%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET853-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:26:32 AM UTC 2025
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET853-2 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 05:46:52 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(c_lessequals_type, type, (
% 0.13/0.39 c_lessequals: ( $i * $i * $i ) > $o)).
% 0.13/0.39 tff(tc_set_type, type, (
% 0.13/0.39 tc_set: $i > $i)).
% 0.13/0.39 tff(t_a_type, type, (
% 0.13/0.39 t_a: $i)).
% 0.13/0.39 tff(c_Zorn_Osucc_type, type, (
% 0.13/0.39 c_Zorn_Osucc: ( $i * $i * $i ) > $i)).
% 0.13/0.39 tff(v_x_type, type, (
% 0.13/0.39 v_x: $i)).
% 0.13/0.39 tff(v_S_type, type, (
% 0.13/0.39 v_S: $i)).
% 0.13/0.39 tff(v_xa_type, type, (
% 0.13/0.39 v_xa: $i)).
% 0.13/0.39 tff(c_Zorn_OTFin__linear__lemma1__1_type, type, (
% 0.13/0.39 c_Zorn_OTFin__linear__lemma1__1: ( $i * $i * $i ) > $i)).
% 0.13/0.39 tff(c_in_type, type, (
% 0.13/0.39 c_in: ( $i * $i * $i ) > $o)).
% 0.13/0.39 tff(c_Zorn_OTFin_type, type, (
% 0.13/0.39 c_Zorn_OTFin: ( $i * $i ) > $i)).
% 0.13/0.39 tff(1,assumption,(~c_lessequals(v_xa, v_x, tc_set(tc_set(t_a)))), introduced(assumption)).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (^[T_a: $i, V_B: $i, V_A: $i] : refl(((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) <=> ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (^[T_a: $i, V_B: $i, V_A: $i] : trans(monotonicity(rewrite(((~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) <=> ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))), ((((~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | (V_A = V_B)) <=> (((~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) | (V_A = V_B)))), rewrite((((~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) | (V_A = V_B)) <=> ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))), ((((~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | (V_A = V_B)) <=> ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (![T_a: $i, V_B: $i, V_A: $i] : (((~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | (V_A = V_B)) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[5])).
% 0.13/0.39 tff(7,axiom,(![T_a: $i, V_B: $i, V_A: $i] : (((~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | (V_A = V_B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_Osubset__antisym_0')).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.13/0.39 tff(10,plain,(
% 0.13/0.39 ![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 0.13/0.39 inference(skolemize,[status(sab)],[9])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 ((~(v_xa = c_Zorn_Osucc(v_S, v_x, t_a))) <=> (~(v_xa = c_Zorn_Osucc(v_S, v_x, t_a)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(13,axiom,(~(v_xa = c_Zorn_Osucc(v_S, v_x, t_a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_3')).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (~(v_xa = c_Zorn_Osucc(v_S, v_x, t_a))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (c_lessequals(v_xa, c_Zorn_Osucc(v_S, v_x, t_a), tc_set(tc_set(t_a))) <=> c_lessequals(v_xa, c_Zorn_Osucc(v_S, v_x, t_a), tc_set(tc_set(t_a)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(16,axiom,(c_lessequals(v_xa, c_Zorn_Osucc(v_S, v_x, t_a), tc_set(tc_set(t_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_2')).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (c_lessequals(v_xa, c_Zorn_Osucc(v_S, v_x, t_a), tc_set(tc_set(t_a)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((v_xa = c_Zorn_Osucc(v_S, v_x, t_a)) | (~c_lessequals(v_xa, c_Zorn_Osucc(v_S, v_x, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), v_xa, tc_set(tc_set(t_a)))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | (v_xa = c_Zorn_Osucc(v_S, v_x, t_a)) | (~c_lessequals(v_xa, c_Zorn_Osucc(v_S, v_x, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), v_xa, tc_set(tc_set(t_a)))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((v_xa = c_Zorn_Osucc(v_S, v_x, t_a)) | (~c_lessequals(v_xa, c_Zorn_Osucc(v_S, v_x, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), v_xa, tc_set(tc_set(t_a)))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | (v_xa = c_Zorn_Osucc(v_S, v_x, t_a)) | (~c_lessequals(v_xa, c_Zorn_Osucc(v_S, v_x, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), v_xa, tc_set(tc_set(t_a))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (~c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), v_xa, tc_set(tc_set(t_a)))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[20, 17, 14, 11])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (^[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)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 (![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))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (![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))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (^[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))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(26,plain,
% 0.13/0.40 (![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (((((~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))))) | 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))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[25])).
% 0.13/0.40 tff(27,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')).
% 0.13/0.40 tff(28,plain,
% 0.13/0.40 (![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))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 (![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))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.13/0.40 tff(30,plain,(
% 0.13/0.40 ![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))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[29])).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 (![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))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 (c_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))) <=> c_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(33,axiom,(c_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_1')).
% 0.13/0.40 tff(34,plain,
% 0.13/0.40 (c_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.13/0.40 tff(35,plain,
% 0.13/0.40 (c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))) <=> c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(36,axiom,(c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.13/0.40 tff(37,plain,
% 0.13/0.40 (c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.13/0.40 tff(38,plain,
% 0.13/0.40 (((~![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_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), v_xa, tc_set(tc_set(t_a))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), v_x, 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_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), v_xa, tc_set(tc_set(t_a))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), v_x, tc_set(tc_set(t_a))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(39,plain,
% 0.13/0.40 ((c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), v_xa, tc_set(tc_set(t_a))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | (~c_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), v_x, tc_set(tc_set(t_a)))) <=> ((~c_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), v_xa, tc_set(tc_set(t_a))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), v_x, tc_set(tc_set(t_a))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(40,plain,
% 0.13/0.40 (((~![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_x, t_a), v_xa, tc_set(tc_set(t_a))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | (~c_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), v_x, 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_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), v_xa, tc_set(tc_set(t_a))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), v_x, tc_set(tc_set(t_a)))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[39])).
% 0.13/0.40 tff(41,plain,
% 0.13/0.40 (((~![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_x, t_a), v_xa, tc_set(tc_set(t_a))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | (~c_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), v_x, 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_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), v_xa, tc_set(tc_set(t_a))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), v_x, tc_set(tc_set(t_a))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[40, 38])).
% 0.13/0.40 tff(42,plain,
% 0.13/0.40 ((~![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_x, t_a), v_xa, tc_set(tc_set(t_a))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | (~c_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), v_x, tc_set(tc_set(t_a))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(43,plain,
% 0.13/0.40 ((~![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_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), v_xa, tc_set(tc_set(t_a))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), v_x, tc_set(tc_set(t_a)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.13/0.40 tff(44,plain,
% 0.13/0.40 (c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), v_x, tc_set(tc_set(t_a)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[43, 37, 34, 31, 21])).
% 0.13/0.40 tff(45,plain,
% 0.13/0.40 (c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), v_x, tc_set(tc_set(t_a)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[44, 1])).
% 0.13/0.40 tff(46,plain,
% 0.13/0.40 (^[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))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(47,plain,
% 0.13/0.40 (![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)))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[46])).
% 0.13/0.40 tff(48,plain,
% 0.13/0.40 (![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)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(49,plain,
% 0.13/0.40 (^[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)))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(50,plain,
% 0.13/0.40 (![V_n: $i, V_S: $i, T_a: $i, V_m: $i] : (((((~c_in(V_m, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a)))) | (~c_in(V_n, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))))) | 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)))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[49])).
% 0.13/0.40 tff(51,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')).
% 0.13/0.40 tff(52,plain,
% 0.13/0.40 (![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)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.13/0.40 tff(53,plain,
% 0.13/0.40 (![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)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.22/0.41 tff(54,plain,(
% 0.22/0.41 ![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)))))),
% 0.22/0.41 inference(skolemize,[status(sab)],[53])).
% 0.22/0.41 tff(55,plain,
% 0.22/0.41 (![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)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.22/0.41 tff(56,plain,
% 0.22/0.41 (((~![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_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), v_xa, tc_set(tc_set(t_a))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, 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_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), v_xa, tc_set(tc_set(t_a))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(57,plain,
% 0.22/0.41 ((c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), v_xa, tc_set(tc_set(t_a))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))) | (~c_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))))) <=> ((~c_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), v_xa, tc_set(tc_set(t_a))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(58,plain,
% 0.22/0.41 (((~![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_x, t_a), v_xa, tc_set(tc_set(t_a))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))) | (~c_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))))) <=> ((~![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_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), v_xa, tc_set(tc_set(t_a))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))))),
% 0.22/0.41 inference(monotonicity,[status(thm)],[57])).
% 0.22/0.41 tff(59,plain,
% 0.22/0.41 (((~![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_x, t_a), v_xa, tc_set(tc_set(t_a))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))) | (~c_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))))) <=> ((~![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_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), v_xa, tc_set(tc_set(t_a))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))))),
% 0.22/0.41 inference(transitivity,[status(thm)],[58, 56])).
% 0.22/0.41 tff(60,plain,
% 0.22/0.41 ((~![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_x, t_a), v_xa, tc_set(tc_set(t_a))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))) | (~c_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(61,plain,
% 0.22/0.41 ((~![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_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), v_xa, tc_set(tc_set(t_a))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_in(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.22/0.41 tff(62,plain,
% 0.22/0.41 (c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[61, 37, 34, 55, 21])).
% 0.22/0.41 tff(63,plain,
% 0.22/0.41 (c_in(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[62, 1])).
% 0.22/0.41 tff(64,plain,
% 0.22/0.41 (^[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))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(65,plain,
% 0.22/0.41 (![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)))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[64])).
% 0.22/0.41 tff(66,plain,
% 0.22/0.41 (![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)))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(67,plain,
% 0.22/0.41 (^[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)))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(68,plain,
% 0.22/0.41 (![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)))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[67])).
% 0.22/0.41 tff(69,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')).
% 0.22/0.41 tff(70,plain,
% 0.22/0.41 (![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)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.22/0.41 tff(71,plain,
% 0.22/0.41 (![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)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.22/0.41 tff(72,plain,(
% 0.22/0.41 ![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)))),
% 0.22/0.42 inference(skolemize,[status(sab)],[71])).
% 0.22/0.42 tff(73,plain,
% 0.22/0.42 (![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(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)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.22/0.42 tff(74,plain,
% 0.22/0.42 (((~![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(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_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), v_xa, tc_set(tc_set(t_a))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a) = v_x)))) <=> ((~![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_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), v_xa, tc_set(tc_set(t_a))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a) = v_x)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(75,plain,
% 0.22/0.42 ((c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), v_xa, tc_set(tc_set(t_a))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | (~c_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a) = v_x))) <=> ((~c_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), v_xa, tc_set(tc_set(t_a))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a) = v_x)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(76,plain,
% 0.22/0.42 (((~![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(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_x, t_a), v_xa, tc_set(tc_set(t_a))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | (~c_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a) = v_x)))) <=> ((~![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_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), v_xa, tc_set(tc_set(t_a))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a) = v_x))))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[75])).
% 0.22/0.42 tff(77,plain,
% 0.22/0.42 (((~![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(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_x, t_a), v_xa, tc_set(tc_set(t_a))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | (~c_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a) = v_x)))) <=> ((~![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_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), v_xa, tc_set(tc_set(t_a))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a) = v_x)))),
% 0.22/0.42 inference(transitivity,[status(thm)],[76, 74])).
% 0.22/0.42 tff(78,plain,
% 0.22/0.42 ((~![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(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_x, t_a), v_xa, tc_set(tc_set(t_a))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | (~c_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a) = v_x)))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(79,plain,
% 0.22/0.42 ((~![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(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_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), v_xa, tc_set(tc_set(t_a))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a) = v_x))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.22/0.42 tff(80,plain,
% 0.22/0.42 (c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | (~(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a) = v_x))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[79, 37, 34, 73, 21])).
% 0.22/0.42 tff(81,plain,
% 0.22/0.42 (~(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a) = v_x)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[80, 1])).
% 0.22/0.42 tff(82,plain,
% 0.22/0.42 (^[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(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))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(83,plain,
% 0.22/0.42 (![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(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)))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[82])).
% 0.22/0.42 tff(84,plain,
% 0.22/0.42 (![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(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)))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(85,plain,
% 0.22/0.42 (^[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_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)))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(86,plain,
% 0.22/0.42 (![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_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)))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[85])).
% 0.22/0.42 tff(87,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')).
% 0.22/0.42 tff(88,plain,
% 0.22/0.42 (![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(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)))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.22/0.42 tff(89,plain,
% 0.22/0.42 (![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(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)))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.22/0.42 tff(90,plain,(
% 0.22/0.42 ![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(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)))))),
% 0.22/0.42 inference(skolemize,[status(sab)],[89])).
% 0.22/0.42 tff(91,plain,
% 0.22/0.42 (![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(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)))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.22/0.42 tff(92,plain,
% 0.22/0.42 (((~![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(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_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), v_xa, tc_set(tc_set(t_a))) | (~c_in(v_x, 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_x, t_a), t_a), v_x, 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_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), v_xa, tc_set(tc_set(t_a))) | (~c_in(v_x, 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_x, t_a), t_a), v_x, tc_set(tc_set(t_a)))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(93,plain,
% 0.22/0.42 ((c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), v_xa, tc_set(tc_set(t_a))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | (~c_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(c_Zorn_Osucc(v_S, c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), t_a), v_x, tc_set(tc_set(t_a))))) <=> ((~c_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), v_xa, tc_set(tc_set(t_a))) | (~c_in(v_x, 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_x, t_a), t_a), v_x, tc_set(tc_set(t_a)))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(94,plain,
% 0.22/0.42 (((~![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(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_x, t_a), v_xa, tc_set(tc_set(t_a))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | (~c_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(c_Zorn_Osucc(v_S, c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), t_a), v_x, 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_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), v_xa, tc_set(tc_set(t_a))) | (~c_in(v_x, 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_x, t_a), t_a), v_x, tc_set(tc_set(t_a))))))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[93])).
% 0.22/0.43 tff(95,plain,
% 0.22/0.43 (((~![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_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_x, t_a), v_xa, tc_set(tc_set(t_a))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | (~c_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(c_Zorn_Osucc(v_S, c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), t_a), v_x, 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_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), v_xa, tc_set(tc_set(t_a))) | (~c_in(v_x, 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_x, t_a), t_a), v_x, tc_set(tc_set(t_a)))))),
% 0.22/0.43 inference(transitivity,[status(thm)],[94, 92])).
% 0.22/0.43 tff(96,plain,
% 0.22/0.43 ((~![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_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_x, t_a), v_xa, tc_set(tc_set(t_a))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | (~c_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_in(v_x, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(c_Zorn_Osucc(v_S, c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), t_a), v_x, tc_set(tc_set(t_a)))))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(97,plain,
% 0.22/0.43 ((~![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_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_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), v_xa, tc_set(tc_set(t_a))) | (~c_in(v_x, 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_x, t_a), t_a), v_x, tc_set(tc_set(t_a))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.22/0.43 tff(98,plain,
% 0.22/0.43 (c_lessequals(v_xa, v_x, tc_set(tc_set(t_a))) | (~c_lessequals(c_Zorn_Osucc(v_S, c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), t_a), v_x, tc_set(tc_set(t_a))))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[97, 37, 34, 91, 21])).
% 0.22/0.43 tff(99,plain,
% 0.22/0.43 (~c_lessequals(c_Zorn_Osucc(v_S, c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), t_a), v_x, tc_set(tc_set(t_a)))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[98, 1])).
% 0.22/0.43 tff(100,plain,
% 0.22/0.43 (^[V_U: $i] : refl(((~c_in(V_U, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(V_U, v_x, tc_set(tc_set(t_a)))) | (V_U = v_x) | c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a)))) <=> ((~c_in(V_U, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(V_U, v_x, tc_set(tc_set(t_a)))) | (V_U = v_x) | c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a)))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(101,plain,
% 0.22/0.43 (![V_U: $i] : ((~c_in(V_U, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(V_U, v_x, tc_set(tc_set(t_a)))) | (V_U = v_x) | c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a)))) <=> ![V_U: $i] : ((~c_in(V_U, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(V_U, v_x, tc_set(tc_set(t_a)))) | (V_U = v_x) | c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[100])).
% 0.22/0.43 tff(102,plain,
% 0.22/0.43 (![V_U: $i] : ((~c_in(V_U, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(V_U, v_x, tc_set(tc_set(t_a)))) | (V_U = v_x) | c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a)))) <=> ![V_U: $i] : ((~c_in(V_U, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(V_U, v_x, tc_set(tc_set(t_a)))) | (V_U = v_x) | c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(103,plain,
% 0.22/0.43 (^[V_U: $i] : trans(monotonicity(trans(monotonicity(rewrite((c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a))) | (V_U = v_x)) <=> ((V_U = v_x) | c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a))))), (((c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a))) | (V_U = v_x)) | (~c_lessequals(V_U, v_x, tc_set(tc_set(t_a))))) <=> (((V_U = v_x) | c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a)))) | (~c_lessequals(V_U, v_x, tc_set(tc_set(t_a))))))), rewrite((((V_U = v_x) | c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a)))) | (~c_lessequals(V_U, v_x, tc_set(tc_set(t_a))))) <=> ((~c_lessequals(V_U, v_x, tc_set(tc_set(t_a)))) | (V_U = v_x) | c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a))))), (((c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a))) | (V_U = v_x)) | (~c_lessequals(V_U, v_x, tc_set(tc_set(t_a))))) <=> ((~c_lessequals(V_U, v_x, tc_set(tc_set(t_a)))) | (V_U = v_x) | c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a)))))), ((((c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a))) | (V_U = v_x)) | (~c_lessequals(V_U, v_x, tc_set(tc_set(t_a))))) | (~c_in(V_U, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))))) <=> (((~c_lessequals(V_U, v_x, tc_set(tc_set(t_a)))) | (V_U = v_x) | c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a)))) | (~c_in(V_U, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))))))), rewrite((((~c_lessequals(V_U, v_x, tc_set(tc_set(t_a)))) | (V_U = v_x) | c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, 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_U, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(V_U, v_x, tc_set(tc_set(t_a)))) | (V_U = v_x) | c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a))))), ((((c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a))) | (V_U = v_x)) | (~c_lessequals(V_U, v_x, 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_U, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(V_U, v_x, tc_set(tc_set(t_a)))) | (V_U = v_x) | c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(104,plain,
% 0.22/0.43 (![V_U: $i] : (((c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a))) | (V_U = v_x)) | (~c_lessequals(V_U, v_x, tc_set(tc_set(t_a))))) | (~c_in(V_U, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))))) <=> ![V_U: $i] : ((~c_in(V_U, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(V_U, v_x, tc_set(tc_set(t_a)))) | (V_U = v_x) | c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[103])).
% 0.22/0.43 tff(105,axiom,(![V_U: $i] : (((c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a))) | (V_U = v_x)) | (~c_lessequals(V_U, v_x, tc_set(tc_set(t_a))))) | (~c_in(V_U, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_5')).
% 0.22/0.43 tff(106,plain,
% 0.22/0.43 (![V_U: $i] : ((~c_in(V_U, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(V_U, v_x, tc_set(tc_set(t_a)))) | (V_U = v_x) | c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.22/0.43 tff(107,plain,
% 0.22/0.43 (![V_U: $i] : ((~c_in(V_U, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(V_U, v_x, tc_set(tc_set(t_a)))) | (V_U = v_x) | c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.22/0.43 tff(108,plain,(
% 0.22/0.43 ![V_U: $i] : ((~c_in(V_U, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(V_U, v_x, tc_set(tc_set(t_a)))) | (V_U = v_x) | c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a))))),
% 0.22/0.43 inference(skolemize,[status(sab)],[107])).
% 0.22/0.43 tff(109,plain,
% 0.22/0.43 (![V_U: $i] : ((~c_in(V_U, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(V_U, v_x, tc_set(tc_set(t_a)))) | (V_U = v_x) | c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[108, 101])).
% 0.22/0.43 tff(110,plain,
% 0.22/0.43 (((~![V_U: $i] : ((~c_in(V_U, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(V_U, v_x, tc_set(tc_set(t_a)))) | (V_U = v_x) | c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a))))) | ((~c_in(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), v_x, tc_set(tc_set(t_a)))) | (c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a) = v_x) | c_lessequals(c_Zorn_Osucc(v_S, c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), t_a), v_x, tc_set(tc_set(t_a))))) <=> ((~![V_U: $i] : ((~c_in(V_U, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(V_U, v_x, tc_set(tc_set(t_a)))) | (V_U = v_x) | c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a))))) | (~c_in(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), v_x, tc_set(tc_set(t_a)))) | (c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a) = v_x) | c_lessequals(c_Zorn_Osucc(v_S, c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), t_a), v_x, tc_set(tc_set(t_a))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(111,plain,
% 0.22/0.43 ((~![V_U: $i] : ((~c_in(V_U, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(V_U, v_x, tc_set(tc_set(t_a)))) | (V_U = v_x) | c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a))))) | ((~c_in(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), v_x, tc_set(tc_set(t_a)))) | (c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a) = v_x) | c_lessequals(c_Zorn_Osucc(v_S, c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), t_a), v_x, tc_set(tc_set(t_a))))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(112,plain,
% 0.22/0.43 ((~![V_U: $i] : ((~c_in(V_U, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(V_U, v_x, tc_set(tc_set(t_a)))) | (V_U = v_x) | c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a))))) | (~c_in(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), v_x, tc_set(tc_set(t_a)))) | (c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a) = v_x) | c_lessequals(c_Zorn_Osucc(v_S, c_Zorn_OTFin__linear__lemma1__1(v_S, v_x, t_a), t_a), v_x, tc_set(tc_set(t_a)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.22/0.44 tff(113,plain,
% 0.22/0.44 ($false),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[112, 109, 99, 81, 63, 45])).
% 0.22/0.44 tff(114,plain,(c_lessequals(v_xa, v_x, tc_set(tc_set(t_a)))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.44 tff(115,plain,
% 0.22/0.44 (^[V_x: $i, V_S: $i, T_a: $i, V_y: $i] : refl(((~c_lessequals(V_x, V_y, tc_set(tc_set(T_a)))) | c_lessequals(V_x, c_Zorn_Osucc(V_S, V_y, T_a), tc_set(tc_set(T_a)))) <=> ((~c_lessequals(V_x, V_y, tc_set(tc_set(T_a)))) | c_lessequals(V_x, c_Zorn_Osucc(V_S, V_y, T_a), tc_set(tc_set(T_a)))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(116,plain,
% 0.22/0.44 (![V_x: $i, V_S: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_x, V_y, tc_set(tc_set(T_a)))) | c_lessequals(V_x, c_Zorn_Osucc(V_S, V_y, T_a), tc_set(tc_set(T_a)))) <=> ![V_x: $i, V_S: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_x, V_y, tc_set(tc_set(T_a)))) | c_lessequals(V_x, c_Zorn_Osucc(V_S, V_y, T_a), tc_set(tc_set(T_a))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[115])).
% 0.22/0.44 tff(117,plain,
% 0.22/0.44 (![V_x: $i, V_S: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_x, V_y, tc_set(tc_set(T_a)))) | c_lessequals(V_x, c_Zorn_Osucc(V_S, V_y, T_a), tc_set(tc_set(T_a)))) <=> ![V_x: $i, V_S: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_x, V_y, tc_set(tc_set(T_a)))) | c_lessequals(V_x, c_Zorn_Osucc(V_S, V_y, T_a), tc_set(tc_set(T_a))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(118,axiom,(![V_x: $i, V_S: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_x, V_y, tc_set(tc_set(T_a)))) | c_lessequals(V_x, c_Zorn_Osucc(V_S, V_y, T_a), tc_set(tc_set(T_a))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Zorn_Osucc__trans_0')).
% 0.22/0.44 tff(119,plain,
% 0.22/0.44 (![V_x: $i, V_S: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_x, V_y, tc_set(tc_set(T_a)))) | c_lessequals(V_x, c_Zorn_Osucc(V_S, V_y, T_a), tc_set(tc_set(T_a))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.22/0.44 tff(120,plain,(
% 0.22/0.44 ![V_x: $i, V_S: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_x, V_y, tc_set(tc_set(T_a)))) | c_lessequals(V_x, c_Zorn_Osucc(V_S, V_y, T_a), tc_set(tc_set(T_a))))),
% 0.22/0.44 inference(skolemize,[status(sab)],[119])).
% 0.22/0.44 tff(121,plain,
% 0.22/0.44 (![V_x: $i, V_S: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_x, V_y, tc_set(tc_set(T_a)))) | c_lessequals(V_x, c_Zorn_Osucc(V_S, V_y, T_a), tc_set(tc_set(T_a))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[120, 116])).
% 0.22/0.44 tff(122,plain,
% 0.22/0.44 ((~c_lessequals(c_Zorn_Osucc(v_S, v_xa, t_a), c_Zorn_Osucc(v_S, v_x, t_a), tc_set(tc_set(t_a)))) <=> (~c_lessequals(c_Zorn_Osucc(v_S, v_xa, t_a), c_Zorn_Osucc(v_S, v_x, t_a), tc_set(tc_set(t_a))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(123,axiom,(~c_lessequals(c_Zorn_Osucc(v_S, v_xa, t_a), c_Zorn_Osucc(v_S, v_x, t_a), tc_set(tc_set(t_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_4')).
% 0.22/0.44 tff(124,plain,
% 0.22/0.44 (~c_lessequals(c_Zorn_Osucc(v_S, v_xa, t_a), c_Zorn_Osucc(v_S, v_x, t_a), tc_set(tc_set(t_a)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.22/0.44 tff(125,plain,
% 0.22/0.44 (((~![V_x: $i, V_S: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_x, V_y, tc_set(tc_set(T_a)))) | c_lessequals(V_x, c_Zorn_Osucc(V_S, V_y, T_a), tc_set(tc_set(T_a))))) | ((~c_lessequals(c_Zorn_Osucc(v_S, v_xa, t_a), v_x, tc_set(tc_set(t_a)))) | c_lessequals(c_Zorn_Osucc(v_S, v_xa, t_a), c_Zorn_Osucc(v_S, v_x, t_a), tc_set(tc_set(t_a))))) <=> ((~![V_x: $i, V_S: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_x, V_y, tc_set(tc_set(T_a)))) | c_lessequals(V_x, c_Zorn_Osucc(V_S, V_y, T_a), tc_set(tc_set(T_a))))) | (~c_lessequals(c_Zorn_Osucc(v_S, v_xa, t_a), v_x, tc_set(tc_set(t_a)))) | c_lessequals(c_Zorn_Osucc(v_S, v_xa, t_a), c_Zorn_Osucc(v_S, v_x, t_a), tc_set(tc_set(t_a))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(126,plain,
% 0.22/0.44 ((~![V_x: $i, V_S: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_x, V_y, tc_set(tc_set(T_a)))) | c_lessequals(V_x, c_Zorn_Osucc(V_S, V_y, T_a), tc_set(tc_set(T_a))))) | ((~c_lessequals(c_Zorn_Osucc(v_S, v_xa, t_a), v_x, tc_set(tc_set(t_a)))) | c_lessequals(c_Zorn_Osucc(v_S, v_xa, t_a), c_Zorn_Osucc(v_S, v_x, t_a), tc_set(tc_set(t_a))))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(127,plain,
% 0.22/0.44 ((~![V_x: $i, V_S: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_x, V_y, tc_set(tc_set(T_a)))) | c_lessequals(V_x, c_Zorn_Osucc(V_S, V_y, T_a), tc_set(tc_set(T_a))))) | (~c_lessequals(c_Zorn_Osucc(v_S, v_xa, t_a), v_x, tc_set(tc_set(t_a)))) | c_lessequals(c_Zorn_Osucc(v_S, v_xa, t_a), c_Zorn_Osucc(v_S, v_x, t_a), tc_set(tc_set(t_a)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.22/0.44 tff(128,plain,
% 0.22/0.44 (~c_lessequals(c_Zorn_Osucc(v_S, v_xa, t_a), v_x, tc_set(tc_set(t_a)))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[127, 124, 121])).
% 0.22/0.44 tff(129,plain,
% 0.22/0.44 (((~![V_U: $i] : ((~c_in(V_U, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(V_U, v_x, tc_set(tc_set(t_a)))) | (V_U = v_x) | c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a))))) | ((~c_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(v_xa, v_x, tc_set(tc_set(t_a)))) | (v_xa = v_x) | c_lessequals(c_Zorn_Osucc(v_S, v_xa, t_a), v_x, tc_set(tc_set(t_a))))) <=> ((~![V_U: $i] : ((~c_in(V_U, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(V_U, v_x, tc_set(tc_set(t_a)))) | (V_U = v_x) | c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a))))) | (~c_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(v_xa, v_x, tc_set(tc_set(t_a)))) | (v_xa = v_x) | c_lessequals(c_Zorn_Osucc(v_S, v_xa, t_a), v_x, tc_set(tc_set(t_a))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(130,plain,
% 0.22/0.44 ((~![V_U: $i] : ((~c_in(V_U, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(V_U, v_x, tc_set(tc_set(t_a)))) | (V_U = v_x) | c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a))))) | ((~c_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(v_xa, v_x, tc_set(tc_set(t_a)))) | (v_xa = v_x) | c_lessequals(c_Zorn_Osucc(v_S, v_xa, t_a), v_x, tc_set(tc_set(t_a))))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(131,plain,
% 0.22/0.44 ((~![V_U: $i] : ((~c_in(V_U, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(V_U, v_x, tc_set(tc_set(t_a)))) | (V_U = v_x) | c_lessequals(c_Zorn_Osucc(v_S, V_U, t_a), v_x, tc_set(tc_set(t_a))))) | (~c_in(v_xa, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a)))) | (~c_lessequals(v_xa, v_x, tc_set(tc_set(t_a)))) | (v_xa = v_x) | c_lessequals(c_Zorn_Osucc(v_S, v_xa, t_a), v_x, tc_set(tc_set(t_a)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.22/0.44 tff(132,plain,
% 0.22/0.44 ((~c_lessequals(v_xa, v_x, tc_set(tc_set(t_a)))) | (v_xa = v_x) | c_lessequals(c_Zorn_Osucc(v_S, v_xa, t_a), v_x, tc_set(tc_set(t_a)))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[131, 34, 109])).
% 0.22/0.44 tff(133,plain,
% 0.22/0.44 ((~c_lessequals(v_xa, v_x, tc_set(tc_set(t_a)))) | (v_xa = v_x)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[132, 128])).
% 0.22/0.44 tff(134,plain,
% 0.22/0.44 (v_xa = v_x),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[133, 114])).
% 0.22/0.44 tff(135,plain,
% 0.22/0.44 (c_Zorn_Osucc(v_S, v_xa, t_a) = c_Zorn_Osucc(v_S, v_x, t_a)),
% 0.22/0.44 inference(monotonicity,[status(thm)],[134])).
% 0.22/0.44 tff(136,plain,
% 0.22/0.44 (c_Zorn_Osucc(v_S, v_x, t_a) = c_Zorn_Osucc(v_S, v_xa, t_a)),
% 0.22/0.44 inference(symmetry,[status(thm)],[135])).
% 0.22/0.44 tff(137,plain,
% 0.22/0.44 (c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), c_Zorn_Osucc(v_S, v_x, t_a), tc_set(tc_set(t_a))) <=> c_lessequals(c_Zorn_Osucc(v_S, v_xa, t_a), c_Zorn_Osucc(v_S, v_x, t_a), tc_set(tc_set(t_a)))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[136])).
% 0.22/0.44 tff(138,plain,
% 0.22/0.44 (c_lessequals(c_Zorn_Osucc(v_S, v_xa, t_a), c_Zorn_Osucc(v_S, v_x, t_a), tc_set(tc_set(t_a))) <=> c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), c_Zorn_Osucc(v_S, v_x, t_a), tc_set(tc_set(t_a)))),
% 0.22/0.44 inference(symmetry,[status(thm)],[137])).
% 0.22/0.44 tff(139,plain,
% 0.22/0.44 ((~c_lessequals(c_Zorn_Osucc(v_S, v_xa, t_a), c_Zorn_Osucc(v_S, v_x, t_a), tc_set(tc_set(t_a)))) <=> (~c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), c_Zorn_Osucc(v_S, v_x, t_a), tc_set(tc_set(t_a))))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[138])).
% 0.22/0.44 tff(140,plain,
% 0.22/0.44 (~c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), c_Zorn_Osucc(v_S, v_x, t_a), tc_set(tc_set(t_a)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[124, 139])).
% 0.22/0.44 tff(141,plain,
% 0.22/0.44 (^[T_a: $i, V_A: $i] : refl(c_lessequals(V_A, V_A, tc_set(T_a)) <=> c_lessequals(V_A, V_A, tc_set(T_a)))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(142,plain,
% 0.22/0.44 (![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a)) <=> ![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[141])).
% 0.22/0.44 tff(143,plain,
% 0.22/0.44 (![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a)) <=> ![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(144,axiom,(![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_Osubset__refl_0')).
% 0.22/0.44 tff(145,plain,
% 0.22/0.44 (![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.22/0.44 tff(146,plain,(
% 0.22/0.44 ![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))),
% 0.22/0.44 inference(skolemize,[status(sab)],[145])).
% 0.22/0.44 tff(147,plain,
% 0.22/0.44 (![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[146, 142])).
% 0.22/0.44 tff(148,plain,
% 0.22/0.44 ((~![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))) | c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), c_Zorn_Osucc(v_S, v_x, t_a), tc_set(tc_set(t_a)))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(149,plain,
% 0.22/0.44 (c_lessequals(c_Zorn_Osucc(v_S, v_x, t_a), c_Zorn_Osucc(v_S, v_x, t_a), tc_set(tc_set(t_a)))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.22/0.44 tff(150,plain,
% 0.22/0.44 ($false),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[149, 140])).
% 0.22/0.44 % SZS output end Proof
% 0.22/0.45 % E exiting
%------------------------------------------------------------------------------