%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM011-2 : 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 05:00:57 AM UTC 2025
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : COM011-2 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Jun 19 12:20:38 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(c_lessequals_type, type, (
% 0.13/0.39 c_lessequals: ( $i * $i * $i ) > $o)).
% 0.13/0.39 tff(tc_set_type, type, (
% 0.13/0.39 tc_set: $i > $i)).
% 0.13/0.39 tff(t_a_type, type, (
% 0.13/0.39 t_a: $i)).
% 0.13/0.39 tff(v_A_type, type, (
% 0.13/0.39 v_A: $i)).
% 0.13/0.39 tff(c_minus_type, type, (
% 0.13/0.39 c_minus: ( $i * $i * $i ) > $i)).
% 0.13/0.39 tff(v_B_type, type, (
% 0.13/0.39 v_B: $i)).
% 0.13/0.39 tff(c_in_type, type, (
% 0.13/0.39 c_in: ( $i * $i * $i ) > $o)).
% 0.13/0.39 tff(c_Main_OsubsetI__1_type, type, (
% 0.13/0.39 c_Main_OsubsetI__1: ( $i * $i * $i ) > $i)).
% 0.13/0.39 tff(tc_UNITY_Oprogram_type, type, (
% 0.13/0.39 tc_UNITY_Oprogram: $i > $i)).
% 0.13/0.39 tff(c_WFair_Otransient_type, type, (
% 0.13/0.39 c_WFair_Otransient: ( $i * $i ) > $i)).
% 0.13/0.39 tff(v_F_type, type, (
% 0.13/0.39 v_F: $i)).
% 0.13/0.39 tff(c_UNITY_Oconstrains_type, type, (
% 0.13/0.39 c_UNITY_Oconstrains: ( $i * $i * $i ) > $i)).
% 0.13/0.39 tff(c_union_type, type, (
% 0.13/0.39 c_union: ( $i * $i * $i ) > $i)).
% 0.13/0.39 tff(c_WFair_Oensures_type, type, (
% 0.13/0.39 c_WFair_Oensures: ( $i * $i * $i ) > $i)).
% 0.13/0.39 tff(c_WFair_OleadsTo_type, type, (
% 0.13/0.39 c_WFair_OleadsTo: ( $i * $i * $i ) > $i)).
% 0.13/0.39 tff(1,assumption,(~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))), introduced(assumption)).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (^[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))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 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/sandbox2/benchmark/theBenchmark.p','cls_Set_OsubsetI_1')).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.13/0.39 tff(7,plain,(
% 0.13/0.39 ![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)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[6])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (((~![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(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), v_A, t_a)) | c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_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(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), v_A, t_a)) | c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 ((~![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(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), v_A, t_a)) | c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 ((~![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(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), v_A, t_a)) | c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (~c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), v_A, t_a)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[11, 8, 1])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (^[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))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[13])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 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/sandbox2/benchmark/theBenchmark.p','cls_Set_OsubsetI_0')).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.13/0.39 tff(18,plain,(
% 0.13/0.39 ![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)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[17])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 (((~![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(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), c_minus(v_A, v_B, tc_set(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_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), c_minus(v_A, v_B, tc_set(t_a)), t_a))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 ((c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), c_minus(v_A, v_B, tc_set(t_a)), t_a) | c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))) <=> (c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), c_minus(v_A, v_B, tc_set(t_a)), t_a))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (((~![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(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), c_minus(v_A, v_B, tc_set(t_a)), t_a) | c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_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(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), c_minus(v_A, v_B, tc_set(t_a)), t_a)))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[21])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 (((~![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(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), c_minus(v_A, v_B, tc_set(t_a)), t_a) | c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_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(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), c_minus(v_A, v_B, tc_set(t_a)), t_a))),
% 0.13/0.39 inference(transitivity,[status(thm)],[22, 20])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 ((~![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(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), c_minus(v_A, v_B, tc_set(t_a)), t_a) | c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 ((~![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(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), c_minus(v_A, v_B, tc_set(t_a)), t_a)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 (c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), c_minus(v_A, v_B, tc_set(t_a)), t_a)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[25, 19, 1])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : refl(((~c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a)) | c_in(V_c, V_A, T_a)) <=> ((~c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a)) | c_in(V_c, V_A, T_a)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a)) | c_in(V_c, V_A, T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a)) | c_in(V_c, V_A, T_a))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[27])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a)) | c_in(V_c, V_A, T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a)) | c_in(V_c, V_A, T_a))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(30,axiom,(![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a)) | c_in(V_c, V_A, T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_ODiffE_1')).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a)) | c_in(V_c, V_A, T_a))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.13/0.39 tff(32,plain,(
% 0.13/0.39 ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a)) | c_in(V_c, V_A, T_a))),
% 0.13/0.39 inference(skolemize,[status(sab)],[31])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a)) | c_in(V_c, V_A, T_a))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a)) | c_in(V_c, V_A, T_a))) | ((~c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), c_minus(v_A, v_B, tc_set(t_a)), t_a)) | c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), v_A, t_a))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a)) | c_in(V_c, V_A, T_a))) | (~c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), c_minus(v_A, v_B, tc_set(t_a)), t_a)) | c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), v_A, t_a))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a)) | c_in(V_c, V_A, T_a))) | ((~c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), c_minus(v_A, v_B, tc_set(t_a)), t_a)) | c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), v_A, t_a))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a)) | c_in(V_c, V_A, T_a))) | (~c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), c_minus(v_A, v_B, tc_set(t_a)), t_a)) | c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), v_A, t_a)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.13/0.39 tff(37,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[36, 33, 26, 12])).
% 0.13/0.39 tff(38,plain,(c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(39,assumption,(~c_in(v_F, c_UNITY_Oconstrains(c_minus(v_A, v_B, tc_set(t_a)), c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a))), introduced(assumption)).
% 0.13/0.39 tff(40,plain,
% 0.13/0.39 (^[V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : refl((c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a)))) <=> (c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 (![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a)))) <=> ![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[40])).
% 0.13/0.39 tff(42,plain,
% 0.13/0.39 (![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a)))) <=> ![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(43,plain,
% 0.13/0.39 (^[V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : rewrite((((~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) | c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a))) <=> (c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(44,plain,
% 0.13/0.39 (![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) | c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a))) <=> ![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[43])).
% 0.13/0.39 tff(45,axiom,(![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) | c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_UNITY_Oconstrains__weaken__L_0')).
% 0.13/0.39 tff(46,plain,
% 0.13/0.39 (![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.13/0.39 tff(47,plain,
% 0.13/0.39 (![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.21/0.40 tff(48,plain,(
% 0.21/0.40 ![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[47])).
% 0.21/0.40 tff(49,plain,
% 0.21/0.40 (![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.21/0.40 tff(50,plain,
% 0.21/0.40 (c_in(v_F, c_UNITY_Oconstrains(v_A, c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a)) <=> c_in(v_F, c_UNITY_Oconstrains(v_A, c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(51,axiom,(c_in(v_F, c_UNITY_Oconstrains(v_A, c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.21/0.40 tff(52,plain,
% 0.21/0.40 (c_in(v_F, c_UNITY_Oconstrains(v_A, c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.21/0.40 tff(53,plain,
% 0.21/0.40 (((~![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a))))) | (c_in(v_F, c_UNITY_Oconstrains(c_minus(v_A, v_B, tc_set(t_a)), c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a)) | (~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))) | (~c_in(v_F, c_UNITY_Oconstrains(v_A, c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a))))) <=> ((~![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a))))) | c_in(v_F, c_UNITY_Oconstrains(c_minus(v_A, v_B, tc_set(t_a)), c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a)) | (~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))) | (~c_in(v_F, c_UNITY_Oconstrains(v_A, c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(54,plain,
% 0.21/0.40 ((~![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a))))) | (c_in(v_F, c_UNITY_Oconstrains(c_minus(v_A, v_B, tc_set(t_a)), c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a)) | (~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))) | (~c_in(v_F, c_UNITY_Oconstrains(v_A, c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(55,plain,
% 0.21/0.40 ((~![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a))))) | c_in(v_F, c_UNITY_Oconstrains(c_minus(v_A, v_B, tc_set(t_a)), c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a)) | (~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))) | (~c_in(v_F, c_UNITY_Oconstrains(v_A, c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.21/0.40 tff(56,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[55, 52, 49, 39, 38])).
% 0.21/0.40 tff(57,plain,(c_in(v_F, c_UNITY_Oconstrains(c_minus(v_A, v_B, tc_set(t_a)), c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40 tff(58,plain,
% 0.21/0.40 (^[V_F: $i, T_a: $i, V_B: $i, V_A: $i] : refl(((~c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) | c_in(V_F, c_WFair_OleadsTo(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) <=> ((~c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) | c_in(V_F, c_WFair_OleadsTo(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(59,plain,
% 0.21/0.40 (![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) | c_in(V_F, c_WFair_OleadsTo(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) <=> ![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) | c_in(V_F, c_WFair_OleadsTo(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[58])).
% 0.21/0.40 tff(60,plain,
% 0.21/0.40 (![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) | c_in(V_F, c_WFair_OleadsTo(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) <=> ![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) | c_in(V_F, c_WFair_OleadsTo(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(61,axiom,(![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) | c_in(V_F, c_WFair_OleadsTo(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_WFair_OleadsTo__Basis_0')).
% 0.21/0.40 tff(62,plain,
% 0.21/0.40 (![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) | c_in(V_F, c_WFair_OleadsTo(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.21/0.40 tff(63,plain,(
% 0.21/0.40 ![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) | c_in(V_F, c_WFair_OleadsTo(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)))),
% 0.21/0.40 inference(skolemize,[status(sab)],[62])).
% 0.21/0.40 tff(64,plain,
% 0.21/0.40 (![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) | c_in(V_F, c_WFair_OleadsTo(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.21/0.40 tff(65,plain,
% 0.21/0.40 ((~c_in(v_F, c_WFair_OleadsTo(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a))) <=> (~c_in(v_F, c_WFair_OleadsTo(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(66,axiom,(~c_in(v_F, c_WFair_OleadsTo(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_2')).
% 0.21/0.40 tff(67,plain,
% 0.21/0.40 (~c_in(v_F, c_WFair_OleadsTo(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.21/0.40 tff(68,plain,
% 0.21/0.40 (((~![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) | c_in(V_F, c_WFair_OleadsTo(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)))) | ((~c_in(v_F, c_WFair_Oensures(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a))) | c_in(v_F, c_WFair_OleadsTo(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a)))) <=> ((~![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) | c_in(V_F, c_WFair_OleadsTo(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)))) | (~c_in(v_F, c_WFair_Oensures(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a))) | c_in(v_F, c_WFair_OleadsTo(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(69,plain,
% 0.21/0.40 ((~![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) | c_in(V_F, c_WFair_OleadsTo(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)))) | ((~c_in(v_F, c_WFair_Oensures(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a))) | c_in(v_F, c_WFair_OleadsTo(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(70,plain,
% 0.21/0.40 ((~![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) | c_in(V_F, c_WFair_OleadsTo(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)))) | (~c_in(v_F, c_WFair_Oensures(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a))) | c_in(v_F, c_WFair_OleadsTo(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.21/0.40 tff(71,plain,
% 0.21/0.40 (~c_in(v_F, c_WFair_Oensures(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[70, 67, 64])).
% 0.21/0.40 tff(72,plain,
% 0.21/0.40 (^[V_F: $i, T_a: $i, V_B: $i, V_A: $i] : refl((c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a)))) <=> (c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(73,plain,
% 0.21/0.40 (![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a)))) <=> ![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[72])).
% 0.21/0.40 tff(74,plain,
% 0.21/0.40 (![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a)))) <=> ![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(75,plain,
% 0.21/0.40 (^[V_F: $i, T_a: $i, V_B: $i, V_A: $i] : trans(monotonicity(rewrite(((~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a)))) <=> ((~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))))), ((((~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a)))) | c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) <=> (((~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a)))) | c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))))), rewrite((((~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a)))) | c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) <=> (c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))))), ((((~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a)))) | c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) <=> (c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(76,plain,
% 0.21/0.40 (![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a)))) | c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) <=> ![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[75])).
% 0.21/0.40 tff(77,axiom,(![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a)))) | c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_WFair_OensuresI_0')).
% 0.21/0.40 tff(78,plain,
% 0.21/0.40 (![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.21/0.40 tff(79,plain,
% 0.21/0.40 (![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.21/0.40 tff(80,plain,(
% 0.21/0.40 ![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[79])).
% 0.21/0.40 tff(81,plain,
% 0.21/0.40 (![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.21/0.40 tff(82,plain,
% 0.21/0.40 (((~![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))))) | (c_in(v_F, c_WFair_Oensures(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a)) | (~c_in(v_F, c_WFair_Otransient(c_minus(v_A, v_B, tc_set(t_a)), t_a), tc_UNITY_Oprogram(t_a))) | (~c_in(v_F, c_UNITY_Oconstrains(c_minus(v_A, v_B, tc_set(t_a)), c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a))))) <=> ((~![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))))) | c_in(v_F, c_WFair_Oensures(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a)) | (~c_in(v_F, c_WFair_Otransient(c_minus(v_A, v_B, tc_set(t_a)), t_a), tc_UNITY_Oprogram(t_a))) | (~c_in(v_F, c_UNITY_Oconstrains(c_minus(v_A, v_B, tc_set(t_a)), c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(83,plain,
% 0.21/0.41 ((~![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))))) | (c_in(v_F, c_WFair_Oensures(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a)) | (~c_in(v_F, c_WFair_Otransient(c_minus(v_A, v_B, tc_set(t_a)), t_a), tc_UNITY_Oprogram(t_a))) | (~c_in(v_F, c_UNITY_Oconstrains(c_minus(v_A, v_B, tc_set(t_a)), c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(84,plain,
% 0.21/0.41 ((~![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))))) | c_in(v_F, c_WFair_Oensures(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a)) | (~c_in(v_F, c_WFair_Otransient(c_minus(v_A, v_B, tc_set(t_a)), t_a), tc_UNITY_Oprogram(t_a))) | (~c_in(v_F, c_UNITY_Oconstrains(c_minus(v_A, v_B, tc_set(t_a)), c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.21/0.41 tff(85,plain,
% 0.21/0.41 ((~c_in(v_F, c_WFair_Otransient(c_minus(v_A, v_B, tc_set(t_a)), t_a), tc_UNITY_Oprogram(t_a))) | (~c_in(v_F, c_UNITY_Oconstrains(c_minus(v_A, v_B, tc_set(t_a)), c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[84, 81, 71])).
% 0.21/0.41 tff(86,plain,
% 0.21/0.41 (~c_in(v_F, c_WFair_Otransient(c_minus(v_A, v_B, tc_set(t_a)), t_a), tc_UNITY_Oprogram(t_a))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[85, 57])).
% 0.21/0.41 tff(87,plain,
% 0.21/0.41 (^[V_F: $i, T_a: $i, V_B: $i, V_A: $i] : refl(((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a)))) <=> ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(88,plain,
% 0.21/0.41 (![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a)))) <=> ![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[87])).
% 0.21/0.41 tff(89,plain,
% 0.21/0.41 (![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a)))) <=> ![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(90,plain,
% 0.21/0.41 (^[V_F: $i, T_a: $i, V_B: $i, V_A: $i] : rewrite((((~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a))) <=> ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(91,plain,
% 0.21/0.41 (![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a))) <=> ![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[90])).
% 0.21/0.41 tff(92,axiom,(![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_WFair_Otransient__strengthen_0')).
% 0.21/0.41 tff(93,plain,
% 0.21/0.41 (![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.21/0.41 tff(94,plain,
% 0.21/0.41 (![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.21/0.41 tff(95,plain,(
% 0.21/0.41 ![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[94])).
% 0.21/0.41 tff(96,plain,
% 0.21/0.41 (![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.21/0.41 tff(97,plain,
% 0.21/0.41 (c_in(v_F, c_WFair_Otransient(v_A, t_a), tc_UNITY_Oprogram(t_a)) <=> c_in(v_F, c_WFair_Otransient(v_A, t_a), tc_UNITY_Oprogram(t_a))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(98,axiom,(c_in(v_F, c_WFair_Otransient(v_A, t_a), tc_UNITY_Oprogram(t_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_1')).
% 0.21/0.41 tff(99,plain,
% 0.21/0.41 (c_in(v_F, c_WFair_Otransient(v_A, t_a), tc_UNITY_Oprogram(t_a))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.21/0.41 tff(100,plain,
% 0.21/0.41 (((~![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))))) | (c_in(v_F, c_WFair_Otransient(c_minus(v_A, v_B, tc_set(t_a)), t_a), tc_UNITY_Oprogram(t_a)) | (~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))) | (~c_in(v_F, c_WFair_Otransient(v_A, t_a), tc_UNITY_Oprogram(t_a))))) <=> ((~![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))))) | c_in(v_F, c_WFair_Otransient(c_minus(v_A, v_B, tc_set(t_a)), t_a), tc_UNITY_Oprogram(t_a)) | (~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))) | (~c_in(v_F, c_WFair_Otransient(v_A, t_a), tc_UNITY_Oprogram(t_a))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(101,plain,
% 0.21/0.41 (((~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))) | c_in(v_F, c_WFair_Otransient(c_minus(v_A, v_B, tc_set(t_a)), t_a), tc_UNITY_Oprogram(t_a)) | (~c_in(v_F, c_WFair_Otransient(v_A, t_a), tc_UNITY_Oprogram(t_a)))) <=> (c_in(v_F, c_WFair_Otransient(c_minus(v_A, v_B, tc_set(t_a)), t_a), tc_UNITY_Oprogram(t_a)) | (~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))) | (~c_in(v_F, c_WFair_Otransient(v_A, t_a), tc_UNITY_Oprogram(t_a))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(102,plain,
% 0.21/0.41 (((~![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))))) | ((~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))) | c_in(v_F, c_WFair_Otransient(c_minus(v_A, v_B, tc_set(t_a)), t_a), tc_UNITY_Oprogram(t_a)) | (~c_in(v_F, c_WFair_Otransient(v_A, t_a), tc_UNITY_Oprogram(t_a))))) <=> ((~![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))))) | (c_in(v_F, c_WFair_Otransient(c_minus(v_A, v_B, tc_set(t_a)), t_a), tc_UNITY_Oprogram(t_a)) | (~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))) | (~c_in(v_F, c_WFair_Otransient(v_A, t_a), tc_UNITY_Oprogram(t_a)))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[101])).
% 0.21/0.41 tff(103,plain,
% 0.21/0.41 (((~![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))))) | ((~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))) | c_in(v_F, c_WFair_Otransient(c_minus(v_A, v_B, tc_set(t_a)), t_a), tc_UNITY_Oprogram(t_a)) | (~c_in(v_F, c_WFair_Otransient(v_A, t_a), tc_UNITY_Oprogram(t_a))))) <=> ((~![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))))) | c_in(v_F, c_WFair_Otransient(c_minus(v_A, v_B, tc_set(t_a)), t_a), tc_UNITY_Oprogram(t_a)) | (~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))) | (~c_in(v_F, c_WFair_Otransient(v_A, t_a), tc_UNITY_Oprogram(t_a))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[102, 100])).
% 0.21/0.41 tff(104,plain,
% 0.21/0.41 ((~![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))))) | ((~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))) | c_in(v_F, c_WFair_Otransient(c_minus(v_A, v_B, tc_set(t_a)), t_a), tc_UNITY_Oprogram(t_a)) | (~c_in(v_F, c_WFair_Otransient(v_A, t_a), tc_UNITY_Oprogram(t_a))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(105,plain,
% 0.21/0.41 ((~![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))))) | c_in(v_F, c_WFair_Otransient(c_minus(v_A, v_B, tc_set(t_a)), t_a), tc_UNITY_Oprogram(t_a)) | (~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))) | (~c_in(v_F, c_WFair_Otransient(v_A, t_a), tc_UNITY_Oprogram(t_a)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.21/0.41 tff(106,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[105, 99, 96, 86, 38])).
% 0.21/0.41 % SZS output end Proof
% 0.21/0.41 % E exiting
%------------------------------------------------------------------------------