%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET837-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:28 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET837-2 : TPTP v9.0.0. Released v3.2.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 05:46:41 EDT 2025
% 0.12/0.35 % CPUTime :
% 0.12/0.39 % SZS status Unsatisfiable
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(c_in_type, type, (
% 0.12/0.39 c_in: ( $i * $i * $i ) > $o)).
% 0.12/0.39 tff(t_a_type, type, (
% 0.12/0.39 t_a: $i)).
% 0.12/0.39 tff(v_Y_type, type, (
% 0.12/0.39 v_Y: $i)).
% 0.12/0.39 tff(c_Main_OsubsetI__1_type, type, (
% 0.12/0.39 c_Main_OsubsetI__1: ( $i * $i * $i ) > $i)).
% 0.12/0.39 tff(v_x_type, type, (
% 0.12/0.39 v_x: $i)).
% 0.12/0.39 tff(c_union_type, type, (
% 0.12/0.39 c_union: ( $i * $i * $i ) > $i)).
% 0.12/0.39 tff(v_Z_type, type, (
% 0.12/0.39 v_Z: $i)).
% 0.12/0.39 tff(c_lessequals_type, type, (
% 0.12/0.39 c_lessequals: ( $i * $i * $i ) > $o)).
% 0.12/0.39 tff(tc_set_type, type, (
% 0.12/0.39 tc_set: $i > $i)).
% 0.12/0.39 tff(v_X_type, type, (
% 0.12/0.39 v_X: $i)).
% 0.12/0.39 tff(1,assumption,(c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_Z, t_a)), introduced(assumption)).
% 0.12/0.39 tff(2,assumption,(~(v_X = c_union(v_Y, v_Z, t_a))), introduced(assumption)).
% 0.12/0.39 tff(3,assumption,(~c_lessequals(v_Y, c_union(v_Y, v_Z, t_a), tc_set(t_a))), introduced(assumption)).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (^[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))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[4])).
% 0.12/0.39 tff(6,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 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')).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.12/0.39 tff(9,plain,(
% 0.12/0.39 ![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)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[8])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 (((~![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_Y, c_union(v_Y, v_Z, t_a), t_a), c_union(v_Y, v_Z, t_a), t_a)) | c_lessequals(v_Y, c_union(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_Y, c_union(v_Y, v_Z, t_a), t_a), c_union(v_Y, v_Z, t_a), t_a)) | c_lessequals(v_Y, c_union(v_Y, v_Z, t_a), tc_set(t_a)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 ((~![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_Y, c_union(v_Y, v_Z, t_a), t_a), c_union(v_Y, v_Z, t_a), t_a)) | c_lessequals(v_Y, c_union(v_Y, v_Z, t_a), tc_set(t_a)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 ((~![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_Y, c_union(v_Y, v_Z, t_a), t_a), c_union(v_Y, v_Z, t_a), t_a)) | c_lessequals(v_Y, c_union(v_Y, v_Z, t_a), tc_set(t_a))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (~c_in(c_Main_OsubsetI__1(v_Y, c_union(v_Y, v_Z, t_a), t_a), c_union(v_Y, v_Z, t_a), t_a)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[13, 10, 3])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (^[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))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[15])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 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')).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.12/0.39 tff(20,plain,(
% 0.12/0.39 ![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)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[19])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (((~![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_Y, c_union(v_Y, v_Z, t_a), tc_set(t_a)) | c_in(c_Main_OsubsetI__1(v_Y, c_union(v_Y, v_Z, t_a), t_a), v_Y, 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_Y, c_union(v_Y, v_Z, t_a), tc_set(t_a)) | c_in(c_Main_OsubsetI__1(v_Y, c_union(v_Y, v_Z, t_a), t_a), v_Y, t_a))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 ((c_in(c_Main_OsubsetI__1(v_Y, c_union(v_Y, v_Z, t_a), t_a), v_Y, t_a) | c_lessequals(v_Y, c_union(v_Y, v_Z, t_a), tc_set(t_a))) <=> (c_lessequals(v_Y, c_union(v_Y, v_Z, t_a), tc_set(t_a)) | c_in(c_Main_OsubsetI__1(v_Y, c_union(v_Y, v_Z, t_a), t_a), v_Y, t_a))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (((~![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_Y, c_union(v_Y, v_Z, t_a), t_a), v_Y, t_a) | c_lessequals(v_Y, c_union(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_Y, c_union(v_Y, v_Z, t_a), tc_set(t_a)) | c_in(c_Main_OsubsetI__1(v_Y, c_union(v_Y, v_Z, t_a), t_a), v_Y, t_a)))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[23])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (((~![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_Y, c_union(v_Y, v_Z, t_a), t_a), v_Y, t_a) | c_lessequals(v_Y, c_union(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_Y, c_union(v_Y, v_Z, t_a), tc_set(t_a)) | c_in(c_Main_OsubsetI__1(v_Y, c_union(v_Y, v_Z, t_a), t_a), v_Y, t_a))),
% 0.12/0.39 inference(transitivity,[status(thm)],[24, 22])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 ((~![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_Y, c_union(v_Y, v_Z, t_a), t_a), v_Y, t_a) | c_lessequals(v_Y, c_union(v_Y, v_Z, t_a), tc_set(t_a)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 ((~![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_Y, c_union(v_Y, v_Z, t_a), tc_set(t_a)) | c_in(c_Main_OsubsetI__1(v_Y, c_union(v_Y, v_Z, t_a), t_a), v_Y, t_a)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.12/0.40 tff(28,plain,
% 0.12/0.40 (c_in(c_Main_OsubsetI__1(v_Y, c_union(v_Y, v_Z, t_a), t_a), v_Y, t_a)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[27, 21, 3])).
% 0.12/0.40 tff(29,plain,
% 0.12/0.40 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : refl(((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a)) <=> ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(30,plain,
% 0.12/0.40 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[29])).
% 0.12/0.40 tff(31,plain,
% 0.12/0.40 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(32,axiom,(![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_OUnCI_1')).
% 0.12/0.40 tff(33,plain,
% 0.12/0.40 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.12/0.40 tff(34,plain,(
% 0.12/0.40 ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.12/0.40 inference(skolemize,[status(sab)],[33])).
% 0.12/0.40 tff(35,plain,
% 0.12/0.40 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.12/0.40 tff(36,plain,
% 0.12/0.40 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | ((~c_in(c_Main_OsubsetI__1(v_Y, c_union(v_Y, v_Z, t_a), t_a), v_Y, t_a)) | c_in(c_Main_OsubsetI__1(v_Y, c_union(v_Y, v_Z, t_a), t_a), c_union(v_Y, v_Z, t_a), t_a))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | (~c_in(c_Main_OsubsetI__1(v_Y, c_union(v_Y, v_Z, t_a), t_a), v_Y, t_a)) | c_in(c_Main_OsubsetI__1(v_Y, c_union(v_Y, v_Z, t_a), t_a), c_union(v_Y, v_Z, t_a), t_a))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(37,plain,
% 0.12/0.40 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | ((~c_in(c_Main_OsubsetI__1(v_Y, c_union(v_Y, v_Z, t_a), t_a), v_Y, t_a)) | c_in(c_Main_OsubsetI__1(v_Y, c_union(v_Y, v_Z, t_a), t_a), c_union(v_Y, v_Z, t_a), t_a))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(38,plain,
% 0.12/0.40 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | (~c_in(c_Main_OsubsetI__1(v_Y, c_union(v_Y, v_Z, t_a), t_a), v_Y, t_a)) | c_in(c_Main_OsubsetI__1(v_Y, c_union(v_Y, v_Z, t_a), t_a), c_union(v_Y, v_Z, t_a), t_a)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.12/0.40 tff(39,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[38, 35, 28, 14])).
% 0.12/0.40 tff(40,plain,(c_lessequals(v_Y, c_union(v_Y, v_Z, t_a), tc_set(t_a))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.40 tff(41,assumption,(~c_lessequals(v_Z, c_union(v_Y, v_Z, t_a), tc_set(t_a))), introduced(assumption)).
% 0.12/0.40 tff(42,plain,
% 0.12/0.40 (((~![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_Z, c_union(v_Y, v_Z, t_a), t_a), c_union(v_Y, v_Z, t_a), t_a)) | c_lessequals(v_Z, c_union(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_Z, c_union(v_Y, v_Z, t_a), t_a), c_union(v_Y, v_Z, t_a), t_a)) | c_lessequals(v_Z, c_union(v_Y, v_Z, t_a), tc_set(t_a)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(43,plain,
% 0.12/0.40 ((~![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_Z, c_union(v_Y, v_Z, t_a), t_a), c_union(v_Y, v_Z, t_a), t_a)) | c_lessequals(v_Z, c_union(v_Y, v_Z, t_a), tc_set(t_a)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(44,plain,
% 0.12/0.40 ((~![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_Z, c_union(v_Y, v_Z, t_a), t_a), c_union(v_Y, v_Z, t_a), t_a)) | c_lessequals(v_Z, c_union(v_Y, v_Z, t_a), tc_set(t_a))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.12/0.40 tff(45,plain,
% 0.12/0.40 ((~c_in(c_Main_OsubsetI__1(v_Z, c_union(v_Y, v_Z, t_a), t_a), c_union(v_Y, v_Z, t_a), t_a)) | c_lessequals(v_Z, c_union(v_Y, v_Z, t_a), tc_set(t_a))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[44, 10])).
% 0.12/0.40 tff(46,plain,
% 0.12/0.40 (~c_in(c_Main_OsubsetI__1(v_Z, c_union(v_Y, v_Z, t_a), t_a), c_union(v_Y, v_Z, t_a), t_a)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[45, 41])).
% 0.12/0.40 tff(47,plain,
% 0.12/0.40 (((~![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_Z, c_union(v_Y, v_Z, t_a), t_a), v_Z, t_a) | c_lessequals(v_Z, c_union(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_Z, c_union(v_Y, v_Z, t_a), t_a), v_Z, t_a) | c_lessequals(v_Z, c_union(v_Y, v_Z, t_a), tc_set(t_a)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(48,plain,
% 0.12/0.40 ((~![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_Z, c_union(v_Y, v_Z, t_a), t_a), v_Z, t_a) | c_lessequals(v_Z, c_union(v_Y, v_Z, t_a), tc_set(t_a)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(49,plain,
% 0.12/0.40 ((~![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_Z, c_union(v_Y, v_Z, t_a), t_a), v_Z, t_a) | c_lessequals(v_Z, c_union(v_Y, v_Z, t_a), tc_set(t_a))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.12/0.40 tff(50,plain,
% 0.12/0.40 (c_in(c_Main_OsubsetI__1(v_Z, c_union(v_Y, v_Z, t_a), t_a), v_Z, t_a) | c_lessequals(v_Z, c_union(v_Y, v_Z, t_a), tc_set(t_a))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[49, 21])).
% 0.12/0.40 tff(51,plain,
% 0.12/0.40 (c_in(c_Main_OsubsetI__1(v_Z, c_union(v_Y, v_Z, t_a), t_a), v_Z, t_a)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[50, 41])).
% 0.12/0.40 tff(52,plain,
% 0.12/0.40 (^[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, c_union(V_A, V_B, T_a), T_a)) <=> ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(53,plain,
% 0.12/0.40 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), 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, c_union(V_A, V_B, T_a), T_a))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[52])).
% 0.12/0.40 tff(54,plain,
% 0.12/0.40 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), 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, c_union(V_A, V_B, T_a), T_a))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(55,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, c_union(V_A, V_B, T_a), T_a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_OUnCI_0')).
% 0.12/0.40 tff(56,plain,
% 0.12/0.40 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.12/0.40 tff(57,plain,(
% 0.12/0.40 ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.12/0.40 inference(skolemize,[status(sab)],[56])).
% 0.12/0.40 tff(58,plain,
% 0.12/0.40 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.12/0.40 tff(59,plain,
% 0.12/0.40 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | ((~c_in(c_Main_OsubsetI__1(v_Z, c_union(v_Y, v_Z, t_a), t_a), v_Z, t_a)) | c_in(c_Main_OsubsetI__1(v_Z, c_union(v_Y, v_Z, t_a), t_a), c_union(v_Y, v_Z, t_a), 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, c_union(V_A, V_B, T_a), T_a))) | (~c_in(c_Main_OsubsetI__1(v_Z, c_union(v_Y, v_Z, t_a), t_a), v_Z, t_a)) | c_in(c_Main_OsubsetI__1(v_Z, c_union(v_Y, v_Z, t_a), t_a), c_union(v_Y, v_Z, t_a), t_a))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(60,plain,
% 0.12/0.40 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | ((~c_in(c_Main_OsubsetI__1(v_Z, c_union(v_Y, v_Z, t_a), t_a), v_Z, t_a)) | c_in(c_Main_OsubsetI__1(v_Z, c_union(v_Y, v_Z, t_a), t_a), c_union(v_Y, v_Z, t_a), t_a))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(61,plain,
% 0.12/0.40 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | (~c_in(c_Main_OsubsetI__1(v_Z, c_union(v_Y, v_Z, t_a), t_a), v_Z, t_a)) | c_in(c_Main_OsubsetI__1(v_Z, c_union(v_Y, v_Z, t_a), t_a), c_union(v_Y, v_Z, t_a), t_a)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.12/0.40 tff(62,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[61, 58, 51, 46])).
% 0.12/0.40 tff(63,plain,(c_lessequals(v_Z, c_union(v_Y, v_Z, t_a), tc_set(t_a))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.40 tff(64,plain,
% 0.12/0.40 (^[V_U: $i] : refl(((v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Y, V_U, tc_set(t_a))) | (~c_lessequals(v_Z, V_U, tc_set(t_a))) | c_lessequals(v_X, V_U, tc_set(t_a))) <=> ((v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Y, V_U, tc_set(t_a))) | (~c_lessequals(v_Z, V_U, tc_set(t_a))) | c_lessequals(v_X, V_U, tc_set(t_a))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(65,plain,
% 0.12/0.40 (![V_U: $i] : ((v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Y, V_U, tc_set(t_a))) | (~c_lessequals(v_Z, V_U, tc_set(t_a))) | c_lessequals(v_X, V_U, tc_set(t_a))) <=> ![V_U: $i] : ((v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Y, V_U, tc_set(t_a))) | (~c_lessequals(v_Z, V_U, tc_set(t_a))) | c_lessequals(v_X, V_U, tc_set(t_a)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[64])).
% 0.12/0.40 tff(66,plain,
% 0.12/0.40 (![V_U: $i] : ((v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Y, V_U, tc_set(t_a))) | (~c_lessequals(v_Z, V_U, tc_set(t_a))) | c_lessequals(v_X, V_U, tc_set(t_a))) <=> ![V_U: $i] : ((v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Y, V_U, tc_set(t_a))) | (~c_lessequals(v_Z, V_U, tc_set(t_a))) | c_lessequals(v_X, V_U, tc_set(t_a)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(67,plain,
% 0.12/0.40 (^[V_U: $i] : trans(monotonicity(rewrite((((v_X = c_union(v_Y, v_Z, t_a)) | c_lessequals(v_X, V_U, tc_set(t_a))) | (~c_lessequals(v_Z, V_U, tc_set(t_a)))) <=> ((v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Z, V_U, tc_set(t_a))) | c_lessequals(v_X, V_U, tc_set(t_a)))), (((((v_X = c_union(v_Y, v_Z, t_a)) | c_lessequals(v_X, V_U, tc_set(t_a))) | (~c_lessequals(v_Z, V_U, tc_set(t_a)))) | (~c_lessequals(v_Y, V_U, tc_set(t_a)))) <=> (((v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Z, V_U, tc_set(t_a))) | c_lessequals(v_X, V_U, tc_set(t_a))) | (~c_lessequals(v_Y, V_U, tc_set(t_a)))))), rewrite((((v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Z, V_U, tc_set(t_a))) | c_lessequals(v_X, V_U, tc_set(t_a))) | (~c_lessequals(v_Y, V_U, tc_set(t_a)))) <=> ((v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Y, V_U, tc_set(t_a))) | (~c_lessequals(v_Z, V_U, tc_set(t_a))) | c_lessequals(v_X, V_U, tc_set(t_a)))), (((((v_X = c_union(v_Y, v_Z, t_a)) | c_lessequals(v_X, V_U, tc_set(t_a))) | (~c_lessequals(v_Z, V_U, tc_set(t_a)))) | (~c_lessequals(v_Y, V_U, tc_set(t_a)))) <=> ((v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Y, V_U, tc_set(t_a))) | (~c_lessequals(v_Z, V_U, tc_set(t_a))) | c_lessequals(v_X, V_U, tc_set(t_a)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 (![V_U: $i] : ((((v_X = c_union(v_Y, v_Z, t_a)) | c_lessequals(v_X, V_U, tc_set(t_a))) | (~c_lessequals(v_Z, V_U, tc_set(t_a)))) | (~c_lessequals(v_Y, V_U, tc_set(t_a)))) <=> ![V_U: $i] : ((v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Y, V_U, tc_set(t_a))) | (~c_lessequals(v_Z, V_U, tc_set(t_a))) | c_lessequals(v_X, V_U, tc_set(t_a)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[67])).
% 0.20/0.41 tff(69,axiom,(![V_U: $i] : ((((v_X = c_union(v_Y, v_Z, t_a)) | c_lessequals(v_X, V_U, tc_set(t_a))) | (~c_lessequals(v_Z, V_U, tc_set(t_a)))) | (~c_lessequals(v_Y, V_U, tc_set(t_a))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_5')).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 (![V_U: $i] : ((v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Y, V_U, tc_set(t_a))) | (~c_lessequals(v_Z, V_U, tc_set(t_a))) | c_lessequals(v_X, V_U, tc_set(t_a)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.41 tff(71,plain,
% 0.20/0.41 (![V_U: $i] : ((v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Y, V_U, tc_set(t_a))) | (~c_lessequals(v_Z, V_U, tc_set(t_a))) | c_lessequals(v_X, V_U, tc_set(t_a)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.20/0.41 tff(72,plain,(
% 0.20/0.41 ![V_U: $i] : ((v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Y, V_U, tc_set(t_a))) | (~c_lessequals(v_Z, V_U, tc_set(t_a))) | c_lessequals(v_X, V_U, tc_set(t_a)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[71])).
% 0.20/0.41 tff(73,plain,
% 0.20/0.41 (![V_U: $i] : ((v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Y, V_U, tc_set(t_a))) | (~c_lessequals(v_Z, V_U, tc_set(t_a))) | c_lessequals(v_X, V_U, tc_set(t_a)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.20/0.41 tff(74,plain,
% 0.20/0.41 (((~![V_U: $i] : ((v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Y, V_U, tc_set(t_a))) | (~c_lessequals(v_Z, V_U, tc_set(t_a))) | c_lessequals(v_X, V_U, tc_set(t_a)))) | ((v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Y, c_union(v_Y, v_Z, t_a), tc_set(t_a))) | c_lessequals(v_X, c_union(v_Y, v_Z, t_a), tc_set(t_a)) | (~c_lessequals(v_Z, c_union(v_Y, v_Z, t_a), tc_set(t_a))))) <=> ((~![V_U: $i] : ((v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Y, V_U, tc_set(t_a))) | (~c_lessequals(v_Z, V_U, tc_set(t_a))) | c_lessequals(v_X, V_U, tc_set(t_a)))) | (v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Y, c_union(v_Y, v_Z, t_a), tc_set(t_a))) | c_lessequals(v_X, c_union(v_Y, v_Z, t_a), tc_set(t_a)) | (~c_lessequals(v_Z, c_union(v_Y, v_Z, t_a), tc_set(t_a))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(75,plain,
% 0.20/0.41 (((v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Y, c_union(v_Y, v_Z, t_a), tc_set(t_a))) | (~c_lessequals(v_Z, c_union(v_Y, v_Z, t_a), tc_set(t_a))) | c_lessequals(v_X, c_union(v_Y, v_Z, t_a), tc_set(t_a))) <=> ((v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Y, c_union(v_Y, v_Z, t_a), tc_set(t_a))) | c_lessequals(v_X, c_union(v_Y, v_Z, t_a), tc_set(t_a)) | (~c_lessequals(v_Z, c_union(v_Y, v_Z, t_a), tc_set(t_a))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(76,plain,
% 0.20/0.41 (((~![V_U: $i] : ((v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Y, V_U, tc_set(t_a))) | (~c_lessequals(v_Z, V_U, tc_set(t_a))) | c_lessequals(v_X, V_U, tc_set(t_a)))) | ((v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Y, c_union(v_Y, v_Z, t_a), tc_set(t_a))) | (~c_lessequals(v_Z, c_union(v_Y, v_Z, t_a), tc_set(t_a))) | c_lessequals(v_X, c_union(v_Y, v_Z, t_a), tc_set(t_a)))) <=> ((~![V_U: $i] : ((v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Y, V_U, tc_set(t_a))) | (~c_lessequals(v_Z, V_U, tc_set(t_a))) | c_lessequals(v_X, V_U, tc_set(t_a)))) | ((v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Y, c_union(v_Y, v_Z, t_a), tc_set(t_a))) | c_lessequals(v_X, c_union(v_Y, v_Z, t_a), tc_set(t_a)) | (~c_lessequals(v_Z, c_union(v_Y, v_Z, t_a), tc_set(t_a)))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[75])).
% 0.20/0.41 tff(77,plain,
% 0.20/0.41 (((~![V_U: $i] : ((v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Y, V_U, tc_set(t_a))) | (~c_lessequals(v_Z, V_U, tc_set(t_a))) | c_lessequals(v_X, V_U, tc_set(t_a)))) | ((v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Y, c_union(v_Y, v_Z, t_a), tc_set(t_a))) | (~c_lessequals(v_Z, c_union(v_Y, v_Z, t_a), tc_set(t_a))) | c_lessequals(v_X, c_union(v_Y, v_Z, t_a), tc_set(t_a)))) <=> ((~![V_U: $i] : ((v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Y, V_U, tc_set(t_a))) | (~c_lessequals(v_Z, V_U, tc_set(t_a))) | c_lessequals(v_X, V_U, tc_set(t_a)))) | (v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Y, c_union(v_Y, v_Z, t_a), tc_set(t_a))) | c_lessequals(v_X, c_union(v_Y, v_Z, t_a), tc_set(t_a)) | (~c_lessequals(v_Z, c_union(v_Y, v_Z, t_a), tc_set(t_a))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[76, 74])).
% 0.20/0.41 tff(78,plain,
% 0.20/0.41 ((~![V_U: $i] : ((v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Y, V_U, tc_set(t_a))) | (~c_lessequals(v_Z, V_U, tc_set(t_a))) | c_lessequals(v_X, V_U, tc_set(t_a)))) | ((v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Y, c_union(v_Y, v_Z, t_a), tc_set(t_a))) | (~c_lessequals(v_Z, c_union(v_Y, v_Z, t_a), tc_set(t_a))) | c_lessequals(v_X, c_union(v_Y, v_Z, t_a), tc_set(t_a)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(79,plain,
% 0.20/0.41 ((~![V_U: $i] : ((v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Y, V_U, tc_set(t_a))) | (~c_lessequals(v_Z, V_U, tc_set(t_a))) | c_lessequals(v_X, V_U, tc_set(t_a)))) | (v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Y, c_union(v_Y, v_Z, t_a), tc_set(t_a))) | c_lessequals(v_X, c_union(v_Y, v_Z, t_a), tc_set(t_a)) | (~c_lessequals(v_Z, c_union(v_Y, v_Z, t_a), tc_set(t_a)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.41 tff(80,plain,
% 0.20/0.41 ((v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(v_Y, c_union(v_Y, v_Z, t_a), tc_set(t_a))) | c_lessequals(v_X, c_union(v_Y, v_Z, t_a), tc_set(t_a))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[79, 73, 63])).
% 0.20/0.41 tff(81,plain,
% 0.20/0.41 ((v_X = c_union(v_Y, v_Z, t_a)) | c_lessequals(v_X, c_union(v_Y, v_Z, t_a), tc_set(t_a))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[80, 40])).
% 0.20/0.41 tff(82,plain,
% 0.20/0.41 (c_lessequals(v_X, c_union(v_Y, v_Z, t_a), tc_set(t_a))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[81, 2])).
% 0.20/0.41 tff(83,plain,
% 0.20/0.41 (^[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)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(84,plain,
% 0.20/0.41 (![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))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[83])).
% 0.20/0.41 tff(85,plain,
% 0.20/0.41 (![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))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(86,plain,
% 0.20/0.41 (^[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))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(87,plain,
% 0.20/0.41 (![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))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[86])).
% 0.20/0.41 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')).
% 0.20/0.41 tff(89,plain,
% 0.20/0.41 (![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))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.20/0.41 tff(90,plain,
% 0.20/0.41 (![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))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.20/0.41 tff(91,plain,(
% 0.20/0.41 ![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))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[90])).
% 0.20/0.41 tff(92,plain,
% 0.20/0.41 (![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))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.20/0.41 tff(93,plain,
% 0.20/0.41 (((~![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_union(v_Y, v_Z, t_a)) | (~c_lessequals(c_union(v_Y, v_Z, t_a), v_X, tc_set(t_a))) | (~c_lessequals(v_X, c_union(v_Y, v_Z, t_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))))) | (v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(c_union(v_Y, v_Z, t_a), v_X, tc_set(t_a))) | (~c_lessequals(v_X, c_union(v_Y, v_Z, t_a), tc_set(t_a))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(94,plain,
% 0.20/0.41 (((~c_lessequals(v_X, c_union(v_Y, v_Z, t_a), tc_set(t_a))) | (v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(c_union(v_Y, v_Z, t_a), v_X, tc_set(t_a)))) <=> ((v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(c_union(v_Y, v_Z, t_a), v_X, tc_set(t_a))) | (~c_lessequals(v_X, c_union(v_Y, v_Z, t_a), tc_set(t_a))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(95,plain,
% 0.20/0.41 (((~![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_union(v_Y, v_Z, t_a), tc_set(t_a))) | (v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(c_union(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_union(v_Y, v_Z, t_a)) | (~c_lessequals(c_union(v_Y, v_Z, t_a), v_X, tc_set(t_a))) | (~c_lessequals(v_X, c_union(v_Y, v_Z, t_a), tc_set(t_a)))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[94])).
% 0.20/0.41 tff(96,plain,
% 0.20/0.41 (((~![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_union(v_Y, v_Z, t_a), tc_set(t_a))) | (v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(c_union(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_union(v_Y, v_Z, t_a)) | (~c_lessequals(c_union(v_Y, v_Z, t_a), v_X, tc_set(t_a))) | (~c_lessequals(v_X, c_union(v_Y, v_Z, t_a), tc_set(t_a))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[95, 93])).
% 0.20/0.41 tff(97,plain,
% 0.20/0.41 ((~![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_union(v_Y, v_Z, t_a), tc_set(t_a))) | (v_X = c_union(v_Y, v_Z, t_a)) | (~c_lessequals(c_union(v_Y, v_Z, t_a), v_X, tc_set(t_a))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(98,plain,
% 0.20/0.41 ((~![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_union(v_Y, v_Z, t_a)) | (~c_lessequals(c_union(v_Y, v_Z, t_a), v_X, tc_set(t_a))) | (~c_lessequals(v_X, c_union(v_Y, v_Z, t_a), tc_set(t_a)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.42 tff(99,plain,
% 0.20/0.42 (~c_lessequals(c_union(v_Y, v_Z, t_a), v_X, tc_set(t_a))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[98, 2, 92, 82])).
% 0.20/0.42 tff(100,plain,
% 0.20/0.42 (((~![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_union(v_Y, v_Z, t_a), v_X, t_a), v_X, t_a)) | c_lessequals(c_union(v_Y, v_Z, t_a), v_X, 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_union(v_Y, v_Z, t_a), v_X, t_a), v_X, t_a)) | c_lessequals(c_union(v_Y, v_Z, t_a), v_X, tc_set(t_a)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(101,plain,
% 0.20/0.42 ((~![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_union(v_Y, v_Z, t_a), v_X, t_a), v_X, t_a)) | c_lessequals(c_union(v_Y, v_Z, t_a), v_X, tc_set(t_a)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(102,plain,
% 0.20/0.42 ((~![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_union(v_Y, v_Z, t_a), v_X, t_a), v_X, t_a)) | c_lessequals(c_union(v_Y, v_Z, t_a), v_X, tc_set(t_a))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.20/0.42 tff(103,plain,
% 0.20/0.42 (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_X, t_a)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[102, 10, 99])).
% 0.20/0.42 tff(104,plain,
% 0.20/0.42 (((v_X = c_union(v_Y, v_Z, t_a)) | c_lessequals(v_Y, v_X, tc_set(t_a))) <=> ((v_X = c_union(v_Y, v_Z, t_a)) | c_lessequals(v_Y, v_X, tc_set(t_a)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(105,axiom,((v_X = c_union(v_Y, v_Z, t_a)) | c_lessequals(v_Y, v_X, tc_set(t_a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.20/0.42 tff(106,plain,
% 0.20/0.42 ((v_X = c_union(v_Y, v_Z, t_a)) | c_lessequals(v_Y, v_X, tc_set(t_a))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.42 tff(107,plain,
% 0.20/0.42 (c_lessequals(v_Y, v_X, tc_set(t_a))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[106, 2])).
% 0.20/0.42 tff(108,assumption,(c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Y, t_a)), introduced(assumption)).
% 0.20/0.42 tff(109,assumption,(~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_X, t_a)), introduced(assumption)).
% 0.20/0.42 tff(110,plain,
% 0.20/0.42 (^[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)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(111,plain,
% 0.20/0.42 (![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)))) <=> ![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))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[110])).
% 0.20/0.42 tff(112,plain,
% 0.20/0.42 (![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)))) <=> ![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))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(113,plain,
% 0.20/0.42 (^[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)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(114,plain,
% 0.20/0.42 (![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))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[113])).
% 0.20/0.42 tff(115,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')).
% 0.20/0.42 tff(116,plain,
% 0.20/0.42 (![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))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.20/0.42 tff(117,plain,
% 0.20/0.42 (![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))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.20/0.42 tff(118,plain,(
% 0.20/0.42 ![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))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[117])).
% 0.20/0.42 tff(119,plain,
% 0.20/0.42 (![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))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[118, 111])).
% 0.20/0.42 tff(120,assumption,(c_lessequals(v_Y, v_X, tc_set(t_a))), introduced(assumption)).
% 0.20/0.42 tff(121,plain,
% 0.20/0.42 (((~![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_Y, v_X, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_X, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Y, 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_Y, v_X, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_X, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Y, t_a)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(122,plain,
% 0.20/0.42 ((c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_X, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Y, t_a)) | (~c_lessequals(v_Y, v_X, tc_set(t_a)))) <=> ((~c_lessequals(v_Y, v_X, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_X, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Y, t_a)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(123,plain,
% 0.20/0.42 (((~![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(c_union(v_Y, v_Z, t_a), v_X, t_a), v_X, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Y, t_a)) | (~c_lessequals(v_Y, 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_lessequals(v_Y, v_X, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_X, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Y, t_a))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[122])).
% 0.20/0.42 tff(124,plain,
% 0.20/0.42 (((~![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(c_union(v_Y, v_Z, t_a), v_X, t_a), v_X, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Y, t_a)) | (~c_lessequals(v_Y, 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_lessequals(v_Y, v_X, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_X, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Y, t_a)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[123, 121])).
% 0.20/0.42 tff(125,plain,
% 0.20/0.42 ((~![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(c_union(v_Y, v_Z, t_a), v_X, t_a), v_X, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Y, t_a)) | (~c_lessequals(v_Y, v_X, tc_set(t_a))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(126,plain,
% 0.20/0.42 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_X, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Y, t_a))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.20/0.43 tff(127,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[126, 120, 119, 109, 108])).
% 0.20/0.43 tff(128,plain,((~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Y, t_a)) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_X, t_a)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(129,plain,
% 0.20/0.43 (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Y, t_a)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[128, 107, 103])).
% 0.20/0.43 tff(130,plain,
% 0.20/0.43 (((~![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_union(v_Y, v_Z, t_a), v_X, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), c_union(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_union(v_Y, v_Z, t_a), v_X, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), c_union(v_Y, v_Z, t_a), t_a))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(131,plain,
% 0.20/0.43 ((c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), c_union(v_Y, v_Z, t_a), t_a) | c_lessequals(c_union(v_Y, v_Z, t_a), v_X, tc_set(t_a))) <=> (c_lessequals(c_union(v_Y, v_Z, t_a), v_X, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), c_union(v_Y, v_Z, t_a), t_a))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(132,plain,
% 0.20/0.43 (((~![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_union(v_Y, v_Z, t_a), v_X, t_a), c_union(v_Y, v_Z, t_a), t_a) | c_lessequals(c_union(v_Y, v_Z, t_a), v_X, 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_union(v_Y, v_Z, t_a), v_X, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), c_union(v_Y, v_Z, t_a), t_a)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[131])).
% 0.20/0.43 tff(133,plain,
% 0.20/0.43 (((~![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_union(v_Y, v_Z, t_a), v_X, t_a), c_union(v_Y, v_Z, t_a), t_a) | c_lessequals(c_union(v_Y, v_Z, t_a), v_X, 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_union(v_Y, v_Z, t_a), v_X, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), c_union(v_Y, v_Z, t_a), t_a))),
% 0.20/0.43 inference(transitivity,[status(thm)],[132, 130])).
% 0.20/0.43 tff(134,plain,
% 0.20/0.43 ((~![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_union(v_Y, v_Z, t_a), v_X, t_a), c_union(v_Y, v_Z, t_a), t_a) | c_lessequals(c_union(v_Y, v_Z, t_a), v_X, tc_set(t_a)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(135,plain,
% 0.20/0.43 ((~![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_union(v_Y, v_Z, t_a), v_X, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), c_union(v_Y, v_Z, t_a), t_a)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.20/0.43 tff(136,plain,
% 0.20/0.43 (c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), c_union(v_Y, v_Z, t_a), t_a)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[135, 21, 99])).
% 0.20/0.43 tff(137,plain,
% 0.20/0.43 (^[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_in(V_c, c_union(V_A, V_B, T_a), T_a))) <=> (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(138,plain,
% 0.20/0.43 (![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_in(V_c, c_union(V_A, V_B, T_a), 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_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[137])).
% 0.20/0.43 tff(139,plain,
% 0.20/0.43 (![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_in(V_c, c_union(V_A, V_B, T_a), 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_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(140,plain,
% 0.20/0.43 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : rewrite((((~c_in(V_c, c_union(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a)) | c_in(V_c, V_A, T_a)) <=> (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(141,plain,
% 0.20/0.43 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_c, c_union(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, 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, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[140])).
% 0.20/0.43 tff(142,axiom,(![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_c, c_union(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a)) | c_in(V_c, V_A, T_a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_OUnE_0')).
% 0.20/0.43 tff(143,plain,
% 0.20/0.43 (![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_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.20/0.43 tff(144,plain,
% 0.20/0.43 (![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_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[143, 139])).
% 0.20/0.43 tff(145,plain,(
% 0.20/0.43 ![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_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[144])).
% 0.20/0.43 tff(146,plain,
% 0.20/0.43 (![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_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[145, 138])).
% 0.20/0.43 tff(147,plain,
% 0.20/0.43 (((~![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_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | (c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Z, t_a) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), c_union(v_Y, v_Z, t_a), 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_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Z, t_a) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), c_union(v_Y, v_Z, t_a), t_a)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(148,plain,
% 0.20/0.43 ((~![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_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | (c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Z, t_a) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), c_union(v_Y, v_Z, t_a), t_a)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(149,plain,
% 0.20/0.43 ((~![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_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Z, t_a) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), c_union(v_Y, v_Z, t_a), t_a))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.20/0.43 tff(150,plain,
% 0.20/0.43 (c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Z, t_a) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Y, t_a)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[149, 146, 136])).
% 0.20/0.43 tff(151,plain,
% 0.20/0.43 (c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Z, t_a)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[150, 129])).
% 0.20/0.43 tff(152,assumption,(~c_lessequals(v_Z, v_X, tc_set(t_a))), introduced(assumption)).
% 0.20/0.43 tff(153,plain,
% 0.20/0.43 (((v_X = c_union(v_Y, v_Z, t_a)) | c_lessequals(v_Z, v_X, tc_set(t_a))) <=> ((v_X = c_union(v_Y, v_Z, t_a)) | c_lessequals(v_Z, v_X, tc_set(t_a)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(154,axiom,((v_X = c_union(v_Y, v_Z, t_a)) | c_lessequals(v_Z, v_X, tc_set(t_a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_1')).
% 0.20/0.43 tff(155,plain,
% 0.20/0.43 ((v_X = c_union(v_Y, v_Z, t_a)) | c_lessequals(v_Z, v_X, tc_set(t_a))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.20/0.43 tff(156,plain,
% 0.20/0.43 (v_X = c_union(v_Y, v_Z, t_a)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[155, 152])).
% 0.20/0.43 tff(157,plain,
% 0.20/0.43 (c_lessequals(v_Z, v_X, tc_set(t_a)) <=> c_lessequals(v_Z, c_union(v_Y, v_Z, t_a), tc_set(t_a))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[156])).
% 0.20/0.43 tff(158,plain,
% 0.20/0.43 (c_lessequals(v_Z, c_union(v_Y, v_Z, t_a), tc_set(t_a)) <=> c_lessequals(v_Z, v_X, tc_set(t_a))),
% 0.20/0.43 inference(symmetry,[status(thm)],[157])).
% 0.20/0.43 tff(159,plain,
% 0.20/0.43 (c_lessequals(v_Z, v_X, tc_set(t_a))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[63, 158])).
% 0.20/0.43 tff(160,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[152, 159])).
% 0.20/0.43 tff(161,plain,(c_lessequals(v_Z, v_X, tc_set(t_a))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(162,plain,
% 0.20/0.43 (((~![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_Z, v_X, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_X, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Z, 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_Z, v_X, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_X, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Z, t_a)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(163,plain,
% 0.20/0.43 ((c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_X, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Z, t_a)) | (~c_lessequals(v_Z, v_X, tc_set(t_a)))) <=> ((~c_lessequals(v_Z, v_X, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_X, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Z, t_a)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(164,plain,
% 0.20/0.43 (((~![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(c_union(v_Y, v_Z, t_a), v_X, t_a), v_X, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Z, t_a)) | (~c_lessequals(v_Z, 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_lessequals(v_Z, v_X, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_X, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Z, t_a))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[163])).
% 0.20/0.43 tff(165,plain,
% 0.20/0.43 (((~![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(c_union(v_Y, v_Z, t_a), v_X, t_a), v_X, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Z, t_a)) | (~c_lessequals(v_Z, 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_lessequals(v_Z, v_X, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_X, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Z, t_a)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[164, 162])).
% 0.20/0.44 tff(166,plain,
% 0.20/0.44 ((~![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(c_union(v_Y, v_Z, t_a), v_X, t_a), v_X, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Z, t_a)) | (~c_lessequals(v_Z, v_X, tc_set(t_a))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(167,plain,
% 0.20/0.44 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (~c_lessequals(v_Z, v_X, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_X, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_X, t_a), v_Z, t_a))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.20/0.44 tff(168,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[167, 161, 119, 103, 151])).
% 0.20/0.44 tff(169,plain,(v_X = c_union(v_Y, v_Z, t_a)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(170,plain,
% 0.20/0.44 (c_union(v_Y, v_Z, t_a) = v_X),
% 0.20/0.44 inference(symmetry,[status(thm)],[169])).
% 0.20/0.44 tff(171,plain,
% 0.20/0.44 (c_lessequals(c_union(v_Y, v_Z, t_a), v_x, tc_set(t_a)) <=> c_lessequals(v_X, v_x, tc_set(t_a))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[170])).
% 0.20/0.44 tff(172,plain,
% 0.20/0.44 (c_lessequals(v_X, v_x, tc_set(t_a)) <=> c_lessequals(c_union(v_Y, v_Z, t_a), v_x, tc_set(t_a))),
% 0.20/0.44 inference(symmetry,[status(thm)],[171])).
% 0.20/0.44 tff(173,plain,
% 0.20/0.44 ((~c_lessequals(v_X, v_x, tc_set(t_a))) <=> (~c_lessequals(c_union(v_Y, v_Z, t_a), v_x, tc_set(t_a)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[172])).
% 0.20/0.44 tff(174,plain,
% 0.20/0.44 (c_lessequals(v_Y, v_X, tc_set(t_a)) <=> c_lessequals(v_Y, c_union(v_Y, v_Z, t_a), tc_set(t_a))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[169])).
% 0.20/0.44 tff(175,plain,
% 0.20/0.44 (c_lessequals(v_Y, c_union(v_Y, v_Z, t_a), tc_set(t_a)) <=> c_lessequals(v_Y, v_X, tc_set(t_a))),
% 0.20/0.44 inference(symmetry,[status(thm)],[174])).
% 0.20/0.44 tff(176,plain,
% 0.20/0.44 (c_lessequals(v_Y, v_X, tc_set(t_a))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[40, 175])).
% 0.20/0.44 tff(177,plain,
% 0.20/0.44 (((~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | (~(v_X = c_union(v_Y, v_Z, t_a))) | (~c_lessequals(v_X, v_x, tc_set(t_a)))) <=> ((~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | (~(v_X = c_union(v_Y, v_Z, t_a))) | (~c_lessequals(v_X, v_x, tc_set(t_a))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(178,plain,
% 0.20/0.44 ((((~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | (~c_lessequals(v_X, v_x, tc_set(t_a)))) | (~(v_X = c_union(v_Y, v_Z, t_a)))) <=> ((~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | (~(v_X = c_union(v_Y, v_Z, t_a))) | (~c_lessequals(v_X, v_x, tc_set(t_a))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(179,plain,
% 0.20/0.44 ((((~c_lessequals(v_X, v_x, tc_set(t_a))) | (~c_lessequals(v_Z, v_X, tc_set(t_a)))) | (~c_lessequals(v_Y, v_X, tc_set(t_a)))) <=> ((~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | (~c_lessequals(v_X, v_x, tc_set(t_a))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(180,plain,
% 0.20/0.44 (((((~c_lessequals(v_X, v_x, tc_set(t_a))) | (~c_lessequals(v_Z, v_X, tc_set(t_a)))) | (~c_lessequals(v_Y, v_X, tc_set(t_a)))) | (~(v_X = c_union(v_Y, v_Z, t_a)))) <=> (((~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | (~c_lessequals(v_X, v_x, tc_set(t_a)))) | (~(v_X = c_union(v_Y, v_Z, t_a))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[179])).
% 0.20/0.44 tff(181,plain,
% 0.20/0.44 (((((~c_lessequals(v_X, v_x, tc_set(t_a))) | (~c_lessequals(v_Z, v_X, tc_set(t_a)))) | (~c_lessequals(v_Y, v_X, tc_set(t_a)))) | (~(v_X = c_union(v_Y, v_Z, t_a)))) <=> ((~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | (~(v_X = c_union(v_Y, v_Z, t_a))) | (~c_lessequals(v_X, v_x, tc_set(t_a))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[180, 178])).
% 0.20/0.44 tff(182,axiom,((((~c_lessequals(v_X, v_x, tc_set(t_a))) | (~c_lessequals(v_Z, v_X, tc_set(t_a)))) | (~c_lessequals(v_Y, v_X, tc_set(t_a)))) | (~(v_X = c_union(v_Y, v_Z, t_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_4')).
% 0.20/0.44 tff(183,plain,
% 0.20/0.44 ((~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | (~(v_X = c_union(v_Y, v_Z, t_a))) | (~c_lessequals(v_X, v_x, tc_set(t_a)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.20/0.44 tff(184,plain,
% 0.20/0.44 ((~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | (~(v_X = c_union(v_Y, v_Z, t_a))) | (~c_lessequals(v_X, v_x, tc_set(t_a)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[183, 177])).
% 0.20/0.44 tff(185,plain,
% 0.20/0.44 ((~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | (~(v_X = c_union(v_Y, v_Z, t_a))) | (~c_lessequals(v_X, v_x, tc_set(t_a)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[184, 177])).
% 0.20/0.44 tff(186,plain,
% 0.20/0.44 ((~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | (~(v_X = c_union(v_Y, v_Z, t_a))) | (~c_lessequals(v_X, v_x, tc_set(t_a)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[185, 177])).
% 0.20/0.44 tff(187,plain,
% 0.20/0.44 ((~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | (~(v_X = c_union(v_Y, v_Z, t_a))) | (~c_lessequals(v_X, v_x, tc_set(t_a)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[186, 177])).
% 0.20/0.44 tff(188,plain,
% 0.20/0.44 (~c_lessequals(v_X, v_x, tc_set(t_a))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[187, 176, 161, 169])).
% 0.20/0.44 tff(189,plain,
% 0.20/0.44 (~c_lessequals(c_union(v_Y, v_Z, t_a), v_x, tc_set(t_a))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[188, 173])).
% 0.20/0.44 tff(190,plain,
% 0.20/0.44 (((~![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_union(v_Y, v_Z, t_a), v_x, t_a), v_x, t_a)) | c_lessequals(c_union(v_Y, v_Z, t_a), v_x, 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_union(v_Y, v_Z, t_a), v_x, t_a), v_x, t_a)) | c_lessequals(c_union(v_Y, v_Z, t_a), v_x, tc_set(t_a)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(191,plain,
% 0.20/0.44 ((~![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_union(v_Y, v_Z, t_a), v_x, t_a), v_x, t_a)) | c_lessequals(c_union(v_Y, v_Z, t_a), v_x, tc_set(t_a)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(192,plain,
% 0.20/0.44 ((~![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_union(v_Y, v_Z, t_a), v_x, t_a), v_x, t_a)) | c_lessequals(c_union(v_Y, v_Z, t_a), v_x, tc_set(t_a))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.20/0.44 tff(193,plain,
% 0.20/0.44 ((~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_x, t_a)) | c_lessequals(c_union(v_Y, v_Z, t_a), v_x, tc_set(t_a))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[192, 10])).
% 0.20/0.44 tff(194,plain,
% 0.20/0.44 (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_x, t_a)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[193, 189])).
% 0.20/0.44 tff(195,plain,
% 0.20/0.44 (((~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | (~(v_X = c_union(v_Y, v_Z, t_a))) | c_lessequals(v_Z, v_x, tc_set(t_a))) <=> ((~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | (~(v_X = c_union(v_Y, v_Z, t_a))) | c_lessequals(v_Z, v_x, tc_set(t_a)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(196,plain,
% 0.20/0.44 ((((~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | c_lessequals(v_Z, v_x, tc_set(t_a))) | (~(v_X = c_union(v_Y, v_Z, t_a)))) <=> ((~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | (~(v_X = c_union(v_Y, v_Z, t_a))) | c_lessequals(v_Z, v_x, tc_set(t_a)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(197,plain,
% 0.20/0.45 ((((~c_lessequals(v_Z, v_X, tc_set(t_a))) | c_lessequals(v_Z, v_x, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a)))) <=> ((~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | c_lessequals(v_Z, v_x, tc_set(t_a)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(198,plain,
% 0.20/0.45 ((c_lessequals(v_Z, v_x, tc_set(t_a)) | (~c_lessequals(v_Z, v_X, tc_set(t_a)))) <=> ((~c_lessequals(v_Z, v_X, tc_set(t_a))) | c_lessequals(v_Z, v_x, tc_set(t_a)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(199,plain,
% 0.20/0.45 (((c_lessequals(v_Z, v_x, tc_set(t_a)) | (~c_lessequals(v_Z, v_X, tc_set(t_a)))) | (~c_lessequals(v_Y, v_X, tc_set(t_a)))) <=> (((~c_lessequals(v_Z, v_X, tc_set(t_a))) | c_lessequals(v_Z, v_x, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[198])).
% 0.20/0.45 tff(200,plain,
% 0.20/0.45 (((c_lessequals(v_Z, v_x, tc_set(t_a)) | (~c_lessequals(v_Z, v_X, tc_set(t_a)))) | (~c_lessequals(v_Y, v_X, tc_set(t_a)))) <=> ((~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | c_lessequals(v_Z, v_x, tc_set(t_a)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[199, 197])).
% 0.20/0.45 tff(201,plain,
% 0.20/0.45 ((((c_lessequals(v_Z, v_x, tc_set(t_a)) | (~c_lessequals(v_Z, v_X, tc_set(t_a)))) | (~c_lessequals(v_Y, v_X, tc_set(t_a)))) | (~(v_X = c_union(v_Y, v_Z, t_a)))) <=> (((~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | c_lessequals(v_Z, v_x, tc_set(t_a))) | (~(v_X = c_union(v_Y, v_Z, t_a))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[200])).
% 0.20/0.45 tff(202,plain,
% 0.20/0.45 ((((c_lessequals(v_Z, v_x, tc_set(t_a)) | (~c_lessequals(v_Z, v_X, tc_set(t_a)))) | (~c_lessequals(v_Y, v_X, tc_set(t_a)))) | (~(v_X = c_union(v_Y, v_Z, t_a)))) <=> ((~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | (~(v_X = c_union(v_Y, v_Z, t_a))) | c_lessequals(v_Z, v_x, tc_set(t_a)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[201, 196])).
% 0.20/0.45 tff(203,axiom,(((c_lessequals(v_Z, v_x, tc_set(t_a)) | (~c_lessequals(v_Z, v_X, tc_set(t_a)))) | (~c_lessequals(v_Y, v_X, tc_set(t_a)))) | (~(v_X = c_union(v_Y, v_Z, t_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_3')).
% 0.20/0.45 tff(204,plain,
% 0.20/0.45 ((~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | (~(v_X = c_union(v_Y, v_Z, t_a))) | c_lessequals(v_Z, v_x, tc_set(t_a))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.20/0.45 tff(205,plain,
% 0.20/0.45 ((~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | (~(v_X = c_union(v_Y, v_Z, t_a))) | c_lessequals(v_Z, v_x, tc_set(t_a))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[204, 195])).
% 0.20/0.45 tff(206,plain,
% 0.20/0.45 ((~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | (~(v_X = c_union(v_Y, v_Z, t_a))) | c_lessequals(v_Z, v_x, tc_set(t_a))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[205, 195])).
% 0.20/0.45 tff(207,plain,
% 0.20/0.45 ((~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | (~(v_X = c_union(v_Y, v_Z, t_a))) | c_lessequals(v_Z, v_x, tc_set(t_a))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[206, 195])).
% 0.20/0.45 tff(208,plain,
% 0.20/0.45 ((~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | (~(v_X = c_union(v_Y, v_Z, t_a))) | c_lessequals(v_Z, v_x, tc_set(t_a))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[207, 195])).
% 0.20/0.45 tff(209,plain,
% 0.20/0.45 (c_lessequals(v_Z, v_x, tc_set(t_a))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[208, 176, 161, 169])).
% 0.20/0.45 tff(210,plain,
% 0.20/0.45 (((~![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_Z, v_x, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_x, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_Z, 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_Z, v_x, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_x, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_Z, t_a)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(211,plain,
% 0.20/0.45 ((c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_x, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_Z, t_a)) | (~c_lessequals(v_Z, v_x, tc_set(t_a)))) <=> ((~c_lessequals(v_Z, v_x, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_x, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_Z, t_a)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(212,plain,
% 0.20/0.45 (((~![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(c_union(v_Y, v_Z, t_a), v_x, t_a), v_x, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_Z, t_a)) | (~c_lessequals(v_Z, 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_lessequals(v_Z, v_x, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_x, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_Z, t_a))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[211])).
% 0.20/0.45 tff(213,plain,
% 0.20/0.45 (((~![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(c_union(v_Y, v_Z, t_a), v_x, t_a), v_x, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_Z, t_a)) | (~c_lessequals(v_Z, 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_lessequals(v_Z, v_x, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_x, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_Z, t_a)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[212, 210])).
% 0.20/0.45 tff(214,plain,
% 0.20/0.45 ((~![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(c_union(v_Y, v_Z, t_a), v_x, t_a), v_x, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_Z, t_a)) | (~c_lessequals(v_Z, v_x, tc_set(t_a))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(215,plain,
% 0.20/0.45 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (~c_lessequals(v_Z, v_x, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_x, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_Z, t_a))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.20/0.45 tff(216,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[215, 209, 119, 194, 1])).
% 0.20/0.45 tff(217,plain,(~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_Z, t_a)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(218,plain,
% 0.20/0.45 (((~![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_union(v_Y, v_Z, t_a), v_x, t_a), c_union(v_Y, v_Z, t_a), t_a) | c_lessequals(c_union(v_Y, v_Z, t_a), v_x, 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_union(v_Y, v_Z, t_a), v_x, t_a), c_union(v_Y, v_Z, t_a), t_a) | c_lessequals(c_union(v_Y, v_Z, t_a), v_x, tc_set(t_a)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(219,plain,
% 0.20/0.45 ((~![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_union(v_Y, v_Z, t_a), v_x, t_a), c_union(v_Y, v_Z, t_a), t_a) | c_lessequals(c_union(v_Y, v_Z, t_a), v_x, tc_set(t_a)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(220,plain,
% 0.20/0.45 ((~![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_union(v_Y, v_Z, t_a), v_x, t_a), c_union(v_Y, v_Z, t_a), t_a) | c_lessequals(c_union(v_Y, v_Z, t_a), v_x, tc_set(t_a))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.20/0.45 tff(221,plain,
% 0.20/0.45 (c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), c_union(v_Y, v_Z, t_a), t_a) | c_lessequals(c_union(v_Y, v_Z, t_a), v_x, tc_set(t_a))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[220, 21])).
% 0.20/0.45 tff(222,plain,
% 0.20/0.45 (c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), c_union(v_Y, v_Z, t_a), t_a)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[221, 189])).
% 0.20/0.45 tff(223,plain,
% 0.20/0.45 (((~![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_union(V_A, V_B, T_a), T_a)))) | (c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_Z, t_a) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), c_union(v_Y, v_Z, t_a), 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_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_Z, t_a) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), c_union(v_Y, v_Z, t_a), t_a)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(224,plain,
% 0.20/0.45 ((~![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_union(V_A, V_B, T_a), T_a)))) | (c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_Z, t_a) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), c_union(v_Y, v_Z, t_a), t_a)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(225,plain,
% 0.20/0.45 ((~![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_union(V_A, V_B, T_a), T_a)))) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_Z, t_a) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), c_union(v_Y, v_Z, t_a), t_a))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.20/0.45 tff(226,plain,
% 0.20/0.45 (c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_Z, t_a) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_Y, t_a)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[225, 146, 222])).
% 0.20/0.45 tff(227,plain,
% 0.20/0.45 (c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_Y, t_a)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[226, 217])).
% 0.20/0.45 tff(228,plain,
% 0.20/0.45 ((c_lessequals(v_Y, v_x, tc_set(t_a)) | (~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | (~(v_X = c_union(v_Y, v_Z, t_a)))) <=> (c_lessequals(v_Y, v_x, tc_set(t_a)) | (~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | (~(v_X = c_union(v_Y, v_Z, t_a))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(229,plain,
% 0.20/0.45 (((c_lessequals(v_Y, v_x, tc_set(t_a)) | (~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a)))) | (~(v_X = c_union(v_Y, v_Z, t_a)))) <=> (c_lessequals(v_Y, v_x, tc_set(t_a)) | (~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | (~(v_X = c_union(v_Y, v_Z, t_a))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(230,plain,
% 0.20/0.45 (((c_lessequals(v_Y, v_x, tc_set(t_a)) | (~c_lessequals(v_Z, v_X, tc_set(t_a)))) | (~c_lessequals(v_Y, v_X, tc_set(t_a)))) <=> (c_lessequals(v_Y, v_x, tc_set(t_a)) | (~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(231,plain,
% 0.20/0.45 ((c_lessequals(v_Y, v_x, tc_set(t_a)) | (~c_lessequals(v_Z, v_X, tc_set(t_a)))) <=> (c_lessequals(v_Y, v_x, tc_set(t_a)) | (~c_lessequals(v_Z, v_X, tc_set(t_a))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(232,plain,
% 0.20/0.45 (((c_lessequals(v_Y, v_x, tc_set(t_a)) | (~c_lessequals(v_Z, v_X, tc_set(t_a)))) | (~c_lessequals(v_Y, v_X, tc_set(t_a)))) <=> ((c_lessequals(v_Y, v_x, tc_set(t_a)) | (~c_lessequals(v_Z, v_X, tc_set(t_a)))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[231])).
% 0.20/0.46 tff(233,plain,
% 0.20/0.46 (((c_lessequals(v_Y, v_x, tc_set(t_a)) | (~c_lessequals(v_Z, v_X, tc_set(t_a)))) | (~c_lessequals(v_Y, v_X, tc_set(t_a)))) <=> (c_lessequals(v_Y, v_x, tc_set(t_a)) | (~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[232, 230])).
% 0.20/0.46 tff(234,plain,
% 0.20/0.46 ((((c_lessequals(v_Y, v_x, tc_set(t_a)) | (~c_lessequals(v_Z, v_X, tc_set(t_a)))) | (~c_lessequals(v_Y, v_X, tc_set(t_a)))) | (~(v_X = c_union(v_Y, v_Z, t_a)))) <=> ((c_lessequals(v_Y, v_x, tc_set(t_a)) | (~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a)))) | (~(v_X = c_union(v_Y, v_Z, t_a))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[233])).
% 0.20/0.46 tff(235,plain,
% 0.20/0.46 ((((c_lessequals(v_Y, v_x, tc_set(t_a)) | (~c_lessequals(v_Z, v_X, tc_set(t_a)))) | (~c_lessequals(v_Y, v_X, tc_set(t_a)))) | (~(v_X = c_union(v_Y, v_Z, t_a)))) <=> (c_lessequals(v_Y, v_x, tc_set(t_a)) | (~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | (~(v_X = c_union(v_Y, v_Z, t_a))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[234, 229])).
% 0.20/0.46 tff(236,axiom,(((c_lessequals(v_Y, v_x, tc_set(t_a)) | (~c_lessequals(v_Z, v_X, tc_set(t_a)))) | (~c_lessequals(v_Y, v_X, tc_set(t_a)))) | (~(v_X = c_union(v_Y, v_Z, t_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_2')).
% 0.20/0.46 tff(237,plain,
% 0.20/0.46 (c_lessequals(v_Y, v_x, tc_set(t_a)) | (~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | (~(v_X = c_union(v_Y, v_Z, t_a)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.20/0.46 tff(238,plain,
% 0.20/0.46 (c_lessequals(v_Y, v_x, tc_set(t_a)) | (~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | (~(v_X = c_union(v_Y, v_Z, t_a)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[237, 228])).
% 0.20/0.46 tff(239,plain,
% 0.20/0.46 (c_lessequals(v_Y, v_x, tc_set(t_a)) | (~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | (~(v_X = c_union(v_Y, v_Z, t_a)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[238, 228])).
% 0.20/0.46 tff(240,plain,
% 0.20/0.46 (c_lessequals(v_Y, v_x, tc_set(t_a)) | (~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | (~(v_X = c_union(v_Y, v_Z, t_a)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[239, 228])).
% 0.20/0.46 tff(241,plain,
% 0.20/0.46 (c_lessequals(v_Y, v_x, tc_set(t_a)) | (~c_lessequals(v_Z, v_X, tc_set(t_a))) | (~c_lessequals(v_Y, v_X, tc_set(t_a))) | (~(v_X = c_union(v_Y, v_Z, t_a)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[240, 228])).
% 0.20/0.46 tff(242,plain,
% 0.20/0.46 (c_lessequals(v_Y, v_x, tc_set(t_a))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[241, 176, 161, 169])).
% 0.20/0.46 tff(243,plain,
% 0.20/0.46 (((~![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_Y, v_x, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_x, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_Y, 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_Y, v_x, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_x, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_Y, t_a)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(244,plain,
% 0.20/0.46 ((c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_x, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_Y, t_a)) | (~c_lessequals(v_Y, v_x, tc_set(t_a)))) <=> ((~c_lessequals(v_Y, v_x, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_x, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_Y, t_a)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(245,plain,
% 0.20/0.46 (((~![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(c_union(v_Y, v_Z, t_a), v_x, t_a), v_x, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_Y, t_a)) | (~c_lessequals(v_Y, 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_lessequals(v_Y, v_x, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_x, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_Y, t_a))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[244])).
% 0.20/0.46 tff(246,plain,
% 0.20/0.46 (((~![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(c_union(v_Y, v_Z, t_a), v_x, t_a), v_x, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_Y, t_a)) | (~c_lessequals(v_Y, 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_lessequals(v_Y, v_x, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_x, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_Y, t_a)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[245, 243])).
% 0.20/0.46 tff(247,plain,
% 0.20/0.46 ((~![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(c_union(v_Y, v_Z, t_a), v_x, t_a), v_x, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_Y, t_a)) | (~c_lessequals(v_Y, v_x, tc_set(t_a))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(248,plain,
% 0.20/0.46 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (~c_lessequals(v_Y, v_x, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_x, t_a) | (~c_in(c_Main_OsubsetI__1(c_union(v_Y, v_Z, t_a), v_x, t_a), v_Y, t_a))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.20/0.46 tff(249,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[248, 242, 119, 194, 227])).
% 0.20/0.46 % SZS output end Proof
% 0.20/0.46 % E exiting
%------------------------------------------------------------------------------