%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWX057+1 : TPTP v9.1.0. Released v9.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:37:50 AM UTC 2025
% Result : Theorem 0.21s 0.52s
% Output : Proof 0.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWX057+1 : TPTP v9.1.0. Released v9.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Jun 20 12:23:57 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.21/0.52 % SZS status Theorem
% 0.21/0.52 % SZS output start Proof
% 0.21/0.52 tff(occ_type, type, (
% 0.21/0.52 occ: ( $i * $i ) > $i)).
% 0.21/0.52 tff(tptp_fun______type, type, (
% 0.21/0.52 tptp_fun_____: ( $i * $i ) > $i)).
% 0.21/0.52 tff(tptp_fun_Xl4_135_type, type, (
% 0.21/0.52 tptp_fun_Xl4_135: $i)).
% 0.21/0.52 tff(tptp_fun_Xl3_136_type, type, (
% 0.21/0.52 tptp_fun_Xl3_136: $i)).
% 0.21/0.52 tff(tptp_fun_Xx_127_type, type, (
% 0.21/0.52 tptp_fun_Xx_127: ( $i * $i ) > $i)).
% 0.21/0.52 tff(tptp_fun_Xl2_137_type, type, (
% 0.21/0.52 tptp_fun_Xl2_137: $i)).
% 0.21/0.52 tff(tptp_fun_Xl1_138_type, type, (
% 0.21/0.52 tptp_fun_Xl1_138: $i)).
% 0.21/0.52 tff(tptp_fun______type, type, (
% 0.21/0.52 tptp_fun_____: ( $i * $i ) > $i)).
% 0.21/0.52 tff(list_succeeds_type, type, (
% 0.21/0.52 list_succeeds: $i > $o)).
% 0.21/0.52 tff(permutation_succeeds_type, type, (
% 0.21/0.52 permutation_succeeds: ( $i * $i ) > $o)).
% 0.21/0.52 tff(1,plain,
% 0.21/0.52 ((~![Xl1: $i, Xl2: $i, Xl3: $i, Xl4: $i] : ((~(permutation_succeeds(Xl1, Xl3) & permutation_succeeds(Xl2, Xl4))) | permutation_succeeds(tptp_fun_____(Xl1, Xl2), tptp_fun_____(Xl3, Xl4)))) <=> (~![Xl1: $i, Xl2: $i, Xl3: $i, Xl4: $i] : ((~(permutation_succeeds(Xl1, Xl3) & permutation_succeeds(Xl2, Xl4))) | permutation_succeeds(tptp_fun_____(Xl1, Xl2), tptp_fun_____(Xl3, Xl4))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(2,plain,
% 0.21/0.52 ((~![Xl1: $i, Xl2: $i, Xl3: $i, Xl4: $i] : ((permutation_succeeds(Xl1, Xl3) & permutation_succeeds(Xl2, Xl4)) => permutation_succeeds(tptp_fun_____(Xl1, Xl2), tptp_fun_____(Xl3, Xl4)))) <=> (~![Xl1: $i, Xl2: $i, Xl3: $i, Xl4: $i] : ((~(permutation_succeeds(Xl1, Xl3) & permutation_succeeds(Xl2, Xl4))) | permutation_succeeds(tptp_fun_____(Xl1, Xl2), tptp_fun_____(Xl3, Xl4))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(3,axiom,(~![Xl1: $i, Xl2: $i, Xl3: $i, Xl4: $i] : ((permutation_succeeds(Xl1, Xl3) & permutation_succeeds(Xl2, Xl4)) => permutation_succeeds(tptp_fun_____(Xl1, Xl2), tptp_fun_____(Xl3, Xl4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''theorem-(permutation:app)'')).
% 0.21/0.52 tff(4,plain,
% 0.21/0.52 (~![Xl1: $i, Xl2: $i, Xl3: $i, Xl4: $i] : ((~(permutation_succeeds(Xl1, Xl3) & permutation_succeeds(Xl2, Xl4))) | permutation_succeeds(tptp_fun_____(Xl1, Xl2), tptp_fun_____(Xl3, Xl4)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.21/0.52 tff(5,plain,
% 0.21/0.52 (~![Xl1: $i, Xl2: $i, Xl3: $i, Xl4: $i] : ((~(permutation_succeeds(Xl1, Xl3) & permutation_succeeds(Xl2, Xl4))) | permutation_succeeds(tptp_fun_____(Xl1, Xl2), tptp_fun_____(Xl3, Xl4)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.21/0.52 tff(6,plain,
% 0.21/0.52 (~![Xl1: $i, Xl2: $i, Xl3: $i, Xl4: $i] : ((~(permutation_succeeds(Xl1, Xl3) & permutation_succeeds(Xl2, Xl4))) | permutation_succeeds(tptp_fun_____(Xl1, Xl2), tptp_fun_____(Xl3, Xl4)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.21/0.52 tff(7,plain,
% 0.21/0.52 (~![Xl1: $i, Xl2: $i, Xl3: $i, Xl4: $i] : ((~(permutation_succeeds(Xl1, Xl3) & permutation_succeeds(Xl2, Xl4))) | permutation_succeeds(tptp_fun_____(Xl1, Xl2), tptp_fun_____(Xl3, Xl4)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.21/0.52 tff(8,plain,(
% 0.21/0.52 ~((~(permutation_succeeds(Xl1!138, Xl3!136) & permutation_succeeds(Xl2!137, Xl4!135))) | permutation_succeeds(tptp_fun_____(Xl1!138, Xl2!137), tptp_fun_____(Xl3!136, Xl4!135)))),
% 0.21/0.52 inference(skolemize,[status(sab)],[7])).
% 0.21/0.52 tff(9,plain,
% 0.21/0.52 (permutation_succeeds(Xl1!138, Xl3!136) & permutation_succeeds(Xl2!137, Xl4!135)),
% 0.21/0.52 inference(or_elim,[status(thm)],[8])).
% 0.21/0.52 tff(10,plain,
% 0.21/0.52 (permutation_succeeds(Xl2!137, Xl4!135)),
% 0.21/0.52 inference(and_elim,[status(thm)],[9])).
% 0.21/0.52 tff(11,plain,
% 0.21/0.52 (^[Xl1: $i, Xl2: $i] : refl(((~permutation_succeeds(Xl1, Xl2)) | (~((~list_succeeds(Xl2)) | (~list_succeeds(Xl1))))) <=> ((~permutation_succeeds(Xl1, Xl2)) | (~((~list_succeeds(Xl2)) | (~list_succeeds(Xl1))))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(12,plain,
% 0.21/0.52 (![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | (~((~list_succeeds(Xl2)) | (~list_succeeds(Xl1))))) <=> ![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | (~((~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[11])).
% 0.21/0.52 tff(13,plain,
% 0.21/0.52 (^[Xl1: $i, Xl2: $i] : rewrite(((~permutation_succeeds(Xl1, Xl2)) | (list_succeeds(Xl1) & list_succeeds(Xl2))) <=> ((~permutation_succeeds(Xl1, Xl2)) | (~((~list_succeeds(Xl2)) | (~list_succeeds(Xl1))))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(14,plain,
% 0.21/0.52 (![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | (list_succeeds(Xl1) & list_succeeds(Xl2))) <=> ![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | (~((~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.52 tff(15,plain,
% 0.21/0.52 (![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | (list_succeeds(Xl1) & list_succeeds(Xl2))) <=> ![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | (list_succeeds(Xl1) & list_succeeds(Xl2)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(16,plain,
% 0.21/0.52 (^[Xl1: $i, Xl2: $i] : rewrite((permutation_succeeds(Xl1, Xl2) => (list_succeeds(Xl1) & list_succeeds(Xl2))) <=> ((~permutation_succeeds(Xl1, Xl2)) | (list_succeeds(Xl1) & list_succeeds(Xl2))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(17,plain,
% 0.21/0.52 (![Xl1: $i, Xl2: $i] : (permutation_succeeds(Xl1, Xl2) => (list_succeeds(Xl1) & list_succeeds(Xl2))) <=> ![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | (list_succeeds(Xl1) & list_succeeds(Xl2)))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[16])).
% 0.21/0.52 tff(18,axiom,(![Xl1: $i, Xl2: $i] : (permutation_succeeds(Xl1, Xl2) => (list_succeeds(Xl1) & list_succeeds(Xl2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''lemma-(permutation:types)'')).
% 0.21/0.52 tff(19,plain,
% 0.21/0.52 (![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | (list_succeeds(Xl1) & list_succeeds(Xl2)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.21/0.52 tff(20,plain,
% 0.21/0.52 (![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | (list_succeeds(Xl1) & list_succeeds(Xl2)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.21/0.52 tff(21,plain,(
% 0.21/0.52 ![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | (list_succeeds(Xl1) & list_succeeds(Xl2)))),
% 0.21/0.52 inference(skolemize,[status(sab)],[20])).
% 0.21/0.52 tff(22,plain,
% 0.21/0.52 (![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | (~((~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.21/0.52 tff(23,plain,
% 0.21/0.52 (![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | (~((~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[22, 12])).
% 0.21/0.52 tff(24,plain,
% 0.21/0.52 (((~![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | (~((~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))))) | ((~permutation_succeeds(Xl2!137, Xl4!135)) | (~((~list_succeeds(Xl4!135)) | (~list_succeeds(Xl2!137)))))) <=> ((~![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | (~((~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))))) | (~permutation_succeeds(Xl2!137, Xl4!135)) | (~((~list_succeeds(Xl4!135)) | (~list_succeeds(Xl2!137)))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(25,plain,
% 0.21/0.52 ((~![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | (~((~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))))) | ((~permutation_succeeds(Xl2!137, Xl4!135)) | (~((~list_succeeds(Xl4!135)) | (~list_succeeds(Xl2!137)))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(26,plain,
% 0.21/0.52 ((~![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | (~((~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))))) | (~permutation_succeeds(Xl2!137, Xl4!135)) | (~((~list_succeeds(Xl4!135)) | (~list_succeeds(Xl2!137))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.21/0.52 tff(27,plain,
% 0.21/0.52 (~((~list_succeeds(Xl4!135)) | (~list_succeeds(Xl2!137)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[26, 23, 10])).
% 0.21/0.52 tff(28,plain,
% 0.21/0.52 (((~list_succeeds(Xl4!135)) | (~list_succeeds(Xl2!137))) | list_succeeds(Xl4!135)),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(29,plain,
% 0.21/0.52 (list_succeeds(Xl4!135)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.21/0.52 tff(30,plain,
% 0.21/0.52 (permutation_succeeds(Xl1!138, Xl3!136)),
% 0.21/0.52 inference(and_elim,[status(thm)],[9])).
% 0.21/0.52 tff(31,plain,
% 0.21/0.52 (((~![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | (~((~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))))) | ((~permutation_succeeds(Xl1!138, Xl3!136)) | (~((~list_succeeds(Xl3!136)) | (~list_succeeds(Xl1!138)))))) <=> ((~![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | (~((~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))))) | (~permutation_succeeds(Xl1!138, Xl3!136)) | (~((~list_succeeds(Xl3!136)) | (~list_succeeds(Xl1!138)))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(32,plain,
% 0.21/0.52 ((~![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | (~((~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))))) | ((~permutation_succeeds(Xl1!138, Xl3!136)) | (~((~list_succeeds(Xl3!136)) | (~list_succeeds(Xl1!138)))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(33,plain,
% 0.21/0.52 ((~![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | (~((~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))))) | (~permutation_succeeds(Xl1!138, Xl3!136)) | (~((~list_succeeds(Xl3!136)) | (~list_succeeds(Xl1!138))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.21/0.52 tff(34,plain,
% 0.21/0.52 (~((~list_succeeds(Xl3!136)) | (~list_succeeds(Xl1!138)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[33, 23, 30])).
% 0.21/0.52 tff(35,plain,
% 0.21/0.52 (((~list_succeeds(Xl3!136)) | (~list_succeeds(Xl1!138))) | list_succeeds(Xl3!136)),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(36,plain,
% 0.21/0.52 (list_succeeds(Xl3!136)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.21/0.52 tff(37,plain,
% 0.21/0.52 (^[Xx: $i, Xl1: $i, Xl2: $i] : refl(((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1))) <=> ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(38,plain,
% 0.21/0.52 (![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1))) <=> ![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[37])).
% 0.21/0.52 tff(39,plain,
% 0.21/0.52 (^[Xx: $i, Xl1: $i, Xl2: $i] : trans(monotonicity(trans(monotonicity(rewrite((list_succeeds(Xl1) & list_succeeds(Xl2)) <=> (~((~list_succeeds(Xl2)) | (~list_succeeds(Xl1))))), ((~(list_succeeds(Xl1) & list_succeeds(Xl2))) <=> (~(~((~list_succeeds(Xl2)) | (~list_succeeds(Xl1))))))), rewrite((~(~((~list_succeeds(Xl2)) | (~list_succeeds(Xl1))))) <=> ((~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))), ((~(list_succeeds(Xl1) & list_succeeds(Xl2))) <=> ((~list_succeeds(Xl2)) | (~list_succeeds(Xl1))))), (((~(list_succeeds(Xl1) & list_succeeds(Xl2))) | (occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2)))) <=> (((~list_succeeds(Xl2)) | (~list_succeeds(Xl1))) | (occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2)))))), rewrite((((~list_succeeds(Xl2)) | (~list_succeeds(Xl1))) | (occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2)))) <=> ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))), (((~(list_succeeds(Xl1) & list_succeeds(Xl2))) | (occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2)))) <=> ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(40,plain,
% 0.21/0.52 (![Xx: $i, Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl1) & list_succeeds(Xl2))) | (occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2)))) <=> ![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[39])).
% 0.21/0.52 tff(41,plain,
% 0.21/0.52 (![Xx: $i, Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl1) & list_succeeds(Xl2))) | (occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2)))) <=> ![Xx: $i, Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl1) & list_succeeds(Xl2))) | (occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(42,plain,
% 0.21/0.52 (^[Xx: $i, Xl1: $i, Xl2: $i] : rewrite(((list_succeeds(Xl1) & list_succeeds(Xl2)) => (occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2)))) <=> ((~(list_succeeds(Xl1) & list_succeeds(Xl2))) | (occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2)))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(43,plain,
% 0.21/0.52 (![Xx: $i, Xl1: $i, Xl2: $i] : ((list_succeeds(Xl1) & list_succeeds(Xl2)) => (occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2)))) <=> ![Xx: $i, Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl1) & list_succeeds(Xl2))) | (occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[42])).
% 0.21/0.52 tff(44,axiom,(![Xx: $i, Xl1: $i, Xl2: $i] : ((list_succeeds(Xl1) & list_succeeds(Xl2)) => (occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''lemma-(occ:app)'')).
% 0.21/0.52 tff(45,plain,
% 0.21/0.52 (![Xx: $i, Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl1) & list_succeeds(Xl2))) | (occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.21/0.52 tff(46,plain,
% 0.21/0.52 (![Xx: $i, Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl1) & list_succeeds(Xl2))) | (occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.21/0.52 tff(47,plain,(
% 0.21/0.52 ![Xx: $i, Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl1) & list_succeeds(Xl2))) | (occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))))),
% 0.21/0.52 inference(skolemize,[status(sab)],[46])).
% 0.21/0.52 tff(48,plain,
% 0.21/0.52 (![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.21/0.52 tff(49,plain,
% 0.21/0.52 (![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[48, 38])).
% 0.21/0.52 tff(50,plain,
% 0.21/0.52 (((~![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | ((~list_succeeds(Xl3!136)) | (~list_succeeds(Xl4!135)) | (occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl3!136, Xl4!135)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl3!136), occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl4!135))))) <=> ((~![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | (~list_succeeds(Xl3!136)) | (~list_succeeds(Xl4!135)) | (occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl3!136, Xl4!135)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl3!136), occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl4!135))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(51,plain,
% 0.21/0.52 (((occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl3!136, Xl4!135)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl3!136), occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl4!135))) | (~list_succeeds(Xl4!135)) | (~list_succeeds(Xl3!136))) <=> ((~list_succeeds(Xl3!136)) | (~list_succeeds(Xl4!135)) | (occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl3!136, Xl4!135)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl3!136), occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl4!135))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(52,plain,
% 0.21/0.52 (((~![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | ((occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl3!136, Xl4!135)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl3!136), occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl4!135))) | (~list_succeeds(Xl4!135)) | (~list_succeeds(Xl3!136)))) <=> ((~![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | ((~list_succeeds(Xl3!136)) | (~list_succeeds(Xl4!135)) | (occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl3!136, Xl4!135)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl3!136), occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl4!135)))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[51])).
% 0.21/0.52 tff(53,plain,
% 0.21/0.52 (((~![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | ((occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl3!136, Xl4!135)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl3!136), occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl4!135))) | (~list_succeeds(Xl4!135)) | (~list_succeeds(Xl3!136)))) <=> ((~![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | (~list_succeeds(Xl3!136)) | (~list_succeeds(Xl4!135)) | (occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl3!136, Xl4!135)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl3!136), occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl4!135))))),
% 0.21/0.52 inference(transitivity,[status(thm)],[52, 50])).
% 0.21/0.52 tff(54,plain,
% 0.21/0.52 ((~![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | ((occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl3!136, Xl4!135)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl3!136), occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl4!135))) | (~list_succeeds(Xl4!135)) | (~list_succeeds(Xl3!136)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(55,plain,
% 0.21/0.52 ((~![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | (~list_succeeds(Xl3!136)) | (~list_succeeds(Xl4!135)) | (occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl3!136, Xl4!135)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl3!136), occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl4!135)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.21/0.52 tff(56,plain,
% 0.21/0.52 (occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl3!136, Xl4!135)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl3!136), occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl4!135))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[55, 49, 36, 29])).
% 0.21/0.52 tff(57,plain,
% 0.21/0.52 (tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl3!136), occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl4!135)) = occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl3!136, Xl4!135))),
% 0.21/0.52 inference(symmetry,[status(thm)],[56])).
% 0.21/0.52 tff(58,plain,
% 0.21/0.52 (^[Xl1: $i, Xl2: $i] : refl(((~permutation_succeeds(Xl1, Xl2)) | ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2))) <=> ((~permutation_succeeds(Xl1, Xl2)) | ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(59,plain,
% 0.21/0.52 (![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2))) <=> ![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[58])).
% 0.21/0.52 tff(60,plain,
% 0.21/0.52 (^[Xl1: $i, Xl2: $i] : rewrite(((~permutation_succeeds(Xl1, Xl2)) | ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2))) <=> ((~permutation_succeeds(Xl1, Xl2)) | ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(61,plain,
% 0.21/0.52 (![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2))) <=> ![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[60])).
% 0.21/0.52 tff(62,plain,
% 0.21/0.52 (![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2))) <=> ![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))),
% 0.21/0.52 inference(transitivity,[status(thm)],[61, 59])).
% 0.21/0.52 tff(63,plain,
% 0.21/0.52 (![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2))) <=> ![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(64,plain,
% 0.21/0.52 (^[Xl1: $i, Xl2: $i] : rewrite((permutation_succeeds(Xl1, Xl2) => ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2))) <=> ((~permutation_succeeds(Xl1, Xl2)) | ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(65,plain,
% 0.21/0.52 (![Xl1: $i, Xl2: $i] : (permutation_succeeds(Xl1, Xl2) => ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2))) <=> ![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[64])).
% 0.21/0.52 tff(66,axiom,(![Xl1: $i, Xl2: $i] : (permutation_succeeds(Xl1, Xl2) => ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''theorem-(permutation:occ)'')).
% 0.21/0.52 tff(67,plain,
% 0.21/0.52 (![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.21/0.52 tff(68,plain,
% 0.21/0.52 (![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.21/0.52 tff(69,plain,(
% 0.21/0.52 ![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))),
% 0.21/0.52 inference(skolemize,[status(sab)],[68])).
% 0.21/0.52 tff(70,plain,
% 0.21/0.52 (![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.21/0.52 tff(71,plain,
% 0.21/0.52 (((~![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))) | ((~permutation_succeeds(Xl2!137, Xl4!135)) | ![Xx: $i] : (occ(Xx, Xl2!137) = occ(Xx, Xl4!135)))) <=> ((~![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))) | (~permutation_succeeds(Xl2!137, Xl4!135)) | ![Xx: $i] : (occ(Xx, Xl2!137) = occ(Xx, Xl4!135)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(72,plain,
% 0.21/0.52 ((~![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))) | ((~permutation_succeeds(Xl2!137, Xl4!135)) | ![Xx: $i] : (occ(Xx, Xl2!137) = occ(Xx, Xl4!135)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(73,plain,
% 0.21/0.52 ((~![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))) | (~permutation_succeeds(Xl2!137, Xl4!135)) | ![Xx: $i] : (occ(Xx, Xl2!137) = occ(Xx, Xl4!135))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.21/0.52 tff(74,plain,
% 0.21/0.52 (![Xx: $i] : (occ(Xx, Xl2!137) = occ(Xx, Xl4!135))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[73, 70, 10])).
% 0.21/0.52 tff(75,plain,
% 0.21/0.52 ((~![Xx: $i] : (occ(Xx, Xl2!137) = occ(Xx, Xl4!135))) | (occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl2!137) = occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl4!135))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(76,plain,
% 0.21/0.52 (occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl2!137) = occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl4!135)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.21/0.52 tff(77,plain,
% 0.21/0.52 (((~![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))) | ((~permutation_succeeds(Xl1!138, Xl3!136)) | ![Xx: $i] : (occ(Xx, Xl1!138) = occ(Xx, Xl3!136)))) <=> ((~![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))) | (~permutation_succeeds(Xl1!138, Xl3!136)) | ![Xx: $i] : (occ(Xx, Xl1!138) = occ(Xx, Xl3!136)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(78,plain,
% 0.21/0.52 ((~![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))) | ((~permutation_succeeds(Xl1!138, Xl3!136)) | ![Xx: $i] : (occ(Xx, Xl1!138) = occ(Xx, Xl3!136)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(79,plain,
% 0.21/0.52 ((~![Xl1: $i, Xl2: $i] : ((~permutation_succeeds(Xl1, Xl2)) | ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))) | (~permutation_succeeds(Xl1!138, Xl3!136)) | ![Xx: $i] : (occ(Xx, Xl1!138) = occ(Xx, Xl3!136))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.21/0.52 tff(80,plain,
% 0.21/0.52 (![Xx: $i] : (occ(Xx, Xl1!138) = occ(Xx, Xl3!136))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[79, 70, 30])).
% 0.21/0.52 tff(81,plain,
% 0.21/0.52 ((~![Xx: $i] : (occ(Xx, Xl1!138) = occ(Xx, Xl3!136))) | (occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl1!138) = occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl3!136))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(82,plain,
% 0.21/0.52 (occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl1!138) = occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl3!136)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.21/0.52 tff(83,plain,
% 0.21/0.52 (tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl1!138), occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl2!137)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl3!136), occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl4!135))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[82, 76])).
% 0.21/0.52 tff(84,plain,
% 0.21/0.52 (((~list_succeeds(Xl4!135)) | (~list_succeeds(Xl2!137))) | list_succeeds(Xl2!137)),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(85,plain,
% 0.21/0.52 (list_succeeds(Xl2!137)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[84, 27])).
% 0.21/0.52 tff(86,plain,
% 0.21/0.52 (((~list_succeeds(Xl3!136)) | (~list_succeeds(Xl1!138))) | list_succeeds(Xl1!138)),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(87,plain,
% 0.21/0.52 (list_succeeds(Xl1!138)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[86, 34])).
% 0.21/0.52 tff(88,plain,
% 0.21/0.52 (((~![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | ((~list_succeeds(Xl1!138)) | (~list_succeeds(Xl2!137)) | (occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl1!138, Xl2!137)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl1!138), occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl2!137))))) <=> ((~![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | (~list_succeeds(Xl1!138)) | (~list_succeeds(Xl2!137)) | (occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl1!138, Xl2!137)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl1!138), occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl2!137))))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(89,plain,
% 0.21/0.53 (((occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl1!138, Xl2!137)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl1!138), occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl2!137))) | (~list_succeeds(Xl2!137)) | (~list_succeeds(Xl1!138))) <=> ((~list_succeeds(Xl1!138)) | (~list_succeeds(Xl2!137)) | (occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl1!138, Xl2!137)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl1!138), occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl2!137))))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(90,plain,
% 0.21/0.53 (((~![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | ((occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl1!138, Xl2!137)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl1!138), occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl2!137))) | (~list_succeeds(Xl2!137)) | (~list_succeeds(Xl1!138)))) <=> ((~![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | ((~list_succeeds(Xl1!138)) | (~list_succeeds(Xl2!137)) | (occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl1!138, Xl2!137)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl1!138), occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl2!137)))))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[89])).
% 0.21/0.53 tff(91,plain,
% 0.21/0.53 (((~![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | ((occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl1!138, Xl2!137)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl1!138), occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl2!137))) | (~list_succeeds(Xl2!137)) | (~list_succeeds(Xl1!138)))) <=> ((~![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | (~list_succeeds(Xl1!138)) | (~list_succeeds(Xl2!137)) | (occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl1!138, Xl2!137)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl1!138), occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl2!137))))),
% 0.21/0.53 inference(transitivity,[status(thm)],[90, 88])).
% 0.21/0.53 tff(92,plain,
% 0.21/0.53 ((~![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | ((occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl1!138, Xl2!137)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl1!138), occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl2!137))) | (~list_succeeds(Xl2!137)) | (~list_succeeds(Xl1!138)))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(93,plain,
% 0.21/0.53 ((~![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | (~list_succeeds(Xl1!138)) | (~list_succeeds(Xl2!137)) | (occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl1!138, Xl2!137)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl1!138), occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl2!137)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.21/0.53 tff(94,plain,
% 0.21/0.53 (occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl1!138, Xl2!137)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl1!138), occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), Xl2!137))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[93, 49, 87, 85])).
% 0.21/0.53 tff(95,plain,
% 0.21/0.53 (occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl1!138, Xl2!137)) = occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl3!136, Xl4!135))),
% 0.21/0.53 inference(transitivity,[status(thm)],[94, 83, 57])).
% 0.21/0.53 tff(96,plain,
% 0.21/0.53 (^[Xl1: $i, Xl2: $i] : refl((list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1))) <=> (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(97,plain,
% 0.21/0.53 (![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1))) <=> ![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[96])).
% 0.21/0.53 tff(98,plain,
% 0.21/0.53 (^[Xl1: $i, Xl2: $i] : trans(monotonicity(trans(monotonicity(rewrite((list_succeeds(Xl1) & list_succeeds(Xl2)) <=> (~((~list_succeeds(Xl2)) | (~list_succeeds(Xl1))))), ((~(list_succeeds(Xl1) & list_succeeds(Xl2))) <=> (~(~((~list_succeeds(Xl2)) | (~list_succeeds(Xl1))))))), rewrite((~(~((~list_succeeds(Xl2)) | (~list_succeeds(Xl1))))) <=> ((~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))), ((~(list_succeeds(Xl1) & list_succeeds(Xl2))) <=> ((~list_succeeds(Xl2)) | (~list_succeeds(Xl1))))), ((list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~(list_succeeds(Xl1) & list_succeeds(Xl2)))) <=> (list_succeeds(tptp_fun_____(Xl1, Xl2)) | ((~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))))), rewrite((list_succeeds(tptp_fun_____(Xl1, Xl2)) | ((~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) <=> (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))), ((list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~(list_succeeds(Xl1) & list_succeeds(Xl2)))) <=> (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(99,plain,
% 0.21/0.53 (![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(Xl2)) | (~list_succeeds(Xl1)))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[98])).
% 0.21/0.53 tff(100,plain,
% 0.21/0.53 (![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))))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(101,plain,
% 0.21/0.53 (^[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)))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(102,plain,
% 0.21/0.53 (![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))))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[101])).
% 0.21/0.53 tff(103,axiom,(![Xl1: $i, Xl2: $i] : ((list_succeeds(Xl1) & list_succeeds(Xl2)) => list_succeeds(tptp_fun_____(Xl1, Xl2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''axiom-(app:types:1)'')).
% 0.21/0.53 tff(104,plain,
% 0.21/0.53 (![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~(list_succeeds(Xl1) & list_succeeds(Xl2))))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.21/0.53 tff(105,plain,
% 0.21/0.53 (![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~(list_succeeds(Xl1) & list_succeeds(Xl2))))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.21/0.53 tff(106,plain,(
% 0.21/0.53 ![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~(list_succeeds(Xl1) & list_succeeds(Xl2))))),
% 0.21/0.53 inference(skolemize,[status(sab)],[105])).
% 0.21/0.53 tff(107,plain,
% 0.21/0.53 (![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.21/0.53 tff(108,plain,
% 0.21/0.53 (![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[107, 97])).
% 0.21/0.53 tff(109,plain,
% 0.21/0.53 (((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | ((~list_succeeds(Xl3!136)) | (~list_succeeds(Xl4!135)) | list_succeeds(tptp_fun_____(Xl3!136, Xl4!135)))) <=> ((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | (~list_succeeds(Xl3!136)) | (~list_succeeds(Xl4!135)) | list_succeeds(tptp_fun_____(Xl3!136, Xl4!135)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(110,plain,
% 0.21/0.53 ((list_succeeds(tptp_fun_____(Xl3!136, Xl4!135)) | (~list_succeeds(Xl4!135)) | (~list_succeeds(Xl3!136))) <=> ((~list_succeeds(Xl3!136)) | (~list_succeeds(Xl4!135)) | list_succeeds(tptp_fun_____(Xl3!136, Xl4!135)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(111,plain,
% 0.21/0.53 (((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | (list_succeeds(tptp_fun_____(Xl3!136, Xl4!135)) | (~list_succeeds(Xl4!135)) | (~list_succeeds(Xl3!136)))) <=> ((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | ((~list_succeeds(Xl3!136)) | (~list_succeeds(Xl4!135)) | list_succeeds(tptp_fun_____(Xl3!136, Xl4!135))))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[110])).
% 0.21/0.53 tff(112,plain,
% 0.21/0.53 (((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | (list_succeeds(tptp_fun_____(Xl3!136, Xl4!135)) | (~list_succeeds(Xl4!135)) | (~list_succeeds(Xl3!136)))) <=> ((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | (~list_succeeds(Xl3!136)) | (~list_succeeds(Xl4!135)) | list_succeeds(tptp_fun_____(Xl3!136, Xl4!135)))),
% 0.21/0.53 inference(transitivity,[status(thm)],[111, 109])).
% 0.21/0.53 tff(113,plain,
% 0.21/0.53 ((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | (list_succeeds(tptp_fun_____(Xl3!136, Xl4!135)) | (~list_succeeds(Xl4!135)) | (~list_succeeds(Xl3!136)))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(114,plain,
% 0.21/0.53 ((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | (~list_succeeds(Xl3!136)) | (~list_succeeds(Xl4!135)) | list_succeeds(tptp_fun_____(Xl3!136, Xl4!135))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.21/0.53 tff(115,plain,
% 0.21/0.53 ((~list_succeeds(Xl3!136)) | (~list_succeeds(Xl4!135)) | list_succeeds(tptp_fun_____(Xl3!136, Xl4!135))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[114, 108])).
% 0.21/0.53 tff(116,plain,
% 0.21/0.53 (list_succeeds(tptp_fun_____(Xl3!136, Xl4!135))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[115, 29, 36])).
% 0.21/0.53 tff(117,plain,
% 0.21/0.53 (((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | ((~list_succeeds(Xl1!138)) | (~list_succeeds(Xl2!137)) | list_succeeds(tptp_fun_____(Xl1!138, Xl2!137)))) <=> ((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | (~list_succeeds(Xl1!138)) | (~list_succeeds(Xl2!137)) | list_succeeds(tptp_fun_____(Xl1!138, Xl2!137)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(118,plain,
% 0.21/0.53 ((list_succeeds(tptp_fun_____(Xl1!138, Xl2!137)) | (~list_succeeds(Xl2!137)) | (~list_succeeds(Xl1!138))) <=> ((~list_succeeds(Xl1!138)) | (~list_succeeds(Xl2!137)) | list_succeeds(tptp_fun_____(Xl1!138, Xl2!137)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(119,plain,
% 0.21/0.53 (((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | (list_succeeds(tptp_fun_____(Xl1!138, Xl2!137)) | (~list_succeeds(Xl2!137)) | (~list_succeeds(Xl1!138)))) <=> ((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | ((~list_succeeds(Xl1!138)) | (~list_succeeds(Xl2!137)) | list_succeeds(tptp_fun_____(Xl1!138, Xl2!137))))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[118])).
% 0.21/0.53 tff(120,plain,
% 0.21/0.53 (((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | (list_succeeds(tptp_fun_____(Xl1!138, Xl2!137)) | (~list_succeeds(Xl2!137)) | (~list_succeeds(Xl1!138)))) <=> ((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | (~list_succeeds(Xl1!138)) | (~list_succeeds(Xl2!137)) | list_succeeds(tptp_fun_____(Xl1!138, Xl2!137)))),
% 0.21/0.53 inference(transitivity,[status(thm)],[119, 117])).
% 0.21/0.53 tff(121,plain,
% 0.21/0.53 ((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | (list_succeeds(tptp_fun_____(Xl1!138, Xl2!137)) | (~list_succeeds(Xl2!137)) | (~list_succeeds(Xl1!138)))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(122,plain,
% 0.21/0.53 ((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | (~list_succeeds(Xl1!138)) | (~list_succeeds(Xl2!137)) | list_succeeds(tptp_fun_____(Xl1!138, Xl2!137))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.21/0.53 tff(123,plain,
% 0.21/0.53 ((~list_succeeds(Xl1!138)) | (~list_succeeds(Xl2!137)) | list_succeeds(tptp_fun_____(Xl1!138, Xl2!137))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[122, 108])).
% 0.21/0.53 tff(124,plain,
% 0.21/0.53 (list_succeeds(tptp_fun_____(Xl1!138, Xl2!137))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[123, 85, 87])).
% 0.21/0.53 tff(125,plain,
% 0.21/0.53 (~permutation_succeeds(tptp_fun_____(Xl1!138, Xl2!137), tptp_fun_____(Xl3!136, Xl4!135))),
% 0.21/0.53 inference(or_elim,[status(thm)],[8])).
% 0.21/0.53 tff(126,plain,
% 0.21/0.53 (^[Xl1: $i, Xl2: $i] : refl((permutation_succeeds(Xl1, Xl2) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)) | (~(occ(tptp_fun_Xx_127(Xl2, Xl1), Xl1) = occ(tptp_fun_Xx_127(Xl2, Xl1), Xl2)))) <=> (permutation_succeeds(Xl1, Xl2) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)) | (~(occ(tptp_fun_Xx_127(Xl2, Xl1), Xl1) = occ(tptp_fun_Xx_127(Xl2, Xl1), Xl2)))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(127,plain,
% 0.21/0.53 (![Xl1: $i, Xl2: $i] : (permutation_succeeds(Xl1, Xl2) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)) | (~(occ(tptp_fun_Xx_127(Xl2, Xl1), Xl1) = occ(tptp_fun_Xx_127(Xl2, Xl1), Xl2)))) <=> ![Xl1: $i, Xl2: $i] : (permutation_succeeds(Xl1, Xl2) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)) | (~(occ(tptp_fun_Xx_127(Xl2, Xl1), Xl1) = occ(tptp_fun_Xx_127(Xl2, Xl1), Xl2))))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[126])).
% 0.21/0.53 tff(128,plain,
% 0.21/0.53 (^[Xl1: $i, Xl2: $i] : rewrite((((~list_succeeds(Xl2)) | (~list_succeeds(Xl1)) | (~(occ(tptp_fun_Xx_127(Xl2, Xl1), Xl1) = occ(tptp_fun_Xx_127(Xl2, Xl1), Xl2)))) | permutation_succeeds(Xl1, Xl2)) <=> (permutation_succeeds(Xl1, Xl2) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)) | (~(occ(tptp_fun_Xx_127(Xl2, Xl1), Xl1) = occ(tptp_fun_Xx_127(Xl2, Xl1), Xl2)))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(129,plain,
% 0.21/0.53 (![Xl1: $i, Xl2: $i] : (((~list_succeeds(Xl2)) | (~list_succeeds(Xl1)) | (~(occ(tptp_fun_Xx_127(Xl2, Xl1), Xl1) = occ(tptp_fun_Xx_127(Xl2, Xl1), Xl2)))) | permutation_succeeds(Xl1, Xl2)) <=> ![Xl1: $i, Xl2: $i] : (permutation_succeeds(Xl1, Xl2) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)) | (~(occ(tptp_fun_Xx_127(Xl2, Xl1), Xl1) = occ(tptp_fun_Xx_127(Xl2, Xl1), Xl2))))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[128])).
% 0.21/0.53 tff(130,plain,
% 0.21/0.53 (![Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl2) & list_succeeds(Xl1) & ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))) | permutation_succeeds(Xl1, Xl2)) <=> ![Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl2) & list_succeeds(Xl1) & ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))) | permutation_succeeds(Xl1, Xl2))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(131,plain,
% 0.21/0.53 (^[Xl1: $i, Xl2: $i] : trans(monotonicity(rewrite(((list_succeeds(Xl2) & list_succeeds(Xl1)) & ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2))) <=> (list_succeeds(Xl2) & list_succeeds(Xl1) & ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))), ((((list_succeeds(Xl2) & list_succeeds(Xl1)) & ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2))) => permutation_succeeds(Xl1, Xl2)) <=> ((list_succeeds(Xl2) & list_succeeds(Xl1) & ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2))) => permutation_succeeds(Xl1, Xl2)))), rewrite(((list_succeeds(Xl2) & list_succeeds(Xl1) & ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2))) => permutation_succeeds(Xl1, Xl2)) <=> ((~(list_succeeds(Xl2) & list_succeeds(Xl1) & ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))) | permutation_succeeds(Xl1, Xl2))), ((((list_succeeds(Xl2) & list_succeeds(Xl1)) & ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2))) => permutation_succeeds(Xl1, Xl2)) <=> ((~(list_succeeds(Xl2) & list_succeeds(Xl1) & ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))) | permutation_succeeds(Xl1, Xl2))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(132,plain,
% 0.21/0.53 (![Xl1: $i, Xl2: $i] : (((list_succeeds(Xl2) & list_succeeds(Xl1)) & ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2))) => permutation_succeeds(Xl1, Xl2)) <=> ![Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl2) & list_succeeds(Xl1) & ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))) | permutation_succeeds(Xl1, Xl2))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[131])).
% 0.21/0.53 tff(133,axiom,(![Xl1: $i, Xl2: $i] : (((list_succeeds(Xl2) & list_succeeds(Xl1)) & ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2))) => permutation_succeeds(Xl1, Xl2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''theorem-(occ:permutation)'')).
% 0.21/0.53 tff(134,plain,
% 0.21/0.53 (![Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl2) & list_succeeds(Xl1) & ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))) | permutation_succeeds(Xl1, Xl2))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.21/0.53 tff(135,plain,
% 0.21/0.53 (![Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl2) & list_succeeds(Xl1) & ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))) | permutation_succeeds(Xl1, Xl2))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[134, 130])).
% 0.21/0.53 tff(136,plain,(
% 0.21/0.53 ![Xl1: $i, Xl2: $i] : (((~list_succeeds(Xl2)) | (~list_succeeds(Xl1)) | (~(occ(tptp_fun_Xx_127(Xl2, Xl1), Xl1) = occ(tptp_fun_Xx_127(Xl2, Xl1), Xl2)))) | permutation_succeeds(Xl1, Xl2))),
% 0.21/0.53 inference(skolemize,[status(sab)],[135])).
% 0.21/0.53 tff(137,plain,
% 0.21/0.53 (![Xl1: $i, Xl2: $i] : (permutation_succeeds(Xl1, Xl2) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)) | (~(occ(tptp_fun_Xx_127(Xl2, Xl1), Xl1) = occ(tptp_fun_Xx_127(Xl2, Xl1), Xl2))))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[136, 129])).
% 0.21/0.53 tff(138,plain,
% 0.21/0.53 (![Xl1: $i, Xl2: $i] : (permutation_succeeds(Xl1, Xl2) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)) | (~(occ(tptp_fun_Xx_127(Xl2, Xl1), Xl1) = occ(tptp_fun_Xx_127(Xl2, Xl1), Xl2))))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[137, 127])).
% 0.37/0.54 tff(139,plain,
% 0.37/0.54 (((~![Xl1: $i, Xl2: $i] : (permutation_succeeds(Xl1, Xl2) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)) | (~(occ(tptp_fun_Xx_127(Xl2, Xl1), Xl1) = occ(tptp_fun_Xx_127(Xl2, Xl1), Xl2))))) | (permutation_succeeds(tptp_fun_____(Xl1!138, Xl2!137), tptp_fun_____(Xl3!136, Xl4!135)) | (~list_succeeds(tptp_fun_____(Xl3!136, Xl4!135))) | (~list_succeeds(tptp_fun_____(Xl1!138, Xl2!137))) | (~(occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl1!138, Xl2!137)) = occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl3!136, Xl4!135)))))) <=> ((~![Xl1: $i, Xl2: $i] : (permutation_succeeds(Xl1, Xl2) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)) | (~(occ(tptp_fun_Xx_127(Xl2, Xl1), Xl1) = occ(tptp_fun_Xx_127(Xl2, Xl1), Xl2))))) | permutation_succeeds(tptp_fun_____(Xl1!138, Xl2!137), tptp_fun_____(Xl3!136, Xl4!135)) | (~list_succeeds(tptp_fun_____(Xl3!136, Xl4!135))) | (~list_succeeds(tptp_fun_____(Xl1!138, Xl2!137))) | (~(occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl1!138, Xl2!137)) = occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl3!136, Xl4!135)))))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(140,plain,
% 0.37/0.54 ((~![Xl1: $i, Xl2: $i] : (permutation_succeeds(Xl1, Xl2) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)) | (~(occ(tptp_fun_Xx_127(Xl2, Xl1), Xl1) = occ(tptp_fun_Xx_127(Xl2, Xl1), Xl2))))) | (permutation_succeeds(tptp_fun_____(Xl1!138, Xl2!137), tptp_fun_____(Xl3!136, Xl4!135)) | (~list_succeeds(tptp_fun_____(Xl3!136, Xl4!135))) | (~list_succeeds(tptp_fun_____(Xl1!138, Xl2!137))) | (~(occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl1!138, Xl2!137)) = occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl3!136, Xl4!135)))))),
% 0.37/0.54 inference(quant_inst,[status(thm)],[])).
% 0.37/0.54 tff(141,plain,
% 0.37/0.54 ((~![Xl1: $i, Xl2: $i] : (permutation_succeeds(Xl1, Xl2) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)) | (~(occ(tptp_fun_Xx_127(Xl2, Xl1), Xl1) = occ(tptp_fun_Xx_127(Xl2, Xl1), Xl2))))) | permutation_succeeds(tptp_fun_____(Xl1!138, Xl2!137), tptp_fun_____(Xl3!136, Xl4!135)) | (~list_succeeds(tptp_fun_____(Xl3!136, Xl4!135))) | (~list_succeeds(tptp_fun_____(Xl1!138, Xl2!137))) | (~(occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl1!138, Xl2!137)) = occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl3!136, Xl4!135))))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.37/0.54 tff(142,plain,
% 0.37/0.54 ((~list_succeeds(tptp_fun_____(Xl3!136, Xl4!135))) | (~list_succeeds(tptp_fun_____(Xl1!138, Xl2!137))) | (~(occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl1!138, Xl2!137)) = occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl3!136, Xl4!135))))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[141, 138, 125])).
% 0.37/0.54 tff(143,plain,
% 0.37/0.54 (~(occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl1!138, Xl2!137)) = occ(tptp_fun_Xx_127(tptp_fun_____(Xl3!136, Xl4!135), tptp_fun_____(Xl1!138, Xl2!137)), tptp_fun_____(Xl3!136, Xl4!135)))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[142, 124, 116])).
% 0.37/0.54 tff(144,plain,
% 0.37/0.54 ($false),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[143, 95])).
% 0.37/0.54 % SZS output end Proof
% 0.37/0.54 % E exiting
%------------------------------------------------------------------------------