%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWX051+1 : TPTP v9.1.0. Released v9.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 0.61s 0.79s
% Output : Proof 0.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SWX051+1 : TPTP v9.1.0. Released v9.1.0.
% 0.13/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 12:20:48 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.61/0.79 % SZS status Theorem
% 0.61/0.79 % SZS output start Proof
% 0.61/0.79 tff(s_type, type, (
% 0.61/0.79 s: $i > $i)).
% 0.61/0.79 tff(occ_type, type, (
% 0.61/0.79 occ: ( $i * $i ) > $i)).
% 0.61/0.79 tff(tptp_fun_Xl2_129_type, type, (
% 0.61/0.79 tptp_fun_Xl2_129: $i)).
% 0.61/0.79 tff(tptp_fun_Xx_131_type, type, (
% 0.61/0.79 tptp_fun_Xx_131: $i)).
% 0.61/0.79 tff(tptp_fun_Xl1_130_type, type, (
% 0.61/0.79 tptp_fun_Xl1_130: $i)).
% 0.61/0.79 tff(tptp_fun______type, type, (
% 0.61/0.79 tptp_fun_____: ( $i * $i ) > $i)).
% 0.61/0.79 tff(tptp_fun_Xl4_119_type, type, (
% 0.61/0.79 tptp_fun_Xl4_119: ( $i * $i * $i ) > $i)).
% 0.61/0.79 tff(tptp_fun_Xl3_120_type, type, (
% 0.61/0.79 tptp_fun_Xl3_120: ( $i * $i * $i ) > $i)).
% 0.61/0.79 tff(tptp_fun______type, type, (
% 0.61/0.79 tptp_fun_____: ( $i * $i ) > $i)).
% 0.61/0.79 tff(list_succeeds_type, type, (
% 0.61/0.79 list_succeeds: $i > $o)).
% 0.61/0.79 tff(cons_type, type, (
% 0.61/0.79 cons: ( $i * $i ) > $i)).
% 0.61/0.79 tff(delete_succeeds_type, type, (
% 0.61/0.79 delete_succeeds: ( $i * $i * $i ) > $o)).
% 0.61/0.79 tff(nat_succeeds_type, type, (
% 0.61/0.79 nat_succeeds: $i > $o)).
% 0.61/0.79 tff(1,plain,
% 0.61/0.79 ((~![Xx: $i, Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl1) & delete_succeeds(Xx, Xl1, Xl2))) | (occ(Xx, Xl1) = s(occ(Xx, Xl2))))) <=> (~![Xx: $i, Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl1) & delete_succeeds(Xx, Xl1, Xl2))) | (occ(Xx, Xl1) = s(occ(Xx, Xl2)))))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(2,plain,
% 0.61/0.79 ((~![Xx: $i, Xl1: $i, Xl2: $i] : ((list_succeeds(Xl1) & delete_succeeds(Xx, Xl1, Xl2)) => (occ(Xx, Xl1) = s(occ(Xx, Xl2))))) <=> (~![Xx: $i, Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl1) & delete_succeeds(Xx, Xl1, Xl2))) | (occ(Xx, Xl1) = s(occ(Xx, Xl2)))))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(3,axiom,(~![Xx: $i, Xl1: $i, Xl2: $i] : ((list_succeeds(Xl1) & delete_succeeds(Xx, Xl1, Xl2)) => (occ(Xx, Xl1) = s(occ(Xx, Xl2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''lemma-(delete:occ:eq)'')).
% 0.61/0.79 tff(4,plain,
% 0.61/0.79 (~![Xx: $i, Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl1) & delete_succeeds(Xx, Xl1, Xl2))) | (occ(Xx, Xl1) = s(occ(Xx, Xl2))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.61/0.79 tff(5,plain,
% 0.61/0.79 (~![Xx: $i, Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl1) & delete_succeeds(Xx, Xl1, Xl2))) | (occ(Xx, Xl1) = s(occ(Xx, Xl2))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.61/0.79 tff(6,plain,
% 0.61/0.79 (~![Xx: $i, Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl1) & delete_succeeds(Xx, Xl1, Xl2))) | (occ(Xx, Xl1) = s(occ(Xx, Xl2))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.61/0.79 tff(7,plain,
% 0.61/0.79 (~![Xx: $i, Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl1) & delete_succeeds(Xx, Xl1, Xl2))) | (occ(Xx, Xl1) = s(occ(Xx, Xl2))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.61/0.79 tff(8,plain,(
% 0.61/0.79 ~((~(list_succeeds(Xl1!130) & delete_succeeds(Xx!131, Xl1!130, Xl2!129))) | (occ(Xx!131, Xl1!130) = s(occ(Xx!131, Xl2!129))))),
% 0.61/0.79 inference(skolemize,[status(sab)],[7])).
% 0.61/0.79 tff(9,plain,
% 0.61/0.79 (list_succeeds(Xl1!130) & delete_succeeds(Xx!131, Xl1!130, Xl2!129)),
% 0.61/0.79 inference(or_elim,[status(thm)],[8])).
% 0.61/0.79 tff(10,plain,
% 0.61/0.79 (delete_succeeds(Xx!131, Xl1!130, Xl2!129)),
% 0.61/0.79 inference(and_elim,[status(thm)],[9])).
% 0.61/0.79 tff(11,plain,
% 0.61/0.79 (^[Xx: $i, Xl1: $i, Xl2: $i] : refl(((~delete_succeeds(Xx, Xl1, Xl2)) | (~((~list_succeeds(tptp_fun_Xl3_120(Xl2, Xl1, Xx))) | (~(Xl1 = tptp_fun_____(tptp_fun_Xl3_120(Xl2, Xl1, Xx), cons(Xx, tptp_fun_Xl4_119(Xl2, Xl1, Xx))))) | (~(Xl2 = tptp_fun_____(tptp_fun_Xl3_120(Xl2, Xl1, Xx), tptp_fun_Xl4_119(Xl2, Xl1, Xx))))))) <=> ((~delete_succeeds(Xx, Xl1, Xl2)) | (~((~list_succeeds(tptp_fun_Xl3_120(Xl2, Xl1, Xx))) | (~(Xl1 = tptp_fun_____(tptp_fun_Xl3_120(Xl2, Xl1, Xx), cons(Xx, tptp_fun_Xl4_119(Xl2, Xl1, Xx))))) | (~(Xl2 = tptp_fun_____(tptp_fun_Xl3_120(Xl2, Xl1, Xx), tptp_fun_Xl4_119(Xl2, Xl1, Xx))))))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(12,plain,
% 0.61/0.79 (![Xx: $i, Xl1: $i, Xl2: $i] : ((~delete_succeeds(Xx, Xl1, Xl2)) | (~((~list_succeeds(tptp_fun_Xl3_120(Xl2, Xl1, Xx))) | (~(Xl1 = tptp_fun_____(tptp_fun_Xl3_120(Xl2, Xl1, Xx), cons(Xx, tptp_fun_Xl4_119(Xl2, Xl1, Xx))))) | (~(Xl2 = tptp_fun_____(tptp_fun_Xl3_120(Xl2, Xl1, Xx), tptp_fun_Xl4_119(Xl2, Xl1, Xx))))))) <=> ![Xx: $i, Xl1: $i, Xl2: $i] : ((~delete_succeeds(Xx, Xl1, Xl2)) | (~((~list_succeeds(tptp_fun_Xl3_120(Xl2, Xl1, Xx))) | (~(Xl1 = tptp_fun_____(tptp_fun_Xl3_120(Xl2, Xl1, Xx), cons(Xx, tptp_fun_Xl4_119(Xl2, Xl1, Xx))))) | (~(Xl2 = tptp_fun_____(tptp_fun_Xl3_120(Xl2, Xl1, Xx), tptp_fun_Xl4_119(Xl2, Xl1, Xx)))))))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[11])).
% 0.61/0.79 tff(13,plain,
% 0.61/0.79 (^[Xx: $i, Xl1: $i, Xl2: $i] : rewrite(((~delete_succeeds(Xx, Xl1, Xl2)) | (list_succeeds(tptp_fun_Xl3_120(Xl2, Xl1, Xx)) & (Xl1 = tptp_fun_____(tptp_fun_Xl3_120(Xl2, Xl1, Xx), cons(Xx, tptp_fun_Xl4_119(Xl2, Xl1, Xx)))) & (Xl2 = tptp_fun_____(tptp_fun_Xl3_120(Xl2, Xl1, Xx), tptp_fun_Xl4_119(Xl2, Xl1, Xx))))) <=> ((~delete_succeeds(Xx, Xl1, Xl2)) | (~((~list_succeeds(tptp_fun_Xl3_120(Xl2, Xl1, Xx))) | (~(Xl1 = tptp_fun_____(tptp_fun_Xl3_120(Xl2, Xl1, Xx), cons(Xx, tptp_fun_Xl4_119(Xl2, Xl1, Xx))))) | (~(Xl2 = tptp_fun_____(tptp_fun_Xl3_120(Xl2, Xl1, Xx), tptp_fun_Xl4_119(Xl2, Xl1, Xx))))))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(14,plain,
% 0.61/0.79 (![Xx: $i, Xl1: $i, Xl2: $i] : ((~delete_succeeds(Xx, Xl1, Xl2)) | (list_succeeds(tptp_fun_Xl3_120(Xl2, Xl1, Xx)) & (Xl1 = tptp_fun_____(tptp_fun_Xl3_120(Xl2, Xl1, Xx), cons(Xx, tptp_fun_Xl4_119(Xl2, Xl1, Xx)))) & (Xl2 = tptp_fun_____(tptp_fun_Xl3_120(Xl2, Xl1, Xx), tptp_fun_Xl4_119(Xl2, Xl1, Xx))))) <=> ![Xx: $i, Xl1: $i, Xl2: $i] : ((~delete_succeeds(Xx, Xl1, Xl2)) | (~((~list_succeeds(tptp_fun_Xl3_120(Xl2, Xl1, Xx))) | (~(Xl1 = tptp_fun_____(tptp_fun_Xl3_120(Xl2, Xl1, Xx), cons(Xx, tptp_fun_Xl4_119(Xl2, Xl1, Xx))))) | (~(Xl2 = tptp_fun_____(tptp_fun_Xl3_120(Xl2, Xl1, Xx), tptp_fun_Xl4_119(Xl2, Xl1, Xx)))))))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[13])).
% 0.61/0.79 tff(15,plain,
% 0.61/0.79 (![Xx: $i, Xl1: $i, Xl2: $i] : ((~delete_succeeds(Xx, Xl1, Xl2)) | ?[Xl3: $i, Xl4: $i] : (list_succeeds(Xl3) & (Xl1 = tptp_fun_____(Xl3, cons(Xx, Xl4))) & (Xl2 = tptp_fun_____(Xl3, Xl4)))) <=> ![Xx: $i, Xl1: $i, Xl2: $i] : ((~delete_succeeds(Xx, Xl1, Xl2)) | ?[Xl3: $i, Xl4: $i] : (list_succeeds(Xl3) & (Xl1 = tptp_fun_____(Xl3, cons(Xx, Xl4))) & (Xl2 = tptp_fun_____(Xl3, Xl4))))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(16,plain,
% 0.61/0.79 (^[Xx: $i, Xl1: $i, Xl2: $i] : trans(monotonicity(quant_intro(proof_bind(^[Xl3: $i, Xl4: $i] : rewrite(((list_succeeds(Xl3) & (Xl1 = tptp_fun_____(Xl3, cons(Xx, Xl4)))) & (Xl2 = tptp_fun_____(Xl3, Xl4))) <=> (list_succeeds(Xl3) & (Xl1 = tptp_fun_____(Xl3, cons(Xx, Xl4))) & (Xl2 = tptp_fun_____(Xl3, Xl4))))), (?[Xl3: $i, Xl4: $i] : ((list_succeeds(Xl3) & (Xl1 = tptp_fun_____(Xl3, cons(Xx, Xl4)))) & (Xl2 = tptp_fun_____(Xl3, Xl4))) <=> ?[Xl3: $i, Xl4: $i] : (list_succeeds(Xl3) & (Xl1 = tptp_fun_____(Xl3, cons(Xx, Xl4))) & (Xl2 = tptp_fun_____(Xl3, Xl4))))), ((delete_succeeds(Xx, Xl1, Xl2) => ?[Xl3: $i, Xl4: $i] : ((list_succeeds(Xl3) & (Xl1 = tptp_fun_____(Xl3, cons(Xx, Xl4)))) & (Xl2 = tptp_fun_____(Xl3, Xl4)))) <=> (delete_succeeds(Xx, Xl1, Xl2) => ?[Xl3: $i, Xl4: $i] : (list_succeeds(Xl3) & (Xl1 = tptp_fun_____(Xl3, cons(Xx, Xl4))) & (Xl2 = tptp_fun_____(Xl3, Xl4)))))), rewrite((delete_succeeds(Xx, Xl1, Xl2) => ?[Xl3: $i, Xl4: $i] : (list_succeeds(Xl3) & (Xl1 = tptp_fun_____(Xl3, cons(Xx, Xl4))) & (Xl2 = tptp_fun_____(Xl3, Xl4)))) <=> ((~delete_succeeds(Xx, Xl1, Xl2)) | ?[Xl3: $i, Xl4: $i] : (list_succeeds(Xl3) & (Xl1 = tptp_fun_____(Xl3, cons(Xx, Xl4))) & (Xl2 = tptp_fun_____(Xl3, Xl4))))), ((delete_succeeds(Xx, Xl1, Xl2) => ?[Xl3: $i, Xl4: $i] : ((list_succeeds(Xl3) & (Xl1 = tptp_fun_____(Xl3, cons(Xx, Xl4)))) & (Xl2 = tptp_fun_____(Xl3, Xl4)))) <=> ((~delete_succeeds(Xx, Xl1, Xl2)) | ?[Xl3: $i, Xl4: $i] : (list_succeeds(Xl3) & (Xl1 = tptp_fun_____(Xl3, cons(Xx, Xl4))) & (Xl2 = tptp_fun_____(Xl3, Xl4))))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(17,plain,
% 0.61/0.79 (![Xx: $i, Xl1: $i, Xl2: $i] : (delete_succeeds(Xx, Xl1, Xl2) => ?[Xl3: $i, Xl4: $i] : ((list_succeeds(Xl3) & (Xl1 = tptp_fun_____(Xl3, cons(Xx, Xl4)))) & (Xl2 = tptp_fun_____(Xl3, Xl4)))) <=> ![Xx: $i, Xl1: $i, Xl2: $i] : ((~delete_succeeds(Xx, Xl1, Xl2)) | ?[Xl3: $i, Xl4: $i] : (list_succeeds(Xl3) & (Xl1 = tptp_fun_____(Xl3, cons(Xx, Xl4))) & (Xl2 = tptp_fun_____(Xl3, Xl4))))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[16])).
% 0.61/0.79 tff(18,axiom,(![Xx: $i, Xl1: $i, Xl2: $i] : (delete_succeeds(Xx, Xl1, Xl2) => ?[Xl3: $i, Xl4: $i] : ((list_succeeds(Xl3) & (Xl1 = tptp_fun_____(Xl3, cons(Xx, Xl4)))) & (Xl2 = tptp_fun_____(Xl3, Xl4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''axiom-(delete:app:2)'')).
% 0.61/0.79 tff(19,plain,
% 0.61/0.79 (![Xx: $i, Xl1: $i, Xl2: $i] : ((~delete_succeeds(Xx, Xl1, Xl2)) | ?[Xl3: $i, Xl4: $i] : (list_succeeds(Xl3) & (Xl1 = tptp_fun_____(Xl3, cons(Xx, Xl4))) & (Xl2 = tptp_fun_____(Xl3, Xl4))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.61/0.79 tff(20,plain,
% 0.61/0.79 (![Xx: $i, Xl1: $i, Xl2: $i] : ((~delete_succeeds(Xx, Xl1, Xl2)) | ?[Xl3: $i, Xl4: $i] : (list_succeeds(Xl3) & (Xl1 = tptp_fun_____(Xl3, cons(Xx, Xl4))) & (Xl2 = tptp_fun_____(Xl3, Xl4))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.61/0.79 tff(21,plain,(
% 0.61/0.79 ![Xx: $i, Xl1: $i, Xl2: $i] : ((~delete_succeeds(Xx, Xl1, Xl2)) | (list_succeeds(tptp_fun_Xl3_120(Xl2, Xl1, Xx)) & (Xl1 = tptp_fun_____(tptp_fun_Xl3_120(Xl2, Xl1, Xx), cons(Xx, tptp_fun_Xl4_119(Xl2, Xl1, Xx)))) & (Xl2 = tptp_fun_____(tptp_fun_Xl3_120(Xl2, Xl1, Xx), tptp_fun_Xl4_119(Xl2, Xl1, Xx)))))),
% 0.61/0.79 inference(skolemize,[status(sab)],[20])).
% 0.61/0.79 tff(22,plain,
% 0.61/0.79 (![Xx: $i, Xl1: $i, Xl2: $i] : ((~delete_succeeds(Xx, Xl1, Xl2)) | (~((~list_succeeds(tptp_fun_Xl3_120(Xl2, Xl1, Xx))) | (~(Xl1 = tptp_fun_____(tptp_fun_Xl3_120(Xl2, Xl1, Xx), cons(Xx, tptp_fun_Xl4_119(Xl2, Xl1, Xx))))) | (~(Xl2 = tptp_fun_____(tptp_fun_Xl3_120(Xl2, Xl1, Xx), tptp_fun_Xl4_119(Xl2, Xl1, Xx)))))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.61/0.79 tff(23,plain,
% 0.61/0.79 (![Xx: $i, Xl1: $i, Xl2: $i] : ((~delete_succeeds(Xx, Xl1, Xl2)) | (~((~list_succeeds(tptp_fun_Xl3_120(Xl2, Xl1, Xx))) | (~(Xl1 = tptp_fun_____(tptp_fun_Xl3_120(Xl2, Xl1, Xx), cons(Xx, tptp_fun_Xl4_119(Xl2, Xl1, Xx))))) | (~(Xl2 = tptp_fun_____(tptp_fun_Xl3_120(Xl2, Xl1, Xx), tptp_fun_Xl4_119(Xl2, Xl1, Xx)))))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[22, 12])).
% 0.61/0.79 tff(24,plain,
% 0.61/0.79 (((~![Xx: $i, Xl1: $i, Xl2: $i] : ((~delete_succeeds(Xx, Xl1, Xl2)) | (~((~list_succeeds(tptp_fun_Xl3_120(Xl2, Xl1, Xx))) | (~(Xl1 = tptp_fun_____(tptp_fun_Xl3_120(Xl2, Xl1, Xx), cons(Xx, tptp_fun_Xl4_119(Xl2, Xl1, Xx))))) | (~(Xl2 = tptp_fun_____(tptp_fun_Xl3_120(Xl2, Xl1, Xx), tptp_fun_Xl4_119(Xl2, Xl1, Xx)))))))) | ((~delete_succeeds(Xx!131, Xl1!130, Xl2!129)) | (~((~list_succeeds(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))) | (~(Xl1!130 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))) | (~(Xl2!129 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))))))) <=> ((~![Xx: $i, Xl1: $i, Xl2: $i] : ((~delete_succeeds(Xx, Xl1, Xl2)) | (~((~list_succeeds(tptp_fun_Xl3_120(Xl2, Xl1, Xx))) | (~(Xl1 = tptp_fun_____(tptp_fun_Xl3_120(Xl2, Xl1, Xx), cons(Xx, tptp_fun_Xl4_119(Xl2, Xl1, Xx))))) | (~(Xl2 = tptp_fun_____(tptp_fun_Xl3_120(Xl2, Xl1, Xx), tptp_fun_Xl4_119(Xl2, Xl1, Xx)))))))) | (~delete_succeeds(Xx!131, Xl1!130, Xl2!129)) | (~((~list_succeeds(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))) | (~(Xl1!130 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))) | (~(Xl2!129 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))))))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(25,plain,
% 0.61/0.79 ((~![Xx: $i, Xl1: $i, Xl2: $i] : ((~delete_succeeds(Xx, Xl1, Xl2)) | (~((~list_succeeds(tptp_fun_Xl3_120(Xl2, Xl1, Xx))) | (~(Xl1 = tptp_fun_____(tptp_fun_Xl3_120(Xl2, Xl1, Xx), cons(Xx, tptp_fun_Xl4_119(Xl2, Xl1, Xx))))) | (~(Xl2 = tptp_fun_____(tptp_fun_Xl3_120(Xl2, Xl1, Xx), tptp_fun_Xl4_119(Xl2, Xl1, Xx)))))))) | ((~delete_succeeds(Xx!131, Xl1!130, Xl2!129)) | (~((~list_succeeds(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))) | (~(Xl1!130 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))) | (~(Xl2!129 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))))))),
% 0.61/0.79 inference(quant_inst,[status(thm)],[])).
% 0.61/0.79 tff(26,plain,
% 0.61/0.79 ((~![Xx: $i, Xl1: $i, Xl2: $i] : ((~delete_succeeds(Xx, Xl1, Xl2)) | (~((~list_succeeds(tptp_fun_Xl3_120(Xl2, Xl1, Xx))) | (~(Xl1 = tptp_fun_____(tptp_fun_Xl3_120(Xl2, Xl1, Xx), cons(Xx, tptp_fun_Xl4_119(Xl2, Xl1, Xx))))) | (~(Xl2 = tptp_fun_____(tptp_fun_Xl3_120(Xl2, Xl1, Xx), tptp_fun_Xl4_119(Xl2, Xl1, Xx)))))))) | (~delete_succeeds(Xx!131, Xl1!130, Xl2!129)) | (~((~list_succeeds(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))) | (~(Xl1!130 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))) | (~(Xl2!129 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.61/0.79 tff(27,plain,
% 0.61/0.79 (~((~list_succeeds(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))) | (~(Xl1!130 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))) | (~(Xl2!129 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[26, 23, 10])).
% 0.61/0.79 tff(28,plain,
% 0.61/0.79 (((~list_succeeds(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))) | (~(Xl1!130 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))) | (~(Xl2!129 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))) | (Xl2!129 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))),
% 0.61/0.79 inference(tautology,[status(thm)],[])).
% 0.61/0.79 tff(29,plain,
% 0.61/0.79 (Xl2!129 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.61/0.79 tff(30,plain,
% 0.61/0.79 (tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)) = Xl2!129),
% 0.61/0.79 inference(symmetry,[status(thm)],[29])).
% 0.61/0.79 tff(31,plain,
% 0.61/0.79 (list_succeeds(tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) <=> list_succeeds(Xl2!129)),
% 0.61/0.79 inference(monotonicity,[status(thm)],[30])).
% 0.61/0.79 tff(32,plain,
% 0.61/0.79 (list_succeeds(Xl2!129) <=> list_succeeds(tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))),
% 0.61/0.79 inference(symmetry,[status(thm)],[31])).
% 0.61/0.79 tff(33,plain,
% 0.61/0.79 (list_succeeds(Xl1!130)),
% 0.61/0.79 inference(and_elim,[status(thm)],[9])).
% 0.61/0.79 tff(34,plain,
% 0.61/0.79 (^[Xx: $i, Xl1: $i, Xl2: $i] : refl((list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~delete_succeeds(Xx, Xl1, Xl2))) <=> (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~delete_succeeds(Xx, Xl1, Xl2))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(35,plain,
% 0.61/0.79 (![Xx: $i, Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~delete_succeeds(Xx, Xl1, Xl2))) <=> ![Xx: $i, Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~delete_succeeds(Xx, Xl1, Xl2)))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[34])).
% 0.61/0.79 tff(36,plain,
% 0.61/0.79 (^[Xx: $i, Xl1: $i, Xl2: $i] : trans(monotonicity(trans(monotonicity(rewrite((delete_succeeds(Xx, Xl1, Xl2) & list_succeeds(Xl1)) <=> (~((~list_succeeds(Xl1)) | (~delete_succeeds(Xx, Xl1, Xl2))))), ((~(delete_succeeds(Xx, Xl1, Xl2) & list_succeeds(Xl1))) <=> (~(~((~list_succeeds(Xl1)) | (~delete_succeeds(Xx, Xl1, Xl2))))))), rewrite((~(~((~list_succeeds(Xl1)) | (~delete_succeeds(Xx, Xl1, Xl2))))) <=> ((~list_succeeds(Xl1)) | (~delete_succeeds(Xx, Xl1, Xl2)))), ((~(delete_succeeds(Xx, Xl1, Xl2) & list_succeeds(Xl1))) <=> ((~list_succeeds(Xl1)) | (~delete_succeeds(Xx, Xl1, Xl2))))), ((list_succeeds(Xl2) | (~(delete_succeeds(Xx, Xl1, Xl2) & list_succeeds(Xl1)))) <=> (list_succeeds(Xl2) | ((~list_succeeds(Xl1)) | (~delete_succeeds(Xx, Xl1, Xl2)))))), rewrite((list_succeeds(Xl2) | ((~list_succeeds(Xl1)) | (~delete_succeeds(Xx, Xl1, Xl2)))) <=> (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~delete_succeeds(Xx, Xl1, Xl2)))), ((list_succeeds(Xl2) | (~(delete_succeeds(Xx, Xl1, Xl2) & list_succeeds(Xl1)))) <=> (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~delete_succeeds(Xx, Xl1, Xl2)))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(37,plain,
% 0.61/0.79 (![Xx: $i, Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~(delete_succeeds(Xx, Xl1, Xl2) & list_succeeds(Xl1)))) <=> ![Xx: $i, Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~delete_succeeds(Xx, Xl1, Xl2)))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[36])).
% 0.61/0.79 tff(38,plain,
% 0.61/0.79 (![Xx: $i, Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~(delete_succeeds(Xx, Xl1, Xl2) & list_succeeds(Xl1)))) <=> ![Xx: $i, Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~(delete_succeeds(Xx, Xl1, Xl2) & list_succeeds(Xl1))))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(39,plain,
% 0.61/0.79 (^[Xx: $i, Xl1: $i, Xl2: $i] : rewrite(((delete_succeeds(Xx, Xl1, Xl2) & list_succeeds(Xl1)) => list_succeeds(Xl2)) <=> (list_succeeds(Xl2) | (~(delete_succeeds(Xx, Xl1, Xl2) & list_succeeds(Xl1)))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(40,plain,
% 0.61/0.79 (![Xx: $i, Xl1: $i, Xl2: $i] : ((delete_succeeds(Xx, Xl1, Xl2) & list_succeeds(Xl1)) => list_succeeds(Xl2)) <=> ![Xx: $i, Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~(delete_succeeds(Xx, Xl1, Xl2) & list_succeeds(Xl1))))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[39])).
% 0.61/0.79 tff(41,axiom,(![Xx: $i, Xl1: $i, Xl2: $i] : ((delete_succeeds(Xx, Xl1, Xl2) & list_succeeds(Xl1)) => list_succeeds(Xl2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''axiom-(delete:types:1)'')).
% 0.61/0.79 tff(42,plain,
% 0.61/0.79 (![Xx: $i, Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~(delete_succeeds(Xx, Xl1, Xl2) & list_succeeds(Xl1))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.61/0.79 tff(43,plain,
% 0.61/0.79 (![Xx: $i, Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~(delete_succeeds(Xx, Xl1, Xl2) & list_succeeds(Xl1))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.61/0.79 tff(44,plain,(
% 0.61/0.79 ![Xx: $i, Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~(delete_succeeds(Xx, Xl1, Xl2) & list_succeeds(Xl1))))),
% 0.61/0.79 inference(skolemize,[status(sab)],[43])).
% 0.61/0.79 tff(45,plain,
% 0.61/0.79 (![Xx: $i, Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~delete_succeeds(Xx, Xl1, Xl2)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.61/0.79 tff(46,plain,
% 0.61/0.79 (![Xx: $i, Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~delete_succeeds(Xx, Xl1, Xl2)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[45, 35])).
% 0.61/0.79 tff(47,plain,
% 0.61/0.79 (((~![Xx: $i, Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~delete_succeeds(Xx, Xl1, Xl2)))) | (list_succeeds(Xl2!129) | (~list_succeeds(Xl1!130)) | (~delete_succeeds(Xx!131, Xl1!130, Xl2!129)))) <=> ((~![Xx: $i, Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~delete_succeeds(Xx, Xl1, Xl2)))) | list_succeeds(Xl2!129) | (~list_succeeds(Xl1!130)) | (~delete_succeeds(Xx!131, Xl1!130, Xl2!129)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(48,plain,
% 0.61/0.79 ((~![Xx: $i, Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~delete_succeeds(Xx, Xl1, Xl2)))) | (list_succeeds(Xl2!129) | (~list_succeeds(Xl1!130)) | (~delete_succeeds(Xx!131, Xl1!130, Xl2!129)))),
% 0.61/0.79 inference(quant_inst,[status(thm)],[])).
% 0.61/0.79 tff(49,plain,
% 0.61/0.79 ((~![Xx: $i, Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~delete_succeeds(Xx, Xl1, Xl2)))) | list_succeeds(Xl2!129) | (~list_succeeds(Xl1!130)) | (~delete_succeeds(Xx!131, Xl1!130, Xl2!129))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.61/0.79 tff(50,plain,
% 0.61/0.79 (list_succeeds(Xl2!129)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[49, 46, 33, 10])).
% 0.61/0.79 tff(51,plain,
% 0.61/0.79 (list_succeeds(tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[50, 32])).
% 0.61/0.79 tff(52,plain,
% 0.61/0.79 (((~list_succeeds(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))) | (~(Xl1!130 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))) | (~(Xl2!129 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))) | list_succeeds(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))),
% 0.61/0.79 inference(tautology,[status(thm)],[])).
% 0.61/0.79 tff(53,plain,
% 0.61/0.79 (list_succeeds(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[52, 27])).
% 0.61/0.79 tff(54,plain,
% 0.61/0.79 (^[Xl1: $i, Xl2: $i] : refl((list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~list_succeeds(tptp_fun_____(Xl1, Xl2)))) <=> (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~list_succeeds(tptp_fun_____(Xl1, Xl2)))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(55,plain,
% 0.61/0.79 (![Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~list_succeeds(tptp_fun_____(Xl1, Xl2)))) <=> ![Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~list_succeeds(tptp_fun_____(Xl1, Xl2))))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[54])).
% 0.61/0.79 tff(56,plain,
% 0.61/0.79 (^[Xl1: $i, Xl2: $i] : trans(monotonicity(trans(monotonicity(rewrite((list_succeeds(Xl1) & list_succeeds(tptp_fun_____(Xl1, Xl2))) <=> (~((~list_succeeds(Xl1)) | (~list_succeeds(tptp_fun_____(Xl1, Xl2)))))), ((~(list_succeeds(Xl1) & list_succeeds(tptp_fun_____(Xl1, Xl2)))) <=> (~(~((~list_succeeds(Xl1)) | (~list_succeeds(tptp_fun_____(Xl1, Xl2)))))))), rewrite((~(~((~list_succeeds(Xl1)) | (~list_succeeds(tptp_fun_____(Xl1, Xl2)))))) <=> ((~list_succeeds(Xl1)) | (~list_succeeds(tptp_fun_____(Xl1, Xl2))))), ((~(list_succeeds(Xl1) & list_succeeds(tptp_fun_____(Xl1, Xl2)))) <=> ((~list_succeeds(Xl1)) | (~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))))))), rewrite((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(Xl2) | (~(list_succeeds(Xl1) & list_succeeds(tptp_fun_____(Xl1, Xl2))))) <=> (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~list_succeeds(tptp_fun_____(Xl1, Xl2))))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(57,plain,
% 0.61/0.79 (![Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~(list_succeeds(Xl1) & list_succeeds(tptp_fun_____(Xl1, Xl2))))) <=> ![Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~list_succeeds(tptp_fun_____(Xl1, Xl2))))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[56])).
% 0.61/0.79 tff(58,plain,
% 0.61/0.79 (![Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~(list_succeeds(Xl1) & list_succeeds(tptp_fun_____(Xl1, Xl2))))) <=> ![Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~(list_succeeds(Xl1) & list_succeeds(tptp_fun_____(Xl1, Xl2)))))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(59,plain,
% 0.61/0.79 (^[Xl1: $i, Xl2: $i] : rewrite(((list_succeeds(Xl1) & list_succeeds(tptp_fun_____(Xl1, Xl2))) => list_succeeds(Xl2)) <=> (list_succeeds(Xl2) | (~(list_succeeds(Xl1) & list_succeeds(tptp_fun_____(Xl1, Xl2))))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(60,plain,
% 0.61/0.79 (![Xl1: $i, Xl2: $i] : ((list_succeeds(Xl1) & list_succeeds(tptp_fun_____(Xl1, Xl2))) => list_succeeds(Xl2)) <=> ![Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~(list_succeeds(Xl1) & list_succeeds(tptp_fun_____(Xl1, Xl2)))))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[59])).
% 0.61/0.79 tff(61,axiom,(![Xl1: $i, Xl2: $i] : ((list_succeeds(Xl1) & list_succeeds(tptp_fun_____(Xl1, Xl2))) => list_succeeds(Xl2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''axiom-(app:types:2)'')).
% 0.61/0.79 tff(62,plain,
% 0.61/0.79 (![Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~(list_succeeds(Xl1) & list_succeeds(tptp_fun_____(Xl1, Xl2)))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.61/0.79 tff(63,plain,
% 0.61/0.79 (![Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~(list_succeeds(Xl1) & list_succeeds(tptp_fun_____(Xl1, Xl2)))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.61/0.79 tff(64,plain,(
% 0.61/0.79 ![Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~(list_succeeds(Xl1) & list_succeeds(tptp_fun_____(Xl1, Xl2)))))),
% 0.61/0.79 inference(skolemize,[status(sab)],[63])).
% 0.61/0.79 tff(65,plain,
% 0.61/0.79 (![Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~list_succeeds(tptp_fun_____(Xl1, Xl2))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.61/0.80 tff(66,plain,
% 0.61/0.80 (![Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~list_succeeds(tptp_fun_____(Xl1, Xl2))))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[65, 55])).
% 0.61/0.80 tff(67,plain,
% 0.61/0.80 (((~![Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~list_succeeds(tptp_fun_____(Xl1, Xl2))))) | (list_succeeds(tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))))) <=> ((~![Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~list_succeeds(tptp_fun_____(Xl1, Xl2))))) | list_succeeds(tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(68,plain,
% 0.61/0.80 ((~![Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~list_succeeds(tptp_fun_____(Xl1, Xl2))))) | (list_succeeds(tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))))),
% 0.61/0.80 inference(quant_inst,[status(thm)],[])).
% 0.61/0.80 tff(69,plain,
% 0.61/0.80 ((~![Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~list_succeeds(tptp_fun_____(Xl1, Xl2))))) | list_succeeds(tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.61/0.80 tff(70,plain,
% 0.61/0.80 (list_succeeds(tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)) | (~list_succeeds(tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[69, 66, 53])).
% 0.61/0.80 tff(71,plain,
% 0.61/0.80 (list_succeeds(tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[70, 51])).
% 0.61/0.80 tff(72,plain,
% 0.61/0.80 (^[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))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(73,plain,
% 0.61/0.80 (![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)))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[72])).
% 0.61/0.80 tff(74,plain,
% 0.61/0.80 (^[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)))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(75,plain,
% 0.61/0.80 (![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)))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[74])).
% 0.61/0.80 tff(76,plain,
% 0.61/0.80 (![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))))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(77,plain,
% 0.61/0.80 (^[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)))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(78,plain,
% 0.61/0.80 (![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))))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[77])).
% 0.61/0.80 tff(79,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)'')).
% 0.61/0.80 tff(80,plain,
% 0.61/0.80 (![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))))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.61/0.80 tff(81,plain,
% 0.61/0.80 (![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))))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.61/0.80 tff(82,plain,(
% 0.61/0.80 ![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))))),
% 0.61/0.80 inference(skolemize,[status(sab)],[81])).
% 0.61/0.80 tff(83,plain,
% 0.61/0.80 (![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)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.61/0.80 tff(84,plain,
% 0.61/0.80 (![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)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[83, 73])).
% 0.61/0.80 tff(85,plain,
% 0.61/0.80 (((~![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(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) | (occ(Xx!131, tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) = tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))))) <=> ((~![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(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) | (occ(Xx!131, tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) = tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(86,plain,
% 0.61/0.80 (((occ(Xx!131, tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) = tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) | (~list_succeeds(tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)))) <=> ((~list_succeeds(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) | (occ(Xx!131, tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) = tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(87,plain,
% 0.61/0.80 (((~![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(Xx!131, tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) = tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) | (~list_succeeds(tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))))) <=> ((~![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(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) | (occ(Xx!131, tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) = tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[86])).
% 0.61/0.80 tff(88,plain,
% 0.61/0.80 (((~![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(Xx!131, tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) = tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) | (~list_succeeds(tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))))) <=> ((~![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(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) | (occ(Xx!131, tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) = tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))))),
% 0.61/0.80 inference(transitivity,[status(thm)],[87, 85])).
% 0.61/0.80 tff(89,plain,
% 0.61/0.80 ((~![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(Xx!131, tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) = tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) | (~list_succeeds(tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))))),
% 0.61/0.80 inference(quant_inst,[status(thm)],[])).
% 0.61/0.80 tff(90,plain,
% 0.61/0.80 ((~![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(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) | (occ(Xx!131, tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) = tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.61/0.80 tff(91,plain,
% 0.61/0.80 ((~list_succeeds(tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) | (occ(Xx!131, tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) = tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[90, 84, 53])).
% 0.61/0.80 tff(92,plain,
% 0.61/0.80 (occ(Xx!131, tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) = tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[91, 71])).
% 0.61/0.80 tff(93,plain,
% 0.61/0.80 (occ(Xx!131, tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) = occ(Xx!131, Xl2!129)),
% 0.61/0.80 inference(monotonicity,[status(thm)],[30])).
% 0.61/0.80 tff(94,plain,
% 0.61/0.80 (occ(Xx!131, Xl2!129) = occ(Xx!131, tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))),
% 0.61/0.80 inference(symmetry,[status(thm)],[93])).
% 0.61/0.80 tff(95,plain,
% 0.61/0.80 (occ(Xx!131, Xl2!129) = tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))),
% 0.61/0.80 inference(transitivity,[status(thm)],[94, 92])).
% 0.61/0.80 tff(96,plain,
% 0.61/0.80 (s(occ(Xx!131, Xl2!129)) = s(tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[95])).
% 0.61/0.80 tff(97,plain,
% 0.61/0.80 (s(tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) = s(occ(Xx!131, Xl2!129))),
% 0.61/0.80 inference(symmetry,[status(thm)],[96])).
% 0.61/0.80 tff(98,plain,
% 0.61/0.80 (^[Xx: $i, Xl: $i] : refl((nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl))) <=> (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(99,plain,
% 0.61/0.80 (![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl))) <=> ![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[98])).
% 0.61/0.80 tff(100,plain,
% 0.61/0.80 (![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl))) <=> ![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(101,plain,
% 0.61/0.80 (^[Xx: $i, Xl: $i] : rewrite((list_succeeds(Xl) => nat_succeeds(occ(Xx, Xl))) <=> (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(102,plain,
% 0.61/0.80 (![Xx: $i, Xl: $i] : (list_succeeds(Xl) => nat_succeeds(occ(Xx, Xl))) <=> ![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[101])).
% 0.61/0.80 tff(103,axiom,(![Xx: $i, Xl: $i] : (list_succeeds(Xl) => nat_succeeds(occ(Xx, Xl)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''corollary-(occ:types)'')).
% 0.61/0.80 tff(104,plain,
% 0.61/0.80 (![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.61/0.80 tff(105,plain,
% 0.61/0.80 (![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.61/0.80 tff(106,plain,(
% 0.61/0.80 ![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))),
% 0.61/0.80 inference(skolemize,[status(sab)],[105])).
% 0.61/0.80 tff(107,plain,
% 0.61/0.80 (![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.61/0.80 tff(108,plain,
% 0.61/0.80 (((~![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))) | (nat_succeeds(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))))) <=> ((~![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))) | nat_succeeds(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(109,plain,
% 0.61/0.80 ((~![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))) | (nat_succeeds(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))))),
% 0.61/0.80 inference(quant_inst,[status(thm)],[])).
% 0.61/0.80 tff(110,plain,
% 0.61/0.80 ((~![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))) | nat_succeeds(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.61/0.80 tff(111,plain,
% 0.61/0.80 (nat_succeeds(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)))),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[110, 107, 53])).
% 0.61/0.80 tff(112,plain,
% 0.61/0.80 (^[Xx: $i, Xy: $i] : refl(((~nat_succeeds(Xx)) | (tptp_fun_____(s(Xx), Xy) = s(tptp_fun_____(Xx, Xy)))) <=> ((~nat_succeeds(Xx)) | (tptp_fun_____(s(Xx), Xy) = s(tptp_fun_____(Xx, Xy)))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(113,plain,
% 0.61/0.80 (![Xx: $i, Xy: $i] : ((~nat_succeeds(Xx)) | (tptp_fun_____(s(Xx), Xy) = s(tptp_fun_____(Xx, Xy)))) <=> ![Xx: $i, Xy: $i] : ((~nat_succeeds(Xx)) | (tptp_fun_____(s(Xx), Xy) = s(tptp_fun_____(Xx, Xy))))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[112])).
% 0.61/0.80 tff(114,plain,
% 0.61/0.80 (![Xx: $i, Xy: $i] : ((~nat_succeeds(Xx)) | (tptp_fun_____(s(Xx), Xy) = s(tptp_fun_____(Xx, Xy)))) <=> ![Xx: $i, Xy: $i] : ((~nat_succeeds(Xx)) | (tptp_fun_____(s(Xx), Xy) = s(tptp_fun_____(Xx, Xy))))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(115,plain,
% 0.61/0.80 (^[Xx: $i, Xy: $i] : rewrite((nat_succeeds(Xx) => (tptp_fun_____(s(Xx), Xy) = s(tptp_fun_____(Xx, Xy)))) <=> ((~nat_succeeds(Xx)) | (tptp_fun_____(s(Xx), Xy) = s(tptp_fun_____(Xx, Xy)))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(116,plain,
% 0.61/0.80 (![Xx: $i, Xy: $i] : (nat_succeeds(Xx) => (tptp_fun_____(s(Xx), Xy) = s(tptp_fun_____(Xx, Xy)))) <=> ![Xx: $i, Xy: $i] : ((~nat_succeeds(Xx)) | (tptp_fun_____(s(Xx), Xy) = s(tptp_fun_____(Xx, Xy))))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[115])).
% 0.61/0.80 tff(117,axiom,(![Xx: $i, Xy: $i] : (nat_succeeds(Xx) => (tptp_fun_____(s(Xx), Xy) = s(tptp_fun_____(Xx, Xy))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''axiom-(plus:successor)'')).
% 0.61/0.80 tff(118,plain,
% 0.61/0.80 (![Xx: $i, Xy: $i] : ((~nat_succeeds(Xx)) | (tptp_fun_____(s(Xx), Xy) = s(tptp_fun_____(Xx, Xy))))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.61/0.80 tff(119,plain,
% 0.61/0.80 (![Xx: $i, Xy: $i] : ((~nat_succeeds(Xx)) | (tptp_fun_____(s(Xx), Xy) = s(tptp_fun_____(Xx, Xy))))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.61/0.80 tff(120,plain,(
% 0.61/0.80 ![Xx: $i, Xy: $i] : ((~nat_succeeds(Xx)) | (tptp_fun_____(s(Xx), Xy) = s(tptp_fun_____(Xx, Xy))))),
% 0.61/0.80 inference(skolemize,[status(sab)],[119])).
% 0.61/0.80 tff(121,plain,
% 0.61/0.80 (![Xx: $i, Xy: $i] : ((~nat_succeeds(Xx)) | (tptp_fun_____(s(Xx), Xy) = s(tptp_fun_____(Xx, Xy))))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.61/0.80 tff(122,plain,
% 0.61/0.80 (((~![Xx: $i, Xy: $i] : ((~nat_succeeds(Xx)) | (tptp_fun_____(s(Xx), Xy) = s(tptp_fun_____(Xx, Xy))))) | ((~nat_succeeds(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)))) | (tptp_fun_____(s(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) = s(tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))))) <=> ((~![Xx: $i, Xy: $i] : ((~nat_succeeds(Xx)) | (tptp_fun_____(s(Xx), Xy) = s(tptp_fun_____(Xx, Xy))))) | (~nat_succeeds(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)))) | (tptp_fun_____(s(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) = s(tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(123,plain,
% 0.61/0.80 ((~![Xx: $i, Xy: $i] : ((~nat_succeeds(Xx)) | (tptp_fun_____(s(Xx), Xy) = s(tptp_fun_____(Xx, Xy))))) | ((~nat_succeeds(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)))) | (tptp_fun_____(s(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) = s(tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))))),
% 0.61/0.80 inference(quant_inst,[status(thm)],[])).
% 0.61/0.80 tff(124,plain,
% 0.61/0.80 ((~![Xx: $i, Xy: $i] : ((~nat_succeeds(Xx)) | (tptp_fun_____(s(Xx), Xy) = s(tptp_fun_____(Xx, Xy))))) | (~nat_succeeds(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)))) | (tptp_fun_____(s(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) = s(tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.61/0.80 tff(125,plain,
% 0.61/0.80 ((~nat_succeeds(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)))) | (tptp_fun_____(s(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) = s(tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))))),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[124, 121])).
% 0.61/0.80 tff(126,plain,
% 0.61/0.80 (tptp_fun_____(s(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) = s(tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[125, 111])).
% 0.61/0.80 tff(127,plain,
% 0.61/0.80 (((~![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))) | (nat_succeeds(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))) <=> ((~![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))) | nat_succeeds(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(128,plain,
% 0.61/0.80 ((~![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))) | (nat_succeeds(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))),
% 0.61/0.80 inference(quant_inst,[status(thm)],[])).
% 0.61/0.80 tff(129,plain,
% 0.61/0.80 ((~![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))) | nat_succeeds(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.61/0.80 tff(130,plain,
% 0.61/0.80 (nat_succeeds(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[129, 107, 71])).
% 0.61/0.80 tff(131,plain,
% 0.61/0.80 (^[Xx: $i, Xy: $i] : refl(((tptp_fun_____(Xx, s(Xy)) = tptp_fun_____(s(Xx), Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx))) <=> ((tptp_fun_____(Xx, s(Xy)) = tptp_fun_____(s(Xx), Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(132,plain,
% 0.61/0.80 (![Xx: $i, Xy: $i] : ((tptp_fun_____(Xx, s(Xy)) = tptp_fun_____(s(Xx), Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx))) <=> ![Xx: $i, Xy: $i] : ((tptp_fun_____(Xx, s(Xy)) = tptp_fun_____(s(Xx), Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[131])).
% 0.61/0.80 tff(133,plain,
% 0.61/0.80 (^[Xx: $i, Xy: $i] : trans(monotonicity(trans(monotonicity(rewrite((nat_succeeds(Xx) & nat_succeeds(Xy)) <=> (~((~nat_succeeds(Xy)) | (~nat_succeeds(Xx))))), ((~(nat_succeeds(Xx) & nat_succeeds(Xy))) <=> (~(~((~nat_succeeds(Xy)) | (~nat_succeeds(Xx))))))), rewrite((~(~((~nat_succeeds(Xy)) | (~nat_succeeds(Xx))))) <=> ((~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))), ((~(nat_succeeds(Xx) & nat_succeeds(Xy))) <=> ((~nat_succeeds(Xy)) | (~nat_succeeds(Xx))))), (((~(nat_succeeds(Xx) & nat_succeeds(Xy))) | (tptp_fun_____(Xx, s(Xy)) = tptp_fun_____(s(Xx), Xy))) <=> (((~nat_succeeds(Xy)) | (~nat_succeeds(Xx))) | (tptp_fun_____(Xx, s(Xy)) = tptp_fun_____(s(Xx), Xy))))), rewrite((((~nat_succeeds(Xy)) | (~nat_succeeds(Xx))) | (tptp_fun_____(Xx, s(Xy)) = tptp_fun_____(s(Xx), Xy))) <=> ((tptp_fun_____(Xx, s(Xy)) = tptp_fun_____(s(Xx), Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))), (((~(nat_succeeds(Xx) & nat_succeeds(Xy))) | (tptp_fun_____(Xx, s(Xy)) = tptp_fun_____(s(Xx), Xy))) <=> ((tptp_fun_____(Xx, s(Xy)) = tptp_fun_____(s(Xx), Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(134,plain,
% 0.61/0.80 (![Xx: $i, Xy: $i] : ((~(nat_succeeds(Xx) & nat_succeeds(Xy))) | (tptp_fun_____(Xx, s(Xy)) = tptp_fun_____(s(Xx), Xy))) <=> ![Xx: $i, Xy: $i] : ((tptp_fun_____(Xx, s(Xy)) = tptp_fun_____(s(Xx), Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[133])).
% 0.61/0.80 tff(135,plain,
% 0.61/0.80 (![Xx: $i, Xy: $i] : ((~(nat_succeeds(Xx) & nat_succeeds(Xy))) | (tptp_fun_____(Xx, s(Xy)) = tptp_fun_____(s(Xx), Xy))) <=> ![Xx: $i, Xy: $i] : ((~(nat_succeeds(Xx) & nat_succeeds(Xy))) | (tptp_fun_____(Xx, s(Xy)) = tptp_fun_____(s(Xx), Xy)))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(136,plain,
% 0.61/0.80 (^[Xx: $i, Xy: $i] : rewrite(((nat_succeeds(Xx) & nat_succeeds(Xy)) => (tptp_fun_____(Xx, s(Xy)) = tptp_fun_____(s(Xx), Xy))) <=> ((~(nat_succeeds(Xx) & nat_succeeds(Xy))) | (tptp_fun_____(Xx, s(Xy)) = tptp_fun_____(s(Xx), Xy))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(137,plain,
% 0.61/0.80 (![Xx: $i, Xy: $i] : ((nat_succeeds(Xx) & nat_succeeds(Xy)) => (tptp_fun_____(Xx, s(Xy)) = tptp_fun_____(s(Xx), Xy))) <=> ![Xx: $i, Xy: $i] : ((~(nat_succeeds(Xx) & nat_succeeds(Xy))) | (tptp_fun_____(Xx, s(Xy)) = tptp_fun_____(s(Xx), Xy)))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[136])).
% 0.61/0.80 tff(138,axiom,(![Xx: $i, Xy: $i] : ((nat_succeeds(Xx) & nat_succeeds(Xy)) => (tptp_fun_____(Xx, s(Xy)) = tptp_fun_____(s(Xx), Xy)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''axiom-(plus:successor)_002'')).
% 0.61/0.80 tff(139,plain,
% 0.61/0.80 (![Xx: $i, Xy: $i] : ((~(nat_succeeds(Xx) & nat_succeeds(Xy))) | (tptp_fun_____(Xx, s(Xy)) = tptp_fun_____(s(Xx), Xy)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.61/0.80 tff(140,plain,
% 0.61/0.80 (![Xx: $i, Xy: $i] : ((~(nat_succeeds(Xx) & nat_succeeds(Xy))) | (tptp_fun_____(Xx, s(Xy)) = tptp_fun_____(s(Xx), Xy)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.61/0.80 tff(141,plain,(
% 0.61/0.80 ![Xx: $i, Xy: $i] : ((~(nat_succeeds(Xx) & nat_succeeds(Xy))) | (tptp_fun_____(Xx, s(Xy)) = tptp_fun_____(s(Xx), Xy)))),
% 0.61/0.80 inference(skolemize,[status(sab)],[140])).
% 0.61/0.80 tff(142,plain,
% 0.61/0.80 (![Xx: $i, Xy: $i] : ((tptp_fun_____(Xx, s(Xy)) = tptp_fun_____(s(Xx), Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[141, 134])).
% 0.61/0.80 tff(143,plain,
% 0.61/0.80 (![Xx: $i, Xy: $i] : ((tptp_fun_____(Xx, s(Xy)) = tptp_fun_____(s(Xx), Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[142, 132])).
% 0.61/0.80 tff(144,plain,
% 0.61/0.80 (((~![Xx: $i, Xy: $i] : ((tptp_fun_____(Xx, s(Xy)) = tptp_fun_____(s(Xx), Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))) | ((~nat_succeeds(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)))) | (~nat_succeeds(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) | (tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), s(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) = tptp_fun_____(s(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))))) <=> ((~![Xx: $i, Xy: $i] : ((tptp_fun_____(Xx, s(Xy)) = tptp_fun_____(s(Xx), Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))) | (~nat_succeeds(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)))) | (~nat_succeeds(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) | (tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), s(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) = tptp_fun_____(s(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))))),
% 0.61/0.81 inference(rewrite,[status(thm)],[])).
% 0.61/0.81 tff(145,plain,
% 0.61/0.81 (((tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), s(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) = tptp_fun_____(s(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) | (~nat_succeeds(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) | (~nat_succeeds(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))))) <=> ((~nat_succeeds(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)))) | (~nat_succeeds(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) | (tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), s(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) = tptp_fun_____(s(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))))),
% 0.61/0.81 inference(rewrite,[status(thm)],[])).
% 0.61/0.81 tff(146,plain,
% 0.61/0.81 (((~![Xx: $i, Xy: $i] : ((tptp_fun_____(Xx, s(Xy)) = tptp_fun_____(s(Xx), Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))) | ((tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), s(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) = tptp_fun_____(s(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) | (~nat_succeeds(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) | (~nat_succeeds(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)))))) <=> ((~![Xx: $i, Xy: $i] : ((tptp_fun_____(Xx, s(Xy)) = tptp_fun_____(s(Xx), Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))) | ((~nat_succeeds(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)))) | (~nat_succeeds(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) | (tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), s(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) = tptp_fun_____(s(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))))),
% 0.61/0.81 inference(monotonicity,[status(thm)],[145])).
% 0.61/0.81 tff(147,plain,
% 0.61/0.81 (((~![Xx: $i, Xy: $i] : ((tptp_fun_____(Xx, s(Xy)) = tptp_fun_____(s(Xx), Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))) | ((tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), s(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) = tptp_fun_____(s(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) | (~nat_succeeds(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) | (~nat_succeeds(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)))))) <=> ((~![Xx: $i, Xy: $i] : ((tptp_fun_____(Xx, s(Xy)) = tptp_fun_____(s(Xx), Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))) | (~nat_succeeds(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)))) | (~nat_succeeds(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) | (tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), s(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) = tptp_fun_____(s(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))))),
% 0.61/0.81 inference(transitivity,[status(thm)],[146, 144])).
% 0.61/0.81 tff(148,plain,
% 0.61/0.81 ((~![Xx: $i, Xy: $i] : ((tptp_fun_____(Xx, s(Xy)) = tptp_fun_____(s(Xx), Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))) | ((tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), s(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) = tptp_fun_____(s(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) | (~nat_succeeds(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) | (~nat_succeeds(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)))))),
% 0.61/0.81 inference(quant_inst,[status(thm)],[])).
% 0.61/0.81 tff(149,plain,
% 0.61/0.81 ((~![Xx: $i, Xy: $i] : ((tptp_fun_____(Xx, s(Xy)) = tptp_fun_____(s(Xx), Xy)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))) | (~nat_succeeds(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)))) | (~nat_succeeds(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) | (tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), s(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) = tptp_fun_____(s(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.61/0.81 tff(150,plain,
% 0.61/0.81 ((~nat_succeeds(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)))) | (~nat_succeeds(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) | (tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), s(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) = tptp_fun_____(s(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[149, 143])).
% 0.61/0.81 tff(151,plain,
% 0.61/0.81 (tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), s(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) = tptp_fun_____(s(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))), occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[150, 130, 111])).
% 0.61/0.81 tff(152,plain,
% 0.61/0.81 (^[Xx: $i, Xl: $i] : refl(((~list_succeeds(Xl)) | (occ(Xx, cons(Xx, Xl)) = s(occ(Xx, Xl)))) <=> ((~list_succeeds(Xl)) | (occ(Xx, cons(Xx, Xl)) = s(occ(Xx, Xl)))))),
% 0.61/0.81 inference(bind,[status(th)],[])).
% 0.61/0.81 tff(153,plain,
% 0.61/0.81 (![Xx: $i, Xl: $i] : ((~list_succeeds(Xl)) | (occ(Xx, cons(Xx, Xl)) = s(occ(Xx, Xl)))) <=> ![Xx: $i, Xl: $i] : ((~list_succeeds(Xl)) | (occ(Xx, cons(Xx, Xl)) = s(occ(Xx, Xl))))),
% 0.61/0.81 inference(quant_intro,[status(thm)],[152])).
% 0.61/0.81 tff(154,plain,
% 0.61/0.81 (![Xx: $i, Xl: $i] : ((~list_succeeds(Xl)) | (occ(Xx, cons(Xx, Xl)) = s(occ(Xx, Xl)))) <=> ![Xx: $i, Xl: $i] : ((~list_succeeds(Xl)) | (occ(Xx, cons(Xx, Xl)) = s(occ(Xx, Xl))))),
% 0.61/0.81 inference(rewrite,[status(thm)],[])).
% 0.61/0.81 tff(155,plain,
% 0.61/0.81 (^[Xx: $i, Xl: $i] : rewrite((list_succeeds(Xl) => (occ(Xx, cons(Xx, Xl)) = s(occ(Xx, Xl)))) <=> ((~list_succeeds(Xl)) | (occ(Xx, cons(Xx, Xl)) = s(occ(Xx, Xl)))))),
% 0.61/0.81 inference(bind,[status(th)],[])).
% 0.61/0.81 tff(156,plain,
% 0.61/0.81 (![Xx: $i, Xl: $i] : (list_succeeds(Xl) => (occ(Xx, cons(Xx, Xl)) = s(occ(Xx, Xl)))) <=> ![Xx: $i, Xl: $i] : ((~list_succeeds(Xl)) | (occ(Xx, cons(Xx, Xl)) = s(occ(Xx, Xl))))),
% 0.61/0.81 inference(quant_intro,[status(thm)],[155])).
% 0.61/0.81 tff(157,axiom,(![Xx: $i, Xl: $i] : (list_succeeds(Xl) => (occ(Xx, cons(Xx, Xl)) = s(occ(Xx, Xl))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''lemma-(occ:cons:eq)'')).
% 0.61/0.81 tff(158,plain,
% 0.61/0.81 (![Xx: $i, Xl: $i] : ((~list_succeeds(Xl)) | (occ(Xx, cons(Xx, Xl)) = s(occ(Xx, Xl))))),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.61/0.81 tff(159,plain,
% 0.61/0.81 (![Xx: $i, Xl: $i] : ((~list_succeeds(Xl)) | (occ(Xx, cons(Xx, Xl)) = s(occ(Xx, Xl))))),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[158, 154])).
% 0.61/0.81 tff(160,plain,(
% 0.61/0.81 ![Xx: $i, Xl: $i] : ((~list_succeeds(Xl)) | (occ(Xx, cons(Xx, Xl)) = s(occ(Xx, Xl))))),
% 0.61/0.81 inference(skolemize,[status(sab)],[159])).
% 0.61/0.81 tff(161,plain,
% 0.61/0.81 (![Xx: $i, Xl: $i] : ((~list_succeeds(Xl)) | (occ(Xx, cons(Xx, Xl)) = s(occ(Xx, Xl))))),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[160, 153])).
% 0.61/0.81 tff(162,plain,
% 0.61/0.81 (((~![Xx: $i, Xl: $i] : ((~list_succeeds(Xl)) | (occ(Xx, cons(Xx, Xl)) = s(occ(Xx, Xl))))) | ((~list_succeeds(tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) | (occ(Xx!131, cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) = s(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))))) <=> ((~![Xx: $i, Xl: $i] : ((~list_succeeds(Xl)) | (occ(Xx, cons(Xx, Xl)) = s(occ(Xx, Xl))))) | (~list_succeeds(tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) | (occ(Xx!131, cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) = s(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))))),
% 0.61/0.81 inference(rewrite,[status(thm)],[])).
% 0.61/0.81 tff(163,plain,
% 0.61/0.81 ((~![Xx: $i, Xl: $i] : ((~list_succeeds(Xl)) | (occ(Xx, cons(Xx, Xl)) = s(occ(Xx, Xl))))) | ((~list_succeeds(tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) | (occ(Xx!131, cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) = s(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))))),
% 0.61/0.81 inference(quant_inst,[status(thm)],[])).
% 0.61/0.81 tff(164,plain,
% 0.61/0.81 ((~![Xx: $i, Xl: $i] : ((~list_succeeds(Xl)) | (occ(Xx, cons(Xx, Xl)) = s(occ(Xx, Xl))))) | (~list_succeeds(tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) | (occ(Xx!131, cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) = s(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.61/0.81 tff(165,plain,
% 0.61/0.81 ((~list_succeeds(tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) | (occ(Xx!131, cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) = s(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[164, 161])).
% 0.61/0.81 tff(166,plain,
% 0.61/0.81 (occ(Xx!131, cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) = s(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[165, 71])).
% 0.61/0.81 tff(167,plain,
% 0.61/0.81 (s(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) = occ(Xx!131, cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))),
% 0.61/0.81 inference(symmetry,[status(thm)],[166])).
% 0.61/0.81 tff(168,plain,
% 0.61/0.81 (tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), s(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) = tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))),
% 0.61/0.81 inference(monotonicity,[status(thm)],[167])).
% 0.61/0.81 tff(169,plain,
% 0.61/0.81 (tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) = tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), s(occ(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))),
% 0.61/0.81 inference(symmetry,[status(thm)],[168])).
% 0.61/0.81 tff(170,plain,
% 0.61/0.81 (((~list_succeeds(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))) | (~(Xl1!130 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))) | (~(Xl2!129 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))) | (Xl1!130 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))),
% 0.61/0.81 inference(tautology,[status(thm)],[])).
% 0.61/0.81 tff(171,plain,
% 0.61/0.81 (Xl1!130 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[170, 27])).
% 0.61/0.81 tff(172,plain,
% 0.61/0.81 (tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) = Xl1!130),
% 0.61/0.81 inference(symmetry,[status(thm)],[171])).
% 0.61/0.81 tff(173,plain,
% 0.61/0.81 (list_succeeds(tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) <=> list_succeeds(Xl1!130)),
% 0.61/0.81 inference(monotonicity,[status(thm)],[172])).
% 0.61/0.81 tff(174,plain,
% 0.61/0.81 (list_succeeds(Xl1!130) <=> list_succeeds(tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))),
% 0.61/0.81 inference(symmetry,[status(thm)],[173])).
% 0.61/0.81 tff(175,plain,
% 0.61/0.81 (list_succeeds(tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[33, 174])).
% 0.61/0.81 tff(176,plain,
% 0.61/0.81 (((~![Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~list_succeeds(tptp_fun_____(Xl1, Xl2))))) | (list_succeeds(cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))))) <=> ((~![Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~list_succeeds(tptp_fun_____(Xl1, Xl2))))) | list_succeeds(cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))))),
% 0.61/0.81 inference(rewrite,[status(thm)],[])).
% 0.61/0.81 tff(177,plain,
% 0.61/0.81 ((~![Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~list_succeeds(tptp_fun_____(Xl1, Xl2))))) | (list_succeeds(cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))))),
% 0.61/0.81 inference(quant_inst,[status(thm)],[])).
% 0.61/0.81 tff(178,plain,
% 0.61/0.81 ((~![Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~list_succeeds(tptp_fun_____(Xl1, Xl2))))) | list_succeeds(cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))))),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.61/0.81 tff(179,plain,
% 0.61/0.81 (list_succeeds(cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))))),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[178, 66, 53])).
% 0.61/0.81 tff(180,plain,
% 0.61/0.81 (list_succeeds(cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[179, 175])).
% 0.61/0.81 tff(181,plain,
% 0.61/0.81 (((~![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(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) | (occ(Xx!131, tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) = tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))))) <=> ((~![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(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) | (occ(Xx!131, tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) = tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))))),
% 0.61/0.81 inference(rewrite,[status(thm)],[])).
% 0.61/0.81 tff(182,plain,
% 0.61/0.81 (((occ(Xx!131, tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) = tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))) | (~list_succeeds(cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)))) <=> ((~list_succeeds(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) | (occ(Xx!131, tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) = tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))))),
% 0.61/0.81 inference(rewrite,[status(thm)],[])).
% 0.61/0.81 tff(183,plain,
% 0.61/0.81 (((~![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(Xx!131, tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) = tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))) | (~list_succeeds(cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))))) <=> ((~![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(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) | (occ(Xx!131, tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) = tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))))))),
% 0.61/0.81 inference(monotonicity,[status(thm)],[182])).
% 0.61/0.81 tff(184,plain,
% 0.61/0.81 (((~![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(Xx!131, tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) = tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))) | (~list_succeeds(cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))))) <=> ((~![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(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) | (occ(Xx!131, tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) = tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))))),
% 0.61/0.81 inference(transitivity,[status(thm)],[183, 181])).
% 0.61/0.81 tff(185,plain,
% 0.61/0.81 ((~![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(Xx!131, tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) = tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))) | (~list_succeeds(cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))))),
% 0.61/0.81 inference(quant_inst,[status(thm)],[])).
% 0.61/0.81 tff(186,plain,
% 0.61/0.81 ((~![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(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131))) | (~list_succeeds(cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) | (occ(Xx!131, tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) = tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))))),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.61/0.81 tff(187,plain,
% 0.61/0.81 ((~list_succeeds(cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) | (occ(Xx!131, tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) = tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))))),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[186, 84, 53])).
% 0.61/0.83 tff(188,plain,
% 0.61/0.83 (occ(Xx!131, tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) = tptp_fun_____(occ(Xx!131, tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131)), occ(Xx!131, cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[187, 180])).
% 0.61/0.83 tff(189,plain,
% 0.61/0.83 (occ(Xx!131, tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131)))) = occ(Xx!131, Xl1!130)),
% 0.61/0.83 inference(monotonicity,[status(thm)],[172])).
% 0.61/0.83 tff(190,plain,
% 0.61/0.83 (occ(Xx!131, Xl1!130) = occ(Xx!131, tptp_fun_____(tptp_fun_Xl3_120(Xl2!129, Xl1!130, Xx!131), cons(Xx!131, tptp_fun_Xl4_119(Xl2!129, Xl1!130, Xx!131))))),
% 0.61/0.83 inference(symmetry,[status(thm)],[189])).
% 0.61/0.83 tff(191,plain,
% 0.61/0.83 (occ(Xx!131, Xl1!130) = s(occ(Xx!131, Xl2!129))),
% 0.61/0.83 inference(transitivity,[status(thm)],[190, 188, 169, 151, 126, 97])).
% 0.61/0.83 tff(192,plain,
% 0.61/0.83 (~(occ(Xx!131, Xl1!130) = s(occ(Xx!131, Xl2!129)))),
% 0.61/0.83 inference(or_elim,[status(thm)],[8])).
% 0.61/0.83 tff(193,plain,
% 0.61/0.83 ($false),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[192, 191])).
% 0.61/0.83 % SZS output end Proof
% 0.61/0.83 % E exiting
%------------------------------------------------------------------------------