%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET843-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:26:29 AM UTC 2025
% Result : Unsatisfiable 0.22s 0.38s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET843-2 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n010.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 05:47:41 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.22/0.38 % SZS status Unsatisfiable
% 0.22/0.38 % SZS output start Proof
% 0.22/0.38 tff(c_lessequals_type, type, (
% 0.22/0.38 c_lessequals: ( $i * $i * $i ) > $o)).
% 0.22/0.38 tff(tc_set_type, type, (
% 0.22/0.38 tc_set: $i > $i)).
% 0.22/0.38 tff(t_a_type, type, (
% 0.22/0.38 t_a: $i)).
% 0.22/0.38 tff(c_Zorn_OTFin_type, type, (
% 0.22/0.38 c_Zorn_OTFin: ( $i * $i ) > $i)).
% 0.22/0.38 tff(v_S_type, type, (
% 0.22/0.38 v_S: $i)).
% 0.22/0.38 tff(c_in_type, type, (
% 0.22/0.38 c_in: ( $i * $i * $i ) > $o)).
% 0.22/0.38 tff(c_Union_type, type, (
% 0.22/0.38 c_Union: ( $i * $i ) > $i)).
% 0.22/0.38 tff(c_Zorn_Osucc_type, type, (
% 0.22/0.38 c_Zorn_Osucc: ( $i * $i * $i ) > $i)).
% 0.22/0.38 tff(v_m_type, type, (
% 0.22/0.38 v_m: $i)).
% 0.22/0.38 tff(1,assumption,(~(v_m = c_Zorn_Osucc(v_S, v_m, t_a))), introduced(assumption)).
% 0.22/0.38 tff(2,plain,
% 0.22/0.38 (((v_m = c_Zorn_Osucc(v_S, v_m, t_a)) | (v_m = c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)))) <=> ((v_m = c_Zorn_Osucc(v_S, v_m, t_a)) | (v_m = c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a))))),
% 0.22/0.38 inference(rewrite,[status(thm)],[])).
% 0.22/0.38 tff(3,axiom,((v_m = c_Zorn_Osucc(v_S, v_m, t_a)) | (v_m = c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_2')).
% 0.22/0.38 tff(4,plain,
% 0.22/0.38 ((v_m = c_Zorn_Osucc(v_S, v_m, t_a)) | (v_m = c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)))),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.22/0.38 tff(5,plain,
% 0.22/0.38 (v_m = c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a))),
% 0.22/0.38 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.22/0.38 tff(6,plain,
% 0.22/0.38 (c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)) = v_m),
% 0.22/0.38 inference(symmetry,[status(thm)],[5])).
% 0.22/0.38 tff(7,plain,
% 0.22/0.38 (c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a) = c_Zorn_Osucc(v_S, v_m, t_a)),
% 0.22/0.38 inference(monotonicity,[status(thm)],[6])).
% 0.22/0.38 tff(8,plain,
% 0.22/0.38 (c_Zorn_Osucc(v_S, v_m, t_a) = c_Zorn_Osucc(v_S, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), t_a)),
% 0.22/0.38 inference(symmetry,[status(thm)],[7])).
% 0.22/0.38 tff(9,plain,
% 0.22/0.38 (c_in(c_Zorn_Osucc(v_S, v_m, 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)))),
% 0.22/0.38 inference(monotonicity,[status(thm)],[8])).
% 0.22/0.39 tff(10,plain,
% 0.22/0.39 (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, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))),
% 0.22/0.39 inference(symmetry,[status(thm)],[9])).
% 0.22/0.39 tff(11,plain,
% 0.22/0.39 (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(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))),
% 0.22/0.39 inference(monotonicity,[status(thm)],[6])).
% 0.22/0.39 tff(12,plain,
% 0.22/0.39 (c_in(v_m, 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)))),
% 0.22/0.39 inference(symmetry,[status(thm)],[11])).
% 0.22/0.39 tff(13,plain,
% 0.22/0.39 (c_in(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))) <=> c_in(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))),
% 0.22/0.39 inference(rewrite,[status(thm)],[])).
% 0.22/0.39 tff(14,axiom,(c_in(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.22/0.39 tff(15,plain,
% 0.22/0.39 (c_in(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.22/0.39 tff(16,plain,
% 0.22/0.39 (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)))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.22/0.39 tff(17,plain,
% 0.22/0.39 (^[V_x: $i, V_S: $i, T_a: $i] : refl(((~c_in(V_x, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | c_in(c_Zorn_Osucc(V_S, V_x, T_a), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) <=> ((~c_in(V_x, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | c_in(c_Zorn_Osucc(V_S, V_x, T_a), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))))),
% 0.22/0.39 inference(bind,[status(th)],[])).
% 0.22/0.39 tff(18,plain,
% 0.22/0.39 (![V_x: $i, V_S: $i, T_a: $i] : ((~c_in(V_x, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | c_in(c_Zorn_Osucc(V_S, V_x, T_a), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) <=> ![V_x: $i, V_S: $i, T_a: $i] : ((~c_in(V_x, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | c_in(c_Zorn_Osucc(V_S, V_x, T_a), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))))),
% 0.22/0.39 inference(quant_intro,[status(thm)],[17])).
% 0.22/0.39 tff(19,plain,
% 0.22/0.39 (![V_x: $i, V_S: $i, T_a: $i] : ((~c_in(V_x, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | c_in(c_Zorn_Osucc(V_S, V_x, T_a), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) <=> ![V_x: $i, V_S: $i, T_a: $i] : ((~c_in(V_x, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | c_in(c_Zorn_Osucc(V_S, V_x, T_a), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))))),
% 0.22/0.39 inference(rewrite,[status(thm)],[])).
% 0.22/0.39 tff(20,axiom,(![V_x: $i, V_S: $i, T_a: $i] : ((~c_in(V_x, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | c_in(c_Zorn_Osucc(V_S, V_x, 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_OsuccI_0')).
% 0.22/0.39 tff(21,plain,
% 0.22/0.39 (![V_x: $i, V_S: $i, T_a: $i] : ((~c_in(V_x, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | c_in(c_Zorn_Osucc(V_S, V_x, T_a), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.22/0.39 tff(22,plain,(
% 0.22/0.39 ![V_x: $i, V_S: $i, T_a: $i] : ((~c_in(V_x, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | c_in(c_Zorn_Osucc(V_S, V_x, T_a), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))))),
% 0.22/0.39 inference(skolemize,[status(sab)],[21])).
% 0.22/0.39 tff(23,plain,
% 0.22/0.39 (![V_x: $i, V_S: $i, T_a: $i] : ((~c_in(V_x, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | c_in(c_Zorn_Osucc(V_S, V_x, T_a), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.22/0.39 tff(24,plain,
% 0.22/0.39 (((~![V_x: $i, V_S: $i, T_a: $i] : ((~c_in(V_x, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | c_in(c_Zorn_Osucc(V_S, V_x, 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)))) | 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))))) <=> ((~![V_x: $i, V_S: $i, T_a: $i] : ((~c_in(V_x, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | c_in(c_Zorn_Osucc(V_S, V_x, 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)))) | 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))))),
% 0.22/0.39 inference(rewrite,[status(thm)],[])).
% 0.22/0.39 tff(25,plain,
% 0.22/0.39 ((~![V_x: $i, V_S: $i, T_a: $i] : ((~c_in(V_x, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | c_in(c_Zorn_Osucc(V_S, V_x, 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)))) | 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))))),
% 0.22/0.39 inference(quant_inst,[status(thm)],[])).
% 0.22/0.39 tff(26,plain,
% 0.22/0.39 ((~![V_x: $i, V_S: $i, T_a: $i] : ((~c_in(V_x, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | c_in(c_Zorn_Osucc(V_S, V_x, 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)))) | 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)))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.22/0.39 tff(27,plain,
% 0.22/0.39 ((~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)))),
% 0.22/0.39 inference(unit_resolution,[status(thm)],[26, 23])).
% 0.22/0.39 tff(28,plain,
% 0.22/0.39 (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)))),
% 0.22/0.39 inference(unit_resolution,[status(thm)],[27, 16])).
% 0.22/0.39 tff(29,plain,
% 0.22/0.39 (c_in(c_Zorn_Osucc(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[28, 10])).
% 0.22/0.39 tff(30,plain,
% 0.22/0.39 ((c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)) = c_Zorn_Osucc(v_S, v_m, t_a)) <=> (v_m = c_Zorn_Osucc(v_S, v_m, t_a))),
% 0.22/0.39 inference(monotonicity,[status(thm)],[6])).
% 0.22/0.39 tff(31,plain,
% 0.22/0.39 ((v_m = c_Zorn_Osucc(v_S, v_m, t_a)) <=> (c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)) = c_Zorn_Osucc(v_S, v_m, t_a))),
% 0.22/0.39 inference(symmetry,[status(thm)],[30])).
% 0.22/0.39 tff(32,plain,
% 0.22/0.39 ((~(v_m = c_Zorn_Osucc(v_S, v_m, t_a))) <=> (~(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)) = c_Zorn_Osucc(v_S, v_m, t_a)))),
% 0.22/0.39 inference(monotonicity,[status(thm)],[31])).
% 0.22/0.39 tff(33,plain,
% 0.22/0.39 (~(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)) = c_Zorn_Osucc(v_S, v_m, t_a))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[1, 32])).
% 0.22/0.39 tff(34,plain,
% 0.22/0.39 (c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_Osucc(v_S, v_m, t_a), tc_set(tc_set(t_a))) <=> c_lessequals(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), tc_set(tc_set(t_a)))),
% 0.22/0.39 inference(monotonicity,[status(thm)],[8])).
% 0.22/0.39 tff(35,plain,
% 0.22/0.39 (c_lessequals(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), tc_set(tc_set(t_a))) <=> c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_Osucc(v_S, v_m, t_a), tc_set(tc_set(t_a)))),
% 0.22/0.39 inference(symmetry,[status(thm)],[34])).
% 0.22/0.39 tff(36,plain,
% 0.22/0.39 (^[V_x: $i, V_S: $i, T_a: $i] : refl(c_lessequals(V_x, c_Zorn_Osucc(V_S, V_x, T_a), tc_set(tc_set(T_a))) <=> c_lessequals(V_x, c_Zorn_Osucc(V_S, V_x, T_a), tc_set(tc_set(T_a))))),
% 0.22/0.39 inference(bind,[status(th)],[])).
% 0.22/0.39 tff(37,plain,
% 0.22/0.39 (![V_x: $i, V_S: $i, T_a: $i] : c_lessequals(V_x, c_Zorn_Osucc(V_S, V_x, T_a), tc_set(tc_set(T_a))) <=> ![V_x: $i, V_S: $i, T_a: $i] : c_lessequals(V_x, c_Zorn_Osucc(V_S, V_x, T_a), tc_set(tc_set(T_a)))),
% 0.22/0.39 inference(quant_intro,[status(thm)],[36])).
% 0.22/0.39 tff(38,plain,
% 0.22/0.39 (![V_x: $i, V_S: $i, T_a: $i] : c_lessequals(V_x, c_Zorn_Osucc(V_S, V_x, T_a), tc_set(tc_set(T_a))) <=> ![V_x: $i, V_S: $i, T_a: $i] : c_lessequals(V_x, c_Zorn_Osucc(V_S, V_x, T_a), tc_set(tc_set(T_a)))),
% 0.22/0.39 inference(rewrite,[status(thm)],[])).
% 0.22/0.39 tff(39,axiom,(![V_x: $i, V_S: $i, T_a: $i] : c_lessequals(V_x, c_Zorn_Osucc(V_S, V_x, T_a), tc_set(tc_set(T_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Zorn_OAbrial__axiom1_0')).
% 0.22/0.39 tff(40,plain,
% 0.22/0.39 (![V_x: $i, V_S: $i, T_a: $i] : c_lessequals(V_x, c_Zorn_Osucc(V_S, V_x, T_a), tc_set(tc_set(T_a)))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.22/0.39 tff(41,plain,(
% 0.22/0.39 ![V_x: $i, V_S: $i, T_a: $i] : c_lessequals(V_x, c_Zorn_Osucc(V_S, V_x, T_a), tc_set(tc_set(T_a)))),
% 0.22/0.39 inference(skolemize,[status(sab)],[40])).
% 0.22/0.39 tff(42,plain,
% 0.22/0.39 (![V_x: $i, V_S: $i, T_a: $i] : c_lessequals(V_x, c_Zorn_Osucc(V_S, V_x, T_a), tc_set(tc_set(T_a)))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.22/0.39 tff(43,plain,
% 0.22/0.39 ((~![V_x: $i, V_S: $i, T_a: $i] : c_lessequals(V_x, c_Zorn_Osucc(V_S, V_x, T_a), tc_set(tc_set(T_a)))) | c_lessequals(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), tc_set(tc_set(t_a)))),
% 0.22/0.39 inference(quant_inst,[status(thm)],[])).
% 0.22/0.39 tff(44,plain,
% 0.22/0.39 (c_lessequals(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), tc_set(tc_set(t_a)))),
% 0.22/0.39 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.22/0.39 tff(45,plain,
% 0.22/0.39 (c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_Osucc(v_S, v_m, t_a), tc_set(tc_set(t_a)))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[44, 35])).
% 0.22/0.39 tff(46,plain,
% 0.22/0.39 (^[T_a: $i, V_B: $i, V_A: $i] : refl(((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) <=> ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))))),
% 0.22/0.39 inference(bind,[status(th)],[])).
% 0.22/0.39 tff(47,plain,
% 0.22/0.39 (![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 0.22/0.39 inference(quant_intro,[status(thm)],[46])).
% 0.22/0.39 tff(48,plain,
% 0.22/0.39 (![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 0.22/0.39 inference(rewrite,[status(thm)],[])).
% 0.22/0.39 tff(49,plain,
% 0.22/0.39 (^[T_a: $i, V_B: $i, V_A: $i] : trans(monotonicity(rewrite(((~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) <=> ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))), ((((~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | (V_A = V_B)) <=> (((~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) | (V_A = V_B)))), rewrite((((~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) | (V_A = V_B)) <=> ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))), ((((~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | (V_A = V_B)) <=> ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))))),
% 0.22/0.39 inference(bind,[status(th)],[])).
% 0.22/0.39 tff(50,plain,
% 0.22/0.39 (![T_a: $i, V_B: $i, V_A: $i] : (((~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | (V_A = V_B)) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 0.22/0.39 inference(quant_intro,[status(thm)],[49])).
% 0.22/0.39 tff(51,axiom,(![T_a: $i, V_B: $i, V_A: $i] : (((~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | (V_A = V_B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_Osubset__antisym_0')).
% 0.22/0.39 tff(52,plain,
% 0.22/0.39 (![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.22/0.39 tff(53,plain,
% 0.22/0.39 (![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.22/0.39 tff(54,plain,(
% 0.22/0.39 ![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 0.22/0.39 inference(skolemize,[status(sab)],[53])).
% 0.22/0.39 tff(55,plain,
% 0.22/0.39 (![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.22/0.39 tff(56,plain,
% 0.22/0.39 (((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)) = c_Zorn_Osucc(v_S, v_m, t_a)) | (~c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_Osucc(v_S, v_m, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), tc_set(tc_set(t_a)))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | (c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)) = c_Zorn_Osucc(v_S, v_m, t_a)) | (~c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_Osucc(v_S, v_m, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), tc_set(tc_set(t_a)))))),
% 0.22/0.39 inference(rewrite,[status(thm)],[])).
% 0.22/0.39 tff(57,plain,
% 0.22/0.39 ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)) = c_Zorn_Osucc(v_S, v_m, t_a)) | (~c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_Osucc(v_S, v_m, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), tc_set(tc_set(t_a)))))),
% 0.22/0.39 inference(quant_inst,[status(thm)],[])).
% 0.22/0.39 tff(58,plain,
% 0.22/0.39 ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | (c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)) = c_Zorn_Osucc(v_S, v_m, t_a)) | (~c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_Osucc(v_S, v_m, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), tc_set(tc_set(t_a))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.22/0.40 tff(59,plain,
% 0.22/0.40 ((c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)) = c_Zorn_Osucc(v_S, v_m, t_a)) | (~c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_Osucc(v_S, v_m, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), tc_set(tc_set(t_a))))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[58, 55])).
% 0.22/0.40 tff(60,plain,
% 0.22/0.40 (~c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), tc_set(tc_set(t_a)))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[59, 45, 33])).
% 0.22/0.40 tff(61,plain,
% 0.22/0.40 (^[T_a: $i, V_B: $i, V_A: $i] : refl(((~c_in(V_B, V_A, tc_set(T_a))) | c_lessequals(V_B, c_Union(V_A, T_a), tc_set(T_a))) <=> ((~c_in(V_B, V_A, tc_set(T_a))) | c_lessequals(V_B, c_Union(V_A, T_a), tc_set(T_a))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(62,plain,
% 0.22/0.40 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_B, V_A, tc_set(T_a))) | c_lessequals(V_B, c_Union(V_A, T_a), tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_B, V_A, tc_set(T_a))) | c_lessequals(V_B, c_Union(V_A, T_a), tc_set(T_a)))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[61])).
% 0.22/0.40 tff(63,plain,
% 0.22/0.40 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_B, V_A, tc_set(T_a))) | c_lessequals(V_B, c_Union(V_A, T_a), tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_B, V_A, tc_set(T_a))) | c_lessequals(V_B, c_Union(V_A, T_a), tc_set(T_a)))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(64,axiom,(![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_B, V_A, tc_set(T_a))) | c_lessequals(V_B, c_Union(V_A, T_a), tc_set(T_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_OUnion__upper_0')).
% 0.22/0.40 tff(65,plain,
% 0.22/0.40 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_B, V_A, tc_set(T_a))) | c_lessequals(V_B, c_Union(V_A, T_a), tc_set(T_a)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.22/0.40 tff(66,plain,(
% 0.22/0.40 ![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_B, V_A, tc_set(T_a))) | c_lessequals(V_B, c_Union(V_A, T_a), tc_set(T_a)))),
% 0.22/0.40 inference(skolemize,[status(sab)],[65])).
% 0.22/0.40 tff(67,plain,
% 0.22/0.40 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_B, V_A, tc_set(T_a))) | c_lessequals(V_B, c_Union(V_A, T_a), tc_set(T_a)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.22/0.40 tff(68,plain,
% 0.22/0.40 (((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_B, V_A, tc_set(T_a))) | c_lessequals(V_B, c_Union(V_A, T_a), tc_set(T_a)))) | ((~c_in(c_Zorn_Osucc(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), tc_set(tc_set(t_a))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_B, V_A, tc_set(T_a))) | c_lessequals(V_B, c_Union(V_A, T_a), tc_set(T_a)))) | (~c_in(c_Zorn_Osucc(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), tc_set(tc_set(t_a))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(69,plain,
% 0.22/0.40 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_B, V_A, tc_set(T_a))) | c_lessequals(V_B, c_Union(V_A, T_a), tc_set(T_a)))) | ((~c_in(c_Zorn_Osucc(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), tc_set(tc_set(t_a))))),
% 0.22/0.40 inference(quant_inst,[status(thm)],[])).
% 0.22/0.40 tff(70,plain,
% 0.22/0.40 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_B, V_A, tc_set(T_a))) | c_lessequals(V_B, c_Union(V_A, T_a), tc_set(T_a)))) | (~c_in(c_Zorn_Osucc(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), tc_set(tc_set(t_a)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.22/0.40 tff(71,plain,
% 0.22/0.40 ((~c_in(c_Zorn_Osucc(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), tc_set(tc_set(t_a)))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[70, 67])).
% 0.22/0.40 tff(72,plain,
% 0.22/0.40 (~c_in(c_Zorn_Osucc(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[71, 60])).
% 0.22/0.40 tff(73,plain,
% 0.22/0.40 ($false),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[72, 29])).
% 0.22/0.40 tff(74,plain,(v_m = c_Zorn_Osucc(v_S, v_m, t_a)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.40 tff(75,plain,
% 0.22/0.40 (c_Zorn_Osucc(v_S, v_m, t_a) = v_m),
% 0.22/0.40 inference(symmetry,[status(thm)],[74])).
% 0.22/0.40 tff(76,plain,
% 0.22/0.40 (c_in(c_Zorn_Osucc(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))) <=> c_in(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))),
% 0.22/0.40 inference(monotonicity,[status(thm)],[75])).
% 0.22/0.40 tff(77,plain,
% 0.22/0.40 (c_in(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))) <=> c_in(c_Zorn_Osucc(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))),
% 0.22/0.40 inference(symmetry,[status(thm)],[76])).
% 0.22/0.40 tff(78,plain,
% 0.22/0.40 (c_in(c_Zorn_Osucc(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[15, 77])).
% 0.22/0.40 tff(79,plain,
% 0.22/0.40 (c_Zorn_Osucc(v_S, c_Zorn_Osucc(v_S, v_m, t_a), t_a) = c_Zorn_Osucc(v_S, v_m, t_a)),
% 0.22/0.40 inference(monotonicity,[status(thm)],[75])).
% 0.22/0.40 tff(80,plain,
% 0.22/0.40 (c_Zorn_Osucc(v_S, v_m, t_a) = c_Zorn_Osucc(v_S, c_Zorn_Osucc(v_S, v_m, t_a), t_a)),
% 0.22/0.40 inference(symmetry,[status(thm)],[79])).
% 0.22/0.40 tff(81,plain,
% 0.22/0.40 (c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_Osucc(v_S, v_m, t_a), tc_set(tc_set(t_a))) <=> c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), v_m, tc_set(tc_set(t_a)))),
% 0.22/0.40 inference(monotonicity,[status(thm)],[75])).
% 0.22/0.40 tff(82,plain,
% 0.22/0.40 (c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), v_m, tc_set(tc_set(t_a))) <=> c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_Osucc(v_S, v_m, t_a), tc_set(tc_set(t_a)))),
% 0.22/0.40 inference(symmetry,[status(thm)],[81])).
% 0.22/0.40 tff(83,plain,
% 0.22/0.40 ((~c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), v_m, tc_set(tc_set(t_a)))) <=> (~c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_Osucc(v_S, v_m, t_a), tc_set(tc_set(t_a))))),
% 0.22/0.40 inference(monotonicity,[status(thm)],[82])).
% 0.22/0.40 tff(84,plain,
% 0.22/0.40 (((~(v_m = c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)))) | (~(v_m = c_Zorn_Osucc(v_S, v_m, t_a)))) <=> ((~(v_m = c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)))) | (~(v_m = c_Zorn_Osucc(v_S, v_m, t_a))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(85,axiom,((~(v_m = c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)))) | (~(v_m = c_Zorn_Osucc(v_S, v_m, t_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_1')).
% 0.22/0.40 tff(86,plain,
% 0.22/0.40 ((~(v_m = c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)))) | (~(v_m = c_Zorn_Osucc(v_S, v_m, t_a)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.22/0.40 tff(87,plain,
% 0.22/0.40 ((~(v_m = c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)))) | (~(v_m = c_Zorn_Osucc(v_S, v_m, t_a)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[86, 84])).
% 0.22/0.40 tff(88,plain,
% 0.22/0.40 ((~(v_m = c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)))) | (~(v_m = c_Zorn_Osucc(v_S, v_m, t_a)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[87, 84])).
% 0.22/0.40 tff(89,plain,
% 0.22/0.40 ((~(v_m = c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)))) | (~(v_m = c_Zorn_Osucc(v_S, v_m, t_a)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.22/0.40 tff(90,plain,
% 0.22/0.40 ((~(v_m = c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)))) | (~(v_m = c_Zorn_Osucc(v_S, v_m, t_a)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[89, 84])).
% 0.22/0.40 tff(91,plain,
% 0.22/0.40 (~(v_m = c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[90, 74])).
% 0.22/0.40 tff(92,plain,
% 0.22/0.40 (((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_B, V_A, tc_set(T_a))) | c_lessequals(V_B, c_Union(V_A, T_a), tc_set(T_a)))) | ((~c_in(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(v_m, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), tc_set(tc_set(t_a))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_B, V_A, tc_set(T_a))) | c_lessequals(V_B, c_Union(V_A, T_a), tc_set(T_a)))) | (~c_in(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(v_m, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), tc_set(tc_set(t_a))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(93,plain,
% 0.22/0.40 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_B, V_A, tc_set(T_a))) | c_lessequals(V_B, c_Union(V_A, T_a), tc_set(T_a)))) | ((~c_in(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(v_m, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), tc_set(tc_set(t_a))))),
% 0.22/0.40 inference(quant_inst,[status(thm)],[])).
% 0.22/0.40 tff(94,plain,
% 0.22/0.40 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_B, V_A, tc_set(T_a))) | c_lessequals(V_B, c_Union(V_A, T_a), tc_set(T_a)))) | (~c_in(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(v_m, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), tc_set(tc_set(t_a)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.22/0.40 tff(95,plain,
% 0.22/0.40 (c_lessequals(v_m, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), tc_set(tc_set(t_a)))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[94, 67, 15])).
% 0.22/0.40 tff(96,plain,
% 0.22/0.40 (((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((v_m = c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a))) | (~c_lessequals(v_m, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), tc_set(tc_set(t_a)))) | (~c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), v_m, tc_set(tc_set(t_a)))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | (v_m = c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a))) | (~c_lessequals(v_m, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), tc_set(tc_set(t_a)))) | (~c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), v_m, tc_set(tc_set(t_a)))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(97,plain,
% 0.22/0.40 ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((v_m = c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a))) | (~c_lessequals(v_m, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), tc_set(tc_set(t_a)))) | (~c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), v_m, tc_set(tc_set(t_a)))))),
% 0.22/0.40 inference(quant_inst,[status(thm)],[])).
% 0.22/0.40 tff(98,plain,
% 0.22/0.40 ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | (v_m = c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a))) | (~c_lessequals(v_m, c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), tc_set(tc_set(t_a)))) | (~c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), v_m, tc_set(tc_set(t_a))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.22/0.40 tff(99,plain,
% 0.22/0.40 ((v_m = c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a))) | (~c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), v_m, tc_set(tc_set(t_a))))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[98, 55, 95])).
% 0.22/0.40 tff(100,plain,
% 0.22/0.40 (~c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), v_m, tc_set(tc_set(t_a)))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[99, 91])).
% 0.22/0.40 tff(101,plain,
% 0.22/0.40 (~c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_Osucc(v_S, v_m, t_a), tc_set(tc_set(t_a)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[100, 83])).
% 0.22/0.40 tff(102,plain,
% 0.22/0.40 (^[V_n: $i, V_S: $i, T_a: $i, V_m: $i] : refl((c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | (~(V_m = c_Zorn_Osucc(V_S, V_m, T_a))) | (~c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))))) <=> (c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | (~(V_m = c_Zorn_Osucc(V_S, V_m, T_a))) | (~c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(103,plain,
% 0.22/0.40 (![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | (~(V_m = c_Zorn_Osucc(V_S, V_m, T_a))) | (~c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))))) <=> ![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | (~(V_m = c_Zorn_Osucc(V_S, V_m, T_a))) | (~c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[102])).
% 0.22/0.40 tff(104,plain,
% 0.22/0.40 (![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | (~(V_m = c_Zorn_Osucc(V_S, V_m, T_a))) | (~c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))))) <=> ![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | (~(V_m = c_Zorn_Osucc(V_S, V_m, T_a))) | (~c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(105,plain,
% 0.22/0.40 (^[V_n: $i, V_S: $i, T_a: $i, V_m: $i] : trans(monotonicity(rewrite((((~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))))) | (~(V_m = c_Zorn_Osucc(V_S, V_m, T_a)))) <=> ((~(V_m = c_Zorn_Osucc(V_S, V_m, T_a))) | (~c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))))), (((((~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))))) | (~(V_m = c_Zorn_Osucc(V_S, V_m, T_a)))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a)))) <=> (((~(V_m = c_Zorn_Osucc(V_S, V_m, T_a))) | (~c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a)))))), rewrite((((~(V_m = c_Zorn_Osucc(V_S, V_m, T_a))) | (~c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a)))) <=> (c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | (~(V_m = c_Zorn_Osucc(V_S, V_m, T_a))) | (~c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))))), (((((~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))))) | (~(V_m = c_Zorn_Osucc(V_S, V_m, T_a)))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a)))) <=> (c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | (~(V_m = c_Zorn_Osucc(V_S, V_m, T_a))) | (~c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(106,plain,
% 0.22/0.40 (![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : ((((~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))))) | (~(V_m = c_Zorn_Osucc(V_S, V_m, T_a)))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a)))) <=> ![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | (~(V_m = c_Zorn_Osucc(V_S, V_m, T_a))) | (~c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[105])).
% 0.22/0.40 tff(107,axiom,(![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : ((((~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))))) | (~(V_m = c_Zorn_Osucc(V_S, V_m, T_a)))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Zorn_Oeq__succ__upper_0')).
% 0.22/0.40 tff(108,plain,
% 0.22/0.40 (![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | (~(V_m = c_Zorn_Osucc(V_S, V_m, T_a))) | (~c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.22/0.40 tff(109,plain,
% 0.22/0.40 (![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | (~(V_m = c_Zorn_Osucc(V_S, V_m, T_a))) | (~c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.22/0.41 tff(110,plain,(
% 0.22/0.41 ![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | (~(V_m = c_Zorn_Osucc(V_S, V_m, T_a))) | (~c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))))),
% 0.22/0.41 inference(skolemize,[status(sab)],[109])).
% 0.22/0.41 tff(111,plain,
% 0.22/0.41 (![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | (~(V_m = c_Zorn_Osucc(V_S, V_m, T_a))) | (~c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.22/0.41 tff(112,plain,
% 0.22/0.41 (((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | (~(V_m = c_Zorn_Osucc(V_S, V_m, T_a))) | (~c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_m, 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)))) | c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_Osucc(v_S, v_m, t_a), tc_set(tc_set(t_a))) | (~(c_Zorn_Osucc(v_S, v_m, t_a) = c_Zorn_Osucc(v_S, c_Zorn_Osucc(v_S, v_m, t_a), t_a))) | (~c_in(c_Zorn_Osucc(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))))) <=> ((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | (~(V_m = c_Zorn_Osucc(V_S, V_m, T_a))) | (~c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_m, 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)))) | c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_Osucc(v_S, v_m, t_a), tc_set(tc_set(t_a))) | (~(c_Zorn_Osucc(v_S, v_m, t_a) = c_Zorn_Osucc(v_S, c_Zorn_Osucc(v_S, v_m, t_a), t_a))) | (~c_in(c_Zorn_Osucc(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(113,plain,
% 0.22/0.41 ((c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_Osucc(v_S, v_m, t_a), tc_set(tc_set(t_a))) | (~(c_Zorn_Osucc(v_S, v_m, t_a) = c_Zorn_Osucc(v_S, c_Zorn_Osucc(v_S, v_m, 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_in(c_Zorn_Osucc(v_S, v_m, 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)))) | c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_Osucc(v_S, v_m, t_a), tc_set(tc_set(t_a))) | (~(c_Zorn_Osucc(v_S, v_m, t_a) = c_Zorn_Osucc(v_S, c_Zorn_Osucc(v_S, v_m, t_a), t_a))) | (~c_in(c_Zorn_Osucc(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(114,plain,
% 0.22/0.41 (((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | (~(V_m = c_Zorn_Osucc(V_S, V_m, T_a))) | (~c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))))) | (c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_Osucc(v_S, v_m, t_a), tc_set(tc_set(t_a))) | (~(c_Zorn_Osucc(v_S, v_m, t_a) = c_Zorn_Osucc(v_S, c_Zorn_Osucc(v_S, v_m, 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_in(c_Zorn_Osucc(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))))) <=> ((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | (~(V_m = c_Zorn_Osucc(V_S, V_m, T_a))) | (~c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_m, 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)))) | c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_Osucc(v_S, v_m, t_a), tc_set(tc_set(t_a))) | (~(c_Zorn_Osucc(v_S, v_m, t_a) = c_Zorn_Osucc(v_S, c_Zorn_Osucc(v_S, v_m, t_a), t_a))) | (~c_in(c_Zorn_Osucc(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))))))),
% 0.22/0.41 inference(monotonicity,[status(thm)],[113])).
% 0.22/0.41 tff(115,plain,
% 0.22/0.41 (((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | (~(V_m = c_Zorn_Osucc(V_S, V_m, T_a))) | (~c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))))) | (c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_Osucc(v_S, v_m, t_a), tc_set(tc_set(t_a))) | (~(c_Zorn_Osucc(v_S, v_m, t_a) = c_Zorn_Osucc(v_S, c_Zorn_Osucc(v_S, v_m, 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_in(c_Zorn_Osucc(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))))) <=> ((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | (~(V_m = c_Zorn_Osucc(V_S, V_m, T_a))) | (~c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_m, 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)))) | c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_Osucc(v_S, v_m, t_a), tc_set(tc_set(t_a))) | (~(c_Zorn_Osucc(v_S, v_m, t_a) = c_Zorn_Osucc(v_S, c_Zorn_Osucc(v_S, v_m, t_a), t_a))) | (~c_in(c_Zorn_Osucc(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))))),
% 0.22/0.41 inference(transitivity,[status(thm)],[114, 112])).
% 0.22/0.41 tff(116,plain,
% 0.22/0.41 ((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | (~(V_m = c_Zorn_Osucc(V_S, V_m, T_a))) | (~c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))))) | (c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_Osucc(v_S, v_m, t_a), tc_set(tc_set(t_a))) | (~(c_Zorn_Osucc(v_S, v_m, t_a) = c_Zorn_Osucc(v_S, c_Zorn_Osucc(v_S, v_m, 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_in(c_Zorn_Osucc(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(117,plain,
% 0.22/0.41 ((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | (~(V_m = c_Zorn_Osucc(V_S, V_m, T_a))) | (~c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_m, 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)))) | c_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_Osucc(v_S, v_m, t_a), tc_set(tc_set(t_a))) | (~(c_Zorn_Osucc(v_S, v_m, t_a) = c_Zorn_Osucc(v_S, c_Zorn_Osucc(v_S, v_m, t_a), t_a))) | (~c_in(c_Zorn_Osucc(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.22/0.41 tff(118,plain,
% 0.22/0.41 ((~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_lessequals(c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), c_Zorn_Osucc(v_S, v_m, t_a), tc_set(tc_set(t_a))) | (~(c_Zorn_Osucc(v_S, v_m, t_a) = c_Zorn_Osucc(v_S, c_Zorn_Osucc(v_S, v_m, t_a), t_a))) | (~c_in(c_Zorn_Osucc(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[117, 111])).
% 0.22/0.41 tff(119,plain,
% 0.22/0.41 (~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)))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[118, 101, 80, 78])).
% 0.22/0.41 tff(120,plain,
% 0.22/0.41 (^[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)))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(121,plain,
% 0.22/0.41 (![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))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[120])).
% 0.22/0.41 tff(122,plain,
% 0.22/0.41 (![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))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(123,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')).
% 0.22/0.41 tff(124,plain,
% 0.22/0.41 (![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))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.22/0.41 tff(125,plain,(
% 0.22/0.41 ![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))))),
% 0.22/0.41 inference(skolemize,[status(sab)],[124])).
% 0.22/0.41 tff(126,plain,
% 0.22/0.41 (![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))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[125, 121])).
% 0.22/0.41 tff(127,plain,
% 0.22/0.41 (((~![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))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(128,plain,
% 0.22/0.41 ((~![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))))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(129,plain,
% 0.22/0.41 ((~![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)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.22/0.41 tff(130,plain,
% 0.22/0.41 (~c_lessequals(c_Zorn_OTFin(v_S, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(tc_set(t_a))))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[129, 126, 119])).
% 0.22/0.41 tff(131,plain,
% 0.22/0.41 (^[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)))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(132,plain,
% 0.22/0.42 (![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))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[131])).
% 0.22/0.42 tff(133,plain,
% 0.22/0.42 (![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))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(134,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')).
% 0.22/0.42 tff(135,plain,
% 0.22/0.42 (![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.22/0.42 tff(136,plain,(
% 0.22/0.42 ![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))),
% 0.22/0.42 inference(skolemize,[status(sab)],[135])).
% 0.22/0.42 tff(137,plain,
% 0.22/0.42 (![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.22/0.42 tff(138,plain,
% 0.22/0.42 ((~![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))) | c_lessequals(c_Zorn_OTFin(v_S, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(tc_set(t_a))))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(139,plain,
% 0.22/0.42 ($false),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[138, 137, 130])).
% 0.22/0.42 % SZS output end Proof
% 0.22/0.42 % E exiting
%------------------------------------------------------------------------------