%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET840-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:29 AM UTC 2025
% Result : Unsatisfiable 49.04s 49.25s
% Output : Proof 49.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET840-2 : TPTP v9.0.0. Released v3.2.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 05:45:08 EDT 2025
% 0.12/0.34 % CPUTime :
% 49.04/49.25 % SZS status Unsatisfiable
% 49.04/49.25 % SZS output start Proof
% 49.04/49.25 tff(c_in_type, type, (
% 49.04/49.25 c_in: ( $i * $i * $i ) > $o)).
% 49.04/49.25 tff(tc_set_type, type, (
% 49.04/49.25 tc_set: $i > $i)).
% 49.04/49.25 tff(t_b_type, type, (
% 49.04/49.25 t_b: $i)).
% 49.04/49.25 tff(c_insert_type, type, (
% 49.04/49.25 c_insert: ( $i * $i * $i ) > $i)).
% 49.04/49.25 tff(c_emptyset_type, type, (
% 49.04/49.25 c_emptyset: $i)).
% 49.04/49.25 tff(c_Union_type, type, (
% 49.04/49.25 c_Union: ( $i * $i ) > $i)).
% 49.04/49.25 tff(v_S_type, type, (
% 49.04/49.25 v_S: $i)).
% 49.04/49.25 tff(c_Main_OsubsetI__1_type, type, (
% 49.04/49.25 c_Main_OsubsetI__1: ( $i * $i * $i ) > $i)).
% 49.04/49.25 tff(c_lessequals_type, type, (
% 49.04/49.25 c_lessequals: ( $i * $i * $i ) > $o)).
% 49.04/49.25 tff(1,assumption,(~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), tc_set(t_b))), introduced(assumption)).
% 49.04/49.25 tff(2,plain,
% 49.04/49.25 (^[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))))),
% 49.04/49.25 inference(bind,[status(th)],[])).
% 49.04/49.25 tff(3,plain,
% 49.04/49.25 (![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)))),
% 49.04/49.25 inference(quant_intro,[status(thm)],[2])).
% 49.04/49.25 tff(4,plain,
% 49.04/49.25 (![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)))),
% 49.04/49.25 inference(rewrite,[status(thm)],[])).
% 49.04/49.25 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_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_OsubsetI_1')).
% 49.04/49.25 tff(6,plain,
% 49.04/49.25 (![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)))),
% 49.04/49.25 inference(modus_ponens,[status(thm)],[5, 4])).
% 49.04/49.25 tff(7,plain,(
% 49.04/49.25 ![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)))),
% 49.04/49.25 inference(skolemize,[status(sab)],[6])).
% 49.04/49.25 tff(8,plain,
% 49.04/49.25 (![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)))),
% 49.04/49.25 inference(modus_ponens,[status(thm)],[7, 3])).
% 49.04/49.25 tff(9,plain,
% 49.04/49.25 (((~![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_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Union(v_S, t_b), t_b)) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), tc_set(t_b)))) <=> ((~![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_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Union(v_S, t_b), t_b)) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), tc_set(t_b)))),
% 49.04/49.25 inference(rewrite,[status(thm)],[])).
% 49.04/49.25 tff(10,plain,
% 49.04/49.25 ((~![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_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Union(v_S, t_b), t_b)) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), tc_set(t_b)))),
% 49.04/49.25 inference(quant_inst,[status(thm)],[])).
% 49.04/49.25 tff(11,plain,
% 49.04/49.25 ((~![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_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Union(v_S, t_b), t_b)) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), tc_set(t_b))),
% 49.04/49.25 inference(modus_ponens,[status(thm)],[10, 9])).
% 49.04/49.25 tff(12,plain,
% 49.04/49.25 (~c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Union(v_S, t_b), t_b)),
% 49.04/49.25 inference(unit_resolution,[status(thm)],[11, 8, 1])).
% 49.04/49.25 tff(13,plain,
% 49.04/49.25 (^[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))))),
% 49.04/49.25 inference(bind,[status(th)],[])).
% 49.04/49.25 tff(14,plain,
% 49.04/49.25 (![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)))),
% 49.04/49.25 inference(quant_intro,[status(thm)],[13])).
% 49.04/49.25 tff(15,plain,
% 49.04/49.25 (![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)))),
% 49.04/49.25 inference(rewrite,[status(thm)],[])).
% 49.04/49.25 tff(16,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')).
% 49.04/49.25 tff(17,plain,
% 49.04/49.25 (![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)))),
% 49.04/49.25 inference(modus_ponens,[status(thm)],[16, 15])).
% 49.04/49.25 tff(18,plain,(
% 49.04/49.25 ![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)))),
% 49.04/49.25 inference(skolemize,[status(sab)],[17])).
% 49.04/49.25 tff(19,plain,
% 49.04/49.25 (![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)))),
% 49.04/49.25 inference(modus_ponens,[status(thm)],[18, 14])).
% 49.04/49.25 tff(20,plain,
% 49.04/49.25 (((~![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_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), tc_set(t_b)) | c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), t_b))) <=> ((~![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_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), tc_set(t_b)) | c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), t_b))),
% 49.04/49.25 inference(rewrite,[status(thm)],[])).
% 49.04/49.25 tff(21,plain,
% 49.04/49.25 ((c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), t_b) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), tc_set(t_b))) <=> (c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), tc_set(t_b)) | c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), t_b))),
% 49.04/49.25 inference(rewrite,[status(thm)],[])).
% 49.04/49.25 tff(22,plain,
% 49.04/49.25 (((~![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_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), t_b) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), tc_set(t_b)))) <=> ((~![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_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), tc_set(t_b)) | c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), t_b)))),
% 49.04/49.25 inference(monotonicity,[status(thm)],[21])).
% 49.04/49.25 tff(23,plain,
% 49.04/49.25 (((~![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_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), t_b) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), tc_set(t_b)))) <=> ((~![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_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), tc_set(t_b)) | c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), t_b))),
% 49.04/49.25 inference(transitivity,[status(thm)],[22, 20])).
% 49.04/49.25 tff(24,plain,
% 49.04/49.25 ((~![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_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), t_b) | c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), tc_set(t_b)))),
% 49.04/49.25 inference(quant_inst,[status(thm)],[])).
% 49.04/49.25 tff(25,plain,
% 49.04/49.25 ((~![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_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), tc_set(t_b)) | c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), t_b)),
% 49.04/49.25 inference(modus_ponens,[status(thm)],[24, 23])).
% 49.04/49.25 tff(26,plain,
% 49.04/49.25 (c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), t_b)),
% 49.04/49.25 inference(unit_resolution,[status(thm)],[25, 19, 1])).
% 49.04/49.25 tff(27,plain,
% 49.04/49.25 (^[V_U: $i] : refl((~c_lessequals(v_S, c_insert(V_U, c_emptyset, tc_set(t_b)), tc_set(tc_set(t_b)))) <=> (~c_lessequals(v_S, c_insert(V_U, c_emptyset, tc_set(t_b)), tc_set(tc_set(t_b)))))),
% 49.04/49.25 inference(bind,[status(th)],[])).
% 49.04/49.25 tff(28,plain,
% 49.04/49.25 (![V_U: $i] : (~c_lessequals(v_S, c_insert(V_U, c_emptyset, tc_set(t_b)), tc_set(tc_set(t_b)))) <=> ![V_U: $i] : (~c_lessequals(v_S, c_insert(V_U, c_emptyset, tc_set(t_b)), tc_set(tc_set(t_b))))),
% 49.04/49.25 inference(quant_intro,[status(thm)],[27])).
% 49.04/49.25 tff(29,plain,
% 49.04/49.25 (![V_U: $i] : (~c_lessequals(v_S, c_insert(V_U, c_emptyset, tc_set(t_b)), tc_set(tc_set(t_b)))) <=> ![V_U: $i] : (~c_lessequals(v_S, c_insert(V_U, c_emptyset, tc_set(t_b)), tc_set(tc_set(t_b))))),
% 49.04/49.25 inference(rewrite,[status(thm)],[])).
% 49.04/49.25 tff(30,axiom,(![V_U: $i] : (~c_lessequals(v_S, c_insert(V_U, c_emptyset, tc_set(t_b)), tc_set(tc_set(t_b))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_0')).
% 49.04/49.25 tff(31,plain,
% 49.04/49.25 (![V_U: $i] : (~c_lessequals(v_S, c_insert(V_U, c_emptyset, tc_set(t_b)), tc_set(tc_set(t_b))))),
% 49.04/49.25 inference(modus_ponens,[status(thm)],[30, 29])).
% 49.04/49.25 tff(32,plain,(
% 49.04/49.25 ![V_U: $i] : (~c_lessequals(v_S, c_insert(V_U, c_emptyset, tc_set(t_b)), tc_set(tc_set(t_b))))),
% 49.04/49.25 inference(skolemize,[status(sab)],[31])).
% 49.04/49.25 tff(33,plain,
% 49.04/49.25 (![V_U: $i] : (~c_lessequals(v_S, c_insert(V_U, c_emptyset, tc_set(t_b)), tc_set(tc_set(t_b))))),
% 49.04/49.25 inference(modus_ponens,[status(thm)],[32, 28])).
% 49.04/49.25 tff(34,plain,
% 49.04/49.25 ((~![V_U: $i] : (~c_lessequals(v_S, c_insert(V_U, c_emptyset, tc_set(t_b)), tc_set(tc_set(t_b))))) | (~c_lessequals(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(tc_set(t_b))))),
% 49.04/49.25 inference(quant_inst,[status(thm)],[])).
% 49.04/49.25 tff(35,plain,
% 49.04/49.25 (~c_lessequals(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(tc_set(t_b)))),
% 49.04/49.25 inference(unit_resolution,[status(thm)],[34, 33])).
% 49.04/49.25 tff(36,plain,
% 49.04/49.25 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), v_S, tc_set(t_b)) | c_lessequals(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(tc_set(t_b))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), v_S, tc_set(t_b)) | c_lessequals(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(tc_set(t_b))))),
% 49.04/49.25 inference(rewrite,[status(thm)],[])).
% 49.04/49.25 tff(37,plain,
% 49.04/49.25 ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), v_S, tc_set(t_b)) | c_lessequals(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(tc_set(t_b))))),
% 49.04/49.25 inference(quant_inst,[status(thm)],[])).
% 49.04/49.25 tff(38,plain,
% 49.04/49.25 ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), v_S, tc_set(t_b)) | c_lessequals(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(tc_set(t_b)))),
% 49.04/49.25 inference(modus_ponens,[status(thm)],[37, 36])).
% 49.04/49.25 tff(39,plain,
% 49.04/49.25 (c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), v_S, tc_set(t_b))),
% 49.04/49.25 inference(unit_resolution,[status(thm)],[38, 19, 35])).
% 49.04/49.25 tff(40,plain,
% 49.04/49.25 (^[T_a: $i, V_X: $i, V_A: $i, V_C: $i] : refl((c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a))) <=> (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a))))),
% 49.04/49.25 inference(bind,[status(th)],[])).
% 49.04/49.25 tff(41,plain,
% 49.04/49.25 (![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a))) <=> ![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))),
% 49.04/49.25 inference(quant_intro,[status(thm)],[40])).
% 49.04/49.25 tff(42,plain,
% 49.04/49.25 (![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a))) <=> ![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))),
% 49.04/49.25 inference(rewrite,[status(thm)],[])).
% 49.04/49.25 tff(43,plain,
% 49.04/49.25 (^[T_a: $i, V_X: $i, V_A: $i, V_C: $i] : rewrite((((~c_in(V_A, V_X, T_a)) | (~c_in(V_X, V_C, tc_set(T_a)))) | c_in(V_A, c_Union(V_C, T_a), T_a)) <=> (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a))))),
% 49.04/49.25 inference(bind,[status(th)],[])).
% 49.04/49.25 tff(44,plain,
% 49.04/49.25 (![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (((~c_in(V_A, V_X, T_a)) | (~c_in(V_X, V_C, tc_set(T_a)))) | c_in(V_A, c_Union(V_C, T_a), T_a)) <=> ![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))),
% 49.04/49.25 inference(quant_intro,[status(thm)],[43])).
% 49.04/49.25 tff(45,axiom,(![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (((~c_in(V_A, V_X, T_a)) | (~c_in(V_X, V_C, tc_set(T_a)))) | c_in(V_A, c_Union(V_C, T_a), T_a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_OUnionI_0')).
% 49.04/49.25 tff(46,plain,
% 49.04/49.25 (![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))),
% 49.04/49.25 inference(modus_ponens,[status(thm)],[45, 44])).
% 49.04/49.25 tff(47,plain,
% 49.04/49.25 (![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))),
% 49.04/49.25 inference(modus_ponens,[status(thm)],[46, 42])).
% 49.04/49.25 tff(48,plain,(
% 49.04/49.25 ![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))),
% 49.04/49.25 inference(skolemize,[status(sab)],[47])).
% 49.04/49.25 tff(49,plain,
% 49.04/49.25 (![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))),
% 49.04/49.25 inference(modus_ponens,[status(thm)],[48, 41])).
% 49.04/49.25 tff(50,plain,
% 49.04/49.25 (((~![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))) | ((~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), v_S, tc_set(t_b))) | c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Union(v_S, t_b), t_b) | (~c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), t_b)))) <=> ((~![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), v_S, tc_set(t_b))) | c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Union(v_S, t_b), t_b) | (~c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), t_b)))),
% 49.04/49.25 inference(rewrite,[status(thm)],[])).
% 49.04/49.25 tff(51,plain,
% 49.04/49.25 ((c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Union(v_S, t_b), t_b) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), v_S, tc_set(t_b))) | (~c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), t_b))) <=> ((~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), v_S, tc_set(t_b))) | c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Union(v_S, t_b), t_b) | (~c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), t_b)))),
% 49.04/49.25 inference(rewrite,[status(thm)],[])).
% 49.04/49.25 tff(52,plain,
% 49.04/49.25 (((~![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))) | (c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Union(v_S, t_b), t_b) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), v_S, tc_set(t_b))) | (~c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), t_b)))) <=> ((~![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))) | ((~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), v_S, tc_set(t_b))) | c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Union(v_S, t_b), t_b) | (~c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), t_b))))),
% 49.04/49.25 inference(monotonicity,[status(thm)],[51])).
% 49.04/49.25 tff(53,plain,
% 49.04/49.25 (((~![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))) | (c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Union(v_S, t_b), t_b) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), v_S, tc_set(t_b))) | (~c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), t_b)))) <=> ((~![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), v_S, tc_set(t_b))) | c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Union(v_S, t_b), t_b) | (~c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), t_b)))),
% 49.04/49.25 inference(transitivity,[status(thm)],[52, 50])).
% 49.04/49.25 tff(54,plain,
% 49.04/49.25 ((~![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))) | (c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Union(v_S, t_b), t_b) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), v_S, tc_set(t_b))) | (~c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), t_b)))),
% 49.04/49.25 inference(quant_inst,[status(thm)],[])).
% 49.04/49.25 tff(55,plain,
% 49.04/49.25 ((~![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), v_S, tc_set(t_b))) | c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Union(v_S, t_b), t_b) | (~c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), t_b))),
% 49.04/49.26 inference(modus_ponens,[status(thm)],[54, 53])).
% 49.04/49.26 tff(56,plain,
% 49.04/49.26 ($false),
% 49.04/49.26 inference(unit_resolution,[status(thm)],[55, 49, 39, 26, 12])).
% 49.04/49.26 tff(57,plain,(c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), tc_set(t_b))), inference(lemma,lemma(discharge,[]))).
% 49.04/49.26 tff(58,plain,
% 49.04/49.26 (^[V_U: $i] : refl(((~c_in(V_U, v_S, tc_set(t_b))) | c_lessequals(c_Union(v_S, t_b), V_U, tc_set(t_b))) <=> ((~c_in(V_U, v_S, tc_set(t_b))) | c_lessequals(c_Union(v_S, t_b), V_U, tc_set(t_b))))),
% 49.04/49.26 inference(bind,[status(th)],[])).
% 49.04/49.26 tff(59,plain,
% 49.04/49.26 (![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_b))) | c_lessequals(c_Union(v_S, t_b), V_U, tc_set(t_b))) <=> ![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_b))) | c_lessequals(c_Union(v_S, t_b), V_U, tc_set(t_b)))),
% 49.04/49.26 inference(quant_intro,[status(thm)],[58])).
% 49.04/49.26 tff(60,plain,
% 49.04/49.26 (![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_b))) | c_lessequals(c_Union(v_S, t_b), V_U, tc_set(t_b))) <=> ![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_b))) | c_lessequals(c_Union(v_S, t_b), V_U, tc_set(t_b)))),
% 49.04/49.26 inference(rewrite,[status(thm)],[])).
% 49.04/49.26 tff(61,plain,
% 49.04/49.26 (^[V_U: $i] : rewrite((c_lessequals(c_Union(v_S, t_b), V_U, tc_set(t_b)) | (~c_in(V_U, v_S, tc_set(t_b)))) <=> ((~c_in(V_U, v_S, tc_set(t_b))) | c_lessequals(c_Union(v_S, t_b), V_U, tc_set(t_b))))),
% 49.04/49.26 inference(bind,[status(th)],[])).
% 49.04/49.26 tff(62,plain,
% 49.04/49.26 (![V_U: $i] : (c_lessequals(c_Union(v_S, t_b), V_U, tc_set(t_b)) | (~c_in(V_U, v_S, tc_set(t_b)))) <=> ![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_b))) | c_lessequals(c_Union(v_S, t_b), V_U, tc_set(t_b)))),
% 49.04/49.26 inference(quant_intro,[status(thm)],[61])).
% 49.04/49.26 tff(63,axiom,(![V_U: $i] : (c_lessequals(c_Union(v_S, t_b), V_U, tc_set(t_b)) | (~c_in(V_U, v_S, tc_set(t_b))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_1')).
% 49.04/49.26 tff(64,plain,
% 49.04/49.26 (![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_b))) | c_lessequals(c_Union(v_S, t_b), V_U, tc_set(t_b)))),
% 49.04/49.26 inference(modus_ponens,[status(thm)],[63, 62])).
% 49.04/49.26 tff(65,plain,
% 49.04/49.26 (![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_b))) | c_lessequals(c_Union(v_S, t_b), V_U, tc_set(t_b)))),
% 49.04/49.26 inference(modus_ponens,[status(thm)],[64, 60])).
% 49.04/49.26 tff(66,plain,(
% 49.04/49.26 ![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_b))) | c_lessequals(c_Union(v_S, t_b), V_U, tc_set(t_b)))),
% 49.04/49.26 inference(skolemize,[status(sab)],[65])).
% 49.04/49.26 tff(67,plain,
% 49.04/49.26 (![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_b))) | c_lessequals(c_Union(v_S, t_b), V_U, tc_set(t_b)))),
% 49.04/49.26 inference(modus_ponens,[status(thm)],[66, 59])).
% 49.04/49.26 tff(68,plain,
% 49.04/49.26 (((~![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_b))) | c_lessequals(c_Union(v_S, t_b), V_U, tc_set(t_b)))) | ((~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), v_S, tc_set(t_b))) | c_lessequals(c_Union(v_S, t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), tc_set(t_b)))) <=> ((~![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_b))) | c_lessequals(c_Union(v_S, t_b), V_U, tc_set(t_b)))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), v_S, tc_set(t_b))) | c_lessequals(c_Union(v_S, t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), tc_set(t_b)))),
% 49.04/49.26 inference(rewrite,[status(thm)],[])).
% 49.04/49.26 tff(69,plain,
% 49.04/49.26 ((~![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_b))) | c_lessequals(c_Union(v_S, t_b), V_U, tc_set(t_b)))) | ((~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), v_S, tc_set(t_b))) | c_lessequals(c_Union(v_S, t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), tc_set(t_b)))),
% 49.04/49.26 inference(quant_inst,[status(thm)],[])).
% 49.04/49.26 tff(70,plain,
% 49.04/49.26 ((~![V_U: $i] : ((~c_in(V_U, v_S, tc_set(t_b))) | c_lessequals(c_Union(v_S, t_b), V_U, tc_set(t_b)))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), v_S, tc_set(t_b))) | c_lessequals(c_Union(v_S, t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), tc_set(t_b))),
% 49.04/49.26 inference(modus_ponens,[status(thm)],[69, 68])).
% 49.04/49.26 tff(71,plain,
% 49.04/49.26 (c_lessequals(c_Union(v_S, t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), tc_set(t_b))),
% 49.04/49.26 inference(unit_resolution,[status(thm)],[70, 67, 39])).
% 49.04/49.26 tff(72,plain,
% 49.04/49.26 (^[T_a: $i, V_B: $i, V_A: $i] : refl(((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) <=> ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))))),
% 49.04/49.26 inference(bind,[status(th)],[])).
% 49.04/49.26 tff(73,plain,
% 49.04/49.26 (![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 49.04/49.26 inference(quant_intro,[status(thm)],[72])).
% 49.04/49.26 tff(74,plain,
% 49.04/49.26 (![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 49.04/49.26 inference(rewrite,[status(thm)],[])).
% 49.04/49.26 tff(75,plain,
% 49.04/49.26 (^[T_a: $i, V_B: $i, V_A: $i] : trans(monotonicity(rewrite(((~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) <=> ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))), ((((~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | (V_A = V_B)) <=> (((~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) | (V_A = V_B)))), rewrite((((~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) | (V_A = V_B)) <=> ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))), ((((~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | (V_A = V_B)) <=> ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))))),
% 49.04/49.26 inference(bind,[status(th)],[])).
% 49.04/49.26 tff(76,plain,
% 49.04/49.26 (![T_a: $i, V_B: $i, V_A: $i] : (((~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | (V_A = V_B)) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 49.04/49.26 inference(quant_intro,[status(thm)],[75])).
% 49.04/49.26 tff(77,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')).
% 49.04/49.26 tff(78,plain,
% 49.04/49.26 (![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 49.04/49.26 inference(modus_ponens,[status(thm)],[77, 76])).
% 49.04/49.26 tff(79,plain,
% 49.04/49.26 (![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 49.04/49.26 inference(modus_ponens,[status(thm)],[78, 74])).
% 49.04/49.26 tff(80,plain,(
% 49.04/49.26 ![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 49.04/49.26 inference(skolemize,[status(sab)],[79])).
% 49.04/49.26 tff(81,plain,
% 49.04/49.26 (![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 49.04/49.26 inference(modus_ponens,[status(thm)],[80, 73])).
% 49.04/49.26 tff(82,plain,
% 49.04/49.26 (((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)) = c_Union(v_S, t_b)) | (~c_lessequals(c_Union(v_S, t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), tc_set(t_b))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), tc_set(t_b))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | (c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)) = c_Union(v_S, t_b)) | (~c_lessequals(c_Union(v_S, t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), tc_set(t_b))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), tc_set(t_b))))),
% 49.08/49.26 inference(rewrite,[status(thm)],[])).
% 49.08/49.26 tff(83,plain,
% 49.08/49.26 (((c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)) = c_Union(v_S, t_b)) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), tc_set(t_b))) | (~c_lessequals(c_Union(v_S, t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), tc_set(t_b)))) <=> ((c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)) = c_Union(v_S, t_b)) | (~c_lessequals(c_Union(v_S, t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), tc_set(t_b))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), tc_set(t_b))))),
% 49.08/49.26 inference(rewrite,[status(thm)],[])).
% 49.08/49.26 tff(84,plain,
% 49.08/49.26 (((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)) = c_Union(v_S, t_b)) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), tc_set(t_b))) | (~c_lessequals(c_Union(v_S, t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), tc_set(t_b))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)) = c_Union(v_S, t_b)) | (~c_lessequals(c_Union(v_S, t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), tc_set(t_b))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), tc_set(t_b)))))),
% 49.08/49.26 inference(monotonicity,[status(thm)],[83])).
% 49.08/49.26 tff(85,plain,
% 49.08/49.26 (((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)) = c_Union(v_S, t_b)) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), tc_set(t_b))) | (~c_lessequals(c_Union(v_S, t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), tc_set(t_b))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | (c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)) = c_Union(v_S, t_b)) | (~c_lessequals(c_Union(v_S, t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), tc_set(t_b))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), tc_set(t_b))))),
% 49.08/49.26 inference(transitivity,[status(thm)],[84, 82])).
% 49.08/49.26 tff(86,plain,
% 49.08/49.26 ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)) = c_Union(v_S, t_b)) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), tc_set(t_b))) | (~c_lessequals(c_Union(v_S, t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), tc_set(t_b))))),
% 49.08/49.26 inference(quant_inst,[status(thm)],[])).
% 49.08/49.26 tff(87,plain,
% 49.08/49.26 ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | (c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)) = c_Union(v_S, t_b)) | (~c_lessequals(c_Union(v_S, t_b), c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), tc_set(t_b))) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), tc_set(t_b)))),
% 49.08/49.26 inference(modus_ponens,[status(thm)],[86, 85])).
% 49.08/49.26 tff(88,plain,
% 49.08/49.26 ((c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)) = c_Union(v_S, t_b)) | (~c_lessequals(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_Union(v_S, t_b), tc_set(t_b)))),
% 49.08/49.26 inference(unit_resolution,[status(thm)],[87, 81, 71])).
% 49.08/49.26 tff(89,plain,
% 49.08/49.26 (c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)) = c_Union(v_S, t_b)),
% 49.08/49.26 inference(unit_resolution,[status(thm)],[88, 57])).
% 49.08/49.26 tff(90,plain,
% 49.08/49.26 (c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)) <=> c_in(c_Union(v_S, t_b), c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b))),
% 49.08/49.26 inference(monotonicity,[status(thm)],[89])).
% 49.08/49.26 tff(91,plain,
% 49.08/49.26 (c_in(c_Union(v_S, t_b), c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)) <=> c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b))),
% 49.08/49.26 inference(symmetry,[status(thm)],[90])).
% 49.08/49.26 tff(92,plain,
% 49.08/49.26 (^[V_x: $i, T_a: $i, V_B: $i] : refl(c_in(V_x, c_insert(V_x, V_B, T_a), T_a) <=> c_in(V_x, c_insert(V_x, V_B, T_a), T_a))),
% 49.08/49.26 inference(bind,[status(th)],[])).
% 49.08/49.26 tff(93,plain,
% 49.08/49.26 (![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a) <=> ![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 49.08/49.26 inference(quant_intro,[status(thm)],[92])).
% 49.08/49.26 tff(94,plain,
% 49.08/49.26 (![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a) <=> ![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 49.08/49.26 inference(rewrite,[status(thm)],[])).
% 49.08/49.26 tff(95,axiom,(![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_OinsertCI_1')).
% 49.08/49.26 tff(96,plain,
% 49.08/49.26 (![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 49.08/49.26 inference(modus_ponens,[status(thm)],[95, 94])).
% 49.08/49.26 tff(97,plain,(
% 49.08/49.26 ![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 49.08/49.26 inference(skolemize,[status(sab)],[96])).
% 49.08/49.26 tff(98,plain,
% 49.08/49.26 (![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 49.08/49.26 inference(modus_ponens,[status(thm)],[97, 93])).
% 49.08/49.26 tff(99,plain,
% 49.08/49.26 ((~![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)) | c_in(c_Union(v_S, t_b), c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b))),
% 49.08/49.26 inference(quant_inst,[status(thm)],[])).
% 49.08/49.26 tff(100,plain,
% 49.08/49.26 (c_in(c_Union(v_S, t_b), c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b))),
% 49.08/49.26 inference(unit_resolution,[status(thm)],[99, 98])).
% 49.08/49.26 tff(101,plain,
% 49.08/49.26 (c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b))),
% 49.08/49.27 inference(modus_ponens,[status(thm)],[100, 91])).
% 49.08/49.27 tff(102,plain,
% 49.08/49.27 (((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b))) | c_lessequals(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(tc_set(t_b))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b))) | c_lessequals(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(tc_set(t_b))))),
% 49.08/49.27 inference(rewrite,[status(thm)],[])).
% 49.08/49.27 tff(103,plain,
% 49.08/49.27 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b))) | c_lessequals(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(tc_set(t_b))))),
% 49.08/49.27 inference(quant_inst,[status(thm)],[])).
% 49.08/49.27 tff(104,plain,
% 49.08/49.27 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b))) | c_lessequals(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(tc_set(t_b)))),
% 49.08/49.27 inference(modus_ponens,[status(thm)],[103, 102])).
% 49.08/49.27 tff(105,plain,
% 49.08/49.27 (~c_in(c_Main_OsubsetI__1(v_S, c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b)), c_insert(c_Union(v_S, t_b), c_emptyset, tc_set(t_b)), tc_set(t_b))),
% 49.08/49.27 inference(unit_resolution,[status(thm)],[104, 8, 35])).
% 49.08/49.27 tff(106,plain,
% 49.08/49.27 ($false),
% 49.08/49.27 inference(unit_resolution,[status(thm)],[105, 101])).
% 49.08/49.27 % SZS output end Proof
% 49.08/49.27 % E exiting
%------------------------------------------------------------------------------