%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET858-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:26:33 AM UTC 2025
% Result : Unsatisfiable 0.23s 0.42s
% Output : Proof 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.15 % Problem : SET858-2 : TPTP v9.0.0. Released v3.2.0.
% 0.04/0.15 % Command : run_E %s %d THM
% 0.16/0.37 % Computer : n015.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Fri Jun 20 05:47:55 EDT 2025
% 0.16/0.37 % CPUTime :
% 0.23/0.42 % SZS status Unsatisfiable
% 0.23/0.42 % SZS output start Proof
% 0.23/0.42 tff(c_in_type, type, (
% 0.23/0.42 c_in: ( $i * $i * $i ) > $o)).
% 0.23/0.42 tff(tc_set_type, type, (
% 0.23/0.42 tc_set: $i > $i)).
% 0.23/0.42 tff(t_a_type, type, (
% 0.23/0.42 t_a: $i)).
% 0.23/0.42 tff(c_Zorn_OTFin_type, type, (
% 0.23/0.42 c_Zorn_OTFin: ( $i * $i ) > $i)).
% 0.23/0.42 tff(v_S_type, type, (
% 0.23/0.42 v_S: $i)).
% 0.23/0.42 tff(c_Zorn_OTFin__linear__lemma1__1_type, type, (
% 0.23/0.42 c_Zorn_OTFin__linear__lemma1__1: ( $i * $i * $i ) > $i)).
% 0.23/0.42 tff(v_m_type, type, (
% 0.23/0.42 v_m: $i)).
% 0.23/0.42 tff(c_lessequals_type, type, (
% 0.23/0.42 c_lessequals: ( $i * $i * $i ) > $o)).
% 0.23/0.42 tff(v_n_type, type, (
% 0.23/0.42 v_n: $i)).
% 0.23/0.42 tff(c_Zorn_Osucc_type, type, (
% 0.23/0.42 c_Zorn_Osucc: ( $i * $i * $i ) > $i)).
% 0.23/0.42 tff(1,plain,
% 0.23/0.42 (^[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))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(2,plain,
% 0.23/0.42 (![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)))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.23/0.42 tff(3,plain,
% 0.23/0.42 (![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)))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(4,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')).
% 0.23/0.42 tff(5,plain,
% 0.23/0.42 (![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)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.23/0.42 tff(6,plain,(
% 0.23/0.42 ![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)))),
% 0.23/0.42 inference(skolemize,[status(sab)],[5])).
% 0.23/0.42 tff(7,plain,
% 0.23/0.42 (![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)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.23/0.42 tff(8,plain,
% 0.23/0.42 ((~![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(v_m, c_Zorn_Osucc(v_S, v_m, t_a), tc_set(tc_set(t_a)))),
% 0.23/0.42 inference(quant_inst,[status(thm)],[])).
% 0.23/0.42 tff(9,plain,
% 0.23/0.42 (c_lessequals(v_m, c_Zorn_Osucc(v_S, v_m, t_a), tc_set(tc_set(t_a)))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.23/0.42 tff(10,assumption,(c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a)))), introduced(assumption)).
% 0.23/0.42 tff(11,plain,
% 0.23/0.42 (^[T_a: $i, V_B: $i, V_A: $i, V_C: $i] : refl((c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a)))) <=> (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a)))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(12,plain,
% 0.23/0.42 (![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a)))) <=> ![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[11])).
% 0.23/0.42 tff(13,plain,
% 0.23/0.42 (![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a)))) <=> ![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(14,plain,
% 0.23/0.42 (^[T_a: $i, V_B: $i, V_A: $i, V_C: $i] : trans(monotonicity(rewrite(((~c_lessequals(V_B, V_C, 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_C, tc_set(T_a))))), ((((~c_lessequals(V_B, V_C, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(V_A, V_C, tc_set(T_a))) <=> (((~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a)))) | c_lessequals(V_A, V_C, tc_set(T_a))))), rewrite((((~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a)))) | c_lessequals(V_A, V_C, tc_set(T_a))) <=> (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))), ((((~c_lessequals(V_B, V_C, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(V_A, V_C, tc_set(T_a))) <=> (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(15,plain,
% 0.23/0.42 (![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (((~c_lessequals(V_B, V_C, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(V_A, V_C, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[14])).
% 0.23/0.42 tff(16,axiom,(![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (((~c_lessequals(V_B, V_C, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(V_A, V_C, tc_set(T_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_Osubset__trans_0')).
% 0.23/0.42 tff(17,plain,
% 0.23/0.42 (![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.23/0.42 tff(18,plain,
% 0.23/0.42 (![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.23/0.42 tff(19,plain,(
% 0.23/0.42 ![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))),
% 0.23/0.42 inference(skolemize,[status(sab)],[18])).
% 0.23/0.42 tff(20,plain,
% 0.23/0.42 (![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.23/0.42 tff(21,plain,
% 0.23/0.42 ((~c_lessequals(v_m, v_n, tc_set(tc_set(t_a)))) <=> (~c_lessequals(v_m, v_n, tc_set(tc_set(t_a))))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(22,axiom,(~c_lessequals(v_m, v_n, tc_set(tc_set(t_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_3')).
% 0.23/0.42 tff(23,plain,
% 0.23/0.42 (~c_lessequals(v_m, v_n, tc_set(tc_set(t_a)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.23/0.42 tff(24,plain,
% 0.23/0.42 (((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))) | (c_lessequals(v_m, v_n, tc_set(tc_set(t_a))) | (~c_lessequals(v_m, 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), v_n, tc_set(tc_set(t_a)))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))) | c_lessequals(v_m, v_n, tc_set(tc_set(t_a))) | (~c_lessequals(v_m, 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), v_n, tc_set(tc_set(t_a)))))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(25,plain,
% 0.23/0.42 ((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))) | (c_lessequals(v_m, v_n, tc_set(tc_set(t_a))) | (~c_lessequals(v_m, 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), v_n, tc_set(tc_set(t_a)))))),
% 0.23/0.42 inference(quant_inst,[status(thm)],[])).
% 0.23/0.42 tff(26,plain,
% 0.23/0.42 ((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))) | c_lessequals(v_m, v_n, tc_set(tc_set(t_a))) | (~c_lessequals(v_m, c_Zorn_Osucc(v_S, v_m, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.23/0.42 tff(27,plain,
% 0.23/0.42 ($false),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[26, 23, 20, 10, 9])).
% 0.23/0.42 tff(28,plain,(~c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a)))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.42 tff(29,plain,
% 0.23/0.42 (^[V_n: $i, V_S: $i, T_a: $i, V_m: $i] : refl((c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))))) <=> (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(30,plain,
% 0.23/0.42 (![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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)))) | (~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(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[29])).
% 0.23/0.42 tff(31,plain,
% 0.23/0.42 (![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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)))) | (~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(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(32,plain,
% 0.23/0.42 (^[V_n: $i, V_S: $i, T_a: $i, V_m: $i] : trans(monotonicity(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))))) | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) <=> (c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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)))) | (~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))))) | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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)))) | (~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(((c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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)))) | (~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))) | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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)))) | (~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))))) | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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))) | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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)))) | (~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))))) | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a)))) <=> ((c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))))) | c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a)))))), rewrite(((c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))))) | c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a)))) <=> (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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)))) | (~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))))) | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a)))) <=> (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(33,plain,
% 0.23/0.42 (![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))))) | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a)))) <=> ![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[32])).
% 0.23/0.42 tff(34,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))))) | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Zorn_OTFin__linear__lemma1_0')).
% 0.23/0.42 tff(35,plain,
% 0.23/0.42 (![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.23/0.42 tff(36,plain,
% 0.23/0.42 (![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.23/0.42 tff(37,plain,(
% 0.23/0.42 ![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))))),
% 0.23/0.42 inference(skolemize,[status(sab)],[36])).
% 0.23/0.42 tff(38,plain,
% 0.23/0.42 (![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.23/0.42 tff(39,plain,
% 0.23/0.42 ((~c_lessequals(v_n, v_m, tc_set(tc_set(t_a)))) <=> (~c_lessequals(v_n, v_m, tc_set(tc_set(t_a))))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(40,axiom,(~c_lessequals(v_n, v_m, tc_set(tc_set(t_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_2')).
% 0.23/0.42 tff(41,plain,
% 0.23/0.42 (~c_lessequals(v_n, v_m, tc_set(tc_set(t_a)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.23/0.42 tff(42,plain,
% 0.23/0.42 (c_in(v_n, 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)))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(43,axiom,(c_in(v_n, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_1')).
% 0.23/0.42 tff(44,plain,
% 0.23/0.42 (c_in(v_n, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.23/0.42 tff(45,plain,
% 0.23/0.42 (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)))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(46,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')).
% 0.23/0.42 tff(47,plain,
% 0.23/0.42 (c_in(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.23/0.42 tff(48,plain,
% 0.23/0.42 (((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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)))) | (~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_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_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(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(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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)))) | (~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_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_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(49,plain,
% 0.23/0.43 ((c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))) | c_lessequals(v_n, v_m, tc_set(tc_set(t_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), 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)))) | (~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_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_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(50,plain,
% 0.23/0.43 (((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))))) | (c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))) | c_lessequals(v_n, v_m, tc_set(tc_set(t_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), 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)))) | (~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(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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)))) | (~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_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_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))))),
% 0.23/0.43 inference(monotonicity,[status(thm)],[49])).
% 0.23/0.43 tff(51,plain,
% 0.23/0.43 (((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))))) | (c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))) | c_lessequals(v_n, v_m, tc_set(tc_set(t_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), 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)))) | (~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(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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)))) | (~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_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_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))))),
% 0.23/0.43 inference(transitivity,[status(thm)],[50, 48])).
% 0.23/0.43 tff(52,plain,
% 0.23/0.43 ((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))))) | (c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))) | c_lessequals(v_n, v_m, tc_set(tc_set(t_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), 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)))) | (~c_in(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))))),
% 0.23/0.43 inference(quant_inst,[status(thm)],[])).
% 0.23/0.43 tff(53,plain,
% 0.23/0.43 ((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), 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)))) | (~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_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_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.23/0.43 tff(54,plain,
% 0.23/0.43 (c_in(c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[53, 47, 44, 41, 38, 28])).
% 0.23/0.43 tff(55,plain,
% 0.23/0.43 (^[V_n: $i, V_S: $i, T_a: $i, V_m: $i] : refl((c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m))) <=> (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(56,plain,
% 0.23/0.43 (![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m))) <=> ![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m)))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[55])).
% 0.23/0.43 tff(57,plain,
% 0.23/0.43 (![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m))) <=> ![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m)))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(58,plain,
% 0.23/0.43 (^[V_n: $i, V_S: $i, T_a: $i, V_m: $i] : trans(monotonicity(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))))) | (~(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m))) <=> ((~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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m)))), (((((~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))))) | (~(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a)))))), rewrite((((~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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a)))) <=> (c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m)))), (((((~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))))) | (~(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a)))) <=> (c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m))))), ((((((~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))))) | (~(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a)))) | c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a)))) <=> ((c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m))) | c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a)))))), rewrite(((c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m))) | c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a)))) <=> (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m)))), ((((((~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))))) | (~(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a)))) | c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a)))) <=> (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m)))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(59,plain,
% 0.23/0.43 (![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))))) | (~(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a)))) | c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a)))) <=> ![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m)))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[58])).
% 0.23/0.43 tff(60,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))))) | (~(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a)))) | c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Zorn_OTFin__linear__lemma1_2')).
% 0.23/0.43 tff(61,plain,
% 0.23/0.43 (![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.23/0.43 tff(62,plain,
% 0.23/0.43 (![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.23/0.43 tff(63,plain,(
% 0.23/0.43 ![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m)))),
% 0.23/0.43 inference(skolemize,[status(sab)],[62])).
% 0.23/0.43 tff(64,plain,
% 0.23/0.43 (![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.23/0.43 tff(65,plain,
% 0.23/0.43 (((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m)))) | (c_lessequals(v_n, v_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a) = v_m)) | c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))))) <=> ((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m)))) | c_lessequals(v_n, v_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a) = v_m)) | c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(66,plain,
% 0.23/0.43 ((c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))) | c_lessequals(v_n, v_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a) = v_m))) <=> (c_lessequals(v_n, v_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a) = v_m)) | c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(67,plain,
% 0.23/0.43 (((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m)))) | (c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))) | c_lessequals(v_n, v_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a) = v_m)))) <=> ((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m)))) | (c_lessequals(v_n, v_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a) = v_m)) | c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a)))))),
% 0.23/0.43 inference(monotonicity,[status(thm)],[66])).
% 0.23/0.43 tff(68,plain,
% 0.23/0.43 (((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m)))) | (c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))) | c_lessequals(v_n, v_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a) = v_m)))) <=> ((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m)))) | c_lessequals(v_n, v_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a) = v_m)) | c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))))),
% 0.23/0.43 inference(transitivity,[status(thm)],[67, 65])).
% 0.23/0.43 tff(69,plain,
% 0.23/0.43 ((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m)))) | (c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))) | c_lessequals(v_n, v_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a) = v_m)))),
% 0.23/0.43 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(70,plain,
% 0.23/0.44 ((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a) = V_m)))) | c_lessequals(v_n, v_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a) = v_m)) | c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.23/0.44 tff(71,plain,
% 0.23/0.44 (~(c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a) = v_m)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[70, 47, 44, 41, 64, 28])).
% 0.23/0.44 tff(72,plain,
% 0.23/0.44 (^[V_n: $i, V_S: $i, T_a: $i, V_m: $i] : refl((c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, tc_set(tc_set(T_a))))) <=> (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, tc_set(tc_set(T_a))))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(73,plain,
% 0.23/0.44 (![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, tc_set(tc_set(T_a))))) <=> ![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, tc_set(tc_set(T_a)))))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[72])).
% 0.23/0.44 tff(74,plain,
% 0.23/0.44 (![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, tc_set(tc_set(T_a))))) <=> ![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, tc_set(tc_set(T_a)))))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(75,plain,
% 0.23/0.44 (^[V_n: $i, V_S: $i, T_a: $i, V_m: $i] : trans(monotonicity(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))))) | (~c_lessequals(c_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, tc_set(tc_set(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_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, 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))))) | (~c_lessequals(c_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, tc_set(tc_set(T_a))))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, tc_set(tc_set(T_a))))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a)))))), rewrite((((~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_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, 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))) | (~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_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, 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))))) | (~c_lessequals(c_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, 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))) | (~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_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, 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))))) | (~c_lessequals(c_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, tc_set(tc_set(T_a))))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a)))) | c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a)))) <=> ((c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, tc_set(tc_set(T_a))))) | c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a)))))), rewrite(((c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, tc_set(tc_set(T_a))))) | c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a)))) <=> (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, 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))))) | (~c_lessequals(c_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, tc_set(tc_set(T_a))))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a)))) | c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a)))) <=> (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, tc_set(tc_set(T_a)))))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(76,plain,
% 0.23/0.44 (![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))))) | (~c_lessequals(c_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, tc_set(tc_set(T_a))))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a)))) | c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a)))) <=> ![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, tc_set(tc_set(T_a)))))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[75])).
% 0.23/0.44 tff(77,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))))) | (~c_lessequals(c_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, tc_set(tc_set(T_a))))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a)))) | c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Zorn_OTFin__linear__lemma1_3')).
% 0.23/0.44 tff(78,plain,
% 0.23/0.44 (![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, tc_set(tc_set(T_a)))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.23/0.44 tff(79,plain,
% 0.23/0.44 (![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, tc_set(tc_set(T_a)))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.23/0.44 tff(80,plain,(
% 0.23/0.44 ![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, tc_set(tc_set(T_a)))))),
% 0.23/0.44 inference(skolemize,[status(sab)],[79])).
% 0.23/0.44 tff(81,plain,
% 0.23/0.44 (![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, tc_set(tc_set(T_a)))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.23/0.44 tff(82,plain,
% 0.23/0.44 (((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, tc_set(tc_set(T_a)))))) | (c_lessequals(v_n, v_m, tc_set(tc_set(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_Zorn_Osucc(v_S, c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), t_a), v_m, tc_set(tc_set(t_a)))) | c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))))) <=> ((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, tc_set(tc_set(T_a)))))) | c_lessequals(v_n, v_m, tc_set(tc_set(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_Zorn_Osucc(v_S, c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), t_a), v_m, tc_set(tc_set(t_a)))) | c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(83,plain,
% 0.23/0.44 ((c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))) | c_lessequals(v_n, v_m, tc_set(tc_set(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_Zorn_Osucc(v_S, c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), t_a), v_m, tc_set(tc_set(t_a))))) <=> (c_lessequals(v_n, v_m, tc_set(tc_set(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_Zorn_Osucc(v_S, c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), t_a), v_m, tc_set(tc_set(t_a)))) | c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(84,plain,
% 0.23/0.44 (((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, tc_set(tc_set(T_a)))))) | (c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))) | c_lessequals(v_n, v_m, tc_set(tc_set(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_Zorn_Osucc(v_S, c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), t_a), v_m, tc_set(tc_set(t_a)))))) <=> ((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, tc_set(tc_set(T_a)))))) | (c_lessequals(v_n, v_m, tc_set(tc_set(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_Zorn_Osucc(v_S, c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), t_a), v_m, tc_set(tc_set(t_a)))) | c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a)))))),
% 0.23/0.44 inference(monotonicity,[status(thm)],[83])).
% 0.23/0.44 tff(85,plain,
% 0.23/0.44 (((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, tc_set(tc_set(T_a)))))) | (c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))) | c_lessequals(v_n, v_m, tc_set(tc_set(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_Zorn_Osucc(v_S, c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), t_a), v_m, tc_set(tc_set(t_a)))))) <=> ((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, tc_set(tc_set(T_a)))))) | c_lessequals(v_n, v_m, tc_set(tc_set(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_Zorn_Osucc(v_S, c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), t_a), v_m, tc_set(tc_set(t_a)))) | c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))))),
% 0.23/0.45 inference(transitivity,[status(thm)],[84, 82])).
% 0.23/0.45 tff(86,plain,
% 0.23/0.45 ((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, tc_set(tc_set(T_a)))))) | (c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))) | c_lessequals(v_n, v_m, tc_set(tc_set(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_Zorn_Osucc(v_S, c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), t_a), v_m, tc_set(tc_set(t_a)))))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(87,plain,
% 0.23/0.45 ((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_Osucc(V_S, c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), T_a), V_m, tc_set(tc_set(T_a)))))) | c_lessequals(v_n, v_m, tc_set(tc_set(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_Zorn_Osucc(v_S, c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), t_a), v_m, tc_set(tc_set(t_a)))) | c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.23/0.45 tff(88,plain,
% 0.23/0.45 (~c_lessequals(c_Zorn_Osucc(v_S, c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), t_a), v_m, tc_set(tc_set(t_a)))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[87, 47, 44, 41, 81, 28])).
% 0.23/0.45 tff(89,plain,
% 0.23/0.45 (^[V_n: $i, V_S: $i, T_a: $i, V_m: $i] : refl((c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), V_m, tc_set(tc_set(T_a)))) <=> (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), V_m, tc_set(tc_set(T_a)))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(90,plain,
% 0.23/0.45 (![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), V_m, tc_set(tc_set(T_a)))) <=> ![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), V_m, tc_set(tc_set(T_a))))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[89])).
% 0.23/0.45 tff(91,plain,
% 0.23/0.45 (![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), V_m, tc_set(tc_set(T_a)))) <=> ![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), V_m, tc_set(tc_set(T_a))))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(92,plain,
% 0.23/0.45 (^[V_n: $i, V_S: $i, T_a: $i, V_m: $i] : trans(monotonicity(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))))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a)))) <=> (c_lessequals(V_n, V_m, tc_set(tc_set(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))))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a)))) | c_lessequals(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), V_m, tc_set(tc_set(T_a)))) <=> ((c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), V_m, tc_set(tc_set(T_a)))))), rewrite(((c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), V_m, tc_set(tc_set(T_a)))) <=> (c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), V_m, 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))))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a)))) | c_lessequals(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), V_m, tc_set(tc_set(T_a)))) <=> (c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), V_m, 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))))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a)))) | c_lessequals(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), V_m, tc_set(tc_set(T_a)))) | c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a)))) <=> ((c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), V_m, tc_set(tc_set(T_a)))) | c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a)))))), rewrite(((c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), V_m, tc_set(tc_set(T_a)))) | c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a)))) <=> (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), V_m, 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))))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a)))) | c_lessequals(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), V_m, tc_set(tc_set(T_a)))) | c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a)))) <=> (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), V_m, tc_set(tc_set(T_a))))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(93,plain,
% 0.23/0.45 (![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))))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a)))) | c_lessequals(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), V_m, tc_set(tc_set(T_a)))) | c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a)))) <=> ![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), V_m, tc_set(tc_set(T_a))))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[92])).
% 0.23/0.45 tff(94,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))))) | c_lessequals(V_n, V_m, tc_set(tc_set(T_a)))) | c_lessequals(c_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), V_m, tc_set(tc_set(T_a)))) | c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Zorn_OTFin__linear__lemma1_1')).
% 0.23/0.45 tff(95,plain,
% 0.23/0.45 (![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), V_m, tc_set(tc_set(T_a))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.23/0.45 tff(96,plain,
% 0.23/0.45 (![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), V_m, tc_set(tc_set(T_a))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.23/0.45 tff(97,plain,(
% 0.23/0.45 ![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), V_m, tc_set(tc_set(T_a))))),
% 0.23/0.45 inference(skolemize,[status(sab)],[96])).
% 0.23/0.45 tff(98,plain,
% 0.23/0.45 (![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), V_m, tc_set(tc_set(T_a))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.23/0.45 tff(99,plain,
% 0.23/0.45 (((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), V_m, tc_set(tc_set(T_a))))) | (c_lessequals(v_n, v_m, tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), v_m, tc_set(tc_set(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_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))))) <=> ((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), V_m, tc_set(tc_set(T_a))))) | c_lessequals(v_n, v_m, tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), v_m, tc_set(tc_set(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_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(100,plain,
% 0.23/0.45 ((c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))) | c_lessequals(v_n, v_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), v_m, tc_set(tc_set(t_a)))) <=> (c_lessequals(v_n, v_m, tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), v_m, tc_set(tc_set(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_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(101,plain,
% 0.23/0.45 (((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), V_m, tc_set(tc_set(T_a))))) | (c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))) | c_lessequals(v_n, v_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), v_m, tc_set(tc_set(t_a))))) <=> ((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), V_m, tc_set(tc_set(T_a))))) | (c_lessequals(v_n, v_m, tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), v_m, tc_set(tc_set(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_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a)))))),
% 0.23/0.45 inference(monotonicity,[status(thm)],[100])).
% 0.23/0.45 tff(102,plain,
% 0.23/0.45 (((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), V_m, tc_set(tc_set(T_a))))) | (c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))) | c_lessequals(v_n, v_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), v_m, tc_set(tc_set(t_a))))) <=> ((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), V_m, tc_set(tc_set(T_a))))) | c_lessequals(v_n, v_m, tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), v_m, tc_set(tc_set(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_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))))),
% 0.23/0.45 inference(transitivity,[status(thm)],[101, 99])).
% 0.23/0.45 tff(103,plain,
% 0.23/0.45 ((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), V_m, tc_set(tc_set(T_a))))) | (c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a))) | c_lessequals(v_n, v_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), v_m, tc_set(tc_set(t_a))))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(104,plain,
% 0.23/0.45 ((~![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (c_lessequals(c_Zorn_Osucc(V_S, V_m, T_a), V_n, tc_set(tc_set(T_a))) | c_lessequals(V_n, V_m, tc_set(tc_set(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_Zorn_OTFin__linear__lemma1__1(V_S, V_m, T_a), V_m, tc_set(tc_set(T_a))))) | c_lessequals(v_n, v_m, tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), v_m, tc_set(tc_set(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_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.23/0.45 tff(105,plain,
% 0.23/0.45 (c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), v_m, tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S, v_m, t_a), v_n, tc_set(tc_set(t_a)))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[104, 47, 44, 41, 98])).
% 0.23/0.45 tff(106,plain,
% 0.23/0.45 (c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), v_m, tc_set(tc_set(t_a)))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[105, 28])).
% 0.23/0.45 tff(107,plain,
% 0.23/0.45 (^[V_U: $i, V_S: $i, T_a: $i, V_m: $i] : refl(((V_U = V_m) | (~c_in(V_U, 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_Zorn_Osucc(V_S, V_U, T_a), V_m, tc_set(tc_set(T_a))) | (~c_lessequals(V_U, V_m, tc_set(tc_set(T_a))))) <=> ((V_U = V_m) | (~c_in(V_U, 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_Zorn_Osucc(V_S, V_U, T_a), V_m, tc_set(tc_set(T_a))) | (~c_lessequals(V_U, V_m, tc_set(tc_set(T_a))))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(108,plain,
% 0.23/0.45 (![V_U: $i, V_S: $i, T_a: $i, V_m: $i] : ((V_U = V_m) | (~c_in(V_U, 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_Zorn_Osucc(V_S, V_U, T_a), V_m, tc_set(tc_set(T_a))) | (~c_lessequals(V_U, V_m, tc_set(tc_set(T_a))))) <=> ![V_U: $i, V_S: $i, T_a: $i, V_m: $i] : ((V_U = V_m) | (~c_in(V_U, 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_Zorn_Osucc(V_S, V_U, T_a), V_m, tc_set(tc_set(T_a))) | (~c_lessequals(V_U, V_m, tc_set(tc_set(T_a)))))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[107])).
% 0.23/0.45 tff(109,plain,
% 0.23/0.45 (![V_U: $i, V_S: $i, T_a: $i, V_m: $i] : ((V_U = V_m) | (~c_in(V_U, 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_Zorn_Osucc(V_S, V_U, T_a), V_m, tc_set(tc_set(T_a))) | (~c_lessequals(V_U, V_m, tc_set(tc_set(T_a))))) <=> ![V_U: $i, V_S: $i, T_a: $i, V_m: $i] : ((V_U = V_m) | (~c_in(V_U, 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_Zorn_Osucc(V_S, V_U, T_a), V_m, tc_set(tc_set(T_a))) | (~c_lessequals(V_U, V_m, tc_set(tc_set(T_a)))))),
% 0.24/0.45 inference(rewrite,[status(thm)],[])).
% 0.24/0.45 tff(110,plain,
% 0.24/0.45 (^[V_U: $i, V_S: $i, T_a: $i, V_m: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c_in(V_U, 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_U, 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_U, 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_U, V_m, tc_set(tc_set(T_a))))) <=> (((~c_in(V_U, 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_U, V_m, tc_set(tc_set(T_a))))))), rewrite((((~c_in(V_U, 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_U, V_m, tc_set(tc_set(T_a))))) <=> ((~c_in(V_U, 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_U, V_m, tc_set(tc_set(T_a)))))), ((((~c_in(V_U, 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_U, V_m, tc_set(tc_set(T_a))))) <=> ((~c_in(V_U, 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_U, V_m, tc_set(tc_set(T_a))))))), (((((~c_in(V_U, 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_U, V_m, tc_set(tc_set(T_a))))) | c_lessequals(c_Zorn_Osucc(V_S, V_U, T_a), V_m, tc_set(tc_set(T_a)))) <=> (((~c_in(V_U, 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_U, V_m, tc_set(tc_set(T_a))))) | c_lessequals(c_Zorn_Osucc(V_S, V_U, T_a), V_m, tc_set(tc_set(T_a)))))), rewrite((((~c_in(V_U, 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_U, V_m, tc_set(tc_set(T_a))))) | c_lessequals(c_Zorn_Osucc(V_S, V_U, T_a), V_m, tc_set(tc_set(T_a)))) <=> ((~c_in(V_U, 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_Zorn_Osucc(V_S, V_U, T_a), V_m, tc_set(tc_set(T_a))) | (~c_lessequals(V_U, V_m, tc_set(tc_set(T_a)))))), (((((~c_in(V_U, 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_U, V_m, tc_set(tc_set(T_a))))) | c_lessequals(c_Zorn_Osucc(V_S, V_U, T_a), V_m, tc_set(tc_set(T_a)))) <=> ((~c_in(V_U, 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_Zorn_Osucc(V_S, V_U, T_a), V_m, tc_set(tc_set(T_a))) | (~c_lessequals(V_U, V_m, tc_set(tc_set(T_a))))))), ((((((~c_in(V_U, 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_U, V_m, tc_set(tc_set(T_a))))) | c_lessequals(c_Zorn_Osucc(V_S, V_U, T_a), V_m, tc_set(tc_set(T_a)))) | (V_U = V_m)) <=> (((~c_in(V_U, 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_Zorn_Osucc(V_S, V_U, T_a), V_m, tc_set(tc_set(T_a))) | (~c_lessequals(V_U, V_m, tc_set(tc_set(T_a))))) | (V_U = V_m)))), rewrite((((~c_in(V_U, 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_Zorn_Osucc(V_S, V_U, T_a), V_m, tc_set(tc_set(T_a))) | (~c_lessequals(V_U, V_m, tc_set(tc_set(T_a))))) | (V_U = V_m)) <=> ((V_U = V_m) | (~c_in(V_U, 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_Zorn_Osucc(V_S, V_U, T_a), V_m, tc_set(tc_set(T_a))) | (~c_lessequals(V_U, V_m, tc_set(tc_set(T_a)))))), ((((((~c_in(V_U, 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_U, V_m, tc_set(tc_set(T_a))))) | c_lessequals(c_Zorn_Osucc(V_S, V_U, T_a), V_m, tc_set(tc_set(T_a)))) | (V_U = V_m)) <=> ((V_U = V_m) | (~c_in(V_U, 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_Zorn_Osucc(V_S, V_U, T_a), V_m, tc_set(tc_set(T_a))) | (~c_lessequals(V_U, V_m, tc_set(tc_set(T_a)))))))),
% 0.24/0.46 inference(bind,[status(th)],[])).
% 0.24/0.46 tff(111,plain,
% 0.24/0.46 (![V_U: $i, V_S: $i, T_a: $i, V_m: $i] : (((((~c_in(V_U, 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_U, V_m, tc_set(tc_set(T_a))))) | c_lessequals(c_Zorn_Osucc(V_S, V_U, T_a), V_m, tc_set(tc_set(T_a)))) | (V_U = V_m)) <=> ![V_U: $i, V_S: $i, T_a: $i, V_m: $i] : ((V_U = V_m) | (~c_in(V_U, 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_Zorn_Osucc(V_S, V_U, T_a), V_m, tc_set(tc_set(T_a))) | (~c_lessequals(V_U, V_m, tc_set(tc_set(T_a)))))),
% 0.24/0.46 inference(quant_intro,[status(thm)],[110])).
% 0.24/0.46 tff(112,axiom,(![V_U: $i, V_S: $i, T_a: $i, V_m: $i] : (((((~c_in(V_U, 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_U, V_m, tc_set(tc_set(T_a))))) | c_lessequals(c_Zorn_Osucc(V_S, V_U, T_a), V_m, tc_set(tc_set(T_a)))) | (V_U = V_m))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Zorn_OTFin__linear__lemma2_0')).
% 0.24/0.46 tff(113,plain,
% 0.24/0.46 (![V_U: $i, V_S: $i, T_a: $i, V_m: $i] : ((V_U = V_m) | (~c_in(V_U, 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_Zorn_Osucc(V_S, V_U, T_a), V_m, tc_set(tc_set(T_a))) | (~c_lessequals(V_U, V_m, tc_set(tc_set(T_a)))))),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.24/0.46 tff(114,plain,
% 0.24/0.46 (![V_U: $i, V_S: $i, T_a: $i, V_m: $i] : ((V_U = V_m) | (~c_in(V_U, 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_Zorn_Osucc(V_S, V_U, T_a), V_m, tc_set(tc_set(T_a))) | (~c_lessequals(V_U, V_m, tc_set(tc_set(T_a)))))),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.24/0.46 tff(115,plain,(
% 0.24/0.46 ![V_U: $i, V_S: $i, T_a: $i, V_m: $i] : ((V_U = V_m) | (~c_in(V_U, 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_Zorn_Osucc(V_S, V_U, T_a), V_m, tc_set(tc_set(T_a))) | (~c_lessequals(V_U, V_m, tc_set(tc_set(T_a)))))),
% 0.24/0.46 inference(skolemize,[status(sab)],[114])).
% 0.24/0.46 tff(116,plain,
% 0.24/0.46 (![V_U: $i, V_S: $i, T_a: $i, V_m: $i] : ((V_U = V_m) | (~c_in(V_U, 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_Zorn_Osucc(V_S, V_U, T_a), V_m, tc_set(tc_set(T_a))) | (~c_lessequals(V_U, V_m, tc_set(tc_set(T_a)))))),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[115, 108])).
% 0.24/0.46 tff(117,plain,
% 0.24/0.46 (((~![V_U: $i, V_S: $i, T_a: $i, V_m: $i] : ((V_U = V_m) | (~c_in(V_U, 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_Zorn_Osucc(V_S, V_U, T_a), V_m, tc_set(tc_set(T_a))) | (~c_lessequals(V_U, V_m, tc_set(tc_set(T_a)))))) | ((~c_in(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a) = v_m) | (~c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), v_m, tc_set(tc_set(t_a)))) | (~c_in(c_Zorn_OTFin__linear__lemma1__1(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, c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), t_a), v_m, tc_set(tc_set(t_a))))) <=> ((~![V_U: $i, V_S: $i, T_a: $i, V_m: $i] : ((V_U = V_m) | (~c_in(V_U, 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_Zorn_Osucc(V_S, V_U, T_a), V_m, tc_set(tc_set(T_a))) | (~c_lessequals(V_U, V_m, tc_set(tc_set(T_a)))))) | (~c_in(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a) = v_m) | (~c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), v_m, tc_set(tc_set(t_a)))) | (~c_in(c_Zorn_OTFin__linear__lemma1__1(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, c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), t_a), v_m, tc_set(tc_set(t_a))))),
% 0.24/0.46 inference(rewrite,[status(thm)],[])).
% 0.24/0.46 tff(118,plain,
% 0.24/0.46 (((c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a) = v_m) | (~c_in(c_Zorn_OTFin__linear__lemma1__1(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)))) | c_lessequals(c_Zorn_Osucc(v_S, c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), t_a), v_m, tc_set(tc_set(t_a))) | (~c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), v_m, tc_set(tc_set(t_a))))) <=> ((~c_in(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a) = v_m) | (~c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), v_m, tc_set(tc_set(t_a)))) | (~c_in(c_Zorn_OTFin__linear__lemma1__1(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, c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), t_a), v_m, tc_set(tc_set(t_a))))),
% 0.24/0.46 inference(rewrite,[status(thm)],[])).
% 0.24/0.46 tff(119,plain,
% 0.24/0.46 (((~![V_U: $i, V_S: $i, T_a: $i, V_m: $i] : ((V_U = V_m) | (~c_in(V_U, 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_Zorn_Osucc(V_S, V_U, T_a), V_m, tc_set(tc_set(T_a))) | (~c_lessequals(V_U, V_m, tc_set(tc_set(T_a)))))) | ((c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a) = v_m) | (~c_in(c_Zorn_OTFin__linear__lemma1__1(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)))) | c_lessequals(c_Zorn_Osucc(v_S, c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), t_a), v_m, tc_set(tc_set(t_a))) | (~c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), v_m, tc_set(tc_set(t_a)))))) <=> ((~![V_U: $i, V_S: $i, T_a: $i, V_m: $i] : ((V_U = V_m) | (~c_in(V_U, 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_Zorn_Osucc(V_S, V_U, T_a), V_m, tc_set(tc_set(T_a))) | (~c_lessequals(V_U, V_m, tc_set(tc_set(T_a)))))) | ((~c_in(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a) = v_m) | (~c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), v_m, tc_set(tc_set(t_a)))) | (~c_in(c_Zorn_OTFin__linear__lemma1__1(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, c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), t_a), v_m, tc_set(tc_set(t_a)))))),
% 0.24/0.46 inference(monotonicity,[status(thm)],[118])).
% 0.24/0.46 tff(120,plain,
% 0.24/0.46 (((~![V_U: $i, V_S: $i, T_a: $i, V_m: $i] : ((V_U = V_m) | (~c_in(V_U, 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_Zorn_Osucc(V_S, V_U, T_a), V_m, tc_set(tc_set(T_a))) | (~c_lessequals(V_U, V_m, tc_set(tc_set(T_a)))))) | ((c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a) = v_m) | (~c_in(c_Zorn_OTFin__linear__lemma1__1(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)))) | c_lessequals(c_Zorn_Osucc(v_S, c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), t_a), v_m, tc_set(tc_set(t_a))) | (~c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), v_m, tc_set(tc_set(t_a)))))) <=> ((~![V_U: $i, V_S: $i, T_a: $i, V_m: $i] : ((V_U = V_m) | (~c_in(V_U, 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_Zorn_Osucc(V_S, V_U, T_a), V_m, tc_set(tc_set(T_a))) | (~c_lessequals(V_U, V_m, tc_set(tc_set(T_a)))))) | (~c_in(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a) = v_m) | (~c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), v_m, tc_set(tc_set(t_a)))) | (~c_in(c_Zorn_OTFin__linear__lemma1__1(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, c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), t_a), v_m, tc_set(tc_set(t_a))))),
% 0.24/0.46 inference(transitivity,[status(thm)],[119, 117])).
% 0.24/0.46 tff(121,plain,
% 0.24/0.46 ((~![V_U: $i, V_S: $i, T_a: $i, V_m: $i] : ((V_U = V_m) | (~c_in(V_U, 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_Zorn_Osucc(V_S, V_U, T_a), V_m, tc_set(tc_set(T_a))) | (~c_lessequals(V_U, V_m, tc_set(tc_set(T_a)))))) | ((c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a) = v_m) | (~c_in(c_Zorn_OTFin__linear__lemma1__1(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)))) | c_lessequals(c_Zorn_Osucc(v_S, c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), t_a), v_m, tc_set(tc_set(t_a))) | (~c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), v_m, tc_set(tc_set(t_a)))))),
% 0.24/0.46 inference(quant_inst,[status(thm)],[])).
% 0.24/0.46 tff(122,plain,
% 0.24/0.46 ((~![V_U: $i, V_S: $i, T_a: $i, V_m: $i] : ((V_U = V_m) | (~c_in(V_U, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | c_lessequals(c_Zorn_Osucc(V_S, V_U, T_a), V_m, tc_set(tc_set(T_a))) | (~c_lessequals(V_U, V_m, tc_set(tc_set(T_a)))))) | (~c_in(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a) = v_m) | (~c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), v_m, tc_set(tc_set(t_a)))) | (~c_in(c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(c_Zorn_Osucc(v_S, c_Zorn_OTFin__linear__lemma1__1(v_S, v_m, t_a), t_a), v_m, tc_set(tc_set(t_a)))),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.24/0.46 tff(123,plain,
% 0.24/0.46 ($false),
% 0.24/0.46 inference(unit_resolution,[status(thm)],[122, 47, 116, 106, 88, 71, 54])).
% 0.24/0.46 % SZS output end Proof
% 0.24/0.47 % E exiting
%------------------------------------------------------------------------------