Z3---4.15.1.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Z3---4.15.1
% Problem  : SET831-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_E %s %d THM

% Computer : n014.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sat Jun 21 05:26:27 AM UTC 2025

% Result   : Unsatisfiable 0.19s 0.37s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SET831-2 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.12  % Command    : run_E %s %d THM
% 0.12/0.33  % Computer : n014.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Fri Jun 20 05:44:54 EDT 2025
% 0.12/0.33  % CPUTime    : 
% 0.19/0.37  % SZS status Unsatisfiable
% 0.19/0.37  % SZS output start Proof
% 0.19/0.37  tff(c_in_type, type, (
% 0.19/0.37     c_in: ( $i * $i * $i ) > $o)).
% 0.19/0.37  tff(t_a_type, type, (
% 0.19/0.37     t_a: $i)).
% 0.19/0.37  tff(v_Z_type, type, (
% 0.19/0.37     v_Z: $i)).
% 0.19/0.37  tff(c_Main_OsubsetI__1_type, type, (
% 0.19/0.37     c_Main_OsubsetI__1: ( $i * $i * $i ) > $i)).
% 0.19/0.37  tff(c_inter_type, type, (
% 0.19/0.37     c_inter: ( $i * $i * $i ) > $i)).
% 0.19/0.37  tff(v_Y_type, type, (
% 0.19/0.37     v_Y: $i)).
% 0.19/0.37  tff(v_x_type, type, (
% 0.19/0.37     v_x: $i)).
% 0.19/0.37  tff(c_lessequals_type, type, (
% 0.19/0.37     c_lessequals: ( $i * $i * $i ) > $o)).
% 0.19/0.37  tff(tc_set_type, type, (
% 0.19/0.37     tc_set: $i > $i)).
% 0.19/0.37  tff(v_X_type, type, (
% 0.19/0.37     v_X: $i)).
% 0.19/0.37  tff(1,assumption,(~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a)), introduced(assumption)).
% 0.19/0.37  tff(2,assumption,(~(v_X = c_inter(v_Y, v_Z, t_a))), introduced(assumption)).
% 0.19/0.37  tff(3,assumption,(~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a))), introduced(assumption)).
% 0.19/0.37  tff(4,plain,
% 0.19/0.37      (^[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))))),
% 0.19/0.37      inference(bind,[status(th)],[])).
% 0.19/0.37  tff(5,plain,
% 0.19/0.37      (![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)))),
% 0.19/0.37      inference(quant_intro,[status(thm)],[4])).
% 0.19/0.37  tff(6,plain,
% 0.19/0.37      (![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)))),
% 0.19/0.37      inference(rewrite,[status(thm)],[])).
% 0.19/0.37  tff(7,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')).
% 0.19/0.37  tff(8,plain,
% 0.19/0.37      (![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)))),
% 0.19/0.37      inference(modus_ponens,[status(thm)],[7, 6])).
% 0.19/0.37  tff(9,plain,(
% 0.19/0.37      ![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)))),
% 0.19/0.37      inference(skolemize,[status(sab)],[8])).
% 0.19/0.37  tff(10,plain,
% 0.19/0.37      (![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)))),
% 0.19/0.37      inference(modus_ponens,[status(thm)],[9, 5])).
% 0.19/0.37  tff(11,plain,
% 0.19/0.37      (((~![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(c_inter(v_Y, v_Z, t_a), v_Y, t_a), v_Y, t_a)) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, 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(c_inter(v_Y, v_Z, t_a), v_Y, t_a), v_Y, t_a)) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a)))),
% 0.19/0.37      inference(rewrite,[status(thm)],[])).
% 0.19/0.37  tff(12,plain,
% 0.19/0.37      ((~![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(c_inter(v_Y, v_Z, t_a), v_Y, t_a), v_Y, t_a)) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a)))),
% 0.19/0.37      inference(quant_inst,[status(thm)],[])).
% 0.19/0.37  tff(13,plain,
% 0.19/0.37      ((~![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(c_inter(v_Y, v_Z, t_a), v_Y, t_a), v_Y, t_a)) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a))),
% 0.19/0.37      inference(modus_ponens,[status(thm)],[12, 11])).
% 0.19/0.37  tff(14,plain,
% 0.19/0.37      (~c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), v_Y, t_a)),
% 0.19/0.37      inference(unit_resolution,[status(thm)],[13, 10, 3])).
% 0.19/0.37  tff(15,plain,
% 0.19/0.37      (^[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))))),
% 0.19/0.37      inference(bind,[status(th)],[])).
% 0.19/0.37  tff(16,plain,
% 0.19/0.37      (![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)))),
% 0.19/0.37      inference(quant_intro,[status(thm)],[15])).
% 0.19/0.37  tff(17,plain,
% 0.19/0.37      (![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)))),
% 0.19/0.37      inference(rewrite,[status(thm)],[])).
% 0.19/0.37  tff(18,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')).
% 0.19/0.37  tff(19,plain,
% 0.19/0.37      (![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)))),
% 0.19/0.37      inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.37  tff(20,plain,(
% 0.19/0.37      ![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)))),
% 0.19/0.37      inference(skolemize,[status(sab)],[19])).
% 0.19/0.37  tff(21,plain,
% 0.19/0.37      (![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)))),
% 0.19/0.37      inference(modus_ponens,[status(thm)],[20, 16])).
% 0.19/0.37  tff(22,plain,
% 0.19/0.37      (((~![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(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), c_inter(v_Y, v_Z, t_a), 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(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), c_inter(v_Y, v_Z, t_a), t_a))),
% 0.19/0.37      inference(rewrite,[status(thm)],[])).
% 0.19/0.37  tff(23,plain,
% 0.19/0.37      ((c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), c_inter(v_Y, v_Z, t_a), t_a) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a))) <=> (c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), c_inter(v_Y, v_Z, t_a), t_a))),
% 0.19/0.37      inference(rewrite,[status(thm)],[])).
% 0.19/0.37  tff(24,plain,
% 0.19/0.37      (((~![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(c_inter(v_Y, v_Z, t_a), v_Y, t_a), c_inter(v_Y, v_Z, t_a), t_a) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, 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(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), c_inter(v_Y, v_Z, t_a), t_a)))),
% 0.19/0.37      inference(monotonicity,[status(thm)],[23])).
% 0.19/0.37  tff(25,plain,
% 0.19/0.37      (((~![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(c_inter(v_Y, v_Z, t_a), v_Y, t_a), c_inter(v_Y, v_Z, t_a), t_a) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, 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(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), c_inter(v_Y, v_Z, t_a), t_a))),
% 0.19/0.37      inference(transitivity,[status(thm)],[24, 22])).
% 0.19/0.37  tff(26,plain,
% 0.19/0.37      ((~![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(c_inter(v_Y, v_Z, t_a), v_Y, t_a), c_inter(v_Y, v_Z, t_a), t_a) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a)))),
% 0.19/0.37      inference(quant_inst,[status(thm)],[])).
% 0.19/0.38  tff(27,plain,
% 0.19/0.38      ((~![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(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), c_inter(v_Y, v_Z, t_a), t_a)),
% 0.19/0.38      inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.38  tff(28,plain,
% 0.19/0.38      (c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), c_inter(v_Y, v_Z, t_a), t_a)),
% 0.19/0.38      inference(unit_resolution,[status(thm)],[27, 21, 3])).
% 0.19/0.38  tff(29,plain,
% 0.19/0.38      (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : refl(((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_A, T_a)) <=> ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_A, T_a)))),
% 0.19/0.38      inference(bind,[status(th)],[])).
% 0.19/0.38  tff(30,plain,
% 0.19/0.38      (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_A, T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_A, T_a))),
% 0.19/0.38      inference(quant_intro,[status(thm)],[29])).
% 0.19/0.38  tff(31,plain,
% 0.19/0.38      (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_A, T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_A, T_a))),
% 0.19/0.38      inference(rewrite,[status(thm)],[])).
% 0.19/0.38  tff(32,axiom,(![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_A, T_a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_OIntE_1')).
% 0.19/0.38  tff(33,plain,
% 0.19/0.38      (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_A, T_a))),
% 0.19/0.38      inference(modus_ponens,[status(thm)],[32, 31])).
% 0.19/0.38  tff(34,plain,(
% 0.19/0.38      ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_A, T_a))),
% 0.19/0.38      inference(skolemize,[status(sab)],[33])).
% 0.19/0.38  tff(35,plain,
% 0.19/0.38      (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_A, T_a))),
% 0.19/0.38      inference(modus_ponens,[status(thm)],[34, 30])).
% 0.19/0.38  tff(36,plain,
% 0.19/0.38      (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_A, T_a))) | ((~c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), v_Y, t_a))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_A, T_a))) | (~c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), v_Y, t_a))),
% 0.19/0.38      inference(rewrite,[status(thm)],[])).
% 0.19/0.38  tff(37,plain,
% 0.19/0.38      ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_A, T_a))) | ((~c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), v_Y, t_a))),
% 0.19/0.38      inference(quant_inst,[status(thm)],[])).
% 0.19/0.38  tff(38,plain,
% 0.19/0.38      ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_A, T_a))) | (~c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), v_Y, t_a)),
% 0.19/0.38      inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.38  tff(39,plain,
% 0.19/0.38      ($false),
% 0.19/0.38      inference(unit_resolution,[status(thm)],[38, 35, 28, 14])).
% 0.19/0.38  tff(40,plain,(c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.38  tff(41,assumption,(~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a))), introduced(assumption)).
% 0.19/0.38  tff(42,plain,
% 0.19/0.38      (((~![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(c_inter(v_Y, v_Z, t_a), v_Z, t_a), v_Z, t_a)) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, 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(c_inter(v_Y, v_Z, t_a), v_Z, t_a), v_Z, t_a)) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a)))),
% 0.19/0.38      inference(rewrite,[status(thm)],[])).
% 0.19/0.38  tff(43,plain,
% 0.19/0.38      ((~![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(c_inter(v_Y, v_Z, t_a), v_Z, t_a), v_Z, t_a)) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a)))),
% 0.19/0.38      inference(quant_inst,[status(thm)],[])).
% 0.19/0.38  tff(44,plain,
% 0.19/0.38      ((~![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(c_inter(v_Y, v_Z, t_a), v_Z, t_a), v_Z, t_a)) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a))),
% 0.19/0.38      inference(modus_ponens,[status(thm)],[43, 42])).
% 0.19/0.38  tff(45,plain,
% 0.19/0.38      ((~c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Z, t_a), v_Z, t_a)) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a))),
% 0.19/0.38      inference(unit_resolution,[status(thm)],[44, 10])).
% 0.19/0.38  tff(46,plain,
% 0.19/0.38      (~c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Z, t_a), v_Z, t_a)),
% 0.19/0.38      inference(unit_resolution,[status(thm)],[45, 41])).
% 0.19/0.38  tff(47,plain,
% 0.19/0.38      (((~![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(c_inter(v_Y, v_Z, t_a), v_Z, t_a), c_inter(v_Y, v_Z, t_a), t_a) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, 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(c_inter(v_Y, v_Z, t_a), v_Z, t_a), c_inter(v_Y, v_Z, t_a), t_a) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a)))),
% 0.19/0.38      inference(rewrite,[status(thm)],[])).
% 0.19/0.38  tff(48,plain,
% 0.19/0.38      ((~![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(c_inter(v_Y, v_Z, t_a), v_Z, t_a), c_inter(v_Y, v_Z, t_a), t_a) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a)))),
% 0.19/0.38      inference(quant_inst,[status(thm)],[])).
% 0.19/0.38  tff(49,plain,
% 0.19/0.38      ((~![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(c_inter(v_Y, v_Z, t_a), v_Z, t_a), c_inter(v_Y, v_Z, t_a), t_a) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a))),
% 0.19/0.38      inference(modus_ponens,[status(thm)],[48, 47])).
% 0.19/0.38  tff(50,plain,
% 0.19/0.38      (c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Z, t_a), c_inter(v_Y, v_Z, t_a), t_a) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a))),
% 0.19/0.38      inference(unit_resolution,[status(thm)],[49, 21])).
% 0.19/0.38  tff(51,plain,
% 0.19/0.38      (c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Z, t_a), c_inter(v_Y, v_Z, t_a), t_a)),
% 0.19/0.38      inference(unit_resolution,[status(thm)],[50, 41])).
% 0.19/0.38  tff(52,plain,
% 0.19/0.38      (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : refl(((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a)) <=> ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a)))),
% 0.19/0.38      inference(bind,[status(th)],[])).
% 0.19/0.38  tff(53,plain,
% 0.19/0.38      (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a))),
% 0.19/0.38      inference(quant_intro,[status(thm)],[52])).
% 0.19/0.38  tff(54,plain,
% 0.19/0.38      (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a))),
% 0.19/0.38      inference(rewrite,[status(thm)],[])).
% 0.19/0.38  tff(55,axiom,(![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_OIntE_0')).
% 0.19/0.38  tff(56,plain,
% 0.19/0.38      (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a))),
% 0.19/0.38      inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.38  tff(57,plain,(
% 0.19/0.38      ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a))),
% 0.19/0.38      inference(skolemize,[status(sab)],[56])).
% 0.19/0.38  tff(58,plain,
% 0.19/0.38      (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a))),
% 0.19/0.38      inference(modus_ponens,[status(thm)],[57, 53])).
% 0.19/0.38  tff(59,plain,
% 0.19/0.38      (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a))) | ((~c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Z, t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Z, t_a), v_Z, t_a))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a))) | (~c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Z, t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Z, t_a), v_Z, t_a))),
% 0.19/0.38      inference(rewrite,[status(thm)],[])).
% 0.19/0.38  tff(60,plain,
% 0.19/0.38      ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a))) | ((~c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Z, t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Z, t_a), v_Z, t_a))),
% 0.19/0.38      inference(quant_inst,[status(thm)],[])).
% 0.19/0.38  tff(61,plain,
% 0.19/0.38      ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a))) | (~c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Z, t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Z, t_a), v_Z, t_a)),
% 0.19/0.38      inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.38  tff(62,plain,
% 0.19/0.38      ($false),
% 0.19/0.38      inference(unit_resolution,[status(thm)],[61, 58, 51, 46])).
% 0.19/0.38  tff(63,plain,(c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.38  tff(64,plain,
% 0.19/0.38      (^[V_U: $i] : refl(((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a))) <=> ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a))))),
% 0.19/0.38      inference(bind,[status(th)],[])).
% 0.19/0.38  tff(65,plain,
% 0.19/0.38      (![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a))) <=> ![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))),
% 0.19/0.38      inference(quant_intro,[status(thm)],[64])).
% 0.19/0.38  tff(66,plain,
% 0.19/0.38      (![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a))) <=> ![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))),
% 0.19/0.38      inference(rewrite,[status(thm)],[])).
% 0.19/0.38  tff(67,plain,
% 0.19/0.38      (^[V_U: $i] : trans(monotonicity(rewrite((((v_X = c_inter(v_Y, v_Z, t_a)) | c_lessequals(V_U, v_X, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a)))) <=> ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))), (((((v_X = c_inter(v_Y, v_Z, t_a)) | c_lessequals(V_U, v_X, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a)))) | (~c_lessequals(V_U, v_Y, tc_set(t_a)))) <=> (((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a))) | (~c_lessequals(V_U, v_Y, tc_set(t_a)))))), rewrite((((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a))) | (~c_lessequals(V_U, v_Y, tc_set(t_a)))) <=> ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))), (((((v_X = c_inter(v_Y, v_Z, t_a)) | c_lessequals(V_U, v_X, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a)))) | (~c_lessequals(V_U, v_Y, tc_set(t_a)))) <=> ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))))),
% 0.19/0.39      inference(bind,[status(th)],[])).
% 0.19/0.39  tff(68,plain,
% 0.19/0.39      (![V_U: $i] : ((((v_X = c_inter(v_Y, v_Z, t_a)) | c_lessequals(V_U, v_X, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a)))) | (~c_lessequals(V_U, v_Y, tc_set(t_a)))) <=> ![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))),
% 0.19/0.39      inference(quant_intro,[status(thm)],[67])).
% 0.19/0.39  tff(69,axiom,(![V_U: $i] : ((((v_X = c_inter(v_Y, v_Z, t_a)) | c_lessequals(V_U, v_X, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a)))) | (~c_lessequals(V_U, v_Y, tc_set(t_a))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_5')).
% 0.19/0.39  tff(70,plain,
% 0.19/0.39      (![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))),
% 0.19/0.39      inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.39  tff(71,plain,
% 0.19/0.39      (![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))),
% 0.19/0.39      inference(modus_ponens,[status(thm)],[70, 66])).
% 0.19/0.39  tff(72,plain,(
% 0.19/0.39      ![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))),
% 0.19/0.39      inference(skolemize,[status(sab)],[71])).
% 0.19/0.39  tff(73,plain,
% 0.19/0.39      (![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))),
% 0.19/0.39      inference(modus_ponens,[status(thm)],[72, 65])).
% 0.19/0.39  tff(74,plain,
% 0.19/0.39      (((~![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))) | ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a))) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a))))) <=> ((~![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))) | (v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a))) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a))))),
% 0.19/0.39      inference(rewrite,[status(thm)],[])).
% 0.19/0.39  tff(75,plain,
% 0.19/0.39      (((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a))) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a))) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a))) <=> ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a))) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a))))),
% 0.19/0.39      inference(rewrite,[status(thm)],[])).
% 0.19/0.39  tff(76,plain,
% 0.19/0.39      (((~![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))) | ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a))) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a))) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a)))) <=> ((~![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))) | ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a))) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a)))))),
% 0.19/0.39      inference(monotonicity,[status(thm)],[75])).
% 0.19/0.39  tff(77,plain,
% 0.19/0.39      (((~![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))) | ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a))) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a))) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a)))) <=> ((~![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))) | (v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a))) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a))))),
% 0.19/0.39      inference(transitivity,[status(thm)],[76, 74])).
% 0.19/0.39  tff(78,plain,
% 0.19/0.39      ((~![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))) | ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a))) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a))) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a)))),
% 0.19/0.39      inference(quant_inst,[status(thm)],[])).
% 0.19/0.39  tff(79,plain,
% 0.19/0.39      ((~![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))) | (v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a))) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a)))),
% 0.19/0.39      inference(modus_ponens,[status(thm)],[78, 77])).
% 0.19/0.39  tff(80,plain,
% 0.19/0.39      ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a))) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a))),
% 0.19/0.39      inference(unit_resolution,[status(thm)],[79, 73, 63])).
% 0.19/0.39  tff(81,plain,
% 0.19/0.39      ((v_X = c_inter(v_Y, v_Z, t_a)) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a))),
% 0.19/0.39      inference(unit_resolution,[status(thm)],[80, 40])).
% 0.19/0.39  tff(82,plain,
% 0.19/0.39      (c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a))),
% 0.19/0.39      inference(unit_resolution,[status(thm)],[81, 2])).
% 0.19/0.39  tff(83,plain,
% 0.19/0.39      (^[T_a: $i, V_B: $i, V_A: $i] : refl(((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~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_B, V_A, tc_set(T_a)))))),
% 0.19/0.39      inference(bind,[status(th)],[])).
% 0.19/0.39  tff(84,plain,
% 0.19/0.39      (![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 0.19/0.39      inference(quant_intro,[status(thm)],[83])).
% 0.19/0.39  tff(85,plain,
% 0.19/0.39      (![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 0.19/0.39      inference(rewrite,[status(thm)],[])).
% 0.19/0.39  tff(86,plain,
% 0.19/0.39      (^[T_a: $i, V_B: $i, V_A: $i] : trans(monotonicity(rewrite(((~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) <=> ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))), ((((~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | (V_A = V_B)) <=> (((~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) | (V_A = V_B)))), rewrite((((~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) | (V_A = V_B)) <=> ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~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))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a))))))),
% 0.19/0.39      inference(bind,[status(th)],[])).
% 0.19/0.39  tff(87,plain,
% 0.19/0.39      (![T_a: $i, V_B: $i, V_A: $i] : (((~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | (V_A = V_B)) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 0.19/0.40      inference(quant_intro,[status(thm)],[86])).
% 0.19/0.40  tff(88,axiom,(![T_a: $i, V_B: $i, V_A: $i] : (((~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | (V_A = V_B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_Osubset__antisym_0')).
% 0.19/0.40  tff(89,plain,
% 0.19/0.40      (![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 0.19/0.40      inference(modus_ponens,[status(thm)],[88, 87])).
% 0.19/0.40  tff(90,plain,
% 0.19/0.40      (![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 0.19/0.40      inference(modus_ponens,[status(thm)],[89, 85])).
% 0.19/0.40  tff(91,plain,(
% 0.19/0.40      ![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 0.19/0.40      inference(skolemize,[status(sab)],[90])).
% 0.19/0.40  tff(92,plain,
% 0.19/0.40      (![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 0.19/0.40      inference(modus_ponens,[status(thm)],[91, 84])).
% 0.19/0.40  tff(93,plain,
% 0.19/0.40      (((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a))) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | (v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a))) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a))))),
% 0.19/0.40      inference(rewrite,[status(thm)],[])).
% 0.19/0.40  tff(94,plain,
% 0.19/0.40      (((~c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a))) | (v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a)))) <=> ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a))) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a))))),
% 0.19/0.40      inference(rewrite,[status(thm)],[])).
% 0.19/0.40  tff(95,plain,
% 0.19/0.40      (((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((~c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a))) | (v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a))) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a)))))),
% 0.19/0.40      inference(monotonicity,[status(thm)],[94])).
% 0.19/0.40  tff(96,plain,
% 0.19/0.40      (((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((~c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a))) | (v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | (v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a))) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a))))),
% 0.19/0.40      inference(transitivity,[status(thm)],[95, 93])).
% 0.19/0.40  tff(97,plain,
% 0.19/0.40      ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((~c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a))) | (v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a))))),
% 0.19/0.40      inference(quant_inst,[status(thm)],[])).
% 0.19/0.40  tff(98,plain,
% 0.19/0.40      ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | (v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a))) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a)))),
% 0.19/0.40      inference(modus_ponens,[status(thm)],[97, 96])).
% 0.19/0.40  tff(99,plain,
% 0.19/0.40      (~c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a))),
% 0.19/0.40      inference(unit_resolution,[status(thm)],[98, 2, 92, 82])).
% 0.19/0.40  tff(100,plain,
% 0.19/0.40      (((~![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_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a)) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, 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_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a)) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a))),
% 0.19/0.40      inference(rewrite,[status(thm)],[])).
% 0.19/0.40  tff(101,plain,
% 0.19/0.40      ((c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a) | c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a))) <=> (c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a)) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a))),
% 0.19/0.40      inference(rewrite,[status(thm)],[])).
% 0.19/0.40  tff(102,plain,
% 0.19/0.40      (((~![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_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a) | c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), 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_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a)) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)))),
% 0.19/0.40      inference(monotonicity,[status(thm)],[101])).
% 0.19/0.40  tff(103,plain,
% 0.19/0.40      (((~![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_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a) | c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), 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_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a)) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a))),
% 0.19/0.40      inference(transitivity,[status(thm)],[102, 100])).
% 0.19/0.40  tff(104,plain,
% 0.19/0.40      ((~![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_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a) | c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a)))),
% 0.19/0.40      inference(quant_inst,[status(thm)],[])).
% 0.19/0.40  tff(105,plain,
% 0.19/0.40      ((~![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_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a)) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)),
% 0.19/0.40      inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.40  tff(106,plain,
% 0.19/0.40      (c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)),
% 0.19/0.40      inference(unit_resolution,[status(thm)],[105, 21, 99])).
% 0.19/0.40  tff(107,assumption,(~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a)), introduced(assumption)).
% 0.19/0.40  tff(108,assumption,(c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)), introduced(assumption)).
% 0.19/0.40  tff(109,plain,
% 0.19/0.40      (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : refl((c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) <=> (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)))))),
% 0.19/0.40      inference(bind,[status(th)],[])).
% 0.19/0.40  tff(110,plain,
% 0.19/0.40      (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))),
% 0.19/0.40      inference(quant_intro,[status(thm)],[109])).
% 0.19/0.40  tff(111,plain,
% 0.19/0.40      (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))),
% 0.19/0.40      inference(rewrite,[status(thm)],[])).
% 0.19/0.40  tff(112,plain,
% 0.19/0.40      (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : rewrite((((~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | c_in(V_c, V_B, T_a)) <=> (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)))))),
% 0.19/0.40      inference(bind,[status(th)],[])).
% 0.19/0.40  tff(113,plain,
% 0.19/0.40      (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | c_in(V_c, V_B, T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))),
% 0.19/0.40      inference(quant_intro,[status(thm)],[112])).
% 0.19/0.40  tff(114,axiom,(![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | c_in(V_c, V_B, T_a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_OsubsetD_0')).
% 0.19/0.40  tff(115,plain,
% 0.19/0.40      (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))),
% 0.19/0.40      inference(modus_ponens,[status(thm)],[114, 113])).
% 0.19/0.40  tff(116,plain,
% 0.19/0.40      (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))),
% 0.19/0.40      inference(modus_ponens,[status(thm)],[115, 111])).
% 0.19/0.40  tff(117,plain,(
% 0.19/0.40      ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))),
% 0.19/0.40      inference(skolemize,[status(sab)],[116])).
% 0.19/0.40  tff(118,plain,
% 0.19/0.40      (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))),
% 0.19/0.40      inference(modus_ponens,[status(thm)],[117, 110])).
% 0.19/0.40  tff(119,assumption,(~c_lessequals(v_X, v_Z, tc_set(t_a))), introduced(assumption)).
% 0.19/0.40  tff(120,plain,
% 0.19/0.40      (((v_X = c_inter(v_Y, v_Z, t_a)) | c_lessequals(v_X, v_Z, tc_set(t_a))) <=> ((v_X = c_inter(v_Y, v_Z, t_a)) | c_lessequals(v_X, v_Z, tc_set(t_a)))),
% 0.19/0.40      inference(rewrite,[status(thm)],[])).
% 0.19/0.40  tff(121,axiom,((v_X = c_inter(v_Y, v_Z, t_a)) | c_lessequals(v_X, v_Z, tc_set(t_a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_1')).
% 0.19/0.40  tff(122,plain,
% 0.19/0.40      ((v_X = c_inter(v_Y, v_Z, t_a)) | c_lessequals(v_X, v_Z, tc_set(t_a))),
% 0.19/0.40      inference(modus_ponens,[status(thm)],[121, 120])).
% 0.19/0.40  tff(123,plain,
% 0.19/0.40      (v_X = c_inter(v_Y, v_Z, t_a)),
% 0.19/0.40      inference(unit_resolution,[status(thm)],[122, 119])).
% 0.19/0.40  tff(124,plain,
% 0.19/0.40      (c_lessequals(v_X, v_Z, tc_set(t_a)) <=> c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a))),
% 0.19/0.40      inference(monotonicity,[status(thm)],[123])).
% 0.19/0.40  tff(125,plain,
% 0.19/0.40      (c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a)) <=> c_lessequals(v_X, v_Z, tc_set(t_a))),
% 0.19/0.40      inference(symmetry,[status(thm)],[124])).
% 0.19/0.40  tff(126,plain,
% 0.19/0.40      (c_lessequals(v_X, v_Z, tc_set(t_a))),
% 0.19/0.40      inference(modus_ponens,[status(thm)],[63, 125])).
% 0.19/0.40  tff(127,plain,
% 0.19/0.40      ($false),
% 0.19/0.40      inference(unit_resolution,[status(thm)],[119, 126])).
% 0.19/0.40  tff(128,plain,(c_lessequals(v_X, v_Z, tc_set(t_a))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40  tff(129,plain,
% 0.19/0.40      (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)))),
% 0.19/0.40      inference(rewrite,[status(thm)],[])).
% 0.19/0.40  tff(130,plain,
% 0.19/0.40      ((c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) <=> ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)))),
% 0.19/0.41      inference(rewrite,[status(thm)],[])).
% 0.19/0.41  tff(131,plain,
% 0.19/0.41      (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a))))),
% 0.19/0.41      inference(monotonicity,[status(thm)],[130])).
% 0.19/0.41  tff(132,plain,
% 0.19/0.41      (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)))),
% 0.19/0.41      inference(transitivity,[status(thm)],[131, 129])).
% 0.19/0.41  tff(133,plain,
% 0.19/0.41      ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))))),
% 0.19/0.41      inference(quant_inst,[status(thm)],[])).
% 0.19/0.41  tff(134,plain,
% 0.19/0.41      ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a))),
% 0.19/0.41      inference(modus_ponens,[status(thm)],[133, 132])).
% 0.19/0.41  tff(135,plain,
% 0.19/0.41      ($false),
% 0.19/0.41      inference(unit_resolution,[status(thm)],[134, 128, 118, 108, 107])).
% 0.19/0.41  tff(136,plain,(c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41  tff(137,plain,
% 0.19/0.41      (c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a)),
% 0.19/0.41      inference(unit_resolution,[status(thm)],[136, 106])).
% 0.19/0.41  tff(138,plain,
% 0.19/0.41      (((~![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_X, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), 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_X, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a)))),
% 0.19/0.41      inference(rewrite,[status(thm)],[])).
% 0.19/0.41  tff(139,plain,
% 0.19/0.41      ((~![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_X, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a)))),
% 0.19/0.41      inference(quant_inst,[status(thm)],[])).
% 0.19/0.41  tff(140,plain,
% 0.19/0.41      ((~![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_X, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a))),
% 0.19/0.41      inference(modus_ponens,[status(thm)],[139, 138])).
% 0.19/0.41  tff(141,plain,
% 0.19/0.41      (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a)),
% 0.19/0.41      inference(unit_resolution,[status(thm)],[140, 10, 99])).
% 0.19/0.41  tff(142,plain,
% 0.19/0.41      (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : refl((c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a))) <=> (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a))))),
% 0.19/0.41      inference(bind,[status(th)],[])).
% 0.19/0.41  tff(143,plain,
% 0.19/0.41      (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a))) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))),
% 0.19/0.41      inference(quant_intro,[status(thm)],[142])).
% 0.19/0.41  tff(144,plain,
% 0.19/0.41      (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a))) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))),
% 0.19/0.41      inference(rewrite,[status(thm)],[])).
% 0.19/0.41  tff(145,plain,
% 0.19/0.41      (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : trans(monotonicity(rewrite(((~c_in(V_c, V_B, T_a)) | (~c_in(V_c, V_A, T_a))) <=> ((~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))), ((((~c_in(V_c, V_B, T_a)) | (~c_in(V_c, V_A, T_a))) | c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) <=> (((~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a))) | c_in(V_c, c_inter(V_A, V_B, T_a), T_a)))), rewrite((((~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a))) | c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) <=> (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))), ((((~c_in(V_c, V_B, T_a)) | (~c_in(V_c, V_A, T_a))) | c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) <=> (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))))),
% 0.19/0.41      inference(bind,[status(th)],[])).
% 0.19/0.41  tff(146,plain,
% 0.19/0.41      (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_c, V_B, T_a)) | (~c_in(V_c, V_A, T_a))) | c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))),
% 0.19/0.41      inference(quant_intro,[status(thm)],[145])).
% 0.19/0.41  tff(147,axiom,(![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_c, V_B, T_a)) | (~c_in(V_c, V_A, T_a))) | c_in(V_c, c_inter(V_A, V_B, T_a), T_a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_OIntI_0')).
% 0.19/0.41  tff(148,plain,
% 0.19/0.41      (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))),
% 0.19/0.41      inference(modus_ponens,[status(thm)],[147, 146])).
% 0.19/0.41  tff(149,plain,
% 0.19/0.41      (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))),
% 0.19/0.41      inference(modus_ponens,[status(thm)],[148, 144])).
% 0.19/0.41  tff(150,plain,(
% 0.19/0.41      ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))),
% 0.19/0.41      inference(skolemize,[status(sab)],[149])).
% 0.19/0.41  tff(151,plain,
% 0.19/0.41      (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))),
% 0.19/0.41      inference(modus_ponens,[status(thm)],[150, 143])).
% 0.19/0.41  tff(152,plain,
% 0.19/0.41      (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))) | (c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a)) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a)) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a)))),
% 0.19/0.41      inference(rewrite,[status(thm)],[])).
% 0.19/0.41  tff(153,plain,
% 0.19/0.41      ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))) | (c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a)) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a)))),
% 0.19/0.41      inference(quant_inst,[status(thm)],[])).
% 0.19/0.41  tff(154,plain,
% 0.19/0.41      ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a)) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a))),
% 0.19/0.41      inference(modus_ponens,[status(thm)],[153, 152])).
% 0.19/0.41  tff(155,plain,
% 0.19/0.41      ((~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a)) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a))),
% 0.19/0.41      inference(unit_resolution,[status(thm)],[154, 151, 141])).
% 0.19/0.41  tff(156,plain,
% 0.19/0.41      (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a)),
% 0.19/0.41      inference(unit_resolution,[status(thm)],[155, 137])).
% 0.19/0.41  tff(157,plain,
% 0.19/0.41      (((v_X = c_inter(v_Y, v_Z, t_a)) | c_lessequals(v_X, v_Y, tc_set(t_a))) <=> ((v_X = c_inter(v_Y, v_Z, t_a)) | c_lessequals(v_X, v_Y, tc_set(t_a)))),
% 0.19/0.41      inference(rewrite,[status(thm)],[])).
% 0.19/0.41  tff(158,axiom,((v_X = c_inter(v_Y, v_Z, t_a)) | c_lessequals(v_X, v_Y, tc_set(t_a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.19/0.41  tff(159,plain,
% 0.19/0.41      ((v_X = c_inter(v_Y, v_Z, t_a)) | c_lessequals(v_X, v_Y, tc_set(t_a))),
% 0.19/0.41      inference(modus_ponens,[status(thm)],[158, 157])).
% 0.19/0.41  tff(160,plain,
% 0.19/0.41      (c_lessequals(v_X, v_Y, tc_set(t_a))),
% 0.19/0.41      inference(unit_resolution,[status(thm)],[159, 2])).
% 0.19/0.41  tff(161,plain,
% 0.19/0.41      (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | ((~c_lessequals(v_X, v_Y, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)))),
% 0.19/0.41      inference(rewrite,[status(thm)],[])).
% 0.19/0.41  tff(162,plain,
% 0.19/0.41      ((c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) <=> ((~c_lessequals(v_X, v_Y, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)))),
% 0.19/0.41      inference(rewrite,[status(thm)],[])).
% 0.19/0.41  tff(163,plain,
% 0.19/0.41      (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)) | (~c_lessequals(v_X, v_Y, tc_set(t_a))))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | ((~c_lessequals(v_X, v_Y, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a))))),
% 0.19/0.41      inference(monotonicity,[status(thm)],[162])).
% 0.19/0.41  tff(164,plain,
% 0.19/0.42      (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)) | (~c_lessequals(v_X, v_Y, tc_set(t_a))))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)))),
% 0.19/0.42      inference(transitivity,[status(thm)],[163, 161])).
% 0.19/0.42  tff(165,plain,
% 0.19/0.42      ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)) | (~c_lessequals(v_X, v_Y, tc_set(t_a))))),
% 0.19/0.42      inference(quant_inst,[status(thm)],[])).
% 0.19/0.42  tff(166,plain,
% 0.19/0.42      ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a))),
% 0.19/0.42      inference(modus_ponens,[status(thm)],[165, 164])).
% 0.19/0.42  tff(167,plain,
% 0.19/0.42      ($false),
% 0.19/0.42      inference(unit_resolution,[status(thm)],[166, 160, 118, 106, 156])).
% 0.19/0.42  tff(168,plain,(v_X = c_inter(v_Y, v_Z, t_a)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42  tff(169,plain,
% 0.19/0.42      (c_inter(v_Y, v_Z, t_a) = v_X),
% 0.19/0.42      inference(symmetry,[status(thm)],[168])).
% 0.19/0.42  tff(170,plain,
% 0.19/0.42      (c_lessequals(v_x, c_inter(v_Y, v_Z, t_a), tc_set(t_a)) <=> c_lessequals(v_x, v_X, tc_set(t_a))),
% 0.19/0.42      inference(monotonicity,[status(thm)],[169])).
% 0.19/0.42  tff(171,plain,
% 0.19/0.42      (c_lessequals(v_x, v_X, tc_set(t_a)) <=> c_lessequals(v_x, c_inter(v_Y, v_Z, t_a), tc_set(t_a))),
% 0.19/0.42      inference(symmetry,[status(thm)],[170])).
% 0.19/0.42  tff(172,plain,
% 0.19/0.42      ((~c_lessequals(v_x, v_X, tc_set(t_a))) <=> (~c_lessequals(v_x, c_inter(v_Y, v_Z, t_a), tc_set(t_a)))),
% 0.19/0.42      inference(monotonicity,[status(thm)],[171])).
% 0.19/0.42  tff(173,plain,
% 0.19/0.42      (c_lessequals(v_X, v_Y, tc_set(t_a)) <=> c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a))),
% 0.19/0.42      inference(monotonicity,[status(thm)],[168])).
% 0.19/0.42  tff(174,plain,
% 0.19/0.42      (c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a)) <=> c_lessequals(v_X, v_Y, tc_set(t_a))),
% 0.19/0.42      inference(symmetry,[status(thm)],[173])).
% 0.19/0.42  tff(175,plain,
% 0.19/0.42      (c_lessequals(v_X, v_Y, tc_set(t_a))),
% 0.19/0.42      inference(modus_ponens,[status(thm)],[40, 174])).
% 0.19/0.42  tff(176,plain,
% 0.19/0.42      (((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a)))) <=> ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a))))),
% 0.19/0.42      inference(rewrite,[status(thm)],[])).
% 0.19/0.42  tff(177,plain,
% 0.19/0.42      ((((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a)))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))) <=> ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a))))),
% 0.19/0.42      inference(rewrite,[status(thm)],[])).
% 0.19/0.42  tff(178,plain,
% 0.19/0.42      ((((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) <=> ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a))))),
% 0.19/0.42      inference(rewrite,[status(thm)],[])).
% 0.19/0.42  tff(179,plain,
% 0.19/0.42      (((~c_lessequals(v_x, v_X, tc_set(t_a))) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) <=> ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a))))),
% 0.19/0.42      inference(rewrite,[status(thm)],[])).
% 0.19/0.42  tff(180,plain,
% 0.19/0.42      ((((~c_lessequals(v_x, v_X, tc_set(t_a))) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) <=> (((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))))),
% 0.19/0.42      inference(monotonicity,[status(thm)],[179])).
% 0.19/0.42  tff(181,plain,
% 0.19/0.42      ((((~c_lessequals(v_x, v_X, tc_set(t_a))) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) <=> ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a))))),
% 0.19/0.42      inference(transitivity,[status(thm)],[180, 178])).
% 0.19/0.42  tff(182,plain,
% 0.19/0.42      (((((~c_lessequals(v_x, v_X, tc_set(t_a))) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))) <=> (((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a)))) | (~(v_X = c_inter(v_Y, v_Z, t_a))))),
% 0.19/0.42      inference(monotonicity,[status(thm)],[181])).
% 0.19/0.42  tff(183,plain,
% 0.19/0.42      (((((~c_lessequals(v_x, v_X, tc_set(t_a))) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))) <=> ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a))))),
% 0.19/0.42      inference(transitivity,[status(thm)],[182, 177])).
% 0.19/0.42  tff(184,axiom,((((~c_lessequals(v_x, v_X, tc_set(t_a))) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_4')).
% 0.19/0.42  tff(185,plain,
% 0.19/0.42      ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a)))),
% 0.19/0.42      inference(modus_ponens,[status(thm)],[184, 183])).
% 0.19/0.42  tff(186,plain,
% 0.19/0.42      ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a)))),
% 0.19/0.42      inference(modus_ponens,[status(thm)],[185, 176])).
% 0.19/0.42  tff(187,plain,
% 0.19/0.42      ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a)))),
% 0.19/0.42      inference(modus_ponens,[status(thm)],[186, 176])).
% 0.19/0.42  tff(188,plain,
% 0.19/0.42      ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a)))),
% 0.19/0.42      inference(modus_ponens,[status(thm)],[187, 176])).
% 0.19/0.42  tff(189,plain,
% 0.19/0.42      ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a)))),
% 0.19/0.42      inference(modus_ponens,[status(thm)],[188, 176])).
% 0.19/0.42  tff(190,plain,
% 0.19/0.42      (~c_lessequals(v_x, v_X, tc_set(t_a))),
% 0.19/0.42      inference(unit_resolution,[status(thm)],[189, 175, 128, 168])).
% 0.19/0.42  tff(191,plain,
% 0.19/0.42      (~c_lessequals(v_x, c_inter(v_Y, v_Z, t_a), tc_set(t_a))),
% 0.19/0.42      inference(modus_ponens,[status(thm)],[190, 172])).
% 0.19/0.42  tff(192,plain,
% 0.19/0.42      (((~![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_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a) | c_lessequals(v_x, c_inter(v_Y, v_Z, t_a), 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_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a) | c_lessequals(v_x, c_inter(v_Y, v_Z, t_a), tc_set(t_a)))),
% 0.19/0.42      inference(rewrite,[status(thm)],[])).
% 0.19/0.42  tff(193,plain,
% 0.19/0.42      ((~![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_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a) | c_lessequals(v_x, c_inter(v_Y, v_Z, t_a), tc_set(t_a)))),
% 0.19/0.42      inference(quant_inst,[status(thm)],[])).
% 0.19/0.42  tff(194,plain,
% 0.19/0.42      ((~![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_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a) | c_lessequals(v_x, c_inter(v_Y, v_Z, t_a), tc_set(t_a))),
% 0.19/0.42      inference(modus_ponens,[status(thm)],[193, 192])).
% 0.19/0.42  tff(195,plain,
% 0.19/0.42      (c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a) | c_lessequals(v_x, c_inter(v_Y, v_Z, t_a), tc_set(t_a))),
% 0.19/0.42      inference(unit_resolution,[status(thm)],[194, 21])).
% 0.19/0.42  tff(196,plain,
% 0.19/0.42      (c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)),
% 0.19/0.42      inference(unit_resolution,[status(thm)],[195, 191])).
% 0.19/0.42  tff(197,plain,
% 0.19/0.42      ((c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))) <=> (c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))))),
% 0.19/0.42      inference(rewrite,[status(thm)],[])).
% 0.19/0.42  tff(198,plain,
% 0.19/0.42      (((c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))) <=> (c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))))),
% 0.19/0.42      inference(rewrite,[status(thm)],[])).
% 0.19/0.42  tff(199,plain,
% 0.19/0.42      (((c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) <=> (c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))))),
% 0.19/0.42      inference(rewrite,[status(thm)],[])).
% 0.19/0.42  tff(200,plain,
% 0.19/0.42      ((c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) <=> (c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))))),
% 0.19/0.42      inference(rewrite,[status(thm)],[])).
% 0.19/0.42  tff(201,plain,
% 0.19/0.42      (((c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) <=> ((c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))))),
% 0.19/0.42      inference(monotonicity,[status(thm)],[200])).
% 0.19/0.42  tff(202,plain,
% 0.19/0.42      (((c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) <=> (c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))))),
% 0.19/0.42      inference(transitivity,[status(thm)],[201, 199])).
% 0.19/0.42  tff(203,plain,
% 0.19/0.42      ((((c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))) <=> ((c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) | (~(v_X = c_inter(v_Y, v_Z, t_a))))),
% 0.19/0.42      inference(monotonicity,[status(thm)],[202])).
% 0.19/0.42  tff(204,plain,
% 0.19/0.42      ((((c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))) <=> (c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))))),
% 0.19/0.42      inference(transitivity,[status(thm)],[203, 198])).
% 0.19/0.42  tff(205,axiom,(((c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_2')).
% 0.19/0.42  tff(206,plain,
% 0.19/0.42      (c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))),
% 0.19/0.42      inference(modus_ponens,[status(thm)],[205, 204])).
% 0.19/0.42  tff(207,plain,
% 0.19/0.42      (c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))),
% 0.19/0.42      inference(modus_ponens,[status(thm)],[206, 197])).
% 0.19/0.42  tff(208,plain,
% 0.19/0.42      (c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))),
% 0.19/0.43      inference(modus_ponens,[status(thm)],[207, 197])).
% 0.19/0.43  tff(209,plain,
% 0.19/0.43      (c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))),
% 0.19/0.43      inference(modus_ponens,[status(thm)],[208, 197])).
% 0.19/0.43  tff(210,plain,
% 0.19/0.43      (c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))),
% 0.19/0.43      inference(modus_ponens,[status(thm)],[209, 197])).
% 0.19/0.43  tff(211,plain,
% 0.19/0.43      (c_lessequals(v_x, v_Y, tc_set(t_a))),
% 0.19/0.43      inference(unit_resolution,[status(thm)],[210, 175, 128, 168])).
% 0.19/0.43  tff(212,plain,
% 0.19/0.43      (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | ((~c_lessequals(v_x, v_Y, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (~c_lessequals(v_x, v_Y, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)))),
% 0.19/0.43      inference(rewrite,[status(thm)],[])).
% 0.19/0.43  tff(213,plain,
% 0.19/0.43      ((c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)) | (~c_lessequals(v_x, v_Y, tc_set(t_a)))) <=> ((~c_lessequals(v_x, v_Y, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)))),
% 0.19/0.43      inference(rewrite,[status(thm)],[])).
% 0.19/0.43  tff(214,plain,
% 0.19/0.43      (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)) | (~c_lessequals(v_x, v_Y, tc_set(t_a))))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | ((~c_lessequals(v_x, v_Y, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a))))),
% 0.19/0.43      inference(monotonicity,[status(thm)],[213])).
% 0.19/0.43  tff(215,plain,
% 0.19/0.43      (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)) | (~c_lessequals(v_x, v_Y, tc_set(t_a))))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (~c_lessequals(v_x, v_Y, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)))),
% 0.19/0.43      inference(transitivity,[status(thm)],[214, 212])).
% 0.19/0.43  tff(216,plain,
% 0.19/0.43      ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)) | (~c_lessequals(v_x, v_Y, tc_set(t_a))))),
% 0.19/0.43      inference(quant_inst,[status(thm)],[])).
% 0.19/0.43  tff(217,plain,
% 0.19/0.43      ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (~c_lessequals(v_x, v_Y, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a))),
% 0.19/0.43      inference(modus_ponens,[status(thm)],[216, 215])).
% 0.19/0.43  tff(218,plain,
% 0.19/0.43      ($false),
% 0.19/0.43      inference(unit_resolution,[status(thm)],[217, 211, 118, 196, 1])).
% 0.19/0.43  tff(219,plain,(c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43  tff(220,plain,
% 0.19/0.43      (((~![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_x, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_lessequals(v_x, c_inter(v_Y, v_Z, t_a), 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_x, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_lessequals(v_x, c_inter(v_Y, v_Z, t_a), tc_set(t_a)))),
% 0.19/0.43      inference(rewrite,[status(thm)],[])).
% 0.19/0.43  tff(221,plain,
% 0.19/0.43      ((~![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_x, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_lessequals(v_x, c_inter(v_Y, v_Z, t_a), tc_set(t_a)))),
% 0.19/0.43      inference(quant_inst,[status(thm)],[])).
% 0.19/0.43  tff(222,plain,
% 0.19/0.43      ((~![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_x, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_lessequals(v_x, c_inter(v_Y, v_Z, t_a), tc_set(t_a))),
% 0.19/0.43      inference(modus_ponens,[status(thm)],[221, 220])).
% 0.19/0.43  tff(223,plain,
% 0.19/0.43      ((~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_lessequals(v_x, c_inter(v_Y, v_Z, t_a), tc_set(t_a))),
% 0.19/0.43      inference(unit_resolution,[status(thm)],[222, 10])).
% 0.19/0.43  tff(224,plain,
% 0.19/0.43      (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a)),
% 0.19/0.43      inference(unit_resolution,[status(thm)],[223, 191])).
% 0.19/0.43  tff(225,plain,
% 0.19/0.43      (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))) | (c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a)) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))) | c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a)) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a)))),
% 0.19/0.43      inference(rewrite,[status(thm)],[])).
% 0.19/0.43  tff(226,plain,
% 0.19/0.43      ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))) | (c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a)) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a)))),
% 0.19/0.43      inference(quant_inst,[status(thm)],[])).
% 0.19/0.43  tff(227,plain,
% 0.19/0.43      ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))) | c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a)) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a))),
% 0.19/0.43      inference(modus_ponens,[status(thm)],[226, 225])).
% 0.19/0.43  tff(228,plain,
% 0.19/0.43      ((~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a)) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a))),
% 0.19/0.43      inference(unit_resolution,[status(thm)],[227, 151, 224])).
% 0.19/0.43  tff(229,plain,
% 0.19/0.43      (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a)),
% 0.19/0.43      inference(unit_resolution,[status(thm)],[228, 219])).
% 0.19/0.43  tff(230,plain,
% 0.19/0.43      (((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a))) <=> ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a)))),
% 0.19/0.44      inference(rewrite,[status(thm)],[])).
% 0.19/0.44  tff(231,plain,
% 0.19/0.44      ((((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))) <=> ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a)))),
% 0.19/0.44      inference(rewrite,[status(thm)],[])).
% 0.19/0.44  tff(232,plain,
% 0.19/0.44      ((((~c_lessequals(v_X, v_Z, tc_set(t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) <=> ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a)))),
% 0.19/0.44      inference(rewrite,[status(thm)],[])).
% 0.19/0.44  tff(233,plain,
% 0.19/0.44      ((c_lessequals(v_x, v_Z, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) <=> ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a)))),
% 0.19/0.44      inference(rewrite,[status(thm)],[])).
% 0.19/0.44  tff(234,plain,
% 0.19/0.44      (((c_lessequals(v_x, v_Z, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) <=> (((~c_lessequals(v_X, v_Z, tc_set(t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))))),
% 0.19/0.44      inference(monotonicity,[status(thm)],[233])).
% 0.19/0.44  tff(235,plain,
% 0.19/0.44      (((c_lessequals(v_x, v_Z, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) <=> ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a)))),
% 0.19/0.44      inference(transitivity,[status(thm)],[234, 232])).
% 0.19/0.44  tff(236,plain,
% 0.19/0.44      ((((c_lessequals(v_x, v_Z, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))) <=> (((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))))),
% 0.19/0.44      inference(monotonicity,[status(thm)],[235])).
% 0.19/0.44  tff(237,plain,
% 0.19/0.44      ((((c_lessequals(v_x, v_Z, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))) <=> ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a)))),
% 0.19/0.44      inference(transitivity,[status(thm)],[236, 231])).
% 0.19/0.44  tff(238,axiom,(((c_lessequals(v_x, v_Z, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_3')).
% 0.19/0.44  tff(239,plain,
% 0.19/0.44      ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a))),
% 0.19/0.44      inference(modus_ponens,[status(thm)],[238, 237])).
% 0.19/0.44  tff(240,plain,
% 0.19/0.44      ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a))),
% 0.19/0.44      inference(modus_ponens,[status(thm)],[239, 230])).
% 0.19/0.44  tff(241,plain,
% 0.19/0.44      ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a))),
% 0.19/0.44      inference(modus_ponens,[status(thm)],[240, 230])).
% 0.19/0.44  tff(242,plain,
% 0.19/0.44      ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a))),
% 0.19/0.44      inference(modus_ponens,[status(thm)],[241, 230])).
% 0.19/0.44  tff(243,plain,
% 0.19/0.44      ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a))),
% 0.19/0.44      inference(modus_ponens,[status(thm)],[242, 230])).
% 0.19/0.44  tff(244,plain,
% 0.19/0.44      (c_lessequals(v_x, v_Z, tc_set(t_a))),
% 0.19/0.44      inference(unit_resolution,[status(thm)],[243, 175, 128, 168])).
% 0.19/0.44  tff(245,plain,
% 0.19/0.44      (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | ((~c_lessequals(v_x, v_Z, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (~c_lessequals(v_x, v_Z, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)))),
% 0.19/0.44      inference(rewrite,[status(thm)],[])).
% 0.19/0.44  tff(246,plain,
% 0.19/0.44      ((c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)) | (~c_lessequals(v_x, v_Z, tc_set(t_a)))) <=> ((~c_lessequals(v_x, v_Z, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)))),
% 0.19/0.44      inference(rewrite,[status(thm)],[])).
% 0.19/0.44  tff(247,plain,
% 0.19/0.44      (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)) | (~c_lessequals(v_x, v_Z, tc_set(t_a))))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | ((~c_lessequals(v_x, v_Z, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a))))),
% 0.19/0.44      inference(monotonicity,[status(thm)],[246])).
% 0.19/0.44  tff(248,plain,
% 0.19/0.44      (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)) | (~c_lessequals(v_x, v_Z, tc_set(t_a))))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (~c_lessequals(v_x, v_Z, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)))),
% 0.19/0.44      inference(transitivity,[status(thm)],[247, 245])).
% 0.19/0.44  tff(249,plain,
% 0.19/0.44      ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)) | (~c_lessequals(v_x, v_Z, tc_set(t_a))))),
% 0.19/0.44      inference(quant_inst,[status(thm)],[])).
% 0.19/0.44  tff(250,plain,
% 0.19/0.44      ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (~c_lessequals(v_x, v_Z, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a))),
% 0.19/0.44      inference(modus_ponens,[status(thm)],[249, 248])).
% 0.19/0.44  tff(251,plain,
% 0.19/0.44      ($false),
% 0.19/0.44      inference(unit_resolution,[status(thm)],[250, 244, 118, 196, 229])).
% 0.19/0.44  % SZS output end Proof
% 0.19/0.44  % E exiting
%------------------------------------------------------------------------------