%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET830-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:26:26 AM UTC 2025
% Result : Unsatisfiable 1.53s 1.70s
% Output : Proof 1.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12 % Problem : SET830-2 : TPTP v9.0.0. Released v3.2.0.
% 0.05/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 05:48:35 EDT 2025
% 0.13/0.34 % CPUTime :
% 1.53/1.70 % SZS status Unsatisfiable
% 1.53/1.70 % SZS output start Proof
% 1.53/1.70 tff(c_in_type, type, (
% 1.53/1.70 c_in: ( $i * $i * $i ) > $o)).
% 1.53/1.70 tff(t_a_type, type, (
% 1.53/1.70 t_a: $i)).
% 1.53/1.70 tff(v_Z_type, type, (
% 1.53/1.70 v_Z: $i)).
% 1.53/1.70 tff(c_Main_OsubsetI__1_type, type, (
% 1.53/1.70 c_Main_OsubsetI__1: ( $i * $i * $i ) > $i)).
% 1.53/1.70 tff(c_inter_type, type, (
% 1.53/1.70 c_inter: ( $i * $i * $i ) > $i)).
% 1.53/1.70 tff(v_Y_type, type, (
% 1.53/1.70 v_Y: $i)).
% 1.53/1.70 tff(c_lessequals_type, type, (
% 1.53/1.70 c_lessequals: ( $i * $i * $i ) > $o)).
% 1.53/1.70 tff(tc_set_type, type, (
% 1.53/1.70 tc_set: $i > $i)).
% 1.53/1.70 tff(v_X_type, type, (
% 1.53/1.70 v_X: $i)).
% 1.53/1.70 tff(v_x_type, type, (
% 1.53/1.70 v_x: $i)).
% 1.53/1.70 tff(1,assumption,(~c_lessequals(c_inter(v_Z, v_Y, t_a), v_Y, tc_set(t_a))), introduced(assumption)).
% 1.53/1.70 tff(2,plain,
% 1.53/1.70 (^[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))))),
% 1.53/1.70 inference(bind,[status(th)],[])).
% 1.53/1.70 tff(3,plain,
% 1.53/1.70 (![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)))),
% 1.53/1.70 inference(quant_intro,[status(thm)],[2])).
% 1.53/1.70 tff(4,plain,
% 1.53/1.70 (![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)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(5,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/sandbox2/benchmark/theBenchmark.p','cls_Set_OsubsetI_0')).
% 1.53/1.70 tff(6,plain,
% 1.53/1.70 (![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)))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[5, 4])).
% 1.53/1.70 tff(7,plain,(
% 1.53/1.70 ![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)))),
% 1.53/1.70 inference(skolemize,[status(sab)],[6])).
% 1.53/1.70 tff(8,plain,
% 1.53/1.70 (![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)))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.53/1.70 tff(9,plain,
% 1.53/1.70 (((~![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_Z, v_Y, t_a), v_Y, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Z, v_Y, t_a), v_Y, t_a), c_inter(v_Z, v_Y, 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_Z, v_Y, t_a), v_Y, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Z, v_Y, t_a), v_Y, t_a), c_inter(v_Z, v_Y, t_a), t_a))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(10,plain,
% 1.53/1.70 ((c_in(c_Main_OsubsetI__1(c_inter(v_Z, v_Y, t_a), v_Y, t_a), c_inter(v_Z, v_Y, t_a), t_a) | c_lessequals(c_inter(v_Z, v_Y, t_a), v_Y, tc_set(t_a))) <=> (c_lessequals(c_inter(v_Z, v_Y, t_a), v_Y, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Z, v_Y, t_a), v_Y, t_a), c_inter(v_Z, v_Y, t_a), t_a))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(11,plain,
% 1.53/1.70 (((~![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_Z, v_Y, t_a), v_Y, t_a), c_inter(v_Z, v_Y, t_a), t_a) | c_lessequals(c_inter(v_Z, v_Y, 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_Z, v_Y, t_a), v_Y, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Z, v_Y, t_a), v_Y, t_a), c_inter(v_Z, v_Y, t_a), t_a)))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[10])).
% 1.53/1.70 tff(12,plain,
% 1.53/1.70 (((~![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_Z, v_Y, t_a), v_Y, t_a), c_inter(v_Z, v_Y, t_a), t_a) | c_lessequals(c_inter(v_Z, v_Y, 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_Z, v_Y, t_a), v_Y, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Z, v_Y, t_a), v_Y, t_a), c_inter(v_Z, v_Y, t_a), t_a))),
% 1.53/1.70 inference(transitivity,[status(thm)],[11, 9])).
% 1.53/1.70 tff(13,plain,
% 1.53/1.70 ((~![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_Z, v_Y, t_a), v_Y, t_a), c_inter(v_Z, v_Y, t_a), t_a) | c_lessequals(c_inter(v_Z, v_Y, t_a), v_Y, tc_set(t_a)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(14,plain,
% 1.53/1.70 ((~![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_Z, v_Y, t_a), v_Y, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Z, v_Y, t_a), v_Y, t_a), c_inter(v_Z, v_Y, t_a), t_a)),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[13, 12])).
% 1.53/1.70 tff(15,plain,
% 1.53/1.70 (c_in(c_Main_OsubsetI__1(c_inter(v_Z, v_Y, t_a), v_Y, t_a), c_inter(v_Z, v_Y, t_a), t_a)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[14, 8, 1])).
% 1.53/1.70 tff(16,plain,
% 1.53/1.70 (^[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))))),
% 1.53/1.70 inference(bind,[status(th)],[])).
% 1.53/1.70 tff(17,plain,
% 1.53/1.70 (![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)))),
% 1.53/1.70 inference(quant_intro,[status(thm)],[16])).
% 1.53/1.70 tff(18,plain,
% 1.53/1.70 (![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)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(19,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/sandbox2/benchmark/theBenchmark.p','cls_Set_OsubsetI_1')).
% 1.53/1.70 tff(20,plain,
% 1.53/1.70 (![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)))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[19, 18])).
% 1.53/1.70 tff(21,plain,(
% 1.53/1.70 ![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)))),
% 1.53/1.70 inference(skolemize,[status(sab)],[20])).
% 1.53/1.70 tff(22,plain,
% 1.53/1.70 (![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)))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[21, 17])).
% 1.53/1.70 tff(23,plain,
% 1.53/1.70 (((~![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_Z, v_Y, t_a), v_Y, t_a), v_Y, t_a)) | c_lessequals(c_inter(v_Z, v_Y, 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_Z, v_Y, t_a), v_Y, t_a), v_Y, t_a)) | c_lessequals(c_inter(v_Z, v_Y, t_a), v_Y, tc_set(t_a)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(24,plain,
% 1.53/1.70 ((~![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_Z, v_Y, t_a), v_Y, t_a), v_Y, t_a)) | c_lessequals(c_inter(v_Z, v_Y, t_a), v_Y, tc_set(t_a)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(25,plain,
% 1.53/1.70 ((~![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_Z, v_Y, t_a), v_Y, t_a), v_Y, t_a)) | c_lessequals(c_inter(v_Z, v_Y, t_a), v_Y, tc_set(t_a))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[24, 23])).
% 1.53/1.70 tff(26,plain,
% 1.53/1.70 ((~c_in(c_Main_OsubsetI__1(c_inter(v_Z, v_Y, t_a), v_Y, t_a), v_Y, t_a)) | c_lessequals(c_inter(v_Z, v_Y, t_a), v_Y, tc_set(t_a))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[25, 22])).
% 1.53/1.70 tff(27,plain,
% 1.53/1.70 (~c_in(c_Main_OsubsetI__1(c_inter(v_Z, v_Y, t_a), v_Y, t_a), v_Y, t_a)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[26, 1])).
% 1.53/1.70 tff(28,plain,
% 1.53/1.70 (^[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)))),
% 1.53/1.70 inference(bind,[status(th)],[])).
% 1.53/1.70 tff(29,plain,
% 1.53/1.70 (![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))),
% 1.53/1.70 inference(quant_intro,[status(thm)],[28])).
% 1.53/1.70 tff(30,plain,
% 1.53/1.70 (![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))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(31,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/sandbox2/benchmark/theBenchmark.p','cls_Set_OIntE_0')).
% 1.53/1.70 tff(32,plain,
% 1.53/1.70 (![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))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[31, 30])).
% 1.53/1.70 tff(33,plain,(
% 1.53/1.70 ![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))),
% 1.53/1.70 inference(skolemize,[status(sab)],[32])).
% 1.53/1.70 tff(34,plain,
% 1.53/1.70 (![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))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[33, 29])).
% 1.53/1.70 tff(35,plain,
% 1.53/1.70 (((~![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_Z, v_Y, t_a), v_Y, t_a), c_inter(v_Z, v_Y, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Z, v_Y, 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_B, T_a))) | (~c_in(c_Main_OsubsetI__1(c_inter(v_Z, v_Y, t_a), v_Y, t_a), c_inter(v_Z, v_Y, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Z, v_Y, t_a), v_Y, t_a), v_Y, t_a))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(36,plain,
% 1.53/1.70 ((~![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_Z, v_Y, t_a), v_Y, t_a), c_inter(v_Z, v_Y, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Z, v_Y, t_a), v_Y, t_a), v_Y, t_a))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(37,plain,
% 1.53/1.70 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a))) | (~c_in(c_Main_OsubsetI__1(c_inter(v_Z, v_Y, t_a), v_Y, t_a), c_inter(v_Z, v_Y, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Z, v_Y, t_a), v_Y, t_a), v_Y, t_a)),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[36, 35])).
% 1.53/1.70 tff(38,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[37, 34, 27, 15])).
% 1.53/1.70 tff(39,plain,(c_lessequals(c_inter(v_Z, v_Y, t_a), v_Y, tc_set(t_a))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(40,plain,
% 1.53/1.70 (c_in(v_x, v_Z, t_a) <=> c_in(v_x, v_Z, t_a)),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(41,axiom,(c_in(v_x, v_Z, t_a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_3')).
% 1.53/1.70 tff(42,plain,
% 1.53/1.70 (c_in(v_x, v_Z, t_a)),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[41, 40])).
% 1.53/1.70 tff(43,plain,
% 1.53/1.70 (c_in(v_x, v_Y, t_a) <=> c_in(v_x, v_Y, t_a)),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(44,axiom,(c_in(v_x, v_Y, t_a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_2')).
% 1.53/1.70 tff(45,plain,
% 1.53/1.70 (c_in(v_x, v_Y, t_a)),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[44, 43])).
% 1.53/1.70 tff(46,plain,
% 1.53/1.70 (^[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))))),
% 1.53/1.70 inference(bind,[status(th)],[])).
% 1.53/1.70 tff(47,plain,
% 1.53/1.70 (![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)))),
% 1.53/1.70 inference(quant_intro,[status(thm)],[46])).
% 1.53/1.70 tff(48,plain,
% 1.53/1.70 (![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)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(49,plain,
% 1.53/1.70 (^[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)))))),
% 1.53/1.70 inference(bind,[status(th)],[])).
% 1.53/1.70 tff(50,plain,
% 1.53/1.70 (![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)))),
% 1.53/1.70 inference(quant_intro,[status(thm)],[49])).
% 1.53/1.70 tff(51,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/sandbox2/benchmark/theBenchmark.p','cls_Set_OIntI_0')).
% 1.53/1.70 tff(52,plain,
% 1.53/1.70 (![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)))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[51, 50])).
% 1.53/1.70 tff(53,plain,
% 1.53/1.70 (![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)))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[52, 48])).
% 1.53/1.70 tff(54,plain,(
% 1.53/1.70 ![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)))),
% 1.53/1.70 inference(skolemize,[status(sab)],[53])).
% 1.53/1.70 tff(55,plain,
% 1.53/1.70 (![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)))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[54, 47])).
% 1.53/1.70 tff(56,plain,
% 1.53/1.70 (((~![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(v_x, v_Y, t_a)) | (~c_in(v_x, v_Z, t_a)) | c_in(v_x, c_inter(v_Z, v_Y, 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)))) | (~c_in(v_x, v_Y, t_a)) | (~c_in(v_x, v_Z, t_a)) | c_in(v_x, c_inter(v_Z, v_Y, t_a), t_a))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(57,plain,
% 1.53/1.70 ((c_in(v_x, c_inter(v_Z, v_Y, t_a), t_a) | (~c_in(v_x, v_Z, t_a)) | (~c_in(v_x, v_Y, t_a))) <=> ((~c_in(v_x, v_Y, t_a)) | (~c_in(v_x, v_Z, t_a)) | c_in(v_x, c_inter(v_Z, v_Y, t_a), t_a))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(58,plain,
% 1.53/1.70 (((~![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(v_x, c_inter(v_Z, v_Y, t_a), t_a) | (~c_in(v_x, v_Z, t_a)) | (~c_in(v_x, 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(V_c, V_B, T_a)))) | ((~c_in(v_x, v_Y, t_a)) | (~c_in(v_x, v_Z, t_a)) | c_in(v_x, c_inter(v_Z, v_Y, t_a), t_a)))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[57])).
% 1.53/1.70 tff(59,plain,
% 1.53/1.70 (((~![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(v_x, c_inter(v_Z, v_Y, t_a), t_a) | (~c_in(v_x, v_Z, t_a)) | (~c_in(v_x, 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(V_c, V_B, T_a)))) | (~c_in(v_x, v_Y, t_a)) | (~c_in(v_x, v_Z, t_a)) | c_in(v_x, c_inter(v_Z, v_Y, t_a), t_a))),
% 1.53/1.70 inference(transitivity,[status(thm)],[58, 56])).
% 1.53/1.70 tff(60,plain,
% 1.53/1.70 ((~![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(v_x, c_inter(v_Z, v_Y, t_a), t_a) | (~c_in(v_x, v_Z, t_a)) | (~c_in(v_x, v_Y, t_a)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(61,plain,
% 1.53/1.70 ((~![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(v_x, v_Y, t_a)) | (~c_in(v_x, v_Z, t_a)) | c_in(v_x, c_inter(v_Z, v_Y, t_a), t_a)),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[60, 59])).
% 1.53/1.70 tff(62,plain,
% 1.53/1.70 (c_in(v_x, c_inter(v_Z, v_Y, t_a), t_a)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[61, 55, 45, 42])).
% 1.53/1.70 tff(63,plain,
% 1.53/1.70 ((~c_in(v_x, v_X, t_a)) <=> (~c_in(v_x, v_X, t_a))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(64,axiom,(~c_in(v_x, v_X, t_a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_4')).
% 1.53/1.70 tff(65,plain,
% 1.53/1.70 (~c_in(v_x, v_X, t_a)),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[64, 63])).
% 1.53/1.70 tff(66,plain,
% 1.53/1.70 (^[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)))))),
% 1.53/1.70 inference(bind,[status(th)],[])).
% 1.53/1.70 tff(67,plain,
% 1.53/1.70 (![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))))),
% 1.53/1.70 inference(quant_intro,[status(thm)],[66])).
% 1.53/1.70 tff(68,plain,
% 1.53/1.70 (![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))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(69,plain,
% 1.53/1.70 (^[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)))))),
% 1.53/1.70 inference(bind,[status(th)],[])).
% 1.53/1.70 tff(70,plain,
% 1.53/1.70 (![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))))),
% 1.53/1.70 inference(quant_intro,[status(thm)],[69])).
% 1.53/1.70 tff(71,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/sandbox2/benchmark/theBenchmark.p','cls_Set_OsubsetD_0')).
% 1.53/1.70 tff(72,plain,
% 1.53/1.70 (![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))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[71, 70])).
% 1.53/1.70 tff(73,plain,
% 1.53/1.70 (![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))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[72, 68])).
% 1.53/1.71 tff(74,plain,(
% 1.53/1.71 ![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))))),
% 1.53/1.71 inference(skolemize,[status(sab)],[73])).
% 1.53/1.71 tff(75,plain,
% 1.53/1.71 (![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))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[74, 67])).
% 1.53/1.71 tff(76,plain,
% 1.53/1.71 (((~![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(v_x, v_X, t_a) | (~c_in(v_x, c_inter(v_Z, v_Y, t_a), t_a)) | (~c_lessequals(c_inter(v_Z, v_Y, t_a), v_X, 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_in(v_x, v_X, t_a) | (~c_in(v_x, c_inter(v_Z, v_Y, t_a), t_a)) | (~c_lessequals(c_inter(v_Z, v_Y, t_a), v_X, tc_set(t_a))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(77,plain,
% 1.53/1.71 ((~![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(v_x, v_X, t_a) | (~c_in(v_x, c_inter(v_Z, v_Y, t_a), t_a)) | (~c_lessequals(c_inter(v_Z, v_Y, t_a), v_X, tc_set(t_a))))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(78,plain,
% 1.53/1.71 ((~![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(v_x, v_X, t_a) | (~c_in(v_x, c_inter(v_Z, v_Y, t_a), t_a)) | (~c_lessequals(c_inter(v_Z, v_Y, t_a), v_X, tc_set(t_a)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[77, 76])).
% 1.53/1.71 tff(79,plain,
% 1.53/1.71 (~c_lessequals(c_inter(v_Z, v_Y, t_a), v_X, tc_set(t_a))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[78, 75, 65, 62])).
% 1.53/1.71 tff(80,plain,
% 1.53/1.71 (^[V_U: $i] : refl(((~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))) <=> ((~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))))),
% 1.53/1.71 inference(bind,[status(th)],[])).
% 1.53/1.71 tff(81,plain,
% 1.53/1.71 (![V_U: $i] : ((~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] : ((~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)))),
% 1.53/1.71 inference(quant_intro,[status(thm)],[80])).
% 1.53/1.71 tff(82,plain,
% 1.53/1.71 (![V_U: $i] : ((~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] : ((~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)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(83,plain,
% 1.53/1.71 (^[V_U: $i] : trans(monotonicity(rewrite((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_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(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)))) <=> (((~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((((~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)))) <=> ((~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)))), (((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)))) <=> ((~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)))))),
% 1.53/1.71 inference(bind,[status(th)],[])).
% 1.53/1.71 tff(84,plain,
% 1.53/1.71 (![V_U: $i] : ((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] : ((~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)))),
% 1.53/1.71 inference(quant_intro,[status(thm)],[83])).
% 1.53/1.71 tff(85,axiom,(![V_U: $i] : ((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/sandbox2/benchmark/theBenchmark.p','cls_conjecture_5')).
% 1.53/1.71 tff(86,plain,
% 1.53/1.71 (![V_U: $i] : ((~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)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[85, 84])).
% 1.53/1.71 tff(87,plain,
% 1.53/1.71 (![V_U: $i] : ((~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)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[86, 82])).
% 1.53/1.71 tff(88,plain,(
% 1.53/1.71 ![V_U: $i] : ((~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)))),
% 1.53/1.71 inference(skolemize,[status(sab)],[87])).
% 1.53/1.71 tff(89,plain,
% 1.53/1.71 (![V_U: $i] : ((~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)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[88, 81])).
% 1.53/1.71 tff(90,plain,
% 1.53/1.71 (((~![V_U: $i] : ((~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)))) | ((~c_lessequals(c_inter(v_Z, v_Y, t_a), v_Y, tc_set(t_a))) | (~c_lessequals(c_inter(v_Z, v_Y, t_a), v_Z, tc_set(t_a))) | c_lessequals(c_inter(v_Z, v_Y, t_a), v_X, tc_set(t_a)))) <=> ((~![V_U: $i] : ((~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)))) | (~c_lessequals(c_inter(v_Z, v_Y, t_a), v_Y, tc_set(t_a))) | (~c_lessequals(c_inter(v_Z, v_Y, t_a), v_Z, tc_set(t_a))) | c_lessequals(c_inter(v_Z, v_Y, t_a), v_X, tc_set(t_a)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(91,plain,
% 1.53/1.71 ((~![V_U: $i] : ((~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)))) | ((~c_lessequals(c_inter(v_Z, v_Y, t_a), v_Y, tc_set(t_a))) | (~c_lessequals(c_inter(v_Z, v_Y, t_a), v_Z, tc_set(t_a))) | c_lessequals(c_inter(v_Z, v_Y, t_a), v_X, tc_set(t_a)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(92,plain,
% 1.53/1.71 ((~![V_U: $i] : ((~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)))) | (~c_lessequals(c_inter(v_Z, v_Y, t_a), v_Y, tc_set(t_a))) | (~c_lessequals(c_inter(v_Z, v_Y, t_a), v_Z, tc_set(t_a))) | c_lessequals(c_inter(v_Z, v_Y, t_a), v_X, tc_set(t_a))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[91, 90])).
% 1.53/1.71 tff(93,plain,
% 1.53/1.71 ((~c_lessequals(c_inter(v_Z, v_Y, t_a), v_Y, tc_set(t_a))) | (~c_lessequals(c_inter(v_Z, v_Y, t_a), v_Z, tc_set(t_a)))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[92, 89, 79])).
% 1.53/1.71 tff(94,plain,
% 1.53/1.71 (~c_lessequals(c_inter(v_Z, v_Y, t_a), v_Z, tc_set(t_a))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[93, 39])).
% 1.53/1.71 tff(95,plain,
% 1.53/1.71 (((~![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_Z, v_Y, t_a), v_Z, t_a), v_Z, t_a)) | c_lessequals(c_inter(v_Z, v_Y, 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_Z, v_Y, t_a), v_Z, t_a), v_Z, t_a)) | c_lessequals(c_inter(v_Z, v_Y, t_a), v_Z, tc_set(t_a)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(96,plain,
% 1.53/1.71 ((~![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_Z, v_Y, t_a), v_Z, t_a), v_Z, t_a)) | c_lessequals(c_inter(v_Z, v_Y, t_a), v_Z, tc_set(t_a)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(97,plain,
% 1.53/1.71 ((~![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_Z, v_Y, t_a), v_Z, t_a), v_Z, t_a)) | c_lessequals(c_inter(v_Z, v_Y, t_a), v_Z, tc_set(t_a))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[96, 95])).
% 1.53/1.71 tff(98,plain,
% 1.53/1.71 (~c_in(c_Main_OsubsetI__1(c_inter(v_Z, v_Y, t_a), v_Z, t_a), v_Z, t_a)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[97, 22, 94])).
% 1.53/1.71 tff(99,plain,
% 1.53/1.71 (((~![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_Z, v_Y, t_a), v_Z, t_a), c_inter(v_Z, v_Y, t_a), t_a) | c_lessequals(c_inter(v_Z, v_Y, 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_Z, v_Y, t_a), v_Z, t_a), c_inter(v_Z, v_Y, t_a), t_a) | c_lessequals(c_inter(v_Z, v_Y, t_a), v_Z, tc_set(t_a)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(100,plain,
% 1.53/1.71 ((~![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_Z, v_Y, t_a), v_Z, t_a), c_inter(v_Z, v_Y, t_a), t_a) | c_lessequals(c_inter(v_Z, v_Y, t_a), v_Z, tc_set(t_a)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(101,plain,
% 1.53/1.71 ((~![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_Z, v_Y, t_a), v_Z, t_a), c_inter(v_Z, v_Y, t_a), t_a) | c_lessequals(c_inter(v_Z, v_Y, t_a), v_Z, tc_set(t_a))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[100, 99])).
% 1.53/1.71 tff(102,plain,
% 1.53/1.71 (c_in(c_Main_OsubsetI__1(c_inter(v_Z, v_Y, t_a), v_Z, t_a), c_inter(v_Z, v_Y, t_a), t_a)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[101, 8, 94])).
% 1.53/1.71 tff(103,plain,
% 1.53/1.71 (^[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)))),
% 1.53/1.71 inference(bind,[status(th)],[])).
% 1.53/1.71 tff(104,plain,
% 1.53/1.71 (![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))),
% 1.53/1.71 inference(quant_intro,[status(thm)],[103])).
% 1.53/1.71 tff(105,plain,
% 1.53/1.71 (![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))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(106,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/sandbox2/benchmark/theBenchmark.p','cls_Set_OIntE_1')).
% 1.53/1.71 tff(107,plain,
% 1.53/1.71 (![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))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[106, 105])).
% 1.53/1.71 tff(108,plain,(
% 1.53/1.71 ![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))),
% 1.53/1.71 inference(skolemize,[status(sab)],[107])).
% 1.53/1.71 tff(109,plain,
% 1.53/1.71 (![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))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[108, 104])).
% 1.53/1.71 tff(110,plain,
% 1.53/1.71 (((~![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_Z, v_Y, t_a), v_Z, t_a), c_inter(v_Z, v_Y, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Z, v_Y, 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_A, T_a))) | (~c_in(c_Main_OsubsetI__1(c_inter(v_Z, v_Y, t_a), v_Z, t_a), c_inter(v_Z, v_Y, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Z, v_Y, t_a), v_Z, t_a), v_Z, t_a))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(111,plain,
% 1.53/1.71 ((~![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_Z, v_Y, t_a), v_Z, t_a), c_inter(v_Z, v_Y, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Z, v_Y, t_a), v_Z, t_a), v_Z, t_a))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(112,plain,
% 1.53/1.71 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_A, T_a))) | (~c_in(c_Main_OsubsetI__1(c_inter(v_Z, v_Y, t_a), v_Z, t_a), c_inter(v_Z, v_Y, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Z, v_Y, t_a), v_Z, t_a), v_Z, t_a)),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[111, 110])).
% 1.53/1.71 tff(113,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[112, 109, 102, 98])).
% 1.53/1.71 % SZS output end Proof
% 1.53/1.71 % E exiting
%------------------------------------------------------------------------------