%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWX217+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 07:08:17 PM UTC 2026
% Result : Theorem 75.11s 75.37s
% Output : Proof 75.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX217+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.16/0.33 % Computer : n003.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 12:14:58 EDT 2026
% 0.16/0.33 % CPUTime :
% 75.11/75.37 % SZS status Theorem
% 75.11/75.37 % SZS output start Proof
% 75.11/75.37 tff(evenNat_type, type, (
% 75.11/75.37 evenNat: $i > $o)).
% 75.11/75.37 tff(suc_type, type, (
% 75.11/75.37 suc: $i > $i)).
% 75.11/75.37 tff(zero_type, type, (
% 75.11/75.37 zero: $i)).
% 75.11/75.37 tff(double_type, type, (
% 75.11/75.37 double: $i > $i)).
% 75.11/75.37 tff(rd_type, type, (
% 75.11/75.37 rd: $i > $i)).
% 75.11/75.37 tff(cons_type, type, (
% 75.11/75.37 cons: ( $i * $i ) > $i)).
% 75.11/75.37 tff(shw_type, type, (
% 75.11/75.37 shw: $i > $i)).
% 75.11/75.37 tff(half_type, type, (
% 75.11/75.37 half: $i > $i)).
% 75.11/75.37 tff(i_type, type, (
% 75.11/75.37 i: $i)).
% 75.11/75.37 tff(o_type, type, (
% 75.11/75.37 o: $i)).
% 75.11/75.37 tff(append_type, type, (
% 75.11/75.37 append: ( $i * $i ) > $i)).
% 75.11/75.37 tff(nil_type, type, (
% 75.11/75.37 nil: $i)).
% 75.11/75.37 tff(x_type, type, (
% 75.11/75.37 x: ( $i * $i ) > $i)).
% 75.11/75.37 tff(addNat_type, type, (
% 75.11/75.37 addNat: ( $i * $i ) > $i)).
% 75.11/75.37 tff(1,plain,
% 75.11/75.37 (^[Xs: $i] : refl((rd(cons(i, Xs)) = suc(double(rd(Xs)))) <=> (rd(cons(i, Xs)) = suc(double(rd(Xs)))))),
% 75.11/75.37 inference(bind,[status(th)],[])).
% 75.11/75.37 tff(2,plain,
% 75.11/75.37 (![Xs: $i] : (rd(cons(i, Xs)) = suc(double(rd(Xs)))) <=> ![Xs: $i] : (rd(cons(i, Xs)) = suc(double(rd(Xs))))),
% 75.11/75.37 inference(quant_intro,[status(thm)],[1])).
% 75.11/75.37 tff(3,plain,
% 75.11/75.37 (![Xs: $i] : (rd(cons(i, Xs)) = suc(double(rd(Xs)))) <=> ![Xs: $i] : (rd(cons(i, Xs)) = suc(double(rd(Xs))))),
% 75.11/75.37 inference(rewrite,[status(thm)],[])).
% 75.11/75.37 tff(4,axiom,(![Xs: $i] : (rd(cons(i, Xs)) = suc(double(rd(Xs))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_021')).
% 75.11/75.37 tff(5,plain,
% 75.11/75.37 (![Xs: $i] : (rd(cons(i, Xs)) = suc(double(rd(Xs))))),
% 75.11/75.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 75.11/75.37 tff(6,plain,(
% 75.11/75.37 ![Xs: $i] : (rd(cons(i, Xs)) = suc(double(rd(Xs))))),
% 75.11/75.37 inference(skolemize,[status(sab)],[5])).
% 75.11/75.37 tff(7,plain,
% 75.11/75.37 (![Xs: $i] : (rd(cons(i, Xs)) = suc(double(rd(Xs))))),
% 75.11/75.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 75.11/75.37 tff(8,plain,
% 75.11/75.37 ((~![Xs: $i] : (rd(cons(i, Xs)) = suc(double(rd(Xs))))) | (rd(cons(i, cons(o, cons(i, shw(half(suc(zero))))))) = suc(double(rd(cons(o, cons(i, shw(half(suc(zero)))))))))),
% 75.11/75.37 inference(quant_inst,[status(thm)],[])).
% 75.11/75.37 tff(9,plain,
% 75.11/75.37 (rd(cons(i, cons(o, cons(i, shw(half(suc(zero))))))) = suc(double(rd(cons(o, cons(i, shw(half(suc(zero))))))))),
% 75.11/75.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 75.11/75.37 tff(10,plain,
% 75.11/75.37 (^[Y: $i] : refl((append(nil, Y) = Y) <=> (append(nil, Y) = Y))),
% 75.11/75.37 inference(bind,[status(th)],[])).
% 75.11/75.37 tff(11,plain,
% 75.11/75.37 (![Y: $i] : (append(nil, Y) = Y) <=> ![Y: $i] : (append(nil, Y) = Y)),
% 75.11/75.37 inference(quant_intro,[status(thm)],[10])).
% 75.11/75.37 tff(12,plain,
% 75.11/75.37 (![Y: $i] : (append(nil, Y) = Y) <=> ![Y: $i] : (append(nil, Y) = Y)),
% 75.11/75.37 inference(rewrite,[status(thm)],[])).
% 75.11/75.37 tff(13,axiom,(![Y: $i] : (append(nil, Y) = Y)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_015')).
% 75.11/75.37 tff(14,plain,
% 75.11/75.37 (![Y: $i] : (append(nil, Y) = Y)),
% 75.11/75.37 inference(modus_ponens,[status(thm)],[13, 12])).
% 75.11/75.37 tff(15,plain,(
% 75.11/75.37 ![Y: $i] : (append(nil, Y) = Y)),
% 75.11/75.37 inference(skolemize,[status(sab)],[14])).
% 75.11/75.37 tff(16,plain,
% 75.11/75.37 (![Y: $i] : (append(nil, Y) = Y)),
% 75.11/75.37 inference(modus_ponens,[status(thm)],[15, 11])).
% 75.11/75.37 tff(17,plain,
% 75.11/75.37 ((~![Y: $i] : (append(nil, Y) = Y)) | (append(nil, cons(o, cons(i, shw(half(suc(zero)))))) = cons(o, cons(i, shw(half(suc(zero))))))),
% 75.11/75.37 inference(quant_inst,[status(thm)],[])).
% 75.11/75.37 tff(18,plain,
% 75.11/75.37 (append(nil, cons(o, cons(i, shw(half(suc(zero)))))) = cons(o, cons(i, shw(half(suc(zero)))))),
% 75.11/75.37 inference(unit_resolution,[status(thm)],[17, 16])).
% 75.11/75.37 tff(19,plain,
% 75.11/75.37 (cons(i, append(nil, cons(o, cons(i, shw(half(suc(zero))))))) = cons(i, cons(o, cons(i, shw(half(suc(zero))))))),
% 75.11/75.37 inference(monotonicity,[status(thm)],[18])).
% 75.11/75.37 tff(20,plain,
% 75.11/75.37 (^[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))))),
% 75.11/75.37 inference(bind,[status(th)],[])).
% 75.11/75.37 tff(21,plain,
% 75.11/75.37 (![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)))),
% 75.11/75.37 inference(quant_intro,[status(thm)],[20])).
% 75.11/75.37 tff(22,plain,
% 75.11/75.37 (![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)))),
% 75.11/75.37 inference(rewrite,[status(thm)],[])).
% 75.11/75.37 tff(23,axiom,(![Y: $i, Z: $i, Xs: $i] : (append(cons(Z, Xs), Y) = cons(Z, append(Xs, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_016')).
% 75.11/75.37 tff(24,plain,
% 75.11/75.37 (![Y: $i, Z: $i, Xs: $i] : (append(cons(Z, Xs), Y) = cons(Z, append(Xs, Y)))),
% 75.11/75.37 inference(modus_ponens,[status(thm)],[23, 22])).
% 75.11/75.37 tff(25,plain,(
% 75.11/75.37 ![Y: $i, Z: $i, Xs: $i] : (append(cons(Z, Xs), Y) = cons(Z, append(Xs, Y)))),
% 75.11/75.37 inference(skolemize,[status(sab)],[24])).
% 75.11/75.37 tff(26,plain,
% 75.11/75.37 (![Y: $i, Z: $i, Xs: $i] : (append(cons(Z, Xs), Y) = cons(Z, append(Xs, Y)))),
% 75.11/75.37 inference(modus_ponens,[status(thm)],[25, 21])).
% 75.11/75.37 tff(27,plain,
% 75.11/75.37 ((~![Y: $i, Z: $i, Xs: $i] : (append(cons(Z, Xs), Y) = cons(Z, append(Xs, Y)))) | (append(cons(i, nil), cons(o, cons(i, shw(half(suc(zero)))))) = cons(i, append(nil, cons(o, cons(i, shw(half(suc(zero))))))))),
% 75.11/75.37 inference(quant_inst,[status(thm)],[])).
% 75.11/75.37 tff(28,plain,
% 75.11/75.37 (append(cons(i, nil), cons(o, cons(i, shw(half(suc(zero)))))) = cons(i, append(nil, cons(o, cons(i, shw(half(suc(zero)))))))),
% 75.11/75.37 inference(unit_resolution,[status(thm)],[27, 26])).
% 75.11/75.37 tff(29,plain,
% 75.11/75.37 (^[N: $i] : refl((~(evenNat(N) <=> evenNat(suc(N)))) <=> (~(evenNat(N) <=> evenNat(suc(N)))))),
% 75.11/75.37 inference(bind,[status(th)],[])).
% 75.11/75.37 tff(30,plain,
% 75.11/75.37 (![N: $i] : (~(evenNat(N) <=> evenNat(suc(N)))) <=> ![N: $i] : (~(evenNat(N) <=> evenNat(suc(N))))),
% 75.11/75.37 inference(quant_intro,[status(thm)],[29])).
% 75.11/75.37 tff(31,plain,
% 75.11/75.37 (![N: $i] : (~(evenNat(N) <=> evenNat(suc(N)))) <=> ![N: $i] : (~(evenNat(N) <=> evenNat(suc(N))))),
% 75.11/75.37 inference(rewrite,[status(thm)],[])).
% 75.11/75.37 tff(32,plain,
% 75.11/75.37 (^[N: $i] : trans(rewrite((evenNat(suc(N)) <=> (~evenNat(N))) <=> (~(evenNat(N) <=> evenNat(suc(N))))), rewrite((~(evenNat(N) <=> evenNat(suc(N)))) <=> (~(evenNat(N) <=> evenNat(suc(N))))), ((evenNat(suc(N)) <=> (~evenNat(N))) <=> (~(evenNat(N) <=> evenNat(suc(N))))))),
% 75.11/75.37 inference(bind,[status(th)],[])).
% 75.11/75.37 tff(33,plain,
% 75.11/75.37 (![N: $i] : (evenNat(suc(N)) <=> (~evenNat(N))) <=> ![N: $i] : (~(evenNat(N) <=> evenNat(suc(N))))),
% 75.11/75.37 inference(quant_intro,[status(thm)],[32])).
% 75.11/75.37 tff(34,axiom,(![N: $i] : (evenNat(suc(N)) <=> (~evenNat(N)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_011')).
% 75.11/75.37 tff(35,plain,
% 75.11/75.37 (![N: $i] : (~(evenNat(N) <=> evenNat(suc(N))))),
% 75.11/75.37 inference(modus_ponens,[status(thm)],[34, 33])).
% 75.11/75.37 tff(36,plain,
% 75.11/75.37 (![N: $i] : (~(evenNat(N) <=> evenNat(suc(N))))),
% 75.11/75.37 inference(modus_ponens,[status(thm)],[35, 31])).
% 75.11/75.37 tff(37,plain,(
% 75.11/75.37 ![N: $i] : (~(evenNat(N) <=> evenNat(suc(N))))),
% 75.11/75.37 inference(skolemize,[status(sab)],[36])).
% 75.11/75.37 tff(38,plain,
% 75.11/75.37 (![N: $i] : (~(evenNat(N) <=> evenNat(suc(N))))),
% 75.11/75.37 inference(modus_ponens,[status(thm)],[37, 30])).
% 75.11/75.37 tff(39,plain,
% 75.11/75.37 ((~![N: $i] : (~(evenNat(N) <=> evenNat(suc(N))))) | (~(evenNat(zero) <=> evenNat(suc(zero))))),
% 75.11/75.37 inference(quant_inst,[status(thm)],[])).
% 75.11/75.37 tff(40,plain,
% 75.11/75.37 (~(evenNat(zero) <=> evenNat(suc(zero)))),
% 75.11/75.37 inference(unit_resolution,[status(thm)],[39, 38])).
% 75.11/75.37 tff(41,plain,
% 75.11/75.37 (evenNat(zero) <=> evenNat(zero)),
% 75.11/75.37 inference(rewrite,[status(thm)],[])).
% 75.11/75.37 tff(42,axiom,(evenNat(zero)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_010')).
% 75.11/75.37 tff(43,plain,
% 75.11/75.37 (evenNat(zero)),
% 75.11/75.37 inference(modus_ponens,[status(thm)],[42, 41])).
% 75.11/75.37 tff(44,plain,
% 75.11/75.37 ((evenNat(zero) <=> evenNat(suc(zero))) | (~evenNat(zero)) | (~evenNat(suc(zero)))),
% 75.11/75.37 inference(tautology,[status(thm)],[])).
% 75.11/75.37 tff(45,plain,
% 75.11/75.37 ((evenNat(zero) <=> evenNat(suc(zero))) | (~evenNat(suc(zero)))),
% 75.11/75.37 inference(unit_resolution,[status(thm)],[44, 43])).
% 75.11/75.37 tff(46,plain,
% 75.11/75.37 (~evenNat(suc(zero))),
% 75.11/75.37 inference(unit_resolution,[status(thm)],[45, 40])).
% 75.11/75.37 tff(47,plain,
% 75.11/75.37 (^[Y: $i] : refl((evenNat(suc(Y)) | (shw(suc(Y)) = cons(i, shw(half(suc(Y)))))) <=> (evenNat(suc(Y)) | (shw(suc(Y)) = cons(i, shw(half(suc(Y)))))))),
% 75.11/75.37 inference(bind,[status(th)],[])).
% 75.11/75.37 tff(48,plain,
% 75.11/75.37 (![Y: $i] : (evenNat(suc(Y)) | (shw(suc(Y)) = cons(i, shw(half(suc(Y)))))) <=> ![Y: $i] : (evenNat(suc(Y)) | (shw(suc(Y)) = cons(i, shw(half(suc(Y))))))),
% 75.11/75.37 inference(quant_intro,[status(thm)],[47])).
% 75.11/75.37 tff(49,plain,
% 75.11/75.37 (![Y: $i] : (evenNat(suc(Y)) | (shw(suc(Y)) = cons(i, shw(half(suc(Y)))))) <=> ![Y: $i] : (evenNat(suc(Y)) | (shw(suc(Y)) = cons(i, shw(half(suc(Y))))))),
% 75.11/75.38 inference(rewrite,[status(thm)],[])).
% 75.11/75.38 tff(50,plain,
% 75.11/75.38 (^[Y: $i] : rewrite(((~evenNat(suc(Y))) => (shw(suc(Y)) = cons(i, shw(half(suc(Y)))))) <=> (evenNat(suc(Y)) | (shw(suc(Y)) = cons(i, shw(half(suc(Y)))))))),
% 75.11/75.38 inference(bind,[status(th)],[])).
% 75.11/75.38 tff(51,plain,
% 75.11/75.38 (![Y: $i] : ((~evenNat(suc(Y))) => (shw(suc(Y)) = cons(i, shw(half(suc(Y)))))) <=> ![Y: $i] : (evenNat(suc(Y)) | (shw(suc(Y)) = cons(i, shw(half(suc(Y))))))),
% 75.11/75.38 inference(quant_intro,[status(thm)],[50])).
% 75.11/75.38 tff(52,axiom,(![Y: $i] : ((~evenNat(suc(Y))) => (shw(suc(Y)) = cons(i, shw(half(suc(Y))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_014')).
% 75.11/75.38 tff(53,plain,
% 75.11/75.38 (![Y: $i] : (evenNat(suc(Y)) | (shw(suc(Y)) = cons(i, shw(half(suc(Y))))))),
% 75.11/75.38 inference(modus_ponens,[status(thm)],[52, 51])).
% 75.11/75.38 tff(54,plain,
% 75.11/75.38 (![Y: $i] : (evenNat(suc(Y)) | (shw(suc(Y)) = cons(i, shw(half(suc(Y))))))),
% 75.11/75.38 inference(modus_ponens,[status(thm)],[53, 49])).
% 75.11/75.38 tff(55,plain,(
% 75.11/75.38 ![Y: $i] : (evenNat(suc(Y)) | (shw(suc(Y)) = cons(i, shw(half(suc(Y))))))),
% 75.11/75.38 inference(skolemize,[status(sab)],[54])).
% 75.11/75.38 tff(56,plain,
% 75.11/75.38 (![Y: $i] : (evenNat(suc(Y)) | (shw(suc(Y)) = cons(i, shw(half(suc(Y))))))),
% 75.11/75.38 inference(modus_ponens,[status(thm)],[55, 48])).
% 75.11/75.38 tff(57,plain,
% 75.11/75.38 (((~![Y: $i] : (evenNat(suc(Y)) | (shw(suc(Y)) = cons(i, shw(half(suc(Y))))))) | (evenNat(suc(zero)) | (shw(suc(zero)) = cons(i, shw(half(suc(zero))))))) <=> ((~![Y: $i] : (evenNat(suc(Y)) | (shw(suc(Y)) = cons(i, shw(half(suc(Y))))))) | evenNat(suc(zero)) | (shw(suc(zero)) = cons(i, shw(half(suc(zero))))))),
% 75.11/75.38 inference(rewrite,[status(thm)],[])).
% 75.11/75.38 tff(58,plain,
% 75.11/75.38 ((~![Y: $i] : (evenNat(suc(Y)) | (shw(suc(Y)) = cons(i, shw(half(suc(Y))))))) | (evenNat(suc(zero)) | (shw(suc(zero)) = cons(i, shw(half(suc(zero))))))),
% 75.11/75.38 inference(quant_inst,[status(thm)],[])).
% 75.11/75.38 tff(59,plain,
% 75.11/75.38 ((~![Y: $i] : (evenNat(suc(Y)) | (shw(suc(Y)) = cons(i, shw(half(suc(Y))))))) | evenNat(suc(zero)) | (shw(suc(zero)) = cons(i, shw(half(suc(zero)))))),
% 75.11/75.38 inference(modus_ponens,[status(thm)],[58, 57])).
% 75.11/75.38 tff(60,plain,
% 75.11/75.38 (evenNat(suc(zero)) | (shw(suc(zero)) = cons(i, shw(half(suc(zero)))))),
% 75.11/75.38 inference(unit_resolution,[status(thm)],[59, 56])).
% 75.11/75.38 tff(61,plain,
% 75.11/75.38 (shw(suc(zero)) = cons(i, shw(half(suc(zero))))),
% 75.11/75.38 inference(unit_resolution,[status(thm)],[60, 46])).
% 75.11/75.38 tff(62,plain,
% 75.11/75.38 ((half(zero) = zero) <=> (half(zero) = zero)),
% 75.11/75.38 inference(rewrite,[status(thm)],[])).
% 75.11/75.38 tff(63,axiom,(half(zero) = zero), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_007')).
% 75.11/75.38 tff(64,plain,
% 75.11/75.38 (half(zero) = zero),
% 75.11/75.38 inference(modus_ponens,[status(thm)],[63, 62])).
% 75.11/75.38 tff(65,plain,
% 75.11/75.38 (zero = half(zero)),
% 75.11/75.38 inference(symmetry,[status(thm)],[64])).
% 75.11/75.38 tff(66,plain,
% 75.11/75.38 (suc(zero) = suc(half(zero))),
% 75.11/75.38 inference(monotonicity,[status(thm)],[65])).
% 75.11/75.38 tff(67,plain,
% 75.11/75.38 (suc(half(zero)) = suc(zero)),
% 75.11/75.38 inference(symmetry,[status(thm)],[66])).
% 75.11/75.38 tff(68,plain,
% 75.11/75.38 (^[N: $i] : refl((half(suc(suc(N))) = suc(half(N))) <=> (half(suc(suc(N))) = suc(half(N))))),
% 75.11/75.38 inference(bind,[status(th)],[])).
% 75.11/75.38 tff(69,plain,
% 75.11/75.38 (![N: $i] : (half(suc(suc(N))) = suc(half(N))) <=> ![N: $i] : (half(suc(suc(N))) = suc(half(N)))),
% 75.11/75.38 inference(quant_intro,[status(thm)],[68])).
% 75.11/75.38 tff(70,plain,
% 75.11/75.38 (![N: $i] : (half(suc(suc(N))) = suc(half(N))) <=> ![N: $i] : (half(suc(suc(N))) = suc(half(N)))),
% 75.11/75.38 inference(rewrite,[status(thm)],[])).
% 75.11/75.38 tff(71,axiom,(![N: $i] : (half(suc(suc(N))) = suc(half(N)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_009')).
% 75.11/75.38 tff(72,plain,
% 75.11/75.38 (![N: $i] : (half(suc(suc(N))) = suc(half(N)))),
% 75.11/75.38 inference(modus_ponens,[status(thm)],[71, 70])).
% 75.11/75.38 tff(73,plain,(
% 75.11/75.38 ![N: $i] : (half(suc(suc(N))) = suc(half(N)))),
% 75.11/75.38 inference(skolemize,[status(sab)],[72])).
% 75.11/75.38 tff(74,plain,
% 75.11/75.38 (![N: $i] : (half(suc(suc(N))) = suc(half(N)))),
% 75.11/75.38 inference(modus_ponens,[status(thm)],[73, 69])).
% 75.11/75.38 tff(75,plain,
% 75.11/75.38 ((~![N: $i] : (half(suc(suc(N))) = suc(half(N)))) | (half(suc(suc(zero))) = suc(half(zero)))),
% 75.11/75.38 inference(quant_inst,[status(thm)],[])).
% 75.11/75.38 tff(76,plain,
% 75.11/75.38 (half(suc(suc(zero))) = suc(half(zero))),
% 75.11/75.38 inference(unit_resolution,[status(thm)],[75, 74])).
% 75.11/75.38 tff(77,plain,
% 75.11/75.38 (suc(suc(half(zero))) = suc(suc(zero))),
% 75.11/75.38 inference(monotonicity,[status(thm)],[67])).
% 75.11/75.38 tff(78,plain,
% 75.11/75.38 (half(suc(suc(half(zero)))) = half(suc(suc(zero)))),
% 75.11/75.38 inference(monotonicity,[status(thm)],[77])).
% 75.11/75.38 tff(79,plain,
% 75.11/75.38 (half(suc(suc(half(zero)))) = suc(zero)),
% 75.11/75.38 inference(transitivity,[status(thm)],[78, 76, 67])).
% 75.11/75.38 tff(80,plain,
% 75.11/75.38 (shw(half(suc(suc(half(zero))))) = shw(suc(zero))),
% 75.11/75.38 inference(monotonicity,[status(thm)],[79])).
% 75.11/75.38 tff(81,plain,
% 75.11/75.38 (shw(half(suc(suc(half(zero))))) = cons(i, shw(half(suc(zero))))),
% 75.11/75.38 inference(transitivity,[status(thm)],[80, 61])).
% 75.11/75.38 tff(82,plain,
% 75.11/75.38 (cons(o, shw(half(suc(suc(half(zero)))))) = cons(o, cons(i, shw(half(suc(zero)))))),
% 75.11/75.38 inference(monotonicity,[status(thm)],[81])).
% 75.11/75.38 tff(83,plain,
% 75.11/75.38 ((~![N: $i] : (~(evenNat(N) <=> evenNat(suc(N))))) | (~(evenNat(suc(half(zero))) <=> evenNat(suc(suc(half(zero))))))),
% 75.11/75.38 inference(quant_inst,[status(thm)],[])).
% 75.11/75.38 tff(84,plain,
% 75.11/75.38 (~(evenNat(suc(half(zero))) <=> evenNat(suc(suc(half(zero)))))),
% 75.11/75.38 inference(unit_resolution,[status(thm)],[83, 38])).
% 75.11/75.38 tff(85,plain,
% 75.11/75.38 (evenNat(suc(half(zero))) <=> evenNat(suc(zero))),
% 75.11/75.38 inference(monotonicity,[status(thm)],[67])).
% 75.11/75.38 tff(86,plain,
% 75.11/75.38 (evenNat(suc(zero)) <=> evenNat(suc(half(zero)))),
% 75.11/75.38 inference(symmetry,[status(thm)],[85])).
% 75.11/75.38 tff(87,plain,
% 75.11/75.38 ((~evenNat(suc(zero))) <=> (~evenNat(suc(half(zero))))),
% 75.11/75.38 inference(monotonicity,[status(thm)],[86])).
% 75.11/75.38 tff(88,plain,
% 75.11/75.38 (~evenNat(suc(half(zero)))),
% 75.11/75.38 inference(modus_ponens,[status(thm)],[46, 87])).
% 75.11/75.38 tff(89,plain,
% 75.11/75.38 ((evenNat(suc(half(zero))) <=> evenNat(suc(suc(half(zero))))) | evenNat(suc(half(zero))) | evenNat(suc(suc(half(zero))))),
% 75.11/75.38 inference(tautology,[status(thm)],[])).
% 75.11/75.38 tff(90,plain,
% 75.11/75.38 (evenNat(suc(suc(half(zero))))),
% 75.11/75.38 inference(unit_resolution,[status(thm)],[89, 88, 84])).
% 75.11/75.38 tff(91,plain,
% 75.11/75.38 (^[Y: $i] : refl(((~evenNat(suc(Y))) | (shw(suc(Y)) = cons(o, shw(half(suc(Y)))))) <=> ((~evenNat(suc(Y))) | (shw(suc(Y)) = cons(o, shw(half(suc(Y)))))))),
% 75.11/75.38 inference(bind,[status(th)],[])).
% 75.11/75.38 tff(92,plain,
% 75.11/75.38 (![Y: $i] : ((~evenNat(suc(Y))) | (shw(suc(Y)) = cons(o, shw(half(suc(Y)))))) <=> ![Y: $i] : ((~evenNat(suc(Y))) | (shw(suc(Y)) = cons(o, shw(half(suc(Y))))))),
% 75.11/75.38 inference(quant_intro,[status(thm)],[91])).
% 75.11/75.38 tff(93,plain,
% 75.11/75.38 (![Y: $i] : ((~evenNat(suc(Y))) | (shw(suc(Y)) = cons(o, shw(half(suc(Y)))))) <=> ![Y: $i] : ((~evenNat(suc(Y))) | (shw(suc(Y)) = cons(o, shw(half(suc(Y))))))),
% 75.11/75.38 inference(rewrite,[status(thm)],[])).
% 75.11/75.38 tff(94,plain,
% 75.11/75.38 (^[Y: $i] : rewrite((evenNat(suc(Y)) => (shw(suc(Y)) = cons(o, shw(half(suc(Y)))))) <=> ((~evenNat(suc(Y))) | (shw(suc(Y)) = cons(o, shw(half(suc(Y)))))))),
% 75.11/75.38 inference(bind,[status(th)],[])).
% 75.11/75.38 tff(95,plain,
% 75.11/75.38 (![Y: $i] : (evenNat(suc(Y)) => (shw(suc(Y)) = cons(o, shw(half(suc(Y)))))) <=> ![Y: $i] : ((~evenNat(suc(Y))) | (shw(suc(Y)) = cons(o, shw(half(suc(Y))))))),
% 75.11/75.38 inference(quant_intro,[status(thm)],[94])).
% 75.11/75.38 tff(96,axiom,(![Y: $i] : (evenNat(suc(Y)) => (shw(suc(Y)) = cons(o, shw(half(suc(Y))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_013')).
% 75.11/75.38 tff(97,plain,
% 75.11/75.38 (![Y: $i] : ((~evenNat(suc(Y))) | (shw(suc(Y)) = cons(o, shw(half(suc(Y))))))),
% 75.11/75.38 inference(modus_ponens,[status(thm)],[96, 95])).
% 75.11/75.38 tff(98,plain,
% 75.11/75.38 (![Y: $i] : ((~evenNat(suc(Y))) | (shw(suc(Y)) = cons(o, shw(half(suc(Y))))))),
% 75.11/75.38 inference(modus_ponens,[status(thm)],[97, 93])).
% 75.11/75.38 tff(99,plain,(
% 75.11/75.38 ![Y: $i] : ((~evenNat(suc(Y))) | (shw(suc(Y)) = cons(o, shw(half(suc(Y))))))),
% 75.11/75.38 inference(skolemize,[status(sab)],[98])).
% 75.11/75.38 tff(100,plain,
% 75.11/75.38 (![Y: $i] : ((~evenNat(suc(Y))) | (shw(suc(Y)) = cons(o, shw(half(suc(Y))))))),
% 75.11/75.38 inference(modus_ponens,[status(thm)],[99, 92])).
% 75.11/75.38 tff(101,plain,
% 75.11/75.38 (((~![Y: $i] : ((~evenNat(suc(Y))) | (shw(suc(Y)) = cons(o, shw(half(suc(Y))))))) | ((~evenNat(suc(suc(half(zero))))) | (shw(suc(suc(half(zero)))) = cons(o, shw(half(suc(suc(half(zero))))))))) <=> ((~![Y: $i] : ((~evenNat(suc(Y))) | (shw(suc(Y)) = cons(o, shw(half(suc(Y))))))) | (~evenNat(suc(suc(half(zero))))) | (shw(suc(suc(half(zero)))) = cons(o, shw(half(suc(suc(half(zero))))))))),
% 75.11/75.38 inference(rewrite,[status(thm)],[])).
% 75.11/75.38 tff(102,plain,
% 75.11/75.38 ((~![Y: $i] : ((~evenNat(suc(Y))) | (shw(suc(Y)) = cons(o, shw(half(suc(Y))))))) | ((~evenNat(suc(suc(half(zero))))) | (shw(suc(suc(half(zero)))) = cons(o, shw(half(suc(suc(half(zero))))))))),
% 75.11/75.38 inference(quant_inst,[status(thm)],[])).
% 75.11/75.38 tff(103,plain,
% 75.11/75.38 ((~![Y: $i] : ((~evenNat(suc(Y))) | (shw(suc(Y)) = cons(o, shw(half(suc(Y))))))) | (~evenNat(suc(suc(half(zero))))) | (shw(suc(suc(half(zero)))) = cons(o, shw(half(suc(suc(half(zero)))))))),
% 75.11/75.38 inference(modus_ponens,[status(thm)],[102, 101])).
% 75.11/75.38 tff(104,plain,
% 75.11/75.38 ((~evenNat(suc(suc(half(zero))))) | (shw(suc(suc(half(zero)))) = cons(o, shw(half(suc(suc(half(zero)))))))),
% 75.11/75.38 inference(unit_resolution,[status(thm)],[103, 100])).
% 75.11/75.38 tff(105,plain,
% 75.11/75.38 (shw(suc(suc(half(zero)))) = cons(o, shw(half(suc(suc(half(zero))))))),
% 75.11/75.38 inference(unit_resolution,[status(thm)],[104, 90])).
% 75.11/75.38 tff(106,plain,
% 75.11/75.38 (suc(suc(zero)) = suc(suc(half(zero)))),
% 75.11/75.38 inference(symmetry,[status(thm)],[77])).
% 75.11/75.38 tff(107,plain,
% 75.11/75.38 (shw(suc(suc(zero))) = shw(suc(suc(half(zero))))),
% 75.11/75.38 inference(monotonicity,[status(thm)],[106])).
% 75.11/75.38 tff(108,plain,
% 75.11/75.38 (shw(suc(suc(zero))) = cons(o, cons(i, shw(half(suc(zero)))))),
% 75.11/75.38 inference(transitivity,[status(thm)],[107, 105, 82])).
% 75.11/75.38 tff(109,plain,
% 75.11/75.38 ((half(suc(zero)) = zero) <=> (half(suc(zero)) = zero)),
% 75.11/75.38 inference(rewrite,[status(thm)],[])).
% 75.11/75.38 tff(110,axiom,(half(suc(zero)) = zero), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_008')).
% 75.11/75.38 tff(111,plain,
% 75.11/75.38 (half(suc(zero)) = zero),
% 75.11/75.38 inference(modus_ponens,[status(thm)],[110, 109])).
% 75.11/75.38 tff(112,plain,
% 75.11/75.38 (shw(half(suc(zero))) = shw(zero)),
% 75.11/75.38 inference(monotonicity,[status(thm)],[111])).
% 75.11/75.38 tff(113,plain,
% 75.11/75.38 (shw(zero) = shw(half(suc(zero)))),
% 75.11/75.38 inference(symmetry,[status(thm)],[112])).
% 75.11/75.38 tff(114,plain,
% 75.11/75.38 ((shw(zero) = nil) <=> (shw(zero) = nil)),
% 75.11/75.38 inference(rewrite,[status(thm)],[])).
% 75.11/75.38 tff(115,axiom,(shw(zero) = nil), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_012')).
% 75.11/75.38 tff(116,plain,
% 75.11/75.38 (shw(zero) = nil),
% 75.11/75.38 inference(modus_ponens,[status(thm)],[115, 114])).
% 75.11/75.38 tff(117,plain,
% 75.11/75.38 (nil = shw(zero)),
% 75.11/75.38 inference(symmetry,[status(thm)],[116])).
% 75.11/75.38 tff(118,plain,
% 75.11/75.38 (nil = shw(half(suc(zero)))),
% 75.11/75.38 inference(transitivity,[status(thm)],[117, 113])).
% 75.11/75.38 tff(119,plain,
% 75.11/75.38 (cons(i, nil) = cons(i, shw(half(suc(zero))))),
% 75.11/75.38 inference(monotonicity,[status(thm)],[118])).
% 75.11/75.38 tff(120,plain,
% 75.11/75.38 (cons(i, shw(half(suc(zero)))) = cons(i, nil)),
% 75.11/75.38 inference(symmetry,[status(thm)],[119])).
% 75.11/75.38 tff(121,plain,
% 75.11/75.38 (shw(suc(half(zero))) = shw(suc(zero))),
% 75.11/75.38 inference(monotonicity,[status(thm)],[67])).
% 75.11/75.38 tff(122,plain,
% 75.11/75.38 (shw(suc(half(zero))) = cons(i, nil)),
% 75.11/75.38 inference(transitivity,[status(thm)],[121, 61, 120])).
% 75.11/75.38 tff(123,plain,
% 75.11/75.38 (append(shw(suc(half(zero))), shw(suc(suc(zero)))) = append(cons(i, nil), cons(o, cons(i, shw(half(suc(zero))))))),
% 75.11/75.38 inference(monotonicity,[status(thm)],[122, 108])).
% 75.11/75.38 tff(124,plain,
% 75.11/75.38 (append(shw(suc(half(zero))), shw(suc(suc(zero)))) = cons(i, cons(o, cons(i, shw(half(suc(zero))))))),
% 75.11/75.38 inference(transitivity,[status(thm)],[123, 28, 19])).
% 75.11/75.38 tff(125,plain,
% 75.11/75.38 (rd(append(shw(suc(half(zero))), shw(suc(suc(zero))))) = rd(cons(i, cons(o, cons(i, shw(half(suc(zero)))))))),
% 75.11/75.38 inference(monotonicity,[status(thm)],[124])).
% 75.11/75.38 tff(126,assumption,(~(x(suc(half(zero)), suc(suc(zero))) = rd(append(shw(suc(half(zero))), shw(suc(suc(zero))))))), introduced(assumption)).
% 75.11/75.38 tff(127,plain,
% 75.11/75.38 (^[X: $i, Y: $i] : refl((x(X, Y) = rd(append(shw(X), shw(Y)))) <=> (x(X, Y) = rd(append(shw(X), shw(Y)))))),
% 75.11/75.38 inference(bind,[status(th)],[])).
% 75.11/75.38 tff(128,plain,
% 75.11/75.38 (![X: $i, Y: $i] : (x(X, Y) = rd(append(shw(X), shw(Y)))) <=> ![X: $i, Y: $i] : (x(X, Y) = rd(append(shw(X), shw(Y))))),
% 75.11/75.38 inference(quant_intro,[status(thm)],[127])).
% 75.11/75.38 tff(129,plain,
% 75.11/75.38 (![X: $i, Y: $i] : (x(X, Y) = rd(append(shw(X), shw(Y)))) <=> ![X: $i, Y: $i] : (x(X, Y) = rd(append(shw(X), shw(Y))))),
% 75.11/75.38 inference(rewrite,[status(thm)],[])).
% 75.11/75.38 tff(130,axiom,(![X: $i, Y: $i] : (x(X, Y) = rd(append(shw(X), shw(Y))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_023')).
% 75.11/75.38 tff(131,plain,
% 75.11/75.38 (![X: $i, Y: $i] : (x(X, Y) = rd(append(shw(X), shw(Y))))),
% 75.11/75.38 inference(modus_ponens,[status(thm)],[130, 129])).
% 75.11/75.38 tff(132,plain,(
% 75.11/75.38 ![X: $i, Y: $i] : (x(X, Y) = rd(append(shw(X), shw(Y))))),
% 75.11/75.38 inference(skolemize,[status(sab)],[131])).
% 75.11/75.38 tff(133,plain,
% 75.11/75.38 (![X: $i, Y: $i] : (x(X, Y) = rd(append(shw(X), shw(Y))))),
% 75.11/75.38 inference(modus_ponens,[status(thm)],[132, 128])).
% 75.11/75.38 tff(134,plain,
% 75.11/75.38 ((~![X: $i, Y: $i] : (x(X, Y) = rd(append(shw(X), shw(Y))))) | (x(suc(half(zero)), suc(suc(zero))) = rd(append(shw(suc(half(zero))), shw(suc(suc(zero))))))),
% 75.11/75.38 inference(quant_inst,[status(thm)],[])).
% 75.11/75.38 tff(135,plain,
% 75.11/75.38 ($false),
% 75.11/75.38 inference(unit_resolution,[status(thm)],[134, 133, 126])).
% 75.11/75.38 tff(136,plain,(x(suc(half(zero)), suc(suc(zero))) = rd(append(shw(suc(half(zero))), shw(suc(suc(zero)))))), inference(lemma,lemma(discharge,[]))).
% 75.11/75.38 tff(137,plain,
% 75.11/75.38 (^[X: $i, Y: $i] : refl((x(X, Y) = x(Y, X)) <=> (x(X, Y) = x(Y, X)))),
% 75.11/75.38 inference(bind,[status(th)],[])).
% 75.11/75.38 tff(138,plain,
% 75.11/75.38 (![X: $i, Y: $i] : (x(X, Y) = x(Y, X)) <=> ![X: $i, Y: $i] : (x(X, Y) = x(Y, X))),
% 75.11/75.38 inference(quant_intro,[status(thm)],[137])).
% 75.11/75.38 tff(139,plain,
% 75.11/75.38 ((~?[X: $i, Y: $i] : (~(x(X, Y) = x(Y, X)))) <=> (~?[X: $i, Y: $i] : (~(x(X, Y) = x(Y, X))))),
% 75.11/75.38 inference(rewrite,[status(thm)],[])).
% 75.11/75.38 tff(140,axiom,(~?[X: $i, Y: $i] : (~(x(X, Y) = x(Y, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goal_024')).
% 75.11/75.38 tff(141,plain,
% 75.11/75.38 (~?[X: $i, Y: $i] : (~(x(X, Y) = x(Y, X)))),
% 75.11/75.38 inference(modus_ponens,[status(thm)],[140, 139])).
% 75.11/75.38 tff(142,plain,
% 75.11/75.38 (~?[X: $i, Y: $i] : (~(x(X, Y) = x(Y, X)))),
% 75.11/75.38 inference(modus_ponens,[status(thm)],[141, 139])).
% 75.11/75.38 tff(143,plain,
% 75.11/75.38 (~?[X: $i, Y: $i] : (~(x(X, Y) = x(Y, X)))),
% 75.11/75.38 inference(modus_ponens,[status(thm)],[142, 139])).
% 75.11/75.38 tff(144,plain,
% 75.11/75.38 (~?[X: $i, Y: $i] : (~(x(X, Y) = x(Y, X)))),
% 75.11/75.38 inference(modus_ponens,[status(thm)],[143, 139])).
% 75.11/75.38 tff(145,plain,
% 75.11/75.38 (^[X: $i, Y: $i] : refl($oeq((x(X, Y) = x(Y, X)), (x(X, Y) = x(Y, X))))),
% 75.11/75.38 inference(bind,[status(th)],[])).
% 75.11/75.38 tff(146,plain,(
% 75.11/75.38 ![X: $i, Y: $i] : (x(X, Y) = x(Y, X))),
% 75.11/75.38 inference(nnf-neg,[status(sab)],[144, 145])).
% 75.11/75.38 tff(147,plain,
% 75.11/75.38 (![X: $i, Y: $i] : (x(X, Y) = x(Y, X))),
% 75.11/75.38 inference(modus_ponens,[status(thm)],[146, 138])).
% 75.11/75.38 tff(148,plain,
% 75.11/75.38 ((~![X: $i, Y: $i] : (x(X, Y) = x(Y, X))) | (x(suc(suc(zero)), suc(half(zero))) = x(suc(half(zero)), suc(suc(zero))))),
% 75.11/75.38 inference(quant_inst,[status(thm)],[])).
% 75.11/75.38 tff(149,plain,
% 75.11/75.38 (x(suc(suc(zero)), suc(half(zero))) = x(suc(half(zero)), suc(suc(zero)))),
% 75.11/75.38 inference(unit_resolution,[status(thm)],[148, 147])).
% 75.11/75.38 tff(150,plain,
% 75.11/75.38 ((~![X: $i, Y: $i] : (x(X, Y) = rd(append(shw(X), shw(Y))))) | (x(suc(suc(zero)), suc(half(zero))) = rd(append(shw(suc(suc(zero))), shw(suc(half(zero))))))),
% 75.11/75.38 inference(quant_inst,[status(thm)],[])).
% 75.11/75.38 tff(151,plain,
% 75.11/75.38 (x(suc(suc(zero)), suc(half(zero))) = rd(append(shw(suc(suc(zero))), shw(suc(half(zero)))))),
% 75.11/75.38 inference(unit_resolution,[status(thm)],[150, 133])).
% 75.11/75.38 tff(152,plain,
% 75.11/75.38 (rd(append(shw(suc(suc(zero))), shw(suc(half(zero))))) = x(suc(suc(zero)), suc(half(zero)))),
% 75.11/75.38 inference(symmetry,[status(thm)],[151])).
% 75.11/75.38 tff(153,plain,
% 75.11/75.38 (shw(suc(half(zero))) = cons(i, shw(half(suc(zero))))),
% 75.11/75.38 inference(transitivity,[status(thm)],[121, 61])).
% 75.11/75.38 tff(154,plain,
% 75.11/75.38 (append(shw(suc(suc(zero))), shw(suc(half(zero)))) = append(cons(o, cons(i, shw(half(suc(zero))))), cons(i, shw(half(suc(zero)))))),
% 75.11/75.38 inference(monotonicity,[status(thm)],[108, 153])).
% 75.11/75.38 tff(155,plain,
% 75.11/75.38 (append(cons(o, cons(i, shw(half(suc(zero))))), cons(i, shw(half(suc(zero))))) = append(shw(suc(suc(zero))), shw(suc(half(zero))))),
% 75.11/75.38 inference(symmetry,[status(thm)],[154])).
% 75.11/75.38 tff(156,plain,
% 75.11/75.38 ((~![Y: $i, Z: $i, Xs: $i] : (append(cons(Z, Xs), Y) = cons(Z, append(Xs, Y)))) | (append(cons(o, cons(i, shw(half(suc(zero))))), cons(i, shw(half(suc(zero))))) = cons(o, append(cons(i, shw(half(suc(zero)))), cons(i, shw(half(suc(zero)))))))),
% 75.11/75.38 inference(quant_inst,[status(thm)],[])).
% 75.11/75.38 tff(157,plain,
% 75.11/75.38 (append(cons(o, cons(i, shw(half(suc(zero))))), cons(i, shw(half(suc(zero))))) = cons(o, append(cons(i, shw(half(suc(zero)))), cons(i, shw(half(suc(zero))))))),
% 75.11/75.38 inference(unit_resolution,[status(thm)],[156, 26])).
% 75.11/75.38 tff(158,plain,
% 75.11/75.38 (cons(o, append(cons(i, shw(half(suc(zero)))), cons(i, shw(half(suc(zero)))))) = append(cons(o, cons(i, shw(half(suc(zero))))), cons(i, shw(half(suc(zero)))))),
% 75.11/75.38 inference(symmetry,[status(thm)],[157])).
% 75.11/75.38 tff(159,plain,
% 75.11/75.38 ((~![Y: $i] : (append(nil, Y) = Y)) | (append(nil, cons(i, shw(half(suc(zero))))) = cons(i, shw(half(suc(zero)))))),
% 75.11/75.38 inference(quant_inst,[status(thm)],[])).
% 75.11/75.38 tff(160,plain,
% 75.11/75.38 (append(nil, cons(i, shw(half(suc(zero))))) = cons(i, shw(half(suc(zero))))),
% 75.11/75.38 inference(unit_resolution,[status(thm)],[159, 16])).
% 75.11/75.38 tff(161,plain,
% 75.11/75.38 (cons(i, append(nil, cons(i, shw(half(suc(zero)))))) = cons(i, cons(i, shw(half(suc(zero)))))),
% 75.11/75.38 inference(monotonicity,[status(thm)],[160])).
% 75.11/75.38 tff(162,plain,
% 75.11/75.38 ((~![Y: $i, Z: $i, Xs: $i] : (append(cons(Z, Xs), Y) = cons(Z, append(Xs, Y)))) | (append(cons(i, nil), cons(i, shw(half(suc(zero))))) = cons(i, append(nil, cons(i, shw(half(suc(zero)))))))),
% 75.11/75.38 inference(quant_inst,[status(thm)],[])).
% 75.11/75.38 tff(163,plain,
% 75.11/75.38 (append(cons(i, nil), cons(i, shw(half(suc(zero))))) = cons(i, append(nil, cons(i, shw(half(suc(zero))))))),
% 75.11/75.38 inference(unit_resolution,[status(thm)],[162, 26])).
% 75.11/75.38 tff(164,plain,
% 75.11/75.38 (append(cons(i, shw(half(suc(zero)))), cons(i, shw(half(suc(zero))))) = append(cons(i, nil), cons(i, shw(half(suc(zero)))))),
% 75.11/75.38 inference(monotonicity,[status(thm)],[120])).
% 75.11/75.38 tff(165,plain,
% 75.11/75.38 (append(cons(i, shw(half(suc(zero)))), cons(i, shw(half(suc(zero))))) = cons(i, cons(i, shw(half(suc(zero)))))),
% 75.11/75.38 inference(transitivity,[status(thm)],[164, 163, 161])).
% 75.11/75.38 tff(166,plain,
% 75.11/75.38 (cons(o, append(cons(i, shw(half(suc(zero)))), cons(i, shw(half(suc(zero)))))) = cons(o, cons(i, cons(i, shw(half(suc(zero))))))),
% 75.11/75.38 inference(monotonicity,[status(thm)],[165])).
% 75.11/75.38 tff(167,plain,
% 75.11/75.38 (cons(o, cons(i, cons(i, shw(half(suc(zero)))))) = cons(o, append(cons(i, shw(half(suc(zero)))), cons(i, shw(half(suc(zero))))))),
% 75.11/75.38 inference(symmetry,[status(thm)],[166])).
% 75.11/75.38 tff(168,plain,
% 75.11/75.38 (cons(o, cons(i, cons(i, shw(half(suc(zero)))))) = append(shw(suc(suc(zero))), shw(suc(half(zero))))),
% 75.11/75.38 inference(transitivity,[status(thm)],[167, 158, 155])).
% 75.11/75.38 tff(169,plain,
% 75.11/75.38 (rd(cons(o, cons(i, cons(i, shw(half(suc(zero))))))) = rd(append(shw(suc(suc(zero))), shw(suc(half(zero)))))),
% 75.11/75.38 inference(monotonicity,[status(thm)],[168])).
% 75.11/75.38 tff(170,plain,
% 75.11/75.38 (^[Xs: $i] : refl((rd(cons(o, Xs)) = double(rd(Xs))) <=> (rd(cons(o, Xs)) = double(rd(Xs))))),
% 75.11/75.38 inference(bind,[status(th)],[])).
% 75.11/75.38 tff(171,plain,
% 75.11/75.38 (![Xs: $i] : (rd(cons(o, Xs)) = double(rd(Xs))) <=> ![Xs: $i] : (rd(cons(o, Xs)) = double(rd(Xs)))),
% 75.11/75.38 inference(quant_intro,[status(thm)],[170])).
% 75.11/75.38 tff(172,plain,
% 75.11/75.38 (![Xs: $i] : (rd(cons(o, Xs)) = double(rd(Xs))) <=> ![Xs: $i] : (rd(cons(o, Xs)) = double(rd(Xs)))),
% 75.11/75.38 inference(rewrite,[status(thm)],[])).
% 75.11/75.38 tff(173,axiom,(![Xs: $i] : (rd(cons(o, Xs)) = double(rd(Xs)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_022')).
% 75.11/75.38 tff(174,plain,
% 75.11/75.38 (![Xs: $i] : (rd(cons(o, Xs)) = double(rd(Xs)))),
% 75.11/75.38 inference(modus_ponens,[status(thm)],[173, 172])).
% 75.11/75.38 tff(175,plain,(
% 75.11/75.38 ![Xs: $i] : (rd(cons(o, Xs)) = double(rd(Xs)))),
% 75.11/75.38 inference(skolemize,[status(sab)],[174])).
% 75.11/75.38 tff(176,plain,
% 75.11/75.38 (![Xs: $i] : (rd(cons(o, Xs)) = double(rd(Xs)))),
% 75.11/75.38 inference(modus_ponens,[status(thm)],[175, 171])).
% 75.11/75.38 tff(177,plain,
% 75.11/75.38 ((~![Xs: $i] : (rd(cons(o, Xs)) = double(rd(Xs)))) | (rd(cons(o, cons(i, cons(i, shw(half(suc(zero))))))) = double(rd(cons(i, cons(i, shw(half(suc(zero))))))))),
% 75.11/75.38 inference(quant_inst,[status(thm)],[])).
% 75.11/75.38 tff(178,plain,
% 75.11/75.38 (rd(cons(o, cons(i, cons(i, shw(half(suc(zero))))))) = double(rd(cons(i, cons(i, shw(half(suc(zero)))))))),
% 75.11/75.38 inference(unit_resolution,[status(thm)],[177, 176])).
% 75.11/75.38 tff(179,plain,
% 75.11/75.38 (double(rd(cons(i, cons(i, shw(half(suc(zero))))))) = rd(cons(o, cons(i, cons(i, shw(half(suc(zero)))))))),
% 75.11/75.38 inference(symmetry,[status(thm)],[178])).
% 75.11/75.38 tff(180,plain,
% 75.11/75.38 ((~![Xs: $i] : (rd(cons(i, Xs)) = suc(double(rd(Xs))))) | (rd(cons(i, cons(i, shw(half(suc(zero)))))) = suc(double(rd(cons(i, shw(half(suc(zero))))))))),
% 75.11/75.38 inference(quant_inst,[status(thm)],[])).
% 75.11/75.38 tff(181,plain,
% 75.11/75.38 (rd(cons(i, cons(i, shw(half(suc(zero)))))) = suc(double(rd(cons(i, shw(half(suc(zero)))))))),
% 75.11/75.38 inference(unit_resolution,[status(thm)],[180, 7])).
% 75.11/75.38 tff(182,plain,
% 75.11/75.38 (suc(double(rd(cons(i, shw(half(suc(zero))))))) = rd(cons(i, cons(i, shw(half(suc(zero))))))),
% 75.11/75.38 inference(symmetry,[status(thm)],[181])).
% 75.11/75.38 tff(183,plain,
% 75.11/75.38 (double(suc(double(rd(cons(i, shw(half(suc(zero)))))))) = double(rd(cons(i, cons(i, shw(half(suc(zero)))))))),
% 75.11/75.38 inference(monotonicity,[status(thm)],[182])).
% 75.11/75.38 tff(184,plain,
% 75.11/75.38 (^[X: $i] : refl((double(X) = addNat(X, X)) <=> (double(X) = addNat(X, X)))),
% 75.11/75.38 inference(bind,[status(th)],[])).
% 75.11/75.38 tff(185,plain,
% 75.11/75.38 (![X: $i] : (double(X) = addNat(X, X)) <=> ![X: $i] : (double(X) = addNat(X, X))),
% 75.11/75.38 inference(quant_intro,[status(thm)],[184])).
% 75.11/75.38 tff(186,plain,
% 75.11/75.38 (![X: $i] : (double(X) = addNat(X, X)) <=> ![X: $i] : (double(X) = addNat(X, X))),
% 75.11/75.38 inference(rewrite,[status(thm)],[])).
% 75.11/75.38 tff(187,axiom,(![X: $i] : (double(X) = addNat(X, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_019')).
% 75.11/75.38 tff(188,plain,
% 75.11/75.38 (![X: $i] : (double(X) = addNat(X, X))),
% 75.11/75.38 inference(modus_ponens,[status(thm)],[187, 186])).
% 75.11/75.38 tff(189,plain,(
% 75.11/75.38 ![X: $i] : (double(X) = addNat(X, X))),
% 75.11/75.38 inference(skolemize,[status(sab)],[188])).
% 75.11/75.38 tff(190,plain,
% 75.11/75.38 (![X: $i] : (double(X) = addNat(X, X))),
% 75.11/75.38 inference(modus_ponens,[status(thm)],[189, 185])).
% 75.11/75.38 tff(191,plain,
% 75.11/75.38 ((~![X: $i] : (double(X) = addNat(X, X))) | (double(suc(double(rd(cons(i, shw(half(suc(zero)))))))) = addNat(suc(double(rd(cons(i, shw(half(suc(zero))))))), suc(double(rd(cons(i, shw(half(suc(zero)))))))))),
% 75.11/75.38 inference(quant_inst,[status(thm)],[])).
% 75.11/75.38 tff(192,plain,
% 75.11/75.38 (double(suc(double(rd(cons(i, shw(half(suc(zero)))))))) = addNat(suc(double(rd(cons(i, shw(half(suc(zero))))))), suc(double(rd(cons(i, shw(half(suc(zero))))))))),
% 75.11/75.38 inference(unit_resolution,[status(thm)],[191, 190])).
% 75.11/75.38 tff(193,plain,
% 75.11/75.38 (addNat(suc(double(rd(cons(i, shw(half(suc(zero))))))), suc(double(rd(cons(i, shw(half(suc(zero)))))))) = double(suc(double(rd(cons(i, shw(half(suc(zero))))))))),
% 75.11/75.38 inference(symmetry,[status(thm)],[192])).
% 75.11/75.38 tff(194,plain,
% 75.11/75.38 (^[Y: $i, Z: $i] : refl((addNat(suc(Z), Y) = suc(addNat(Z, Y))) <=> (addNat(suc(Z), Y) = suc(addNat(Z, Y))))),
% 75.11/75.38 inference(bind,[status(th)],[])).
% 75.11/75.38 tff(195,plain,
% 75.11/75.38 (![Y: $i, Z: $i] : (addNat(suc(Z), Y) = suc(addNat(Z, Y))) <=> ![Y: $i, Z: $i] : (addNat(suc(Z), Y) = suc(addNat(Z, Y)))),
% 75.11/75.38 inference(quant_intro,[status(thm)],[194])).
% 75.11/75.38 tff(196,plain,
% 75.11/75.38 (![Y: $i, Z: $i] : (addNat(suc(Z), Y) = suc(addNat(Z, Y))) <=> ![Y: $i, Z: $i] : (addNat(suc(Z), Y) = suc(addNat(Z, Y)))),
% 75.11/75.38 inference(rewrite,[status(thm)],[])).
% 75.11/75.38 tff(197,axiom,(![Y: $i, Z: $i] : (addNat(suc(Z), Y) = suc(addNat(Z, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_018')).
% 75.11/75.38 tff(198,plain,
% 75.11/75.38 (![Y: $i, Z: $i] : (addNat(suc(Z), Y) = suc(addNat(Z, Y)))),
% 75.11/75.38 inference(modus_ponens,[status(thm)],[197, 196])).
% 75.11/75.38 tff(199,plain,(
% 75.11/75.38 ![Y: $i, Z: $i] : (addNat(suc(Z), Y) = suc(addNat(Z, Y)))),
% 75.11/75.38 inference(skolemize,[status(sab)],[198])).
% 75.11/75.38 tff(200,plain,
% 75.11/75.38 (![Y: $i, Z: $i] : (addNat(suc(Z), Y) = suc(addNat(Z, Y)))),
% 75.11/75.38 inference(modus_ponens,[status(thm)],[199, 195])).
% 75.11/75.38 tff(201,plain,
% 75.11/75.38 ((~![Y: $i, Z: $i] : (addNat(suc(Z), Y) = suc(addNat(Z, Y)))) | (addNat(suc(double(rd(cons(i, shw(half(suc(zero))))))), suc(double(rd(cons(i, shw(half(suc(zero)))))))) = suc(addNat(double(rd(cons(i, shw(half(suc(zero)))))), suc(double(rd(cons(i, shw(half(suc(zero))))))))))),
% 75.11/75.38 inference(quant_inst,[status(thm)],[])).
% 75.11/75.38 tff(202,plain,
% 75.11/75.38 (addNat(suc(double(rd(cons(i, shw(half(suc(zero))))))), suc(double(rd(cons(i, shw(half(suc(zero)))))))) = suc(addNat(double(rd(cons(i, shw(half(suc(zero)))))), suc(double(rd(cons(i, shw(half(suc(zero)))))))))),
% 75.11/75.38 inference(unit_resolution,[status(thm)],[201, 200])).
% 75.11/75.38 tff(203,plain,
% 75.11/75.38 (suc(addNat(double(rd(cons(i, shw(half(suc(zero)))))), suc(double(rd(cons(i, shw(half(suc(zero))))))))) = addNat(suc(double(rd(cons(i, shw(half(suc(zero))))))), suc(double(rd(cons(i, shw(half(suc(zero))))))))),
% 75.11/75.38 inference(symmetry,[status(thm)],[202])).
% 75.11/75.38 tff(204,plain,
% 75.11/75.38 (^[Y: $i] : refl((addNat(zero, Y) = Y) <=> (addNat(zero, Y) = Y))),
% 75.11/75.38 inference(bind,[status(th)],[])).
% 75.11/75.38 tff(205,plain,
% 75.11/75.38 (![Y: $i] : (addNat(zero, Y) = Y) <=> ![Y: $i] : (addNat(zero, Y) = Y)),
% 75.11/75.38 inference(quant_intro,[status(thm)],[204])).
% 75.11/75.38 tff(206,plain,
% 75.11/75.38 (![Y: $i] : (addNat(zero, Y) = Y) <=> ![Y: $i] : (addNat(zero, Y) = Y)),
% 75.11/75.38 inference(rewrite,[status(thm)],[])).
% 75.11/75.38 tff(207,axiom,(![Y: $i] : (addNat(zero, Y) = Y)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_017')).
% 75.11/75.38 tff(208,plain,
% 75.11/75.38 (![Y: $i] : (addNat(zero, Y) = Y)),
% 75.11/75.38 inference(modus_ponens,[status(thm)],[207, 206])).
% 75.11/75.38 tff(209,plain,(
% 75.11/75.38 ![Y: $i] : (addNat(zero, Y) = Y)),
% 75.11/75.38 inference(skolemize,[status(sab)],[208])).
% 75.11/75.38 tff(210,plain,
% 75.11/75.38 (![Y: $i] : (addNat(zero, Y) = Y)),
% 75.11/75.38 inference(modus_ponens,[status(thm)],[209, 205])).
% 75.11/75.38 tff(211,plain,
% 75.11/75.38 ((~![Y: $i] : (addNat(zero, Y) = Y)) | (addNat(zero, suc(half(zero))) = suc(half(zero)))),
% 75.11/75.38 inference(quant_inst,[status(thm)],[])).
% 75.11/75.38 tff(212,plain,
% 75.11/75.38 (addNat(zero, suc(half(zero))) = suc(half(zero))),
% 75.11/75.38 inference(unit_resolution,[status(thm)],[211, 210])).
% 75.11/75.38 tff(213,plain,
% 75.11/75.38 (addNat(zero, suc(half(zero))) = suc(zero)),
% 75.11/75.38 inference(transitivity,[status(thm)],[212, 67])).
% 75.11/75.38 tff(214,plain,
% 75.11/75.38 (suc(addNat(zero, suc(half(zero)))) = suc(suc(zero))),
% 75.11/75.38 inference(monotonicity,[status(thm)],[213])).
% 75.11/75.38 tff(215,plain,
% 75.11/75.38 ((~![Y: $i, Z: $i] : (addNat(suc(Z), Y) = suc(addNat(Z, Y)))) | (addNat(suc(zero), suc(half(zero))) = suc(addNat(zero, suc(half(zero)))))),
% 75.11/75.38 inference(quant_inst,[status(thm)],[])).
% 75.11/75.38 tff(216,plain,
% 75.11/75.38 (addNat(suc(zero), suc(half(zero))) = suc(addNat(zero, suc(half(zero))))),
% 75.11/75.38 inference(unit_resolution,[status(thm)],[215, 200])).
% 75.11/75.38 tff(217,plain,
% 75.11/75.38 ((~![Y: $i] : (addNat(zero, Y) = Y)) | (addNat(zero, zero) = zero)),
% 75.11/75.38 inference(quant_inst,[status(thm)],[])).
% 75.11/75.38 tff(218,plain,
% 75.11/75.38 (addNat(zero, zero) = zero),
% 75.11/75.38 inference(unit_resolution,[status(thm)],[217, 210])).
% 75.11/75.38 tff(219,plain,
% 75.11/75.38 ((~![X: $i] : (double(X) = addNat(X, X))) | (double(zero) = addNat(zero, zero))),
% 75.11/75.38 inference(quant_inst,[status(thm)],[])).
% 75.11/75.38 tff(220,plain,
% 75.11/75.38 (double(zero) = addNat(zero, zero)),
% 75.11/75.38 inference(unit_resolution,[status(thm)],[219, 190])).
% 75.11/75.38 tff(221,plain,
% 75.11/75.38 ((rd(nil) = zero) <=> (rd(nil) = zero)),
% 75.11/75.38 inference(rewrite,[status(thm)],[])).
% 75.11/75.38 tff(222,axiom,(rd(nil) = zero), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_020')).
% 75.11/75.38 tff(223,plain,
% 75.11/75.38 (rd(nil) = zero),
% 75.11/75.38 inference(modus_ponens,[status(thm)],[222, 221])).
% 75.11/75.38 tff(224,plain,
% 75.11/75.38 (double(rd(nil)) = double(zero)),
% 75.11/75.38 inference(monotonicity,[status(thm)],[223])).
% 75.11/75.38 tff(225,plain,
% 75.11/75.38 (double(rd(nil)) = zero),
% 75.11/75.38 inference(transitivity,[status(thm)],[224, 220, 218])).
% 75.11/75.38 tff(226,plain,
% 75.11/75.38 (suc(double(rd(nil))) = suc(zero)),
% 75.11/75.38 inference(monotonicity,[status(thm)],[225])).
% 75.11/75.38 tff(227,plain,
% 75.11/75.38 (suc(double(rd(nil))) = suc(half(zero))),
% 75.11/75.38 inference(transitivity,[status(thm)],[226, 66])).
% 75.11/75.38 tff(228,plain,
% 75.11/75.38 (addNat(suc(double(rd(nil))), suc(double(rd(nil)))) = addNat(suc(zero), suc(half(zero)))),
% 75.11/75.38 inference(monotonicity,[status(thm)],[226, 227])).
% 75.11/75.38 tff(229,plain,
% 75.11/75.38 ((~![X: $i] : (double(X) = addNat(X, X))) | (double(suc(double(rd(nil)))) = addNat(suc(double(rd(nil))), suc(double(rd(nil)))))),
% 75.11/75.38 inference(quant_inst,[status(thm)],[])).
% 75.11/75.38 tff(230,plain,
% 75.11/75.38 (double(suc(double(rd(nil)))) = addNat(suc(double(rd(nil))), suc(double(rd(nil))))),
% 75.11/75.38 inference(unit_resolution,[status(thm)],[229, 190])).
% 75.11/75.38 tff(231,plain,
% 75.11/75.38 ((~![Xs: $i] : (rd(cons(i, Xs)) = suc(double(rd(Xs))))) | (rd(cons(i, nil)) = suc(double(rd(nil))))),
% 75.11/75.38 inference(quant_inst,[status(thm)],[])).
% 75.11/75.38 tff(232,plain,
% 75.11/75.38 (rd(cons(i, nil)) = suc(double(rd(nil)))),
% 75.11/75.38 inference(unit_resolution,[status(thm)],[231, 7])).
% 75.11/75.38 tff(233,plain,
% 75.11/75.38 (rd(cons(i, shw(half(suc(zero))))) = rd(cons(i, nil))),
% 75.11/75.38 inference(monotonicity,[status(thm)],[120])).
% 75.11/75.38 tff(234,plain,
% 75.11/75.38 (rd(cons(i, shw(half(suc(zero))))) = suc(double(rd(nil)))),
% 75.11/75.38 inference(transitivity,[status(thm)],[233, 232])).
% 75.11/75.38 tff(235,plain,
% 75.11/75.38 (double(rd(cons(i, shw(half(suc(zero)))))) = double(suc(double(rd(nil))))),
% 75.11/75.38 inference(monotonicity,[status(thm)],[234])).
% 75.11/75.38 tff(236,plain,
% 75.11/75.38 (double(rd(cons(i, shw(half(suc(zero)))))) = suc(suc(half(zero)))),
% 75.11/75.38 inference(transitivity,[status(thm)],[235, 230, 228, 216, 214, 106])).
% 75.11/75.38 tff(237,plain,
% 75.11/75.38 (addNat(double(rd(cons(i, shw(half(suc(zero)))))), suc(double(rd(cons(i, shw(half(suc(zero)))))))) = addNat(suc(suc(half(zero))), suc(double(rd(cons(i, shw(half(suc(zero))))))))),
% 75.11/75.38 inference(monotonicity,[status(thm)],[236])).
% 75.11/75.38 tff(238,plain,
% 75.11/75.38 (addNat(suc(suc(half(zero))), suc(double(rd(cons(i, shw(half(suc(zero)))))))) = addNat(double(rd(cons(i, shw(half(suc(zero)))))), suc(double(rd(cons(i, shw(half(suc(zero))))))))),
% 75.11/75.38 inference(symmetry,[status(thm)],[237])).
% 75.11/75.38 tff(239,plain,
% 75.11/75.38 ((~![Y: $i, Z: $i] : (addNat(suc(Z), Y) = suc(addNat(Z, Y)))) | (addNat(suc(suc(half(zero))), suc(double(rd(cons(i, shw(half(suc(zero)))))))) = suc(addNat(suc(half(zero)), suc(double(rd(cons(i, shw(half(suc(zero))))))))))),
% 75.11/75.38 inference(quant_inst,[status(thm)],[])).
% 75.11/75.38 tff(240,plain,
% 75.11/75.38 (addNat(suc(suc(half(zero))), suc(double(rd(cons(i, shw(half(suc(zero)))))))) = suc(addNat(suc(half(zero)), suc(double(rd(cons(i, shw(half(suc(zero)))))))))),
% 75.11/75.38 inference(unit_resolution,[status(thm)],[239, 200])).
% 75.11/75.38 tff(241,plain,
% 75.11/75.38 (suc(addNat(suc(half(zero)), suc(double(rd(cons(i, shw(half(suc(zero))))))))) = addNat(suc(suc(half(zero))), suc(double(rd(cons(i, shw(half(suc(zero))))))))),
% 75.11/75.38 inference(symmetry,[status(thm)],[240])).
% 75.11/75.38 tff(242,plain,
% 75.11/75.38 (double(rd(cons(i, shw(half(suc(zero)))))) = suc(suc(zero))),
% 75.11/75.38 inference(transitivity,[status(thm)],[235, 230, 228, 216, 214])).
% 75.11/75.38 tff(243,plain,
% 75.11/75.38 (suc(double(rd(cons(i, shw(half(suc(zero))))))) = suc(suc(suc(zero)))),
% 75.11/75.38 inference(monotonicity,[status(thm)],[242])).
% 75.11/75.38 tff(244,plain,
% 75.11/75.38 (suc(suc(double(rd(cons(i, shw(half(suc(zero)))))))) = suc(suc(suc(suc(zero))))),
% 75.11/75.38 inference(monotonicity,[status(thm)],[243])).
% 75.11/75.38 tff(245,plain,
% 75.11/75.38 ((~![Y: $i] : (addNat(zero, Y) = Y)) | (addNat(zero, suc(double(rd(cons(i, shw(half(suc(zero)))))))) = suc(double(rd(cons(i, shw(half(suc(zero))))))))),
% 75.11/75.38 inference(quant_inst,[status(thm)],[])).
% 75.11/75.38 tff(246,plain,
% 75.11/75.38 (addNat(zero, suc(double(rd(cons(i, shw(half(suc(zero)))))))) = suc(double(rd(cons(i, shw(half(suc(zero)))))))),
% 75.11/75.38 inference(unit_resolution,[status(thm)],[245, 210])).
% 75.11/75.38 tff(247,plain,
% 75.11/75.38 (suc(addNat(zero, suc(double(rd(cons(i, shw(half(suc(zero))))))))) = suc(suc(double(rd(cons(i, shw(half(suc(zero))))))))),
% 75.11/75.38 inference(monotonicity,[status(thm)],[246])).
% 75.11/75.38 tff(248,plain,
% 75.11/75.38 ((~![Y: $i, Z: $i] : (addNat(suc(Z), Y) = suc(addNat(Z, Y)))) | (addNat(suc(zero), suc(double(rd(cons(i, shw(half(suc(zero)))))))) = suc(addNat(zero, suc(double(rd(cons(i, shw(half(suc(zero))))))))))),
% 75.11/75.38 inference(quant_inst,[status(thm)],[])).
% 75.11/75.38 tff(249,plain,
% 75.11/75.38 (addNat(suc(zero), suc(double(rd(cons(i, shw(half(suc(zero)))))))) = suc(addNat(zero, suc(double(rd(cons(i, shw(half(suc(zero)))))))))),
% 75.11/75.38 inference(unit_resolution,[status(thm)],[248, 200])).
% 75.11/75.38 tff(250,plain,
% 75.11/75.38 (addNat(suc(half(zero)), suc(double(rd(cons(i, shw(half(suc(zero)))))))) = addNat(suc(zero), suc(double(rd(cons(i, shw(half(suc(zero))))))))),
% 75.11/75.38 inference(monotonicity,[status(thm)],[67])).
% 75.11/75.38 tff(251,plain,
% 75.11/75.38 (addNat(suc(half(zero)), suc(double(rd(cons(i, shw(half(suc(zero)))))))) = suc(suc(suc(suc(zero))))),
% 75.11/75.38 inference(transitivity,[status(thm)],[250, 249, 247, 244])).
% 75.11/75.38 tff(252,plain,
% 75.11/75.38 (suc(addNat(suc(half(zero)), suc(double(rd(cons(i, shw(half(suc(zero))))))))) = suc(suc(suc(suc(suc(zero)))))),
% 75.11/75.38 inference(monotonicity,[status(thm)],[251])).
% 75.11/75.38 tff(253,plain,
% 75.11/75.38 (suc(suc(suc(suc(suc(zero))))) = suc(addNat(suc(half(zero)), suc(double(rd(cons(i, shw(half(suc(zero)))))))))),
% 75.11/75.38 inference(symmetry,[status(thm)],[252])).
% 75.11/75.38 tff(254,plain,
% 75.11/75.38 ((~![Xs: $i] : (rd(cons(o, Xs)) = double(rd(Xs)))) | (rd(cons(o, cons(i, shw(half(suc(zero)))))) = double(rd(cons(i, shw(half(suc(zero)))))))),
% 75.11/75.39 inference(quant_inst,[status(thm)],[])).
% 75.11/75.39 tff(255,plain,
% 75.11/75.39 (rd(cons(o, cons(i, shw(half(suc(zero)))))) = double(rd(cons(i, shw(half(suc(zero))))))),
% 75.11/75.39 inference(unit_resolution,[status(thm)],[254, 176])).
% 75.11/75.39 tff(256,plain,
% 75.11/75.39 (double(rd(cons(o, cons(i, shw(half(suc(zero))))))) = double(double(rd(cons(i, shw(half(suc(zero)))))))),
% 75.11/75.39 inference(monotonicity,[status(thm)],[255])).
% 75.11/75.39 tff(257,plain,
% 75.11/75.39 (double(double(rd(cons(i, shw(half(suc(zero))))))) = double(rd(cons(o, cons(i, shw(half(suc(zero)))))))),
% 75.11/75.39 inference(symmetry,[status(thm)],[256])).
% 75.11/75.39 tff(258,plain,
% 75.11/75.39 ((~![X: $i] : (double(X) = addNat(X, X))) | (double(double(rd(cons(i, shw(half(suc(zero))))))) = addNat(double(rd(cons(i, shw(half(suc(zero)))))), double(rd(cons(i, shw(half(suc(zero))))))))),
% 75.11/75.39 inference(quant_inst,[status(thm)],[])).
% 75.11/75.39 tff(259,plain,
% 75.11/75.39 (double(double(rd(cons(i, shw(half(suc(zero))))))) = addNat(double(rd(cons(i, shw(half(suc(zero)))))), double(rd(cons(i, shw(half(suc(zero)))))))),
% 75.11/75.39 inference(unit_resolution,[status(thm)],[258, 190])).
% 75.11/75.39 tff(260,plain,
% 75.11/75.39 (addNat(double(rd(cons(i, shw(half(suc(zero)))))), double(rd(cons(i, shw(half(suc(zero))))))) = double(double(rd(cons(i, shw(half(suc(zero)))))))),
% 75.11/75.39 inference(symmetry,[status(thm)],[259])).
% 75.11/75.39 tff(261,plain,
% 75.11/75.39 (double(rd(cons(i, shw(half(suc(zero)))))) = suc(addNat(zero, suc(half(zero))))),
% 75.11/75.39 inference(transitivity,[status(thm)],[235, 230, 228, 216])).
% 75.11/75.39 tff(262,plain,
% 75.11/75.39 (addNat(double(rd(cons(i, shw(half(suc(zero)))))), double(rd(cons(i, shw(half(suc(zero))))))) = addNat(suc(addNat(zero, suc(half(zero)))), double(rd(cons(i, shw(half(suc(zero)))))))),
% 75.11/75.39 inference(monotonicity,[status(thm)],[261])).
% 75.11/75.39 tff(263,plain,
% 75.11/75.39 (addNat(suc(addNat(zero, suc(half(zero)))), double(rd(cons(i, shw(half(suc(zero))))))) = addNat(double(rd(cons(i, shw(half(suc(zero)))))), double(rd(cons(i, shw(half(suc(zero)))))))),
% 75.11/75.39 inference(symmetry,[status(thm)],[262])).
% 75.11/75.39 tff(264,plain,
% 75.11/75.39 ((~![Y: $i, Z: $i] : (addNat(suc(Z), Y) = suc(addNat(Z, Y)))) | (addNat(suc(addNat(zero, suc(half(zero)))), double(rd(cons(i, shw(half(suc(zero))))))) = suc(addNat(addNat(zero, suc(half(zero))), double(rd(cons(i, shw(half(suc(zero)))))))))),
% 75.11/75.39 inference(quant_inst,[status(thm)],[])).
% 75.11/75.39 tff(265,plain,
% 75.11/75.39 (addNat(suc(addNat(zero, suc(half(zero)))), double(rd(cons(i, shw(half(suc(zero))))))) = suc(addNat(addNat(zero, suc(half(zero))), double(rd(cons(i, shw(half(suc(zero))))))))),
% 75.11/75.39 inference(unit_resolution,[status(thm)],[264, 200])).
% 75.11/75.39 tff(266,plain,
% 75.11/75.39 (suc(addNat(addNat(zero, suc(half(zero))), double(rd(cons(i, shw(half(suc(zero)))))))) = addNat(suc(addNat(zero, suc(half(zero)))), double(rd(cons(i, shw(half(suc(zero)))))))),
% 75.11/75.39 inference(symmetry,[status(thm)],[265])).
% 75.11/75.39 tff(267,plain,
% 75.11/75.39 (suc(suc(suc(zero))) = suc(double(rd(cons(i, shw(half(suc(zero)))))))),
% 75.11/75.39 inference(symmetry,[status(thm)],[243])).
% 75.11/75.39 tff(268,plain,
% 75.11/75.39 ((~![Y: $i] : (addNat(zero, Y) = Y)) | (addNat(zero, suc(suc(zero))) = suc(suc(zero)))),
% 75.11/75.39 inference(quant_inst,[status(thm)],[])).
% 75.11/75.39 tff(269,plain,
% 75.11/75.39 (addNat(zero, suc(suc(zero))) = suc(suc(zero))),
% 75.11/75.39 inference(unit_resolution,[status(thm)],[268, 210])).
% 75.11/75.39 tff(270,plain,
% 75.11/75.39 (suc(addNat(zero, suc(suc(zero)))) = suc(suc(suc(zero)))),
% 75.11/75.39 inference(monotonicity,[status(thm)],[269])).
% 75.11/75.39 tff(271,plain,
% 75.11/75.39 ((~![Y: $i, Z: $i] : (addNat(suc(Z), Y) = suc(addNat(Z, Y)))) | (addNat(suc(zero), suc(suc(zero))) = suc(addNat(zero, suc(suc(zero)))))),
% 75.11/75.39 inference(quant_inst,[status(thm)],[])).
% 75.11/75.39 tff(272,plain,
% 75.11/75.39 (addNat(suc(zero), suc(suc(zero))) = suc(addNat(zero, suc(suc(zero))))),
% 75.11/75.39 inference(unit_resolution,[status(thm)],[271, 200])).
% 75.11/75.39 tff(273,plain,
% 75.11/75.39 (addNat(addNat(zero, suc(half(zero))), double(rd(cons(i, shw(half(suc(zero))))))) = addNat(suc(zero), suc(suc(zero)))),
% 75.11/75.39 inference(monotonicity,[status(thm)],[213, 242])).
% 75.11/75.39 tff(274,plain,
% 75.11/75.39 (addNat(addNat(zero, suc(half(zero))), double(rd(cons(i, shw(half(suc(zero))))))) = suc(double(rd(cons(i, shw(half(suc(zero)))))))),
% 75.11/75.39 inference(transitivity,[status(thm)],[273, 272, 270, 267])).
% 75.11/75.39 tff(275,plain,
% 75.11/75.39 (suc(addNat(addNat(zero, suc(half(zero))), double(rd(cons(i, shw(half(suc(zero)))))))) = suc(suc(double(rd(cons(i, shw(half(suc(zero))))))))),
% 75.11/75.39 inference(monotonicity,[status(thm)],[274])).
% 75.11/75.39 tff(276,plain,
% 75.11/75.39 (suc(suc(double(rd(cons(i, shw(half(suc(zero)))))))) = suc(addNat(addNat(zero, suc(half(zero))), double(rd(cons(i, shw(half(suc(zero))))))))),
% 75.11/75.39 inference(symmetry,[status(thm)],[275])).
% 75.11/75.39 tff(277,plain,
% 75.11/75.39 (suc(suc(suc(suc(zero)))) = suc(suc(double(rd(cons(i, shw(half(suc(zero))))))))),
% 75.11/75.39 inference(symmetry,[status(thm)],[244])).
% 75.11/75.39 tff(278,plain,
% 75.11/75.39 (suc(suc(suc(suc(zero)))) = double(rd(cons(o, cons(i, shw(half(suc(zero)))))))),
% 75.11/75.39 inference(transitivity,[status(thm)],[277, 276, 266, 263, 260, 257])).
% 75.11/75.39 tff(279,plain,
% 75.11/75.39 (suc(suc(suc(suc(suc(zero))))) = suc(double(rd(cons(o, cons(i, shw(half(suc(zero))))))))),
% 75.11/75.39 inference(monotonicity,[status(thm)],[278])).
% 75.11/75.39 tff(280,plain,
% 75.11/75.39 (suc(double(rd(cons(o, cons(i, shw(half(suc(zero)))))))) = suc(suc(suc(suc(suc(zero)))))),
% 75.11/75.39 inference(symmetry,[status(thm)],[279])).
% 75.11/75.39 tff(281,plain,
% 75.11/75.39 (suc(double(rd(cons(o, cons(i, shw(half(suc(zero)))))))) = addNat(double(rd(cons(i, shw(half(suc(zero)))))), suc(double(rd(cons(i, shw(half(suc(zero))))))))),
% 75.11/75.39 inference(transitivity,[status(thm)],[280, 253, 241, 238])).
% 75.11/75.39 tff(282,plain,
% 75.11/75.39 (suc(suc(double(rd(cons(o, cons(i, shw(half(suc(zero))))))))) = suc(addNat(double(rd(cons(i, shw(half(suc(zero)))))), suc(double(rd(cons(i, shw(half(suc(zero)))))))))),
% 75.11/75.39 inference(monotonicity,[status(thm)],[281])).
% 75.11/75.39 tff(283,plain,
% 75.11/75.39 (suc(suc(suc(suc(suc(suc(zero)))))) = suc(suc(double(rd(cons(o, cons(i, shw(half(suc(zero)))))))))),
% 75.11/75.39 inference(monotonicity,[status(thm)],[279])).
% 75.11/75.39 tff(284,plain,
% 75.11/75.39 (suc(suc(suc(suc(suc(suc(zero)))))) = suc(double(rd(cons(o, cons(i, shw(half(suc(zero))))))))),
% 75.11/75.39 inference(transitivity,[status(thm)],[283, 282, 203, 193, 183, 179, 169, 152, 149, 136, 125, 9])).
% 75.11/75.39 tff(285,plain,
% 75.11/75.39 (evenNat(suc(suc(suc(suc(suc(suc(zero))))))) <=> evenNat(suc(double(rd(cons(o, cons(i, shw(half(suc(zero)))))))))),
% 75.11/75.39 inference(monotonicity,[status(thm)],[284])).
% 75.11/75.39 tff(286,plain,
% 75.11/75.39 (evenNat(suc(double(rd(cons(o, cons(i, shw(half(suc(zero))))))))) <=> evenNat(suc(suc(suc(suc(suc(suc(zero)))))))),
% 75.11/75.39 inference(symmetry,[status(thm)],[285])).
% 75.11/75.39 tff(287,plain,
% 75.11/75.39 ((~evenNat(suc(double(rd(cons(o, cons(i, shw(half(suc(zero)))))))))) <=> (~evenNat(suc(suc(suc(suc(suc(suc(zero))))))))),
% 75.11/75.39 inference(monotonicity,[status(thm)],[286])).
% 75.11/75.39 tff(288,plain,
% 75.11/75.39 (evenNat(suc(double(rd(cons(o, cons(i, shw(half(suc(zero))))))))) <=> evenNat(suc(suc(suc(suc(suc(zero))))))),
% 75.11/75.39 inference(monotonicity,[status(thm)],[280])).
% 75.11/75.39 tff(289,plain,
% 75.11/75.39 (evenNat(suc(suc(suc(suc(suc(zero)))))) <=> evenNat(suc(double(rd(cons(o, cons(i, shw(half(suc(zero)))))))))),
% 75.11/75.39 inference(symmetry,[status(thm)],[288])).
% 75.11/75.39 tff(290,plain,
% 75.11/75.39 ((~evenNat(suc(suc(suc(suc(suc(zero))))))) <=> (~evenNat(suc(double(rd(cons(o, cons(i, shw(half(suc(zero))))))))))),
% 75.11/75.39 inference(monotonicity,[status(thm)],[289])).
% 75.11/75.39 tff(291,plain,
% 75.11/75.39 ((~![N: $i] : (~(evenNat(N) <=> evenNat(suc(N))))) | (~(evenNat(suc(suc(suc(suc(zero))))) <=> evenNat(suc(suc(suc(suc(suc(zero))))))))),
% 75.11/75.39 inference(quant_inst,[status(thm)],[])).
% 75.11/75.39 tff(292,plain,
% 75.11/75.39 (~(evenNat(suc(suc(suc(suc(zero))))) <=> evenNat(suc(suc(suc(suc(suc(zero)))))))),
% 75.11/75.39 inference(unit_resolution,[status(thm)],[291, 38])).
% 75.11/75.39 tff(293,plain,
% 75.11/75.39 ((~![N: $i] : (~(evenNat(N) <=> evenNat(suc(N))))) | (~(evenNat(suc(suc(suc(zero)))) <=> evenNat(suc(suc(suc(suc(zero)))))))),
% 75.11/75.39 inference(quant_inst,[status(thm)],[])).
% 75.11/75.39 tff(294,plain,
% 75.11/75.39 (~(evenNat(suc(suc(suc(zero)))) <=> evenNat(suc(suc(suc(suc(zero))))))),
% 75.11/75.39 inference(unit_resolution,[status(thm)],[293, 38])).
% 75.11/75.39 tff(295,plain,
% 75.11/75.39 ((~![N: $i] : (~(evenNat(N) <=> evenNat(suc(N))))) | (~(evenNat(suc(suc(zero))) <=> evenNat(suc(suc(suc(zero))))))),
% 75.11/75.39 inference(quant_inst,[status(thm)],[])).
% 75.11/75.39 tff(296,plain,
% 75.11/75.39 (~(evenNat(suc(suc(zero))) <=> evenNat(suc(suc(suc(zero)))))),
% 75.11/75.39 inference(unit_resolution,[status(thm)],[295, 38])).
% 75.31/75.55 tff(297,plain,
% 75.31/75.55 (evenNat(suc(suc(half(zero)))) <=> evenNat(suc(suc(zero)))),
% 75.31/75.55 inference(monotonicity,[status(thm)],[77])).
% 75.31/75.55 tff(298,plain,
% 75.31/75.55 (evenNat(suc(suc(zero)))),
% 75.31/75.55 inference(modus_ponens,[status(thm)],[90, 297])).
% 75.31/75.55 tff(299,plain,
% 75.31/75.55 ((evenNat(suc(suc(zero))) <=> evenNat(suc(suc(suc(zero))))) | (~evenNat(suc(suc(zero)))) | (~evenNat(suc(suc(suc(zero)))))),
% 75.31/75.55 inference(tautology,[status(thm)],[])).
% 75.31/75.55 tff(300,plain,
% 75.31/75.55 (~evenNat(suc(suc(suc(zero))))),
% 75.31/75.55 inference(unit_resolution,[status(thm)],[299, 298, 296])).
% 75.31/75.55 tff(301,plain,
% 75.31/75.55 ((evenNat(suc(suc(suc(zero)))) <=> evenNat(suc(suc(suc(suc(zero)))))) | evenNat(suc(suc(suc(zero)))) | evenNat(suc(suc(suc(suc(zero)))))),
% 75.31/75.55 inference(tautology,[status(thm)],[])).
% 75.31/75.55 tff(302,plain,
% 75.31/75.55 (evenNat(suc(suc(suc(suc(zero)))))),
% 75.31/75.55 inference(unit_resolution,[status(thm)],[301, 300, 294])).
% 75.31/75.55 tff(303,plain,
% 75.31/75.55 ((evenNat(suc(suc(suc(suc(zero))))) <=> evenNat(suc(suc(suc(suc(suc(zero))))))) | (~evenNat(suc(suc(suc(suc(zero)))))) | (~evenNat(suc(suc(suc(suc(suc(zero)))))))),
% 75.31/75.55 inference(tautology,[status(thm)],[])).
% 75.31/75.55 tff(304,plain,
% 75.31/75.55 (~evenNat(suc(suc(suc(suc(suc(zero))))))),
% 75.31/75.55 inference(unit_resolution,[status(thm)],[303, 302, 292])).
% 75.31/75.55 tff(305,plain,
% 75.31/75.55 (~evenNat(suc(double(rd(cons(o, cons(i, shw(half(suc(zero)))))))))),
% 75.31/75.55 inference(modus_ponens,[status(thm)],[304, 290])).
% 75.31/75.55 tff(306,plain,
% 75.31/75.55 (~evenNat(suc(suc(suc(suc(suc(suc(zero)))))))),
% 75.31/75.55 inference(modus_ponens,[status(thm)],[305, 287])).
% 75.31/75.55 tff(307,plain,
% 75.31/75.55 ((~![N: $i] : (~(evenNat(N) <=> evenNat(suc(N))))) | (~(evenNat(suc(suc(suc(suc(suc(zero)))))) <=> evenNat(suc(suc(suc(suc(suc(suc(zero)))))))))),
% 75.31/75.55 inference(quant_inst,[status(thm)],[])).
% 75.31/75.55 tff(308,plain,
% 75.31/75.55 (~(evenNat(suc(suc(suc(suc(suc(zero)))))) <=> evenNat(suc(suc(suc(suc(suc(suc(zero))))))))),
% 75.31/75.55 inference(unit_resolution,[status(thm)],[307, 38])).
% 75.31/75.55 tff(309,plain,
% 75.31/75.55 ((evenNat(suc(suc(suc(suc(suc(zero)))))) <=> evenNat(suc(suc(suc(suc(suc(suc(zero)))))))) | evenNat(suc(suc(suc(suc(suc(zero)))))) | evenNat(suc(suc(suc(suc(suc(suc(zero)))))))),
% 75.31/75.55 inference(tautology,[status(thm)],[])).
% 75.31/75.55 tff(310,plain,
% 75.31/75.55 (evenNat(suc(suc(suc(suc(suc(suc(zero)))))))),
% 75.31/75.55 inference(unit_resolution,[status(thm)],[309, 304, 308])).
% 75.31/75.55 tff(311,plain,
% 75.31/75.55 ($false),
% 75.31/75.55 inference(unit_resolution,[status(thm)],[310, 306])).
% 75.31/75.55 % SZS output end Proof
% 75.31/75.55 % E exiting
%------------------------------------------------------------------------------