V_U, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))) <=> (~c_in(V_U, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(84,plain,
% 0.19/0.51 (![V_U: $i] : (~c_in(V_U, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))) <=> ![V_U: $i] : (~c_in(V_U, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[83])).
% 0.19/0.51 tff(85,plain,
% 0.19/0.51 (![V_U: $i] : (~c_in(V_U, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))) <=> ![V_U: $i] : (~c_in(V_U, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(86,axiom,(![V_U: $i] : (~c_in(V_U, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.19/0.51 tff(87,plain,
% 0.19/0.51 (![V_U: $i] : (~c_in(V_U, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.51 tff(88,plain,(
% 0.19/0.51 ![V_U: $i] : (~c_in(V_U, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))))),
% 0.19/0.51 inference(skolemize,[status(sab)],[87])).
% 0.19/0.51 tff(89,plain,
% 0.19/0.51 (![V_U: $i] : (~c_in(V_U, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.19/0.51 tff(90,plain,
% 0.19/0.51 ((~![V_U: $i] : (~c_in(V_U, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))))) | (~c_in(c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(91,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[90, 89, 82])).
% 0.19/0.51 % SZS output end Proof
% 0.19/0.51 % E exiting
%------------------------------------------------------------------------------