%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWX058+1 : TPTP v9.1.0. Released v9.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:37:50 AM UTC 2025
% Result : Theorem 0.22s 0.53s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWX058+1 : TPTP v9.1.0. Released v9.1.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 12:22:24 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.22/0.53 % SZS status Theorem
% 0.22/0.53 % SZS output start Proof
% 0.22/0.53 tff(occ_type, type, (
% 0.22/0.53 occ: ( $i * $i ) > $i)).
% 0.22/0.53 tff(tptp_fun______type, type, (
% 0.22/0.53 tptp_fun_____: ( $i * $i ) > $i)).
% 0.22/0.53 tff(tptp_fun_Xl1_133_type, type, (
% 0.22/0.53 tptp_fun_Xl1_133: $i)).
% 0.22/0.53 tff(tptp_fun_Xl2_132_type, type, (
% 0.22/0.53 tptp_fun_Xl2_132: $i)).
% 0.22/0.53 tff(tptp_fun_Xx_127_type, type, (
% 0.22/0.53 tptp_fun_Xx_127: ( $i * $i ) > $i)).
% 0.22/0.53 tff(tptp_fun______type, type, (
% 0.22/0.53 tptp_fun_____: ( $i * $i ) > $i)).
% 0.22/0.53 tff(list_succeeds_type, type, (
% 0.22/0.53 list_succeeds: $i > $o)).
% 0.22/0.53 tff(permutation_succeeds_type, type, (
% 0.22/0.53 permutation_succeeds: ( $i * $i ) > $o)).
% 0.22/0.53 tff(nat_succeeds_type, type, (
% 0.22/0.53 nat_succeeds: $i > $o)).
% 0.22/0.53 tff(1,plain,
% 0.22/0.53 ((~![Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl1) & list_succeeds(Xl2))) | permutation_succeeds(tptp_fun_____(Xl1, Xl2), tptp_fun_____(Xl2, Xl1)))) <=> (~![Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl1) & list_succeeds(Xl2))) | permutation_succeeds(tptp_fun_____(Xl1, Xl2), tptp_fun_____(Xl2, Xl1))))),
% 0.22/0.53 inference(rewrite,[status(thm)],[])).
% 0.22/0.53 tff(2,plain,
% 0.22/0.53 ((~![Xl1: $i, Xl2: $i] : ((list_succeeds(Xl1) & list_succeeds(Xl2)) => permutation_succeeds(tptp_fun_____(Xl1, Xl2), tptp_fun_____(Xl2, Xl1)))) <=> (~![Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl1) & list_succeeds(Xl2))) | permutation_succeeds(tptp_fun_____(Xl1, Xl2), tptp_fun_____(Xl2, Xl1))))),
% 0.22/0.53 inference(rewrite,[status(thm)],[])).
% 0.22/0.53 tff(3,axiom,(~![Xl1: $i, Xl2: $i] : ((list_succeeds(Xl1) & list_succeeds(Xl2)) => permutation_succeeds(tptp_fun_____(Xl1, Xl2), tptp_fun_____(Xl2, Xl1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''theorem-(permutation:app:commutative)'')).
% 0.22/0.53 tff(4,plain,
% 0.22/0.53 (~![Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl1) & list_succeeds(Xl2))) | permutation_succeeds(tptp_fun_____(Xl1, Xl2), tptp_fun_____(Xl2, Xl1)))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.22/0.53 tff(5,plain,
% 0.22/0.53 (~![Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl1) & list_succeeds(Xl2))) | permutation_succeeds(tptp_fun_____(Xl1, Xl2), tptp_fun_____(Xl2, Xl1)))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.22/0.53 tff(6,plain,
% 0.22/0.53 (~![Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl1) & list_succeeds(Xl2))) | permutation_succeeds(tptp_fun_____(Xl1, Xl2), tptp_fun_____(Xl2, Xl1)))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.22/0.53 tff(7,plain,
% 0.22/0.53 (~![Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl1) & list_succeeds(Xl2))) | permutation_succeeds(tptp_fun_____(Xl1, Xl2), tptp_fun_____(Xl2, Xl1)))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.22/0.53 tff(8,plain,(
% 0.22/0.53 ~((~(list_succeeds(Xl1!133) & list_succeeds(Xl2!132))) | permutation_succeeds(tptp_fun_____(Xl1!133, Xl2!132), tptp_fun_____(Xl2!132, Xl1!133)))),
% 0.22/0.53 inference(skolemize,[status(sab)],[7])).
% 0.22/0.53 tff(9,plain,
% 0.22/0.53 (list_succeeds(Xl1!133) & list_succeeds(Xl2!132)),
% 0.22/0.53 inference(or_elim,[status(thm)],[8])).
% 0.22/0.53 tff(10,plain,
% 0.22/0.53 (list_succeeds(Xl2!132)),
% 0.22/0.53 inference(and_elim,[status(thm)],[9])).
% 0.22/0.53 tff(11,plain,
% 0.22/0.53 (list_succeeds(Xl1!133)),
% 0.22/0.53 inference(and_elim,[status(thm)],[9])).
% 0.22/0.53 tff(12,plain,
% 0.22/0.53 (^[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))))),
% 0.22/0.53 inference(bind,[status(th)],[])).
% 0.22/0.53 tff(13,plain,
% 0.22/0.53 (![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1))) <=> ![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)))),
% 0.22/0.53 inference(quant_intro,[status(thm)],[12])).
% 0.22/0.53 tff(14,plain,
% 0.22/0.53 (^[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)))))),
% 0.22/0.53 inference(bind,[status(th)],[])).
% 0.22/0.53 tff(15,plain,
% 0.22/0.53 (![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)))),
% 0.22/0.53 inference(quant_intro,[status(thm)],[14])).
% 0.22/0.53 tff(16,plain,
% 0.22/0.53 (![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))))),
% 0.22/0.53 inference(rewrite,[status(thm)],[])).
% 0.22/0.53 tff(17,plain,
% 0.22/0.53 (^[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)))))),
% 0.22/0.53 inference(bind,[status(th)],[])).
% 0.22/0.53 tff(18,plain,
% 0.22/0.53 (![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))))),
% 0.22/0.53 inference(quant_intro,[status(thm)],[17])).
% 0.22/0.53 tff(19,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)'')).
% 0.22/0.53 tff(20,plain,
% 0.22/0.53 (![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))))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.22/0.53 tff(21,plain,
% 0.22/0.53 (![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))))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.22/0.53 tff(22,plain,(
% 0.22/0.53 ![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))))),
% 0.22/0.53 inference(skolemize,[status(sab)],[21])).
% 0.22/0.53 tff(23,plain,
% 0.22/0.53 (![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.22/0.53 tff(24,plain,
% 0.22/0.53 (![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.22/0.53 tff(25,plain,
% 0.22/0.53 (((~![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | ((~list_succeeds(Xl1!133)) | (~list_succeeds(Xl2!132)) | (occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl2!132, Xl1!133)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!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(Xl1!133)) | (~list_succeeds(Xl2!132)) | (occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl2!132, Xl1!133)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133))))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(26,plain,
% 0.22/0.54 (((occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl2!132, Xl1!133)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133))) | (~list_succeeds(Xl1!133)) | (~list_succeeds(Xl2!132))) <=> ((~list_succeeds(Xl1!133)) | (~list_succeeds(Xl2!132)) | (occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl2!132, Xl1!133)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133))))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(27,plain,
% 0.22/0.54 (((~![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | ((occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl2!132, Xl1!133)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133))) | (~list_succeeds(Xl1!133)) | (~list_succeeds(Xl2!132)))) <=> ((~![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | ((~list_succeeds(Xl1!133)) | (~list_succeeds(Xl2!132)) | (occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl2!132, Xl1!133)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133)))))),
% 0.22/0.54 inference(monotonicity,[status(thm)],[26])).
% 0.22/0.54 tff(28,plain,
% 0.22/0.54 (((~![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | ((occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl2!132, Xl1!133)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133))) | (~list_succeeds(Xl1!133)) | (~list_succeeds(Xl2!132)))) <=> ((~![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | (~list_succeeds(Xl1!133)) | (~list_succeeds(Xl2!132)) | (occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl2!132, Xl1!133)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133))))),
% 0.22/0.54 inference(transitivity,[status(thm)],[27, 25])).
% 0.22/0.54 tff(29,plain,
% 0.22/0.54 ((~![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | ((occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl2!132, Xl1!133)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133))) | (~list_succeeds(Xl1!133)) | (~list_succeeds(Xl2!132)))),
% 0.22/0.54 inference(quant_inst,[status(thm)],[])).
% 0.22/0.54 tff(30,plain,
% 0.22/0.54 ((~![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | (~list_succeeds(Xl1!133)) | (~list_succeeds(Xl2!132)) | (occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl2!132, Xl1!133)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133)))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.22/0.54 tff(31,plain,
% 0.22/0.54 (occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl2!132, Xl1!133)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[30, 24, 11, 10])).
% 0.22/0.54 tff(32,plain,
% 0.22/0.54 (tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133)) = occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl2!132, Xl1!133))),
% 0.22/0.54 inference(symmetry,[status(thm)],[31])).
% 0.22/0.54 tff(33,plain,
% 0.22/0.54 (^[Xx: $i, Xl: $i] : refl((nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl))) <=> (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl))))),
% 0.22/0.54 inference(bind,[status(th)],[])).
% 0.22/0.54 tff(34,plain,
% 0.22/0.54 (![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl))) <=> ![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))),
% 0.22/0.54 inference(quant_intro,[status(thm)],[33])).
% 0.22/0.54 tff(35,plain,
% 0.22/0.54 (![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl))) <=> ![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(36,plain,
% 0.22/0.54 (^[Xx: $i, Xl: $i] : rewrite((list_succeeds(Xl) => nat_succeeds(occ(Xx, Xl))) <=> (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl))))),
% 0.22/0.54 inference(bind,[status(th)],[])).
% 0.22/0.54 tff(37,plain,
% 0.22/0.54 (![Xx: $i, Xl: $i] : (list_succeeds(Xl) => nat_succeeds(occ(Xx, Xl))) <=> ![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))),
% 0.22/0.54 inference(quant_intro,[status(thm)],[36])).
% 0.22/0.54 tff(38,axiom,(![Xx: $i, Xl: $i] : (list_succeeds(Xl) => nat_succeeds(occ(Xx, Xl)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''corollary-(occ:types)'')).
% 0.22/0.54 tff(39,plain,
% 0.22/0.54 (![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.22/0.54 tff(40,plain,
% 0.22/0.54 (![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.22/0.54 tff(41,plain,(
% 0.22/0.54 ![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))),
% 0.22/0.54 inference(skolemize,[status(sab)],[40])).
% 0.22/0.54 tff(42,plain,
% 0.22/0.54 (![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.22/0.54 tff(43,plain,
% 0.22/0.54 (((~![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))) | ((~list_succeeds(Xl2!132)) | nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132)))) <=> ((~![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))) | (~list_succeeds(Xl2!132)) | nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132)))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(44,plain,
% 0.22/0.54 ((nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132)) | (~list_succeeds(Xl2!132))) <=> ((~list_succeeds(Xl2!132)) | nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132)))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(45,plain,
% 0.22/0.54 (((~![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))) | (nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132)) | (~list_succeeds(Xl2!132)))) <=> ((~![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))) | ((~list_succeeds(Xl2!132)) | nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132))))),
% 0.22/0.54 inference(monotonicity,[status(thm)],[44])).
% 0.22/0.54 tff(46,plain,
% 0.22/0.54 (((~![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))) | (nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132)) | (~list_succeeds(Xl2!132)))) <=> ((~![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))) | (~list_succeeds(Xl2!132)) | nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132)))),
% 0.22/0.54 inference(transitivity,[status(thm)],[45, 43])).
% 0.22/0.54 tff(47,plain,
% 0.22/0.54 ((~![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))) | (nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132)) | (~list_succeeds(Xl2!132)))),
% 0.22/0.54 inference(quant_inst,[status(thm)],[])).
% 0.22/0.54 tff(48,plain,
% 0.22/0.54 ((~![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))) | (~list_succeeds(Xl2!132)) | nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.22/0.54 tff(49,plain,
% 0.22/0.54 (nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[48, 42, 10])).
% 0.22/0.54 tff(50,plain,
% 0.22/0.54 (((~![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))) | ((~list_succeeds(Xl1!133)) | nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133)))) <=> ((~![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))) | (~list_succeeds(Xl1!133)) | nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133)))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(51,plain,
% 0.22/0.54 ((nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133)) | (~list_succeeds(Xl1!133))) <=> ((~list_succeeds(Xl1!133)) | nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133)))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(52,plain,
% 0.22/0.54 (((~![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))) | (nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133)) | (~list_succeeds(Xl1!133)))) <=> ((~![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))) | ((~list_succeeds(Xl1!133)) | nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133))))),
% 0.22/0.54 inference(monotonicity,[status(thm)],[51])).
% 0.22/0.54 tff(53,plain,
% 0.22/0.54 (((~![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))) | (nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133)) | (~list_succeeds(Xl1!133)))) <=> ((~![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))) | (~list_succeeds(Xl1!133)) | nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133)))),
% 0.22/0.54 inference(transitivity,[status(thm)],[52, 50])).
% 0.22/0.54 tff(54,plain,
% 0.22/0.54 ((~![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))) | (nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133)) | (~list_succeeds(Xl1!133)))),
% 0.22/0.54 inference(quant_inst,[status(thm)],[])).
% 0.22/0.54 tff(55,plain,
% 0.22/0.54 ((~![Xx: $i, Xl: $i] : (nat_succeeds(occ(Xx, Xl)) | (~list_succeeds(Xl)))) | (~list_succeeds(Xl1!133)) | nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.22/0.54 tff(56,plain,
% 0.22/0.54 (nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[55, 42, 11])).
% 0.22/0.54 tff(57,plain,
% 0.22/0.54 (^[Xx: $i, Xy: $i] : refl(((tptp_fun_____(Xx, Xy) = tptp_fun_____(Xy, Xx)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx))) <=> ((tptp_fun_____(Xx, Xy) = tptp_fun_____(Xy, Xx)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx))))),
% 0.22/0.54 inference(bind,[status(th)],[])).
% 0.22/0.54 tff(58,plain,
% 0.22/0.54 (![Xx: $i, Xy: $i] : ((tptp_fun_____(Xx, Xy) = tptp_fun_____(Xy, Xx)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx))) <=> ![Xx: $i, Xy: $i] : ((tptp_fun_____(Xx, Xy) = tptp_fun_____(Xy, Xx)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))),
% 0.22/0.54 inference(quant_intro,[status(thm)],[57])).
% 0.22/0.54 tff(59,plain,
% 0.22/0.54 (^[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, Xy) = tptp_fun_____(Xy, Xx))) <=> (((~nat_succeeds(Xy)) | (~nat_succeeds(Xx))) | (tptp_fun_____(Xx, Xy) = tptp_fun_____(Xy, Xx))))), rewrite((((~nat_succeeds(Xy)) | (~nat_succeeds(Xx))) | (tptp_fun_____(Xx, Xy) = tptp_fun_____(Xy, Xx))) <=> ((tptp_fun_____(Xx, Xy) = tptp_fun_____(Xy, Xx)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))), (((~(nat_succeeds(Xx) & nat_succeeds(Xy))) | (tptp_fun_____(Xx, Xy) = tptp_fun_____(Xy, Xx))) <=> ((tptp_fun_____(Xx, Xy) = tptp_fun_____(Xy, Xx)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))))),
% 0.22/0.54 inference(bind,[status(th)],[])).
% 0.22/0.54 tff(60,plain,
% 0.22/0.54 (![Xx: $i, Xy: $i] : ((~(nat_succeeds(Xx) & nat_succeeds(Xy))) | (tptp_fun_____(Xx, Xy) = tptp_fun_____(Xy, Xx))) <=> ![Xx: $i, Xy: $i] : ((tptp_fun_____(Xx, Xy) = tptp_fun_____(Xy, Xx)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))),
% 0.22/0.54 inference(quant_intro,[status(thm)],[59])).
% 0.22/0.54 tff(61,plain,
% 0.22/0.54 (![Xx: $i, Xy: $i] : ((~(nat_succeeds(Xx) & nat_succeeds(Xy))) | (tptp_fun_____(Xx, Xy) = tptp_fun_____(Xy, Xx))) <=> ![Xx: $i, Xy: $i] : ((~(nat_succeeds(Xx) & nat_succeeds(Xy))) | (tptp_fun_____(Xx, Xy) = tptp_fun_____(Xy, Xx)))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(62,plain,
% 0.22/0.54 (^[Xx: $i, Xy: $i] : rewrite(((nat_succeeds(Xx) & nat_succeeds(Xy)) => (tptp_fun_____(Xx, Xy) = tptp_fun_____(Xy, Xx))) <=> ((~(nat_succeeds(Xx) & nat_succeeds(Xy))) | (tptp_fun_____(Xx, Xy) = tptp_fun_____(Xy, Xx))))),
% 0.22/0.54 inference(bind,[status(th)],[])).
% 0.22/0.54 tff(63,plain,
% 0.22/0.54 (![Xx: $i, Xy: $i] : ((nat_succeeds(Xx) & nat_succeeds(Xy)) => (tptp_fun_____(Xx, Xy) = tptp_fun_____(Xy, Xx))) <=> ![Xx: $i, Xy: $i] : ((~(nat_succeeds(Xx) & nat_succeeds(Xy))) | (tptp_fun_____(Xx, Xy) = tptp_fun_____(Xy, Xx)))),
% 0.22/0.54 inference(quant_intro,[status(thm)],[62])).
% 0.22/0.54 tff(64,axiom,(![Xx: $i, Xy: $i] : ((nat_succeeds(Xx) & nat_succeeds(Xy)) => (tptp_fun_____(Xx, Xy) = tptp_fun_____(Xy, Xx)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''axiom-(plus:commutative)'')).
% 0.22/0.54 tff(65,plain,
% 0.22/0.54 (![Xx: $i, Xy: $i] : ((~(nat_succeeds(Xx) & nat_succeeds(Xy))) | (tptp_fun_____(Xx, Xy) = tptp_fun_____(Xy, Xx)))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.22/0.54 tff(66,plain,
% 0.22/0.54 (![Xx: $i, Xy: $i] : ((~(nat_succeeds(Xx) & nat_succeeds(Xy))) | (tptp_fun_____(Xx, Xy) = tptp_fun_____(Xy, Xx)))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.22/0.54 tff(67,plain,(
% 0.22/0.54 ![Xx: $i, Xy: $i] : ((~(nat_succeeds(Xx) & nat_succeeds(Xy))) | (tptp_fun_____(Xx, Xy) = tptp_fun_____(Xy, Xx)))),
% 0.22/0.54 inference(skolemize,[status(sab)],[66])).
% 0.22/0.54 tff(68,plain,
% 0.22/0.54 (![Xx: $i, Xy: $i] : ((tptp_fun_____(Xx, Xy) = tptp_fun_____(Xy, Xx)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.22/0.54 tff(69,plain,
% 0.22/0.54 (![Xx: $i, Xy: $i] : ((tptp_fun_____(Xx, Xy) = tptp_fun_____(Xy, Xx)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[68, 58])).
% 0.22/0.54 tff(70,plain,
% 0.22/0.54 (((~![Xx: $i, Xy: $i] : ((tptp_fun_____(Xx, Xy) = tptp_fun_____(Xy, Xx)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))) | ((~nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132))) | (~nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133))) | (tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133))))) <=> ((~![Xx: $i, Xy: $i] : ((tptp_fun_____(Xx, Xy) = tptp_fun_____(Xy, Xx)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))) | (~nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132))) | (~nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133))) | (tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133))))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(71,plain,
% 0.22/0.54 (((tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133))) | (~nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132))) | (~nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133)))) <=> ((~nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132))) | (~nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133))) | (tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133))))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(72,plain,
% 0.22/0.54 (((~![Xx: $i, Xy: $i] : ((tptp_fun_____(Xx, Xy) = tptp_fun_____(Xy, Xx)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))) | ((tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133))) | (~nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132))) | (~nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133))))) <=> ((~![Xx: $i, Xy: $i] : ((tptp_fun_____(Xx, Xy) = tptp_fun_____(Xy, Xx)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))) | ((~nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132))) | (~nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133))) | (tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133)))))),
% 0.22/0.54 inference(monotonicity,[status(thm)],[71])).
% 0.22/0.54 tff(73,plain,
% 0.22/0.54 (((~![Xx: $i, Xy: $i] : ((tptp_fun_____(Xx, Xy) = tptp_fun_____(Xy, Xx)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))) | ((tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133))) | (~nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132))) | (~nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133))))) <=> ((~![Xx: $i, Xy: $i] : ((tptp_fun_____(Xx, Xy) = tptp_fun_____(Xy, Xx)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))) | (~nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132))) | (~nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133))) | (tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133))))),
% 0.22/0.54 inference(transitivity,[status(thm)],[72, 70])).
% 0.22/0.54 tff(74,plain,
% 0.22/0.54 ((~![Xx: $i, Xy: $i] : ((tptp_fun_____(Xx, Xy) = tptp_fun_____(Xy, Xx)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))) | ((tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133))) | (~nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132))) | (~nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133))))),
% 0.22/0.54 inference(quant_inst,[status(thm)],[])).
% 0.22/0.54 tff(75,plain,
% 0.22/0.54 ((~![Xx: $i, Xy: $i] : ((tptp_fun_____(Xx, Xy) = tptp_fun_____(Xy, Xx)) | (~nat_succeeds(Xy)) | (~nat_succeeds(Xx)))) | (~nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132))) | (~nat_succeeds(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133))) | (tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133)))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.22/0.54 tff(76,plain,
% 0.22/0.54 (tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[75, 69, 56, 49])).
% 0.22/0.54 tff(77,plain,
% 0.22/0.54 (((~![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | ((~list_succeeds(Xl1!133)) | (~list_succeeds(Xl2!132)) | (occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl1!133, Xl2!132)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132))))) <=> ((~![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | (~list_succeeds(Xl1!133)) | (~list_succeeds(Xl2!132)) | (occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl1!133, Xl2!132)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132))))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(78,plain,
% 0.22/0.54 (((occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl1!133, Xl2!132)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132))) | (~list_succeeds(Xl2!132)) | (~list_succeeds(Xl1!133))) <=> ((~list_succeeds(Xl1!133)) | (~list_succeeds(Xl2!132)) | (occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl1!133, Xl2!132)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132))))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(79,plain,
% 0.22/0.54 (((~![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | ((occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl1!133, Xl2!132)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132))) | (~list_succeeds(Xl2!132)) | (~list_succeeds(Xl1!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(Xl1!133)) | (~list_succeeds(Xl2!132)) | (occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl1!133, Xl2!132)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132)))))),
% 0.22/0.55 inference(monotonicity,[status(thm)],[78])).
% 0.22/0.55 tff(80,plain,
% 0.22/0.55 (((~![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | ((occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl1!133, Xl2!132)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132))) | (~list_succeeds(Xl2!132)) | (~list_succeeds(Xl1!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(Xl1!133)) | (~list_succeeds(Xl2!132)) | (occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl1!133, Xl2!132)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132))))),
% 0.22/0.55 inference(transitivity,[status(thm)],[79, 77])).
% 0.22/0.55 tff(81,plain,
% 0.22/0.55 ((~![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | ((occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl1!133, Xl2!132)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132))) | (~list_succeeds(Xl2!132)) | (~list_succeeds(Xl1!133)))),
% 0.22/0.55 inference(quant_inst,[status(thm)],[])).
% 0.22/0.55 tff(82,plain,
% 0.22/0.55 ((~![Xx: $i, Xl1: $i, Xl2: $i] : ((occ(Xx, tptp_fun_____(Xl1, Xl2)) = tptp_fun_____(occ(Xx, Xl1), occ(Xx, Xl2))) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | (~list_succeeds(Xl1!133)) | (~list_succeeds(Xl2!132)) | (occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl1!133, Xl2!132)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132)))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.22/0.55 tff(83,plain,
% 0.22/0.55 (occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl1!133, Xl2!132)) = tptp_fun_____(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl1!133), occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), Xl2!132))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[82, 24, 11, 10])).
% 0.22/0.55 tff(84,plain,
% 0.22/0.55 (occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl1!133, Xl2!132)) = occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl2!132, Xl1!133))),
% 0.22/0.55 inference(transitivity,[status(thm)],[83, 76, 32])).
% 0.22/0.55 tff(85,plain,
% 0.22/0.55 (^[Xl1: $i, Xl2: $i] : refl((list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1))) <=> (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1))))),
% 0.22/0.55 inference(bind,[status(th)],[])).
% 0.22/0.55 tff(86,plain,
% 0.22/0.55 (![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1))) <=> ![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))),
% 0.22/0.55 inference(quant_intro,[status(thm)],[85])).
% 0.22/0.55 tff(87,plain,
% 0.22/0.55 (^[Xl1: $i, Xl2: $i] : trans(monotonicity(trans(monotonicity(rewrite((list_succeeds(Xl1) & list_succeeds(Xl2)) <=> (~((~list_succeeds(Xl2)) | (~list_succeeds(Xl1))))), ((~(list_succeeds(Xl1) & list_succeeds(Xl2))) <=> (~(~((~list_succeeds(Xl2)) | (~list_succeeds(Xl1))))))), rewrite((~(~((~list_succeeds(Xl2)) | (~list_succeeds(Xl1))))) <=> ((~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))), ((~(list_succeeds(Xl1) & list_succeeds(Xl2))) <=> ((~list_succeeds(Xl2)) | (~list_succeeds(Xl1))))), ((list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~(list_succeeds(Xl1) & list_succeeds(Xl2)))) <=> (list_succeeds(tptp_fun_____(Xl1, Xl2)) | ((~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))))), rewrite((list_succeeds(tptp_fun_____(Xl1, Xl2)) | ((~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) <=> (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))), ((list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~(list_succeeds(Xl1) & list_succeeds(Xl2)))) <=> (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))))),
% 0.22/0.55 inference(bind,[status(th)],[])).
% 0.22/0.55 tff(88,plain,
% 0.22/0.55 (![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~(list_succeeds(Xl1) & list_succeeds(Xl2)))) <=> ![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))),
% 0.22/0.55 inference(quant_intro,[status(thm)],[87])).
% 0.22/0.55 tff(89,plain,
% 0.22/0.55 (![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~(list_succeeds(Xl1) & list_succeeds(Xl2)))) <=> ![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~(list_succeeds(Xl1) & list_succeeds(Xl2))))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(90,plain,
% 0.22/0.55 (^[Xl1: $i, Xl2: $i] : rewrite(((list_succeeds(Xl1) & list_succeeds(Xl2)) => list_succeeds(tptp_fun_____(Xl1, Xl2))) <=> (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~(list_succeeds(Xl1) & list_succeeds(Xl2)))))),
% 0.22/0.55 inference(bind,[status(th)],[])).
% 0.22/0.55 tff(91,plain,
% 0.22/0.55 (![Xl1: $i, Xl2: $i] : ((list_succeeds(Xl1) & list_succeeds(Xl2)) => list_succeeds(tptp_fun_____(Xl1, Xl2))) <=> ![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~(list_succeeds(Xl1) & list_succeeds(Xl2))))),
% 0.22/0.55 inference(quant_intro,[status(thm)],[90])).
% 0.22/0.55 tff(92,axiom,(![Xl1: $i, Xl2: $i] : ((list_succeeds(Xl1) & list_succeeds(Xl2)) => list_succeeds(tptp_fun_____(Xl1, Xl2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''axiom-(app:types:1)'')).
% 0.22/0.55 tff(93,plain,
% 0.22/0.55 (![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~(list_succeeds(Xl1) & list_succeeds(Xl2))))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.22/0.55 tff(94,plain,
% 0.22/0.55 (![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~(list_succeeds(Xl1) & list_succeeds(Xl2))))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.22/0.55 tff(95,plain,(
% 0.22/0.55 ![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~(list_succeeds(Xl1) & list_succeeds(Xl2))))),
% 0.22/0.55 inference(skolemize,[status(sab)],[94])).
% 0.22/0.55 tff(96,plain,
% 0.22/0.55 (![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.22/0.55 tff(97,plain,
% 0.22/0.55 (![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[96, 86])).
% 0.22/0.55 tff(98,plain,
% 0.22/0.55 (((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | (list_succeeds(tptp_fun_____(Xl1!133, Xl2!132)) | (~list_succeeds(Xl1!133)) | (~list_succeeds(Xl2!132)))) <=> ((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | list_succeeds(tptp_fun_____(Xl1!133, Xl2!132)) | (~list_succeeds(Xl1!133)) | (~list_succeeds(Xl2!132)))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(99,plain,
% 0.22/0.55 ((list_succeeds(tptp_fun_____(Xl1!133, Xl2!132)) | (~list_succeeds(Xl2!132)) | (~list_succeeds(Xl1!133))) <=> (list_succeeds(tptp_fun_____(Xl1!133, Xl2!132)) | (~list_succeeds(Xl1!133)) | (~list_succeeds(Xl2!132)))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(100,plain,
% 0.22/0.55 (((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | (list_succeeds(tptp_fun_____(Xl1!133, Xl2!132)) | (~list_succeeds(Xl2!132)) | (~list_succeeds(Xl1!133)))) <=> ((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | (list_succeeds(tptp_fun_____(Xl1!133, Xl2!132)) | (~list_succeeds(Xl1!133)) | (~list_succeeds(Xl2!132))))),
% 0.22/0.55 inference(monotonicity,[status(thm)],[99])).
% 0.22/0.55 tff(101,plain,
% 0.22/0.55 (((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | (list_succeeds(tptp_fun_____(Xl1!133, Xl2!132)) | (~list_succeeds(Xl2!132)) | (~list_succeeds(Xl1!133)))) <=> ((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | list_succeeds(tptp_fun_____(Xl1!133, Xl2!132)) | (~list_succeeds(Xl1!133)) | (~list_succeeds(Xl2!132)))),
% 0.22/0.55 inference(transitivity,[status(thm)],[100, 98])).
% 0.22/0.55 tff(102,plain,
% 0.22/0.55 ((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | (list_succeeds(tptp_fun_____(Xl1!133, Xl2!132)) | (~list_succeeds(Xl2!132)) | (~list_succeeds(Xl1!133)))),
% 0.22/0.55 inference(quant_inst,[status(thm)],[])).
% 0.22/0.55 tff(103,plain,
% 0.22/0.55 ((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | list_succeeds(tptp_fun_____(Xl1!133, Xl2!132)) | (~list_succeeds(Xl1!133)) | (~list_succeeds(Xl2!132))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.22/0.55 tff(104,plain,
% 0.22/0.55 (list_succeeds(tptp_fun_____(Xl1!133, Xl2!132))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[103, 97, 11, 10])).
% 0.22/0.55 tff(105,plain,
% 0.22/0.55 (((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | (list_succeeds(tptp_fun_____(Xl2!132, Xl1!133)) | (~list_succeeds(Xl1!133)) | (~list_succeeds(Xl2!132)))) <=> ((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | list_succeeds(tptp_fun_____(Xl2!132, Xl1!133)) | (~list_succeeds(Xl1!133)) | (~list_succeeds(Xl2!132)))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(106,plain,
% 0.22/0.55 ((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | (list_succeeds(tptp_fun_____(Xl2!132, Xl1!133)) | (~list_succeeds(Xl1!133)) | (~list_succeeds(Xl2!132)))),
% 0.22/0.55 inference(quant_inst,[status(thm)],[])).
% 0.22/0.55 tff(107,plain,
% 0.22/0.55 ((~![Xl1: $i, Xl2: $i] : (list_succeeds(tptp_fun_____(Xl1, Xl2)) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)))) | list_succeeds(tptp_fun_____(Xl2!132, Xl1!133)) | (~list_succeeds(Xl1!133)) | (~list_succeeds(Xl2!132))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.22/0.55 tff(108,plain,
% 0.22/0.55 (list_succeeds(tptp_fun_____(Xl2!132, Xl1!133))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[107, 97, 11, 10])).
% 0.22/0.55 tff(109,plain,
% 0.22/0.55 (~permutation_succeeds(tptp_fun_____(Xl1!133, Xl2!132), tptp_fun_____(Xl2!132, Xl1!133))),
% 0.22/0.55 inference(or_elim,[status(thm)],[8])).
% 0.22/0.55 tff(110,plain,
% 0.22/0.55 (^[Xl1: $i, Xl2: $i] : refl((permutation_succeeds(Xl1, Xl2) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)) | (~(occ(tptp_fun_Xx_127(Xl2, Xl1), Xl1) = occ(tptp_fun_Xx_127(Xl2, Xl1), Xl2)))) <=> (permutation_succeeds(Xl1, Xl2) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)) | (~(occ(tptp_fun_Xx_127(Xl2, Xl1), Xl1) = occ(tptp_fun_Xx_127(Xl2, Xl1), Xl2)))))),
% 0.22/0.55 inference(bind,[status(th)],[])).
% 0.22/0.55 tff(111,plain,
% 0.22/0.55 (![Xl1: $i, Xl2: $i] : (permutation_succeeds(Xl1, Xl2) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)) | (~(occ(tptp_fun_Xx_127(Xl2, Xl1), Xl1) = occ(tptp_fun_Xx_127(Xl2, Xl1), Xl2)))) <=> ![Xl1: $i, Xl2: $i] : (permutation_succeeds(Xl1, Xl2) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)) | (~(occ(tptp_fun_Xx_127(Xl2, Xl1), Xl1) = occ(tptp_fun_Xx_127(Xl2, Xl1), Xl2))))),
% 0.22/0.55 inference(quant_intro,[status(thm)],[110])).
% 0.22/0.55 tff(112,plain,
% 0.22/0.55 (^[Xl1: $i, Xl2: $i] : rewrite((((~list_succeeds(Xl2)) | (~list_succeeds(Xl1)) | (~(occ(tptp_fun_Xx_127(Xl2, Xl1), Xl1) = occ(tptp_fun_Xx_127(Xl2, Xl1), Xl2)))) | permutation_succeeds(Xl1, Xl2)) <=> (permutation_succeeds(Xl1, Xl2) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)) | (~(occ(tptp_fun_Xx_127(Xl2, Xl1), Xl1) = occ(tptp_fun_Xx_127(Xl2, Xl1), Xl2)))))),
% 0.22/0.55 inference(bind,[status(th)],[])).
% 0.22/0.55 tff(113,plain,
% 0.22/0.55 (![Xl1: $i, Xl2: $i] : (((~list_succeeds(Xl2)) | (~list_succeeds(Xl1)) | (~(occ(tptp_fun_Xx_127(Xl2, Xl1), Xl1) = occ(tptp_fun_Xx_127(Xl2, Xl1), Xl2)))) | permutation_succeeds(Xl1, Xl2)) <=> ![Xl1: $i, Xl2: $i] : (permutation_succeeds(Xl1, Xl2) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)) | (~(occ(tptp_fun_Xx_127(Xl2, Xl1), Xl1) = occ(tptp_fun_Xx_127(Xl2, Xl1), Xl2))))),
% 0.22/0.55 inference(quant_intro,[status(thm)],[112])).
% 0.22/0.55 tff(114,plain,
% 0.22/0.55 (![Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl2) & list_succeeds(Xl1) & ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))) | permutation_succeeds(Xl1, Xl2)) <=> ![Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl2) & list_succeeds(Xl1) & ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))) | permutation_succeeds(Xl1, Xl2))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(115,plain,
% 0.22/0.55 (^[Xl1: $i, Xl2: $i] : trans(monotonicity(rewrite(((list_succeeds(Xl2) & list_succeeds(Xl1)) & ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2))) <=> (list_succeeds(Xl2) & list_succeeds(Xl1) & ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))), ((((list_succeeds(Xl2) & list_succeeds(Xl1)) & ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2))) => permutation_succeeds(Xl1, Xl2)) <=> ((list_succeeds(Xl2) & list_succeeds(Xl1) & ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2))) => permutation_succeeds(Xl1, Xl2)))), rewrite(((list_succeeds(Xl2) & list_succeeds(Xl1) & ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2))) => permutation_succeeds(Xl1, Xl2)) <=> ((~(list_succeeds(Xl2) & list_succeeds(Xl1) & ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))) | permutation_succeeds(Xl1, Xl2))), ((((list_succeeds(Xl2) & list_succeeds(Xl1)) & ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2))) => permutation_succeeds(Xl1, Xl2)) <=> ((~(list_succeeds(Xl2) & list_succeeds(Xl1) & ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))) | permutation_succeeds(Xl1, Xl2))))),
% 0.22/0.55 inference(bind,[status(th)],[])).
% 0.22/0.55 tff(116,plain,
% 0.22/0.55 (![Xl1: $i, Xl2: $i] : (((list_succeeds(Xl2) & list_succeeds(Xl1)) & ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2))) => permutation_succeeds(Xl1, Xl2)) <=> ![Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl2) & list_succeeds(Xl1) & ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))) | permutation_succeeds(Xl1, Xl2))),
% 0.22/0.55 inference(quant_intro,[status(thm)],[115])).
% 0.22/0.55 tff(117,axiom,(![Xl1: $i, Xl2: $i] : (((list_succeeds(Xl2) & list_succeeds(Xl1)) & ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2))) => permutation_succeeds(Xl1, Xl2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''theorem-(occ:permutation)'')).
% 0.22/0.55 tff(118,plain,
% 0.22/0.55 (![Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl2) & list_succeeds(Xl1) & ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))) | permutation_succeeds(Xl1, Xl2))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.22/0.55 tff(119,plain,
% 0.22/0.55 (![Xl1: $i, Xl2: $i] : ((~(list_succeeds(Xl2) & list_succeeds(Xl1) & ![Xx: $i] : (occ(Xx, Xl1) = occ(Xx, Xl2)))) | permutation_succeeds(Xl1, Xl2))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.22/0.55 tff(120,plain,(
% 0.22/0.55 ![Xl1: $i, Xl2: $i] : (((~list_succeeds(Xl2)) | (~list_succeeds(Xl1)) | (~(occ(tptp_fun_Xx_127(Xl2, Xl1), Xl1) = occ(tptp_fun_Xx_127(Xl2, Xl1), Xl2)))) | permutation_succeeds(Xl1, Xl2))),
% 0.22/0.55 inference(skolemize,[status(sab)],[119])).
% 0.22/0.55 tff(121,plain,
% 0.22/0.55 (![Xl1: $i, Xl2: $i] : (permutation_succeeds(Xl1, Xl2) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)) | (~(occ(tptp_fun_Xx_127(Xl2, Xl1), Xl1) = occ(tptp_fun_Xx_127(Xl2, Xl1), Xl2))))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.22/0.55 tff(122,plain,
% 0.22/0.55 (![Xl1: $i, Xl2: $i] : (permutation_succeeds(Xl1, Xl2) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)) | (~(occ(tptp_fun_Xx_127(Xl2, Xl1), Xl1) = occ(tptp_fun_Xx_127(Xl2, Xl1), Xl2))))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[121, 111])).
% 0.22/0.55 tff(123,plain,
% 0.22/0.55 (((~![Xl1: $i, Xl2: $i] : (permutation_succeeds(Xl1, Xl2) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)) | (~(occ(tptp_fun_Xx_127(Xl2, Xl1), Xl1) = occ(tptp_fun_Xx_127(Xl2, Xl1), Xl2))))) | (permutation_succeeds(tptp_fun_____(Xl1!133, Xl2!132), tptp_fun_____(Xl2!132, Xl1!133)) | (~list_succeeds(tptp_fun_____(Xl2!132, Xl1!133))) | (~list_succeeds(tptp_fun_____(Xl1!133, Xl2!132))) | (~(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl1!133, Xl2!132)) = occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl2!132, Xl1!133)))))) <=> ((~![Xl1: $i, Xl2: $i] : (permutation_succeeds(Xl1, Xl2) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)) | (~(occ(tptp_fun_Xx_127(Xl2, Xl1), Xl1) = occ(tptp_fun_Xx_127(Xl2, Xl1), Xl2))))) | permutation_succeeds(tptp_fun_____(Xl1!133, Xl2!132), tptp_fun_____(Xl2!132, Xl1!133)) | (~list_succeeds(tptp_fun_____(Xl2!132, Xl1!133))) | (~list_succeeds(tptp_fun_____(Xl1!133, Xl2!132))) | (~(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl1!133, Xl2!132)) = occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl2!132, Xl1!133)))))),
% 0.22/0.56 inference(rewrite,[status(thm)],[])).
% 0.22/0.56 tff(124,plain,
% 0.22/0.56 ((~![Xl1: $i, Xl2: $i] : (permutation_succeeds(Xl1, Xl2) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)) | (~(occ(tptp_fun_Xx_127(Xl2, Xl1), Xl1) = occ(tptp_fun_Xx_127(Xl2, Xl1), Xl2))))) | (permutation_succeeds(tptp_fun_____(Xl1!133, Xl2!132), tptp_fun_____(Xl2!132, Xl1!133)) | (~list_succeeds(tptp_fun_____(Xl2!132, Xl1!133))) | (~list_succeeds(tptp_fun_____(Xl1!133, Xl2!132))) | (~(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl1!133, Xl2!132)) = occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl2!132, Xl1!133)))))),
% 0.22/0.56 inference(quant_inst,[status(thm)],[])).
% 0.22/0.56 tff(125,plain,
% 0.22/0.56 ((~![Xl1: $i, Xl2: $i] : (permutation_succeeds(Xl1, Xl2) | (~list_succeeds(Xl2)) | (~list_succeeds(Xl1)) | (~(occ(tptp_fun_Xx_127(Xl2, Xl1), Xl1) = occ(tptp_fun_Xx_127(Xl2, Xl1), Xl2))))) | permutation_succeeds(tptp_fun_____(Xl1!133, Xl2!132), tptp_fun_____(Xl2!132, Xl1!133)) | (~list_succeeds(tptp_fun_____(Xl2!132, Xl1!133))) | (~list_succeeds(tptp_fun_____(Xl1!133, Xl2!132))) | (~(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl1!133, Xl2!132)) = occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl2!132, Xl1!133))))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.22/0.56 tff(126,plain,
% 0.22/0.56 ((~list_succeeds(tptp_fun_____(Xl2!132, Xl1!133))) | (~list_succeeds(tptp_fun_____(Xl1!133, Xl2!132))) | (~(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl1!133, Xl2!132)) = occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl2!132, Xl1!133))))),
% 0.22/0.56 inference(unit_resolution,[status(thm)],[125, 122, 109])).
% 0.22/0.56 tff(127,plain,
% 0.22/0.56 (~(occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl1!133, Xl2!132)) = occ(tptp_fun_Xx_127(tptp_fun_____(Xl2!132, Xl1!133), tptp_fun_____(Xl1!133, Xl2!132)), tptp_fun_____(Xl2!132, Xl1!133)))),
% 0.22/0.56 inference(unit_resolution,[status(thm)],[126, 108, 104])).
% 0.22/0.56 tff(128,plain,
% 0.22/0.56 ($false),
% 0.22/0.56 inference(unit_resolution,[status(thm)],[127, 84])).
% 0.22/0.56 % SZS output end Proof
% 0.22/0.56 % E exiting
%------------------------------------------------------------------------------