%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV776-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:36:04 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.51s
% Output : Proof 0.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV776-1 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 10:50:54 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.51 % SZS status Unsatisfiable
% 0.19/0.51 % SZS output start Proof
% 0.19/0.51 tff(c_Event_Oknows_type, type, (
% 0.19/0.51 c_Event_Oknows: ( $i * $i ) > $i)).
% 0.19/0.51 tff(c_List_Olist_ONil_type, type, (
% 0.19/0.51 c_List_Olist_ONil: $i > $i)).
% 0.19/0.51 tff(tc_Event_Oevent_type, type, (
% 0.19/0.51 tc_Event_Oevent: $i)).
% 0.19/0.51 tff(c_Message_Oagent_OSpy_type, type, (
% 0.19/0.51 c_Message_Oagent_OSpy: $i)).
% 0.19/0.51 tff(c_List_Oappend_type, type, (
% 0.19/0.51 c_List_Oappend: ( $i * $i * $i ) > $i)).
% 0.19/0.51 tff(c_List_Olist_OCons_type, type, (
% 0.19/0.51 c_List_Olist_OCons: ( $i * $i * $i ) > $i)).
% 0.19/0.51 tff(c_Event_Oevent_ONotes_type, type, (
% 0.19/0.51 c_Event_Oevent_ONotes: ( $i * $i ) > $i)).
% 0.19/0.51 tff(v_X_type, type, (
% 0.19/0.51 v_X: $i)).
% 0.19/0.51 tff(v_A_type, type, (
% 0.19/0.51 v_A: $i)).
% 0.19/0.51 tff(c_in_type, type, (
% 0.19/0.51 c_in: ( $i * $i * $i ) > $o)).
% 0.19/0.51 tff(tc_Message_Oagent_type, type, (
% 0.19/0.51 tc_Message_Oagent: $i)).
% 0.19/0.51 tff(c_Event_Obad_type, type, (
% 0.19/0.51 c_Event_Obad: $i)).
% 0.19/0.51 tff(c_Set_Oinsert_type, type, (
% 0.19/0.51 c_Set_Oinsert: ( $i * $i * $i ) > $i)).
% 0.19/0.51 tff(tc_Message_Omsg_type, type, (
% 0.19/0.51 tc_Message_Omsg: $i)).
% 0.19/0.51 tff(1,plain,
% 0.19/0.51 (^[T_a: $i] : refl((c_List_Olist_ONil(T_a) = c_List_Oappend(c_List_Olist_ONil(T_a), c_List_Olist_ONil(T_a), T_a)) <=> (c_List_Olist_ONil(T_a) = c_List_Oappend(c_List_Olist_ONil(T_a), c_List_Olist_ONil(T_a), T_a)))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(2,plain,
% 0.19/0.51 (![T_a: $i] : (c_List_Olist_ONil(T_a) = c_List_Oappend(c_List_Olist_ONil(T_a), c_List_Olist_ONil(T_a), T_a)) <=> ![T_a: $i] : (c_List_Olist_ONil(T_a) = c_List_Oappend(c_List_Olist_ONil(T_a), c_List_Olist_ONil(T_a), T_a))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.51 tff(3,plain,
% 0.19/0.51 (![T_a: $i] : (c_List_Olist_ONil(T_a) = c_List_Oappend(c_List_Olist_ONil(T_a), c_List_Olist_ONil(T_a), T_a)) <=> ![T_a: $i] : (c_List_Olist_ONil(T_a) = c_List_Oappend(c_List_Olist_ONil(T_a), c_List_Olist_ONil(T_a), T_a))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(4,axiom,(![T_a: $i] : (c_List_Olist_ONil(T_a) = c_List_Oappend(c_List_Olist_ONil(T_a), c_List_Olist_ONil(T_a), T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Nil__is__append__conv_2')).
% 0.19/0.51 tff(5,plain,
% 0.19/0.51 (![T_a: $i] : (c_List_Olist_ONil(T_a) = c_List_Oappend(c_List_Olist_ONil(T_a), c_List_Olist_ONil(T_a), T_a))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.51 tff(6,plain,(
% 0.19/0.51 ![T_a: $i] : (c_List_Olist_ONil(T_a) = c_List_Oappend(c_List_Olist_ONil(T_a), c_List_Olist_ONil(T_a), T_a))),
% 0.19/0.51 inference(skolemize,[status(sab)],[5])).
% 0.19/0.51 tff(7,plain,
% 0.19/0.51 (![T_a: $i] : (c_List_Olist_ONil(T_a) = c_List_Oappend(c_List_Olist_ONil(T_a), c_List_Olist_ONil(T_a), T_a))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.51 tff(8,plain,
% 0.19/0.51 ((~![T_a: $i] : (c_List_Olist_ONil(T_a) = c_List_Oappend(c_List_Olist_ONil(T_a), c_List_Olist_ONil(T_a), T_a))) | (c_List_Olist_ONil(tc_Event_Oevent) = c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(9,plain,
% 0.19/0.51 (c_List_Olist_ONil(tc_Event_Oevent) = c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.51 tff(10,plain,
% 0.19/0.51 (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[9])).
% 0.19/0.51 tff(11,plain,
% 0.19/0.51 (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent))),
% 0.19/0.51 inference(symmetry,[status(thm)],[10])).
% 0.19/0.51 tff(12,plain,
% 0.19/0.51 (c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent) = c_List_Olist_ONil(tc_Event_Oevent)),
% 0.19/0.51 inference(symmetry,[status(thm)],[9])).
% 0.19/0.51 tff(13,plain,
% 0.19/0.51 (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[12])).
% 0.19/0.52 tff(14,plain,
% 0.19/0.52 (^[V_x: $i, T_a: $i] : refl((V_x = c_List_Oappend(c_List_Olist_ONil(T_a), V_x, T_a)) <=> (V_x = c_List_Oappend(c_List_Olist_ONil(T_a), V_x, T_a)))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(15,plain,
% 0.19/0.52 (![V_x: $i, T_a: $i] : (V_x = c_List_Oappend(c_List_Olist_ONil(T_a), V_x, T_a)) <=> ![V_x: $i, T_a: $i] : (V_x = c_List_Oappend(c_List_Olist_ONil(T_a), V_x, T_a))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.52 tff(16,plain,
% 0.19/0.52 (![V_x: $i, T_a: $i] : (V_x = c_List_Oappend(c_List_Olist_ONil(T_a), V_x, T_a)) <=> ![V_x: $i, T_a: $i] : (V_x = c_List_Oappend(c_List_Olist_ONil(T_a), V_x, T_a))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(17,axiom,(![V_x: $i, T_a: $i] : (V_x = c_List_Oappend(c_List_Olist_ONil(T_a), V_x, T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_eq__Nil__appendI_0')).
% 0.19/0.52 tff(18,plain,
% 0.19/0.52 (![V_x: $i, T_a: $i] : (V_x = c_List_Oappend(c_List_Olist_ONil(T_a), V_x, T_a))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.19/0.52 tff(19,plain,(
% 0.19/0.52 ![V_x: $i, T_a: $i] : (V_x = c_List_Oappend(c_List_Olist_ONil(T_a), V_x, T_a))),
% 0.19/0.52 inference(skolemize,[status(sab)],[18])).
% 0.19/0.52 tff(20,plain,
% 0.19/0.52 (![V_x: $i, T_a: $i] : (V_x = c_List_Oappend(c_List_Olist_ONil(T_a), V_x, T_a))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.19/0.52 tff(21,plain,
% 0.19/0.52 ((~![V_x: $i, T_a: $i] : (V_x = c_List_Oappend(c_List_Olist_ONil(T_a), V_x, T_a))) | (c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent) = c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(22,plain,
% 0.19/0.52 (c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent) = c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.19/0.52 tff(23,plain,
% 0.19/0.52 (c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent) = c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent)),
% 0.19/0.52 inference(monotonicity,[status(thm)],[12])).
% 0.19/0.52 tff(24,plain,
% 0.19/0.52 (c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent) = c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)),
% 0.19/0.52 inference(transitivity,[status(thm)],[23, 22])).
% 0.19/0.52 tff(25,plain,
% 0.19/0.52 (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[24])).
% 0.19/0.52 tff(26,plain,
% 0.19/0.52 ((c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent))) <=> (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent)))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[25, 13])).
% 0.19/0.52 tff(27,plain,
% 0.19/0.52 (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent))),
% 0.19/0.52 inference(symmetry,[status(thm)],[13])).
% 0.19/0.52 tff(28,plain,
% 0.19/0.52 (c_Set_Oinsert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent)), tc_Message_Omsg) = c_Set_Oinsert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent)), tc_Message_Omsg)),
% 0.19/0.52 inference(monotonicity,[status(thm)],[27])).
% 0.19/0.52 tff(29,plain,
% 0.19/0.52 (c_Set_Oinsert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent)), tc_Message_Omsg) = c_Set_Oinsert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent)), tc_Message_Omsg)),
% 0.19/0.52 inference(symmetry,[status(thm)],[28])).
% 0.19/0.52 tff(30,plain,
% 0.19/0.52 ((c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Set_Oinsert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent)), tc_Message_Omsg)) <=> (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Set_Oinsert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent)), tc_Message_Omsg))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[25, 29])).
% 0.19/0.52 tff(31,plain,
% 0.19/0.52 ((c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Set_Oinsert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent)), tc_Message_Omsg)) <=> (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Set_Oinsert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent)), tc_Message_Omsg))),
% 0.19/0.52 inference(symmetry,[status(thm)],[30])).
% 0.19/0.52 tff(32,plain,
% 0.19/0.52 ((~(c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Set_Oinsert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent)), tc_Message_Omsg))) <=> (~(c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Set_Oinsert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent)), tc_Message_Omsg)))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[31])).
% 0.19/0.52 tff(33,assumption,(~(c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Set_Oinsert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent)), tc_Message_Omsg))), introduced(assumption)).
% 0.19/0.52 tff(34,plain,
% 0.19/0.52 (~(c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Set_Oinsert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent)), tc_Message_Omsg))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.19/0.52 tff(35,plain,
% 0.19/0.52 (^[V_X: $i, V_A: $i, V_evs: $i] : refl(((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A, V_X), V_evs, tc_Event_Oevent)) = c_Set_Oinsert(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg))) <=> ((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A, V_X), V_evs, tc_Event_Oevent)) = c_Set_Oinsert(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(36,plain,
% 0.19/0.52 (![V_X: $i, V_A: $i, V_evs: $i] : ((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A, V_X), V_evs, tc_Event_Oevent)) = c_Set_Oinsert(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg))) <=> ![V_X: $i, V_A: $i, V_evs: $i] : ((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A, V_X), V_evs, tc_Event_Oevent)) = c_Set_Oinsert(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[35])).
% 0.19/0.52 tff(37,plain,
% 0.19/0.52 (![V_X: $i, V_A: $i, V_evs: $i] : ((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A, V_X), V_evs, tc_Event_Oevent)) = c_Set_Oinsert(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg))) <=> ![V_X: $i, V_A: $i, V_evs: $i] : ((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A, V_X), V_evs, tc_Event_Oevent)) = c_Set_Oinsert(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(38,plain,
% 0.19/0.52 (^[V_X: $i, V_A: $i, V_evs: $i] : rewrite(((c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A, V_X), V_evs, tc_Event_Oevent)) = c_Set_Oinsert(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent))) <=> ((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A, V_X), V_evs, tc_Event_Oevent)) = c_Set_Oinsert(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(39,plain,
% 0.19/0.52 (![V_X: $i, V_A: $i, V_evs: $i] : ((c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A, V_X), V_evs, tc_Event_Oevent)) = c_Set_Oinsert(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent))) <=> ![V_X: $i, V_A: $i, V_evs: $i] : ((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A, V_X), V_evs, tc_Event_Oevent)) = c_Set_Oinsert(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[38])).
% 0.19/0.52 tff(40,axiom,(![V_X: $i, V_A: $i, V_evs: $i] : ((c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A, V_X), V_evs, tc_Event_Oevent)) = c_Set_Oinsert(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_knows__Spy__Notes_0')).
% 0.19/0.52 tff(41,plain,
% 0.19/0.52 (![V_X: $i, V_A: $i, V_evs: $i] : ((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A, V_X), V_evs, tc_Event_Oevent)) = c_Set_Oinsert(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.52 tff(42,plain,
% 0.19/0.52 (![V_X: $i, V_A: $i, V_evs: $i] : ((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A, V_X), V_evs, tc_Event_Oevent)) = c_Set_Oinsert(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.19/0.52 tff(43,plain,(
% 0.19/0.52 ![V_X: $i, V_A: $i, V_evs: $i] : ((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A, V_X), V_evs, tc_Event_Oevent)) = c_Set_Oinsert(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)))),
% 0.19/0.52 inference(skolemize,[status(sab)],[42])).
% 0.19/0.52 tff(44,plain,
% 0.19/0.52 (![V_X: $i, V_A: $i, V_evs: $i] : ((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A, V_X), V_evs, tc_Event_Oevent)) = c_Set_Oinsert(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.19/0.52 tff(45,plain,
% 0.19/0.52 (((~![V_X: $i, V_A: $i, V_evs: $i] : ((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A, V_X), V_evs, tc_Event_Oevent)) = c_Set_Oinsert(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)))) | ((~c_in(v_A, c_Event_Obad, tc_Message_Oagent)) | (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Set_Oinsert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent)), tc_Message_Omsg)))) <=> ((~![V_X: $i, V_A: $i, V_evs: $i] : ((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A, V_X), V_evs, tc_Event_Oevent)) = c_Set_Oinsert(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)))) | (~c_in(v_A, c_Event_Obad, tc_Message_Oagent)) | (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Set_Oinsert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent)), tc_Message_Omsg)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(46,plain,
% 0.19/0.52 ((~![V_X: $i, V_A: $i, V_evs: $i] : ((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A, V_X), V_evs, tc_Event_Oevent)) = c_Set_Oinsert(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)))) | ((~c_in(v_A, c_Event_Obad, tc_Message_Oagent)) | (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Set_Oinsert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent)), tc_Message_Omsg)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(47,plain,
% 0.19/0.52 ((~![V_X: $i, V_A: $i, V_evs: $i] : ((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A, V_X), V_evs, tc_Event_Oevent)) = c_Set_Oinsert(V_X, c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)))) | (~c_in(v_A, c_Event_Obad, tc_Message_Oagent)) | (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Set_Oinsert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent)), tc_Message_Omsg))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.19/0.52 tff(48,plain,
% 0.19/0.52 ((~c_in(v_A, c_Event_Obad, tc_Message_Oagent)) | (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Set_Oinsert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent)), tc_Message_Omsg))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[47, 44])).
% 0.19/0.52 tff(49,plain,
% 0.19/0.52 (~c_in(v_A, c_Event_Obad, tc_Message_Oagent)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[48, 34])).
% 0.19/0.52 tff(50,plain,
% 0.19/0.52 (^[V_X: $i, V_A: $i, V_evs: $i] : refl(((c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A, V_X), V_evs, tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)) | c_in(V_A, c_Event_Obad, tc_Message_Oagent)) <=> ((c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A, V_X), V_evs, tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)) | c_in(V_A, c_Event_Obad, tc_Message_Oagent)))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(51,plain,
% 0.19/0.52 (![V_X: $i, V_A: $i, V_evs: $i] : ((c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A, V_X), V_evs, tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)) | c_in(V_A, c_Event_Obad, tc_Message_Oagent)) <=> ![V_X: $i, V_A: $i, V_evs: $i] : ((c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A, V_X), V_evs, tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)) | c_in(V_A, c_Event_Obad, tc_Message_Oagent))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.52 tff(52,plain,
% 0.19/0.52 (![V_X: $i, V_A: $i, V_evs: $i] : ((c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A, V_X), V_evs, tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)) | c_in(V_A, c_Event_Obad, tc_Message_Oagent)) <=> ![V_X: $i, V_A: $i, V_evs: $i] : ((c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A, V_X), V_evs, tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)) | c_in(V_A, c_Event_Obad, tc_Message_Oagent))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(53,axiom,(![V_X: $i, V_A: $i, V_evs: $i] : ((c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A, V_X), V_evs, tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)) | c_in(V_A, c_Event_Obad, tc_Message_Oagent))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_knows__Spy__Notes_1')).
% 0.19/0.52 tff(54,plain,
% 0.19/0.52 (![V_X: $i, V_A: $i, V_evs: $i] : ((c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A, V_X), V_evs, tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)) | c_in(V_A, c_Event_Obad, tc_Message_Oagent))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.19/0.52 tff(55,plain,(
% 0.19/0.52 ![V_X: $i, V_A: $i, V_evs: $i] : ((c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A, V_X), V_evs, tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)) | c_in(V_A, c_Event_Obad, tc_Message_Oagent))),
% 0.19/0.52 inference(skolemize,[status(sab)],[54])).
% 0.19/0.52 tff(56,plain,
% 0.19/0.52 (![V_X: $i, V_A: $i, V_evs: $i] : ((c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A, V_X), V_evs, tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)) | c_in(V_A, c_Event_Obad, tc_Message_Oagent))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.19/0.52 tff(57,plain,
% 0.19/0.52 (((~![V_X: $i, V_A: $i, V_evs: $i] : ((c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A, V_X), V_evs, tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)) | c_in(V_A, c_Event_Obad, tc_Message_Oagent))) | ((c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent))) | c_in(v_A, c_Event_Obad, tc_Message_Oagent))) <=> ((~![V_X: $i, V_A: $i, V_evs: $i] : ((c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A, V_X), V_evs, tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)) | c_in(V_A, c_Event_Obad, tc_Message_Oagent))) | (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent))) | c_in(v_A, c_Event_Obad, tc_Message_Oagent))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(58,plain,
% 0.19/0.52 ((~![V_X: $i, V_A: $i, V_evs: $i] : ((c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A, V_X), V_evs, tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)) | c_in(V_A, c_Event_Obad, tc_Message_Oagent))) | ((c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent))) | c_in(v_A, c_Event_Obad, tc_Message_Oagent))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(59,plain,
% 0.19/0.52 ((~![V_X: $i, V_A: $i, V_evs: $i] : ((c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A, V_X), V_evs, tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)) | c_in(V_A, c_Event_Obad, tc_Message_Oagent))) | (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent))) | c_in(v_A, c_Event_Obad, tc_Message_Oagent)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.52 tff(60,plain,
% 0.19/0.52 ((c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent))) | c_in(v_A, c_Event_Obad, tc_Message_Oagent)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[59, 56])).
% 0.19/0.52 tff(61,plain,
% 0.19/0.52 (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[60, 49])).
% 0.19/0.52 tff(62,plain,
% 0.19/0.52 (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[61, 26])).
% 0.19/0.52 tff(63,plain,
% 0.19/0.52 (((~(c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent)))) | c_in(v_A, c_Event_Obad, tc_Message_Oagent)) <=> ((~(c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent)))) | c_in(v_A, c_Event_Obad, tc_Message_Oagent))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(64,axiom,((~(c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent)))) | c_in(v_A, c_Event_Obad, tc_Message_Oagent)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.19/0.52 tff(65,plain,
% 0.19/0.52 ((~(c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent)))) | c_in(v_A, c_Event_Obad, tc_Message_Oagent)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.52 tff(66,plain,
% 0.19/0.52 (~(c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[65, 49])).
% 0.19/0.52 tff(67,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[66, 62])).
% 0.19/0.52 tff(68,plain,(c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Set_Oinsert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent)), tc_Message_Omsg)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.52 tff(69,plain,
% 0.19/0.52 (((~(c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Set_Oinsert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent)), tc_Message_Omsg))) | (~c_in(v_A, c_Event_Obad, tc_Message_Oagent))) <=> ((~(c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Set_Oinsert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent)), tc_Message_Omsg))) | (~c_in(v_A, c_Event_Obad, tc_Message_Oagent)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(70,axiom,((~(c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Set_Oinsert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent)), tc_Message_Omsg))) | (~c_in(v_A, c_Event_Obad, tc_Message_Oagent))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_1')).
% 0.19/0.52 tff(71,plain,
% 0.19/0.52 ((~(c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Set_Oinsert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent)), tc_Message_Omsg))) | (~c_in(v_A, c_Event_Obad, tc_Message_Oagent))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.52 tff(72,plain,
% 0.19/0.52 ((~(c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Set_Oinsert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent)), tc_Message_Omsg))) | (~c_in(v_A, c_Event_Obad, tc_Message_Oagent))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[71, 69])).
% 0.19/0.52 tff(73,plain,
% 0.19/0.52 ((~(c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Set_Oinsert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent)), tc_Message_Omsg))) | (~c_in(v_A, c_Event_Obad, tc_Message_Oagent))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[72, 69])).
% 0.19/0.52 tff(74,plain,
% 0.19/0.52 ((~(c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Set_Oinsert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent)), tc_Message_Omsg))) | (~c_in(v_A, c_Event_Obad, tc_Message_Oagent))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.19/0.52 tff(75,plain,
% 0.19/0.52 ((~(c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Set_Oinsert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent)), tc_Message_Omsg))) | (~c_in(v_A, c_Event_Obad, tc_Message_Oagent))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[74, 69])).
% 0.19/0.52 tff(76,plain,
% 0.19/0.52 (~c_in(v_A, c_Event_Obad, tc_Message_Oagent)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[75, 68])).
% 0.19/0.52 tff(77,plain,
% 0.19/0.52 (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[59, 56, 76])).
% 0.19/0.52 tff(78,plain,
% 0.19/0.52 (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent))),
% 0.19/0.52 inference(symmetry,[status(thm)],[25])).
% 0.19/0.52 tff(79,plain,
% 0.19/0.52 (c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent))),
% 0.19/0.52 inference(transitivity,[status(thm)],[78, 77, 11])).
% 0.19/0.52 tff(80,plain,
% 0.19/0.52 (((~(c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent)))) | (~(c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Set_Oinsert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent)), tc_Message_Omsg)))) <=> ((~(c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent)))) | (~(c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Set_Oinsert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent)), tc_Message_Omsg))))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(81,axiom,((~(c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent)))) | (~(c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Set_Oinsert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent)), tc_Message_Omsg)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_2')).
% 0.37/0.54 tff(82,plain,
% 0.37/0.54 ((~(c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent)))) | (~(c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Set_Oinsert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent)), tc_Message_Omsg)))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.37/0.54 tff(83,plain,
% 0.37/0.54 (~(c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent), c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A, v_X), c_List_Olist_ONil(tc_Event_Oevent), tc_Event_Oevent), tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy, c_List_Olist_ONil(tc_Event_Oevent)))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[82, 68])).
% 0.37/0.54 tff(84,plain,
% 0.37/0.54 ($false),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[83, 79])).
% 0.37/0.54 % SZS output end Proof
% 0.37/0.55 % E exiting
%------------------------------------------------------------------------------