%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWX050+1 : TPTP v9.1.0. Released v9.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:37:50 AM UTC 2025
% Result : Theorem 0.49s 0.65s
% Output : Proof 0.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWX050+1 : TPTP v9.1.0. Released v9.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 12:20:38 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.49/0.65 % SZS status Theorem
% 0.49/0.65 % SZS output start Proof
% 0.49/0.65 tff(occ_type, type, (
% 0.49/0.65 occ: ( $i * $i ) > $i)).
% 0.49/0.65 tff(tptp_fun_Xl2_130_type, type, (
% 0.49/0.65 tptp_fun_Xl2_130: $i)).
% 0.49/0.65 tff(tptp_fun_Xy_132_type, type, (
% 0.49/0.65 tptp_fun_Xy_132: $i)).
% 0.49/0.65 tff(tptp_fun_Xl1_131_type, type, (
% 0.49/0.65 tptp_fun_Xl1_131: $i)).
% 0.49/0.65 tff(tptp_fun______type, type, (
% 0.49/0.65 tptp_fun_____: ( $i * $i ) > $i)).
% 0.49/0.65 tff(tptp_fun_Xl4_119_type, type, (
% 0.49/0.65 tptp_fun_Xl4_119: ( $i * $i * $i ) > $i)).
% 0.49/0.65 tff(tptp_fun_Xx_133_type, type, (
% 0.49/0.65 tptp_fun_Xx_133: $i)).
% 0.49/0.65 tff(tptp_fun_Xl3_120_type, type, (
% 0.49/0.65 tptp_fun_Xl3_120: ( $i * $i * $i ) > $i)).
% 0.49/0.65 tff(cons_type, type, (
% 0.49/0.65 cons: ( $i * $i ) > $i)).
% 0.49/0.65 tff(list_succeeds_type, type, (
% 0.49/0.65 list_succeeds: $i > $o)).
% 0.49/0.65 tff(delete_succeeds_type, type, (
% 0.49/0.65 delete_succeeds: ( $i * $i * $i ) > $o)).
% 0.49/0.65 tff(tptp_fun______type, type, (
% 0.49/0.65 tptp_fun_____: ( $i * $i ) > $i)).
% 0.49/0.65 tff(1,plain,
% 0.49/0.65 ((~![Xx: $i, Xy: $i, Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl1) & delete_succeeds(Xx, Xl1, Xl2) & (~(Xx = Xy)))) | (occ(Xy, Xl1) = occ(Xy, Xl2)))) <=> (~![Xx: $i, Xy: $i, Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl1) & delete_succeeds(Xx, Xl1, Xl2) & (~(Xx = Xy)))) | (occ(Xy, Xl1) = occ(Xy, Xl2))))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(2,plain,
% 0.49/0.65 ((~![Xx: $i, Xy: $i, Xl1: $i, Xl2: $i] : (((list_succeeds(Xl1) & delete_succeeds(Xx, Xl1, Xl2)) & (~(Xx = Xy))) => (occ(Xy, Xl1) = occ(Xy, Xl2)))) <=> (~![Xx: $i, Xy: $i, Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl1) & delete_succeeds(Xx, Xl1, Xl2) & (~(Xx = Xy)))) | (occ(Xy, Xl1) = occ(Xy, Xl2))))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(3,axiom,(~![Xx: $i, Xy: $i, Xl1: $i, Xl2: $i] : (((list_succeeds(Xl1) & delete_succeeds(Xx, Xl1, Xl2)) & (~(Xx = Xy))) => (occ(Xy, Xl1) = occ(Xy, Xl2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''lemma-(delete:occ:diff)'')).
% 0.49/0.65 tff(4,plain,
% 0.49/0.65 (~![Xx: $i, Xy: $i, Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl1) & delete_succeeds(Xx, Xl1, Xl2) & (~(Xx = Xy)))) | (occ(Xy, Xl1) = occ(Xy, Xl2)))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.49/0.65 tff(5,plain,
% 0.49/0.65 (~![Xx: $i, Xy: $i, Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl1) & delete_succeeds(Xx, Xl1, Xl2) & (~(Xx = Xy)))) | (occ(Xy, Xl1) = occ(Xy, Xl2)))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.49/0.65 tff(6,plain,
% 0.49/0.65 (~![Xx: $i, Xy: $i, Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl1) & delete_succeeds(Xx, Xl1, Xl2) & (~(Xx = Xy)))) | (occ(Xy, Xl1) = occ(Xy, Xl2)))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.49/0.65 tff(7,plain,
% 0.49/0.65 (~![Xx: $i, Xy: $i, Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl1) & delete_succeeds(Xx, Xl1, Xl2) & (~(Xx = Xy)))) | (occ(Xy, Xl1) = occ(Xy, Xl2)))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.49/0.65 tff(8,plain,(
% 0.49/0.65 ~((~(list_succeeds(Xl1!131) & delete_succeeds(Xx!133, Xl1!131, Xl2!130) & (~(Xx!133 = Xy!132)))) | (occ(Xy!132, Xl1!131) = occ(Xy!132, Xl2!130)))),
% 0.49/0.65 inference(skolemize,[status(sab)],[7])).
% 0.49/0.65 tff(9,plain,
% 0.49/0.65 (list_succeeds(Xl1!131) & delete_succeeds(Xx!133, Xl1!131, Xl2!130) & (~(Xx!133 = Xy!132))),
% 0.49/0.65 inference(or_elim,[status(thm)],[8])).
% 0.49/0.65 tff(10,plain,
% 0.49/0.65 (delete_succeeds(Xx!133, Xl1!131, Xl2!130)),
% 0.49/0.65 inference(and_elim,[status(thm)],[9])).
% 0.49/0.65 tff(11,plain,
% 0.49/0.65 (^[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))))))))),
% 0.49/0.65 inference(bind,[status(th)],[])).
% 0.49/0.65 tff(12,plain,
% 0.49/0.65 (![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)))))))),
% 0.49/0.65 inference(quant_intro,[status(thm)],[11])).
% 0.49/0.65 tff(13,plain,
% 0.49/0.65 (^[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))))))))),
% 0.49/0.65 inference(bind,[status(th)],[])).
% 0.49/0.65 tff(14,plain,
% 0.49/0.65 (![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)))))))),
% 0.49/0.65 inference(quant_intro,[status(thm)],[13])).
% 0.49/0.65 tff(15,plain,
% 0.49/0.65 (![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))))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(16,plain,
% 0.49/0.65 (^[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))))))),
% 0.49/0.65 inference(bind,[status(th)],[])).
% 0.49/0.65 tff(17,plain,
% 0.49/0.65 (![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))))),
% 0.49/0.65 inference(quant_intro,[status(thm)],[16])).
% 0.49/0.65 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/sandbox2/benchmark/theBenchmark.p',''axiom-(delete:app:2)'')).
% 0.49/0.65 tff(19,plain,
% 0.49/0.65 (![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))))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.49/0.65 tff(20,plain,
% 0.49/0.65 (![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))))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.49/0.65 tff(21,plain,(
% 0.49/0.65 ![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)))))),
% 0.49/0.65 inference(skolemize,[status(sab)],[20])).
% 0.49/0.65 tff(22,plain,
% 0.49/0.65 (![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)))))))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.49/0.65 tff(23,plain,
% 0.49/0.65 (![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)))))))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[22, 12])).
% 0.49/0.65 tff(24,plain,
% 0.49/0.65 (((~![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!133, Xl1!131, Xl2!130)) | (~((~list_succeeds(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133))) | (~(Xl1!131 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))) | (~(Xl2!130 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))))))) <=> ((~![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!133, Xl1!131, Xl2!130)) | (~((~list_succeeds(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133))) | (~(Xl1!131 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))) | (~(Xl2!130 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))))))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(25,plain,
% 0.49/0.65 ((~![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!133, Xl1!131, Xl2!130)) | (~((~list_succeeds(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133))) | (~(Xl1!131 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))) | (~(Xl2!130 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))))))),
% 0.49/0.65 inference(quant_inst,[status(thm)],[])).
% 0.49/0.65 tff(26,plain,
% 0.49/0.65 ((~![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!133, Xl1!131, Xl2!130)) | (~((~list_succeeds(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133))) | (~(Xl1!131 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))) | (~(Xl2!130 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.49/0.65 tff(27,plain,
% 0.49/0.65 (~((~list_succeeds(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133))) | (~(Xl1!131 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))) | (~(Xl2!130 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))))),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[26, 23, 10])).
% 0.49/0.65 tff(28,plain,
% 0.49/0.65 (((~list_succeeds(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133))) | (~(Xl1!131 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))) | (~(Xl2!130 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))) | (Xl2!130 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))),
% 0.49/0.65 inference(tautology,[status(thm)],[])).
% 0.49/0.65 tff(29,plain,
% 0.49/0.65 (Xl2!130 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.49/0.65 tff(30,plain,
% 0.49/0.65 (occ(Xy!132, Xl2!130) = occ(Xy!132, tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[29])).
% 0.49/0.65 tff(31,plain,
% 0.49/0.65 (occ(Xy!132, tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) = occ(Xy!132, Xl2!130)),
% 0.49/0.65 inference(symmetry,[status(thm)],[30])).
% 0.49/0.65 tff(32,plain,
% 0.49/0.65 (tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)) = Xl2!130),
% 0.49/0.65 inference(symmetry,[status(thm)],[29])).
% 0.49/0.65 tff(33,plain,
% 0.49/0.65 (list_succeeds(tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) <=> list_succeeds(Xl2!130)),
% 0.49/0.65 inference(monotonicity,[status(thm)],[32])).
% 0.49/0.65 tff(34,plain,
% 0.49/0.65 (list_succeeds(Xl2!130) <=> list_succeeds(tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))),
% 0.49/0.65 inference(symmetry,[status(thm)],[33])).
% 0.49/0.65 tff(35,plain,
% 0.49/0.65 (list_succeeds(Xl1!131)),
% 0.49/0.65 inference(and_elim,[status(thm)],[9])).
% 0.49/0.65 tff(36,plain,
% 0.49/0.65 (^[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))))),
% 0.49/0.65 inference(bind,[status(th)],[])).
% 0.49/0.65 tff(37,plain,
% 0.49/0.65 (![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)))),
% 0.49/0.65 inference(quant_intro,[status(thm)],[36])).
% 0.49/0.65 tff(38,plain,
% 0.49/0.65 (^[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)))))),
% 0.49/0.65 inference(bind,[status(th)],[])).
% 0.49/0.65 tff(39,plain,
% 0.49/0.65 (![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)))),
% 0.49/0.65 inference(quant_intro,[status(thm)],[38])).
% 0.49/0.65 tff(40,plain,
% 0.49/0.65 (![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))))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(41,plain,
% 0.49/0.65 (^[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)))))),
% 0.49/0.65 inference(bind,[status(th)],[])).
% 0.49/0.65 tff(42,plain,
% 0.49/0.65 (![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))))),
% 0.49/0.65 inference(quant_intro,[status(thm)],[41])).
% 0.49/0.65 tff(43,axiom,(![Xx: $i, Xl1: $i, Xl2: $i] : ((delete_succeeds(Xx, Xl1, Xl2) & list_succeeds(Xl1)) => list_succeeds(Xl2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''axiom-(delete:types:1)'')).
% 0.49/0.65 tff(44,plain,
% 0.49/0.65 (![Xx: $i, Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~(delete_succeeds(Xx, Xl1, Xl2) & list_succeeds(Xl1))))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.49/0.65 tff(45,plain,
% 0.49/0.65 (![Xx: $i, Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~(delete_succeeds(Xx, Xl1, Xl2) & list_succeeds(Xl1))))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.49/0.65 tff(46,plain,(
% 0.49/0.65 ![Xx: $i, Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~(delete_succeeds(Xx, Xl1, Xl2) & list_succeeds(Xl1))))),
% 0.49/0.65 inference(skolemize,[status(sab)],[45])).
% 0.49/0.65 tff(47,plain,
% 0.49/0.65 (![Xx: $i, Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~delete_succeeds(Xx, Xl1, Xl2)))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.49/0.65 tff(48,plain,
% 0.49/0.65 (![Xx: $i, Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~delete_succeeds(Xx, Xl1, Xl2)))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[47, 37])).
% 0.49/0.65 tff(49,plain,
% 0.49/0.65 (((~![Xx: $i, Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~delete_succeeds(Xx, Xl1, Xl2)))) | (list_succeeds(Xl2!130) | (~list_succeeds(Xl1!131)) | (~delete_succeeds(Xx!133, Xl1!131, Xl2!130)))) <=> ((~![Xx: $i, Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~delete_succeeds(Xx, Xl1, Xl2)))) | list_succeeds(Xl2!130) | (~list_succeeds(Xl1!131)) | (~delete_succeeds(Xx!133, Xl1!131, Xl2!130)))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(50,plain,
% 0.49/0.65 ((~![Xx: $i, Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~delete_succeeds(Xx, Xl1, Xl2)))) | (list_succeeds(Xl2!130) | (~list_succeeds(Xl1!131)) | (~delete_succeeds(Xx!133, Xl1!131, Xl2!130)))),
% 0.49/0.65 inference(quant_inst,[status(thm)],[])).
% 0.49/0.65 tff(51,plain,
% 0.49/0.65 ((~![Xx: $i, Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~delete_succeeds(Xx, Xl1, Xl2)))) | list_succeeds(Xl2!130) | (~list_succeeds(Xl1!131)) | (~delete_succeeds(Xx!133, Xl1!131, Xl2!130))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.49/0.65 tff(52,plain,
% 0.49/0.65 (list_succeeds(Xl2!130)),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[51, 48, 35, 10])).
% 0.49/0.65 tff(53,plain,
% 0.49/0.65 (list_succeeds(tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[52, 34])).
% 0.49/0.65 tff(54,plain,
% 0.49/0.65 (((~list_succeeds(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133))) | (~(Xl1!131 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))) | (~(Xl2!130 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))) | list_succeeds(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133))),
% 0.49/0.65 inference(tautology,[status(thm)],[])).
% 0.49/0.65 tff(55,plain,
% 0.49/0.65 (list_succeeds(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133))),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[54, 27])).
% 0.49/0.65 tff(56,plain,
% 0.49/0.65 (^[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)))))),
% 0.49/0.65 inference(bind,[status(th)],[])).
% 0.49/0.65 tff(57,plain,
% 0.49/0.65 (![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))))),
% 0.49/0.65 inference(quant_intro,[status(thm)],[56])).
% 0.49/0.65 tff(58,plain,
% 0.49/0.65 (^[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))))))),
% 0.49/0.65 inference(bind,[status(th)],[])).
% 0.49/0.65 tff(59,plain,
% 0.49/0.65 (![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))))),
% 0.49/0.65 inference(quant_intro,[status(thm)],[58])).
% 0.49/0.65 tff(60,plain,
% 0.49/0.65 (![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)))))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(61,plain,
% 0.49/0.65 (^[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))))))),
% 0.49/0.65 inference(bind,[status(th)],[])).
% 0.49/0.65 tff(62,plain,
% 0.49/0.65 (![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)))))),
% 0.49/0.65 inference(quant_intro,[status(thm)],[61])).
% 0.49/0.65 tff(63,axiom,(![Xl1: $i, Xl2: $i] : ((list_succeeds(Xl1) & list_succeeds(tptp_fun_____(Xl1, Xl2))) => list_succeeds(Xl2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''axiom-(app:types:2)'')).
% 0.49/0.65 tff(64,plain,
% 0.49/0.65 (![Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~(list_succeeds(Xl1) & list_succeeds(tptp_fun_____(Xl1, Xl2)))))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.49/0.65 tff(65,plain,
% 0.49/0.65 (![Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~(list_succeeds(Xl1) & list_succeeds(tptp_fun_____(Xl1, Xl2)))))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.49/0.65 tff(66,plain,(
% 0.49/0.65 ![Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~(list_succeeds(Xl1) & list_succeeds(tptp_fun_____(Xl1, Xl2)))))),
% 0.49/0.65 inference(skolemize,[status(sab)],[65])).
% 0.49/0.65 tff(67,plain,
% 0.49/0.65 (![Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~list_succeeds(tptp_fun_____(Xl1, Xl2))))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.49/0.65 tff(68,plain,
% 0.49/0.65 (![Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~list_succeeds(tptp_fun_____(Xl1, Xl2))))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[67, 57])).
% 0.49/0.65 tff(69,plain,
% 0.49/0.65 (((~![Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~list_succeeds(tptp_fun_____(Xl1, Xl2))))) | (list_succeeds(tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133))) | (~list_succeeds(tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))))) <=> ((~![Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~list_succeeds(tptp_fun_____(Xl1, Xl2))))) | list_succeeds(tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133))) | (~list_succeeds(tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(70,plain,
% 0.49/0.65 ((~![Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~list_succeeds(tptp_fun_____(Xl1, Xl2))))) | (list_succeeds(tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133))) | (~list_succeeds(tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))))),
% 0.49/0.65 inference(quant_inst,[status(thm)],[])).
% 0.49/0.65 tff(71,plain,
% 0.49/0.65 ((~![Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~list_succeeds(tptp_fun_____(Xl1, Xl2))))) | list_succeeds(tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133))) | (~list_succeeds(tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.49/0.65 tff(72,plain,
% 0.49/0.65 (list_succeeds(tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)) | (~list_succeeds(tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[71, 68, 55])).
% 0.49/0.65 tff(73,plain,
% 0.49/0.65 (list_succeeds(tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[72, 53])).
% 0.49/0.65 tff(74,plain,
% 0.49/0.65 (^[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))))),
% 0.49/0.65 inference(bind,[status(th)],[])).
% 0.49/0.65 tff(75,plain,
% 0.49/0.65 (![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)))),
% 0.49/0.65 inference(quant_intro,[status(thm)],[74])).
% 0.49/0.65 tff(76,plain,
% 0.49/0.65 (^[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)))))),
% 0.49/0.65 inference(bind,[status(th)],[])).
% 0.49/0.65 tff(77,plain,
% 0.49/0.65 (![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)))),
% 0.49/0.65 inference(quant_intro,[status(thm)],[76])).
% 0.49/0.65 tff(78,plain,
% 0.49/0.65 (![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))))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(79,plain,
% 0.49/0.65 (^[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)))))),
% 0.49/0.65 inference(bind,[status(th)],[])).
% 0.49/0.65 tff(80,plain,
% 0.49/0.65 (![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))))),
% 0.49/0.65 inference(quant_intro,[status(thm)],[79])).
% 0.49/0.65 tff(81,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/sandbox2/benchmark/theBenchmark.p',''lemma-(occ:app)'')).
% 0.49/0.65 tff(82,plain,
% 0.49/0.65 (![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))))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.49/0.65 tff(83,plain,
% 0.49/0.65 (![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))))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.49/0.65 tff(84,plain,(
% 0.49/0.65 ![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))))),
% 0.49/0.65 inference(skolemize,[status(sab)],[83])).
% 0.49/0.65 tff(85,plain,
% 0.49/0.65 (![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)))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.49/0.65 tff(86,plain,
% 0.49/0.65 (![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)))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[85, 75])).
% 0.49/0.65 tff(87,plain,
% 0.49/0.65 (((~![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!130, Xl1!131, Xx!133))) | (~list_succeeds(tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) | (occ(Xy!132, tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) = tptp_fun_____(occ(Xy!132, tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133)), occ(Xy!132, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))))) <=> ((~![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!130, Xl1!131, Xx!133))) | (~list_succeeds(tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) | (occ(Xy!132, tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) = tptp_fun_____(occ(Xy!132, tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133)), occ(Xy!132, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(88,plain,
% 0.49/0.65 (((occ(Xy!132, tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) = tptp_fun_____(occ(Xy!132, tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133)), occ(Xy!132, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))) | (~list_succeeds(tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133)))) <=> ((~list_succeeds(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133))) | (~list_succeeds(tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) | (occ(Xy!132, tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) = tptp_fun_____(occ(Xy!132, tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133)), occ(Xy!132, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(89,plain,
% 0.49/0.65 (((~![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(Xy!132, tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) = tptp_fun_____(occ(Xy!132, tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133)), occ(Xy!132, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))) | (~list_succeeds(tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133))))) <=> ((~![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!130, Xl1!131, Xx!133))) | (~list_succeeds(tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) | (occ(Xy!132, tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) = tptp_fun_____(occ(Xy!132, tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133)), occ(Xy!132, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[88])).
% 0.49/0.65 tff(90,plain,
% 0.49/0.65 (((~![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(Xy!132, tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) = tptp_fun_____(occ(Xy!132, tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133)), occ(Xy!132, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))) | (~list_succeeds(tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133))))) <=> ((~![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!130, Xl1!131, Xx!133))) | (~list_succeeds(tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) | (occ(Xy!132, tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) = tptp_fun_____(occ(Xy!132, tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133)), occ(Xy!132, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))))),
% 0.49/0.65 inference(transitivity,[status(thm)],[89, 87])).
% 0.49/0.65 tff(91,plain,
% 0.49/0.65 ((~![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(Xy!132, tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) = tptp_fun_____(occ(Xy!132, tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133)), occ(Xy!132, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))) | (~list_succeeds(tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133))))),
% 0.49/0.65 inference(quant_inst,[status(thm)],[])).
% 0.49/0.65 tff(92,plain,
% 0.49/0.65 ((~![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!130, Xl1!131, Xx!133))) | (~list_succeeds(tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) | (occ(Xy!132, tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) = tptp_fun_____(occ(Xy!132, tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133)), occ(Xy!132, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.49/0.65 tff(93,plain,
% 0.49/0.65 ((~list_succeeds(tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) | (occ(Xy!132, tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) = tptp_fun_____(occ(Xy!132, tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133)), occ(Xy!132, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[92, 86, 55])).
% 0.49/0.65 tff(94,plain,
% 0.49/0.65 (occ(Xy!132, tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) = tptp_fun_____(occ(Xy!132, tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133)), occ(Xy!132, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[93, 73])).
% 0.49/0.65 tff(95,plain,
% 0.49/0.65 (tptp_fun_____(occ(Xy!132, tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133)), occ(Xy!132, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) = occ(Xy!132, tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))),
% 0.49/0.65 inference(symmetry,[status(thm)],[94])).
% 0.49/0.65 tff(96,plain,
% 0.49/0.65 ((Xy!132 = Xx!133) <=> (Xx!133 = Xy!132)),
% 0.49/0.65 inference(commutativity,[status(thm)],[])).
% 0.49/0.65 tff(97,plain,
% 0.49/0.65 ((Xx!133 = Xy!132) <=> (Xy!132 = Xx!133)),
% 0.49/0.65 inference(symmetry,[status(thm)],[96])).
% 0.49/0.65 tff(98,plain,
% 0.49/0.65 ((~(Xx!133 = Xy!132)) <=> (~(Xy!132 = Xx!133))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[97])).
% 0.49/0.65 tff(99,plain,
% 0.49/0.65 (~(Xx!133 = Xy!132)),
% 0.49/0.65 inference(and_elim,[status(thm)],[9])).
% 0.49/0.65 tff(100,plain,
% 0.49/0.65 (~(Xy!132 = Xx!133)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.49/0.65 tff(101,plain,
% 0.49/0.65 (^[Xx: $i, Xy: $i, Xl: $i] : refl(((Xx = Xy) | (occ(Xx, cons(Xy, Xl)) = occ(Xx, Xl)) | (~list_succeeds(Xl))) <=> ((Xx = Xy) | (occ(Xx, cons(Xy, Xl)) = occ(Xx, Xl)) | (~list_succeeds(Xl))))),
% 0.49/0.65 inference(bind,[status(th)],[])).
% 0.49/0.65 tff(102,plain,
% 0.49/0.65 (![Xx: $i, Xy: $i, Xl: $i] : ((Xx = Xy) | (occ(Xx, cons(Xy, Xl)) = occ(Xx, Xl)) | (~list_succeeds(Xl))) <=> ![Xx: $i, Xy: $i, Xl: $i] : ((Xx = Xy) | (occ(Xx, cons(Xy, Xl)) = occ(Xx, Xl)) | (~list_succeeds(Xl)))),
% 0.49/0.65 inference(quant_intro,[status(thm)],[101])).
% 0.49/0.65 tff(103,plain,
% 0.49/0.65 (^[Xx: $i, Xy: $i, Xl: $i] : trans(monotonicity(trans(monotonicity(rewrite((list_succeeds(Xl) & (~(Xx = Xy))) <=> (~((~list_succeeds(Xl)) | (Xx = Xy)))), ((~(list_succeeds(Xl) & (~(Xx = Xy)))) <=> (~(~((~list_succeeds(Xl)) | (Xx = Xy)))))), rewrite((~(~((~list_succeeds(Xl)) | (Xx = Xy)))) <=> ((~list_succeeds(Xl)) | (Xx = Xy))), ((~(list_succeeds(Xl) & (~(Xx = Xy)))) <=> ((~list_succeeds(Xl)) | (Xx = Xy)))), (((~(list_succeeds(Xl) & (~(Xx = Xy)))) | (occ(Xx, cons(Xy, Xl)) = occ(Xx, Xl))) <=> (((~list_succeeds(Xl)) | (Xx = Xy)) | (occ(Xx, cons(Xy, Xl)) = occ(Xx, Xl))))), rewrite((((~list_succeeds(Xl)) | (Xx = Xy)) | (occ(Xx, cons(Xy, Xl)) = occ(Xx, Xl))) <=> ((Xx = Xy) | (occ(Xx, cons(Xy, Xl)) = occ(Xx, Xl)) | (~list_succeeds(Xl)))), (((~(list_succeeds(Xl) & (~(Xx = Xy)))) | (occ(Xx, cons(Xy, Xl)) = occ(Xx, Xl))) <=> ((Xx = Xy) | (occ(Xx, cons(Xy, Xl)) = occ(Xx, Xl)) | (~list_succeeds(Xl)))))),
% 0.49/0.65 inference(bind,[status(th)],[])).
% 0.49/0.65 tff(104,plain,
% 0.49/0.65 (![Xx: $i, Xy: $i, Xl: $i] : ((~(list_succeeds(Xl) & (~(Xx = Xy)))) | (occ(Xx, cons(Xy, Xl)) = occ(Xx, Xl))) <=> ![Xx: $i, Xy: $i, Xl: $i] : ((Xx = Xy) | (occ(Xx, cons(Xy, Xl)) = occ(Xx, Xl)) | (~list_succeeds(Xl)))),
% 0.49/0.65 inference(quant_intro,[status(thm)],[103])).
% 0.49/0.65 tff(105,plain,
% 0.49/0.65 (![Xx: $i, Xy: $i, Xl: $i] : ((~(list_succeeds(Xl) & (~(Xx = Xy)))) | (occ(Xx, cons(Xy, Xl)) = occ(Xx, Xl))) <=> ![Xx: $i, Xy: $i, Xl: $i] : ((~(list_succeeds(Xl) & (~(Xx = Xy)))) | (occ(Xx, cons(Xy, Xl)) = occ(Xx, Xl)))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(106,plain,
% 0.49/0.65 (^[Xx: $i, Xy: $i, Xl: $i] : rewrite(((list_succeeds(Xl) & (~(Xx = Xy))) => (occ(Xx, cons(Xy, Xl)) = occ(Xx, Xl))) <=> ((~(list_succeeds(Xl) & (~(Xx = Xy)))) | (occ(Xx, cons(Xy, Xl)) = occ(Xx, Xl))))),
% 0.49/0.65 inference(bind,[status(th)],[])).
% 0.49/0.65 tff(107,plain,
% 0.49/0.65 (![Xx: $i, Xy: $i, Xl: $i] : ((list_succeeds(Xl) & (~(Xx = Xy))) => (occ(Xx, cons(Xy, Xl)) = occ(Xx, Xl))) <=> ![Xx: $i, Xy: $i, Xl: $i] : ((~(list_succeeds(Xl) & (~(Xx = Xy)))) | (occ(Xx, cons(Xy, Xl)) = occ(Xx, Xl)))),
% 0.49/0.65 inference(quant_intro,[status(thm)],[106])).
% 0.49/0.65 tff(108,axiom,(![Xx: $i, Xy: $i, Xl: $i] : ((list_succeeds(Xl) & (~(Xx = Xy))) => (occ(Xx, cons(Xy, Xl)) = occ(Xx, Xl)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''lemma-(occ:cons:diff)'')).
% 0.49/0.65 tff(109,plain,
% 0.49/0.65 (![Xx: $i, Xy: $i, Xl: $i] : ((~(list_succeeds(Xl) & (~(Xx = Xy)))) | (occ(Xx, cons(Xy, Xl)) = occ(Xx, Xl)))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.49/0.65 tff(110,plain,
% 0.49/0.65 (![Xx: $i, Xy: $i, Xl: $i] : ((~(list_succeeds(Xl) & (~(Xx = Xy)))) | (occ(Xx, cons(Xy, Xl)) = occ(Xx, Xl)))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.49/0.65 tff(111,plain,(
% 0.49/0.65 ![Xx: $i, Xy: $i, Xl: $i] : ((~(list_succeeds(Xl) & (~(Xx = Xy)))) | (occ(Xx, cons(Xy, Xl)) = occ(Xx, Xl)))),
% 0.49/0.65 inference(skolemize,[status(sab)],[110])).
% 0.49/0.65 tff(112,plain,
% 0.49/0.65 (![Xx: $i, Xy: $i, Xl: $i] : ((Xx = Xy) | (occ(Xx, cons(Xy, Xl)) = occ(Xx, Xl)) | (~list_succeeds(Xl)))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.49/0.65 tff(113,plain,
% 0.49/0.65 (![Xx: $i, Xy: $i, Xl: $i] : ((Xx = Xy) | (occ(Xx, cons(Xy, Xl)) = occ(Xx, Xl)) | (~list_succeeds(Xl)))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[112, 102])).
% 0.49/0.65 tff(114,plain,
% 0.49/0.65 (((~![Xx: $i, Xy: $i, Xl: $i] : ((Xx = Xy) | (occ(Xx, cons(Xy, Xl)) = occ(Xx, Xl)) | (~list_succeeds(Xl)))) | ((~list_succeeds(tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) | (Xy!132 = Xx!133) | (occ(Xy!132, cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) = occ(Xy!132, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))) <=> ((~![Xx: $i, Xy: $i, Xl: $i] : ((Xx = Xy) | (occ(Xx, cons(Xy, Xl)) = occ(Xx, Xl)) | (~list_succeeds(Xl)))) | (~list_succeeds(tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) | (Xy!132 = Xx!133) | (occ(Xy!132, cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) = occ(Xy!132, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(115,plain,
% 0.49/0.65 (((Xy!132 = Xx!133) | (occ(Xy!132, cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) = occ(Xy!132, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) | (~list_succeeds(tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))) <=> ((~list_succeeds(tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) | (Xy!132 = Xx!133) | (occ(Xy!132, cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) = occ(Xy!132, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(116,plain,
% 0.49/0.65 (((~![Xx: $i, Xy: $i, Xl: $i] : ((Xx = Xy) | (occ(Xx, cons(Xy, Xl)) = occ(Xx, Xl)) | (~list_succeeds(Xl)))) | ((Xy!132 = Xx!133) | (occ(Xy!132, cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) = occ(Xy!132, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) | (~list_succeeds(tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))) <=> ((~![Xx: $i, Xy: $i, Xl: $i] : ((Xx = Xy) | (occ(Xx, cons(Xy, Xl)) = occ(Xx, Xl)) | (~list_succeeds(Xl)))) | ((~list_succeeds(tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) | (Xy!132 = Xx!133) | (occ(Xy!132, cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) = occ(Xy!132, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[115])).
% 0.49/0.66 tff(117,plain,
% 0.49/0.66 (((~![Xx: $i, Xy: $i, Xl: $i] : ((Xx = Xy) | (occ(Xx, cons(Xy, Xl)) = occ(Xx, Xl)) | (~list_succeeds(Xl)))) | ((Xy!132 = Xx!133) | (occ(Xy!132, cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) = occ(Xy!132, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) | (~list_succeeds(tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))) <=> ((~![Xx: $i, Xy: $i, Xl: $i] : ((Xx = Xy) | (occ(Xx, cons(Xy, Xl)) = occ(Xx, Xl)) | (~list_succeeds(Xl)))) | (~list_succeeds(tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) | (Xy!132 = Xx!133) | (occ(Xy!132, cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) = occ(Xy!132, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))),
% 0.49/0.66 inference(transitivity,[status(thm)],[116, 114])).
% 0.49/0.66 tff(118,plain,
% 0.49/0.66 ((~![Xx: $i, Xy: $i, Xl: $i] : ((Xx = Xy) | (occ(Xx, cons(Xy, Xl)) = occ(Xx, Xl)) | (~list_succeeds(Xl)))) | ((Xy!132 = Xx!133) | (occ(Xy!132, cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) = occ(Xy!132, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) | (~list_succeeds(tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))),
% 0.49/0.66 inference(quant_inst,[status(thm)],[])).
% 0.49/0.66 tff(119,plain,
% 0.49/0.66 ((~![Xx: $i, Xy: $i, Xl: $i] : ((Xx = Xy) | (occ(Xx, cons(Xy, Xl)) = occ(Xx, Xl)) | (~list_succeeds(Xl)))) | (~list_succeeds(tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) | (Xy!132 = Xx!133) | (occ(Xy!132, cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) = occ(Xy!132, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.49/0.66 tff(120,plain,
% 0.49/0.66 (occ(Xy!132, cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) = occ(Xy!132, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[119, 113, 73, 100])).
% 0.49/0.66 tff(121,plain,
% 0.49/0.66 (occ(Xy!132, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)) = occ(Xy!132, cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))),
% 0.49/0.66 inference(symmetry,[status(thm)],[120])).
% 0.49/0.66 tff(122,plain,
% 0.49/0.66 (tptp_fun_____(occ(Xy!132, tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133)), occ(Xy!132, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) = tptp_fun_____(occ(Xy!132, tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133)), occ(Xy!132, cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[121])).
% 0.49/0.66 tff(123,plain,
% 0.49/0.66 (tptp_fun_____(occ(Xy!132, tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133)), occ(Xy!132, cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))) = tptp_fun_____(occ(Xy!132, tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133)), occ(Xy!132, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))),
% 0.49/0.66 inference(symmetry,[status(thm)],[122])).
% 0.49/0.66 tff(124,plain,
% 0.49/0.66 (((~list_succeeds(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133))) | (~(Xl1!131 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))) | (~(Xl2!130 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))) | (Xl1!131 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))),
% 0.49/0.66 inference(tautology,[status(thm)],[])).
% 0.49/0.66 tff(125,plain,
% 0.49/0.66 (Xl1!131 = tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[124, 27])).
% 0.49/0.66 tff(126,plain,
% 0.49/0.66 (tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) = Xl1!131),
% 0.49/0.66 inference(symmetry,[status(thm)],[125])).
% 0.49/0.66 tff(127,plain,
% 0.49/0.66 (list_succeeds(tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))) <=> list_succeeds(Xl1!131)),
% 0.49/0.66 inference(monotonicity,[status(thm)],[126])).
% 0.49/0.66 tff(128,plain,
% 0.49/0.66 (list_succeeds(Xl1!131) <=> list_succeeds(tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))),
% 0.49/0.66 inference(symmetry,[status(thm)],[127])).
% 0.49/0.66 tff(129,plain,
% 0.49/0.66 (list_succeeds(tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[35, 128])).
% 0.49/0.66 tff(130,plain,
% 0.49/0.66 (((~![Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~list_succeeds(tptp_fun_____(Xl1, Xl2))))) | (list_succeeds(cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133))) | (~list_succeeds(tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))))) <=> ((~![Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~list_succeeds(tptp_fun_____(Xl1, Xl2))))) | list_succeeds(cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133))) | (~list_succeeds(tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(131,plain,
% 0.49/0.66 ((~![Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~list_succeeds(tptp_fun_____(Xl1, Xl2))))) | (list_succeeds(cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133))) | (~list_succeeds(tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))))),
% 0.49/0.66 inference(quant_inst,[status(thm)],[])).
% 0.49/0.66 tff(132,plain,
% 0.49/0.66 ((~![Xl1: $i, Xl2: $i] : (list_succeeds(Xl2) | (~list_succeeds(Xl1)) | (~list_succeeds(tptp_fun_____(Xl1, Xl2))))) | list_succeeds(cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133))) | (~list_succeeds(tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.49/0.66 tff(133,plain,
% 0.49/0.66 (list_succeeds(cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))) | (~list_succeeds(tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))))),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[132, 68, 55])).
% 0.49/0.66 tff(134,plain,
% 0.49/0.66 (list_succeeds(cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[133, 129])).
% 0.49/0.66 tff(135,plain,
% 0.49/0.66 (((~![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!130, Xl1!131, Xx!133))) | (~list_succeeds(cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))) | (occ(Xy!132, tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))) = tptp_fun_____(occ(Xy!132, tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133)), occ(Xy!132, cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))))) <=> ((~![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!130, Xl1!131, Xx!133))) | (~list_succeeds(cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))) | (occ(Xy!132, tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))) = tptp_fun_____(occ(Xy!132, tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133)), occ(Xy!132, cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(136,plain,
% 0.49/0.66 (((occ(Xy!132, tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))) = tptp_fun_____(occ(Xy!132, tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133)), occ(Xy!132, cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))) | (~list_succeeds(cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133)))) <=> ((~list_succeeds(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133))) | (~list_succeeds(cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))) | (occ(Xy!132, tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))) = tptp_fun_____(occ(Xy!132, tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133)), occ(Xy!132, cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(137,plain,
% 0.49/0.66 (((~![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(Xy!132, tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))) = tptp_fun_____(occ(Xy!132, tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133)), occ(Xy!132, cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))) | (~list_succeeds(cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133))))) <=> ((~![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!130, Xl1!131, Xx!133))) | (~list_succeeds(cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))) | (occ(Xy!132, tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))) = tptp_fun_____(occ(Xy!132, tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133)), occ(Xy!132, cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))))))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[136])).
% 0.49/0.66 tff(138,plain,
% 0.49/0.66 (((~![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(Xy!132, tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))) = tptp_fun_____(occ(Xy!132, tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133)), occ(Xy!132, cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))) | (~list_succeeds(cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133))))) <=> ((~![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!130, Xl1!131, Xx!133))) | (~list_succeeds(cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))) | (occ(Xy!132, tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))) = tptp_fun_____(occ(Xy!132, tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133)), occ(Xy!132, cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))))),
% 0.49/0.66 inference(transitivity,[status(thm)],[137, 135])).
% 0.49/0.66 tff(139,plain,
% 0.49/0.66 ((~![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(Xy!132, tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))) = tptp_fun_____(occ(Xy!132, tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133)), occ(Xy!132, cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))) | (~list_succeeds(cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))) | (~list_succeeds(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133))))),
% 0.49/0.66 inference(quant_inst,[status(thm)],[])).
% 0.49/0.66 tff(140,plain,
% 0.49/0.66 ((~![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!130, Xl1!131, Xx!133))) | (~list_succeeds(cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))) | (occ(Xy!132, tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))) = tptp_fun_____(occ(Xy!132, tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133)), occ(Xy!132, cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))))),
% 0.52/0.67 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.52/0.67 tff(141,plain,
% 0.52/0.67 ((~list_succeeds(cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))) | (occ(Xy!132, tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))) = tptp_fun_____(occ(Xy!132, tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133)), occ(Xy!132, cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))))),
% 0.52/0.67 inference(unit_resolution,[status(thm)],[140, 86, 55])).
% 0.52/0.67 tff(142,plain,
% 0.52/0.67 (occ(Xy!132, tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))) = tptp_fun_____(occ(Xy!132, tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133)), occ(Xy!132, cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))),
% 0.52/0.67 inference(unit_resolution,[status(thm)],[141, 134])).
% 0.52/0.67 tff(143,plain,
% 0.52/0.67 (occ(Xy!132, tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133)))) = occ(Xy!132, Xl1!131)),
% 0.52/0.67 inference(monotonicity,[status(thm)],[126])).
% 0.52/0.67 tff(144,plain,
% 0.52/0.67 (occ(Xy!132, Xl1!131) = occ(Xy!132, tptp_fun_____(tptp_fun_Xl3_120(Xl2!130, Xl1!131, Xx!133), cons(Xx!133, tptp_fun_Xl4_119(Xl2!130, Xl1!131, Xx!133))))),
% 0.52/0.67 inference(symmetry,[status(thm)],[143])).
% 0.52/0.67 tff(145,plain,
% 0.52/0.67 (occ(Xy!132, Xl1!131) = occ(Xy!132, Xl2!130)),
% 0.52/0.67 inference(transitivity,[status(thm)],[144, 142, 123, 95, 31])).
% 0.52/0.67 tff(146,plain,
% 0.52/0.67 (~(occ(Xy!132, Xl1!131) = occ(Xy!132, Xl2!130))),
% 0.52/0.67 inference(or_elim,[status(thm)],[8])).
% 0.52/0.67 tff(147,plain,
% 0.52/0.67 ($false),
% 0.52/0.67 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.52/0.67 % SZS output end Proof
% 0.52/0.67 % E exiting
%------------------------------------------------------------------------------