Z3---4.15.1.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Z3---4.15.1
% Problem  : SET839-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_E %s %d THM

% Computer : n010.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sat Jun 21 05:26:28 AM UTC 2025

% Result   : Unsatisfiable 9.54s 9.74s
% Output   : Proof 9.62s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13  % Problem    : SET839-2 : TPTP v9.0.0. Released v3.2.0.
% 0.05/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n010.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Fri Jun 20 05:46:56 EDT 2025
% 0.13/0.34  % CPUTime    : 
% 9.54/9.74  % SZS status Unsatisfiable
% 9.54/9.74  % SZS output start Proof
% 9.54/9.74  tff(c_in_type, type, (
% 9.54/9.74     c_in: ( $i * $i * $i ) > $o)).
% 9.54/9.74  tff(tc_set_type, type, (
% 9.54/9.74     tc_set: $i > $i)).
% 9.54/9.74  tff(t_a_type, type, (
% 9.54/9.74     t_a: $i)).
% 9.54/9.74  tff(c_insert_type, type, (
% 9.54/9.74     c_insert: ( $i * $i * $i ) > $i)).
% 9.54/9.74  tff(c_emptyset_type, type, (
% 9.54/9.74     c_emptyset: $i)).
% 9.54/9.74  tff(c_Main_OsubsetI__1_type, type, (
% 9.54/9.74     c_Main_OsubsetI__1: ( $i * $i * $i ) > $i)).
% 9.54/9.74  tff(elem_0_type, type, (
% 9.54/9.74     elem_0: $i)).
% 9.54/9.74  tff(v_S_type, type, (
% 9.54/9.74     v_S: $i)).
% 9.54/9.74  tff(c_lessequals_type, type, (
% 9.54/9.74     c_lessequals: ( $i * $i * $i ) > $o)).
% 9.54/9.74  tff(1,assumption,(~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))), introduced(assumption)).
% 9.54/9.74  tff(2,plain,
% 9.54/9.74      (^[V_U: $i] : refl((~c_lessequals(v_S, c_insert(V_U, c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a)))) <=> (~c_lessequals(v_S, c_insert(V_U, c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a)))))),
% 9.54/9.74      inference(bind,[status(th)],[])).
% 9.54/9.74  tff(3,plain,
% 9.54/9.74      (![V_U: $i] : (~c_lessequals(v_S, c_insert(V_U, c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a)))) <=> ![V_U: $i] : (~c_lessequals(v_S, c_insert(V_U, c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))))),
% 9.54/9.74      inference(quant_intro,[status(thm)],[2])).
% 9.54/9.74  tff(4,plain,
% 9.54/9.74      (![V_U: $i] : (~c_lessequals(v_S, c_insert(V_U, c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a)))) <=> ![V_U: $i] : (~c_lessequals(v_S, c_insert(V_U, c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))))),
% 9.54/9.74      inference(rewrite,[status(thm)],[])).
% 9.54/9.74  tff(5,axiom,(![V_U: $i] : (~c_lessequals(v_S, c_insert(V_U, c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_0')).
% 9.54/9.74  tff(6,plain,
% 9.54/9.74      (![V_U: $i] : (~c_lessequals(v_S, c_insert(V_U, c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))))),
% 9.54/9.74      inference(modus_ponens,[status(thm)],[5, 4])).
% 9.54/9.74  tff(7,plain,(
% 9.54/9.74      ![V_U: $i] : (~c_lessequals(v_S, c_insert(V_U, c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))))),
% 9.54/9.74      inference(skolemize,[status(sab)],[6])).
% 9.54/9.74  tff(8,plain,
% 9.54/9.74      (![V_U: $i] : (~c_lessequals(v_S, c_insert(V_U, c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))))),
% 9.54/9.74      inference(modus_ponens,[status(thm)],[7, 3])).
% 9.54/9.74  tff(9,plain,
% 9.54/9.74      ((~![V_U: $i] : (~c_lessequals(v_S, c_insert(V_U, c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))))) | (~c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))))),
% 9.54/9.74      inference(quant_inst,[status(thm)],[])).
% 9.54/9.74  tff(10,plain,
% 9.54/9.74      (~c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a)))),
% 9.54/9.74      inference(unit_resolution,[status(thm)],[9, 8])).
% 9.54/9.74  tff(11,plain,
% 9.54/9.74      (^[T_a: $i, V_B: $i, V_A: $i] : refl((c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a))))),
% 9.54/9.74      inference(bind,[status(th)],[])).
% 9.54/9.74  tff(12,plain,
% 9.54/9.74      (![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 9.54/9.74      inference(quant_intro,[status(thm)],[11])).
% 9.54/9.74  tff(13,plain,
% 9.54/9.74      (![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 9.54/9.74      inference(rewrite,[status(thm)],[])).
% 9.54/9.74  tff(14,axiom,(![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_OsubsetI_0')).
% 9.54/9.74  tff(15,plain,
% 9.54/9.74      (![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 9.54/9.74      inference(modus_ponens,[status(thm)],[14, 13])).
% 9.54/9.74  tff(16,plain,(
% 9.54/9.74      ![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 9.54/9.74      inference(skolemize,[status(sab)],[15])).
% 9.54/9.74  tff(17,plain,
% 9.54/9.74      (![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 9.54/9.74      inference(modus_ponens,[status(thm)],[16, 12])).
% 9.54/9.74  tff(18,plain,
% 9.54/9.74      (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a)))),
% 9.54/9.74      inference(rewrite,[status(thm)],[])).
% 9.54/9.74  tff(19,plain,
% 9.54/9.74      ((c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a)) | c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a)))) <=> (c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a)))),
% 9.54/9.74      inference(rewrite,[status(thm)],[])).
% 9.54/9.74  tff(20,plain,
% 9.54/9.74      (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a)) | c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))))),
% 9.54/9.74      inference(monotonicity,[status(thm)],[19])).
% 9.54/9.74  tff(21,plain,
% 9.54/9.74      (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a)) | c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a)))),
% 9.54/9.74      inference(transitivity,[status(thm)],[20, 18])).
% 9.54/9.74  tff(22,plain,
% 9.54/9.74      ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a)) | c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))))),
% 9.54/9.74      inference(quant_inst,[status(thm)],[])).
% 9.54/9.74  tff(23,plain,
% 9.54/9.74      ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))),
% 9.54/9.74      inference(modus_ponens,[status(thm)],[22, 21])).
% 9.54/9.74  tff(24,plain,
% 9.54/9.74      (c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))),
% 9.54/9.74      inference(unit_resolution,[status(thm)],[23, 17, 10])).
% 9.54/9.74  tff(25,plain,
% 9.54/9.74      ((~![V_U: $i] : (~c_lessequals(v_S, c_insert(V_U, c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))))) | (~c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))))),
% 9.54/9.74      inference(quant_inst,[status(thm)],[])).
% 9.54/9.74  tff(26,plain,
% 9.54/9.74      (~c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a)))),
% 9.54/9.74      inference(unit_resolution,[status(thm)],[25, 8])).
% 9.54/9.74  tff(27,plain,
% 9.54/9.74      (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a)))),
% 9.54/9.74      inference(rewrite,[status(thm)],[])).
% 9.54/9.74  tff(28,plain,
% 9.54/9.74      ((c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a)) | c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a)))) <=> (c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a)))),
% 9.54/9.74      inference(rewrite,[status(thm)],[])).
% 9.54/9.74  tff(29,plain,
% 9.54/9.74      (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a)) | c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))))),
% 9.54/9.74      inference(monotonicity,[status(thm)],[28])).
% 9.54/9.74  tff(30,plain,
% 9.54/9.74      (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a)) | c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a)))),
% 9.54/9.74      inference(transitivity,[status(thm)],[29, 27])).
% 9.54/9.74  tff(31,plain,
% 9.54/9.74      ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a)) | c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))))),
% 9.54/9.74      inference(quant_inst,[status(thm)],[])).
% 9.54/9.74  tff(32,plain,
% 9.54/9.74      ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))),
% 9.54/9.74      inference(modus_ponens,[status(thm)],[31, 30])).
% 9.54/9.74  tff(33,plain,
% 9.54/9.74      (c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))),
% 9.54/9.74      inference(unit_resolution,[status(thm)],[32, 17, 26])).
% 9.54/9.74  tff(34,plain,
% 9.54/9.74      (^[V_V: $i, V_U: $i] : refl(((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a))) <=> ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a))))),
% 9.54/9.74      inference(bind,[status(th)],[])).
% 9.54/9.74  tff(35,plain,
% 9.54/9.74      (![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a))) <=> ![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))),
% 9.54/9.74      inference(quant_intro,[status(thm)],[34])).
% 9.54/9.74  tff(36,plain,
% 9.54/9.74      (![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a))) <=> ![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))),
% 9.54/9.74      inference(rewrite,[status(thm)],[])).
% 9.54/9.74  tff(37,plain,
% 9.54/9.74      (^[V_V: $i, V_U: $i] : trans(monotonicity(rewrite((c_lessequals(V_U, V_V, tc_set(t_a)) | (~c_in(V_V, v_S, tc_set(t_a)))) <=> ((~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))), (((c_lessequals(V_U, V_V, tc_set(t_a)) | (~c_in(V_V, v_S, tc_set(t_a)))) | (~c_in(V_U, v_S, tc_set(t_a)))) <=> (((~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a))) | (~c_in(V_U, v_S, tc_set(t_a)))))), rewrite((((~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a))) | (~c_in(V_U, v_S, tc_set(t_a)))) <=> ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))), (((c_lessequals(V_U, V_V, tc_set(t_a)) | (~c_in(V_V, v_S, tc_set(t_a)))) | (~c_in(V_U, v_S, tc_set(t_a)))) <=> ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))))),
% 9.54/9.74      inference(bind,[status(th)],[])).
% 9.54/9.74  tff(38,plain,
% 9.54/9.74      (![V_V: $i, V_U: $i] : ((c_lessequals(V_U, V_V, tc_set(t_a)) | (~c_in(V_V, v_S, tc_set(t_a)))) | (~c_in(V_U, v_S, tc_set(t_a)))) <=> ![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))),
% 9.54/9.74      inference(quant_intro,[status(thm)],[37])).
% 9.54/9.74  tff(39,axiom,(![V_V: $i, V_U: $i] : ((c_lessequals(V_U, V_V, tc_set(t_a)) | (~c_in(V_V, v_S, tc_set(t_a)))) | (~c_in(V_U, v_S, tc_set(t_a))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_1')).
% 9.54/9.74  tff(40,plain,
% 9.54/9.74      (![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))),
% 9.54/9.74      inference(modus_ponens,[status(thm)],[39, 38])).
% 9.54/9.74  tff(41,plain,
% 9.54/9.74      (![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))),
% 9.54/9.74      inference(modus_ponens,[status(thm)],[40, 36])).
% 9.54/9.74  tff(42,plain,(
% 9.54/9.74      ![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))),
% 9.54/9.74      inference(skolemize,[status(sab)],[41])).
% 9.54/9.74  tff(43,plain,
% 9.54/9.74      (![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))),
% 9.54/9.74      inference(modus_ponens,[status(thm)],[42, 35])).
% 9.54/9.74  tff(44,plain,
% 9.54/9.74      (((~![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))) | ((~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)))) <=> ((~![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)))),
% 9.54/9.74      inference(rewrite,[status(thm)],[])).
% 9.54/9.74  tff(45,plain,
% 9.54/9.74      (((~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) <=> ((~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)))),
% 9.54/9.74      inference(rewrite,[status(thm)],[])).
% 9.54/9.74  tff(46,plain,
% 9.54/9.74      (((~![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))) | ((~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)))) <=> ((~![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))) | ((~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))))),
% 9.54/9.75      inference(monotonicity,[status(thm)],[45])).
% 9.54/9.75  tff(47,plain,
% 9.54/9.75      (((~![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))) | ((~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)))) <=> ((~![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)))),
% 9.54/9.75      inference(transitivity,[status(thm)],[46, 44])).
% 9.54/9.75  tff(48,plain,
% 9.54/9.75      ((~![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))) | ((~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)))),
% 9.54/9.75      inference(quant_inst,[status(thm)],[])).
% 9.54/9.75  tff(49,plain,
% 9.54/9.75      ((~![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))),
% 9.54/9.75      inference(modus_ponens,[status(thm)],[48, 47])).
% 9.54/9.75  tff(50,plain,
% 9.54/9.75      ($false),
% 9.54/9.75      inference(unit_resolution,[status(thm)],[49, 43, 33, 24, 1])).
% 9.54/9.75  tff(51,plain,(c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))), inference(lemma,lemma(discharge,[]))).
% 9.54/9.75  tff(52,plain,
% 9.54/9.75      (((~![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))) | ((~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)))) <=> ((~![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)))),
% 9.54/9.75      inference(rewrite,[status(thm)],[])).
% 9.54/9.75  tff(53,plain,
% 9.54/9.75      ((~![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))) | ((~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)))),
% 9.54/9.75      inference(quant_inst,[status(thm)],[])).
% 9.54/9.75  tff(54,plain,
% 9.54/9.75      ((~![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))),
% 9.54/9.75      inference(modus_ponens,[status(thm)],[53, 52])).
% 9.54/9.75  tff(55,plain,
% 9.54/9.75      (c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))),
% 9.54/9.75      inference(unit_resolution,[status(thm)],[54, 43, 33, 24])).
% 9.54/9.75  tff(56,plain,
% 9.54/9.75      (^[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)))))),
% 9.54/9.75      inference(bind,[status(th)],[])).
% 9.54/9.75  tff(57,plain,
% 9.54/9.75      (![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))))),
% 9.54/9.75      inference(quant_intro,[status(thm)],[56])).
% 9.54/9.75  tff(58,plain,
% 9.54/9.75      (![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))))),
% 9.54/9.75      inference(rewrite,[status(thm)],[])).
% 9.54/9.75  tff(59,plain,
% 9.54/9.75      (^[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))))))),
% 9.61/9.75      inference(bind,[status(th)],[])).
% 9.61/9.75  tff(60,plain,
% 9.61/9.75      (![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))))),
% 9.61/9.75      inference(quant_intro,[status(thm)],[59])).
% 9.61/9.75  tff(61,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')).
% 9.61/9.75  tff(62,plain,
% 9.61/9.75      (![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))))),
% 9.61/9.75      inference(modus_ponens,[status(thm)],[61, 60])).
% 9.61/9.75  tff(63,plain,
% 9.61/9.75      (![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))))),
% 9.61/9.75      inference(modus_ponens,[status(thm)],[62, 58])).
% 9.61/9.75  tff(64,plain,(
% 9.61/9.75      ![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))))),
% 9.61/9.75      inference(skolemize,[status(sab)],[63])).
% 9.61/9.75  tff(65,plain,
% 9.61/9.75      (![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))))),
% 9.61/9.75      inference(modus_ponens,[status(thm)],[64, 57])).
% 9.61/9.75  tff(66,plain,
% 9.61/9.75      (((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) | (c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)) = c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_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))))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) | (c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)) = c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))))),
% 9.61/9.75      inference(rewrite,[status(thm)],[])).
% 9.61/9.75  tff(67,plain,
% 9.61/9.75      (((c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)) = c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)))) <=> ((~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) | (c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)) = c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))))),
% 9.61/9.75      inference(rewrite,[status(thm)],[])).
% 9.61/9.75  tff(68,plain,
% 9.61/9.75      (((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)) = c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_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))))) | ((~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) | (c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)) = c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)))))),
% 9.62/9.76      inference(monotonicity,[status(thm)],[67])).
% 9.62/9.76  tff(69,plain,
% 9.62/9.76      (((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)) = c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_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))))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) | (c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)) = c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))))),
% 9.62/9.76      inference(transitivity,[status(thm)],[68, 66])).
% 9.62/9.76  tff(70,plain,
% 9.62/9.76      ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)) = c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))))),
% 9.62/9.76      inference(quant_inst,[status(thm)],[])).
% 9.62/9.76  tff(71,plain,
% 9.62/9.76      ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) | (c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)) = c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)))),
% 9.62/9.76      inference(modus_ponens,[status(thm)],[70, 69])).
% 9.62/9.76  tff(72,plain,
% 9.62/9.76      ((c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)) = c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)))),
% 9.62/9.76      inference(unit_resolution,[status(thm)],[71, 65, 55])).
% 9.62/9.76  tff(73,plain,
% 9.62/9.76      (c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)) = c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))),
% 9.62/9.76      inference(unit_resolution,[status(thm)],[72, 51])).
% 9.62/9.76  tff(74,plain,
% 9.62/9.76      (c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)) = c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))),
% 9.62/9.76      inference(symmetry,[status(thm)],[73])).
% 9.62/9.76  tff(75,plain,
% 9.62/9.76      (c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)) <=> c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))),
% 9.62/9.76      inference(monotonicity,[status(thm)],[74])).
% 9.62/9.76  tff(76,plain,
% 9.62/9.76      (c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)) <=> c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))),
% 9.62/9.76      inference(symmetry,[status(thm)],[75])).
% 9.62/9.76  tff(77,plain,
% 9.62/9.76      ((~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) <=> (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)))),
% 9.62/9.76      inference(monotonicity,[status(thm)],[76])).
% 9.62/9.76  tff(78,assumption,(~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))), introduced(assumption)).
% 9.62/9.76  tff(79,plain,
% 9.62/9.76      (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))),
% 9.62/9.76      inference(modus_ponens,[status(thm)],[78, 77])).
% 9.62/9.76  tff(80,plain,
% 9.62/9.76      ((~![V_U: $i] : (~c_lessequals(v_S, c_insert(V_U, c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))))) | (~c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))))),
% 9.62/9.76      inference(quant_inst,[status(thm)],[])).
% 9.62/9.76  tff(81,plain,
% 9.62/9.76      (~c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a)))),
% 9.62/9.76      inference(unit_resolution,[status(thm)],[80, 8])).
% 9.62/9.76  tff(82,plain,
% 9.62/9.76      (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a)))),
% 9.62/9.76      inference(rewrite,[status(thm)],[])).
% 9.62/9.76  tff(83,plain,
% 9.62/9.76      ((c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a)) | c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a)))) <=> (c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a)))),
% 9.62/9.76      inference(rewrite,[status(thm)],[])).
% 9.62/9.76  tff(84,plain,
% 9.62/9.76      (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a)) | c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))))),
% 9.62/9.76      inference(monotonicity,[status(thm)],[83])).
% 9.62/9.76  tff(85,plain,
% 9.62/9.76      (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a)) | c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a)))),
% 9.62/9.76      inference(transitivity,[status(thm)],[84, 82])).
% 9.62/9.76  tff(86,plain,
% 9.62/9.76      ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a)) | c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))))),
% 9.62/9.76      inference(quant_inst,[status(thm)],[])).
% 9.62/9.76  tff(87,plain,
% 9.62/9.76      ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))),
% 9.62/9.76      inference(modus_ponens,[status(thm)],[86, 85])).
% 9.62/9.76  tff(88,plain,
% 9.62/9.76      (c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))),
% 9.62/9.76      inference(unit_resolution,[status(thm)],[87, 17, 81])).
% 9.62/9.76  tff(89,plain,
% 9.62/9.76      (((~![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))) | ((~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)))) <=> ((~![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)))),
% 9.62/9.76      inference(rewrite,[status(thm)],[])).
% 9.62/9.76  tff(90,plain,
% 9.62/9.76      ((~![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))) | ((~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)))),
% 9.62/9.76      inference(quant_inst,[status(thm)],[])).
% 9.62/9.76  tff(91,plain,
% 9.62/9.76      ((~![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))),
% 9.62/9.76      inference(modus_ponens,[status(thm)],[90, 89])).
% 9.62/9.76  tff(92,plain,
% 9.62/9.76      (c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))),
% 9.62/9.76      inference(unit_resolution,[status(thm)],[91, 43, 88, 33])).
% 9.62/9.76  tff(93,plain,
% 9.62/9.76      ($false),
% 9.62/9.76      inference(unit_resolution,[status(thm)],[92, 79])).
% 9.62/9.76  tff(94,plain,(c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))), inference(lemma,lemma(discharge,[]))).
% 9.62/9.76  tff(95,plain,
% 9.62/9.76      (((~![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))) | ((~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)))) <=> ((~![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)))),
% 9.62/9.77      inference(rewrite,[status(thm)],[])).
% 9.62/9.77  tff(96,plain,
% 9.62/9.77      ((~![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))) | ((~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)))),
% 9.62/9.77      inference(quant_inst,[status(thm)],[])).
% 9.62/9.77  tff(97,plain,
% 9.62/9.77      ((~![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))),
% 9.62/9.77      inference(modus_ponens,[status(thm)],[96, 95])).
% 9.62/9.77  tff(98,plain,
% 9.62/9.77      (c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))),
% 9.62/9.77      inference(unit_resolution,[status(thm)],[97, 43, 88, 24])).
% 9.62/9.77  tff(99,plain,
% 9.62/9.77      (((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) | (c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)) = c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_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))))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) | (c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)) = c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))))),
% 9.62/9.77      inference(rewrite,[status(thm)],[])).
% 9.62/9.77  tff(100,plain,
% 9.62/9.77      (((c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)) = c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)))) <=> ((~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) | (c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)) = c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))))),
% 9.62/9.77      inference(rewrite,[status(thm)],[])).
% 9.62/9.77  tff(101,plain,
% 9.62/9.77      (((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)) = c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_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))))) | ((~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) | (c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)) = c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)))))),
% 9.62/9.77      inference(monotonicity,[status(thm)],[100])).
% 9.62/9.77  tff(102,plain,
% 9.62/9.77      (((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)) = c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_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))))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) | (c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)) = c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))))),
% 9.62/9.77      inference(transitivity,[status(thm)],[101, 99])).
% 9.62/9.77  tff(103,plain,
% 9.62/9.77      ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)) = c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))))),
% 9.62/9.77      inference(quant_inst,[status(thm)],[])).
% 9.62/9.77  tff(104,plain,
% 9.62/9.77      ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) | (c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)) = c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)))),
% 9.62/9.77      inference(modus_ponens,[status(thm)],[103, 102])).
% 9.62/9.77  tff(105,plain,
% 9.62/9.77      ((~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) | (c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)) = c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)))),
% 9.62/9.77      inference(unit_resolution,[status(thm)],[104, 65, 98])).
% 9.62/9.77  tff(106,plain,
% 9.62/9.77      (c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)) = c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))),
% 9.62/9.77      inference(unit_resolution,[status(thm)],[105, 94])).
% 9.62/9.77  tff(107,plain,
% 9.62/9.77      (c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)) <=> c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))),
% 9.62/9.78      inference(monotonicity,[status(thm)],[74])).
% 9.62/9.78  tff(108,plain,
% 9.62/9.78      (c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)) <=> c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))),
% 9.62/9.78      inference(symmetry,[status(thm)],[107])).
% 9.62/9.78  tff(109,plain,
% 9.62/9.78      ((~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) <=> (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)))),
% 9.62/9.78      inference(monotonicity,[status(thm)],[108])).
% 9.62/9.78  tff(110,assumption,(~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))), introduced(assumption)).
% 9.62/9.78  tff(111,plain,
% 9.62/9.78      (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))),
% 9.62/9.78      inference(modus_ponens,[status(thm)],[110, 109])).
% 9.62/9.78  tff(112,plain,
% 9.62/9.78      ((~![V_U: $i] : (~c_lessequals(v_S, c_insert(V_U, c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))))) | (~c_lessequals(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))))),
% 9.62/9.78      inference(quant_inst,[status(thm)],[])).
% 9.62/9.78  tff(113,plain,
% 9.62/9.78      (~c_lessequals(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a)))),
% 9.62/9.78      inference(unit_resolution,[status(thm)],[112, 8])).
% 9.62/9.78  tff(114,plain,
% 9.62/9.78      (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a)) | c_lessequals(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_in(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a)) | c_lessequals(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))))),
% 9.62/9.78      inference(rewrite,[status(thm)],[])).
% 9.62/9.78  tff(115,plain,
% 9.62/9.78      ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a)) | c_lessequals(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))))),
% 9.62/9.78      inference(quant_inst,[status(thm)],[])).
% 9.62/9.78  tff(116,plain,
% 9.62/9.78      ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_in(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a)) | c_lessequals(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a)))),
% 9.62/9.78      inference(modus_ponens,[status(thm)],[115, 114])).
% 9.62/9.78  tff(117,plain,
% 9.62/9.78      (c_in(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))),
% 9.62/9.78      inference(unit_resolution,[status(thm)],[116, 17, 113])).
% 9.62/9.78  tff(118,plain,
% 9.62/9.78      (((~![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))) | ((~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)))) <=> ((~![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)))),
% 9.62/9.78      inference(rewrite,[status(thm)],[])).
% 9.62/9.78  tff(119,plain,
% 9.62/9.78      ((~![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))) | ((~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)))),
% 9.62/9.78      inference(quant_inst,[status(thm)],[])).
% 9.62/9.78  tff(120,plain,
% 9.62/9.78      ((~![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))),
% 9.62/9.78      inference(modus_ponens,[status(thm)],[119, 118])).
% 9.62/9.78  tff(121,plain,
% 9.62/9.78      (c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))),
% 9.62/9.78      inference(unit_resolution,[status(thm)],[120, 43, 117, 33])).
% 9.62/9.78  tff(122,plain,
% 9.62/9.78      ($false),
% 9.62/9.78      inference(unit_resolution,[status(thm)],[121, 111])).
% 9.62/9.78  tff(123,plain,(c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))), inference(lemma,lemma(discharge,[]))).
% 9.62/9.78  tff(124,plain,
% 9.62/9.78      (((~![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))) | ((~c_in(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)))) <=> ((~![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)))),
% 9.62/9.78      inference(rewrite,[status(thm)],[])).
% 9.62/9.78  tff(125,plain,
% 9.62/9.78      ((~![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))) | ((~c_in(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)))),
% 9.62/9.78      inference(quant_inst,[status(thm)],[])).
% 9.62/9.78  tff(126,plain,
% 9.62/9.78      ((~![V_V: $i, V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_a))) | (~c_in(V_V, v_S, tc_set(t_a))) | c_lessequals(V_U, V_V, tc_set(t_a)))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), v_S, tc_set(t_a))) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))),
% 9.62/9.78      inference(modus_ponens,[status(thm)],[125, 124])).
% 9.62/9.78  tff(127,plain,
% 9.62/9.78      (c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))),
% 9.62/9.78      inference(unit_resolution,[status(thm)],[126, 43, 117, 24])).
% 9.62/9.78  tff(128,plain,
% 9.62/9.78      (((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)) = c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_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))))) | (c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)) = c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))))),
% 9.62/9.78      inference(rewrite,[status(thm)],[])).
% 9.62/9.78  tff(129,plain,
% 9.62/9.78      ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)) = c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))))),
% 9.62/9.78      inference(quant_inst,[status(thm)],[])).
% 9.62/9.78  tff(130,plain,
% 9.62/9.78      ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | (c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)) = c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)))),
% 9.62/9.78      inference(modus_ponens,[status(thm)],[129, 128])).
% 9.62/9.78  tff(131,plain,
% 9.62/9.78      ((c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)) = c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)))),
% 9.62/9.78      inference(unit_resolution,[status(thm)],[130, 65, 127])).
% 9.62/9.78  tff(132,plain,
% 9.62/9.78      (c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)) = c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a))),
% 9.62/9.78      inference(unit_resolution,[status(thm)],[131, 123])).
% 9.62/9.78  tff(133,plain,
% 9.62/9.78      (c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)) = c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(c_Main_OsubsetI__1(c_insert(elem!0, elem!0, elem!0), c_insert(elem!0, c_emptyset, tc_set(t_a)), t_a), c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))),
% 9.62/9.78      inference(symmetry,[status(thm)],[132])).
% 9.62/9.78  tff(134,plain,
% 9.62/9.78      (c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)) = c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))),
% 9.62/9.78      inference(transitivity,[status(thm)],[133, 106])).
% 9.62/9.78  tff(135,plain,
% 9.62/9.78      (c_in(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)) <=> c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))),
% 9.62/9.78      inference(monotonicity,[status(thm)],[134])).
% 9.62/9.78  tff(136,plain,
% 9.62/9.78      (c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)) <=> c_in(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))),
% 9.62/9.78      inference(symmetry,[status(thm)],[135])).
% 9.62/9.78  tff(137,plain,
% 9.62/9.78      ((~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))) <=> (~c_in(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)))),
% 9.62/9.78      inference(monotonicity,[status(thm)],[136])).
% 9.62/9.78  tff(138,plain,
% 9.62/9.78      (^[T_a: $i, V_B: $i, V_A: $i] : refl(((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a))))),
% 9.62/9.78      inference(bind,[status(th)],[])).
% 9.62/9.78  tff(139,plain,
% 9.62/9.78      (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 9.62/9.78      inference(quant_intro,[status(thm)],[138])).
% 9.62/9.78  tff(140,plain,
% 9.62/9.78      (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 9.62/9.78      inference(rewrite,[status(thm)],[])).
% 9.62/9.78  tff(141,axiom,(![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_OsubsetI_1')).
% 9.62/9.78  tff(142,plain,
% 9.62/9.78      (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 9.62/9.78      inference(modus_ponens,[status(thm)],[141, 140])).
% 9.62/9.78  tff(143,plain,(
% 9.62/9.78      ![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 9.62/9.78      inference(skolemize,[status(sab)],[142])).
% 9.62/9.78  tff(144,plain,
% 9.62/9.78      (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 9.62/9.78      inference(modus_ponens,[status(thm)],[143, 139])).
% 9.62/9.78  tff(145,plain,
% 9.62/9.78      (((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))) | c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))) | c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))))),
% 9.62/9.78      inference(rewrite,[status(thm)],[])).
% 9.62/9.78  tff(146,plain,
% 9.62/9.78      ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))) | c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a))))),
% 9.62/9.78      inference(quant_inst,[status(thm)],[])).
% 9.62/9.78  tff(147,plain,
% 9.62/9.78      ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))) | c_lessequals(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(tc_set(t_a)))),
% 9.62/9.78      inference(modus_ponens,[status(thm)],[146, 145])).
% 9.62/9.78  tff(148,plain,
% 9.62/9.78      (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))),
% 9.62/9.78      inference(unit_resolution,[status(thm)],[147, 144, 81])).
% 9.62/9.78  tff(149,plain,
% 9.62/9.78      (~c_in(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))),
% 9.62/9.78      inference(modus_ponens,[status(thm)],[148, 137])).
% 9.62/9.78  tff(150,plain,
% 9.62/9.78      (^[V_x: $i, T_a: $i, V_B: $i] : refl(c_in(V_x, c_insert(V_x, V_B, T_a), T_a) <=> c_in(V_x, c_insert(V_x, V_B, T_a), T_a))),
% 9.62/9.78      inference(bind,[status(th)],[])).
% 9.62/9.78  tff(151,plain,
% 9.62/9.78      (![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a) <=> ![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 9.62/9.78      inference(quant_intro,[status(thm)],[150])).
% 9.62/9.78  tff(152,plain,
% 9.62/9.78      (![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a) <=> ![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 9.62/9.78      inference(rewrite,[status(thm)],[])).
% 9.62/9.78  tff(153,axiom,(![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_OinsertCI_1')).
% 9.62/9.78  tff(154,plain,
% 9.62/9.78      (![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 9.62/9.78      inference(modus_ponens,[status(thm)],[153, 152])).
% 9.62/9.78  tff(155,plain,(
% 9.62/9.78      ![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 9.62/9.78      inference(skolemize,[status(sab)],[154])).
% 9.62/9.78  tff(156,plain,
% 9.62/9.78      (![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 9.62/9.78      inference(modus_ponens,[status(thm)],[155, 151])).
% 9.62/9.78  tff(157,plain,
% 9.62/9.78      ((~![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)) | c_in(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))),
% 9.62/9.78      inference(quant_inst,[status(thm)],[])).
% 9.62/9.78  tff(158,plain,
% 9.62/9.78      (c_in(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_insert(c_Main_OsubsetI__1(v_S, c_insert(elem!0, c_emptyset, tc_set(t_a)), tc_set(t_a)), c_emptyset, tc_set(t_a)), tc_set(t_a))),
% 9.62/9.79      inference(unit_resolution,[status(thm)],[157, 156])).
% 9.62/9.79  tff(159,plain,
% 9.62/9.79      ($false),
% 9.62/9.79      inference(unit_resolution,[status(thm)],[158, 149])).
% 9.62/9.79  % SZS output end Proof
% 9.62/9.79  % E exiting
%------------------------------------------------------------------------------