%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWX203+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 07:08:16 PM UTC 2026
% Result : Theorem 20.87s 21.03s
% Output : Proof 20.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX203+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.15/0.33 % Computer : n010.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 11:25:53 EDT 2026
% 0.15/0.33 % CPUTime :
% 20.87/21.03 % SZS status Theorem
% 20.87/21.03 % SZS output start Proof
% 20.87/21.03 tff(leqNat_type, type, (
% 20.87/21.03 leqNat: ( $i * $i ) > $o)).
% 20.87/21.03 tff(s_type, type, (
% 20.87/21.03 s: $i > $i)).
% 20.87/21.03 tff(z_type, type, (
% 20.87/21.03 z: $i)).
% 20.87/21.03 tff(elemNat_type, type, (
% 20.87/21.03 elemNat: ( $i * $i ) > $o)).
% 20.87/21.03 tff(cons_type, type, (
% 20.87/21.03 cons: ( $i * $i ) > $i)).
% 20.87/21.03 tff(append_type, type, (
% 20.87/21.03 append: ( $i * $i ) > $i)).
% 20.87/21.03 tff(nil_type, type, (
% 20.87/21.03 nil: $i)).
% 20.87/21.03 tff(rev_type, type, (
% 20.87/21.03 rev: $i > $i)).
% 20.87/21.03 tff(unique_type, type, (
% 20.87/21.03 unique: $i > $o)).
% 20.87/21.03 tff(lengthNat_type, type, (
% 20.87/21.03 lengthNat: $i > $i)).
% 20.87/21.03 tff(sorted_type, type, (
% 20.87/21.03 sorted: $i > $o)).
% 20.87/21.03 tff(1,assumption,(s(s(s(z))) = s(z)), introduced(assumption)).
% 20.87/21.03 tff(2,plain,
% 20.87/21.03 (s(s(s(s(z)))) = s(s(z))),
% 20.87/21.03 inference(monotonicity,[status(thm)],[1])).
% 20.87/21.03 tff(3,assumption,(s(s(s(s(z)))) = s(s(z))), introduced(assumption)).
% 20.87/21.03 tff(4,plain,
% 20.87/21.03 (s(s(z)) = s(s(s(s(z))))),
% 20.87/21.03 inference(symmetry,[status(thm)],[3])).
% 20.87/21.03 tff(5,plain,
% 20.87/21.03 (leqNat(s(s(z)), s(s(s(z)))) <=> leqNat(s(s(s(s(z)))), s(s(s(z))))),
% 20.87/21.03 inference(monotonicity,[status(thm)],[4])).
% 20.87/21.03 tff(6,plain,
% 20.87/21.03 (leqNat(s(s(s(s(z)))), s(s(s(z)))) <=> leqNat(s(s(z)), s(s(s(z))))),
% 20.87/21.03 inference(symmetry,[status(thm)],[5])).
% 20.87/21.03 tff(7,plain,
% 20.87/21.03 ((~leqNat(s(s(s(s(z)))), s(s(s(z))))) <=> (~leqNat(s(s(z)), s(s(s(z)))))),
% 20.87/21.03 inference(monotonicity,[status(thm)],[6])).
% 20.87/21.03 tff(8,plain,
% 20.87/21.03 (^[Z: $i, M: $i] : refl((leqNat(s(Z), s(M)) <=> leqNat(Z, M)) <=> (leqNat(s(Z), s(M)) <=> leqNat(Z, M)))),
% 20.87/21.03 inference(bind,[status(th)],[])).
% 20.87/21.03 tff(9,plain,
% 20.87/21.03 (![Z: $i, M: $i] : (leqNat(s(Z), s(M)) <=> leqNat(Z, M)) <=> ![Z: $i, M: $i] : (leqNat(s(Z), s(M)) <=> leqNat(Z, M))),
% 20.87/21.03 inference(quant_intro,[status(thm)],[8])).
% 20.87/21.03 tff(10,plain,
% 20.87/21.03 (![Z: $i, M: $i] : (leqNat(s(Z), s(M)) <=> leqNat(Z, M)) <=> ![Z: $i, M: $i] : (leqNat(s(Z), s(M)) <=> leqNat(Z, M))),
% 20.87/21.03 inference(rewrite,[status(thm)],[])).
% 20.87/21.03 tff(11,axiom,(![Z: $i, M: $i] : (leqNat(s(Z), s(M)) <=> leqNat(Z, M))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_008')).
% 20.87/21.03 tff(12,plain,
% 20.87/21.03 (![Z: $i, M: $i] : (leqNat(s(Z), s(M)) <=> leqNat(Z, M))),
% 20.87/21.03 inference(modus_ponens,[status(thm)],[11, 10])).
% 20.87/21.03 tff(13,plain,(
% 20.87/21.03 ![Z: $i, M: $i] : (leqNat(s(Z), s(M)) <=> leqNat(Z, M))),
% 20.87/21.03 inference(skolemize,[status(sab)],[12])).
% 20.87/21.03 tff(14,plain,
% 20.87/21.03 (![Z: $i, M: $i] : (leqNat(s(Z), s(M)) <=> leqNat(Z, M))),
% 20.87/21.03 inference(modus_ponens,[status(thm)],[13, 9])).
% 20.87/21.03 tff(15,plain,
% 20.87/21.03 ((~![Z: $i, M: $i] : (leqNat(s(Z), s(M)) <=> leqNat(Z, M))) | (leqNat(s(s(s(s(z)))), s(s(s(z)))) <=> leqNat(s(s(s(z))), s(s(z))))),
% 20.87/21.03 inference(quant_inst,[status(thm)],[])).
% 20.87/21.03 tff(16,plain,
% 20.87/21.03 (leqNat(s(s(s(s(z)))), s(s(s(z)))) <=> leqNat(s(s(s(z))), s(s(z)))),
% 20.87/21.03 inference(unit_resolution,[status(thm)],[15, 14])).
% 20.87/21.03 tff(17,plain,
% 20.87/21.03 ((~![Z: $i, M: $i] : (leqNat(s(Z), s(M)) <=> leqNat(Z, M))) | (leqNat(s(s(s(z))), s(s(z))) <=> leqNat(s(s(z)), s(z)))),
% 20.87/21.03 inference(quant_inst,[status(thm)],[])).
% 20.87/21.03 tff(18,plain,
% 20.87/21.03 (leqNat(s(s(s(z))), s(s(z))) <=> leqNat(s(s(z)), s(z))),
% 20.87/21.03 inference(unit_resolution,[status(thm)],[17, 14])).
% 20.87/21.03 tff(19,plain,
% 20.87/21.03 ((~![Z: $i, M: $i] : (leqNat(s(Z), s(M)) <=> leqNat(Z, M))) | (leqNat(s(s(z)), s(z)) <=> leqNat(s(z), z))),
% 20.87/21.03 inference(quant_inst,[status(thm)],[])).
% 20.87/21.03 tff(20,plain,
% 20.87/21.03 (leqNat(s(s(z)), s(z)) <=> leqNat(s(z), z)),
% 20.87/21.03 inference(unit_resolution,[status(thm)],[19, 14])).
% 20.87/21.03 tff(21,plain,
% 20.87/21.03 (^[Z: $i] : refl((~leqNat(s(Z), z)) <=> (~leqNat(s(Z), z)))),
% 20.87/21.03 inference(bind,[status(th)],[])).
% 20.87/21.03 tff(22,plain,
% 20.87/21.03 (![Z: $i] : (~leqNat(s(Z), z)) <=> ![Z: $i] : (~leqNat(s(Z), z))),
% 20.87/21.03 inference(quant_intro,[status(thm)],[21])).
% 20.87/21.03 tff(23,plain,
% 20.87/21.03 (![Z: $i] : (~leqNat(s(Z), z)) <=> ![Z: $i] : (~leqNat(s(Z), z))),
% 20.87/21.03 inference(rewrite,[status(thm)],[])).
% 20.87/21.03 tff(24,axiom,(![Z: $i] : (~leqNat(s(Z), z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_007')).
% 20.87/21.03 tff(25,plain,
% 20.87/21.03 (![Z: $i] : (~leqNat(s(Z), z))),
% 20.87/21.03 inference(modus_ponens,[status(thm)],[24, 23])).
% 20.87/21.03 tff(26,plain,(
% 20.87/21.03 ![Z: $i] : (~leqNat(s(Z), z))),
% 20.87/21.03 inference(skolemize,[status(sab)],[25])).
% 20.87/21.03 tff(27,plain,
% 20.87/21.03 (![Z: $i] : (~leqNat(s(Z), z))),
% 20.87/21.03 inference(modus_ponens,[status(thm)],[26, 22])).
% 20.87/21.03 tff(28,plain,
% 20.87/21.03 ((~![Z: $i] : (~leqNat(s(Z), z))) | (~leqNat(s(z), z))),
% 20.87/21.03 inference(quant_inst,[status(thm)],[])).
% 20.87/21.03 tff(29,plain,
% 20.87/21.03 (~leqNat(s(z), z)),
% 20.87/21.03 inference(unit_resolution,[status(thm)],[28, 27])).
% 20.87/21.03 tff(30,plain,
% 20.87/21.03 ((~(leqNat(s(s(z)), s(z)) <=> leqNat(s(z), z))) | (~leqNat(s(s(z)), s(z))) | leqNat(s(z), z)),
% 20.87/21.03 inference(tautology,[status(thm)],[])).
% 20.87/21.03 tff(31,plain,
% 20.87/21.03 (~leqNat(s(s(z)), s(z))),
% 20.87/21.03 inference(unit_resolution,[status(thm)],[30, 29, 20])).
% 20.87/21.03 tff(32,plain,
% 20.87/21.03 ((~(leqNat(s(s(s(z))), s(s(z))) <=> leqNat(s(s(z)), s(z)))) | (~leqNat(s(s(s(z))), s(s(z)))) | leqNat(s(s(z)), s(z))),
% 20.87/21.03 inference(tautology,[status(thm)],[])).
% 20.87/21.03 tff(33,plain,
% 20.87/21.03 (~leqNat(s(s(s(z))), s(s(z)))),
% 20.87/21.03 inference(unit_resolution,[status(thm)],[32, 31, 18])).
% 20.87/21.03 tff(34,plain,
% 20.87/21.03 ((~(leqNat(s(s(s(s(z)))), s(s(s(z)))) <=> leqNat(s(s(s(z))), s(s(z))))) | (~leqNat(s(s(s(s(z)))), s(s(s(z))))) | leqNat(s(s(s(z))), s(s(z)))),
% 20.87/21.03 inference(tautology,[status(thm)],[])).
% 20.87/21.03 tff(35,plain,
% 20.87/21.03 ((~(leqNat(s(s(s(s(z)))), s(s(s(z)))) <=> leqNat(s(s(s(z))), s(s(z))))) | (~leqNat(s(s(s(s(z)))), s(s(s(z)))))),
% 20.87/21.03 inference(unit_resolution,[status(thm)],[34, 33])).
% 20.87/21.03 tff(36,plain,
% 20.87/21.03 (~leqNat(s(s(s(s(z)))), s(s(s(z))))),
% 20.87/21.03 inference(unit_resolution,[status(thm)],[35, 16])).
% 20.87/21.03 tff(37,plain,
% 20.87/21.03 (~leqNat(s(s(z)), s(s(s(z))))),
% 20.87/21.03 inference(modus_ponens,[status(thm)],[36, 7])).
% 20.87/21.03 tff(38,plain,
% 20.87/21.03 ((~![Z: $i, M: $i] : (leqNat(s(Z), s(M)) <=> leqNat(Z, M))) | (leqNat(s(s(z)), s(s(s(z)))) <=> leqNat(s(z), s(s(z))))),
% 20.87/21.03 inference(quant_inst,[status(thm)],[])).
% 20.87/21.03 tff(39,plain,
% 20.87/21.03 (leqNat(s(s(z)), s(s(s(z)))) <=> leqNat(s(z), s(s(z)))),
% 20.87/21.03 inference(unit_resolution,[status(thm)],[38, 14])).
% 20.87/21.03 tff(40,plain,
% 20.87/21.03 ((~![Z: $i, M: $i] : (leqNat(s(Z), s(M)) <=> leqNat(Z, M))) | (leqNat(s(z), s(s(z))) <=> leqNat(z, s(z)))),
% 20.87/21.03 inference(quant_inst,[status(thm)],[])).
% 20.87/21.03 tff(41,plain,
% 20.87/21.03 (leqNat(s(z), s(s(z))) <=> leqNat(z, s(z))),
% 20.87/21.03 inference(unit_resolution,[status(thm)],[40, 14])).
% 20.87/21.03 tff(42,plain,
% 20.87/21.03 (^[Y: $i] : refl(leqNat(z, Y) <=> leqNat(z, Y))),
% 20.87/21.03 inference(bind,[status(th)],[])).
% 20.87/21.03 tff(43,plain,
% 20.87/21.03 (![Y: $i] : leqNat(z, Y) <=> ![Y: $i] : leqNat(z, Y)),
% 20.87/21.03 inference(quant_intro,[status(thm)],[42])).
% 20.87/21.03 tff(44,plain,
% 20.87/21.03 (![Y: $i] : leqNat(z, Y) <=> ![Y: $i] : leqNat(z, Y)),
% 20.87/21.03 inference(rewrite,[status(thm)],[])).
% 20.87/21.03 tff(45,axiom,(![Y: $i] : leqNat(z, Y)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_006')).
% 20.87/21.03 tff(46,plain,
% 20.87/21.03 (![Y: $i] : leqNat(z, Y)),
% 20.87/21.03 inference(modus_ponens,[status(thm)],[45, 44])).
% 20.87/21.03 tff(47,plain,(
% 20.87/21.03 ![Y: $i] : leqNat(z, Y)),
% 20.87/21.03 inference(skolemize,[status(sab)],[46])).
% 20.87/21.03 tff(48,plain,
% 20.87/21.03 (![Y: $i] : leqNat(z, Y)),
% 20.87/21.03 inference(modus_ponens,[status(thm)],[47, 43])).
% 20.87/21.03 tff(49,plain,
% 20.87/21.03 ((~![Y: $i] : leqNat(z, Y)) | leqNat(z, s(z))),
% 20.87/21.03 inference(quant_inst,[status(thm)],[])).
% 20.87/21.03 tff(50,plain,
% 20.87/21.03 (leqNat(z, s(z))),
% 20.87/21.03 inference(unit_resolution,[status(thm)],[49, 48])).
% 20.87/21.03 tff(51,plain,
% 20.87/21.03 ((~(leqNat(s(z), s(s(z))) <=> leqNat(z, s(z)))) | leqNat(s(z), s(s(z))) | (~leqNat(z, s(z)))),
% 20.87/21.03 inference(tautology,[status(thm)],[])).
% 20.87/21.03 tff(52,plain,
% 20.87/21.03 (leqNat(s(z), s(s(z)))),
% 20.87/21.03 inference(unit_resolution,[status(thm)],[51, 50, 41])).
% 20.87/21.03 tff(53,plain,
% 20.87/21.03 ((~(leqNat(s(s(z)), s(s(s(z)))) <=> leqNat(s(z), s(s(z))))) | leqNat(s(s(z)), s(s(s(z)))) | (~leqNat(s(z), s(s(z))))),
% 20.87/21.03 inference(tautology,[status(thm)],[])).
% 20.87/21.03 tff(54,plain,
% 20.87/21.03 (leqNat(s(s(z)), s(s(s(z))))),
% 20.87/21.03 inference(unit_resolution,[status(thm)],[53, 52, 39])).
% 20.87/21.03 tff(55,plain,
% 20.87/21.03 ($false),
% 20.87/21.03 inference(unit_resolution,[status(thm)],[54, 37])).
% 20.87/21.03 tff(56,plain,(~(s(s(s(s(z)))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 20.87/21.03 tff(57,plain,
% 20.87/21.03 ($false),
% 20.87/21.03 inference(unit_resolution,[status(thm)],[56, 2])).
% 20.87/21.03 tff(58,plain,(~(s(s(s(z))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 20.87/21.03 tff(59,assumption,(~(elemNat(s(s(s(z))), cons(z, nil)) <=> ((s(s(s(z))) = z) | elemNat(s(s(s(z))), nil)))), introduced(assumption)).
% 20.87/21.03 tff(60,plain,
% 20.87/21.03 (^[X: $i, Z: $i, Xs: $i] : refl((elemNat(X, cons(Z, Xs)) <=> ((X = Z) | elemNat(X, Xs))) <=> (elemNat(X, cons(Z, Xs)) <=> ((X = Z) | elemNat(X, Xs))))),
% 20.87/21.03 inference(bind,[status(th)],[])).
% 20.87/21.03 tff(61,plain,
% 20.87/21.03 (![X: $i, Z: $i, Xs: $i] : (elemNat(X, cons(Z, Xs)) <=> ((X = Z) | elemNat(X, Xs))) <=> ![X: $i, Z: $i, Xs: $i] : (elemNat(X, cons(Z, Xs)) <=> ((X = Z) | elemNat(X, Xs)))),
% 20.87/21.03 inference(quant_intro,[status(thm)],[60])).
% 20.87/21.03 tff(62,plain,
% 20.87/21.03 (![X: $i, Z: $i, Xs: $i] : (elemNat(X, cons(Z, Xs)) <=> ((X = Z) | elemNat(X, Xs))) <=> ![X: $i, Z: $i, Xs: $i] : (elemNat(X, cons(Z, Xs)) <=> ((X = Z) | elemNat(X, Xs)))),
% 20.87/21.03 inference(rewrite,[status(thm)],[])).
% 20.87/21.03 tff(63,axiom,(![X: $i, Z: $i, Xs: $i] : (elemNat(X, cons(Z, Xs)) <=> ((X = Z) | elemNat(X, Xs)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_015')).
% 20.87/21.03 tff(64,plain,
% 20.87/21.03 (![X: $i, Z: $i, Xs: $i] : (elemNat(X, cons(Z, Xs)) <=> ((X = Z) | elemNat(X, Xs)))),
% 20.87/21.03 inference(modus_ponens,[status(thm)],[63, 62])).
% 20.87/21.03 tff(65,plain,(
% 20.87/21.03 ![X: $i, Z: $i, Xs: $i] : (elemNat(X, cons(Z, Xs)) <=> ((X = Z) | elemNat(X, Xs)))),
% 20.87/21.03 inference(skolemize,[status(sab)],[64])).
% 20.87/21.03 tff(66,plain,
% 20.87/21.03 (![X: $i, Z: $i, Xs: $i] : (elemNat(X, cons(Z, Xs)) <=> ((X = Z) | elemNat(X, Xs)))),
% 20.87/21.03 inference(modus_ponens,[status(thm)],[65, 61])).
% 20.87/21.03 tff(67,plain,
% 20.87/21.03 ((~![X: $i, Z: $i, Xs: $i] : (elemNat(X, cons(Z, Xs)) <=> ((X = Z) | elemNat(X, Xs)))) | (elemNat(s(s(s(z))), cons(z, nil)) <=> ((s(s(s(z))) = z) | elemNat(s(s(s(z))), nil)))),
% 20.87/21.03 inference(quant_inst,[status(thm)],[])).
% 20.87/21.03 tff(68,plain,
% 20.87/21.03 ($false),
% 20.87/21.03 inference(unit_resolution,[status(thm)],[67, 66, 59])).
% 20.87/21.03 tff(69,plain,(elemNat(s(s(s(z))), cons(z, nil)) <=> ((s(s(s(z))) = z) | elemNat(s(s(s(z))), nil))), inference(lemma,lemma(discharge,[]))).
% 20.87/21.03 tff(70,plain,
% 20.87/21.03 ((s(s(s(z))) = z) <=> (z = s(s(s(z))))),
% 20.87/21.03 inference(commutativity,[status(thm)],[])).
% 20.87/21.03 tff(71,plain,
% 20.87/21.03 ((z = s(s(s(z)))) <=> (s(s(s(z))) = z)),
% 20.87/21.03 inference(symmetry,[status(thm)],[70])).
% 20.87/21.03 tff(72,plain,
% 20.87/21.03 ((~(z = s(s(s(z))))) <=> (~(s(s(s(z))) = z))),
% 20.87/21.03 inference(monotonicity,[status(thm)],[71])).
% 20.87/21.03 tff(73,plain,
% 20.87/21.03 (^[X: $i] : refl((~(z = s(X))) <=> (~(z = s(X))))),
% 20.87/21.03 inference(bind,[status(th)],[])).
% 20.87/21.03 tff(74,plain,
% 20.87/21.03 (![X: $i] : (~(z = s(X))) <=> ![X: $i] : (~(z = s(X)))),
% 20.87/21.03 inference(quant_intro,[status(thm)],[73])).
% 20.87/21.03 tff(75,plain,
% 20.87/21.03 (![X: $i] : (~(z = s(X))) <=> ![X: $i] : (~(z = s(X)))),
% 20.87/21.03 inference(rewrite,[status(thm)],[])).
% 20.87/21.03 tff(76,axiom,(![X: $i] : (~(z = s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_005')).
% 20.87/21.03 tff(77,plain,
% 20.87/21.03 (![X: $i] : (~(z = s(X)))),
% 20.87/21.03 inference(modus_ponens,[status(thm)],[76, 75])).
% 20.87/21.03 tff(78,plain,(
% 20.87/21.03 ![X: $i] : (~(z = s(X)))),
% 20.87/21.03 inference(skolemize,[status(sab)],[77])).
% 20.87/21.03 tff(79,plain,
% 20.87/21.03 (![X: $i] : (~(z = s(X)))),
% 20.87/21.03 inference(modus_ponens,[status(thm)],[78, 74])).
% 20.87/21.03 tff(80,plain,
% 20.87/21.03 ((~![X: $i] : (~(z = s(X)))) | (~(z = s(s(s(z)))))),
% 20.87/21.03 inference(quant_inst,[status(thm)],[])).
% 20.87/21.03 tff(81,plain,
% 20.87/21.03 (~(z = s(s(s(z))))),
% 20.87/21.03 inference(unit_resolution,[status(thm)],[80, 79])).
% 20.87/21.03 tff(82,plain,
% 20.87/21.03 (~(s(s(s(z))) = z)),
% 20.87/21.03 inference(modus_ponens,[status(thm)],[81, 72])).
% 20.87/21.03 tff(83,assumption,(elemNat(s(s(s(z))), nil)), introduced(assumption)).
% 20.87/21.03 tff(84,plain,
% 20.87/21.03 (^[X: $i] : refl((~elemNat(X, nil)) <=> (~elemNat(X, nil)))),
% 20.87/21.03 inference(bind,[status(th)],[])).
% 20.87/21.03 tff(85,plain,
% 20.87/21.03 (![X: $i] : (~elemNat(X, nil)) <=> ![X: $i] : (~elemNat(X, nil))),
% 20.87/21.03 inference(quant_intro,[status(thm)],[84])).
% 20.87/21.03 tff(86,plain,
% 20.87/21.03 (![X: $i] : (~elemNat(X, nil)) <=> ![X: $i] : (~elemNat(X, nil))),
% 20.87/21.03 inference(rewrite,[status(thm)],[])).
% 20.87/21.03 tff(87,axiom,(![X: $i] : (~elemNat(X, nil))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_014')).
% 20.87/21.03 tff(88,plain,
% 20.87/21.03 (![X: $i] : (~elemNat(X, nil))),
% 20.87/21.03 inference(modus_ponens,[status(thm)],[87, 86])).
% 20.87/21.03 tff(89,plain,(
% 20.87/21.03 ![X: $i] : (~elemNat(X, nil))),
% 20.87/21.03 inference(skolemize,[status(sab)],[88])).
% 20.87/21.03 tff(90,plain,
% 20.87/21.03 (![X: $i] : (~elemNat(X, nil))),
% 20.87/21.03 inference(modus_ponens,[status(thm)],[89, 85])).
% 20.87/21.03 tff(91,plain,
% 20.87/21.03 ((~![X: $i] : (~elemNat(X, nil))) | (~elemNat(s(s(s(z))), nil))),
% 20.87/21.03 inference(quant_inst,[status(thm)],[])).
% 20.87/21.03 tff(92,plain,
% 20.87/21.03 ($false),
% 20.87/21.03 inference(unit_resolution,[status(thm)],[91, 90, 83])).
% 20.87/21.03 tff(93,plain,(~elemNat(s(s(s(z))), nil)), inference(lemma,lemma(discharge,[]))).
% 20.87/21.03 tff(94,plain,
% 20.87/21.03 ((~((s(s(s(z))) = z) | elemNat(s(s(s(z))), nil))) | (s(s(s(z))) = z) | elemNat(s(s(s(z))), nil)),
% 20.87/21.03 inference(tautology,[status(thm)],[])).
% 20.87/21.03 tff(95,plain,
% 20.87/21.03 (~((s(s(s(z))) = z) | elemNat(s(s(s(z))), nil))),
% 20.87/21.03 inference(unit_resolution,[status(thm)],[94, 93, 82])).
% 20.87/21.03 tff(96,plain,
% 20.87/21.03 ((~(elemNat(s(s(s(z))), cons(z, nil)) <=> ((s(s(s(z))) = z) | elemNat(s(s(s(z))), nil)))) | (~elemNat(s(s(s(z))), cons(z, nil))) | ((s(s(s(z))) = z) | elemNat(s(s(s(z))), nil))),
% 20.87/21.03 inference(tautology,[status(thm)],[])).
% 20.87/21.03 tff(97,plain,
% 20.87/21.03 ((~(elemNat(s(s(s(z))), cons(z, nil)) <=> ((s(s(s(z))) = z) | elemNat(s(s(s(z))), nil)))) | (~elemNat(s(s(s(z))), cons(z, nil)))),
% 20.87/21.03 inference(unit_resolution,[status(thm)],[96, 95])).
% 20.87/21.03 tff(98,plain,
% 20.87/21.03 (~elemNat(s(s(s(z))), cons(z, nil))),
% 20.87/21.03 inference(unit_resolution,[status(thm)],[97, 69])).
% 20.87/21.03 tff(99,plain,
% 20.87/21.03 (^[Y: $i] : refl((append(nil, Y) = Y) <=> (append(nil, Y) = Y))),
% 20.87/21.03 inference(bind,[status(th)],[])).
% 20.87/21.03 tff(100,plain,
% 20.87/21.03 (![Y: $i] : (append(nil, Y) = Y) <=> ![Y: $i] : (append(nil, Y) = Y)),
% 20.87/21.03 inference(quant_intro,[status(thm)],[99])).
% 20.87/21.03 tff(101,plain,
% 20.87/21.03 (![Y: $i] : (append(nil, Y) = Y) <=> ![Y: $i] : (append(nil, Y) = Y)),
% 20.87/21.03 inference(rewrite,[status(thm)],[])).
% 20.87/21.03 tff(102,axiom,(![Y: $i] : (append(nil, Y) = Y)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_018')).
% 20.87/21.03 tff(103,plain,
% 20.87/21.03 (![Y: $i] : (append(nil, Y) = Y)),
% 20.87/21.03 inference(modus_ponens,[status(thm)],[102, 101])).
% 20.87/21.03 tff(104,plain,(
% 20.87/21.03 ![Y: $i] : (append(nil, Y) = Y)),
% 20.87/21.03 inference(skolemize,[status(sab)],[103])).
% 20.87/21.03 tff(105,plain,
% 20.87/21.03 (![Y: $i] : (append(nil, Y) = Y)),
% 20.87/21.03 inference(modus_ponens,[status(thm)],[104, 100])).
% 20.87/21.03 tff(106,plain,
% 20.87/21.03 ((~![Y: $i] : (append(nil, Y) = Y)) | (append(nil, cons(z, nil)) = cons(z, nil))),
% 20.87/21.03 inference(quant_inst,[status(thm)],[])).
% 20.87/21.03 tff(107,plain,
% 20.87/21.03 (append(nil, cons(z, nil)) = cons(z, nil)),
% 20.87/21.03 inference(unit_resolution,[status(thm)],[106, 105])).
% 20.87/21.03 tff(108,plain,
% 20.87/21.03 (cons(z, nil) = append(nil, cons(z, nil))),
% 20.87/21.03 inference(symmetry,[status(thm)],[107])).
% 20.87/21.03 tff(109,plain,
% 20.87/21.03 (cons(s(z), cons(z, nil)) = cons(s(z), append(nil, cons(z, nil)))),
% 20.87/21.03 inference(monotonicity,[status(thm)],[108])).
% 20.87/21.03 tff(110,plain,
% 20.87/21.03 (elemNat(s(s(s(z))), cons(s(z), cons(z, nil))) <=> elemNat(s(s(s(z))), cons(s(z), append(nil, cons(z, nil))))),
% 20.87/21.03 inference(monotonicity,[status(thm)],[109])).
% 20.87/21.03 tff(111,plain,
% 20.87/21.03 (elemNat(s(s(s(z))), cons(s(z), append(nil, cons(z, nil)))) <=> elemNat(s(s(s(z))), cons(s(z), cons(z, nil)))),
% 20.87/21.03 inference(symmetry,[status(thm)],[110])).
% 20.87/21.03 tff(112,assumption,(elemNat(s(s(s(z))), cons(s(z), append(nil, cons(z, nil))))), introduced(assumption)).
% 20.87/21.03 tff(113,plain,
% 20.87/21.03 (elemNat(s(s(s(z))), cons(s(z), cons(z, nil)))),
% 20.87/21.03 inference(modus_ponens,[status(thm)],[112, 111])).
% 20.87/21.03 tff(114,plain,
% 20.87/21.03 ((~![X: $i, Z: $i, Xs: $i] : (elemNat(X, cons(Z, Xs)) <=> ((X = Z) | elemNat(X, Xs)))) | (elemNat(s(s(s(z))), cons(s(z), cons(z, nil))) <=> ((s(s(s(z))) = s(z)) | elemNat(s(s(s(z))), cons(z, nil))))),
% 20.87/21.03 inference(quant_inst,[status(thm)],[])).
% 20.87/21.03 tff(115,plain,
% 20.87/21.03 (elemNat(s(s(s(z))), cons(s(z), cons(z, nil))) <=> ((s(s(s(z))) = s(z)) | elemNat(s(s(s(z))), cons(z, nil)))),
% 20.87/21.03 inference(unit_resolution,[status(thm)],[114, 66])).
% 20.87/21.03 tff(116,assumption,(~(s(s(s(z))) = s(z))), introduced(assumption)).
% 20.87/21.03 tff(117,assumption,(~elemNat(s(s(s(z))), cons(z, nil))), introduced(assumption)).
% 20.87/21.03 tff(118,plain,
% 20.87/21.03 ((~((s(s(s(z))) = s(z)) | elemNat(s(s(s(z))), cons(z, nil)))) | (s(s(s(z))) = s(z)) | elemNat(s(s(s(z))), cons(z, nil))),
% 20.87/21.03 inference(tautology,[status(thm)],[])).
% 20.87/21.03 tff(119,plain,
% 20.87/21.03 (~((s(s(s(z))) = s(z)) | elemNat(s(s(s(z))), cons(z, nil)))),
% 20.87/21.03 inference(unit_resolution,[status(thm)],[118, 117, 116])).
% 20.87/21.03 tff(120,plain,
% 20.87/21.03 ((~(elemNat(s(s(s(z))), cons(s(z), cons(z, nil))) <=> ((s(s(s(z))) = s(z)) | elemNat(s(s(s(z))), cons(z, nil))))) | (~elemNat(s(s(s(z))), cons(s(z), cons(z, nil)))) | ((s(s(s(z))) = s(z)) | elemNat(s(s(s(z))), cons(z, nil)))),
% 20.87/21.03 inference(tautology,[status(thm)],[])).
% 20.87/21.03 tff(121,plain,
% 20.87/21.03 ((~(elemNat(s(s(s(z))), cons(s(z), cons(z, nil))) <=> ((s(s(s(z))) = s(z)) | elemNat(s(s(s(z))), cons(z, nil))))) | (~elemNat(s(s(s(z))), cons(s(z), cons(z, nil))))),
% 20.87/21.03 inference(unit_resolution,[status(thm)],[120, 119])).
% 20.87/21.03 tff(122,plain,
% 20.87/21.03 (~elemNat(s(s(s(z))), cons(s(z), cons(z, nil)))),
% 20.87/21.03 inference(unit_resolution,[status(thm)],[121, 115])).
% 20.87/21.03 tff(123,plain,
% 20.87/21.03 ($false),
% 20.87/21.03 inference(unit_resolution,[status(thm)],[122, 113])).
% 20.87/21.03 tff(124,plain,((~elemNat(s(s(s(z))), cons(s(z), append(nil, cons(z, nil))))) | elemNat(s(s(s(z))), cons(z, nil)) | (s(s(s(z))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 20.87/21.03 tff(125,plain,
% 20.87/21.03 ((~elemNat(s(s(s(z))), cons(s(z), append(nil, cons(z, nil))))) | (s(s(s(z))) = s(z))),
% 20.87/21.03 inference(unit_resolution,[status(thm)],[124, 98])).
% 20.87/21.03 tff(126,plain,
% 20.87/21.03 (~elemNat(s(s(s(z))), cons(s(z), append(nil, cons(z, nil))))),
% 20.87/21.03 inference(unit_resolution,[status(thm)],[125, 58])).
% 20.87/21.03 tff(127,assumption,(((~unique(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) | elemNat(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) <=> unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))), introduced(assumption)).
% 20.87/21.03 tff(128,plain,
% 20.87/21.03 (^[Y: $i, Xs: $i] : refl((~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs)))) <=> (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs)))))),
% 20.87/21.03 inference(bind,[status(th)],[])).
% 20.87/21.03 tff(129,plain,
% 20.87/21.03 (![Y: $i, Xs: $i] : (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs)))) <=> ![Y: $i, Xs: $i] : (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs))))),
% 20.87/21.03 inference(quant_intro,[status(thm)],[128])).
% 20.87/21.03 tff(130,plain,
% 20.87/21.03 (^[Y: $i, Xs: $i] : trans(trans(monotonicity(rewrite(((~elemNat(Y, Xs)) & unique(Xs)) <=> (~(elemNat(Y, Xs) | (~unique(Xs))))), ((unique(cons(Y, Xs)) <=> ((~elemNat(Y, Xs)) & unique(Xs))) <=> (unique(cons(Y, Xs)) <=> (~(elemNat(Y, Xs) | (~unique(Xs))))))), rewrite((unique(cons(Y, Xs)) <=> (~(elemNat(Y, Xs) | (~unique(Xs))))) <=> (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs))))), ((unique(cons(Y, Xs)) <=> ((~elemNat(Y, Xs)) & unique(Xs))) <=> (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs)))))), rewrite((~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs)))) <=> (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs))))), ((unique(cons(Y, Xs)) <=> ((~elemNat(Y, Xs)) & unique(Xs))) <=> (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs))))))),
% 20.87/21.03 inference(bind,[status(th)],[])).
% 20.87/21.03 tff(131,plain,
% 20.87/21.03 (![Y: $i, Xs: $i] : (unique(cons(Y, Xs)) <=> ((~elemNat(Y, Xs)) & unique(Xs))) <=> ![Y: $i, Xs: $i] : (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs))))),
% 20.87/21.03 inference(quant_intro,[status(thm)],[130])).
% 20.87/21.03 tff(132,plain,
% 20.87/21.03 (![Y: $i, Xs: $i] : (unique(cons(Y, Xs)) <=> ((~elemNat(Y, Xs)) & unique(Xs))) <=> ![Y: $i, Xs: $i] : (unique(cons(Y, Xs)) <=> ((~elemNat(Y, Xs)) & unique(Xs)))),
% 20.87/21.03 inference(rewrite,[status(thm)],[])).
% 20.87/21.03 tff(133,axiom,(![Y: $i, Xs: $i] : (unique(cons(Y, Xs)) <=> ((~elemNat(Y, Xs)) & unique(Xs)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_017')).
% 20.87/21.03 tff(134,plain,
% 20.87/21.03 (![Y: $i, Xs: $i] : (unique(cons(Y, Xs)) <=> ((~elemNat(Y, Xs)) & unique(Xs)))),
% 20.87/21.03 inference(modus_ponens,[status(thm)],[133, 132])).
% 20.87/21.03 tff(135,plain,(
% 20.87/21.03 ![Y: $i, Xs: $i] : (unique(cons(Y, Xs)) <=> ((~elemNat(Y, Xs)) & unique(Xs)))),
% 20.87/21.03 inference(skolemize,[status(sab)],[134])).
% 20.87/21.03 tff(136,plain,
% 20.87/21.03 (![Y: $i, Xs: $i] : (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs))))),
% 20.87/21.03 inference(modus_ponens,[status(thm)],[135, 131])).
% 20.87/21.03 tff(137,plain,
% 20.87/21.03 (![Y: $i, Xs: $i] : (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs))))),
% 20.87/21.03 inference(modus_ponens,[status(thm)],[136, 129])).
% 20.87/21.03 tff(138,plain,
% 20.87/21.03 (((~![Y: $i, Xs: $i] : (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs))))) | (~(((~unique(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) | elemNat(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) <=> unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))))) <=> ((~![Y: $i, Xs: $i] : (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs))))) | (~(((~unique(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) | elemNat(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) <=> unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))))))),
% 20.87/21.03 inference(rewrite,[status(thm)],[])).
% 20.87/21.03 tff(139,plain,
% 20.87/21.03 ((~(((~unique(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) | elemNat(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) <=> unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))))) <=> (~(((~unique(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) | elemNat(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) <=> unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))))),
% 20.87/21.03 inference(rewrite,[status(thm)],[])).
% 20.87/21.03 tff(140,plain,
% 20.87/21.03 (((elemNat(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))) | (~unique(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))) <=> unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))) <=> (((~unique(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) | elemNat(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) <=> unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))))),
% 20.87/21.03 inference(rewrite,[status(thm)],[])).
% 20.87/21.03 tff(141,plain,
% 20.87/21.03 ((~((elemNat(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))) | (~unique(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))) <=> unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))))) <=> (~(((~unique(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) | elemNat(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) <=> unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))))),
% 20.87/21.03 inference(monotonicity,[status(thm)],[140])).
% 20.87/21.03 tff(142,plain,
% 20.87/21.03 ((~((elemNat(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))) | (~unique(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))) <=> unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))))) <=> (~(((~unique(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) | elemNat(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) <=> unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))))),
% 20.87/21.03 inference(transitivity,[status(thm)],[141, 139])).
% 20.87/21.03 tff(143,plain,
% 20.87/21.03 (((~![Y: $i, Xs: $i] : (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs))))) | (~((elemNat(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))) | (~unique(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))) <=> unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))))) <=> ((~![Y: $i, Xs: $i] : (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs))))) | (~(((~unique(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) | elemNat(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) <=> unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))))))),
% 20.87/21.03 inference(monotonicity,[status(thm)],[142])).
% 20.87/21.03 tff(144,plain,
% 20.87/21.03 (((~![Y: $i, Xs: $i] : (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs))))) | (~((elemNat(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))) | (~unique(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))) <=> unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))))) <=> ((~![Y: $i, Xs: $i] : (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs))))) | (~(((~unique(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) | elemNat(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) <=> unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))))))),
% 20.87/21.03 inference(transitivity,[status(thm)],[143, 138])).
% 20.87/21.03 tff(145,plain,
% 20.87/21.03 ((~![Y: $i, Xs: $i] : (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs))))) | (~((elemNat(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))) | (~unique(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))) <=> unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))))),
% 20.87/21.03 inference(quant_inst,[status(thm)],[])).
% 20.87/21.03 tff(146,plain,
% 20.87/21.03 ((~![Y: $i, Xs: $i] : (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs))))) | (~(((~unique(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) | elemNat(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) <=> unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))))),
% 20.87/21.03 inference(modus_ponens,[status(thm)],[145, 144])).
% 20.87/21.03 tff(147,plain,
% 20.87/21.03 ($false),
% 20.87/21.03 inference(unit_resolution,[status(thm)],[146, 137, 127])).
% 20.87/21.03 tff(148,plain,(~(((~unique(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) | elemNat(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) <=> unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))))), inference(lemma,lemma(discharge,[]))).
% 20.87/21.03 tff(149,assumption,(~(lengthNat(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) = s(lengthNat(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))))), introduced(assumption)).
% 20.87/21.03 tff(150,plain,
% 20.87/21.03 (^[Y: $i, Xs: $i] : refl((lengthNat(cons(Y, Xs)) = s(lengthNat(Xs))) <=> (lengthNat(cons(Y, Xs)) = s(lengthNat(Xs))))),
% 20.87/21.03 inference(bind,[status(th)],[])).
% 20.87/21.03 tff(151,plain,
% 20.87/21.03 (![Y: $i, Xs: $i] : (lengthNat(cons(Y, Xs)) = s(lengthNat(Xs))) <=> ![Y: $i, Xs: $i] : (lengthNat(cons(Y, Xs)) = s(lengthNat(Xs)))),
% 20.87/21.03 inference(quant_intro,[status(thm)],[150])).
% 20.87/21.03 tff(152,plain,
% 20.87/21.03 (![Y: $i, Xs: $i] : (lengthNat(cons(Y, Xs)) = s(lengthNat(Xs))) <=> ![Y: $i, Xs: $i] : (lengthNat(cons(Y, Xs)) = s(lengthNat(Xs)))),
% 20.87/21.03 inference(rewrite,[status(thm)],[])).
% 20.87/21.03 tff(153,axiom,(![Y: $i, Xs: $i] : (lengthNat(cons(Y, Xs)) = s(lengthNat(Xs)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_013')).
% 20.87/21.04 tff(154,plain,
% 20.87/21.04 (![Y: $i, Xs: $i] : (lengthNat(cons(Y, Xs)) = s(lengthNat(Xs)))),
% 20.87/21.04 inference(modus_ponens,[status(thm)],[153, 152])).
% 20.87/21.04 tff(155,plain,(
% 20.87/21.04 ![Y: $i, Xs: $i] : (lengthNat(cons(Y, Xs)) = s(lengthNat(Xs)))),
% 20.87/21.04 inference(skolemize,[status(sab)],[154])).
% 20.87/21.04 tff(156,plain,
% 20.87/21.04 (![Y: $i, Xs: $i] : (lengthNat(cons(Y, Xs)) = s(lengthNat(Xs)))),
% 20.87/21.04 inference(modus_ponens,[status(thm)],[155, 151])).
% 20.87/21.04 tff(157,plain,
% 20.87/21.04 ((~![Y: $i, Xs: $i] : (lengthNat(cons(Y, Xs)) = s(lengthNat(Xs)))) | (lengthNat(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) = s(lengthNat(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))))),
% 20.87/21.04 inference(quant_inst,[status(thm)],[])).
% 20.87/21.04 tff(158,plain,
% 20.87/21.04 ($false),
% 20.87/21.04 inference(unit_resolution,[status(thm)],[157, 156, 149])).
% 20.87/21.04 tff(159,plain,(lengthNat(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) = s(lengthNat(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))), inference(lemma,lemma(discharge,[]))).
% 20.87/21.04 tff(160,plain,
% 20.87/21.04 ((lengthNat(nil) = z) <=> (lengthNat(nil) = z)),
% 20.87/21.04 inference(rewrite,[status(thm)],[])).
% 20.87/21.04 tff(161,axiom,(lengthNat(nil) = z), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_012')).
% 20.87/21.04 tff(162,plain,
% 20.87/21.04 (lengthNat(nil) = z),
% 20.87/21.04 inference(modus_ponens,[status(thm)],[161, 160])).
% 20.87/21.04 tff(163,plain,
% 20.87/21.04 (s(lengthNat(nil)) = s(z)),
% 20.87/21.04 inference(monotonicity,[status(thm)],[162])).
% 20.87/21.04 tff(164,plain,
% 20.87/21.04 ((~![Y: $i, Xs: $i] : (lengthNat(cons(Y, Xs)) = s(lengthNat(Xs)))) | (lengthNat(cons(z, nil)) = s(lengthNat(nil)))),
% 20.87/21.04 inference(quant_inst,[status(thm)],[])).
% 20.87/21.04 tff(165,plain,
% 20.87/21.04 (lengthNat(cons(z, nil)) = s(lengthNat(nil))),
% 20.87/21.04 inference(unit_resolution,[status(thm)],[164, 156])).
% 20.87/21.04 tff(166,plain,
% 20.87/21.04 (lengthNat(cons(z, nil)) = s(z)),
% 20.87/21.04 inference(transitivity,[status(thm)],[165, 163])).
% 20.87/21.04 tff(167,plain,
% 20.87/21.04 (s(lengthNat(cons(z, nil))) = s(s(z))),
% 20.87/21.04 inference(monotonicity,[status(thm)],[166])).
% 20.87/21.04 tff(168,plain,
% 20.87/21.04 ((~![Y: $i, Xs: $i] : (lengthNat(cons(Y, Xs)) = s(lengthNat(Xs)))) | (lengthNat(cons(s(z), cons(z, nil))) = s(lengthNat(cons(z, nil))))),
% 20.87/21.04 inference(quant_inst,[status(thm)],[])).
% 20.87/21.04 tff(169,plain,
% 20.87/21.04 (lengthNat(cons(s(z), cons(z, nil))) = s(lengthNat(cons(z, nil)))),
% 20.87/21.04 inference(unit_resolution,[status(thm)],[168, 156])).
% 20.87/21.04 tff(170,plain,
% 20.87/21.04 (cons(s(z), append(nil, cons(z, nil))) = cons(s(z), cons(z, nil))),
% 20.87/21.04 inference(symmetry,[status(thm)],[109])).
% 20.87/21.04 tff(171,plain,
% 20.87/21.04 (lengthNat(cons(s(z), append(nil, cons(z, nil)))) = lengthNat(cons(s(z), cons(z, nil)))),
% 20.87/21.04 inference(monotonicity,[status(thm)],[170])).
% 20.87/21.04 tff(172,plain,
% 20.87/21.04 (lengthNat(cons(s(z), append(nil, cons(z, nil)))) = s(s(z))),
% 20.87/21.04 inference(transitivity,[status(thm)],[171, 169, 167])).
% 20.87/21.04 tff(173,plain,
% 20.87/21.04 (s(lengthNat(cons(s(z), append(nil, cons(z, nil))))) = s(s(s(z)))),
% 20.87/21.04 inference(monotonicity,[status(thm)],[172])).
% 20.87/21.04 tff(174,assumption,(~(lengthNat(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil))))) = s(lengthNat(cons(s(z), append(nil, cons(z, nil))))))), introduced(assumption)).
% 20.87/21.04 tff(175,plain,
% 20.87/21.04 ((~![Y: $i, Xs: $i] : (lengthNat(cons(Y, Xs)) = s(lengthNat(Xs)))) | (lengthNat(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil))))) = s(lengthNat(cons(s(z), append(nil, cons(z, nil))))))),
% 20.87/21.04 inference(quant_inst,[status(thm)],[])).
% 20.87/21.04 tff(176,plain,
% 20.87/21.04 ($false),
% 20.87/21.04 inference(unit_resolution,[status(thm)],[175, 156, 174])).
% 20.87/21.04 tff(177,plain,(lengthNat(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil))))) = s(lengthNat(cons(s(z), append(nil, cons(z, nil)))))), inference(lemma,lemma(discharge,[]))).
% 20.87/21.04 tff(178,plain,
% 20.87/21.04 ((~![Y: $i] : (append(nil, Y) = Y)) | (append(nil, cons(s(z), nil)) = cons(s(z), nil))),
% 20.87/21.04 inference(quant_inst,[status(thm)],[])).
% 20.87/21.04 tff(179,plain,
% 20.87/21.04 (append(nil, cons(s(z), nil)) = cons(s(z), nil)),
% 20.87/21.04 inference(unit_resolution,[status(thm)],[178, 105])).
% 20.87/21.04 tff(180,plain,
% 20.87/21.04 ((rev(nil) = nil) <=> (rev(nil) = nil)),
% 20.87/21.04 inference(rewrite,[status(thm)],[])).
% 20.87/21.04 tff(181,axiom,(rev(nil) = nil), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_020')).
% 20.87/21.04 tff(182,plain,
% 20.87/21.04 (rev(nil) = nil),
% 20.87/21.04 inference(modus_ponens,[status(thm)],[181, 180])).
% 20.87/21.04 tff(183,plain,
% 20.87/21.04 (nil = rev(nil)),
% 20.87/21.04 inference(symmetry,[status(thm)],[182])).
% 20.87/21.04 tff(184,plain,
% 20.87/21.04 (append(nil, cons(s(z), nil)) = append(rev(nil), cons(s(z), nil))),
% 20.87/21.04 inference(monotonicity,[status(thm)],[183])).
% 20.87/21.04 tff(185,plain,
% 20.87/21.04 (append(rev(nil), cons(s(z), nil)) = append(nil, cons(s(z), nil))),
% 20.87/21.04 inference(symmetry,[status(thm)],[184])).
% 20.87/21.04 tff(186,plain,
% 20.87/21.04 (append(rev(nil), cons(s(z), nil)) = cons(s(z), nil)),
% 20.87/21.04 inference(transitivity,[status(thm)],[185, 179])).
% 20.87/21.04 tff(187,plain,
% 20.87/21.04 (append(append(rev(nil), cons(s(z), nil)), cons(z, nil)) = append(cons(s(z), nil), cons(z, nil))),
% 20.87/21.04 inference(monotonicity,[status(thm)],[186])).
% 20.87/21.04 tff(188,plain,
% 20.87/21.04 (append(cons(s(z), nil), cons(z, nil)) = append(append(rev(nil), cons(s(z), nil)), cons(z, nil))),
% 20.87/21.04 inference(symmetry,[status(thm)],[187])).
% 20.87/21.04 tff(189,plain,
% 20.87/21.04 (^[Y: $i, Z: $i, Xs: $i] : refl((append(cons(Z, Xs), Y) = cons(Z, append(Xs, Y))) <=> (append(cons(Z, Xs), Y) = cons(Z, append(Xs, Y))))),
% 20.87/21.04 inference(bind,[status(th)],[])).
% 20.87/21.04 tff(190,plain,
% 20.87/21.04 (![Y: $i, Z: $i, Xs: $i] : (append(cons(Z, Xs), Y) = cons(Z, append(Xs, Y))) <=> ![Y: $i, Z: $i, Xs: $i] : (append(cons(Z, Xs), Y) = cons(Z, append(Xs, Y)))),
% 20.87/21.04 inference(quant_intro,[status(thm)],[189])).
% 20.87/21.04 tff(191,plain,
% 20.87/21.04 (![Y: $i, Z: $i, Xs: $i] : (append(cons(Z, Xs), Y) = cons(Z, append(Xs, Y))) <=> ![Y: $i, Z: $i, Xs: $i] : (append(cons(Z, Xs), Y) = cons(Z, append(Xs, Y)))),
% 20.87/21.04 inference(rewrite,[status(thm)],[])).
% 20.87/21.04 tff(192,axiom,(![Y: $i, Z: $i, Xs: $i] : (append(cons(Z, Xs), Y) = cons(Z, append(Xs, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_019')).
% 20.87/21.04 tff(193,plain,
% 20.87/21.04 (![Y: $i, Z: $i, Xs: $i] : (append(cons(Z, Xs), Y) = cons(Z, append(Xs, Y)))),
% 20.87/21.04 inference(modus_ponens,[status(thm)],[192, 191])).
% 20.87/21.04 tff(194,plain,(
% 20.87/21.04 ![Y: $i, Z: $i, Xs: $i] : (append(cons(Z, Xs), Y) = cons(Z, append(Xs, Y)))),
% 20.87/21.04 inference(skolemize,[status(sab)],[193])).
% 20.87/21.04 tff(195,plain,
% 20.87/21.04 (![Y: $i, Z: $i, Xs: $i] : (append(cons(Z, Xs), Y) = cons(Z, append(Xs, Y)))),
% 20.87/21.04 inference(modus_ponens,[status(thm)],[194, 190])).
% 20.87/21.04 tff(196,plain,
% 20.87/21.04 ((~![Y: $i, Z: $i, Xs: $i] : (append(cons(Z, Xs), Y) = cons(Z, append(Xs, Y)))) | (append(cons(s(z), nil), cons(z, nil)) = cons(s(z), append(nil, cons(z, nil))))),
% 20.87/21.04 inference(quant_inst,[status(thm)],[])).
% 20.87/21.04 tff(197,plain,
% 20.87/21.04 (append(cons(s(z), nil), cons(z, nil)) = cons(s(z), append(nil, cons(z, nil)))),
% 20.87/21.04 inference(unit_resolution,[status(thm)],[196, 195])).
% 20.87/21.04 tff(198,plain,
% 20.87/21.04 (cons(s(z), append(nil, cons(z, nil))) = append(cons(s(z), nil), cons(z, nil))),
% 20.87/21.04 inference(symmetry,[status(thm)],[197])).
% 20.87/21.04 tff(199,plain,
% 20.87/21.04 (cons(s(z), append(nil, cons(z, nil))) = append(append(rev(nil), cons(s(z), nil)), cons(z, nil))),
% 20.87/21.04 inference(transitivity,[status(thm)],[198, 188])).
% 20.87/21.04 tff(200,plain,
% 20.87/21.04 (cons(s(s(z)), cons(s(z), append(nil, cons(z, nil)))) = cons(s(s(z)), append(append(rev(nil), cons(s(z), nil)), cons(z, nil)))),
% 20.87/21.04 inference(monotonicity,[status(thm)],[199])).
% 20.87/21.04 tff(201,plain,
% 20.87/21.04 (cons(s(s(z)), append(append(rev(nil), cons(s(z), nil)), cons(z, nil))) = cons(s(s(z)), cons(s(z), append(nil, cons(z, nil))))),
% 20.87/21.04 inference(symmetry,[status(thm)],[200])).
% 20.87/21.04 tff(202,plain,
% 20.87/21.04 ((~![Y: $i, Z: $i, Xs: $i] : (append(cons(Z, Xs), Y) = cons(Z, append(Xs, Y)))) | (append(cons(s(s(z)), append(rev(nil), cons(s(z), nil))), cons(z, nil)) = cons(s(s(z)), append(append(rev(nil), cons(s(z), nil)), cons(z, nil))))),
% 20.87/21.04 inference(quant_inst,[status(thm)],[])).
% 20.87/21.04 tff(203,plain,
% 20.87/21.04 (append(cons(s(s(z)), append(rev(nil), cons(s(z), nil))), cons(z, nil)) = cons(s(s(z)), append(append(rev(nil), cons(s(z), nil)), cons(z, nil)))),
% 20.87/21.04 inference(unit_resolution,[status(thm)],[202, 195])).
% 20.87/21.04 tff(204,plain,
% 20.87/21.04 ((~![Y: $i] : (append(nil, Y) = Y)) | (append(nil, cons(s(s(z)), nil)) = cons(s(s(z)), nil))),
% 20.87/21.04 inference(quant_inst,[status(thm)],[])).
% 20.87/21.04 tff(205,plain,
% 20.87/21.04 (append(nil, cons(s(s(z)), nil)) = cons(s(s(z)), nil)),
% 20.87/21.04 inference(unit_resolution,[status(thm)],[204, 105])).
% 20.87/21.04 tff(206,plain,
% 20.87/21.04 (cons(s(s(z)), nil) = append(nil, cons(s(s(z)), nil))),
% 20.87/21.04 inference(symmetry,[status(thm)],[205])).
% 20.87/21.04 tff(207,plain,
% 20.87/21.04 (cons(s(z), cons(s(s(z)), nil)) = cons(s(z), append(nil, cons(s(s(z)), nil)))),
% 20.87/21.04 inference(monotonicity,[status(thm)],[206])).
% 20.87/21.04 tff(208,plain,
% 20.87/21.04 (cons(s(z), append(nil, cons(s(s(z)), nil))) = cons(s(z), cons(s(s(z)), nil))),
% 20.87/21.04 inference(symmetry,[status(thm)],[207])).
% 20.87/21.04 tff(209,plain,
% 20.87/21.04 ((~![Y: $i, Z: $i, Xs: $i] : (append(cons(Z, Xs), Y) = cons(Z, append(Xs, Y)))) | (append(cons(s(z), nil), cons(s(s(z)), nil)) = cons(s(z), append(nil, cons(s(s(z)), nil))))),
% 20.87/21.04 inference(quant_inst,[status(thm)],[])).
% 20.87/21.04 tff(210,plain,
% 20.87/21.04 (append(cons(s(z), nil), cons(s(s(z)), nil)) = cons(s(z), append(nil, cons(s(s(z)), nil)))),
% 20.87/21.04 inference(unit_resolution,[status(thm)],[209, 195])).
% 20.87/21.04 tff(211,plain,
% 20.87/21.04 (rev(append(rev(nil), cons(s(z), nil))) = rev(cons(s(z), nil))),
% 20.87/21.04 inference(monotonicity,[status(thm)],[186])).
% 20.87/21.04 tff(212,plain,
% 20.87/21.04 (rev(cons(s(z), nil)) = rev(append(rev(nil), cons(s(z), nil)))),
% 20.87/21.04 inference(symmetry,[status(thm)],[211])).
% 20.87/21.04 tff(213,plain,
% 20.87/21.04 (^[Y: $i, Xs: $i] : refl((rev(cons(Y, Xs)) = append(rev(Xs), cons(Y, nil))) <=> (rev(cons(Y, Xs)) = append(rev(Xs), cons(Y, nil))))),
% 20.87/21.04 inference(bind,[status(th)],[])).
% 20.87/21.04 tff(214,plain,
% 20.87/21.04 (![Y: $i, Xs: $i] : (rev(cons(Y, Xs)) = append(rev(Xs), cons(Y, nil))) <=> ![Y: $i, Xs: $i] : (rev(cons(Y, Xs)) = append(rev(Xs), cons(Y, nil)))),
% 20.87/21.04 inference(quant_intro,[status(thm)],[213])).
% 20.87/21.04 tff(215,plain,
% 20.87/21.04 (![Y: $i, Xs: $i] : (rev(cons(Y, Xs)) = append(rev(Xs), cons(Y, nil))) <=> ![Y: $i, Xs: $i] : (rev(cons(Y, Xs)) = append(rev(Xs), cons(Y, nil)))),
% 20.87/21.04 inference(rewrite,[status(thm)],[])).
% 20.87/21.04 tff(216,axiom,(![Y: $i, Xs: $i] : (rev(cons(Y, Xs)) = append(rev(Xs), cons(Y, nil)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_021')).
% 20.87/21.04 tff(217,plain,
% 20.87/21.04 (![Y: $i, Xs: $i] : (rev(cons(Y, Xs)) = append(rev(Xs), cons(Y, nil)))),
% 20.87/21.04 inference(modus_ponens,[status(thm)],[216, 215])).
% 20.87/21.04 tff(218,plain,(
% 20.87/21.04 ![Y: $i, Xs: $i] : (rev(cons(Y, Xs)) = append(rev(Xs), cons(Y, nil)))),
% 20.87/21.04 inference(skolemize,[status(sab)],[217])).
% 20.87/21.04 tff(219,plain,
% 20.87/21.04 (![Y: $i, Xs: $i] : (rev(cons(Y, Xs)) = append(rev(Xs), cons(Y, nil)))),
% 20.87/21.04 inference(modus_ponens,[status(thm)],[218, 214])).
% 20.87/21.04 tff(220,plain,
% 20.87/21.04 ((~![Y: $i, Xs: $i] : (rev(cons(Y, Xs)) = append(rev(Xs), cons(Y, nil)))) | (rev(cons(s(z), nil)) = append(rev(nil), cons(s(z), nil)))),
% 20.87/21.04 inference(quant_inst,[status(thm)],[])).
% 20.87/21.04 tff(221,plain,
% 20.87/21.04 (rev(cons(s(z), nil)) = append(rev(nil), cons(s(z), nil))),
% 20.87/21.04 inference(unit_resolution,[status(thm)],[220, 219])).
% 20.87/21.04 tff(222,plain,
% 20.87/21.04 (append(rev(nil), cons(s(z), nil)) = rev(cons(s(z), nil))),
% 20.87/21.04 inference(symmetry,[status(thm)],[221])).
% 20.87/21.04 tff(223,plain,
% 20.87/21.04 (cons(s(z), nil) = append(nil, cons(s(z), nil))),
% 20.87/21.04 inference(symmetry,[status(thm)],[179])).
% 20.87/21.04 tff(224,plain,
% 20.87/21.04 (cons(s(z), nil) = rev(append(rev(nil), cons(s(z), nil)))),
% 20.87/21.04 inference(transitivity,[status(thm)],[223, 184, 222, 212])).
% 20.87/21.04 tff(225,plain,
% 20.87/21.04 (append(cons(s(z), nil), cons(s(s(z)), nil)) = append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))),
% 20.87/21.04 inference(monotonicity,[status(thm)],[224])).
% 20.87/21.04 tff(226,plain,
% 20.87/21.04 (append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil)) = append(cons(s(z), nil), cons(s(s(z)), nil))),
% 20.87/21.04 inference(symmetry,[status(thm)],[225])).
% 20.87/21.04 tff(227,plain,
% 20.87/21.04 (append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil)) = cons(s(z), cons(s(s(z)), nil))),
% 20.87/21.04 inference(transitivity,[status(thm)],[226, 210, 208])).
% 20.87/21.04 tff(228,plain,
% 20.87/21.04 (rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))) = rev(cons(s(z), cons(s(s(z)), nil)))),
% 20.87/21.04 inference(monotonicity,[status(thm)],[227])).
% 20.87/21.04 tff(229,plain,
% 20.87/21.04 (rev(cons(s(z), cons(s(s(z)), nil))) = rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil)))),
% 20.87/21.04 inference(symmetry,[status(thm)],[228])).
% 20.87/21.04 tff(230,plain,
% 20.87/21.04 ((~![Y: $i, Xs: $i] : (rev(cons(Y, Xs)) = append(rev(Xs), cons(Y, nil)))) | (rev(cons(s(z), cons(s(s(z)), nil))) = append(rev(cons(s(s(z)), nil)), cons(s(z), nil)))),
% 20.87/21.04 inference(quant_inst,[status(thm)],[])).
% 20.87/21.04 tff(231,plain,
% 20.87/21.04 (rev(cons(s(z), cons(s(s(z)), nil))) = append(rev(cons(s(s(z)), nil)), cons(s(z), nil))),
% 20.87/21.04 inference(unit_resolution,[status(thm)],[230, 219])).
% 20.87/21.04 tff(232,plain,
% 20.87/21.04 (append(rev(cons(s(s(z)), nil)), cons(s(z), nil)) = rev(cons(s(z), cons(s(s(z)), nil)))),
% 20.87/21.04 inference(symmetry,[status(thm)],[231])).
% 20.87/21.04 tff(233,plain,
% 20.87/21.04 (cons(s(z), nil) = append(rev(nil), cons(s(z), nil))),
% 20.87/21.04 inference(transitivity,[status(thm)],[223, 184])).
% 20.87/21.04 tff(234,plain,
% 20.87/21.04 (append(rev(nil), cons(s(s(z)), nil)) = append(nil, cons(s(s(z)), nil))),
% 20.87/21.04 inference(monotonicity,[status(thm)],[182])).
% 20.87/21.04 tff(235,plain,
% 20.87/21.04 ((~![Y: $i, Xs: $i] : (rev(cons(Y, Xs)) = append(rev(Xs), cons(Y, nil)))) | (rev(cons(s(s(z)), nil)) = append(rev(nil), cons(s(s(z)), nil)))),
% 20.87/21.04 inference(quant_inst,[status(thm)],[])).
% 20.87/21.04 tff(236,plain,
% 20.87/21.04 (rev(cons(s(s(z)), nil)) = append(rev(nil), cons(s(s(z)), nil))),
% 20.87/21.04 inference(unit_resolution,[status(thm)],[235, 219])).
% 20.87/21.04 tff(237,plain,
% 20.87/21.04 (rev(cons(s(s(z)), nil)) = cons(s(s(z)), nil)),
% 20.87/21.04 inference(transitivity,[status(thm)],[236, 234, 205])).
% 20.87/21.04 tff(238,plain,
% 20.87/21.04 (append(rev(cons(s(s(z)), nil)), cons(s(z), nil)) = append(cons(s(s(z)), nil), append(rev(nil), cons(s(z), nil)))),
% 20.87/21.04 inference(monotonicity,[status(thm)],[237, 233])).
% 20.87/21.04 tff(239,plain,
% 20.87/21.04 (append(cons(s(s(z)), nil), append(rev(nil), cons(s(z), nil))) = append(rev(cons(s(s(z)), nil)), cons(s(z), nil))),
% 20.87/21.04 inference(symmetry,[status(thm)],[238])).
% 20.87/21.04 tff(240,plain,
% 20.87/21.04 ((~![Y: $i, Z: $i, Xs: $i] : (append(cons(Z, Xs), Y) = cons(Z, append(Xs, Y)))) | (append(cons(s(s(z)), nil), append(rev(nil), cons(s(z), nil))) = cons(s(s(z)), append(nil, append(rev(nil), cons(s(z), nil)))))),
% 20.87/21.04 inference(quant_inst,[status(thm)],[])).
% 20.87/21.04 tff(241,plain,
% 20.87/21.04 (append(cons(s(s(z)), nil), append(rev(nil), cons(s(z), nil))) = cons(s(s(z)), append(nil, append(rev(nil), cons(s(z), nil))))),
% 20.87/21.04 inference(unit_resolution,[status(thm)],[240, 195])).
% 20.87/21.04 tff(242,plain,
% 20.87/21.04 (cons(s(s(z)), append(nil, append(rev(nil), cons(s(z), nil)))) = append(cons(s(s(z)), nil), append(rev(nil), cons(s(z), nil)))),
% 20.87/21.04 inference(symmetry,[status(thm)],[241])).
% 20.87/21.04 tff(243,plain,
% 20.87/21.04 (append(nil, append(rev(nil), cons(s(z), nil))) = append(rev(nil), cons(s(z), nil))),
% 20.87/21.04 inference(monotonicity,[status(thm)],[183, 186])).
% 20.87/21.04 tff(244,plain,
% 20.87/21.04 (cons(s(s(z)), append(nil, append(rev(nil), cons(s(z), nil)))) = cons(s(s(z)), append(rev(nil), cons(s(z), nil)))),
% 20.87/21.04 inference(monotonicity,[status(thm)],[243])).
% 20.87/21.04 tff(245,plain,
% 20.87/21.04 (cons(s(s(z)), append(rev(nil), cons(s(z), nil))) = cons(s(s(z)), append(nil, append(rev(nil), cons(s(z), nil))))),
% 20.87/21.04 inference(symmetry,[status(thm)],[244])).
% 20.87/21.04 tff(246,plain,
% 20.87/21.04 (cons(s(s(z)), append(rev(nil), cons(s(z), nil))) = rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil)))),
% 20.87/21.04 inference(transitivity,[status(thm)],[245, 242, 239, 232, 229])).
% 20.87/21.04 tff(247,plain,
% 20.87/21.04 (append(cons(s(s(z)), append(rev(nil), cons(s(z), nil))), cons(z, nil)) = append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))),
% 20.87/21.04 inference(monotonicity,[status(thm)],[246])).
% 20.87/21.04 tff(248,plain,
% 20.87/21.04 (append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)) = append(cons(s(s(z)), append(rev(nil), cons(s(z), nil))), cons(z, nil))),
% 20.87/21.04 inference(symmetry,[status(thm)],[247])).
% 20.87/21.04 tff(249,plain,
% 20.87/21.04 (append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)) = cons(s(s(z)), cons(s(z), append(nil, cons(z, nil))))),
% 20.87/21.04 inference(transitivity,[status(thm)],[248, 203, 201])).
% 20.87/21.04 tff(250,plain,
% 20.87/21.04 (lengthNat(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))) = lengthNat(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil)))))),
% 20.87/21.04 inference(monotonicity,[status(thm)],[249])).
% 20.87/21.04 tff(251,plain,
% 20.87/21.04 (lengthNat(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))) = s(s(s(z)))),
% 20.87/21.04 inference(transitivity,[status(thm)],[250, 177, 173])).
% 20.87/21.04 tff(252,plain,
% 20.87/21.04 (s(lengthNat(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) = s(s(s(s(z))))),
% 20.87/21.04 inference(monotonicity,[status(thm)],[251])).
% 20.87/21.04 tff(253,assumption,(lengthNat(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) = s(lengthNat(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))), introduced(assumption)).
% 20.87/21.04 tff(254,plain,
% 20.87/21.04 (lengthNat(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) = s(s(s(s(z))))),
% 20.87/21.04 inference(transitivity,[status(thm)],[253, 252])).
% 20.87/21.04 tff(255,plain,
% 20.87/21.04 (leqNat(lengthNat(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))), s(s(s(z)))) <=> leqNat(s(s(s(s(z)))), s(s(s(z))))),
% 20.87/21.04 inference(monotonicity,[status(thm)],[254])).
% 20.87/21.04 tff(256,plain,
% 20.87/21.04 (leqNat(s(s(s(s(z)))), s(s(s(z)))) <=> leqNat(lengthNat(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))), s(s(s(z))))),
% 20.87/21.04 inference(symmetry,[status(thm)],[255])).
% 20.87/21.04 tff(257,plain,
% 20.87/21.04 ((~leqNat(s(s(s(s(z)))), s(s(s(z))))) <=> (~leqNat(lengthNat(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))), s(s(s(z)))))),
% 20.87/21.04 inference(monotonicity,[status(thm)],[256])).
% 20.87/21.04 tff(258,plain,
% 20.87/21.04 (~leqNat(lengthNat(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))), s(s(s(z))))),
% 20.87/21.04 inference(modus_ponens,[status(thm)],[36, 257])).
% 20.87/21.04 tff(259,assumption,(unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))), introduced(assumption)).
% 20.87/21.04 tff(260,assumption,(((~leqNat(z, s(z))) | (~sorted(cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil))))))) <=> sorted(cons(z, cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil))))))), introduced(assumption)).
% 20.87/21.04 tff(261,plain,
% 20.87/21.04 (^[Y: $i, Y2: $i, Xs: $i] : refl((~(((~leqNat(Y, Y2)) | (~sorted(cons(Y2, Xs)))) <=> sorted(cons(Y, cons(Y2, Xs))))) <=> (~(((~leqNat(Y, Y2)) | (~sorted(cons(Y2, Xs)))) <=> sorted(cons(Y, cons(Y2, Xs))))))),
% 20.87/21.04 inference(bind,[status(th)],[])).
% 20.87/21.04 tff(262,plain,
% 20.87/21.04 (![Y: $i, Y2: $i, Xs: $i] : (~(((~leqNat(Y, Y2)) | (~sorted(cons(Y2, Xs)))) <=> sorted(cons(Y, cons(Y2, Xs))))) <=> ![Y: $i, Y2: $i, Xs: $i] : (~(((~leqNat(Y, Y2)) | (~sorted(cons(Y2, Xs)))) <=> sorted(cons(Y, cons(Y2, Xs)))))),
% 20.87/21.04 inference(quant_intro,[status(thm)],[261])).
% 20.87/21.04 tff(263,plain,
% 20.87/21.04 (^[Y: $i, Y2: $i, Xs: $i] : trans(trans(monotonicity(rewrite((leqNat(Y, Y2) & sorted(cons(Y2, Xs))) <=> (~((~leqNat(Y, Y2)) | (~sorted(cons(Y2, Xs)))))), ((sorted(cons(Y, cons(Y2, Xs))) <=> (leqNat(Y, Y2) & sorted(cons(Y2, Xs)))) <=> (sorted(cons(Y, cons(Y2, Xs))) <=> (~((~leqNat(Y, Y2)) | (~sorted(cons(Y2, Xs)))))))), rewrite((sorted(cons(Y, cons(Y2, Xs))) <=> (~((~leqNat(Y, Y2)) | (~sorted(cons(Y2, Xs)))))) <=> (~(((~leqNat(Y, Y2)) | (~sorted(cons(Y2, Xs)))) <=> sorted(cons(Y, cons(Y2, Xs)))))), ((sorted(cons(Y, cons(Y2, Xs))) <=> (leqNat(Y, Y2) & sorted(cons(Y2, Xs)))) <=> (~(((~leqNat(Y, Y2)) | (~sorted(cons(Y2, Xs)))) <=> sorted(cons(Y, cons(Y2, Xs))))))), rewrite((~(((~leqNat(Y, Y2)) | (~sorted(cons(Y2, Xs)))) <=> sorted(cons(Y, cons(Y2, Xs))))) <=> (~(((~leqNat(Y, Y2)) | (~sorted(cons(Y2, Xs)))) <=> sorted(cons(Y, cons(Y2, Xs)))))), ((sorted(cons(Y, cons(Y2, Xs))) <=> (leqNat(Y, Y2) & sorted(cons(Y2, Xs)))) <=> (~(((~leqNat(Y, Y2)) | (~sorted(cons(Y2, Xs)))) <=> sorted(cons(Y, cons(Y2, Xs)))))))),
% 20.87/21.04 inference(bind,[status(th)],[])).
% 20.87/21.04 tff(264,plain,
% 20.87/21.04 (![Y: $i, Y2: $i, Xs: $i] : (sorted(cons(Y, cons(Y2, Xs))) <=> (leqNat(Y, Y2) & sorted(cons(Y2, Xs)))) <=> ![Y: $i, Y2: $i, Xs: $i] : (~(((~leqNat(Y, Y2)) | (~sorted(cons(Y2, Xs)))) <=> sorted(cons(Y, cons(Y2, Xs)))))),
% 20.87/21.04 inference(quant_intro,[status(thm)],[263])).
% 20.87/21.04 tff(265,plain,
% 20.87/21.04 (![Y: $i, Y2: $i, Xs: $i] : (sorted(cons(Y, cons(Y2, Xs))) <=> (leqNat(Y, Y2) & sorted(cons(Y2, Xs)))) <=> ![Y: $i, Y2: $i, Xs: $i] : (sorted(cons(Y, cons(Y2, Xs))) <=> (leqNat(Y, Y2) & sorted(cons(Y2, Xs))))),
% 20.87/21.04 inference(rewrite,[status(thm)],[])).
% 20.87/21.04 tff(266,axiom,(![Y: $i, Y2: $i, Xs: $i] : (sorted(cons(Y, cons(Y2, Xs))) <=> (leqNat(Y, Y2) & sorted(cons(Y2, Xs))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_011')).
% 20.87/21.04 tff(267,plain,
% 20.87/21.04 (![Y: $i, Y2: $i, Xs: $i] : (sorted(cons(Y, cons(Y2, Xs))) <=> (leqNat(Y, Y2) & sorted(cons(Y2, Xs))))),
% 20.87/21.04 inference(modus_ponens,[status(thm)],[266, 265])).
% 20.87/21.04 tff(268,plain,(
% 20.87/21.04 ![Y: $i, Y2: $i, Xs: $i] : (sorted(cons(Y, cons(Y2, Xs))) <=> (leqNat(Y, Y2) & sorted(cons(Y2, Xs))))),
% 20.87/21.04 inference(skolemize,[status(sab)],[267])).
% 20.87/21.04 tff(269,plain,
% 20.87/21.04 (![Y: $i, Y2: $i, Xs: $i] : (~(((~leqNat(Y, Y2)) | (~sorted(cons(Y2, Xs)))) <=> sorted(cons(Y, cons(Y2, Xs)))))),
% 20.87/21.04 inference(modus_ponens,[status(thm)],[268, 264])).
% 20.87/21.04 tff(270,plain,
% 20.87/21.04 (![Y: $i, Y2: $i, Xs: $i] : (~(((~leqNat(Y, Y2)) | (~sorted(cons(Y2, Xs)))) <=> sorted(cons(Y, cons(Y2, Xs)))))),
% 20.87/21.04 inference(modus_ponens,[status(thm)],[269, 262])).
% 20.87/21.04 tff(271,plain,
% 20.87/21.04 ((~![Y: $i, Y2: $i, Xs: $i] : (~(((~leqNat(Y, Y2)) | (~sorted(cons(Y2, Xs)))) <=> sorted(cons(Y, cons(Y2, Xs)))))) | (~(((~leqNat(z, s(z))) | (~sorted(cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil))))))) <=> sorted(cons(z, cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil))))))))),
% 20.87/21.04 inference(quant_inst,[status(thm)],[])).
% 20.87/21.04 tff(272,plain,
% 20.87/21.04 ($false),
% 20.87/21.04 inference(unit_resolution,[status(thm)],[271, 270, 260])).
% 20.87/21.04 tff(273,plain,(~(((~leqNat(z, s(z))) | (~sorted(cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil))))))) <=> sorted(cons(z, cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil)))))))), inference(lemma,lemma(discharge,[]))).
% 20.87/21.04 tff(274,assumption,(~(((~leqNat(z, s(z))) | (~sorted(cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil))))))) <=> sorted(cons(z, cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil)))))))), introduced(assumption)).
% 20.87/21.04 tff(275,plain,
% 20.87/21.04 ((~![Y: $i, Xs: $i] : (rev(cons(Y, Xs)) = append(rev(Xs), cons(Y, nil)))) | (rev(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) = append(rev(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))), cons(s(s(s(z))), nil)))),
% 20.87/21.04 inference(quant_inst,[status(thm)],[])).
% 20.87/21.04 tff(276,plain,
% 20.87/21.04 (rev(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) = append(rev(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))), cons(s(s(s(z))), nil))),
% 20.87/21.04 inference(unit_resolution,[status(thm)],[275, 219])).
% 20.87/21.04 tff(277,plain,
% 20.87/21.04 (append(rev(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))), cons(s(s(s(z))), nil)) = rev(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))),
% 20.87/21.04 inference(symmetry,[status(thm)],[276])).
% 20.87/21.04 tff(278,plain,
% 20.87/21.04 ((~![Y: $i] : (append(nil, Y) = Y)) | (append(nil, cons(s(s(s(z))), nil)) = cons(s(s(s(z))), nil))),
% 20.87/21.04 inference(quant_inst,[status(thm)],[])).
% 20.87/21.04 tff(279,plain,
% 20.87/21.04 (append(nil, cons(s(s(s(z))), nil)) = cons(s(s(s(z))), nil)),
% 20.87/21.04 inference(unit_resolution,[status(thm)],[278, 105])).
% 20.87/21.04 tff(280,plain,
% 20.87/21.04 (append(nil, cons(s(s(s(z))), nil)) = append(rev(nil), cons(s(s(s(z))), nil))),
% 20.87/21.04 inference(monotonicity,[status(thm)],[183])).
% 20.87/21.04 tff(281,plain,
% 20.87/21.04 (append(rev(nil), cons(s(s(s(z))), nil)) = append(nil, cons(s(s(s(z))), nil))),
% 20.87/21.04 inference(symmetry,[status(thm)],[280])).
% 20.87/21.04 tff(282,plain,
% 20.87/21.04 (append(rev(nil), cons(s(s(s(z))), nil)) = cons(s(s(s(z))), nil)),
% 20.87/21.04 inference(transitivity,[status(thm)],[281, 279])).
% 20.87/21.04 tff(283,plain,
% 20.87/21.04 (rev(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))) = rev(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil)))))),
% 20.87/21.04 inference(monotonicity,[status(thm)],[249])).
% 20.87/21.04 tff(284,plain,
% 20.87/21.04 (rev(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil))))) = rev(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))),
% 20.87/21.04 inference(symmetry,[status(thm)],[283])).
% 20.87/21.04 tff(285,plain,
% 20.87/21.04 ((~![Y: $i, Xs: $i] : (rev(cons(Y, Xs)) = append(rev(Xs), cons(Y, nil)))) | (rev(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil))))) = append(rev(cons(s(z), append(nil, cons(z, nil)))), cons(s(s(z)), nil)))),
% 20.87/21.04 inference(quant_inst,[status(thm)],[])).
% 20.87/21.04 tff(286,plain,
% 20.87/21.04 (rev(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil))))) = append(rev(cons(s(z), append(nil, cons(z, nil)))), cons(s(s(z)), nil))),
% 20.87/21.04 inference(unit_resolution,[status(thm)],[285, 219])).
% 20.87/21.04 tff(287,plain,
% 20.87/21.04 (append(rev(cons(s(z), append(nil, cons(z, nil)))), cons(s(s(z)), nil)) = rev(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil)))))),
% 20.87/21.04 inference(symmetry,[status(thm)],[286])).
% 20.87/21.04 tff(288,plain,
% 20.87/21.04 (append(rev(nil), cons(s(z), nil)) = append(nil, append(rev(nil), cons(s(z), nil)))),
% 20.87/21.04 inference(symmetry,[status(thm)],[243])).
% 20.87/21.04 tff(289,plain,
% 20.87/21.04 (cons(z, append(rev(nil), cons(s(z), nil))) = cons(z, append(nil, append(rev(nil), cons(s(z), nil))))),
% 20.87/21.04 inference(monotonicity,[status(thm)],[288])).
% 20.87/21.04 tff(290,plain,
% 20.87/21.04 (cons(z, append(nil, append(rev(nil), cons(s(z), nil)))) = cons(z, append(rev(nil), cons(s(z), nil)))),
% 20.87/21.04 inference(symmetry,[status(thm)],[289])).
% 20.87/21.04 tff(291,plain,
% 20.87/21.04 ((~![Y: $i, Z: $i, Xs: $i] : (append(cons(Z, Xs), Y) = cons(Z, append(Xs, Y)))) | (append(cons(z, nil), append(rev(nil), cons(s(z), nil))) = cons(z, append(nil, append(rev(nil), cons(s(z), nil)))))),
% 20.87/21.04 inference(quant_inst,[status(thm)],[])).
% 20.87/21.04 tff(292,plain,
% 20.87/21.04 (append(cons(z, nil), append(rev(nil), cons(s(z), nil))) = cons(z, append(nil, append(rev(nil), cons(s(z), nil))))),
% 20.87/21.04 inference(unit_resolution,[status(thm)],[291, 195])).
% 20.87/21.04 tff(293,plain,
% 20.87/21.04 ((~![Y: $i, Xs: $i] : (rev(cons(Y, Xs)) = append(rev(Xs), cons(Y, nil)))) | (rev(cons(z, nil)) = append(rev(nil), cons(z, nil)))),
% 20.87/21.04 inference(quant_inst,[status(thm)],[])).
% 20.87/21.04 tff(294,plain,
% 20.87/21.04 (rev(cons(z, nil)) = append(rev(nil), cons(z, nil))),
% 20.87/21.04 inference(unit_resolution,[status(thm)],[293, 219])).
% 20.87/21.04 tff(295,plain,
% 20.87/21.04 (append(rev(nil), cons(z, nil)) = rev(cons(z, nil))),
% 20.87/21.04 inference(symmetry,[status(thm)],[294])).
% 20.87/21.04 tff(296,plain,
% 20.87/21.04 (append(rev(nil), cons(z, nil)) = append(nil, cons(z, nil))),
% 20.87/21.04 inference(monotonicity,[status(thm)],[182])).
% 20.87/21.04 tff(297,plain,
% 20.87/21.04 (append(nil, cons(z, nil)) = append(rev(nil), cons(z, nil))),
% 20.87/21.04 inference(symmetry,[status(thm)],[296])).
% 20.87/21.04 tff(298,plain,
% 20.87/21.04 (cons(z, nil) = rev(cons(z, nil))),
% 20.87/21.04 inference(transitivity,[status(thm)],[108, 297, 295])).
% 20.87/21.04 tff(299,plain,
% 20.87/21.04 (append(cons(z, nil), append(rev(nil), cons(s(z), nil))) = append(rev(cons(z, nil)), cons(s(z), nil))),
% 20.87/21.04 inference(monotonicity,[status(thm)],[298, 186])).
% 20.87/21.04 tff(300,plain,
% 20.87/21.04 (append(rev(cons(z, nil)), cons(s(z), nil)) = append(cons(z, nil), append(rev(nil), cons(s(z), nil)))),
% 20.87/21.04 inference(symmetry,[status(thm)],[299])).
% 20.87/21.04 tff(301,plain,
% 20.87/21.04 ((~![Y: $i, Xs: $i] : (rev(cons(Y, Xs)) = append(rev(Xs), cons(Y, nil)))) | (rev(cons(s(z), cons(z, nil))) = append(rev(cons(z, nil)), cons(s(z), nil)))),
% 20.87/21.04 inference(quant_inst,[status(thm)],[])).
% 20.87/21.04 tff(302,plain,
% 20.87/21.04 (rev(cons(s(z), cons(z, nil))) = append(rev(cons(z, nil)), cons(s(z), nil))),
% 20.87/21.04 inference(unit_resolution,[status(thm)],[301, 219])).
% 20.87/21.04 tff(303,plain,
% 20.87/21.04 (rev(cons(s(z), append(nil, cons(z, nil)))) = rev(cons(s(z), cons(z, nil)))),
% 20.87/21.04 inference(monotonicity,[status(thm)],[170])).
% 20.87/21.04 tff(304,plain,
% 20.87/21.04 (rev(cons(s(z), append(nil, cons(z, nil)))) = cons(z, append(rev(nil), cons(s(z), nil)))),
% 20.87/21.04 inference(transitivity,[status(thm)],[303, 302, 300, 292, 290])).
% 20.87/21.04 tff(305,plain,
% 20.87/21.04 (append(rev(cons(s(z), append(nil, cons(z, nil)))), cons(s(s(z)), nil)) = append(cons(z, append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))),
% 20.87/21.04 inference(monotonicity,[status(thm)],[304])).
% 20.87/21.05 tff(306,plain,
% 20.87/21.05 (append(cons(z, append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil)) = append(rev(cons(s(z), append(nil, cons(z, nil)))), cons(s(s(z)), nil))),
% 20.87/21.05 inference(symmetry,[status(thm)],[305])).
% 20.87/21.05 tff(307,plain,
% 20.87/21.05 ((~![Y: $i, Z: $i, Xs: $i] : (append(cons(Z, Xs), Y) = cons(Z, append(Xs, Y)))) | (append(cons(z, append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil)) = cons(z, append(append(rev(nil), cons(s(z), nil)), cons(s(s(z)), nil))))),
% 20.87/21.05 inference(quant_inst,[status(thm)],[])).
% 20.87/21.05 tff(308,plain,
% 20.87/21.05 (append(cons(z, append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil)) = cons(z, append(append(rev(nil), cons(s(z), nil)), cons(s(s(z)), nil)))),
% 20.87/21.05 inference(unit_resolution,[status(thm)],[307, 195])).
% 20.87/21.05 tff(309,plain,
% 20.87/21.05 (cons(z, append(append(rev(nil), cons(s(z), nil)), cons(s(s(z)), nil))) = append(cons(z, append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))),
% 20.87/21.05 inference(symmetry,[status(thm)],[308])).
% 20.87/21.05 tff(310,plain,
% 20.87/21.05 (append(rev(nil), cons(s(z), nil)) = rev(append(rev(nil), cons(s(z), nil)))),
% 20.87/21.05 inference(transitivity,[status(thm)],[222, 212])).
% 20.87/21.05 tff(311,plain,
% 20.87/21.05 (append(append(rev(nil), cons(s(z), nil)), cons(s(s(z)), nil)) = append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))),
% 20.87/21.05 inference(monotonicity,[status(thm)],[310])).
% 20.87/21.05 tff(312,plain,
% 20.87/21.05 (append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil)) = append(append(rev(nil), cons(s(z), nil)), cons(s(s(z)), nil))),
% 20.87/21.05 inference(symmetry,[status(thm)],[311])).
% 20.87/21.05 tff(313,plain,
% 20.87/21.05 (cons(z, append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))) = cons(z, append(append(rev(nil), cons(s(z), nil)), cons(s(s(z)), nil)))),
% 20.87/21.05 inference(monotonicity,[status(thm)],[312])).
% 20.87/21.05 tff(314,plain,
% 20.87/21.05 (cons(z, append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))) = rev(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))),
% 20.87/21.05 inference(transitivity,[status(thm)],[313, 309, 306, 287, 284])).
% 20.87/21.05 tff(315,plain,
% 20.87/21.05 (append(cons(z, append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), append(rev(nil), cons(s(s(s(z))), nil))) = append(rev(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))), cons(s(s(s(z))), nil))),
% 20.87/21.05 inference(monotonicity,[status(thm)],[314, 282])).
% 20.87/21.05 tff(316,plain,
% 20.87/21.05 ((~![Y: $i, Z: $i, Xs: $i] : (append(cons(Z, Xs), Y) = cons(Z, append(Xs, Y)))) | (append(cons(z, append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), append(rev(nil), cons(s(s(s(z))), nil))) = cons(z, append(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil)), append(rev(nil), cons(s(s(s(z))), nil)))))),
% 20.87/21.05 inference(quant_inst,[status(thm)],[])).
% 20.87/21.05 tff(317,plain,
% 20.87/21.05 (append(cons(z, append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), append(rev(nil), cons(s(s(s(z))), nil))) = cons(z, append(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil)), append(rev(nil), cons(s(s(s(z))), nil))))),
% 20.87/21.05 inference(unit_resolution,[status(thm)],[316, 195])).
% 20.87/21.05 tff(318,plain,
% 20.87/21.05 (cons(z, append(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil)), append(rev(nil), cons(s(s(s(z))), nil)))) = append(cons(z, append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), append(rev(nil), cons(s(s(s(z))), nil)))),
% 20.87/21.05 inference(symmetry,[status(thm)],[317])).
% 20.87/21.05 tff(319,plain,
% 20.87/21.05 ((~![Y: $i, Xs: $i] : (rev(cons(Y, Xs)) = append(rev(Xs), cons(Y, nil)))) | (rev(cons(s(s(z)), append(rev(nil), cons(s(z), nil)))) = append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil)))),
% 20.87/21.05 inference(quant_inst,[status(thm)],[])).
% 20.87/21.05 tff(320,plain,
% 20.87/21.05 (rev(cons(s(s(z)), append(rev(nil), cons(s(z), nil)))) = append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))),
% 20.87/21.05 inference(unit_resolution,[status(thm)],[319, 219])).
% 20.87/21.05 tff(321,plain,
% 20.87/21.05 (append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil)) = rev(cons(s(s(z)), append(rev(nil), cons(s(z), nil))))),
% 20.87/21.05 inference(symmetry,[status(thm)],[320])).
% 20.87/21.05 tff(322,plain,
% 20.87/21.05 (append(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil)), append(rev(nil), cons(s(s(s(z))), nil))) = append(rev(cons(s(s(z)), append(rev(nil), cons(s(z), nil)))), cons(s(s(s(z))), nil))),
% 20.87/21.05 inference(monotonicity,[status(thm)],[321, 282])).
% 20.87/21.05 tff(323,plain,
% 20.87/21.05 (append(rev(cons(s(s(z)), append(rev(nil), cons(s(z), nil)))), cons(s(s(s(z))), nil)) = append(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil)), append(rev(nil), cons(s(s(s(z))), nil)))),
% 20.87/21.05 inference(symmetry,[status(thm)],[322])).
% 20.87/21.05 tff(324,plain,
% 20.87/21.05 (cons(s(z), append(nil, cons(s(s(z)), nil))) = append(cons(s(z), nil), cons(s(s(z)), nil))),
% 20.87/21.05 inference(symmetry,[status(thm)],[210])).
% 20.87/21.05 tff(325,plain,
% 20.87/21.05 (cons(s(z), cons(s(s(z)), nil)) = rev(cons(s(s(z)), append(rev(nil), cons(s(z), nil))))),
% 20.87/21.05 inference(transitivity,[status(thm)],[207, 324, 225, 321])).
% 20.87/21.05 tff(326,plain,
% 20.87/21.05 (append(cons(s(z), cons(s(s(z)), nil)), append(rev(nil), cons(s(s(s(z))), nil))) = append(rev(cons(s(s(z)), append(rev(nil), cons(s(z), nil)))), cons(s(s(s(z))), nil))),
% 20.87/21.05 inference(monotonicity,[status(thm)],[325, 282])).
% 20.87/21.05 tff(327,plain,
% 20.87/21.05 ((~![Y: $i, Z: $i, Xs: $i] : (append(cons(Z, Xs), Y) = cons(Z, append(Xs, Y)))) | (append(cons(s(z), cons(s(s(z)), nil)), append(rev(nil), cons(s(s(s(z))), nil))) = cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil)))))),
% 20.87/21.05 inference(quant_inst,[status(thm)],[])).
% 20.87/21.05 tff(328,plain,
% 20.87/21.05 (append(cons(s(z), cons(s(s(z)), nil)), append(rev(nil), cons(s(s(s(z))), nil))) = cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil))))),
% 20.87/21.05 inference(unit_resolution,[status(thm)],[327, 195])).
% 20.87/21.05 tff(329,plain,
% 20.87/21.05 (cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil)))) = append(cons(s(z), cons(s(s(z)), nil)), append(rev(nil), cons(s(s(s(z))), nil)))),
% 20.87/21.05 inference(symmetry,[status(thm)],[328])).
% 20.87/21.05 tff(330,plain,
% 20.87/21.05 (cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil)))) = append(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil)), append(rev(nil), cons(s(s(s(z))), nil)))),
% 20.87/21.05 inference(transitivity,[status(thm)],[329, 326, 323])).
% 20.87/21.05 tff(331,plain,
% 20.87/21.05 (cons(z, cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil))))) = cons(z, append(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil)), append(rev(nil), cons(s(s(s(z))), nil))))),
% 20.87/21.05 inference(monotonicity,[status(thm)],[330])).
% 20.87/21.05 tff(332,plain,
% 20.87/21.05 (cons(z, cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil))))) = rev(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))),
% 20.87/21.05 inference(transitivity,[status(thm)],[331, 318, 315, 277])).
% 20.87/21.05 tff(333,plain,
% 20.87/21.05 (sorted(cons(z, cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil)))))) <=> sorted(rev(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))))),
% 20.87/21.05 inference(monotonicity,[status(thm)],[332])).
% 20.87/21.05 tff(334,plain,
% 20.87/21.05 (sorted(rev(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))) <=> sorted(cons(z, cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil))))))),
% 20.87/21.05 inference(symmetry,[status(thm)],[333])).
% 20.87/21.05 tff(335,plain,
% 20.87/21.05 ((~sorted(rev(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))))) <=> (~sorted(cons(z, cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil)))))))),
% 20.87/21.05 inference(monotonicity,[status(thm)],[334])).
% 20.87/21.05 tff(336,assumption,(~sorted(rev(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))))), introduced(assumption)).
% 20.87/21.05 tff(337,plain,
% 20.87/21.05 (~sorted(cons(z, cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil))))))),
% 20.87/21.05 inference(modus_ponens,[status(thm)],[336, 335])).
% 20.87/21.05 tff(338,plain,
% 20.87/21.05 ((~![Y: $i, Xs: $i] : (rev(cons(Y, Xs)) = append(rev(Xs), cons(Y, nil)))) | (rev(cons(s(s(s(z))), cons(s(s(z)), append(rev(nil), cons(s(z), nil))))) = append(rev(cons(s(s(z)), append(rev(nil), cons(s(z), nil)))), cons(s(s(s(z))), nil)))),
% 20.87/21.05 inference(quant_inst,[status(thm)],[])).
% 20.87/21.05 tff(339,plain,
% 20.87/21.05 (rev(cons(s(s(s(z))), cons(s(s(z)), append(rev(nil), cons(s(z), nil))))) = append(rev(cons(s(s(z)), append(rev(nil), cons(s(z), nil)))), cons(s(s(s(z))), nil))),
% 20.87/21.05 inference(unit_resolution,[status(thm)],[338, 219])).
% 20.87/21.05 tff(340,plain,
% 20.87/21.05 (append(rev(cons(s(s(z)), append(rev(nil), cons(s(z), nil)))), cons(s(s(s(z))), nil)) = rev(cons(s(s(s(z))), cons(s(s(z)), append(rev(nil), cons(s(z), nil)))))),
% 20.87/21.05 inference(symmetry,[status(thm)],[339])).
% 20.87/21.05 tff(341,plain,
% 20.87/21.05 (cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil)))) = rev(cons(s(s(s(z))), cons(s(s(z)), append(rev(nil), cons(s(z), nil)))))),
% 20.87/21.05 inference(transitivity,[status(thm)],[329, 326, 340])).
% 20.87/21.05 tff(342,plain,
% 20.87/21.05 (sorted(cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil))))) <=> sorted(rev(cons(s(s(s(z))), cons(s(s(z)), append(rev(nil), cons(s(z), nil))))))),
% 20.87/21.05 inference(monotonicity,[status(thm)],[341])).
% 20.87/21.05 tff(343,plain,
% 20.87/21.05 (sorted(rev(cons(s(s(s(z))), cons(s(s(z)), append(rev(nil), cons(s(z), nil)))))) <=> sorted(cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil)))))),
% 20.87/21.05 inference(symmetry,[status(thm)],[342])).
% 20.87/21.05 tff(344,assumption,(((~leqNat(s(s(z)), s(s(s(z))))) | (~sorted(cons(s(s(s(z))), nil)))) <=> sorted(cons(s(s(z)), cons(s(s(s(z))), nil)))), introduced(assumption)).
% 20.87/21.05 tff(345,plain,
% 20.87/21.05 ((~![Y: $i, Y2: $i, Xs: $i] : (~(((~leqNat(Y, Y2)) | (~sorted(cons(Y2, Xs)))) <=> sorted(cons(Y, cons(Y2, Xs)))))) | (~(((~leqNat(s(s(z)), s(s(s(z))))) | (~sorted(cons(s(s(s(z))), nil)))) <=> sorted(cons(s(s(z)), cons(s(s(s(z))), nil)))))),
% 20.87/21.05 inference(quant_inst,[status(thm)],[])).
% 20.87/21.05 tff(346,plain,
% 20.87/21.05 ($false),
% 20.87/21.05 inference(unit_resolution,[status(thm)],[345, 270, 344])).
% 20.87/21.05 tff(347,plain,(~(((~leqNat(s(s(z)), s(s(s(z))))) | (~sorted(cons(s(s(s(z))), nil)))) <=> sorted(cons(s(s(z)), cons(s(s(s(z))), nil))))), inference(lemma,lemma(discharge,[]))).
% 20.87/21.05 tff(348,plain,
% 20.87/21.05 (^[Y: $i] : refl(sorted(cons(Y, nil)) <=> sorted(cons(Y, nil)))),
% 20.87/21.05 inference(bind,[status(th)],[])).
% 20.87/21.05 tff(349,plain,
% 20.87/21.05 (![Y: $i] : sorted(cons(Y, nil)) <=> ![Y: $i] : sorted(cons(Y, nil))),
% 20.87/21.05 inference(quant_intro,[status(thm)],[348])).
% 20.87/21.05 tff(350,plain,
% 20.87/21.05 (![Y: $i] : sorted(cons(Y, nil)) <=> ![Y: $i] : sorted(cons(Y, nil))),
% 20.87/21.05 inference(rewrite,[status(thm)],[])).
% 20.87/21.05 tff(351,axiom,(![Y: $i] : sorted(cons(Y, nil))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_010')).
% 20.87/21.05 tff(352,plain,
% 20.87/21.05 (![Y: $i] : sorted(cons(Y, nil))),
% 20.87/21.05 inference(modus_ponens,[status(thm)],[351, 350])).
% 20.87/21.05 tff(353,plain,(
% 20.87/21.05 ![Y: $i] : sorted(cons(Y, nil))),
% 20.87/21.05 inference(skolemize,[status(sab)],[352])).
% 20.87/21.05 tff(354,plain,
% 20.87/21.05 (![Y: $i] : sorted(cons(Y, nil))),
% 20.87/21.05 inference(modus_ponens,[status(thm)],[353, 349])).
% 20.87/21.05 tff(355,plain,
% 20.87/21.05 ((~![Y: $i] : sorted(cons(Y, nil))) | sorted(cons(s(s(s(z))), nil))),
% 20.87/21.05 inference(quant_inst,[status(thm)],[])).
% 20.87/21.05 tff(356,plain,
% 20.87/21.05 (sorted(cons(s(s(s(z))), nil))),
% 20.87/21.05 inference(unit_resolution,[status(thm)],[355, 354])).
% 20.87/21.05 tff(357,plain,
% 20.87/21.05 ((~((~leqNat(s(s(z)), s(s(s(z))))) | (~sorted(cons(s(s(s(z))), nil))))) | (~leqNat(s(s(z)), s(s(s(z))))) | (~sorted(cons(s(s(s(z))), nil)))),
% 20.87/21.05 inference(tautology,[status(thm)],[])).
% 20.87/21.05 tff(358,plain,
% 20.87/21.05 (~((~leqNat(s(s(z)), s(s(s(z))))) | (~sorted(cons(s(s(s(z))), nil))))),
% 20.87/21.05 inference(unit_resolution,[status(thm)],[357, 54, 356])).
% 20.87/21.05 tff(359,plain,
% 20.87/21.05 ((((~leqNat(s(s(z)), s(s(s(z))))) | (~sorted(cons(s(s(s(z))), nil)))) <=> sorted(cons(s(s(z)), cons(s(s(s(z))), nil)))) | ((~leqNat(s(s(z)), s(s(s(z))))) | (~sorted(cons(s(s(s(z))), nil)))) | sorted(cons(s(s(z)), cons(s(s(s(z))), nil)))),
% 20.87/21.05 inference(tautology,[status(thm)],[])).
% 20.87/21.05 tff(360,plain,
% 20.87/21.05 ((((~leqNat(s(s(z)), s(s(s(z))))) | (~sorted(cons(s(s(s(z))), nil)))) <=> sorted(cons(s(s(z)), cons(s(s(s(z))), nil)))) | sorted(cons(s(s(z)), cons(s(s(s(z))), nil)))),
% 20.87/21.05 inference(unit_resolution,[status(thm)],[359, 358])).
% 20.87/21.05 tff(361,plain,
% 20.87/21.05 (sorted(cons(s(s(z)), cons(s(s(s(z))), nil)))),
% 20.87/21.05 inference(unit_resolution,[status(thm)],[360, 347])).
% 20.87/21.05 tff(362,plain,
% 20.87/21.05 (cons(s(s(s(z))), nil) = append(nil, cons(s(s(s(z))), nil))),
% 20.87/21.05 inference(symmetry,[status(thm)],[279])).
% 20.87/21.05 tff(363,plain,
% 20.87/21.05 (cons(s(s(s(z))), nil) = append(rev(nil), cons(s(s(s(z))), nil))),
% 20.87/21.05 inference(transitivity,[status(thm)],[362, 280])).
% 20.87/21.05 tff(364,plain,
% 20.87/21.05 (cons(s(s(z)), cons(s(s(s(z))), nil)) = cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil)))),
% 20.87/21.05 inference(monotonicity,[status(thm)],[363])).
% 20.87/21.05 tff(365,plain,
% 20.87/21.05 (sorted(cons(s(s(z)), cons(s(s(s(z))), nil))) <=> sorted(cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil))))),
% 20.87/21.05 inference(monotonicity,[status(thm)],[364])).
% 20.87/21.05 tff(366,plain,
% 20.87/21.05 (sorted(cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil)))) <=> sorted(cons(s(s(z)), cons(s(s(s(z))), nil)))),
% 20.87/21.05 inference(symmetry,[status(thm)],[365])).
% 20.87/21.05 tff(367,plain,
% 20.87/21.05 ((~sorted(cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil))))) <=> (~sorted(cons(s(s(z)), cons(s(s(s(z))), nil))))),
% 20.87/21.05 inference(monotonicity,[status(thm)],[366])).
% 20.87/21.05 tff(368,assumption,(~sorted(cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil))))), introduced(assumption)).
% 20.87/21.05 tff(369,plain,
% 20.87/21.05 (~sorted(cons(s(s(z)), cons(s(s(s(z))), nil)))),
% 20.87/21.05 inference(modus_ponens,[status(thm)],[368, 367])).
% 20.87/21.05 tff(370,assumption,(sorted(cons(s(s(z)), cons(s(s(s(z))), nil)))), introduced(assumption)).
% 20.87/21.05 tff(371,plain,
% 20.87/21.05 ($false),
% 20.87/21.05 inference(unit_resolution,[status(thm)],[370, 369])).
% 20.87/21.05 tff(372,plain,((~sorted(cons(s(s(z)), cons(s(s(s(z))), nil)))) | sorted(cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil))))), inference(lemma,lemma(discharge,[]))).
% 20.87/21.05 tff(373,plain,
% 20.87/21.05 (sorted(cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil))))),
% 20.87/21.05 inference(unit_resolution,[status(thm)],[372, 361])).
% 20.87/21.05 tff(374,plain,
% 20.87/21.05 ((~((~leqNat(s(z), s(s(z)))) | (~sorted(cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil))))))) | (~leqNat(s(z), s(s(z)))) | (~sorted(cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil)))))),
% 20.87/21.05 inference(tautology,[status(thm)],[])).
% 20.87/21.05 tff(375,plain,
% 20.87/21.05 ((~((~leqNat(s(z), s(s(z)))) | (~sorted(cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil))))))) | (~sorted(cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil)))))),
% 20.87/21.05 inference(unit_resolution,[status(thm)],[374, 52])).
% 20.87/21.05 tff(376,plain,
% 20.87/21.05 (~((~leqNat(s(z), s(s(z)))) | (~sorted(cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil))))))),
% 20.87/21.05 inference(unit_resolution,[status(thm)],[375, 373])).
% 20.87/21.05 tff(377,assumption,(((~leqNat(s(z), s(s(z)))) | (~sorted(cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil)))))) <=> sorted(cons(s(z), cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil)))))), introduced(assumption)).
% 20.87/21.05 tff(378,plain,
% 20.87/21.05 ((~![Y: $i, Y2: $i, Xs: $i] : (~(((~leqNat(Y, Y2)) | (~sorted(cons(Y2, Xs)))) <=> sorted(cons(Y, cons(Y2, Xs)))))) | (~(((~leqNat(s(z), s(s(z)))) | (~sorted(cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil)))))) <=> sorted(cons(s(z), cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil)))))))),
% 20.87/21.05 inference(quant_inst,[status(thm)],[])).
% 20.87/21.05 tff(379,plain,
% 20.87/21.05 ($false),
% 20.87/21.05 inference(unit_resolution,[status(thm)],[378, 270, 377])).
% 20.87/21.05 tff(380,plain,(~(((~leqNat(s(z), s(s(z)))) | (~sorted(cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil)))))) <=> sorted(cons(s(z), cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil))))))), inference(lemma,lemma(discharge,[]))).
% 20.87/21.05 tff(381,plain,
% 20.87/21.05 ((((~leqNat(s(z), s(s(z)))) | (~sorted(cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil)))))) <=> sorted(cons(s(z), cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil)))))) | ((~leqNat(s(z), s(s(z)))) | (~sorted(cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil)))))) | sorted(cons(s(z), cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil)))))),
% 20.87/21.05 inference(tautology,[status(thm)],[])).
% 20.87/21.05 tff(382,plain,
% 20.87/21.05 (((~leqNat(s(z), s(s(z)))) | (~sorted(cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil)))))) | sorted(cons(s(z), cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil)))))),
% 20.87/21.05 inference(unit_resolution,[status(thm)],[381, 380])).
% 20.87/21.05 tff(383,plain,
% 20.87/21.05 (sorted(cons(s(z), cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil)))))),
% 20.87/21.05 inference(unit_resolution,[status(thm)],[382, 376])).
% 20.87/21.05 tff(384,plain,
% 20.87/21.05 ((~![Y: $i, Z: $i, Xs: $i] : (append(cons(Z, Xs), Y) = cons(Z, append(Xs, Y)))) | (append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil))) = cons(s(s(z)), append(nil, append(rev(nil), cons(s(s(s(z))), nil)))))),
% 20.87/21.05 inference(quant_inst,[status(thm)],[])).
% 20.87/21.05 tff(385,plain,
% 20.87/21.05 (append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil))) = cons(s(s(z)), append(nil, append(rev(nil), cons(s(s(s(z))), nil))))),
% 20.87/21.05 inference(unit_resolution,[status(thm)],[384, 195])).
% 20.87/21.05 tff(386,plain,
% 20.87/21.05 (cons(s(s(z)), append(nil, append(rev(nil), cons(s(s(s(z))), nil)))) = append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil)))),
% 20.87/21.05 inference(symmetry,[status(thm)],[385])).
% 20.87/21.05 tff(387,plain,
% 20.87/21.05 (append(nil, append(rev(nil), cons(s(s(s(z))), nil))) = append(rev(nil), cons(s(s(s(z))), nil))),
% 20.87/21.05 inference(monotonicity,[status(thm)],[183, 282])).
% 20.87/21.05 tff(388,plain,
% 20.87/21.05 (append(rev(nil), cons(s(s(s(z))), nil)) = append(nil, append(rev(nil), cons(s(s(s(z))), nil)))),
% 20.87/21.05 inference(symmetry,[status(thm)],[387])).
% 20.87/21.05 tff(389,plain,
% 20.87/21.05 (cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil))) = cons(s(s(z)), append(nil, append(rev(nil), cons(s(s(s(z))), nil))))),
% 20.87/21.05 inference(monotonicity,[status(thm)],[388])).
% 20.87/21.05 tff(390,plain,
% 20.87/21.05 (cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil))) = append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil)))),
% 20.87/21.05 inference(transitivity,[status(thm)],[389, 386])).
% 20.87/21.05 tff(391,plain,
% 20.87/21.05 (cons(s(z), cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil)))) = cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil))))),
% 20.87/21.05 inference(monotonicity,[status(thm)],[390])).
% 20.87/21.05 tff(392,plain,
% 20.87/21.05 (cons(s(z), cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil)))) = rev(cons(s(s(s(z))), cons(s(s(z)), append(rev(nil), cons(s(z), nil)))))),
% 20.87/21.05 inference(transitivity,[status(thm)],[391, 329, 326, 340])).
% 20.87/21.05 tff(393,plain,
% 20.87/21.05 (sorted(cons(s(z), cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil))))) <=> sorted(rev(cons(s(s(s(z))), cons(s(s(z)), append(rev(nil), cons(s(z), nil))))))),
% 20.87/21.05 inference(monotonicity,[status(thm)],[392])).
% 20.87/21.05 tff(394,plain,
% 20.87/21.05 (sorted(rev(cons(s(s(s(z))), cons(s(s(z)), append(rev(nil), cons(s(z), nil)))))) <=> sorted(cons(s(z), cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil)))))),
% 20.87/21.05 inference(symmetry,[status(thm)],[393])).
% 20.87/21.05 tff(395,plain,
% 20.87/21.05 ((~sorted(rev(cons(s(s(s(z))), cons(s(s(z)), append(rev(nil), cons(s(z), nil))))))) <=> (~sorted(cons(s(z), cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil))))))),
% 20.87/21.05 inference(monotonicity,[status(thm)],[394])).
% 20.87/21.05 tff(396,assumption,(~sorted(rev(cons(s(s(s(z))), cons(s(s(z)), append(rev(nil), cons(s(z), nil))))))), introduced(assumption)).
% 20.87/21.05 tff(397,plain,
% 20.87/21.05 (~sorted(cons(s(z), cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil)))))),
% 20.87/21.05 inference(modus_ponens,[status(thm)],[396, 395])).
% 20.87/21.05 tff(398,assumption,(sorted(cons(s(z), cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil)))))), introduced(assumption)).
% 20.87/21.05 tff(399,plain,
% 20.87/21.05 ($false),
% 20.87/21.05 inference(unit_resolution,[status(thm)],[398, 397])).
% 20.87/21.05 tff(400,plain,((~sorted(cons(s(z), cons(s(s(z)), append(rev(nil), cons(s(s(s(z))), nil)))))) | sorted(rev(cons(s(s(s(z))), cons(s(s(z)), append(rev(nil), cons(s(z), nil))))))), inference(lemma,lemma(discharge,[]))).
% 20.87/21.05 tff(401,plain,
% 20.87/21.05 (sorted(rev(cons(s(s(s(z))), cons(s(s(z)), append(rev(nil), cons(s(z), nil))))))),
% 20.87/21.05 inference(unit_resolution,[status(thm)],[400, 383])).
% 20.87/21.05 tff(402,plain,
% 20.87/21.05 (sorted(cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil)))))),
% 20.87/21.05 inference(modus_ponens,[status(thm)],[401, 343])).
% 20.87/21.05 tff(403,plain,
% 20.87/21.05 ((~((~leqNat(z, s(z))) | (~sorted(cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil)))))))) | (~leqNat(z, s(z))) | (~sorted(cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil))))))),
% 20.87/21.05 inference(tautology,[status(thm)],[])).
% 20.87/21.05 tff(404,plain,
% 20.87/21.05 ((~((~leqNat(z, s(z))) | (~sorted(cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil)))))))) | (~sorted(cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil))))))),
% 20.87/21.05 inference(unit_resolution,[status(thm)],[403, 50])).
% 20.87/21.05 tff(405,plain,
% 20.87/21.05 (~((~leqNat(z, s(z))) | (~sorted(cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil)))))))),
% 20.87/21.05 inference(unit_resolution,[status(thm)],[404, 402])).
% 20.87/21.05 tff(406,plain,
% 20.87/21.05 ((((~leqNat(z, s(z))) | (~sorted(cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil))))))) <=> sorted(cons(z, cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil))))))) | ((~leqNat(z, s(z))) | (~sorted(cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil))))))) | sorted(cons(z, cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil))))))),
% 20.87/21.05 inference(tautology,[status(thm)],[])).
% 20.87/21.05 tff(407,plain,
% 20.87/21.05 ($false),
% 20.87/21.05 inference(unit_resolution,[status(thm)],[406, 405, 337, 274])).
% 20.87/21.05 tff(408,plain,((((~leqNat(z, s(z))) | (~sorted(cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil))))))) <=> sorted(cons(z, cons(s(z), append(cons(s(s(z)), nil), append(rev(nil), cons(s(s(s(z))), nil))))))) | sorted(rev(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))))), inference(lemma,lemma(discharge,[]))).
% 20.87/21.05 tff(409,plain,
% 20.87/21.05 (sorted(rev(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))))),
% 20.87/21.05 inference(unit_resolution,[status(thm)],[408, 273])).
% 20.87/21.05 tff(410,plain,
% 20.87/21.05 (^[Xs: $i] : refl((leqNat(lengthNat(Xs), s(s(s(z)))) | (~unique(Xs)) | (~sorted(rev(Xs)))) <=> (leqNat(lengthNat(Xs), s(s(s(z)))) | (~unique(Xs)) | (~sorted(rev(Xs)))))),
% 20.87/21.05 inference(bind,[status(th)],[])).
% 20.87/21.05 tff(411,plain,
% 20.87/21.05 (![Xs: $i] : (leqNat(lengthNat(Xs), s(s(s(z)))) | (~unique(Xs)) | (~sorted(rev(Xs)))) <=> ![Xs: $i] : (leqNat(lengthNat(Xs), s(s(s(z)))) | (~unique(Xs)) | (~sorted(rev(Xs))))),
% 20.87/21.05 inference(quant_intro,[status(thm)],[410])).
% 20.87/21.05 tff(412,plain,
% 20.87/21.05 ((~?[Xs: $i] : (~(leqNat(lengthNat(Xs), s(s(s(z)))) | (~unique(Xs)) | (~sorted(rev(Xs)))))) <=> (~?[Xs: $i] : (~(leqNat(lengthNat(Xs), s(s(s(z)))) | (~unique(Xs)) | (~sorted(rev(Xs))))))),
% 20.87/21.05 inference(rewrite,[status(thm)],[])).
% 20.87/21.05 tff(413,plain,
% 20.87/21.05 ((~?[Xs: $i] : (~(sorted(rev(Xs)) => (unique(Xs) => leqNat(lengthNat(Xs), s(s(s(z)))))))) <=> (~?[Xs: $i] : (~(leqNat(lengthNat(Xs), s(s(s(z)))) | (~unique(Xs)) | (~sorted(rev(Xs))))))),
% 20.87/21.05 inference(rewrite,[status(thm)],[])).
% 20.87/21.05 tff(414,axiom,(~?[Xs: $i] : (~(sorted(rev(Xs)) => (unique(Xs) => leqNat(lengthNat(Xs), s(s(s(z)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goal_022')).
% 20.87/21.05 tff(415,plain,
% 20.87/21.05 (~?[Xs: $i] : (~(leqNat(lengthNat(Xs), s(s(s(z)))) | (~unique(Xs)) | (~sorted(rev(Xs)))))),
% 20.87/21.05 inference(modus_ponens,[status(thm)],[414, 413])).
% 20.87/21.05 tff(416,plain,
% 20.87/21.05 (~?[Xs: $i] : (~(leqNat(lengthNat(Xs), s(s(s(z)))) | (~unique(Xs)) | (~sorted(rev(Xs)))))),
% 20.87/21.05 inference(modus_ponens,[status(thm)],[415, 412])).
% 20.87/21.05 tff(417,plain,
% 20.87/21.05 (~?[Xs: $i] : (~(leqNat(lengthNat(Xs), s(s(s(z)))) | (~unique(Xs)) | (~sorted(rev(Xs)))))),
% 20.87/21.05 inference(modus_ponens,[status(thm)],[416, 412])).
% 20.87/21.05 tff(418,plain,
% 20.87/21.05 (~?[Xs: $i] : (~(leqNat(lengthNat(Xs), s(s(s(z)))) | (~unique(Xs)) | (~sorted(rev(Xs)))))),
% 20.87/21.05 inference(modus_ponens,[status(thm)],[417, 412])).
% 20.87/21.05 tff(419,plain,
% 20.87/21.05 (^[Xs: $i] : refl($oeq((leqNat(lengthNat(Xs), s(s(s(z)))) | (~unique(Xs)) | (~sorted(rev(Xs)))), (leqNat(lengthNat(Xs), s(s(s(z)))) | (~unique(Xs)) | (~sorted(rev(Xs))))))),
% 20.87/21.05 inference(bind,[status(th)],[])).
% 20.87/21.05 tff(420,plain,(
% 20.87/21.05 ![Xs: $i] : (leqNat(lengthNat(Xs), s(s(s(z)))) | (~unique(Xs)) | (~sorted(rev(Xs))))),
% 20.87/21.05 inference(nnf-neg,[status(sab)],[418, 419])).
% 20.87/21.05 tff(421,plain,
% 20.87/21.05 (![Xs: $i] : (leqNat(lengthNat(Xs), s(s(s(z)))) | (~unique(Xs)) | (~sorted(rev(Xs))))),
% 20.87/21.05 inference(modus_ponens,[status(thm)],[420, 411])).
% 20.87/21.05 tff(422,plain,
% 20.87/21.05 (((~![Xs: $i] : (leqNat(lengthNat(Xs), s(s(s(z)))) | (~unique(Xs)) | (~sorted(rev(Xs))))) | ((~unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))) | leqNat(lengthNat(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))), s(s(s(z)))) | (~sorted(rev(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))))))) <=> ((~![Xs: $i] : (leqNat(lengthNat(Xs), s(s(s(z)))) | (~unique(Xs)) | (~sorted(rev(Xs))))) | (~unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))) | leqNat(lengthNat(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))), s(s(s(z)))) | (~sorted(rev(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))))))),
% 20.87/21.06 inference(rewrite,[status(thm)],[])).
% 20.87/21.06 tff(423,plain,
% 20.87/21.06 ((leqNat(lengthNat(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))), s(s(s(z)))) | (~unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))) | (~sorted(rev(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))))) <=> ((~unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))) | leqNat(lengthNat(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))), s(s(s(z)))) | (~sorted(rev(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))))))),
% 20.87/21.06 inference(rewrite,[status(thm)],[])).
% 20.87/21.06 tff(424,plain,
% 20.87/21.06 (((~![Xs: $i] : (leqNat(lengthNat(Xs), s(s(s(z)))) | (~unique(Xs)) | (~sorted(rev(Xs))))) | (leqNat(lengthNat(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))), s(s(s(z)))) | (~unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))) | (~sorted(rev(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))))))) <=> ((~![Xs: $i] : (leqNat(lengthNat(Xs), s(s(s(z)))) | (~unique(Xs)) | (~sorted(rev(Xs))))) | ((~unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))) | leqNat(lengthNat(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))), s(s(s(z)))) | (~sorted(rev(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))))))),
% 20.87/21.06 inference(monotonicity,[status(thm)],[423])).
% 20.87/21.06 tff(425,plain,
% 20.87/21.06 (((~![Xs: $i] : (leqNat(lengthNat(Xs), s(s(s(z)))) | (~unique(Xs)) | (~sorted(rev(Xs))))) | (leqNat(lengthNat(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))), s(s(s(z)))) | (~unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))) | (~sorted(rev(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))))))) <=> ((~![Xs: $i] : (leqNat(lengthNat(Xs), s(s(s(z)))) | (~unique(Xs)) | (~sorted(rev(Xs))))) | (~unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))) | leqNat(lengthNat(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))), s(s(s(z)))) | (~sorted(rev(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))))))),
% 20.87/21.06 inference(transitivity,[status(thm)],[424, 422])).
% 20.87/21.06 tff(426,plain,
% 20.87/21.06 ((~![Xs: $i] : (leqNat(lengthNat(Xs), s(s(s(z)))) | (~unique(Xs)) | (~sorted(rev(Xs))))) | (leqNat(lengthNat(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))), s(s(s(z)))) | (~unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))) | (~sorted(rev(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))))))),
% 20.87/21.06 inference(quant_inst,[status(thm)],[])).
% 20.87/21.06 tff(427,plain,
% 20.87/21.06 ((~![Xs: $i] : (leqNat(lengthNat(Xs), s(s(s(z)))) | (~unique(Xs)) | (~sorted(rev(Xs))))) | (~unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))) | leqNat(lengthNat(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))), s(s(s(z)))) | (~sorted(rev(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))))),
% 20.87/21.06 inference(modus_ponens,[status(thm)],[426, 425])).
% 20.87/21.06 tff(428,plain,
% 20.87/21.06 (leqNat(lengthNat(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))), s(s(s(z))))),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[427, 421, 409, 259])).
% 20.87/21.06 tff(429,plain,
% 20.87/21.06 ($false),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[428, 258])).
% 20.87/21.06 tff(430,plain,((~(lengthNat(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) = s(lengthNat(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))))) | (~unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))))), inference(lemma,lemma(discharge,[]))).
% 20.87/21.06 tff(431,plain,
% 20.87/21.06 (~unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[430, 159])).
% 20.87/21.06 tff(432,plain,
% 20.87/21.06 ((((~unique(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) | elemNat(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) <=> unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))) | ((~unique(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) | elemNat(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) | unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))),
% 20.87/21.06 inference(tautology,[status(thm)],[])).
% 20.87/21.06 tff(433,plain,
% 20.87/21.06 ((((~unique(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) | elemNat(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) <=> unique(cons(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))) | ((~unique(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) | elemNat(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[432, 431])).
% 20.87/21.06 tff(434,plain,
% 20.87/21.06 ((~unique(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) | elemNat(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[433, 148])).
% 20.87/21.06 tff(435,plain,
% 20.87/21.06 (elemNat(s(s(z)), cons(s(z), cons(z, nil))) <=> elemNat(s(s(z)), cons(s(z), append(nil, cons(z, nil))))),
% 20.87/21.06 inference(monotonicity,[status(thm)],[109])).
% 20.87/21.06 tff(436,plain,
% 20.87/21.06 (elemNat(s(s(z)), cons(s(z), append(nil, cons(z, nil)))) <=> elemNat(s(s(z)), cons(s(z), cons(z, nil)))),
% 20.87/21.06 inference(symmetry,[status(thm)],[435])).
% 20.87/21.06 tff(437,assumption,(elemNat(s(s(z)), cons(s(z), append(nil, cons(z, nil))))), introduced(assumption)).
% 20.87/21.06 tff(438,plain,
% 20.87/21.06 (elemNat(s(s(z)), cons(s(z), cons(z, nil)))),
% 20.87/21.06 inference(modus_ponens,[status(thm)],[437, 436])).
% 20.87/21.06 tff(439,plain,
% 20.87/21.06 ((~![X: $i, Z: $i, Xs: $i] : (elemNat(X, cons(Z, Xs)) <=> ((X = Z) | elemNat(X, Xs)))) | (elemNat(s(s(z)), cons(s(z), cons(z, nil))) <=> ((s(s(z)) = s(z)) | elemNat(s(s(z)), cons(z, nil))))),
% 20.87/21.06 inference(quant_inst,[status(thm)],[])).
% 20.87/21.06 tff(440,plain,
% 20.87/21.06 (elemNat(s(s(z)), cons(s(z), cons(z, nil))) <=> ((s(s(z)) = s(z)) | elemNat(s(s(z)), cons(z, nil)))),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[439, 66])).
% 20.87/21.06 tff(441,assumption,(elemNat(s(s(z)), nil)), introduced(assumption)).
% 20.87/21.06 tff(442,plain,
% 20.87/21.06 ((~![X: $i] : (~elemNat(X, nil))) | (~elemNat(s(s(z)), nil))),
% 20.87/21.06 inference(quant_inst,[status(thm)],[])).
% 20.87/21.06 tff(443,plain,
% 20.87/21.06 ($false),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[442, 90, 441])).
% 20.87/21.06 tff(444,plain,(~elemNat(s(s(z)), nil)), inference(lemma,lemma(discharge,[]))).
% 20.87/21.06 tff(445,assumption,(s(s(z)) = z), introduced(assumption)).
% 20.87/21.06 tff(446,plain,
% 20.87/21.06 (z = s(s(z))),
% 20.87/21.06 inference(symmetry,[status(thm)],[445])).
% 20.87/21.06 tff(447,plain,
% 20.87/21.06 ((~![X: $i] : (~(z = s(X)))) | (~(z = s(s(z))))),
% 20.87/21.06 inference(quant_inst,[status(thm)],[])).
% 20.87/21.06 tff(448,plain,
% 20.87/21.06 (~(z = s(s(z)))),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[447, 79])).
% 20.87/21.06 tff(449,plain,
% 20.87/21.06 ($false),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[448, 446])).
% 20.87/21.06 tff(450,plain,(~(s(s(z)) = z)), inference(lemma,lemma(discharge,[]))).
% 20.87/21.06 tff(451,plain,
% 20.87/21.06 ((~((s(s(z)) = z) | elemNat(s(s(z)), nil))) | (s(s(z)) = z) | elemNat(s(s(z)), nil)),
% 20.87/21.06 inference(tautology,[status(thm)],[])).
% 20.87/21.06 tff(452,plain,
% 20.87/21.06 ((~((s(s(z)) = z) | elemNat(s(s(z)), nil))) | elemNat(s(s(z)), nil)),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[451, 450])).
% 20.87/21.06 tff(453,plain,
% 20.87/21.06 (~((s(s(z)) = z) | elemNat(s(s(z)), nil))),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[452, 444])).
% 20.87/21.06 tff(454,assumption,(~(elemNat(s(s(z)), cons(z, nil)) <=> ((s(s(z)) = z) | elemNat(s(s(z)), nil)))), introduced(assumption)).
% 20.87/21.06 tff(455,plain,
% 20.87/21.06 ((~![X: $i, Z: $i, Xs: $i] : (elemNat(X, cons(Z, Xs)) <=> ((X = Z) | elemNat(X, Xs)))) | (elemNat(s(s(z)), cons(z, nil)) <=> ((s(s(z)) = z) | elemNat(s(s(z)), nil)))),
% 20.87/21.06 inference(quant_inst,[status(thm)],[])).
% 20.87/21.06 tff(456,plain,
% 20.87/21.06 ($false),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[455, 66, 454])).
% 20.87/21.06 tff(457,plain,(elemNat(s(s(z)), cons(z, nil)) <=> ((s(s(z)) = z) | elemNat(s(s(z)), nil))), inference(lemma,lemma(discharge,[]))).
% 20.87/21.06 tff(458,plain,
% 20.87/21.06 ((~(elemNat(s(s(z)), cons(z, nil)) <=> ((s(s(z)) = z) | elemNat(s(s(z)), nil)))) | (~elemNat(s(s(z)), cons(z, nil))) | ((s(s(z)) = z) | elemNat(s(s(z)), nil))),
% 20.87/21.06 inference(tautology,[status(thm)],[])).
% 20.87/21.06 tff(459,plain,
% 20.87/21.06 ((~elemNat(s(s(z)), cons(z, nil))) | ((s(s(z)) = z) | elemNat(s(s(z)), nil))),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[458, 457])).
% 20.87/21.06 tff(460,plain,
% 20.87/21.06 (~elemNat(s(s(z)), cons(z, nil))),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[459, 453])).
% 20.87/21.06 tff(461,assumption,(s(s(z)) = s(z)), introduced(assumption)).
% 20.87/21.06 tff(462,plain,
% 20.87/21.06 (s(z) = s(s(z))),
% 20.87/21.06 inference(symmetry,[status(thm)],[461])).
% 20.87/21.06 tff(463,plain,
% 20.87/21.06 (leqNat(s(s(z)), s(z)) <=> leqNat(s(s(z)), s(s(z)))),
% 20.87/21.06 inference(monotonicity,[status(thm)],[462])).
% 20.87/21.06 tff(464,plain,
% 20.87/21.06 (leqNat(s(s(z)), s(s(z))) <=> leqNat(s(s(z)), s(z))),
% 20.87/21.06 inference(symmetry,[status(thm)],[463])).
% 20.87/21.06 tff(465,plain,
% 20.87/21.06 ((~![Z: $i, M: $i] : (leqNat(s(Z), s(M)) <=> leqNat(Z, M))) | (leqNat(s(s(z)), s(s(z))) <=> leqNat(s(z), s(z)))),
% 20.87/21.06 inference(quant_inst,[status(thm)],[])).
% 20.87/21.06 tff(466,plain,
% 20.87/21.06 (leqNat(s(s(z)), s(s(z))) <=> leqNat(s(z), s(z))),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[465, 14])).
% 20.87/21.06 tff(467,plain,
% 20.87/21.06 ((~![Z: $i, M: $i] : (leqNat(s(Z), s(M)) <=> leqNat(Z, M))) | (leqNat(s(z), s(z)) <=> leqNat(z, z))),
% 20.87/21.06 inference(quant_inst,[status(thm)],[])).
% 20.87/21.06 tff(468,plain,
% 20.87/21.06 (leqNat(s(z), s(z)) <=> leqNat(z, z)),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[467, 14])).
% 20.87/21.06 tff(469,plain,
% 20.87/21.06 ((~![Y: $i] : leqNat(z, Y)) | leqNat(z, z)),
% 20.87/21.06 inference(quant_inst,[status(thm)],[])).
% 20.87/21.06 tff(470,plain,
% 20.87/21.06 (leqNat(z, z)),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[469, 48])).
% 20.87/21.06 tff(471,plain,
% 20.87/21.06 ((~(leqNat(s(z), s(z)) <=> leqNat(z, z))) | leqNat(s(z), s(z)) | (~leqNat(z, z))),
% 20.87/21.06 inference(tautology,[status(thm)],[])).
% 20.87/21.06 tff(472,plain,
% 20.87/21.06 (leqNat(s(z), s(z))),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[471, 470, 468])).
% 20.87/21.06 tff(473,plain,
% 20.87/21.06 ((~(leqNat(s(s(z)), s(s(z))) <=> leqNat(s(z), s(z)))) | leqNat(s(s(z)), s(s(z))) | (~leqNat(s(z), s(z)))),
% 20.87/21.06 inference(tautology,[status(thm)],[])).
% 20.87/21.06 tff(474,plain,
% 20.87/21.06 (leqNat(s(s(z)), s(s(z)))),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[473, 472, 466])).
% 20.87/21.06 tff(475,plain,
% 20.87/21.06 (leqNat(s(s(z)), s(z))),
% 20.87/21.06 inference(modus_ponens,[status(thm)],[474, 464])).
% 20.87/21.06 tff(476,plain,
% 20.87/21.06 ($false),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[31, 475])).
% 20.87/21.06 tff(477,plain,(~(s(s(z)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 20.87/21.06 tff(478,plain,
% 20.87/21.06 ((~((s(s(z)) = s(z)) | elemNat(s(s(z)), cons(z, nil)))) | (s(s(z)) = s(z)) | elemNat(s(s(z)), cons(z, nil))),
% 20.87/21.06 inference(tautology,[status(thm)],[])).
% 20.87/21.06 tff(479,plain,
% 20.87/21.06 (~((s(s(z)) = s(z)) | elemNat(s(s(z)), cons(z, nil)))),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[478, 477, 460])).
% 20.87/21.06 tff(480,plain,
% 20.87/21.06 ((~(elemNat(s(s(z)), cons(s(z), cons(z, nil))) <=> ((s(s(z)) = s(z)) | elemNat(s(s(z)), cons(z, nil))))) | (~elemNat(s(s(z)), cons(s(z), cons(z, nil)))) | ((s(s(z)) = s(z)) | elemNat(s(s(z)), cons(z, nil)))),
% 20.87/21.06 inference(tautology,[status(thm)],[])).
% 20.87/21.06 tff(481,plain,
% 20.87/21.06 ((~(elemNat(s(s(z)), cons(s(z), cons(z, nil))) <=> ((s(s(z)) = s(z)) | elemNat(s(s(z)), cons(z, nil))))) | (~elemNat(s(s(z)), cons(s(z), cons(z, nil))))),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[480, 479])).
% 20.87/21.06 tff(482,plain,
% 20.87/21.06 (~elemNat(s(s(z)), cons(s(z), cons(z, nil)))),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[481, 440])).
% 20.87/21.06 tff(483,plain,
% 20.87/21.06 ($false),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[482, 438])).
% 20.87/21.06 tff(484,plain,(~elemNat(s(s(z)), cons(s(z), append(nil, cons(z, nil))))), inference(lemma,lemma(discharge,[]))).
% 20.87/21.06 tff(485,plain,
% 20.87/21.06 (unique(cons(s(z), append(nil, cons(z, nil)))) <=> unique(cons(s(z), cons(z, nil)))),
% 20.87/21.06 inference(monotonicity,[status(thm)],[170])).
% 20.87/21.06 tff(486,plain,
% 20.87/21.06 (unique(cons(s(z), cons(z, nil))) <=> unique(cons(s(z), append(nil, cons(z, nil))))),
% 20.87/21.06 inference(symmetry,[status(thm)],[485])).
% 20.87/21.06 tff(487,assumption,(~(elemNat(s(z), cons(z, nil)) <=> ((s(z) = z) | elemNat(s(z), nil)))), introduced(assumption)).
% 20.87/21.06 tff(488,plain,
% 20.87/21.06 ((~![X: $i, Z: $i, Xs: $i] : (elemNat(X, cons(Z, Xs)) <=> ((X = Z) | elemNat(X, Xs)))) | (elemNat(s(z), cons(z, nil)) <=> ((s(z) = z) | elemNat(s(z), nil)))),
% 20.87/21.06 inference(quant_inst,[status(thm)],[])).
% 20.87/21.06 tff(489,plain,
% 20.87/21.06 ($false),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[488, 66, 487])).
% 20.87/21.06 tff(490,plain,(elemNat(s(z), cons(z, nil)) <=> ((s(z) = z) | elemNat(s(z), nil))), inference(lemma,lemma(discharge,[]))).
% 20.87/21.06 tff(491,plain,
% 20.87/21.06 ((s(z) = z) <=> (z = s(z))),
% 20.87/21.06 inference(commutativity,[status(thm)],[])).
% 20.87/21.06 tff(492,plain,
% 20.87/21.06 ((z = s(z)) <=> (s(z) = z)),
% 20.87/21.06 inference(symmetry,[status(thm)],[491])).
% 20.87/21.06 tff(493,plain,
% 20.87/21.06 ((~(z = s(z))) <=> (~(s(z) = z))),
% 20.87/21.06 inference(monotonicity,[status(thm)],[492])).
% 20.87/21.06 tff(494,plain,
% 20.87/21.06 ((~![X: $i] : (~(z = s(X)))) | (~(z = s(z)))),
% 20.87/21.06 inference(quant_inst,[status(thm)],[])).
% 20.87/21.06 tff(495,plain,
% 20.87/21.06 (~(z = s(z))),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[494, 79])).
% 20.87/21.06 tff(496,plain,
% 20.87/21.06 (~(s(z) = z)),
% 20.87/21.06 inference(modus_ponens,[status(thm)],[495, 493])).
% 20.87/21.06 tff(497,assumption,(elemNat(s(z), nil)), introduced(assumption)).
% 20.87/21.06 tff(498,plain,
% 20.87/21.06 ((~![X: $i] : (~elemNat(X, nil))) | (~elemNat(s(z), nil))),
% 20.87/21.06 inference(quant_inst,[status(thm)],[])).
% 20.87/21.06 tff(499,plain,
% 20.87/21.06 ($false),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[498, 90, 497])).
% 20.87/21.06 tff(500,plain,(~elemNat(s(z), nil)), inference(lemma,lemma(discharge,[]))).
% 20.87/21.06 tff(501,plain,
% 20.87/21.06 ((~((s(z) = z) | elemNat(s(z), nil))) | (s(z) = z) | elemNat(s(z), nil)),
% 20.87/21.06 inference(tautology,[status(thm)],[])).
% 20.87/21.06 tff(502,plain,
% 20.87/21.06 (~((s(z) = z) | elemNat(s(z), nil))),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[501, 500, 496])).
% 20.87/21.06 tff(503,plain,
% 20.87/21.06 ((~(elemNat(s(z), cons(z, nil)) <=> ((s(z) = z) | elemNat(s(z), nil)))) | (~elemNat(s(z), cons(z, nil))) | ((s(z) = z) | elemNat(s(z), nil))),
% 20.87/21.06 inference(tautology,[status(thm)],[])).
% 20.87/21.06 tff(504,plain,
% 20.87/21.06 ((~(elemNat(s(z), cons(z, nil)) <=> ((s(z) = z) | elemNat(s(z), nil)))) | (~elemNat(s(z), cons(z, nil)))),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[503, 502])).
% 20.87/21.06 tff(505,plain,
% 20.87/21.06 (~elemNat(s(z), cons(z, nil))),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[504, 490])).
% 20.87/21.06 tff(506,assumption,(elemNat(z, nil)), introduced(assumption)).
% 20.87/21.06 tff(507,plain,
% 20.87/21.06 ((~![X: $i] : (~elemNat(X, nil))) | (~elemNat(z, nil))),
% 20.87/21.06 inference(quant_inst,[status(thm)],[])).
% 20.87/21.06 tff(508,plain,
% 20.87/21.06 ($false),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[507, 90, 506])).
% 20.87/21.06 tff(509,plain,(~elemNat(z, nil)), inference(lemma,lemma(discharge,[]))).
% 20.87/21.06 tff(510,plain,
% 20.87/21.06 (unique(nil) <=> unique(nil)),
% 20.87/21.06 inference(rewrite,[status(thm)],[])).
% 20.87/21.06 tff(511,axiom,(unique(nil)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_016')).
% 20.87/21.06 tff(512,plain,
% 20.87/21.06 (unique(nil)),
% 20.87/21.06 inference(modus_ponens,[status(thm)],[511, 510])).
% 20.87/21.06 tff(513,plain,
% 20.87/21.06 ((~((~unique(nil)) | elemNat(z, nil))) | (~unique(nil)) | elemNat(z, nil)),
% 20.87/21.06 inference(tautology,[status(thm)],[])).
% 20.87/21.06 tff(514,plain,
% 20.87/21.06 ((~((~unique(nil)) | elemNat(z, nil))) | elemNat(z, nil)),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[513, 512])).
% 20.87/21.06 tff(515,plain,
% 20.87/21.06 (~((~unique(nil)) | elemNat(z, nil))),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[514, 509])).
% 20.87/21.06 tff(516,plain,
% 20.87/21.06 (((~![Y: $i, Xs: $i] : (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs))))) | (~(((~unique(nil)) | elemNat(z, nil)) <=> unique(cons(z, nil))))) <=> ((~![Y: $i, Xs: $i] : (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs))))) | (~(((~unique(nil)) | elemNat(z, nil)) <=> unique(cons(z, nil)))))),
% 20.87/21.06 inference(rewrite,[status(thm)],[])).
% 20.87/21.06 tff(517,plain,
% 20.87/21.06 ((~(((~unique(nil)) | elemNat(z, nil)) <=> unique(cons(z, nil)))) <=> (~(((~unique(nil)) | elemNat(z, nil)) <=> unique(cons(z, nil))))),
% 20.87/21.06 inference(rewrite,[status(thm)],[])).
% 20.87/21.06 tff(518,plain,
% 20.87/21.06 (((elemNat(z, nil) | (~unique(nil))) <=> unique(cons(z, nil))) <=> (((~unique(nil)) | elemNat(z, nil)) <=> unique(cons(z, nil)))),
% 20.87/21.06 inference(rewrite,[status(thm)],[])).
% 20.87/21.06 tff(519,plain,
% 20.87/21.06 ((~((elemNat(z, nil) | (~unique(nil))) <=> unique(cons(z, nil)))) <=> (~(((~unique(nil)) | elemNat(z, nil)) <=> unique(cons(z, nil))))),
% 20.87/21.06 inference(monotonicity,[status(thm)],[518])).
% 20.87/21.06 tff(520,plain,
% 20.87/21.06 ((~((elemNat(z, nil) | (~unique(nil))) <=> unique(cons(z, nil)))) <=> (~(((~unique(nil)) | elemNat(z, nil)) <=> unique(cons(z, nil))))),
% 20.87/21.06 inference(transitivity,[status(thm)],[519, 517])).
% 20.87/21.06 tff(521,plain,
% 20.87/21.06 (((~![Y: $i, Xs: $i] : (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs))))) | (~((elemNat(z, nil) | (~unique(nil))) <=> unique(cons(z, nil))))) <=> ((~![Y: $i, Xs: $i] : (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs))))) | (~(((~unique(nil)) | elemNat(z, nil)) <=> unique(cons(z, nil)))))),
% 20.87/21.06 inference(monotonicity,[status(thm)],[520])).
% 20.87/21.06 tff(522,plain,
% 20.87/21.06 (((~![Y: $i, Xs: $i] : (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs))))) | (~((elemNat(z, nil) | (~unique(nil))) <=> unique(cons(z, nil))))) <=> ((~![Y: $i, Xs: $i] : (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs))))) | (~(((~unique(nil)) | elemNat(z, nil)) <=> unique(cons(z, nil)))))),
% 20.87/21.06 inference(transitivity,[status(thm)],[521, 516])).
% 20.87/21.06 tff(523,plain,
% 20.87/21.06 ((~![Y: $i, Xs: $i] : (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs))))) | (~((elemNat(z, nil) | (~unique(nil))) <=> unique(cons(z, nil))))),
% 20.87/21.06 inference(quant_inst,[status(thm)],[])).
% 20.87/21.06 tff(524,plain,
% 20.87/21.06 ((~![Y: $i, Xs: $i] : (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs))))) | (~(((~unique(nil)) | elemNat(z, nil)) <=> unique(cons(z, nil))))),
% 20.87/21.06 inference(modus_ponens,[status(thm)],[523, 522])).
% 20.87/21.06 tff(525,plain,
% 20.87/21.06 (~(((~unique(nil)) | elemNat(z, nil)) <=> unique(cons(z, nil)))),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[524, 137])).
% 20.87/21.06 tff(526,plain,
% 20.87/21.06 ((((~unique(nil)) | elemNat(z, nil)) <=> unique(cons(z, nil))) | ((~unique(nil)) | elemNat(z, nil)) | unique(cons(z, nil))),
% 20.87/21.06 inference(tautology,[status(thm)],[])).
% 20.87/21.06 tff(527,plain,
% 20.87/21.06 (((~unique(nil)) | elemNat(z, nil)) | unique(cons(z, nil))),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[526, 525])).
% 20.87/21.06 tff(528,plain,
% 20.87/21.06 (unique(cons(z, nil))),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[527, 515])).
% 20.87/21.06 tff(529,plain,
% 20.87/21.06 ((~(elemNat(s(z), cons(z, nil)) | (~unique(cons(z, nil))))) | elemNat(s(z), cons(z, nil)) | (~unique(cons(z, nil)))),
% 20.87/21.06 inference(tautology,[status(thm)],[])).
% 20.87/21.06 tff(530,plain,
% 20.87/21.06 ((~(elemNat(s(z), cons(z, nil)) | (~unique(cons(z, nil))))) | elemNat(s(z), cons(z, nil))),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[529, 528])).
% 20.87/21.06 tff(531,plain,
% 20.87/21.06 (~(elemNat(s(z), cons(z, nil)) | (~unique(cons(z, nil))))),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[530, 505])).
% 20.87/21.06 tff(532,plain,
% 20.87/21.06 ((~![Y: $i, Xs: $i] : (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs))))) | (~((elemNat(s(z), cons(z, nil)) | (~unique(cons(z, nil)))) <=> unique(cons(s(z), cons(z, nil)))))),
% 20.87/21.06 inference(quant_inst,[status(thm)],[])).
% 20.87/21.06 tff(533,plain,
% 20.87/21.06 (~((elemNat(s(z), cons(z, nil)) | (~unique(cons(z, nil)))) <=> unique(cons(s(z), cons(z, nil))))),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[532, 137])).
% 20.87/21.06 tff(534,plain,
% 20.87/21.06 (((elemNat(s(z), cons(z, nil)) | (~unique(cons(z, nil)))) <=> unique(cons(s(z), cons(z, nil)))) | (elemNat(s(z), cons(z, nil)) | (~unique(cons(z, nil)))) | unique(cons(s(z), cons(z, nil)))),
% 20.87/21.06 inference(tautology,[status(thm)],[])).
% 20.87/21.06 tff(535,plain,
% 20.87/21.06 ((elemNat(s(z), cons(z, nil)) | (~unique(cons(z, nil)))) | unique(cons(s(z), cons(z, nil)))),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[534, 533])).
% 20.87/21.06 tff(536,plain,
% 20.87/21.06 (unique(cons(s(z), cons(z, nil)))),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[535, 531])).
% 20.87/21.06 tff(537,plain,
% 20.87/21.06 (unique(cons(s(z), append(nil, cons(z, nil))))),
% 20.87/21.06 inference(modus_ponens,[status(thm)],[536, 486])).
% 20.87/21.06 tff(538,plain,
% 20.87/21.06 ((~((~unique(cons(s(z), append(nil, cons(z, nil))))) | elemNat(s(s(z)), cons(s(z), append(nil, cons(z, nil)))))) | (~unique(cons(s(z), append(nil, cons(z, nil))))) | elemNat(s(s(z)), cons(s(z), append(nil, cons(z, nil))))),
% 20.87/21.06 inference(tautology,[status(thm)],[])).
% 20.87/21.06 tff(539,plain,
% 20.87/21.06 (~((~unique(cons(s(z), append(nil, cons(z, nil))))) | elemNat(s(s(z)), cons(s(z), append(nil, cons(z, nil)))))),
% 20.87/21.06 inference(unit_resolution,[status(thm)],[538, 537, 484])).
% 20.87/21.06 tff(540,plain,
% 20.87/21.06 (((~![Y: $i, Xs: $i] : (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs))))) | (~(((~unique(cons(s(z), append(nil, cons(z, nil))))) | elemNat(s(s(z)), cons(s(z), append(nil, cons(z, nil))))) <=> unique(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil)))))))) <=> ((~![Y: $i, Xs: $i] : (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs))))) | (~(((~unique(cons(s(z), append(nil, cons(z, nil))))) | elemNat(s(s(z)), cons(s(z), append(nil, cons(z, nil))))) <=> unique(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil))))))))),
% 20.87/21.06 inference(rewrite,[status(thm)],[])).
% 20.87/21.06 tff(541,plain,
% 20.87/21.06 ((~(((~unique(cons(s(z), append(nil, cons(z, nil))))) | elemNat(s(s(z)), cons(s(z), append(nil, cons(z, nil))))) <=> unique(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil))))))) <=> (~(((~unique(cons(s(z), append(nil, cons(z, nil))))) | elemNat(s(s(z)), cons(s(z), append(nil, cons(z, nil))))) <=> unique(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil)))))))),
% 20.87/21.06 inference(rewrite,[status(thm)],[])).
% 20.87/21.06 tff(542,plain,
% 20.87/21.06 (((elemNat(s(s(z)), cons(s(z), append(nil, cons(z, nil)))) | (~unique(cons(s(z), append(nil, cons(z, nil)))))) <=> unique(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil)))))) <=> (((~unique(cons(s(z), append(nil, cons(z, nil))))) | elemNat(s(s(z)), cons(s(z), append(nil, cons(z, nil))))) <=> unique(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil))))))),
% 20.87/21.06 inference(rewrite,[status(thm)],[])).
% 20.87/21.06 tff(543,plain,
% 20.87/21.06 ((~((elemNat(s(s(z)), cons(s(z), append(nil, cons(z, nil)))) | (~unique(cons(s(z), append(nil, cons(z, nil)))))) <=> unique(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil))))))) <=> (~(((~unique(cons(s(z), append(nil, cons(z, nil))))) | elemNat(s(s(z)), cons(s(z), append(nil, cons(z, nil))))) <=> unique(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil)))))))),
% 20.87/21.07 inference(monotonicity,[status(thm)],[542])).
% 20.87/21.07 tff(544,plain,
% 20.87/21.07 ((~((elemNat(s(s(z)), cons(s(z), append(nil, cons(z, nil)))) | (~unique(cons(s(z), append(nil, cons(z, nil)))))) <=> unique(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil))))))) <=> (~(((~unique(cons(s(z), append(nil, cons(z, nil))))) | elemNat(s(s(z)), cons(s(z), append(nil, cons(z, nil))))) <=> unique(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil)))))))),
% 20.87/21.07 inference(transitivity,[status(thm)],[543, 541])).
% 20.87/21.07 tff(545,plain,
% 20.87/21.07 (((~![Y: $i, Xs: $i] : (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs))))) | (~((elemNat(s(s(z)), cons(s(z), append(nil, cons(z, nil)))) | (~unique(cons(s(z), append(nil, cons(z, nil)))))) <=> unique(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil)))))))) <=> ((~![Y: $i, Xs: $i] : (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs))))) | (~(((~unique(cons(s(z), append(nil, cons(z, nil))))) | elemNat(s(s(z)), cons(s(z), append(nil, cons(z, nil))))) <=> unique(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil))))))))),
% 20.87/21.07 inference(monotonicity,[status(thm)],[544])).
% 20.87/21.07 tff(546,plain,
% 20.87/21.07 (((~![Y: $i, Xs: $i] : (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs))))) | (~((elemNat(s(s(z)), cons(s(z), append(nil, cons(z, nil)))) | (~unique(cons(s(z), append(nil, cons(z, nil)))))) <=> unique(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil)))))))) <=> ((~![Y: $i, Xs: $i] : (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs))))) | (~(((~unique(cons(s(z), append(nil, cons(z, nil))))) | elemNat(s(s(z)), cons(s(z), append(nil, cons(z, nil))))) <=> unique(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil))))))))),
% 20.87/21.07 inference(transitivity,[status(thm)],[545, 540])).
% 20.87/21.07 tff(547,plain,
% 20.87/21.07 ((~![Y: $i, Xs: $i] : (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs))))) | (~((elemNat(s(s(z)), cons(s(z), append(nil, cons(z, nil)))) | (~unique(cons(s(z), append(nil, cons(z, nil)))))) <=> unique(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil)))))))),
% 20.87/21.07 inference(quant_inst,[status(thm)],[])).
% 20.87/21.07 tff(548,plain,
% 20.87/21.07 ((~![Y: $i, Xs: $i] : (~((elemNat(Y, Xs) | (~unique(Xs))) <=> unique(cons(Y, Xs))))) | (~(((~unique(cons(s(z), append(nil, cons(z, nil))))) | elemNat(s(s(z)), cons(s(z), append(nil, cons(z, nil))))) <=> unique(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil)))))))),
% 20.87/21.07 inference(modus_ponens,[status(thm)],[547, 546])).
% 20.87/21.07 tff(549,plain,
% 20.87/21.07 (~(((~unique(cons(s(z), append(nil, cons(z, nil))))) | elemNat(s(s(z)), cons(s(z), append(nil, cons(z, nil))))) <=> unique(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil))))))),
% 20.87/21.07 inference(unit_resolution,[status(thm)],[548, 137])).
% 20.87/21.07 tff(550,plain,
% 20.87/21.07 ((((~unique(cons(s(z), append(nil, cons(z, nil))))) | elemNat(s(s(z)), cons(s(z), append(nil, cons(z, nil))))) <=> unique(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil)))))) | ((~unique(cons(s(z), append(nil, cons(z, nil))))) | elemNat(s(s(z)), cons(s(z), append(nil, cons(z, nil))))) | unique(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil)))))),
% 20.87/21.07 inference(tautology,[status(thm)],[])).
% 20.87/21.07 tff(551,plain,
% 20.87/21.07 (((~unique(cons(s(z), append(nil, cons(z, nil))))) | elemNat(s(s(z)), cons(s(z), append(nil, cons(z, nil))))) | unique(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil)))))),
% 20.87/21.07 inference(unit_resolution,[status(thm)],[550, 549])).
% 20.87/21.07 tff(552,plain,
% 20.87/21.07 (unique(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil)))))),
% 20.87/21.07 inference(unit_resolution,[status(thm)],[551, 539])).
% 20.87/21.07 tff(553,plain,
% 20.87/21.07 (unique(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))) <=> unique(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil)))))),
% 20.87/21.07 inference(monotonicity,[status(thm)],[249])).
% 20.87/21.07 tff(554,plain,
% 20.87/21.07 (unique(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil))))) <=> unique(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))),
% 20.87/21.07 inference(symmetry,[status(thm)],[553])).
% 20.87/21.07 tff(555,assumption,(unique(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil)))))), introduced(assumption)).
% 20.87/21.07 tff(556,plain,
% 20.87/21.07 (unique(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))),
% 20.87/21.07 inference(modus_ponens,[status(thm)],[555, 554])).
% 20.87/21.07 tff(557,assumption,(~unique(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))), introduced(assumption)).
% 20.87/21.07 tff(558,plain,
% 20.87/21.07 ($false),
% 20.87/21.07 inference(unit_resolution,[status(thm)],[557, 556])).
% 20.87/21.07 tff(559,plain,(unique(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))) | (~unique(cons(s(s(z)), cons(s(z), append(nil, cons(z, nil))))))), inference(lemma,lemma(discharge,[]))).
% 20.87/21.07 tff(560,plain,
% 20.87/21.07 (unique(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))),
% 20.87/21.07 inference(unit_resolution,[status(thm)],[559, 552])).
% 20.87/21.07 tff(561,plain,
% 20.87/21.07 ((~((~unique(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) | elemNat(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))))) | (~unique(append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) | elemNat(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))),
% 20.87/21.07 inference(tautology,[status(thm)],[])).
% 20.87/21.07 tff(562,plain,
% 20.87/21.07 (elemNat(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))),
% 20.87/21.07 inference(unit_resolution,[status(thm)],[561, 560, 434])).
% 20.87/21.07 tff(563,plain,
% 20.87/21.07 (cons(s(s(z)), append(append(rev(nil), cons(s(z), nil)), cons(z, nil))) = append(cons(s(s(z)), append(rev(nil), cons(s(z), nil))), cons(z, nil))),
% 20.87/21.07 inference(symmetry,[status(thm)],[203])).
% 20.87/21.07 tff(564,plain,
% 20.87/21.07 (cons(s(s(z)), cons(s(z), append(nil, cons(z, nil)))) = append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))),
% 20.87/21.07 inference(transitivity,[status(thm)],[200, 563, 247])).
% 20.87/21.07 tff(565,plain,
% 20.87/21.07 (elemNat(s(s(s(z))), cons(s(s(z)), cons(s(z), append(nil, cons(z, nil))))) <=> elemNat(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))),
% 20.87/21.07 inference(monotonicity,[status(thm)],[564])).
% 20.87/21.07 tff(566,plain,
% 20.87/21.07 (elemNat(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil))) <=> elemNat(s(s(s(z))), cons(s(s(z)), cons(s(z), append(nil, cons(z, nil)))))),
% 20.87/21.07 inference(symmetry,[status(thm)],[565])).
% 20.87/21.07 tff(567,assumption,(elemNat(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))), introduced(assumption)).
% 20.87/21.07 tff(568,plain,
% 20.87/21.07 (elemNat(s(s(s(z))), cons(s(s(z)), cons(s(z), append(nil, cons(z, nil)))))),
% 20.87/21.07 inference(modus_ponens,[status(thm)],[567, 566])).
% 20.87/21.07 tff(569,plain,
% 20.87/21.07 ((~![X: $i, Z: $i, Xs: $i] : (elemNat(X, cons(Z, Xs)) <=> ((X = Z) | elemNat(X, Xs)))) | (elemNat(s(s(s(z))), cons(s(s(z)), cons(s(z), append(nil, cons(z, nil))))) <=> ((s(s(s(z))) = s(s(z))) | elemNat(s(s(s(z))), cons(s(z), append(nil, cons(z, nil))))))),
% 20.87/21.07 inference(quant_inst,[status(thm)],[])).
% 20.87/21.07 tff(570,plain,
% 20.87/21.07 (elemNat(s(s(s(z))), cons(s(s(z)), cons(s(z), append(nil, cons(z, nil))))) <=> ((s(s(s(z))) = s(s(z))) | elemNat(s(s(s(z))), cons(s(z), append(nil, cons(z, nil)))))),
% 20.87/21.07 inference(unit_resolution,[status(thm)],[569, 66])).
% 20.87/21.07 tff(571,assumption,(~elemNat(s(s(s(z))), cons(s(z), append(nil, cons(z, nil))))), introduced(assumption)).
% 20.87/21.07 tff(572,assumption,(~(s(s(s(z))) = s(s(z)))), introduced(assumption)).
% 20.87/21.07 tff(573,plain,
% 20.87/21.07 ((~((s(s(s(z))) = s(s(z))) | elemNat(s(s(s(z))), cons(s(z), append(nil, cons(z, nil)))))) | (s(s(s(z))) = s(s(z))) | elemNat(s(s(s(z))), cons(s(z), append(nil, cons(z, nil))))),
% 20.87/21.07 inference(tautology,[status(thm)],[])).
% 20.87/21.07 tff(574,plain,
% 20.87/21.07 (~((s(s(s(z))) = s(s(z))) | elemNat(s(s(s(z))), cons(s(z), append(nil, cons(z, nil)))))),
% 20.87/21.07 inference(unit_resolution,[status(thm)],[573, 572, 571])).
% 20.87/21.07 tff(575,plain,
% 20.87/21.07 ((~(elemNat(s(s(s(z))), cons(s(s(z)), cons(s(z), append(nil, cons(z, nil))))) <=> ((s(s(s(z))) = s(s(z))) | elemNat(s(s(s(z))), cons(s(z), append(nil, cons(z, nil))))))) | (~elemNat(s(s(s(z))), cons(s(s(z)), cons(s(z), append(nil, cons(z, nil)))))) | ((s(s(s(z))) = s(s(z))) | elemNat(s(s(s(z))), cons(s(z), append(nil, cons(z, nil)))))),
% 20.87/21.07 inference(tautology,[status(thm)],[])).
% 20.87/21.07 tff(576,plain,
% 20.87/21.07 ((~(elemNat(s(s(s(z))), cons(s(s(z)), cons(s(z), append(nil, cons(z, nil))))) <=> ((s(s(s(z))) = s(s(z))) | elemNat(s(s(s(z))), cons(s(z), append(nil, cons(z, nil))))))) | (~elemNat(s(s(s(z))), cons(s(s(z)), cons(s(z), append(nil, cons(z, nil))))))),
% 20.87/21.07 inference(unit_resolution,[status(thm)],[575, 574])).
% 20.87/21.07 tff(577,plain,
% 20.87/21.07 (~elemNat(s(s(s(z))), cons(s(s(z)), cons(s(z), append(nil, cons(z, nil)))))),
% 20.87/21.07 inference(unit_resolution,[status(thm)],[576, 570])).
% 20.87/21.07 tff(578,plain,
% 20.87/21.07 ($false),
% 20.87/21.07 inference(unit_resolution,[status(thm)],[577, 568])).
% 20.87/21.07 tff(579,plain,((~elemNat(s(s(s(z))), append(rev(append(rev(append(rev(nil), cons(s(z), nil))), cons(s(s(z)), nil))), cons(z, nil)))) | (s(s(s(z))) = s(s(z))) | elemNat(s(s(s(z))), cons(s(z), append(nil, cons(z, nil))))), inference(lemma,lemma(discharge,[]))).
% 20.87/21.07 tff(580,plain,
% 20.87/21.07 ((s(s(s(z))) = s(s(z))) | elemNat(s(s(s(z))), cons(s(z), append(nil, cons(z, nil))))),
% 20.87/21.07 inference(unit_resolution,[status(thm)],[579, 562])).
% 20.87/21.07 tff(581,plain,
% 20.87/21.07 (s(s(s(z))) = s(s(z))),
% 20.87/21.07 inference(unit_resolution,[status(thm)],[580, 126])).
% 20.87/21.07 tff(582,plain,
% 20.87/21.07 (leqNat(s(s(s(z))), s(s(z))) <=> leqNat(s(s(z)), s(s(z)))),
% 20.87/21.07 inference(monotonicity,[status(thm)],[581])).
% 20.87/21.07 tff(583,plain,
% 20.87/21.07 (leqNat(s(s(z)), s(s(z))) <=> leqNat(s(s(s(z))), s(s(z)))),
% 20.87/21.07 inference(symmetry,[status(thm)],[582])).
% 20.87/21.07 tff(584,plain,
% 20.87/21.07 (leqNat(s(s(s(z))), s(s(z)))),
% 20.87/21.07 inference(modus_ponens,[status(thm)],[474, 583])).
% 20.87/21.07 tff(585,plain,
% 20.87/21.07 ($false),
% 20.87/21.07 inference(unit_resolution,[status(thm)],[33, 584])).
% 20.87/21.07 % SZS output end Proof
% 20.87/21.08 % E exiting
%------------------------------------------------------------------------------