%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWX022+1 : TPTP v9.1.0. Released v9.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:37:48 AM UTC 2025
% Result : Theorem 0.20s 0.46s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWX022+1 : TPTP v9.1.0. Released v9.1.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n011.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 : Fri Jun 20 12:19:41 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 % SZS output start Proof
% 0.20/0.46 tff(tptp_fun______type, type, (
% 0.20/0.46 tptp_fun_____: ( $i * $i ) > $i)).
% 0.20/0.46 tff(tptp_fun_Xl1_92_type, type, (
% 0.20/0.46 tptp_fun_Xl1_92: $i)).
% 0.20/0.46 tff(list_succeeds_type, type, (
% 0.20/0.46 list_succeeds: $i > $o)).
% 0.20/0.46 tff(tptp_fun_Xl2_91_type, type, (
% 0.20/0.46 tptp_fun_Xl2_91: $i)).
% 0.20/0.46 tff(tptp_fun_Xl3_90_type, type, (
% 0.20/0.46 tptp_fun_Xl3_90: $i)).
% 0.20/0.46 tff(tptp_fun_Xx3_86_type, type, (
% 0.20/0.46 tptp_fun_Xx3_86: $i)).
% 0.20/0.46 tff(cons_type, type, (
% 0.20/0.46 cons: ( $i * $i ) > $i)).
% 0.20/0.46 tff(tptp_fun_Xx2_87_type, type, (
% 0.20/0.46 tptp_fun_Xx2_87: $i)).
% 0.20/0.46 tff(tptp_fun_Xl1_85_type, type, (
% 0.20/0.46 tptp_fun_Xl1_85: $i)).
% 0.20/0.46 tff(nil_type, type, (
% 0.20/0.46 nil: $i)).
% 0.20/0.46 tff(tptp_fun_Xl3_88_type, type, (
% 0.20/0.46 tptp_fun_Xl3_88: $i)).
% 0.20/0.46 tff(tptp_fun_Xl2_89_type, type, (
% 0.20/0.46 tptp_fun_Xl2_89: $i)).
% 0.20/0.46 tff(1,plain,
% 0.20/0.46 ((~![Xl1: $i, Xl2: $i, Xl3: $i] : ((~(list_succeeds(Xl1) & list_succeeds(Xl2))) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3))))) <=> (~![Xl1: $i, Xl2: $i, Xl3: $i] : ((~(list_succeeds(Xl1) & list_succeeds(Xl2))) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(2,plain,
% 0.20/0.46 ((~![Xl1: $i, Xl2: $i, Xl3: $i] : ((list_succeeds(Xl1) & list_succeeds(Xl2)) => (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3))))) <=> (~![Xl1: $i, Xl2: $i, Xl3: $i] : ((~(list_succeeds(Xl1) & list_succeeds(Xl2))) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(3,axiom,(~![Xl1: $i, Xl2: $i, Xl3: $i] : ((list_succeeds(Xl1) & list_succeeds(Xl2)) => (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''theorem-(app:associative)'')).
% 0.20/0.46 tff(4,plain,
% 0.20/0.46 (~![Xl1: $i, Xl2: $i, Xl3: $i] : ((~(list_succeeds(Xl1) & list_succeeds(Xl2))) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.20/0.46 tff(5,plain,
% 0.20/0.46 (~![Xl1: $i, Xl2: $i, Xl3: $i] : ((~(list_succeeds(Xl1) & list_succeeds(Xl2))) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.20/0.46 tff(6,plain,
% 0.20/0.46 (~![Xl1: $i, Xl2: $i, Xl3: $i] : ((~(list_succeeds(Xl1) & list_succeeds(Xl2))) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.20/0.46 tff(7,plain,
% 0.20/0.46 (~![Xl1: $i, Xl2: $i, Xl3: $i] : ((~(list_succeeds(Xl1) & list_succeeds(Xl2))) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.20/0.46 tff(8,plain,(
% 0.20/0.46 ~((~(list_succeeds(Xl1!92) & list_succeeds(Xl2!91))) | (tptp_fun_____(tptp_fun_____(Xl1!92, Xl2!91), Xl3!90) = tptp_fun_____(Xl1!92, tptp_fun_____(Xl2!91, Xl3!90))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[7])).
% 0.20/0.46 tff(9,plain,
% 0.20/0.46 (list_succeeds(Xl1!92) & list_succeeds(Xl2!91)),
% 0.20/0.46 inference(or_elim,[status(thm)],[8])).
% 0.20/0.46 tff(10,plain,
% 0.20/0.46 (list_succeeds(Xl1!92)),
% 0.20/0.46 inference(and_elim,[status(thm)],[9])).
% 0.20/0.46 tff(11,assumption,(~((~list_succeeds(Xl2!89)) | (tptp_fun_____(tptp_fun_____(Xl1!85, Xl2!89), Xl3!88) = tptp_fun_____(Xl1!85, tptp_fun_____(Xl2!89, Xl3!88))) | (~((Xl1!85 = nil) | (~((~(Xl1!85 = cons(Xx2!87, Xx3!86))) | (~list_succeeds(Xx3!86)) | (~![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2), Xl3) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2, Xl3))))))))))), introduced(assumption)).
% 0.20/0.46 tff(12,plain,
% 0.20/0.46 (((~list_succeeds(Xl2!89)) | (tptp_fun_____(tptp_fun_____(Xl1!85, Xl2!89), Xl3!88) = tptp_fun_____(Xl1!85, tptp_fun_____(Xl2!89, Xl3!88))) | (~((Xl1!85 = nil) | (~((~(Xl1!85 = cons(Xx2!87, Xx3!86))) | (~list_succeeds(Xx3!86)) | (~![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2), Xl3) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2, Xl3)))))))))) | ((Xl1!85 = nil) | (~((~(Xl1!85 = cons(Xx2!87, Xx3!86))) | (~list_succeeds(Xx3!86)) | (~![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2), Xl3) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2, Xl3))))))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(13,plain,
% 0.20/0.46 ((Xl1!85 = nil) | (~((~(Xl1!85 = cons(Xx2!87, Xx3!86))) | (~list_succeeds(Xx3!86)) | (~![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2), Xl3) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2, Xl3)))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.20/0.46 tff(14,plain,
% 0.20/0.46 (((~list_succeeds(Xl2!89)) | (tptp_fun_____(tptp_fun_____(Xl1!85, Xl2!89), Xl3!88) = tptp_fun_____(Xl1!85, tptp_fun_____(Xl2!89, Xl3!88))) | (~((Xl1!85 = nil) | (~((~(Xl1!85 = cons(Xx2!87, Xx3!86))) | (~list_succeeds(Xx3!86)) | (~![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2), Xl3) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2, Xl3)))))))))) | list_succeeds(Xl2!89)),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(15,plain,
% 0.20/0.46 (list_succeeds(Xl2!89)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[14, 11])).
% 0.20/0.46 tff(16,plain,
% 0.20/0.46 (((~list_succeeds(Xl2!89)) | (tptp_fun_____(tptp_fun_____(Xl1!85, Xl2!89), Xl3!88) = tptp_fun_____(Xl1!85, tptp_fun_____(Xl2!89, Xl3!88))) | (~((Xl1!85 = nil) | (~((~(Xl1!85 = cons(Xx2!87, Xx3!86))) | (~list_succeeds(Xx3!86)) | (~![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2), Xl3) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2, Xl3)))))))))) | (~(tptp_fun_____(tptp_fun_____(Xl1!85, Xl2!89), Xl3!88) = tptp_fun_____(Xl1!85, tptp_fun_____(Xl2!89, Xl3!88))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(17,plain,
% 0.20/0.46 (~(tptp_fun_____(tptp_fun_____(Xl1!85, Xl2!89), Xl3!88) = tptp_fun_____(Xl1!85, tptp_fun_____(Xl2!89, Xl3!88)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[16, 11])).
% 0.20/0.46 tff(18,assumption,(~((~(Xl1!85 = cons(Xx2!87, Xx3!86))) | (~list_succeeds(Xx3!86)) | (~![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2), Xl3) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2, Xl3))))))), introduced(assumption)).
% 0.20/0.46 tff(19,plain,
% 0.20/0.46 (((~(Xl1!85 = cons(Xx2!87, Xx3!86))) | (~list_succeeds(Xx3!86)) | (~![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2), Xl3) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2, Xl3)))))) | (Xl1!85 = cons(Xx2!87, Xx3!86))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(20,plain,
% 0.20/0.46 (Xl1!85 = cons(Xx2!87, Xx3!86)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.20/0.46 tff(21,plain,
% 0.20/0.46 (tptp_fun_____(Xl1!85, tptp_fun_____(Xl2!89, Xl3!88)) = tptp_fun_____(cons(Xx2!87, Xx3!86), tptp_fun_____(Xl2!89, Xl3!88))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[20])).
% 0.20/0.46 tff(22,plain,
% 0.20/0.46 (tptp_fun_____(cons(Xx2!87, Xx3!86), tptp_fun_____(Xl2!89, Xl3!88)) = tptp_fun_____(Xl1!85, tptp_fun_____(Xl2!89, Xl3!88))),
% 0.20/0.46 inference(symmetry,[status(thm)],[21])).
% 0.20/0.46 tff(23,plain,
% 0.20/0.46 (((~(Xl1!85 = cons(Xx2!87, Xx3!86))) | (~list_succeeds(Xx3!86)) | (~![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2), Xl3) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2, Xl3)))))) | list_succeeds(Xx3!86)),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(24,plain,
% 0.20/0.46 (list_succeeds(Xx3!86)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[23, 18])).
% 0.20/0.46 tff(25,plain,
% 0.20/0.46 (^[Xx: $i, Xl1: $i, Xl2: $i] : refl(((~list_succeeds(Xl1)) | (tptp_fun_____(cons(Xx, Xl1), Xl2) = cons(Xx, tptp_fun_____(Xl1, Xl2)))) <=> ((~list_succeeds(Xl1)) | (tptp_fun_____(cons(Xx, Xl1), Xl2) = cons(Xx, tptp_fun_____(Xl1, Xl2)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(26,plain,
% 0.20/0.46 (![Xx: $i, Xl1: $i, Xl2: $i] : ((~list_succeeds(Xl1)) | (tptp_fun_____(cons(Xx, Xl1), Xl2) = cons(Xx, tptp_fun_____(Xl1, Xl2)))) <=> ![Xx: $i, Xl1: $i, Xl2: $i] : ((~list_succeeds(Xl1)) | (tptp_fun_____(cons(Xx, Xl1), Xl2) = cons(Xx, tptp_fun_____(Xl1, Xl2))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.46 tff(27,plain,
% 0.20/0.46 (![Xx: $i, Xl1: $i, Xl2: $i] : ((~list_succeeds(Xl1)) | (tptp_fun_____(cons(Xx, Xl1), Xl2) = cons(Xx, tptp_fun_____(Xl1, Xl2)))) <=> ![Xx: $i, Xl1: $i, Xl2: $i] : ((~list_succeeds(Xl1)) | (tptp_fun_____(cons(Xx, Xl1), Xl2) = cons(Xx, tptp_fun_____(Xl1, Xl2))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(28,plain,
% 0.20/0.47 (^[Xx: $i, Xl1: $i, Xl2: $i] : rewrite((list_succeeds(Xl1) => (tptp_fun_____(cons(Xx, Xl1), Xl2) = cons(Xx, tptp_fun_____(Xl1, Xl2)))) <=> ((~list_succeeds(Xl1)) | (tptp_fun_____(cons(Xx, Xl1), Xl2) = cons(Xx, tptp_fun_____(Xl1, Xl2)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(29,plain,
% 0.20/0.47 (![Xx: $i, Xl1: $i, Xl2: $i] : (list_succeeds(Xl1) => (tptp_fun_____(cons(Xx, Xl1), Xl2) = cons(Xx, tptp_fun_____(Xl1, Xl2)))) <=> ![Xx: $i, Xl1: $i, Xl2: $i] : ((~list_succeeds(Xl1)) | (tptp_fun_____(cons(Xx, Xl1), Xl2) = cons(Xx, tptp_fun_____(Xl1, Xl2))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.47 tff(30,axiom,(![Xx: $i, Xl1: $i, Xl2: $i] : (list_succeeds(Xl1) => (tptp_fun_____(cons(Xx, Xl1), Xl2) = cons(Xx, tptp_fun_____(Xl1, Xl2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''corollary-(app:cons)'')).
% 0.20/0.47 tff(31,plain,
% 0.20/0.47 (![Xx: $i, Xl1: $i, Xl2: $i] : ((~list_succeeds(Xl1)) | (tptp_fun_____(cons(Xx, Xl1), Xl2) = cons(Xx, tptp_fun_____(Xl1, Xl2))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.47 tff(32,plain,
% 0.20/0.47 (![Xx: $i, Xl1: $i, Xl2: $i] : ((~list_succeeds(Xl1)) | (tptp_fun_____(cons(Xx, Xl1), Xl2) = cons(Xx, tptp_fun_____(Xl1, Xl2))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.20/0.47 tff(33,plain,(
% 0.20/0.47 ![Xx: $i, Xl1: $i, Xl2: $i] : ((~list_succeeds(Xl1)) | (tptp_fun_____(cons(Xx, Xl1), Xl2) = cons(Xx, tptp_fun_____(Xl1, Xl2))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[32])).
% 0.20/0.47 tff(34,plain,
% 0.20/0.47 (![Xx: $i, Xl1: $i, Xl2: $i] : ((~list_succeeds(Xl1)) | (tptp_fun_____(cons(Xx, Xl1), Xl2) = cons(Xx, tptp_fun_____(Xl1, Xl2))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.20/0.47 tff(35,plain,
% 0.20/0.47 (((~![Xx: $i, Xl1: $i, Xl2: $i] : ((~list_succeeds(Xl1)) | (tptp_fun_____(cons(Xx, Xl1), Xl2) = cons(Xx, tptp_fun_____(Xl1, Xl2))))) | ((~list_succeeds(Xx3!86)) | (tptp_fun_____(cons(Xx2!87, Xx3!86), tptp_fun_____(Xl2!89, Xl3!88)) = cons(Xx2!87, tptp_fun_____(Xx3!86, tptp_fun_____(Xl2!89, Xl3!88)))))) <=> ((~![Xx: $i, Xl1: $i, Xl2: $i] : ((~list_succeeds(Xl1)) | (tptp_fun_____(cons(Xx, Xl1), Xl2) = cons(Xx, tptp_fun_____(Xl1, Xl2))))) | (~list_succeeds(Xx3!86)) | (tptp_fun_____(cons(Xx2!87, Xx3!86), tptp_fun_____(Xl2!89, Xl3!88)) = cons(Xx2!87, tptp_fun_____(Xx3!86, tptp_fun_____(Xl2!89, Xl3!88)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(36,plain,
% 0.20/0.47 ((~![Xx: $i, Xl1: $i, Xl2: $i] : ((~list_succeeds(Xl1)) | (tptp_fun_____(cons(Xx, Xl1), Xl2) = cons(Xx, tptp_fun_____(Xl1, Xl2))))) | ((~list_succeeds(Xx3!86)) | (tptp_fun_____(cons(Xx2!87, Xx3!86), tptp_fun_____(Xl2!89, Xl3!88)) = cons(Xx2!87, tptp_fun_____(Xx3!86, tptp_fun_____(Xl2!89, Xl3!88)))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(37,plain,
% 0.20/0.47 ((~![Xx: $i, Xl1: $i, Xl2: $i] : ((~list_succeeds(Xl1)) | (tptp_fun_____(cons(Xx, Xl1), Xl2) = cons(Xx, tptp_fun_____(Xl1, Xl2))))) | (~list_succeeds(Xx3!86)) | (tptp_fun_____(cons(Xx2!87, Xx3!86), tptp_fun_____(Xl2!89, Xl3!88)) = cons(Xx2!87, tptp_fun_____(Xx3!86, tptp_fun_____(Xl2!89, Xl3!88))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.47 tff(38,plain,
% 0.20/0.47 (tptp_fun_____(cons(Xx2!87, Xx3!86), tptp_fun_____(Xl2!89, Xl3!88)) = cons(Xx2!87, tptp_fun_____(Xx3!86, tptp_fun_____(Xl2!89, Xl3!88)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[37, 34, 24])).
% 0.20/0.47 tff(39,plain,
% 0.20/0.47 (cons(Xx2!87, tptp_fun_____(Xx3!86, tptp_fun_____(Xl2!89, Xl3!88))) = tptp_fun_____(cons(Xx2!87, Xx3!86), tptp_fun_____(Xl2!89, Xl3!88))),
% 0.20/0.47 inference(symmetry,[status(thm)],[38])).
% 0.20/0.47 tff(40,plain,
% 0.20/0.47 (((~(Xl1!85 = cons(Xx2!87, Xx3!86))) | (~list_succeeds(Xx3!86)) | (~![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2), Xl3) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2, Xl3)))))) | ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2), Xl3) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2, Xl3))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(41,plain,
% 0.20/0.47 (![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2), Xl3) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2, Xl3))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[40, 18])).
% 0.20/0.47 tff(42,assumption,(list_succeeds(Xl2!89)), introduced(assumption)).
% 0.20/0.47 tff(43,plain,
% 0.20/0.47 (((~![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2), Xl3) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2, Xl3))))) | ((~list_succeeds(Xl2!89)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2!89), Xl3!88) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2!89, Xl3!88))))) <=> ((~![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2), Xl3) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2, Xl3))))) | (~list_succeeds(Xl2!89)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2!89), Xl3!88) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2!89, Xl3!88))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(44,plain,
% 0.20/0.47 ((~![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2), Xl3) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2, Xl3))))) | ((~list_succeeds(Xl2!89)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2!89), Xl3!88) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2!89, Xl3!88))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(45,plain,
% 0.20/0.47 ((~![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2), Xl3) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2, Xl3))))) | (~list_succeeds(Xl2!89)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2!89), Xl3!88) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2!89, Xl3!88)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.47 tff(46,plain,
% 0.20/0.47 (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2!89), Xl3!88) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2!89, Xl3!88))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[45, 42, 41])).
% 0.20/0.47 tff(47,plain,
% 0.20/0.47 (cons(Xx2!87, tptp_fun_____(tptp_fun_____(Xx3!86, Xl2!89), Xl3!88)) = cons(Xx2!87, tptp_fun_____(Xx3!86, tptp_fun_____(Xl2!89, Xl3!88)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[46])).
% 0.20/0.47 tff(48,plain,
% 0.20/0.47 (^[Xl1: $i, Xl2: $i] : refl((list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl1)) | (~list_succeeds(Xl2))) <=> (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl1)) | (~list_succeeds(Xl2))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(49,plain,
% 0.20/0.47 (![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl1)) | (~list_succeeds(Xl2))) <=> ![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl1)) | (~list_succeeds(Xl2)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.47 tff(50,plain,
% 0.20/0.47 (^[Xl1: $i, Xl2: $i] : trans(monotonicity(trans(monotonicity(rewrite((list_succeeds(Xl1) & list_succeeds(Xl2)) <=> (~((~list_succeeds(Xl1)) | (~list_succeeds(Xl2))))), ((~(list_succeeds(Xl1) & list_succeeds(Xl2))) <=> (~(~((~list_succeeds(Xl1)) | (~list_succeeds(Xl2))))))), rewrite((~(~((~list_succeeds(Xl1)) | (~list_succeeds(Xl2))))) <=> ((~list_succeeds(Xl1)) | (~list_succeeds(Xl2)))), ((~(list_succeeds(Xl1) & list_succeeds(Xl2))) <=> ((~list_succeeds(Xl1)) | (~list_succeeds(Xl2))))), ((list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~(list_succeeds(Xl1) & list_succeeds(Xl2)))) <=> (list_succeeds(tptp_fun_____(Xl1, Xl2)) | ((~list_succeeds(Xl1)) | (~list_succeeds(Xl2)))))), rewrite((list_succeeds(tptp_fun_____(Xl1, Xl2)) | ((~list_succeeds(Xl1)) | (~list_succeeds(Xl2)))) <=> (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl1)) | (~list_succeeds(Xl2)))), ((list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~(list_succeeds(Xl1) & list_succeeds(Xl2)))) <=> (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl1)) | (~list_succeeds(Xl2)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(51,plain,
% 0.20/0.47 (![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~(list_succeeds(Xl1) & list_succeeds(Xl2)))) <=> ![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl1)) | (~list_succeeds(Xl2)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.47 tff(52,plain,
% 0.20/0.47 (![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~(list_succeeds(Xl1) & list_succeeds(Xl2)))) <=> ![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~(list_succeeds(Xl1) & list_succeeds(Xl2))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(53,plain,
% 0.20/0.47 (^[Xl1: $i, Xl2: $i] : rewrite(((list_succeeds(Xl1) & list_succeeds(Xl2)) => list_succeeds(tptp_fun_____(Xl1, Xl2))) <=> (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~(list_succeeds(Xl1) & list_succeeds(Xl2)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(54,plain,
% 0.20/0.47 (![Xl1: $i, Xl2: $i] : ((list_succeeds(Xl1) & list_succeeds(Xl2)) => list_succeeds(tptp_fun_____(Xl1, Xl2))) <=> ![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~(list_succeeds(Xl1) & list_succeeds(Xl2))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[53])).
% 0.20/0.47 tff(55,axiom,(![Xl1: $i, Xl2: $i] : ((list_succeeds(Xl1) & list_succeeds(Xl2)) => list_succeeds(tptp_fun_____(Xl1, Xl2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''corollary-(app:types:1)'')).
% 0.20/0.47 tff(56,plain,
% 0.20/0.47 (![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~(list_succeeds(Xl1) & list_succeeds(Xl2))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.20/0.47 tff(57,plain,
% 0.20/0.47 (![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~(list_succeeds(Xl1) & list_succeeds(Xl2))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.20/0.47 tff(58,plain,(
% 0.20/0.47 ![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~(list_succeeds(Xl1) & list_succeeds(Xl2))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[57])).
% 0.20/0.47 tff(59,plain,
% 0.20/0.47 (![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl1)) | (~list_succeeds(Xl2)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.20/0.47 tff(60,plain,
% 0.20/0.47 (![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl1)) | (~list_succeeds(Xl2)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[59, 49])).
% 0.20/0.47 tff(61,plain,
% 0.20/0.47 (((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl1)) | (~list_succeeds(Xl2)))) | ((~list_succeeds(Xl2!89)) | (~list_succeeds(Xx3!86)) | list_succeeds(tptp_fun_____(Xx3!86, Xl2!89)))) <=> ((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl1)) | (~list_succeeds(Xl2)))) | (~list_succeeds(Xl2!89)) | (~list_succeeds(Xx3!86)) | list_succeeds(tptp_fun_____(Xx3!86, Xl2!89)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(62,plain,
% 0.20/0.47 ((list_succeeds(tptp_fun_____(Xx3!86, Xl2!89)) | (~list_succeeds(Xx3!86)) | (~list_succeeds(Xl2!89))) <=> ((~list_succeeds(Xl2!89)) | (~list_succeeds(Xx3!86)) | list_succeeds(tptp_fun_____(Xx3!86, Xl2!89)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(63,plain,
% 0.20/0.47 (((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl1)) | (~list_succeeds(Xl2)))) | (list_succeeds(tptp_fun_____(Xx3!86, Xl2!89)) | (~list_succeeds(Xx3!86)) | (~list_succeeds(Xl2!89)))) <=> ((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl1)) | (~list_succeeds(Xl2)))) | ((~list_succeeds(Xl2!89)) | (~list_succeeds(Xx3!86)) | list_succeeds(tptp_fun_____(Xx3!86, Xl2!89))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[62])).
% 0.20/0.47 tff(64,plain,
% 0.20/0.47 (((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl1)) | (~list_succeeds(Xl2)))) | (list_succeeds(tptp_fun_____(Xx3!86, Xl2!89)) | (~list_succeeds(Xx3!86)) | (~list_succeeds(Xl2!89)))) <=> ((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl1)) | (~list_succeeds(Xl2)))) | (~list_succeeds(Xl2!89)) | (~list_succeeds(Xx3!86)) | list_succeeds(tptp_fun_____(Xx3!86, Xl2!89)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[63, 61])).
% 0.20/0.47 tff(65,plain,
% 0.20/0.47 ((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl1)) | (~list_succeeds(Xl2)))) | (list_succeeds(tptp_fun_____(Xx3!86, Xl2!89)) | (~list_succeeds(Xx3!86)) | (~list_succeeds(Xl2!89)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(66,plain,
% 0.20/0.47 ((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl1)) | (~list_succeeds(Xl2)))) | (~list_succeeds(Xl2!89)) | (~list_succeeds(Xx3!86)) | list_succeeds(tptp_fun_____(Xx3!86, Xl2!89))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.20/0.47 tff(67,plain,
% 0.20/0.47 (list_succeeds(tptp_fun_____(Xx3!86, Xl2!89))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[66, 60, 42, 24])).
% 0.20/0.47 tff(68,plain,
% 0.20/0.47 (((~![Xx: $i, Xl1: $i, Xl2: $i] : ((~list_succeeds(Xl1)) | (tptp_fun_____(cons(Xx, Xl1), Xl2) = cons(Xx, tptp_fun_____(Xl1, Xl2))))) | ((~list_succeeds(tptp_fun_____(Xx3!86, Xl2!89))) | (tptp_fun_____(cons(Xx2!87, tptp_fun_____(Xx3!86, Xl2!89)), Xl3!88) = cons(Xx2!87, tptp_fun_____(tptp_fun_____(Xx3!86, Xl2!89), Xl3!88))))) <=> ((~![Xx: $i, Xl1: $i, Xl2: $i] : ((~list_succeeds(Xl1)) | (tptp_fun_____(cons(Xx, Xl1), Xl2) = cons(Xx, tptp_fun_____(Xl1, Xl2))))) | (~list_succeeds(tptp_fun_____(Xx3!86, Xl2!89))) | (tptp_fun_____(cons(Xx2!87, tptp_fun_____(Xx3!86, Xl2!89)), Xl3!88) = cons(Xx2!87, tptp_fun_____(tptp_fun_____(Xx3!86, Xl2!89), Xl3!88))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(69,plain,
% 0.20/0.47 ((~![Xx: $i, Xl1: $i, Xl2: $i] : ((~list_succeeds(Xl1)) | (tptp_fun_____(cons(Xx, Xl1), Xl2) = cons(Xx, tptp_fun_____(Xl1, Xl2))))) | ((~list_succeeds(tptp_fun_____(Xx3!86, Xl2!89))) | (tptp_fun_____(cons(Xx2!87, tptp_fun_____(Xx3!86, Xl2!89)), Xl3!88) = cons(Xx2!87, tptp_fun_____(tptp_fun_____(Xx3!86, Xl2!89), Xl3!88))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(70,plain,
% 0.20/0.47 ((~![Xx: $i, Xl1: $i, Xl2: $i] : ((~list_succeeds(Xl1)) | (tptp_fun_____(cons(Xx, Xl1), Xl2) = cons(Xx, tptp_fun_____(Xl1, Xl2))))) | (~list_succeeds(tptp_fun_____(Xx3!86, Xl2!89))) | (tptp_fun_____(cons(Xx2!87, tptp_fun_____(Xx3!86, Xl2!89)), Xl3!88) = cons(Xx2!87, tptp_fun_____(tptp_fun_____(Xx3!86, Xl2!89), Xl3!88)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.47 tff(71,plain,
% 0.20/0.47 ((~list_succeeds(tptp_fun_____(Xx3!86, Xl2!89))) | (tptp_fun_____(cons(Xx2!87, tptp_fun_____(Xx3!86, Xl2!89)), Xl3!88) = cons(Xx2!87, tptp_fun_____(tptp_fun_____(Xx3!86, Xl2!89), Xl3!88)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[70, 34])).
% 0.20/0.47 tff(72,plain,
% 0.20/0.47 (tptp_fun_____(cons(Xx2!87, tptp_fun_____(Xx3!86, Xl2!89)), Xl3!88) = cons(Xx2!87, tptp_fun_____(tptp_fun_____(Xx3!86, Xl2!89), Xl3!88))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[71, 67])).
% 0.20/0.47 tff(73,plain,
% 0.20/0.47 (((~![Xx: $i, Xl1: $i, Xl2: $i] : ((~list_succeeds(Xl1)) | (tptp_fun_____(cons(Xx, Xl1), Xl2) = cons(Xx, tptp_fun_____(Xl1, Xl2))))) | ((~list_succeeds(Xx3!86)) | (tptp_fun_____(cons(Xx2!87, Xx3!86), Xl2!89) = cons(Xx2!87, tptp_fun_____(Xx3!86, Xl2!89))))) <=> ((~![Xx: $i, Xl1: $i, Xl2: $i] : ((~list_succeeds(Xl1)) | (tptp_fun_____(cons(Xx, Xl1), Xl2) = cons(Xx, tptp_fun_____(Xl1, Xl2))))) | (~list_succeeds(Xx3!86)) | (tptp_fun_____(cons(Xx2!87, Xx3!86), Xl2!89) = cons(Xx2!87, tptp_fun_____(Xx3!86, Xl2!89))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(74,plain,
% 0.20/0.47 ((~![Xx: $i, Xl1: $i, Xl2: $i] : ((~list_succeeds(Xl1)) | (tptp_fun_____(cons(Xx, Xl1), Xl2) = cons(Xx, tptp_fun_____(Xl1, Xl2))))) | ((~list_succeeds(Xx3!86)) | (tptp_fun_____(cons(Xx2!87, Xx3!86), Xl2!89) = cons(Xx2!87, tptp_fun_____(Xx3!86, Xl2!89))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(75,plain,
% 0.20/0.47 ((~![Xx: $i, Xl1: $i, Xl2: $i] : ((~list_succeeds(Xl1)) | (tptp_fun_____(cons(Xx, Xl1), Xl2) = cons(Xx, tptp_fun_____(Xl1, Xl2))))) | (~list_succeeds(Xx3!86)) | (tptp_fun_____(cons(Xx2!87, Xx3!86), Xl2!89) = cons(Xx2!87, tptp_fun_____(Xx3!86, Xl2!89)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.47 tff(76,plain,
% 0.20/0.47 (tptp_fun_____(cons(Xx2!87, Xx3!86), Xl2!89) = cons(Xx2!87, tptp_fun_____(Xx3!86, Xl2!89))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[75, 34, 24])).
% 0.20/0.47 tff(77,plain,
% 0.20/0.47 (tptp_fun_____(Xl1!85, Xl2!89) = tptp_fun_____(cons(Xx2!87, Xx3!86), Xl2!89)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[20])).
% 0.20/0.47 tff(78,plain,
% 0.20/0.47 (tptp_fun_____(Xl1!85, Xl2!89) = cons(Xx2!87, tptp_fun_____(Xx3!86, Xl2!89))),
% 0.20/0.47 inference(transitivity,[status(thm)],[77, 76])).
% 0.20/0.47 tff(79,plain,
% 0.20/0.47 (tptp_fun_____(tptp_fun_____(Xl1!85, Xl2!89), Xl3!88) = tptp_fun_____(cons(Xx2!87, tptp_fun_____(Xx3!86, Xl2!89)), Xl3!88)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[78])).
% 0.20/0.47 tff(80,plain,
% 0.20/0.47 (tptp_fun_____(tptp_fun_____(Xl1!85, Xl2!89), Xl3!88) = tptp_fun_____(Xl1!85, tptp_fun_____(Xl2!89, Xl3!88))),
% 0.20/0.47 inference(transitivity,[status(thm)],[79, 72, 47, 39, 22])).
% 0.20/0.47 tff(81,assumption,(~(tptp_fun_____(tptp_fun_____(Xl1!85, Xl2!89), Xl3!88) = tptp_fun_____(Xl1!85, tptp_fun_____(Xl2!89, Xl3!88)))), introduced(assumption)).
% 0.20/0.47 tff(82,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.20/0.47 tff(83,plain,(((~(Xl1!85 = cons(Xx2!87, Xx3!86))) | (~list_succeeds(Xx3!86)) | (~![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2), Xl3) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2, Xl3)))))) | (tptp_fun_____(tptp_fun_____(Xl1!85, Xl2!89), Xl3!88) = tptp_fun_____(Xl1!85, tptp_fun_____(Xl2!89, Xl3!88))) | (~list_succeeds(Xl2!89))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(84,plain,
% 0.20/0.47 ((~(Xl1!85 = cons(Xx2!87, Xx3!86))) | (~list_succeeds(Xx3!86)) | (~![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2), Xl3) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2, Xl3)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[83, 17, 15])).
% 0.20/0.47 tff(85,plain,
% 0.20/0.47 ((~((Xl1!85 = nil) | (~((~(Xl1!85 = cons(Xx2!87, Xx3!86))) | (~list_succeeds(Xx3!86)) | (~![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2), Xl3) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2, Xl3))))))))) | (Xl1!85 = nil) | (~((~(Xl1!85 = cons(Xx2!87, Xx3!86))) | (~list_succeeds(Xx3!86)) | (~![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2), Xl3) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2, Xl3)))))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(86,plain,
% 0.20/0.47 (Xl1!85 = nil),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[85, 84, 13])).
% 0.20/0.47 tff(87,plain,
% 0.20/0.47 (tptp_fun_____(Xl1!85, tptp_fun_____(Xl2!89, Xl3!88)) = tptp_fun_____(nil, tptp_fun_____(Xl2!89, Xl3!88))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[86])).
% 0.20/0.47 tff(88,plain,
% 0.20/0.47 (tptp_fun_____(nil, tptp_fun_____(Xl2!89, Xl3!88)) = tptp_fun_____(Xl1!85, tptp_fun_____(Xl2!89, Xl3!88))),
% 0.20/0.47 inference(symmetry,[status(thm)],[87])).
% 0.20/0.47 tff(89,plain,
% 0.20/0.47 (^[Xl: $i] : refl((tptp_fun_____(nil, Xl) = Xl) <=> (tptp_fun_____(nil, Xl) = Xl))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(90,plain,
% 0.20/0.47 (![Xl: $i] : (tptp_fun_____(nil, Xl) = Xl) <=> ![Xl: $i] : (tptp_fun_____(nil, Xl) = Xl)),
% 0.20/0.47 inference(quant_intro,[status(thm)],[89])).
% 0.20/0.47 tff(91,plain,
% 0.20/0.47 (![Xl: $i] : (tptp_fun_____(nil, Xl) = Xl) <=> ![Xl: $i] : (tptp_fun_____(nil, Xl) = Xl)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(92,axiom,(![Xl: $i] : (tptp_fun_____(nil, Xl) = Xl)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''corollary-(app:nil)'')).
% 0.20/0.47 tff(93,plain,
% 0.20/0.47 (![Xl: $i] : (tptp_fun_____(nil, Xl) = Xl)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.47 tff(94,plain,(
% 0.20/0.47 ![Xl: $i] : (tptp_fun_____(nil, Xl) = Xl)),
% 0.20/0.47 inference(skolemize,[status(sab)],[93])).
% 0.20/0.47 tff(95,plain,
% 0.20/0.47 (![Xl: $i] : (tptp_fun_____(nil, Xl) = Xl)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.20/0.47 tff(96,plain,
% 0.20/0.47 ((~![Xl: $i] : (tptp_fun_____(nil, Xl) = Xl)) | (tptp_fun_____(nil, tptp_fun_____(Xl2!89, Xl3!88)) = tptp_fun_____(Xl2!89, Xl3!88))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(97,plain,
% 0.20/0.47 (tptp_fun_____(nil, tptp_fun_____(Xl2!89, Xl3!88)) = tptp_fun_____(Xl2!89, Xl3!88)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.20/0.47 tff(98,plain,
% 0.20/0.47 (tptp_fun_____(Xl2!89, Xl3!88) = tptp_fun_____(nil, tptp_fun_____(Xl2!89, Xl3!88))),
% 0.20/0.47 inference(symmetry,[status(thm)],[97])).
% 0.20/0.47 tff(99,plain,
% 0.20/0.47 ((~![Xl: $i] : (tptp_fun_____(nil, Xl) = Xl)) | (tptp_fun_____(nil, Xl2!89) = Xl2!89)),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(100,plain,
% 0.20/0.47 (tptp_fun_____(nil, Xl2!89) = Xl2!89),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[99, 95])).
% 0.20/0.47 tff(101,plain,
% 0.20/0.47 (tptp_fun_____(Xl1!85, Xl2!89) = tptp_fun_____(nil, Xl2!89)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[86])).
% 0.20/0.47 tff(102,plain,
% 0.20/0.47 (tptp_fun_____(Xl1!85, Xl2!89) = Xl2!89),
% 0.20/0.47 inference(transitivity,[status(thm)],[101, 100])).
% 0.20/0.47 tff(103,plain,
% 0.20/0.47 (tptp_fun_____(tptp_fun_____(Xl1!85, Xl2!89), Xl3!88) = tptp_fun_____(Xl2!89, Xl3!88)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[102])).
% 0.20/0.47 tff(104,plain,
% 0.20/0.47 (tptp_fun_____(tptp_fun_____(Xl1!85, Xl2!89), Xl3!88) = tptp_fun_____(Xl1!85, tptp_fun_____(Xl2!89, Xl3!88))),
% 0.20/0.47 inference(transitivity,[status(thm)],[103, 98, 88])).
% 0.20/0.47 tff(105,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[17, 104])).
% 0.20/0.47 tff(106,plain,((~list_succeeds(Xl2!89)) | (tptp_fun_____(tptp_fun_____(Xl1!85, Xl2!89), Xl3!88) = tptp_fun_____(Xl1!85, tptp_fun_____(Xl2!89, Xl3!88))) | (~((Xl1!85 = nil) | (~((~(Xl1!85 = cons(Xx2!87, Xx3!86))) | (~list_succeeds(Xx3!86)) | (~![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2), Xl3) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2, Xl3)))))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(107,plain,
% 0.20/0.47 (((~((~list_succeeds(Xl2!89)) | (tptp_fun_____(tptp_fun_____(Xl1!85, Xl2!89), Xl3!88) = tptp_fun_____(Xl1!85, tptp_fun_____(Xl2!89, Xl3!88))) | (~((Xl1!85 = nil) | (~((~(Xl1!85 = cons(Xx2!87, Xx3!86))) | (~list_succeeds(Xx3!86)) | (~![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2), Xl3) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2, Xl3))))))))))) | ![Xl1: $i] : ((~list_succeeds(Xl1)) | ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))))) <=> ((~((~list_succeeds(Xl2!89)) | (tptp_fun_____(tptp_fun_____(Xl1!85, Xl2!89), Xl3!88) = tptp_fun_____(Xl1!85, tptp_fun_____(Xl2!89, Xl3!88))) | (~((Xl1!85 = nil) | (~((~(Xl1!85 = cons(Xx2!87, Xx3!86))) | (~list_succeeds(Xx3!86)) | (~![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2), Xl3) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2, Xl3))))))))))) | ![Xl1: $i] : ((~list_succeeds(Xl1)) | ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(108,plain,
% 0.20/0.47 (((((Xl1!85 = nil) | ((Xl1!85 = cons(Xx2!87, Xx3!86)) & list_succeeds(Xx3!86) & ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2), Xl3) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2, Xl3)))))) & (~((~list_succeeds(Xl2!89)) | (tptp_fun_____(tptp_fun_____(Xl1!85, Xl2!89), Xl3!88) = tptp_fun_____(Xl1!85, tptp_fun_____(Xl2!89, Xl3!88)))))) | ![Xl1: $i] : ((~list_succeeds(Xl1)) | ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))))) <=> ((~((~list_succeeds(Xl2!89)) | (tptp_fun_____(tptp_fun_____(Xl1!85, Xl2!89), Xl3!88) = tptp_fun_____(Xl1!85, tptp_fun_____(Xl2!89, Xl3!88))) | (~((Xl1!85 = nil) | (~((~(Xl1!85 = cons(Xx2!87, Xx3!86))) | (~list_succeeds(Xx3!86)) | (~![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2), Xl3) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2, Xl3))))))))))) | ![Xl1: $i] : ((~list_succeeds(Xl1)) | ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(109,plain,
% 0.20/0.47 (((Xl1!85 = cons(Xx2!87, Xx3!86)) & list_succeeds(Xx3!86) & ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2), Xl3) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2, Xl3))))) <=> ((Xl1!85 = cons(Xx2!87, Xx3!86)) & list_succeeds(Xx3!86) & ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2), Xl3) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2, Xl3)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(110,plain,
% 0.20/0.47 (((Xl1!85 = nil) | ((Xl1!85 = cons(Xx2!87, Xx3!86)) & list_succeeds(Xx3!86) & ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2), Xl3) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2, Xl3)))))) <=> ((Xl1!85 = nil) | ((Xl1!85 = cons(Xx2!87, Xx3!86)) & list_succeeds(Xx3!86) & ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2), Xl3) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2, Xl3))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[109])).
% 0.20/0.48 tff(111,plain,
% 0.20/0.48 ((((Xl1!85 = nil) | ((Xl1!85 = cons(Xx2!87, Xx3!86)) & list_succeeds(Xx3!86) & ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2), Xl3) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2, Xl3)))))) & (~((~list_succeeds(Xl2!89)) | (tptp_fun_____(tptp_fun_____(Xl1!85, Xl2!89), Xl3!88) = tptp_fun_____(Xl1!85, tptp_fun_____(Xl2!89, Xl3!88)))))) <=> (((Xl1!85 = nil) | ((Xl1!85 = cons(Xx2!87, Xx3!86)) & list_succeeds(Xx3!86) & ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2), Xl3) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2, Xl3)))))) & (~((~list_succeeds(Xl2!89)) | (tptp_fun_____(tptp_fun_____(Xl1!85, Xl2!89), Xl3!88) = tptp_fun_____(Xl1!85, tptp_fun_____(Xl2!89, Xl3!88))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[110])).
% 0.20/0.48 tff(112,plain,
% 0.20/0.48 (((((Xl1!85 = nil) | ((Xl1!85 = cons(Xx2!87, Xx3!86)) & list_succeeds(Xx3!86) & ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2), Xl3) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2, Xl3)))))) & (~((~list_succeeds(Xl2!89)) | (tptp_fun_____(tptp_fun_____(Xl1!85, Xl2!89), Xl3!88) = tptp_fun_____(Xl1!85, tptp_fun_____(Xl2!89, Xl3!88)))))) | ![Xl1: $i] : ((~list_succeeds(Xl1)) | ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))))) <=> ((((Xl1!85 = nil) | ((Xl1!85 = cons(Xx2!87, Xx3!86)) & list_succeeds(Xx3!86) & ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3!86, Xl2), Xl3) = tptp_fun_____(Xx3!86, tptp_fun_____(Xl2, Xl3)))))) & (~((~list_succeeds(Xl2!89)) | (tptp_fun_____(tptp_fun_____(Xl1!85, Xl2!89), Xl3!88) = tptp_fun_____(Xl1!85, tptp_fun_____(Xl2!89, Xl3!88)))))) | ![Xl1: $i] : ((~list_succeeds(Xl1)) | ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[111])).
% 0.20/0.48 tff(113,plain,
% 0.20/0.48 (((~![Xl1: $i] : ((~((Xl1 = nil) | ?[Xx2: $i, Xx3: $i] : ((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3) & ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3))))))) | ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))))) | ![Xl1: $i] : ((~list_succeeds(Xl1)) | ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))))) <=> ((~![Xl1: $i] : ((~((Xl1 = nil) | ?[Xx2: $i, Xx3: $i] : ((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3) & ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3))))))) | ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))))) | ![Xl1: $i] : ((~list_succeeds(Xl1)) | ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(114,plain,
% 0.20/0.48 ((![Xl1: $i] : ((~((Xl1 = nil) | ?[Xx2: $i, Xx3: $i] : ((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3) & ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3))))))) | ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3))))) => ![Xl1: $i] : ((~list_succeeds(Xl1)) | ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))))) <=> ((~![Xl1: $i] : ((~((Xl1 = nil) | ?[Xx2: $i, Xx3: $i] : ((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3) & ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3))))))) | ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))))) | ![Xl1: $i] : ((~list_succeeds(Xl1)) | ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(115,plain,
% 0.20/0.48 (^[Xl1: $i] : trans(monotonicity(quant_intro(proof_bind(^[Xl2: $i, Xl3: $i] : rewrite((list_succeeds(Xl2) => (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))) <=> ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))))), (![Xl2: $i, Xl3: $i] : (list_succeeds(Xl2) => (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))) <=> ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))))), ((list_succeeds(Xl1) => ![Xl2: $i, Xl3: $i] : (list_succeeds(Xl2) => (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3))))) <=> (list_succeeds(Xl1) => ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3))))))), rewrite((list_succeeds(Xl1) => ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3))))) <=> ((~list_succeeds(Xl1)) | ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))))), ((list_succeeds(Xl1) => ![Xl2: $i, Xl3: $i] : (list_succeeds(Xl2) => (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3))))) <=> ((~list_succeeds(Xl1)) | ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(116,plain,
% 0.20/0.48 (![Xl1: $i] : (list_succeeds(Xl1) => ![Xl2: $i, Xl3: $i] : (list_succeeds(Xl2) => (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3))))) <=> ![Xl1: $i] : ((~list_succeeds(Xl1)) | ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[115])).
% 0.20/0.48 tff(117,plain,
% 0.20/0.48 (^[Xl1: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Xx2: $i, Xx3: $i] : trans(monotonicity(quant_intro(proof_bind(^[Xl2: $i, Xl3: $i] : rewrite((list_succeeds(Xl2) => (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3)))) <=> ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3)))))), (![Xl2: $i, Xl3: $i] : (list_succeeds(Xl2) => (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3)))) <=> ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3)))))), ((((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3)) & ![Xl2: $i, Xl3: $i] : (list_succeeds(Xl2) => (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3))))) <=> (((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3)) & ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3))))))), rewrite((((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3)) & ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3))))) <=> ((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3) & ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3)))))), ((((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3)) & ![Xl2: $i, Xl3: $i] : (list_succeeds(Xl2) => (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3))))) <=> ((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3) & ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3)))))))), (?[Xx2: $i, Xx3: $i] : (((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3)) & ![Xl2: $i, Xl3: $i] : (list_succeeds(Xl2) => (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3))))) <=> ?[Xx2: $i, Xx3: $i] : ((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3) & ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3))))))), ((?[Xx2: $i, Xx3: $i] : (((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3)) & ![Xl2: $i, Xl3: $i] : (list_succeeds(Xl2) => (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3))))) | (Xl1 = nil)) <=> (?[Xx2: $i, Xx3: $i] : ((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3) & ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3))))) | (Xl1 = nil)))), rewrite((?[Xx2: $i, Xx3: $i] : ((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3) & ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3))))) | (Xl1 = nil)) <=> ((Xl1 = nil) | ?[Xx2: $i, Xx3: $i] : ((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3) & ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3))))))), ((?[Xx2: $i, Xx3: $i] : (((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3)) & ![Xl2: $i, Xl3: $i] : (list_succeeds(Xl2) => (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3))))) | (Xl1 = nil)) <=> ((Xl1 = nil) | ?[Xx2: $i, Xx3: $i] : ((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3) & ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3)))))))), quant_intro(proof_bind(^[Xl2: $i, Xl3: $i] : rewrite((list_succeeds(Xl2) => (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))) <=> ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))))), (![Xl2: $i, Xl3: $i] : (list_succeeds(Xl2) => (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))) <=> ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))))), (((?[Xx2: $i, Xx3: $i] : (((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3)) & ![Xl2: $i, Xl3: $i] : (list_succeeds(Xl2) => (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3))))) | (Xl1 = nil)) => ![Xl2: $i, Xl3: $i] : (list_succeeds(Xl2) => (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3))))) <=> (((Xl1 = nil) | ?[Xx2: $i, Xx3: $i] : ((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3) & ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3)))))) => ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3))))))), rewrite((((Xl1 = nil) | ?[Xx2: $i, Xx3: $i] : ((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3) & ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3)))))) => ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3))))) <=> ((~((Xl1 = nil) | ?[Xx2: $i, Xx3: $i] : ((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3) & ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3))))))) | ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))))), (((?[Xx2: $i, Xx3: $i] : (((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3)) & ![Xl2: $i, Xl3: $i] : (list_succeeds(Xl2) => (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3))))) | (Xl1 = nil)) => ![Xl2: $i, Xl3: $i] : (list_succeeds(Xl2) => (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3))))) <=> ((~((Xl1 = nil) | ?[Xx2: $i, Xx3: $i] : ((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3) & ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3))))))) | ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(118,plain,
% 0.20/0.48 (![Xl1: $i] : ((?[Xx2: $i, Xx3: $i] : (((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3)) & ![Xl2: $i, Xl3: $i] : (list_succeeds(Xl2) => (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3))))) | (Xl1 = nil)) => ![Xl2: $i, Xl3: $i] : (list_succeeds(Xl2) => (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3))))) <=> ![Xl1: $i] : ((~((Xl1 = nil) | ?[Xx2: $i, Xx3: $i] : ((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3) & ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3))))))) | ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[117])).
% 0.20/0.48 tff(119,plain,
% 0.20/0.48 ((![Xl1: $i] : ((?[Xx2: $i, Xx3: $i] : (((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3)) & ![Xl2: $i, Xl3: $i] : (list_succeeds(Xl2) => (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3))))) | (Xl1 = nil)) => ![Xl2: $i, Xl3: $i] : (list_succeeds(Xl2) => (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3))))) => ![Xl1: $i] : (list_succeeds(Xl1) => ![Xl2: $i, Xl3: $i] : (list_succeeds(Xl2) => (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))))) <=> (![Xl1: $i] : ((~((Xl1 = nil) | ?[Xx2: $i, Xx3: $i] : ((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3) & ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3))))))) | ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3))))) => ![Xl1: $i] : ((~list_succeeds(Xl1)) | ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[118, 116])).
% 0.20/0.48 tff(120,plain,
% 0.20/0.48 ((![Xl1: $i] : ((?[Xx2: $i, Xx3: $i] : (((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3)) & ![Xl2: $i, Xl3: $i] : (list_succeeds(Xl2) => (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3))))) | (Xl1 = nil)) => ![Xl2: $i, Xl3: $i] : (list_succeeds(Xl2) => (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3))))) => ![Xl1: $i] : (list_succeeds(Xl1) => ![Xl2: $i, Xl3: $i] : (list_succeeds(Xl2) => (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))))) <=> ((~![Xl1: $i] : ((~((Xl1 = nil) | ?[Xx2: $i, Xx3: $i] : ((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3) & ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3))))))) | ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))))) | ![Xl1: $i] : ((~list_succeeds(Xl1)) | ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[119, 114])).
% 0.20/0.48 tff(121,axiom,(![Xl1: $i] : ((?[Xx2: $i, Xx3: $i] : (((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3)) & ![Xl2: $i, Xl3: $i] : (list_succeeds(Xl2) => (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3))))) | (Xl1 = nil)) => ![Xl2: $i, Xl3: $i] : (list_succeeds(Xl2) => (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3))))) => ![Xl1: $i] : (list_succeeds(Xl1) => ![Xl2: $i, Xl3: $i] : (list_succeeds(Xl2) => (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','induction')).
% 0.20/0.48 tff(122,plain,
% 0.20/0.48 ((~![Xl1: $i] : ((~((Xl1 = nil) | ?[Xx2: $i, Xx3: $i] : ((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3) & ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3))))))) | ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))))) | ![Xl1: $i] : ((~list_succeeds(Xl1)) | ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.20/0.48 tff(123,plain,
% 0.20/0.48 ((~![Xl1: $i] : ((~((Xl1 = nil) | ?[Xx2: $i, Xx3: $i] : ((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3) & ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3))))))) | ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))))) | ![Xl1: $i] : ((~list_succeeds(Xl1)) | ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[122, 113])).
% 0.20/0.48 tff(124,plain,
% 0.20/0.48 ((~![Xl1: $i] : ((~((Xl1 = nil) | ?[Xx2: $i, Xx3: $i] : ((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3) & ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3))))))) | ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))))) | ![Xl1: $i] : ((~list_succeeds(Xl1)) | ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[123, 113])).
% 0.20/0.48 tff(125,plain,
% 0.20/0.48 ((~![Xl1: $i] : ((~((Xl1 = nil) | ?[Xx2: $i, Xx3: $i] : ((Xl1 = cons(Xx2, Xx3)) & list_succeeds(Xx3) & ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xx3, Xl2), Xl3) = tptp_fun_____(Xx3, tptp_fun_____(Xl2, Xl3))))))) | ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))))) | ![Xl1: $i] : ((~list_succeeds(Xl1)) | ![Xl2: $i, Xl3: $i] : ((~list_succeeds(Xl2)) | (tptp_fun_____(tptp_fun_____(Xl1, Xl2), Xl3) = tptp_fun_____(Xl1, tptp_fun_____(Xl2, Xl3)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[124, 113])).
% 0.20/0.48 Proof display could not be completed: monotonicity rule is not handled
% 0.20/0.49 % E exiting
%------------------------------------------------------------------------------