%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWX069+1 : TPTP v9.1.0. Released v9.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:37:51 AM UTC 2025
% Result : Theorem 0.57s 0.72s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.15 % Problem : SWX069+1 : TPTP v9.1.0. Released v9.1.0.
% 0.08/0.15 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n016.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 12:24:32 EDT 2025
% 0.14/0.37 % CPUTime :
% 0.57/0.72 % SZS status Theorem
% 0.57/0.72 % SZS output start Proof
% 0.57/0.72 tff(neg_type, type, (
% 0.57/0.72 neg: $i > $i)).
% 0.57/0.72 tff(tptp_fun_Xx16_33_type, type, (
% 0.57/0.72 tptp_fun_Xx16_33: ( $i * $i * $i ) > $i)).
% 0.57/0.72 tff(tptp_fun_Xa_174_type, type, (
% 0.57/0.72 tptp_fun_Xa_174: $i)).
% 0.57/0.72 tff(tptp_fun_Xi_173_type, type, (
% 0.57/0.72 tptp_fun_Xi_173: $i)).
% 0.57/0.72 tff(tptp_fun_Xy_175_type, type, (
% 0.57/0.72 tptp_fun_Xy_175: $i)).
% 0.57/0.72 tff(p_type, type, (
% 0.57/0.72 p: $i > $i)).
% 0.57/0.72 tff(tptp_fun_Xx19_177_type, type, (
% 0.57/0.72 tptp_fun_Xx19_177: $i)).
% 0.57/0.72 tff(eval_succeeds_type, type, (
% 0.57/0.72 eval_succeeds: ( $i * $i * $i ) > $o)).
% 0.57/0.72 tff(tptp_fun__1__type, type, (
% 0.57/0.72 tptp_fun__1_: $i)).
% 0.57/0.72 tff(tptp_fun__0__type, type, (
% 0.57/0.72 tptp_fun__0_: $i)).
% 0.57/0.72 tff(and_type, type, (
% 0.57/0.72 and: ( $i * $i ) > $i)).
% 0.57/0.72 tff(tptp_fun_Xx13_29_type, type, (
% 0.57/0.72 tptp_fun_Xx13_29: ( $i * $i * $i ) > $i)).
% 0.57/0.72 tff(tptp_fun_Xx12_30_type, type, (
% 0.57/0.72 tptp_fun_Xx12_30: ( $i * $i * $i ) > $i)).
% 0.57/0.72 tff(tptp_fun_Xx15_188_type, type, (
% 0.57/0.72 tptp_fun_Xx15_188: $i)).
% 0.57/0.72 tff(interpretation_succeeds_type, type, (
% 0.57/0.72 interpretation_succeeds: $i > $o)).
% 0.57/0.72 tff(tptp_fun_Xx14_189_type, type, (
% 0.57/0.72 tptp_fun_Xx14_189: $i)).
% 0.57/0.72 tff(tptp_fun_Xx_172_type, type, (
% 0.57/0.72 tptp_fun_Xx_172: $i)).
% 0.57/0.72 tff(or_type, type, (
% 0.57/0.72 or: ( $i * $i ) > $i)).
% 0.57/0.72 tff(tptp_fun_Xx5_21_type, type, (
% 0.57/0.72 tptp_fun_Xx5_21: ( $i * $i * $i ) > $i)).
% 0.57/0.72 tff(tptp_fun_Xx4_22_type, type, (
% 0.57/0.72 tptp_fun_Xx4_22: ( $i * $i * $i ) > $i)).
% 0.57/0.72 tff(tptp_fun_Xx5_182_type, type, (
% 0.57/0.72 tptp_fun_Xx5_182: $i)).
% 0.57/0.72 tff(tptp_fun_Xx4_183_type, type, (
% 0.57/0.72 tptp_fun_Xx4_183: $i)).
% 0.57/0.72 tff(tptp_fun_Xx17_191_type, type, (
% 0.57/0.72 tptp_fun_Xx17_191: $i)).
% 0.57/0.72 tff(tptp_fun_Xx16_190_type, type, (
% 0.57/0.72 tptp_fun_Xx16_190: $i)).
% 0.57/0.72 tff(tptp_fun_Xx12_187_type, type, (
% 0.57/0.72 tptp_fun_Xx12_187: $i)).
% 0.57/0.72 tff(tptp_fun_Xx13_186_type, type, (
% 0.57/0.72 tptp_fun_Xx13_186: $i)).
% 0.57/0.72 tff(tptp_fun_Xx7_184_type, type, (
% 0.57/0.72 tptp_fun_Xx7_184: $i)).
% 0.57/0.72 tff(tptp_fun_Xx6_185_type, type, (
% 0.57/0.72 tptp_fun_Xx6_185: $i)).
% 0.57/0.72 tff(tptp_fun_Xx11_180_type, type, (
% 0.57/0.72 tptp_fun_Xx11_180: $i)).
% 0.57/0.72 tff(tptp_fun_Xx10_181_type, type, (
% 0.57/0.72 tptp_fun_Xx10_181: $i)).
% 0.57/0.72 tff(tptp_fun_Xx8_179_type, type, (
% 0.57/0.72 tptp_fun_Xx8_179: $i)).
% 0.57/0.72 tff(tptp_fun_Xx9_178_type, type, (
% 0.57/0.72 tptp_fun_Xx9_178: $i)).
% 0.57/0.72 tff(member_succeeds_type, type, (
% 0.57/0.72 member_succeeds: ( $i * $i ) > $o)).
% 0.57/0.72 tff(tptp_fun_Xx18_176_type, type, (
% 0.57/0.72 tptp_fun_Xx18_176: $i)).
% 0.57/0.72 tff(tptp_fun_Xx_192_type, type, (
% 0.57/0.72 tptp_fun_Xx_192: $i)).
% 0.57/0.72 tff(tptp_fun_Xi_193_type, type, (
% 0.57/0.72 tptp_fun_Xi_193: $i)).
% 0.57/0.72 tff(tptp_fun_Xa_194_type, type, (
% 0.57/0.72 tptp_fun_Xa_194: $i)).
% 0.57/0.72 tff(tptp_fun_Xy_195_type, type, (
% 0.57/0.72 tptp_fun_Xy_195: $i)).
% 0.57/0.72 tff(tptp_fun_Xx11_23_type, type, (
% 0.57/0.72 tptp_fun_Xx11_23: ( $i * $i * $i ) > $i)).
% 0.57/0.72 tff(tptp_fun_Xx10_24_type, type, (
% 0.57/0.72 tptp_fun_Xx10_24: ( $i * $i * $i ) > $i)).
% 0.57/0.72 tff(tptp_fun_Xx19_36_type, type, (
% 0.57/0.72 tptp_fun_Xx19_36: ( $i * $i * $i ) > $i)).
% 0.57/0.72 tff(tptp_fun_Xx17_34_type, type, (
% 0.57/0.72 tptp_fun_Xx17_34: ( $i * $i * $i ) > $i)).
% 0.57/0.72 tff(tptp_fun_Xx7_25_type, type, (
% 0.57/0.72 tptp_fun_Xx7_25: ( $i * $i * $i ) > $i)).
% 0.57/0.72 tff(tptp_fun_Xx6_26_type, type, (
% 0.57/0.72 tptp_fun_Xx6_26: ( $i * $i * $i ) > $i)).
% 0.57/0.72 tff(tptp_fun_Xx9_27_type, type, (
% 0.57/0.72 tptp_fun_Xx9_27: ( $i * $i * $i ) > $i)).
% 0.57/0.72 tff(tptp_fun_Xx8_28_type, type, (
% 0.57/0.72 tptp_fun_Xx8_28: ( $i * $i * $i ) > $i)).
% 0.57/0.73 tff(tptp_fun_Xx15_31_type, type, (
% 0.57/0.73 tptp_fun_Xx15_31: ( $i * $i * $i ) > $i)).
% 0.57/0.73 tff(tptp_fun_Xx14_32_type, type, (
% 0.57/0.73 tptp_fun_Xx14_32: ( $i * $i * $i ) > $i)).
% 0.57/0.73 tff(tptp_fun_Xx18_35_type, type, (
% 0.57/0.73 tptp_fun_Xx18_35: ( $i * $i * $i ) > $i)).
% 0.57/0.73 tff(incon_succeeds_type, type, (
% 0.57/0.73 incon_succeeds: $i > $o)).
% 0.57/0.73 tff(tptp_fun_Xx2_126_type, type, (
% 0.57/0.73 tptp_fun_Xx2_126: $i > $i)).
% 0.57/0.73 tff(incon_fails_type, type, (
% 0.57/0.73 incon_fails: $i > $o)).
% 0.57/0.73 tff(literal_list_succeeds_type, type, (
% 0.57/0.73 literal_list_succeeds: $i > $o)).
% 0.57/0.73 tff(inj_197_type, type, (
% 0.57/0.73 inj_197: $i > $i)).
% 0.57/0.73 tff(1,assumption,(~((~(Xx!172 = |'1'|)) | (~(Xa!174 = and(Xx14!189, Xx15!188))) | (~eval_succeeds(Xx14!189, Xi!173, |'1'|)) | (~eval_succeeds(Xx15!188, Xi!173, |'1'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx14!189, Xi!173, Xy)) | (|'1'| = Xy)))) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx15!188, Xi!173, Xy)) | (|'1'| = Xy)))))), introduced(assumption)).
% 0.57/0.73 tff(2,plain,
% 0.57/0.73 (((~(Xx!172 = |'1'|)) | (~(Xa!174 = and(Xx14!189, Xx15!188))) | (~eval_succeeds(Xx14!189, Xi!173, |'1'|)) | (~eval_succeeds(Xx15!188, Xi!173, |'1'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx14!189, Xi!173, Xy)) | (|'1'| = Xy)))) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx15!188, Xi!173, Xy)) | (|'1'| = Xy))))) | ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx14!189, Xi!173, Xy)) | (|'1'| = Xy)))),
% 0.57/0.73 inference(tautology,[status(thm)],[])).
% 0.57/0.73 tff(3,plain,
% 0.57/0.73 ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx14!189, Xi!173, Xy)) | (|'1'| = Xy))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.57/0.73 tff(4,assumption,(~((~(Xy!175 = |'0'|)) | (~eval_succeeds(tptp_fun_Xx12_30(Xy!175, Xi!173, Xa!174), Xi!173, |'0'|)) | (~(Xa!174 = and(tptp_fun_Xx12_30(Xy!175, Xi!173, Xa!174), tptp_fun_Xx13_29(Xy!175, Xi!173, Xa!174)))))), introduced(assumption)).
% 0.57/0.73 tff(5,plain,
% 0.57/0.73 (((~(Xx!172 = |'1'|)) | (~(Xa!174 = and(Xx14!189, Xx15!188))) | (~eval_succeeds(Xx14!189, Xi!173, |'1'|)) | (~eval_succeeds(Xx15!188, Xi!173, |'1'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx14!189, Xi!173, Xy)) | (|'1'| = Xy)))) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx15!188, Xi!173, Xy)) | (|'1'| = Xy))))) | (Xa!174 = and(Xx14!189, Xx15!188))),
% 0.57/0.73 inference(tautology,[status(thm)],[])).
% 0.57/0.73 tff(6,plain,
% 0.57/0.73 (Xa!174 = and(Xx14!189, Xx15!188)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[5, 1])).
% 0.57/0.73 tff(7,plain,
% 0.57/0.73 (((~(Xy!175 = |'0'|)) | (~eval_succeeds(tptp_fun_Xx12_30(Xy!175, Xi!173, Xa!174), Xi!173, |'0'|)) | (~(Xa!174 = and(tptp_fun_Xx12_30(Xy!175, Xi!173, Xa!174), tptp_fun_Xx13_29(Xy!175, Xi!173, Xa!174))))) | (Xa!174 = and(tptp_fun_Xx12_30(Xy!175, Xi!173, Xa!174), tptp_fun_Xx13_29(Xy!175, Xi!173, Xa!174)))),
% 0.57/0.73 inference(tautology,[status(thm)],[])).
% 0.57/0.73 tff(8,plain,
% 0.57/0.73 (Xa!174 = and(tptp_fun_Xx12_30(Xy!175, Xi!173, Xa!174), tptp_fun_Xx13_29(Xy!175, Xi!173, Xa!174))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[7, 4])).
% 0.57/0.73 tff(9,assumption,(Xa!174 = and(Xx14!189, Xx15!188)), introduced(assumption)).
% 0.57/0.73 tff(10,plain,
% 0.57/0.73 (and(Xx14!189, Xx15!188) = Xa!174),
% 0.57/0.73 inference(symmetry,[status(thm)],[9])).
% 0.57/0.73 tff(11,plain,
% 0.57/0.73 (and(Xx14!189, Xx15!188) = and(tptp_fun_Xx12_30(Xy!175, Xi!173, Xa!174), tptp_fun_Xx13_29(Xy!175, Xi!173, Xa!174))),
% 0.57/0.73 inference(transitivity,[status(thm)],[10, 8])).
% 0.57/0.73 tff(12,plain,
% 0.57/0.73 (^[Xx72: $i, Xx73: $i, Xx74: $i, Xx75: $i] : refl(((~(and(Xx72, Xx73) = and(Xx74, Xx75))) | (Xx72 = Xx74)) <=> ((~(and(Xx72, Xx73) = and(Xx74, Xx75))) | (Xx72 = Xx74)))),
% 0.57/0.73 inference(bind,[status(th)],[])).
% 0.57/0.73 tff(13,plain,
% 0.57/0.73 (![Xx72: $i, Xx73: $i, Xx74: $i, Xx75: $i] : ((~(and(Xx72, Xx73) = and(Xx74, Xx75))) | (Xx72 = Xx74)) <=> ![Xx72: $i, Xx73: $i, Xx74: $i, Xx75: $i] : ((~(and(Xx72, Xx73) = and(Xx74, Xx75))) | (Xx72 = Xx74))),
% 0.57/0.73 inference(quant_intro,[status(thm)],[12])).
% 0.57/0.73 tff(14,plain,
% 0.57/0.73 (![Xx72: $i, Xx73: $i, Xx74: $i, Xx75: $i] : ((~(and(Xx72, Xx73) = and(Xx74, Xx75))) | (Xx72 = Xx74)) <=> ![Xx72: $i, Xx73: $i, Xx74: $i, Xx75: $i] : ((~(and(Xx72, Xx73) = and(Xx74, Xx75))) | (Xx72 = Xx74))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(15,plain,
% 0.57/0.73 (^[Xx72: $i, Xx73: $i, Xx74: $i, Xx75: $i] : rewrite(((and(Xx72, Xx73) = and(Xx74, Xx75)) => (Xx72 = Xx74)) <=> ((~(and(Xx72, Xx73) = and(Xx74, Xx75))) | (Xx72 = Xx74)))),
% 0.57/0.73 inference(bind,[status(th)],[])).
% 0.57/0.73 tff(16,plain,
% 0.57/0.73 (![Xx72: $i, Xx73: $i, Xx74: $i, Xx75: $i] : ((and(Xx72, Xx73) = and(Xx74, Xx75)) => (Xx72 = Xx74)) <=> ![Xx72: $i, Xx73: $i, Xx74: $i, Xx75: $i] : ((~(and(Xx72, Xx73) = and(Xx74, Xx75))) | (Xx72 = Xx74))),
% 0.57/0.73 inference(quant_intro,[status(thm)],[15])).
% 0.57/0.73 tff(17,axiom,(![Xx72: $i, Xx73: $i, Xx74: $i, Xx75: $i] : ((and(Xx72, Xx73) = and(Xx74, Xx75)) => (Xx72 = Xx74))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','id33')).
% 0.57/0.73 tff(18,plain,
% 0.57/0.73 (![Xx72: $i, Xx73: $i, Xx74: $i, Xx75: $i] : ((~(and(Xx72, Xx73) = and(Xx74, Xx75))) | (Xx72 = Xx74))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.57/0.73 tff(19,plain,
% 0.57/0.73 (![Xx72: $i, Xx73: $i, Xx74: $i, Xx75: $i] : ((~(and(Xx72, Xx73) = and(Xx74, Xx75))) | (Xx72 = Xx74))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.57/0.73 tff(20,plain,(
% 0.57/0.73 ![Xx72: $i, Xx73: $i, Xx74: $i, Xx75: $i] : ((~(and(Xx72, Xx73) = and(Xx74, Xx75))) | (Xx72 = Xx74))),
% 0.57/0.73 inference(skolemize,[status(sab)],[19])).
% 0.57/0.73 tff(21,plain,
% 0.57/0.73 (![Xx72: $i, Xx73: $i, Xx74: $i, Xx75: $i] : ((~(and(Xx72, Xx73) = and(Xx74, Xx75))) | (Xx72 = Xx74))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.57/0.73 tff(22,plain,
% 0.57/0.73 (((~![Xx72: $i, Xx73: $i, Xx74: $i, Xx75: $i] : ((~(and(Xx72, Xx73) = and(Xx74, Xx75))) | (Xx72 = Xx74))) | ((~(and(Xx14!189, Xx15!188) = and(tptp_fun_Xx12_30(Xy!175, Xi!173, Xa!174), tptp_fun_Xx13_29(Xy!175, Xi!173, Xa!174)))) | (Xx14!189 = tptp_fun_Xx12_30(Xy!175, Xi!173, Xa!174)))) <=> ((~![Xx72: $i, Xx73: $i, Xx74: $i, Xx75: $i] : ((~(and(Xx72, Xx73) = and(Xx74, Xx75))) | (Xx72 = Xx74))) | (~(and(Xx14!189, Xx15!188) = and(tptp_fun_Xx12_30(Xy!175, Xi!173, Xa!174), tptp_fun_Xx13_29(Xy!175, Xi!173, Xa!174)))) | (Xx14!189 = tptp_fun_Xx12_30(Xy!175, Xi!173, Xa!174)))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(23,plain,
% 0.57/0.73 ((~![Xx72: $i, Xx73: $i, Xx74: $i, Xx75: $i] : ((~(and(Xx72, Xx73) = and(Xx74, Xx75))) | (Xx72 = Xx74))) | ((~(and(Xx14!189, Xx15!188) = and(tptp_fun_Xx12_30(Xy!175, Xi!173, Xa!174), tptp_fun_Xx13_29(Xy!175, Xi!173, Xa!174)))) | (Xx14!189 = tptp_fun_Xx12_30(Xy!175, Xi!173, Xa!174)))),
% 0.57/0.73 inference(quant_inst,[status(thm)],[])).
% 0.57/0.73 tff(24,plain,
% 0.57/0.73 ((~![Xx72: $i, Xx73: $i, Xx74: $i, Xx75: $i] : ((~(and(Xx72, Xx73) = and(Xx74, Xx75))) | (Xx72 = Xx74))) | (~(and(Xx14!189, Xx15!188) = and(tptp_fun_Xx12_30(Xy!175, Xi!173, Xa!174), tptp_fun_Xx13_29(Xy!175, Xi!173, Xa!174)))) | (Xx14!189 = tptp_fun_Xx12_30(Xy!175, Xi!173, Xa!174))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.57/0.73 tff(25,plain,
% 0.57/0.73 (Xx14!189 = tptp_fun_Xx12_30(Xy!175, Xi!173, Xa!174)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[24, 21, 11])).
% 0.57/0.73 tff(26,plain,
% 0.57/0.73 (eval_succeeds(Xx14!189, Xi!173, |'0'|) <=> eval_succeeds(tptp_fun_Xx12_30(Xy!175, Xi!173, Xa!174), Xi!173, |'0'|)),
% 0.57/0.73 inference(monotonicity,[status(thm)],[25])).
% 0.57/0.73 tff(27,plain,
% 0.57/0.73 (eval_succeeds(tptp_fun_Xx12_30(Xy!175, Xi!173, Xa!174), Xi!173, |'0'|) <=> eval_succeeds(Xx14!189, Xi!173, |'0'|)),
% 0.57/0.73 inference(symmetry,[status(thm)],[26])).
% 0.57/0.73 tff(28,plain,
% 0.57/0.73 (((~(Xy!175 = |'0'|)) | (~eval_succeeds(tptp_fun_Xx12_30(Xy!175, Xi!173, Xa!174), Xi!173, |'0'|)) | (~(Xa!174 = and(tptp_fun_Xx12_30(Xy!175, Xi!173, Xa!174), tptp_fun_Xx13_29(Xy!175, Xi!173, Xa!174))))) | eval_succeeds(tptp_fun_Xx12_30(Xy!175, Xi!173, Xa!174), Xi!173, |'0'|)),
% 0.57/0.73 inference(tautology,[status(thm)],[])).
% 0.57/0.73 tff(29,plain,
% 0.57/0.73 (eval_succeeds(tptp_fun_Xx12_30(Xy!175, Xi!173, Xa!174), Xi!173, |'0'|)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[28, 4])).
% 0.57/0.73 tff(30,plain,
% 0.57/0.73 (eval_succeeds(Xx14!189, Xi!173, |'0'|)),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[29, 27])).
% 0.57/0.73 tff(31,assumption,(![Xy: $i] : ((~eval_succeeds(Xx14!189, Xi!173, Xy)) | (|'1'| = Xy))), introduced(assumption)).
% 0.57/0.73 tff(32,plain,
% 0.57/0.73 ((~(|'1'| = |'0'|)) <=> (~(|'1'| = |'0'|))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(33,axiom,(~(|'1'| = |'0'|)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','id16')).
% 0.57/0.73 tff(34,plain,
% 0.57/0.73 (~(|'1'| = |'0'|)),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.57/0.73 tff(35,plain,
% 0.57/0.73 (((~![Xy: $i] : ((~eval_succeeds(Xx14!189, Xi!173, Xy)) | (|'1'| = Xy))) | ((~eval_succeeds(Xx14!189, Xi!173, |'0'|)) | (|'1'| = |'0'|))) <=> ((~![Xy: $i] : ((~eval_succeeds(Xx14!189, Xi!173, Xy)) | (|'1'| = Xy))) | (~eval_succeeds(Xx14!189, Xi!173, |'0'|)) | (|'1'| = |'0'|))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(36,plain,
% 0.57/0.73 ((~![Xy: $i] : ((~eval_succeeds(Xx14!189, Xi!173, Xy)) | (|'1'| = Xy))) | ((~eval_succeeds(Xx14!189, Xi!173, |'0'|)) | (|'1'| = |'0'|))),
% 0.57/0.73 inference(quant_inst,[status(thm)],[])).
% 0.57/0.73 tff(37,plain,
% 0.57/0.73 ((~![Xy: $i] : ((~eval_succeeds(Xx14!189, Xi!173, Xy)) | (|'1'| = Xy))) | (~eval_succeeds(Xx14!189, Xi!173, |'0'|)) | (|'1'| = |'0'|)),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.57/0.73 tff(38,plain,
% 0.57/0.73 (~eval_succeeds(Xx14!189, Xi!173, |'0'|)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[37, 34, 31])).
% 0.57/0.73 tff(39,plain,
% 0.57/0.73 ($false),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[38, 30])).
% 0.57/0.73 tff(40,plain,(((~(Xy!175 = |'0'|)) | (~eval_succeeds(tptp_fun_Xx12_30(Xy!175, Xi!173, Xa!174), Xi!173, |'0'|)) | (~(Xa!174 = and(tptp_fun_Xx12_30(Xy!175, Xi!173, Xa!174), tptp_fun_Xx13_29(Xy!175, Xi!173, Xa!174))))) | (~![Xy: $i] : ((~eval_succeeds(Xx14!189, Xi!173, Xy)) | (|'1'| = Xy))) | (~(Xa!174 = and(Xx14!189, Xx15!188)))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.73 tff(41,plain,
% 0.57/0.73 (~![Xy: $i] : ((~eval_succeeds(Xx14!189, Xi!173, Xy)) | (|'1'| = Xy))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[40, 6, 4])).
% 0.57/0.73 tff(42,assumption,(![Xy: $i] : ((~eval_succeeds(Xa!194, Xi!193, Xy)) | (Xx!192 = Xy))), introduced(assumption)).
% 0.57/0.73 tff(43,plain,
% 0.57/0.73 ((~![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | (~eval_succeeds(Xa, Xi, Xx)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)))) <=> (~![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | (~eval_succeeds(Xa, Xi, Xx)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy))))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(44,plain,
% 0.57/0.73 ((~![Xa: $i, Xi: $i, Xx: $i] : (eval_succeeds(Xa, Xi, Xx) => (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xa, Xi, Xy) => (Xx = Xy))))) <=> (~![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | (~eval_succeeds(Xa, Xi, Xx)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy))))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(45,axiom,(~![Xa: $i, Xi: $i, Xx: $i] : (eval_succeeds(Xa, Xi, Xx) => (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xa, Xi, Xy) => (Xx = Xy))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''lemma-(eval:function)'')).
% 0.57/0.73 tff(46,plain,
% 0.57/0.73 (~![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | (~eval_succeeds(Xa, Xi, Xx)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.57/0.73 tff(47,plain,
% 0.57/0.73 (~![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | (~eval_succeeds(Xa, Xi, Xx)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[46, 43])).
% 0.57/0.73 tff(48,plain,
% 0.57/0.73 (~((~eval_succeeds(Xa!194, Xi!193, Xy!195)) | (Xx!192 = Xy!195))),
% 0.57/0.73 inference(and_elim,[status(thm)],[47])).
% 0.57/0.73 tff(49,plain,
% 0.57/0.73 (~(Xx!192 = Xy!195)),
% 0.57/0.73 inference(or_elim,[status(thm)],[48])).
% 0.57/0.73 tff(50,plain,
% 0.57/0.73 (eval_succeeds(Xa!194, Xi!193, Xy!195)),
% 0.57/0.73 inference(or_elim,[status(thm)],[48])).
% 0.57/0.73 tff(51,plain,
% 0.57/0.73 (((~![Xy: $i] : ((~eval_succeeds(Xa!194, Xi!193, Xy)) | (Xx!192 = Xy))) | ((~eval_succeeds(Xa!194, Xi!193, Xy!195)) | (Xx!192 = Xy!195))) <=> ((~![Xy: $i] : ((~eval_succeeds(Xa!194, Xi!193, Xy)) | (Xx!192 = Xy))) | (~eval_succeeds(Xa!194, Xi!193, Xy!195)) | (Xx!192 = Xy!195))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(52,plain,
% 0.57/0.73 ((~![Xy: $i] : ((~eval_succeeds(Xa!194, Xi!193, Xy)) | (Xx!192 = Xy))) | ((~eval_succeeds(Xa!194, Xi!193, Xy!195)) | (Xx!192 = Xy!195))),
% 0.57/0.73 inference(quant_inst,[status(thm)],[])).
% 0.57/0.73 tff(53,plain,
% 0.57/0.73 ((~![Xy: $i] : ((~eval_succeeds(Xa!194, Xi!193, Xy)) | (Xx!192 = Xy))) | (~eval_succeeds(Xa!194, Xi!193, Xy!195)) | (Xx!192 = Xy!195)),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.57/0.73 tff(54,plain,
% 0.57/0.73 ($false),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[53, 50, 49, 42])).
% 0.57/0.73 tff(55,plain,(~![Xy: $i] : ((~eval_succeeds(Xa!194, Xi!193, Xy)) | (Xx!192 = Xy))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.73 tff(56,plain,
% 0.57/0.73 (eval_succeeds(Xa!194, Xi!193, Xx!192)),
% 0.57/0.73 inference(and_elim,[status(thm)],[47])).
% 0.57/0.73 tff(57,plain,
% 0.57/0.73 (interpretation_succeeds(Xi!193)),
% 0.57/0.73 inference(and_elim,[status(thm)],[47])).
% 0.57/0.73 tff(58,assumption,(![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | (~eval_succeeds(Xa, Xi, Xx)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)))), introduced(assumption)).
% 0.57/0.73 tff(59,plain,
% 0.57/0.73 (((~![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | (~eval_succeeds(Xa, Xi, Xx)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)))) | ((~interpretation_succeeds(Xi!193)) | (~eval_succeeds(Xa!194, Xi!193, Xx!192)) | ![Xy: $i] : ((~eval_succeeds(Xa!194, Xi!193, Xy)) | (Xx!192 = Xy)))) <=> ((~![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | (~eval_succeeds(Xa, Xi, Xx)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)))) | (~interpretation_succeeds(Xi!193)) | (~eval_succeeds(Xa!194, Xi!193, Xx!192)) | ![Xy: $i] : ((~eval_succeeds(Xa!194, Xi!193, Xy)) | (Xx!192 = Xy)))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(60,plain,
% 0.57/0.73 ((~![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | (~eval_succeeds(Xa, Xi, Xx)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)))) | ((~interpretation_succeeds(Xi!193)) | (~eval_succeeds(Xa!194, Xi!193, Xx!192)) | ![Xy: $i] : ((~eval_succeeds(Xa!194, Xi!193, Xy)) | (Xx!192 = Xy)))),
% 0.57/0.73 inference(quant_inst,[status(thm)],[])).
% 0.57/0.73 tff(61,plain,
% 0.57/0.73 ((~![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | (~eval_succeeds(Xa, Xi, Xx)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)))) | (~interpretation_succeeds(Xi!193)) | (~eval_succeeds(Xa!194, Xi!193, Xx!192)) | ![Xy: $i] : ((~eval_succeeds(Xa!194, Xi!193, Xy)) | (Xx!192 = Xy))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.57/0.73 tff(62,plain,
% 0.57/0.73 ($false),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[61, 58, 57, 56, 55])).
% 0.57/0.73 tff(63,plain,(~![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | (~eval_succeeds(Xa, Xi, Xx)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.73 tff(64,plain,
% 0.57/0.73 (((~((~interpretation_succeeds(Xi!173)) | (~eval_succeeds(Xa!174, Xi!173, Xy!175)) | (Xx!172 = Xy!175) | (~((~((~(Xa!174 = p(Xx18!176))) | (~(Xx!172 = |'0'|)) | (~member_succeeds(neg(p(Xx18!176)), Xi!173)))) | (~((~(Xa!174 = p(Xx19!177))) | (~(Xx!172 = |'1'|)) | (~member_succeeds(p(Xx19!177), Xi!173)))) | (~((~(Xx!172 = |'1'|)) | (~(Xa!174 = or(Xx8!179, Xx9!178))) | (~eval_succeeds(Xx8!179, Xi!173, |'1'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx8!179, Xi!173, Xy)) | (|'1'| = Xy)))))) | (~((~(Xx!172 = |'0'|)) | (~(Xa!174 = and(Xx10!181, Xx11!180))) | (~eval_succeeds(Xx11!180, Xi!173, |'0'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx11!180, Xi!173, Xy)) | (|'0'| = Xy)))))) | (~((~(Xx!172 = |'0'|)) | (~(Xa!174 = or(Xx4!183, Xx5!182))) | (~eval_succeeds(Xx4!183, Xi!173, |'0'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx4!183, Xi!173, Xy)) | (|'0'| = Xy)))) | (~eval_succeeds(Xx5!182, Xi!173, |'0'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx5!182, Xi!173, Xy)) | (|'0'| = Xy)))))) | (~((~(Xx!172 = |'1'|)) | (~(Xa!174 = or(Xx6!185, Xx7!184))) | (~eval_succeeds(Xx7!184, Xi!173, |'1'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx7!184, Xi!173, Xy)) | (|'1'| = Xy)))))) | (~((~(Xx!172 = |'0'|)) | (~(Xa!174 = and(Xx12!187, Xx13!186))) | (~eval_succeeds(Xx12!187, Xi!173, |'0'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx12!187, Xi!173, Xy)) | (|'0'| = Xy)))))) | (~((~(Xx!172 = |'1'|)) | (~(Xa!174 = and(Xx14!189, Xx15!188))) | (~eval_succeeds(Xx14!189, Xi!173, |'1'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx14!189, Xi!173, Xy)) | (|'1'| = Xy)))) | (~eval_succeeds(Xx15!188, Xi!173, |'1'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx15!188, Xi!173, Xy)) | (|'1'| = Xy)))))) | (~((~(Xx!172 = |'0'|)) | (~(Xa!174 = neg(Xx16!190))) | (~eval_succeeds(Xx16!190, Xi!173, |'1'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx16!190, Xi!173, Xy)) | (|'1'| = Xy)))))) | (~((~(Xx!172 = |'1'|)) | (~(Xa!174 = neg(Xx17!191))) | (~eval_succeeds(Xx17!191, Xi!173, |'0'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx17!191, Xi!173, Xy)) | (|'0'| = Xy)))))))))) | ![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | (~eval_succeeds(Xa, Xi, Xx)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)))) <=> ((~((~interpretation_succeeds(Xi!173)) | (~eval_succeeds(Xa!174, Xi!173, Xy!175)) | (Xx!172 = Xy!175) | (~((~((~(Xa!174 = p(Xx18!176))) | (~(Xx!172 = |'0'|)) | (~member_succeeds(neg(p(Xx18!176)), Xi!173)))) | (~((~(Xa!174 = p(Xx19!177))) | (~(Xx!172 = |'1'|)) | (~member_succeeds(p(Xx19!177), Xi!173)))) | (~((~(Xx!172 = |'1'|)) | (~(Xa!174 = or(Xx8!179, Xx9!178))) | (~eval_succeeds(Xx8!179, Xi!173, |'1'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx8!179, Xi!173, Xy)) | (|'1'| = Xy)))))) | (~((~(Xx!172 = |'0'|)) | (~(Xa!174 = and(Xx10!181, Xx11!180))) | (~eval_succeeds(Xx11!180, Xi!173, |'0'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx11!180, Xi!173, Xy)) | (|'0'| = Xy)))))) | (~((~(Xx!172 = |'1'|)) | (~(Xa!174 = or(Xx6!185, Xx7!184))) | (~eval_succeeds(Xx7!184, Xi!173, |'1'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx7!184, Xi!173, Xy)) | (|'1'| = Xy)))))) | (~((~(Xx!172 = |'0'|)) | (~(Xa!174 = and(Xx12!187, Xx13!186))) | (~eval_succeeds(Xx12!187, Xi!173, |'0'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx12!187, Xi!173, Xy)) | (|'0'| = Xy)))))) | (~((~(Xx!172 = |'0'|)) | (~(Xa!174 = neg(Xx16!190))) | (~eval_succeeds(Xx16!190, Xi!173, |'1'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx16!190, Xi!173, Xy)) | (|'1'| = Xy)))))) | (~((~(Xx!172 = |'1'|)) | (~(Xa!174 = neg(Xx17!191))) | (~eval_succeeds(Xx17!191, Xi!173, |'0'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx17!191, Xi!173, Xy)) | (|'0'| = Xy)))))) | (~((~(Xx!172 = |'0'|)) | (~(Xa!174 = or(Xx4!183, Xx5!182))) | (~eval_succeeds(Xx4!183, Xi!173, |'0'|)) | (~eval_succeeds(Xx5!182, Xi!173, |'0'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx4!183, Xi!173, Xy)) | (|'0'| = Xy)))) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx5!182, Xi!173, Xy)) | (|'0'| = Xy)))))) | (~((~(Xx!172 = |'1'|)) | (~(Xa!174 = and(Xx14!189, Xx15!188))) | (~eval_succeeds(Xx14!189, Xi!173, |'1'|)) | (~eval_succeeds(Xx15!188, Xi!173, |'1'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx14!189, Xi!173, Xy)) | (|'1'| = Xy)))) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx15!188, Xi!173, Xy)) | (|'1'| = Xy)))))))))) | ![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | (~eval_succeeds(Xa, Xi, Xx)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy))))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(65,plain,
% 0.57/0.73 (((~((~interpretation_succeeds(Xi!173)) | (~eval_succeeds(Xa!174, Xi!173, Xy!175)) | (Xx!172 = Xy!175) | (~((~((~(Xa!174 = p(Xx18!176))) | (~(Xx!172 = |'0'|)) | (~member_succeeds(neg(p(Xx18!176)), Xi!173)))) | (~((~(Xa!174 = p(Xx19!177))) | (~(Xx!172 = |'1'|)) | (~member_succeeds(p(Xx19!177), Xi!173)))) | (~((~(Xx!172 = |'1'|)) | (~(Xa!174 = or(Xx8!179, Xx9!178))) | (~eval_succeeds(Xx8!179, Xi!173, |'1'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx8!179, Xi!173, Xy)) | (|'1'| = Xy)))))) | (~((~(Xx!172 = |'0'|)) | (~(Xa!174 = and(Xx10!181, Xx11!180))) | (~eval_succeeds(Xx11!180, Xi!173, |'0'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx11!180, Xi!173, Xy)) | (|'0'| = Xy)))))) | (~((~(Xx!172 = |'0'|)) | (~(Xa!174 = or(Xx4!183, Xx5!182))) | (~eval_succeeds(Xx4!183, Xi!173, |'0'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx4!183, Xi!173, Xy)) | (|'0'| = Xy)))) | (~eval_succeeds(Xx5!182, Xi!173, |'0'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx5!182, Xi!173, Xy)) | (|'0'| = Xy)))))) | (~((~(Xx!172 = |'1'|)) | (~(Xa!174 = or(Xx6!185, Xx7!184))) | (~eval_succeeds(Xx7!184, Xi!173, |'1'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx7!184, Xi!173, Xy)) | (|'1'| = Xy)))))) | (~((~(Xx!172 = |'0'|)) | (~(Xa!174 = and(Xx12!187, Xx13!186))) | (~eval_succeeds(Xx12!187, Xi!173, |'0'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx12!187, Xi!173, Xy)) | (|'0'| = Xy)))))) | (~((~(Xx!172 = |'1'|)) | (~(Xa!174 = and(Xx14!189, Xx15!188))) | (~eval_succeeds(Xx14!189, Xi!173, |'1'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx14!189, Xi!173, Xy)) | (|'1'| = Xy)))) | (~eval_succeeds(Xx15!188, Xi!173, |'1'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx15!188, Xi!173, Xy)) | (|'1'| = Xy)))))) | (~((~(Xx!172 = |'0'|)) | (~(Xa!174 = neg(Xx16!190))) | (~eval_succeeds(Xx16!190, Xi!173, |'1'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx16!190, Xi!173, Xy)) | (|'1'| = Xy)))))) | (~((~(Xx!172 = |'1'|)) | (~(Xa!174 = neg(Xx17!191))) | (~eval_succeeds(Xx17!191, Xi!173, |'0'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx17!191, Xi!173, Xy)) | (|'0'| = Xy)))))))))) | ![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | (~eval_succeeds(Xa, Xi, Xx)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)))) <=> ((~((~interpretation_succeeds(Xi!173)) | (~eval_succeeds(Xa!174, Xi!173, Xy!175)) | (Xx!172 = Xy!175) | (~((~((~(Xa!174 = p(Xx18!176))) | (~(Xx!172 = |'0'|)) | (~member_succeeds(neg(p(Xx18!176)), Xi!173)))) | (~((~(Xa!174 = p(Xx19!177))) | (~(Xx!172 = |'1'|)) | (~member_succeeds(p(Xx19!177), Xi!173)))) | (~((~(Xx!172 = |'1'|)) | (~(Xa!174 = or(Xx8!179, Xx9!178))) | (~eval_succeeds(Xx8!179, Xi!173, |'1'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx8!179, Xi!173, Xy)) | (|'1'| = Xy)))))) | (~((~(Xx!172 = |'0'|)) | (~(Xa!174 = and(Xx10!181, Xx11!180))) | (~eval_succeeds(Xx11!180, Xi!173, |'0'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx11!180, Xi!173, Xy)) | (|'0'| = Xy)))))) | (~((~(Xx!172 = |'0'|)) | (~(Xa!174 = or(Xx4!183, Xx5!182))) | (~eval_succeeds(Xx4!183, Xi!173, |'0'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx4!183, Xi!173, Xy)) | (|'0'| = Xy)))) | (~eval_succeeds(Xx5!182, Xi!173, |'0'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx5!182, Xi!173, Xy)) | (|'0'| = Xy)))))) | (~((~(Xx!172 = |'1'|)) | (~(Xa!174 = or(Xx6!185, Xx7!184))) | (~eval_succeeds(Xx7!184, Xi!173, |'1'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx7!184, Xi!173, Xy)) | (|'1'| = Xy)))))) | (~((~(Xx!172 = |'0'|)) | (~(Xa!174 = and(Xx12!187, Xx13!186))) | (~eval_succeeds(Xx12!187, Xi!173, |'0'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx12!187, Xi!173, Xy)) | (|'0'| = Xy)))))) | (~((~(Xx!172 = |'1'|)) | (~(Xa!174 = and(Xx14!189, Xx15!188))) | (~eval_succeeds(Xx14!189, Xi!173, |'1'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx14!189, Xi!173, Xy)) | (|'1'| = Xy)))) | (~eval_succeeds(Xx15!188, Xi!173, |'1'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx15!188, Xi!173, Xy)) | (|'1'| = Xy)))))) | (~((~(Xx!172 = |'0'|)) | (~(Xa!174 = neg(Xx16!190))) | (~eval_succeeds(Xx16!190, Xi!173, |'1'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx16!190, Xi!173, Xy)) | (|'1'| = Xy)))))) | (~((~(Xx!172 = |'1'|)) | (~(Xa!174 = neg(Xx17!191))) | (~eval_succeeds(Xx17!191, Xi!173, |'0'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx17!191, Xi!173, Xy)) | (|'0'| = Xy)))))))))) | ![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | (~eval_succeeds(Xa, Xi, Xx)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy))))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(66,plain,
% 0.57/0.74 (((interpretation_succeeds(Xi!173) & (~((~eval_succeeds(Xa!174, Xi!173, Xy!175)) | (Xx!172 = Xy!175))) & (((Xa!174 = p(Xx18!176)) & (Xx!172 = |'0'|) & member_succeeds(neg(p(Xx18!176)), Xi!173)) | ((Xa!174 = p(Xx19!177)) & (Xx!172 = |'1'|) & member_succeeds(p(Xx19!177), Xi!173)) | ((Xa!174 = or(Xx8!179, Xx9!178)) & (Xx!172 = |'1'|) & eval_succeeds(Xx8!179, Xi!173, |'1'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx8!179, Xi!173, Xy)) | (|'1'| = Xy)))) | ((Xa!174 = and(Xx10!181, Xx11!180)) & (Xx!172 = |'0'|) & eval_succeeds(Xx11!180, Xi!173, |'0'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx11!180, Xi!173, Xy)) | (|'0'| = Xy)))) | ((Xa!174 = or(Xx4!183, Xx5!182)) & (Xx!172 = |'0'|) & eval_succeeds(Xx4!183, Xi!173, |'0'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx4!183, Xi!173, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5!182, Xi!173, |'0'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx5!182, Xi!173, Xy)) | (|'0'| = Xy)))) | ((Xa!174 = or(Xx6!185, Xx7!184)) & (Xx!172 = |'1'|) & eval_succeeds(Xx7!184, Xi!173, |'1'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx7!184, Xi!173, Xy)) | (|'1'| = Xy)))) | ((Xa!174 = and(Xx12!187, Xx13!186)) & (Xx!172 = |'0'|) & eval_succeeds(Xx12!187, Xi!173, |'0'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx12!187, Xi!173, Xy)) | (|'0'| = Xy)))) | ((Xa!174 = and(Xx14!189, Xx15!188)) & (Xx!172 = |'1'|) & eval_succeeds(Xx14!189, Xi!173, |'1'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx14!189, Xi!173, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15!188, Xi!173, |'1'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx15!188, Xi!173, Xy)) | (|'1'| = Xy)))) | ((Xa!174 = neg(Xx16!190)) & (Xx!172 = |'0'|) & eval_succeeds(Xx16!190, Xi!173, |'1'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx16!190, Xi!173, Xy)) | (|'1'| = Xy)))) | ((Xa!174 = neg(Xx17!191)) & (Xx!172 = |'1'|) & eval_succeeds(Xx17!191, Xi!173, |'0'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx17!191, Xi!173, Xy)) | (|'0'| = Xy)))))) | ![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | (~eval_succeeds(Xa, Xi, Xx)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)))) <=> ((~((~interpretation_succeeds(Xi!173)) | (~eval_succeeds(Xa!174, Xi!173, Xy!175)) | (Xx!172 = Xy!175) | (~((~((~(Xa!174 = p(Xx18!176))) | (~(Xx!172 = |'0'|)) | (~member_succeeds(neg(p(Xx18!176)), Xi!173)))) | (~((~(Xa!174 = p(Xx19!177))) | (~(Xx!172 = |'1'|)) | (~member_succeeds(p(Xx19!177), Xi!173)))) | (~((~(Xx!172 = |'1'|)) | (~(Xa!174 = or(Xx8!179, Xx9!178))) | (~eval_succeeds(Xx8!179, Xi!173, |'1'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx8!179, Xi!173, Xy)) | (|'1'| = Xy)))))) | (~((~(Xx!172 = |'0'|)) | (~(Xa!174 = and(Xx10!181, Xx11!180))) | (~eval_succeeds(Xx11!180, Xi!173, |'0'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx11!180, Xi!173, Xy)) | (|'0'| = Xy)))))) | (~((~(Xx!172 = |'0'|)) | (~(Xa!174 = or(Xx4!183, Xx5!182))) | (~eval_succeeds(Xx4!183, Xi!173, |'0'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx4!183, Xi!173, Xy)) | (|'0'| = Xy)))) | (~eval_succeeds(Xx5!182, Xi!173, |'0'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx5!182, Xi!173, Xy)) | (|'0'| = Xy)))))) | (~((~(Xx!172 = |'1'|)) | (~(Xa!174 = or(Xx6!185, Xx7!184))) | (~eval_succeeds(Xx7!184, Xi!173, |'1'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx7!184, Xi!173, Xy)) | (|'1'| = Xy)))))) | (~((~(Xx!172 = |'0'|)) | (~(Xa!174 = and(Xx12!187, Xx13!186))) | (~eval_succeeds(Xx12!187, Xi!173, |'0'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx12!187, Xi!173, Xy)) | (|'0'| = Xy)))))) | (~((~(Xx!172 = |'1'|)) | (~(Xa!174 = and(Xx14!189, Xx15!188))) | (~eval_succeeds(Xx14!189, Xi!173, |'1'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx14!189, Xi!173, Xy)) | (|'1'| = Xy)))) | (~eval_succeeds(Xx15!188, Xi!173, |'1'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx15!188, Xi!173, Xy)) | (|'1'| = Xy)))))) | (~((~(Xx!172 = |'0'|)) | (~(Xa!174 = neg(Xx16!190))) | (~eval_succeeds(Xx16!190, Xi!173, |'1'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx16!190, Xi!173, Xy)) | (|'1'| = Xy)))))) | (~((~(Xx!172 = |'1'|)) | (~(Xa!174 = neg(Xx17!191))) | (~eval_succeeds(Xx17!191, Xi!173, |'0'|)) | (~((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx17!191, Xi!173, Xy)) | (|'0'| = Xy)))))))))) | ![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | (~eval_succeeds(Xa, Xi, Xx)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy))))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(67,plain,
% 0.57/0.74 ((interpretation_succeeds(Xi!173) & (~((~eval_succeeds(Xa!174, Xi!173, Xy!175)) | (Xx!172 = Xy!175))) & (((Xa!174 = p(Xx18!176)) & (Xx!172 = |'0'|) & member_succeeds(neg(p(Xx18!176)), Xi!173)) | ((Xa!174 = p(Xx19!177)) & (Xx!172 = |'1'|) & member_succeeds(p(Xx19!177), Xi!173)) | ((Xa!174 = or(Xx8!179, Xx9!178)) & (Xx!172 = |'1'|) & eval_succeeds(Xx8!179, Xi!173, |'1'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx8!179, Xi!173, Xy)) | (|'1'| = Xy)))) | ((Xa!174 = and(Xx10!181, Xx11!180)) & (Xx!172 = |'0'|) & eval_succeeds(Xx11!180, Xi!173, |'0'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx11!180, Xi!173, Xy)) | (|'0'| = Xy)))) | ((Xa!174 = or(Xx4!183, Xx5!182)) & (Xx!172 = |'0'|) & eval_succeeds(Xx4!183, Xi!173, |'0'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx4!183, Xi!173, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5!182, Xi!173, |'0'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx5!182, Xi!173, Xy)) | (|'0'| = Xy)))) | ((Xa!174 = or(Xx6!185, Xx7!184)) & (Xx!172 = |'1'|) & eval_succeeds(Xx7!184, Xi!173, |'1'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx7!184, Xi!173, Xy)) | (|'1'| = Xy)))) | ((Xa!174 = and(Xx12!187, Xx13!186)) & (Xx!172 = |'0'|) & eval_succeeds(Xx12!187, Xi!173, |'0'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx12!187, Xi!173, Xy)) | (|'0'| = Xy)))) | ((Xa!174 = and(Xx14!189, Xx15!188)) & (Xx!172 = |'1'|) & eval_succeeds(Xx14!189, Xi!173, |'1'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx14!189, Xi!173, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15!188, Xi!173, |'1'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx15!188, Xi!173, Xy)) | (|'1'| = Xy)))) | ((Xa!174 = neg(Xx16!190)) & (Xx!172 = |'0'|) & eval_succeeds(Xx16!190, Xi!173, |'1'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx16!190, Xi!173, Xy)) | (|'1'| = Xy)))) | ((Xa!174 = neg(Xx17!191)) & (Xx!172 = |'1'|) & eval_succeeds(Xx17!191, Xi!173, |'0'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx17!191, Xi!173, Xy)) | (|'0'| = Xy)))))) <=> (interpretation_succeeds(Xi!173) & (~((~eval_succeeds(Xa!174, Xi!173, Xy!175)) | (Xx!172 = Xy!175))) & (((Xa!174 = p(Xx18!176)) & (Xx!172 = |'0'|) & member_succeeds(neg(p(Xx18!176)), Xi!173)) | ((Xa!174 = p(Xx19!177)) & (Xx!172 = |'1'|) & member_succeeds(p(Xx19!177), Xi!173)) | ((Xa!174 = or(Xx8!179, Xx9!178)) & (Xx!172 = |'1'|) & eval_succeeds(Xx8!179, Xi!173, |'1'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx8!179, Xi!173, Xy)) | (|'1'| = Xy)))) | ((Xa!174 = and(Xx10!181, Xx11!180)) & (Xx!172 = |'0'|) & eval_succeeds(Xx11!180, Xi!173, |'0'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx11!180, Xi!173, Xy)) | (|'0'| = Xy)))) | ((Xa!174 = or(Xx4!183, Xx5!182)) & (Xx!172 = |'0'|) & eval_succeeds(Xx4!183, Xi!173, |'0'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx4!183, Xi!173, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5!182, Xi!173, |'0'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx5!182, Xi!173, Xy)) | (|'0'| = Xy)))) | ((Xa!174 = or(Xx6!185, Xx7!184)) & (Xx!172 = |'1'|) & eval_succeeds(Xx7!184, Xi!173, |'1'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx7!184, Xi!173, Xy)) | (|'1'| = Xy)))) | ((Xa!174 = and(Xx12!187, Xx13!186)) & (Xx!172 = |'0'|) & eval_succeeds(Xx12!187, Xi!173, |'0'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx12!187, Xi!173, Xy)) | (|'0'| = Xy)))) | ((Xa!174 = and(Xx14!189, Xx15!188)) & (Xx!172 = |'1'|) & eval_succeeds(Xx14!189, Xi!173, |'1'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx14!189, Xi!173, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15!188, Xi!173, |'1'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx15!188, Xi!173, Xy)) | (|'1'| = Xy)))) | ((Xa!174 = neg(Xx16!190)) & (Xx!172 = |'0'|) & eval_succeeds(Xx16!190, Xi!173, |'1'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx16!190, Xi!173, Xy)) | (|'1'| = Xy)))) | ((Xa!174 = neg(Xx17!191)) & (Xx!172 = |'1'|) & eval_succeeds(Xx17!191, Xi!173, |'0'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx17!191, Xi!173, Xy)) | (|'0'| = Xy))))))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(68,plain,
% 0.57/0.74 (((interpretation_succeeds(Xi!173) & (~((~eval_succeeds(Xa!174, Xi!173, Xy!175)) | (Xx!172 = Xy!175))) & (((Xa!174 = p(Xx18!176)) & (Xx!172 = |'0'|) & member_succeeds(neg(p(Xx18!176)), Xi!173)) | ((Xa!174 = p(Xx19!177)) & (Xx!172 = |'1'|) & member_succeeds(p(Xx19!177), Xi!173)) | ((Xa!174 = or(Xx8!179, Xx9!178)) & (Xx!172 = |'1'|) & eval_succeeds(Xx8!179, Xi!173, |'1'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx8!179, Xi!173, Xy)) | (|'1'| = Xy)))) | ((Xa!174 = and(Xx10!181, Xx11!180)) & (Xx!172 = |'0'|) & eval_succeeds(Xx11!180, Xi!173, |'0'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx11!180, Xi!173, Xy)) | (|'0'| = Xy)))) | ((Xa!174 = or(Xx4!183, Xx5!182)) & (Xx!172 = |'0'|) & eval_succeeds(Xx4!183, Xi!173, |'0'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx4!183, Xi!173, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5!182, Xi!173, |'0'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx5!182, Xi!173, Xy)) | (|'0'| = Xy)))) | ((Xa!174 = or(Xx6!185, Xx7!184)) & (Xx!172 = |'1'|) & eval_succeeds(Xx7!184, Xi!173, |'1'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx7!184, Xi!173, Xy)) | (|'1'| = Xy)))) | ((Xa!174 = and(Xx12!187, Xx13!186)) & (Xx!172 = |'0'|) & eval_succeeds(Xx12!187, Xi!173, |'0'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx12!187, Xi!173, Xy)) | (|'0'| = Xy)))) | ((Xa!174 = and(Xx14!189, Xx15!188)) & (Xx!172 = |'1'|) & eval_succeeds(Xx14!189, Xi!173, |'1'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx14!189, Xi!173, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15!188, Xi!173, |'1'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx15!188, Xi!173, Xy)) | (|'1'| = Xy)))) | ((Xa!174 = neg(Xx16!190)) & (Xx!172 = |'0'|) & eval_succeeds(Xx16!190, Xi!173, |'1'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx16!190, Xi!173, Xy)) | (|'1'| = Xy)))) | ((Xa!174 = neg(Xx17!191)) & (Xx!172 = |'1'|) & eval_succeeds(Xx17!191, Xi!173, |'0'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx17!191, Xi!173, Xy)) | (|'0'| = Xy)))))) | ![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | (~eval_succeeds(Xa, Xi, Xx)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)))) <=> ((interpretation_succeeds(Xi!173) & (~((~eval_succeeds(Xa!174, Xi!173, Xy!175)) | (Xx!172 = Xy!175))) & (((Xa!174 = p(Xx18!176)) & (Xx!172 = |'0'|) & member_succeeds(neg(p(Xx18!176)), Xi!173)) | ((Xa!174 = p(Xx19!177)) & (Xx!172 = |'1'|) & member_succeeds(p(Xx19!177), Xi!173)) | ((Xa!174 = or(Xx8!179, Xx9!178)) & (Xx!172 = |'1'|) & eval_succeeds(Xx8!179, Xi!173, |'1'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx8!179, Xi!173, Xy)) | (|'1'| = Xy)))) | ((Xa!174 = and(Xx10!181, Xx11!180)) & (Xx!172 = |'0'|) & eval_succeeds(Xx11!180, Xi!173, |'0'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx11!180, Xi!173, Xy)) | (|'0'| = Xy)))) | ((Xa!174 = or(Xx4!183, Xx5!182)) & (Xx!172 = |'0'|) & eval_succeeds(Xx4!183, Xi!173, |'0'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx4!183, Xi!173, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5!182, Xi!173, |'0'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx5!182, Xi!173, Xy)) | (|'0'| = Xy)))) | ((Xa!174 = or(Xx6!185, Xx7!184)) & (Xx!172 = |'1'|) & eval_succeeds(Xx7!184, Xi!173, |'1'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx7!184, Xi!173, Xy)) | (|'1'| = Xy)))) | ((Xa!174 = and(Xx12!187, Xx13!186)) & (Xx!172 = |'0'|) & eval_succeeds(Xx12!187, Xi!173, |'0'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx12!187, Xi!173, Xy)) | (|'0'| = Xy)))) | ((Xa!174 = and(Xx14!189, Xx15!188)) & (Xx!172 = |'1'|) & eval_succeeds(Xx14!189, Xi!173, |'1'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx14!189, Xi!173, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15!188, Xi!173, |'1'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx15!188, Xi!173, Xy)) | (|'1'| = Xy)))) | ((Xa!174 = neg(Xx16!190)) & (Xx!172 = |'0'|) & eval_succeeds(Xx16!190, Xi!173, |'1'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx16!190, Xi!173, Xy)) | (|'1'| = Xy)))) | ((Xa!174 = neg(Xx17!191)) & (Xx!172 = |'1'|) & eval_succeeds(Xx17!191, Xi!173, |'0'|) & ((~interpretation_succeeds(Xi!173)) | ![Xy: $i] : ((~eval_succeeds(Xx17!191, Xi!173, Xy)) | (|'0'| = Xy)))))) | ![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | (~eval_succeeds(Xa, Xi, Xx)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy))))),
% 0.57/0.75 inference(monotonicity,[status(thm)],[67])).
% 0.57/0.75 tff(69,plain,
% 0.57/0.75 (((~![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)) | (~(?[Xx18: $i] : ((Xa = p(Xx18)) & (Xx = |'0'|) & member_succeeds(neg(p(Xx18)), Xi)) | ?[Xx19: $i] : ((Xa = p(Xx19)) & (Xx = |'1'|) & member_succeeds(p(Xx19), Xi)) | ?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx16: $i] : ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx17: $i] : ((Xa = neg(Xx17)) & (Xx = |'1'|) & eval_succeeds(Xx17, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy)))))))) | ![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | (~eval_succeeds(Xa, Xi, Xx)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)))) <=> ((~![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)) | (~(?[Xx18: $i] : ((Xa = p(Xx18)) & (Xx = |'0'|) & member_succeeds(neg(p(Xx18)), Xi)) | ?[Xx19: $i] : ((Xa = p(Xx19)) & (Xx = |'1'|) & member_succeeds(p(Xx19), Xi)) | ?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx16: $i] : ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx17: $i] : ((Xa = neg(Xx17)) & (Xx = |'1'|) & eval_succeeds(Xx17, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy)))))))) | ![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | (~eval_succeeds(Xa, Xi, Xx)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy))))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(70,plain,
% 0.57/0.75 ((![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)) | (~(?[Xx18: $i] : ((Xa = p(Xx18)) & (Xx = |'0'|) & member_succeeds(neg(p(Xx18)), Xi)) | ?[Xx19: $i] : ((Xa = p(Xx19)) & (Xx = |'1'|) & member_succeeds(p(Xx19), Xi)) | ?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx16: $i] : ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx17: $i] : ((Xa = neg(Xx17)) & (Xx = |'1'|) & eval_succeeds(Xx17, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy))))))) => ![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | (~eval_succeeds(Xa, Xi, Xx)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)))) <=> ((~![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)) | (~(?[Xx18: $i] : ((Xa = p(Xx18)) & (Xx = |'0'|) & member_succeeds(neg(p(Xx18)), Xi)) | ?[Xx19: $i] : ((Xa = p(Xx19)) & (Xx = |'1'|) & member_succeeds(p(Xx19), Xi)) | ?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx16: $i] : ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx17: $i] : ((Xa = neg(Xx17)) & (Xx = |'1'|) & eval_succeeds(Xx17, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy)))))))) | ![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | (~eval_succeeds(Xa, Xi, Xx)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy))))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(71,plain,
% 0.57/0.75 (^[Xa: $i, Xi: $i, Xx: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Xy: $i] : rewrite((eval_succeeds(Xa, Xi, Xy) => (Xx = Xy)) <=> ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)))), (![Xy: $i] : (eval_succeeds(Xa, Xi, Xy) => (Xx = Xy)) <=> ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)))), ((interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xa, Xi, Xy) => (Xx = Xy))) <=> (interpretation_succeeds(Xi) => ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy))))), rewrite((interpretation_succeeds(Xi) => ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy))) <=> ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)))), ((interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xa, Xi, Xy) => (Xx = Xy))) <=> ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy))))), ((eval_succeeds(Xa, Xi, Xx) => (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xa, Xi, Xy) => (Xx = Xy)))) <=> (eval_succeeds(Xa, Xi, Xx) => ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)))))), rewrite((eval_succeeds(Xa, Xi, Xx) => ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)))) <=> ((~interpretation_succeeds(Xi)) | (~eval_succeeds(Xa, Xi, Xx)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)))), ((eval_succeeds(Xa, Xi, Xx) => (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xa, Xi, Xy) => (Xx = Xy)))) <=> ((~interpretation_succeeds(Xi)) | (~eval_succeeds(Xa, Xi, Xx)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)))))),
% 0.57/0.75 inference(bind,[status(th)],[])).
% 0.57/0.75 tff(72,plain,
% 0.57/0.75 (![Xa: $i, Xi: $i, Xx: $i] : (eval_succeeds(Xa, Xi, Xx) => (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xa, Xi, Xy) => (Xx = Xy)))) <=> ![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | (~eval_succeeds(Xa, Xi, Xx)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)))),
% 0.57/0.75 inference(quant_intro,[status(thm)],[71])).
% 0.57/0.75 tff(73,plain,
% 0.57/0.75 (^[Xa: $i, Xi: $i, Xx: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((?[Xx4: $i, Xx5: $i] : ((((((Xa = or(Xx4, Xx5)) & (Xx = |'0'|)) & eval_succeeds(Xx4, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx4, Xi, Xy) => (|'0'| = Xy)))) & eval_succeeds(Xx5, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx5, Xi, Xy) => (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((((Xa = or(Xx6, Xx7)) & (Xx = |'1'|)) & eval_succeeds(Xx7, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx7, Xi, Xy) => (|'1'| = Xy))))) <=> (?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))))), quant_intro(proof_bind(^[Xx8: $i, Xx9: $i] : trans(monotonicity(rewrite((((Xa = or(Xx8, Xx9)) & (Xx = |'1'|)) & eval_succeeds(Xx8, Xi, |'1'|)) <=> ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|))), trans(monotonicity(quant_intro(proof_bind(^[Xy: $i] : rewrite((eval_succeeds(Xx8, Xi, Xy) => (|'1'| = Xy)) <=> ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))), (![Xy: $i] : (eval_succeeds(Xx8, Xi, Xy) => (|'1'| = Xy)) <=> ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))), ((interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx8, Xi, Xy) => (|'1'| = Xy))) <=> (interpretation_succeeds(Xi) => ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy))))), rewrite((interpretation_succeeds(Xi) => ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy))) <=> ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))), ((interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx8, Xi, Xy) => (|'1'| = Xy))) <=> ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy))))), (((((Xa = or(Xx8, Xx9)) & (Xx = |'1'|)) & eval_succeeds(Xx8, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx8, Xi, Xy) => (|'1'| = Xy)))) <=> (((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|)) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))))), rewrite((((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|)) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) <=> ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy))))), (((((Xa = or(Xx8, Xx9)) & (Xx = |'1'|)) & eval_succeeds(Xx8, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx8, Xi, Xy) => (|'1'| = Xy)))) <=> ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy))))))), (?[Xx8: $i, Xx9: $i] : ((((Xa = or(Xx8, Xx9)) & (Xx = |'1'|)) & eval_succeeds(Xx8, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx8, Xi, Xy) => (|'1'| = Xy)))) <=> ?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))))), (((?[Xx4: $i, Xx5: $i] : ((((((Xa = or(Xx4, Xx5)) & (Xx = |'0'|)) & eval_succeeds(Xx4, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx4, Xi, Xy) => (|'0'| = Xy)))) & eval_succeeds(Xx5, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx5, Xi, Xy) => (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((((Xa = or(Xx6, Xx7)) & (Xx = |'1'|)) & eval_succeeds(Xx7, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx7, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx8: $i, Xx9: $i] : ((((Xa = or(Xx8, Xx9)) & (Xx = |'1'|)) & eval_succeeds(Xx8, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx8, Xi, Xy) => (|'1'| = Xy))))) <=> ((?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy))))) | ?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy))))))), rewrite(((?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy))))) | ?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy))))) <=> (?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))))), (((?[Xx4: $i, Xx5: $i] : ((((((Xa = or(Xx4, Xx5)) & (Xx = |'0'|)) & eval_succeeds(Xx4, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx4, Xi, Xy) => (|'0'| = Xy)))) & eval_succeeds(Xx5, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx5, Xi, Xy) => (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((((Xa = or(Xx6, Xx7)) & (Xx = |'1'|)) & eval_succeeds(Xx7, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx7, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx8: $i, Xx9: $i] : ((((Xa = or(Xx8, Xx9)) & (Xx = |'1'|)) & eval_succeeds(Xx8, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx8, Xi, Xy) => (|'1'| = Xy))))) <=> (?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy))))))), quant_intro(proof_bind(^[Xx10: $i, Xx11: $i] : trans(monotonicity(rewrite((((Xa = and(Xx10, Xx11)) & (Xx = |'0'|)) & eval_succeeds(Xx11, Xi, |'0'|)) <=> ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|))), trans(monotonicity(quant_intro(proof_bind(^[Xy: $i] : rewrite((eval_succeeds(Xx11, Xi, Xy) => (|'0'| = Xy)) <=> ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))), (![Xy: $i] : (eval_succeeds(Xx11, Xi, Xy) => (|'0'| = Xy)) <=> ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))), ((interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx11, Xi, Xy) => (|'0'| = Xy))) <=> (interpretation_succeeds(Xi) => ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy))))), rewrite((interpretation_succeeds(Xi) => ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy))) <=> ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))), ((interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx11, Xi, Xy) => (|'0'| = Xy))) <=> ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy))))), (((((Xa = and(Xx10, Xx11)) & (Xx = |'0'|)) & eval_succeeds(Xx11, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx11, Xi, Xy) => (|'0'| = Xy)))) <=> (((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|)) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))))), rewrite((((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|)) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) <=> ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy))))), (((((Xa = and(Xx10, Xx11)) & (Xx = |'0'|)) & eval_succeeds(Xx11, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx11, Xi, Xy) => (|'0'| = Xy)))) <=> ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy))))))), (?[Xx10: $i, Xx11: $i] : ((((Xa = and(Xx10, Xx11)) & (Xx = |'0'|)) & eval_succeeds(Xx11, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx11, Xi, Xy) => (|'0'| = Xy)))) <=> ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))))), ((((?[Xx4: $i, Xx5: $i] : ((((((Xa = or(Xx4, Xx5)) & (Xx = |'0'|)) & eval_succeeds(Xx4, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx4, Xi, Xy) => (|'0'| = Xy)))) & eval_succeeds(Xx5, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx5, Xi, Xy) => (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((((Xa = or(Xx6, Xx7)) & (Xx = |'1'|)) & eval_succeeds(Xx7, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx7, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx8: $i, Xx9: $i] : ((((Xa = or(Xx8, Xx9)) & (Xx = |'1'|)) & eval_succeeds(Xx8, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx8, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx10: $i, Xx11: $i] : ((((Xa = and(Xx10, Xx11)) & (Xx = |'0'|)) & eval_succeeds(Xx11, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx11, Xi, Xy) => (|'0'| = Xy))))) <=> ((?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy))))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy))))))), rewrite(((?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy))))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy))))) <=> (?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))))), ((((?[Xx4: $i, Xx5: $i] : ((((((Xa = or(Xx4, Xx5)) & (Xx = |'0'|)) & eval_succeeds(Xx4, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx4, Xi, Xy) => (|'0'| = Xy)))) & eval_succeeds(Xx5, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx5, Xi, Xy) => (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((((Xa = or(Xx6, Xx7)) & (Xx = |'1'|)) & eval_succeeds(Xx7, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx7, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx8: $i, Xx9: $i] : ((((Xa = or(Xx8, Xx9)) & (Xx = |'1'|)) & eval_succeeds(Xx8, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx8, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx10: $i, Xx11: $i] : ((((Xa = and(Xx10, Xx11)) & (Xx = |'0'|)) & eval_succeeds(Xx11, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx11, Xi, Xy) => (|'0'| = Xy))))) <=> (?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy))))))), quant_intro(proof_bind(^[Xx12: $i, Xx13: $i] : trans(monotonicity(rewrite((((Xa = and(Xx12, Xx13)) & (Xx = |'0'|)) & eval_succeeds(Xx12, Xi, |'0'|)) <=> ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|))), trans(monotonicity(quant_intro(proof_bind(^[Xy: $i] : rewrite((eval_succeeds(Xx12, Xi, Xy) => (|'0'| = Xy)) <=> ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))), (![Xy: $i] : (eval_succeeds(Xx12, Xi, Xy) => (|'0'| = Xy)) <=> ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))), ((interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx12, Xi, Xy) => (|'0'| = Xy))) <=> (interpretation_succeeds(Xi) => ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy))))), rewrite((interpretation_succeeds(Xi) => ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy))) <=> ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))), ((interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx12, Xi, Xy) => (|'0'| = Xy))) <=> ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy))))), (((((Xa = and(Xx12, Xx13)) & (Xx = |'0'|)) & eval_succeeds(Xx12, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx12, Xi, Xy) => (|'0'| = Xy)))) <=> (((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|)) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))))), rewrite((((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|)) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) <=> ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy))))), (((((Xa = and(Xx12, Xx13)) & (Xx = |'0'|)) & eval_succeeds(Xx12, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx12, Xi, Xy) => (|'0'| = Xy)))) <=> ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy))))))), (?[Xx12: $i, Xx13: $i] : ((((Xa = and(Xx12, Xx13)) & (Xx = |'0'|)) & eval_succeeds(Xx12, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx12, Xi, Xy) => (|'0'| = Xy)))) <=> ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))))), (((((?[Xx4: $i, Xx5: $i] : ((((((Xa = or(Xx4, Xx5)) & (Xx = |'0'|)) & eval_succeeds(Xx4, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx4, Xi, Xy) => (|'0'| = Xy)))) & eval_succeeds(Xx5, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx5, Xi, Xy) => (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((((Xa = or(Xx6, Xx7)) & (Xx = |'1'|)) & eval_succeeds(Xx7, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx7, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx8: $i, Xx9: $i] : ((((Xa = or(Xx8, Xx9)) & (Xx = |'1'|)) & eval_succeeds(Xx8, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx8, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx10: $i, Xx11: $i] : ((((Xa = and(Xx10, Xx11)) & (Xx = |'0'|)) & eval_succeeds(Xx11, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx11, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx12: $i, Xx13: $i] : ((((Xa = and(Xx12, Xx13)) & (Xx = |'0'|)) & eval_succeeds(Xx12, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx12, Xi, Xy) => (|'0'| = Xy))))) <=> ((?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy))))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy))))))), rewrite(((?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy))))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy))))) <=> (?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))))), (((((?[Xx4: $i, Xx5: $i] : ((((((Xa = or(Xx4, Xx5)) & (Xx = |'0'|)) & eval_succeeds(Xx4, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx4, Xi, Xy) => (|'0'| = Xy)))) & eval_succeeds(Xx5, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx5, Xi, Xy) => (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((((Xa = or(Xx6, Xx7)) & (Xx = |'1'|)) & eval_succeeds(Xx7, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx7, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx8: $i, Xx9: $i] : ((((Xa = or(Xx8, Xx9)) & (Xx = |'1'|)) & eval_succeeds(Xx8, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx8, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx10: $i, Xx11: $i] : ((((Xa = and(Xx10, Xx11)) & (Xx = |'0'|)) & eval_succeeds(Xx11, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx11, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx12: $i, Xx13: $i] : ((((Xa = and(Xx12, Xx13)) & (Xx = |'0'|)) & eval_succeeds(Xx12, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx12, Xi, Xy) => (|'0'| = Xy))))) <=> (?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy))))))), quant_intro(proof_bind(^[Xx14: $i, Xx15: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((Xa = and(Xx14, Xx15)) & (Xx = |'1'|)) & eval_succeeds(Xx14, Xi, |'1'|)) <=> ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|))), trans(monotonicity(quant_intro(proof_bind(^[Xy: $i] : rewrite((eval_succeeds(Xx14, Xi, Xy) => (|'1'| = Xy)) <=> ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy)))), (![Xy: $i] : (eval_succeeds(Xx14, Xi, Xy) => (|'1'| = Xy)) <=> ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy)))), ((interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx14, Xi, Xy) => (|'1'| = Xy))) <=> (interpretation_succeeds(Xi) => ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))))), rewrite((interpretation_succeeds(Xi) => ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) <=> ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy)))), ((interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx14, Xi, Xy) => (|'1'| = Xy))) <=> ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))))), (((((Xa = and(Xx14, Xx15)) & (Xx = |'1'|)) & eval_succeeds(Xx14, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx14, Xi, Xy) => (|'1'| = Xy)))) <=> (((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|)) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy)))))), rewrite((((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|)) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy)))) <=> ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))))), (((((Xa = and(Xx14, Xx15)) & (Xx = |'1'|)) & eval_succeeds(Xx14, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx14, Xi, Xy) => (|'1'| = Xy)))) <=> ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy)))))), ((((((Xa = and(Xx14, Xx15)) & (Xx = |'1'|)) & eval_succeeds(Xx14, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx14, Xi, Xy) => (|'1'| = Xy)))) & eval_succeeds(Xx15, Xi, |'1'|)) <=> (((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy)))) & eval_succeeds(Xx15, Xi, |'1'|)))), rewrite((((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy)))) & eval_succeeds(Xx15, Xi, |'1'|)) <=> ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|))), ((((((Xa = and(Xx14, Xx15)) & (Xx = |'1'|)) & eval_succeeds(Xx14, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx14, Xi, Xy) => (|'1'| = Xy)))) & eval_succeeds(Xx15, Xi, |'1'|)) <=> ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|)))), trans(monotonicity(quant_intro(proof_bind(^[Xy: $i] : rewrite((eval_succeeds(Xx15, Xi, Xy) => (|'1'| = Xy)) <=> ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))), (![Xy: $i] : (eval_succeeds(Xx15, Xi, Xy) => (|'1'| = Xy)) <=> ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))), ((interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx15, Xi, Xy) => (|'1'| = Xy))) <=> (interpretation_succeeds(Xi) => ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy))))), rewrite((interpretation_succeeds(Xi) => ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy))) <=> ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))), ((interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx15, Xi, Xy) => (|'1'| = Xy))) <=> ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy))))), (((((((Xa = and(Xx14, Xx15)) & (Xx = |'1'|)) & eval_succeeds(Xx14, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx14, Xi, Xy) => (|'1'| = Xy)))) & eval_succeeds(Xx15, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx15, Xi, Xy) => (|'1'| = Xy)))) <=> (((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|)) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))))), rewrite((((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|)) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))) <=> ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy))))), (((((((Xa = and(Xx14, Xx15)) & (Xx = |'1'|)) & eval_succeeds(Xx14, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx14, Xi, Xy) => (|'1'| = Xy)))) & eval_succeeds(Xx15, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx15, Xi, Xy) => (|'1'| = Xy)))) <=> ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy))))))), (?[Xx14: $i, Xx15: $i] : ((((((Xa = and(Xx14, Xx15)) & (Xx = |'1'|)) & eval_succeeds(Xx14, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx14, Xi, Xy) => (|'1'| = Xy)))) & eval_succeeds(Xx15, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx15, Xi, Xy) => (|'1'| = Xy)))) <=> ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))))), ((((((?[Xx4: $i, Xx5: $i] : ((((((Xa = or(Xx4, Xx5)) & (Xx = |'0'|)) & eval_succeeds(Xx4, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx4, Xi, Xy) => (|'0'| = Xy)))) & eval_succeeds(Xx5, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx5, Xi, Xy) => (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((((Xa = or(Xx6, Xx7)) & (Xx = |'1'|)) & eval_succeeds(Xx7, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx7, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx8: $i, Xx9: $i] : ((((Xa = or(Xx8, Xx9)) & (Xx = |'1'|)) & eval_succeeds(Xx8, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx8, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx10: $i, Xx11: $i] : ((((Xa = and(Xx10, Xx11)) & (Xx = |'0'|)) & eval_succeeds(Xx11, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx11, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx12: $i, Xx13: $i] : ((((Xa = and(Xx12, Xx13)) & (Xx = |'0'|)) & eval_succeeds(Xx12, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx12, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx14: $i, Xx15: $i] : ((((((Xa = and(Xx14, Xx15)) & (Xx = |'1'|)) & eval_succeeds(Xx14, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx14, Xi, Xy) => (|'1'| = Xy)))) & eval_succeeds(Xx15, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx15, Xi, Xy) => (|'1'| = Xy))))) <=> ((?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy))))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy))))))), rewrite(((?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy))))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy))))) <=> (?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))))), ((((((?[Xx4: $i, Xx5: $i] : ((((((Xa = or(Xx4, Xx5)) & (Xx = |'0'|)) & eval_succeeds(Xx4, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx4, Xi, Xy) => (|'0'| = Xy)))) & eval_succeeds(Xx5, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx5, Xi, Xy) => (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((((Xa = or(Xx6, Xx7)) & (Xx = |'1'|)) & eval_succeeds(Xx7, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx7, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx8: $i, Xx9: $i] : ((((Xa = or(Xx8, Xx9)) & (Xx = |'1'|)) & eval_succeeds(Xx8, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx8, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx10: $i, Xx11: $i] : ((((Xa = and(Xx10, Xx11)) & (Xx = |'0'|)) & eval_succeeds(Xx11, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx11, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx12: $i, Xx13: $i] : ((((Xa = and(Xx12, Xx13)) & (Xx = |'0'|)) & eval_succeeds(Xx12, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx12, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx14: $i, Xx15: $i] : ((((((Xa = and(Xx14, Xx15)) & (Xx = |'1'|)) & eval_succeeds(Xx14, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx14, Xi, Xy) => (|'1'| = Xy)))) & eval_succeeds(Xx15, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx15, Xi, Xy) => (|'1'| = Xy))))) <=> (?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy))))))), quant_intro(proof_bind(^[Xx16: $i] : trans(monotonicity(rewrite((((Xa = neg(Xx16)) & (Xx = |'0'|)) & eval_succeeds(Xx16, Xi, |'1'|)) <=> ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|))), trans(monotonicity(quant_intro(proof_bind(^[Xy: $i] : rewrite((eval_succeeds(Xx16, Xi, Xy) => (|'1'| = Xy)) <=> ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy)))), (![Xy: $i] : (eval_succeeds(Xx16, Xi, Xy) => (|'1'| = Xy)) <=> ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy)))), ((interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx16, Xi, Xy) => (|'1'| = Xy))) <=> (interpretation_succeeds(Xi) => ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy))))), rewrite((interpretation_succeeds(Xi) => ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy))) <=> ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy)))), ((interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx16, Xi, Xy) => (|'1'| = Xy))) <=> ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy))))), (((((Xa = neg(Xx16)) & (Xx = |'0'|)) & eval_succeeds(Xx16, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx16, Xi, Xy) => (|'1'| = Xy)))) <=> (((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|)) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy)))))), rewrite((((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|)) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy)))) <=> ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy))))), (((((Xa = neg(Xx16)) & (Xx = |'0'|)) & eval_succeeds(Xx16, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx16, Xi, Xy) => (|'1'| = Xy)))) <=> ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy))))))), (?[Xx16: $i] : ((((Xa = neg(Xx16)) & (Xx = |'0'|)) & eval_succeeds(Xx16, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx16, Xi, Xy) => (|'1'| = Xy)))) <=> ?[Xx16: $i] : ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy)))))), (((((((?[Xx4: $i, Xx5: $i] : ((((((Xa = or(Xx4, Xx5)) & (Xx = |'0'|)) & eval_succeeds(Xx4, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx4, Xi, Xy) => (|'0'| = Xy)))) & eval_succeeds(Xx5, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx5, Xi, Xy) => (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((((Xa = or(Xx6, Xx7)) & (Xx = |'1'|)) & eval_succeeds(Xx7, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx7, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx8: $i, Xx9: $i] : ((((Xa = or(Xx8, Xx9)) & (Xx = |'1'|)) & eval_succeeds(Xx8, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx8, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx10: $i, Xx11: $i] : ((((Xa = and(Xx10, Xx11)) & (Xx = |'0'|)) & eval_succeeds(Xx11, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx11, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx12: $i, Xx13: $i] : ((((Xa = and(Xx12, Xx13)) & (Xx = |'0'|)) & eval_succeeds(Xx12, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx12, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx14: $i, Xx15: $i] : ((((((Xa = and(Xx14, Xx15)) & (Xx = |'1'|)) & eval_succeeds(Xx14, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx14, Xi, Xy) => (|'1'| = Xy)))) & eval_succeeds(Xx15, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx15, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx16: $i] : ((((Xa = neg(Xx16)) & (Xx = |'0'|)) & eval_succeeds(Xx16, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx16, Xi, Xy) => (|'1'| = Xy))))) <=> ((?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy))))) | ?[Xx16: $i] : ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy))))))), rewrite(((?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy))))) | ?[Xx16: $i] : ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy))))) <=> (?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx16: $i] : ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy)))))), (((((((?[Xx4: $i, Xx5: $i] : ((((((Xa = or(Xx4, Xx5)) & (Xx = |'0'|)) & eval_succeeds(Xx4, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx4, Xi, Xy) => (|'0'| = Xy)))) & eval_succeeds(Xx5, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx5, Xi, Xy) => (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((((Xa = or(Xx6, Xx7)) & (Xx = |'1'|)) & eval_succeeds(Xx7, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx7, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx8: $i, Xx9: $i] : ((((Xa = or(Xx8, Xx9)) & (Xx = |'1'|)) & eval_succeeds(Xx8, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx8, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx10: $i, Xx11: $i] : ((((Xa = and(Xx10, Xx11)) & (Xx = |'0'|)) & eval_succeeds(Xx11, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx11, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx12: $i, Xx13: $i] : ((((Xa = and(Xx12, Xx13)) & (Xx = |'0'|)) & eval_succeeds(Xx12, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx12, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx14: $i, Xx15: $i] : ((((((Xa = and(Xx14, Xx15)) & (Xx = |'1'|)) & eval_succeeds(Xx14, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx14, Xi, Xy) => (|'1'| = Xy)))) & eval_succeeds(Xx15, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx15, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx16: $i] : ((((Xa = neg(Xx16)) & (Xx = |'0'|)) & eval_succeeds(Xx16, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx16, Xi, Xy) => (|'1'| = Xy))))) <=> (?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx16: $i] : ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy))))))), quant_intro(proof_bind(^[Xx17: $i] : trans(monotonicity(rewrite((((Xa = neg(Xx17)) & (Xx = |'1'|)) & eval_succeeds(Xx17, Xi, |'0'|)) <=> ((Xa = neg(Xx17)) & (Xx = |'1'|) & eval_succeeds(Xx17, Xi, |'0'|))), trans(monotonicity(quant_intro(proof_bind(^[Xy: $i] : rewrite((eval_succeeds(Xx17, Xi, Xy) => (|'0'| = Xy)) <=> ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy)))), (![Xy: $i] : (eval_succeeds(Xx17, Xi, Xy) => (|'0'| = Xy)) <=> ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy)))), ((interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx17, Xi, Xy) => (|'0'| = Xy))) <=> (interpretation_succeeds(Xi) => ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy))))), rewrite((interpretation_succeeds(Xi) => ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy))) <=> ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy)))), ((interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx17, Xi, Xy) => (|'0'| = Xy))) <=> ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy))))), (((((Xa = neg(Xx17)) & (Xx = |'1'|)) & eval_succeeds(Xx17, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx17, Xi, Xy) => (|'0'| = Xy)))) <=> (((Xa = neg(Xx17)) & (Xx = |'1'|) & eval_succeeds(Xx17, Xi, |'0'|)) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy)))))), rewrite((((Xa = neg(Xx17)) & (Xx = |'1'|) & eval_succeeds(Xx17, Xi, |'0'|)) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy)))) <=> ((Xa = neg(Xx17)) & (Xx = |'1'|) & eval_succeeds(Xx17, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy))))), (((((Xa = neg(Xx17)) & (Xx = |'1'|)) & eval_succeeds(Xx17, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx17, Xi, Xy) => (|'0'| = Xy)))) <=> ((Xa = neg(Xx17)) & (Xx = |'1'|) & eval_succeeds(Xx17, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy))))))), (?[Xx17: $i] : ((((Xa = neg(Xx17)) & (Xx = |'1'|)) & eval_succeeds(Xx17, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx17, Xi, Xy) => (|'0'| = Xy)))) <=> ?[Xx17: $i] : ((Xa = neg(Xx17)) & (Xx = |'1'|) & eval_succeeds(Xx17, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy)))))), ((((((((?[Xx4: $i, Xx5: $i] : ((((((Xa = or(Xx4, Xx5)) & (Xx = |'0'|)) & eval_succeeds(Xx4, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx4, Xi, Xy) => (|'0'| = Xy)))) & eval_succeeds(Xx5, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx5, Xi, Xy) => (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((((Xa = or(Xx6, Xx7)) & (Xx = |'1'|)) & eval_succeeds(Xx7, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx7, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx8: $i, Xx9: $i] : ((((Xa = or(Xx8, Xx9)) & (Xx = |'1'|)) & eval_succeeds(Xx8, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx8, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx10: $i, Xx11: $i] : ((((Xa = and(Xx10, Xx11)) & (Xx = |'0'|)) & eval_succeeds(Xx11, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx11, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx12: $i, Xx13: $i] : ((((Xa = and(Xx12, Xx13)) & (Xx = |'0'|)) & eval_succeeds(Xx12, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx12, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx14: $i, Xx15: $i] : ((((((Xa = and(Xx14, Xx15)) & (Xx = |'1'|)) & eval_succeeds(Xx14, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx14, Xi, Xy) => (|'1'| = Xy)))) & eval_succeeds(Xx15, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx15, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx16: $i] : ((((Xa = neg(Xx16)) & (Xx = |'0'|)) & eval_succeeds(Xx16, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx16, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx17: $i] : ((((Xa = neg(Xx17)) & (Xx = |'1'|)) & eval_succeeds(Xx17, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx17, Xi, Xy) => (|'0'| = Xy))))) <=> ((?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx16: $i] : ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy))))) | ?[Xx17: $i] : ((Xa = neg(Xx17)) & (Xx = |'1'|) & eval_succeeds(Xx17, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy))))))), rewrite(((?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx16: $i] : ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy))))) | ?[Xx17: $i] : ((Xa = neg(Xx17)) & (Xx = |'1'|) & eval_succeeds(Xx17, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy))))) <=> (?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx16: $i] : ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx17: $i] : ((Xa = neg(Xx17)) & (Xx = |'1'|) & eval_succeeds(Xx17, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy)))))), ((((((((?[Xx4: $i, Xx5: $i] : ((((((Xa = or(Xx4, Xx5)) & (Xx = |'0'|)) & eval_succeeds(Xx4, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx4, Xi, Xy) => (|'0'| = Xy)))) & eval_succeeds(Xx5, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx5, Xi, Xy) => (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((((Xa = or(Xx6, Xx7)) & (Xx = |'1'|)) & eval_succeeds(Xx7, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx7, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx8: $i, Xx9: $i] : ((((Xa = or(Xx8, Xx9)) & (Xx = |'1'|)) & eval_succeeds(Xx8, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx8, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx10: $i, Xx11: $i] : ((((Xa = and(Xx10, Xx11)) & (Xx = |'0'|)) & eval_succeeds(Xx11, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx11, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx12: $i, Xx13: $i] : ((((Xa = and(Xx12, Xx13)) & (Xx = |'0'|)) & eval_succeeds(Xx12, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx12, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx14: $i, Xx15: $i] : ((((((Xa = and(Xx14, Xx15)) & (Xx = |'1'|)) & eval_succeeds(Xx14, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx14, Xi, Xy) => (|'1'| = Xy)))) & eval_succeeds(Xx15, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx15, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx16: $i] : ((((Xa = neg(Xx16)) & (Xx = |'0'|)) & eval_succeeds(Xx16, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx16, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx17: $i] : ((((Xa = neg(Xx17)) & (Xx = |'1'|)) & eval_succeeds(Xx17, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx17, Xi, Xy) => (|'0'| = Xy))))) <=> (?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx16: $i] : ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx17: $i] : ((Xa = neg(Xx17)) & (Xx = |'1'|) & eval_succeeds(Xx17, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy))))))), quant_intro(proof_bind(^[Xx18: $i] : rewrite((((Xa = p(Xx18)) & (Xx = |'0'|)) & member_succeeds(neg(p(Xx18)), Xi)) <=> ((Xa = p(Xx18)) & (Xx = |'0'|) & member_succeeds(neg(p(Xx18)), Xi)))), (?[Xx18: $i] : (((Xa = p(Xx18)) & (Xx = |'0'|)) & member_succeeds(neg(p(Xx18)), Xi)) <=> ?[Xx18: $i] : ((Xa = p(Xx18)) & (Xx = |'0'|) & member_succeeds(neg(p(Xx18)), Xi)))), (((((((((?[Xx4: $i, Xx5: $i] : ((((((Xa = or(Xx4, Xx5)) & (Xx = |'0'|)) & eval_succeeds(Xx4, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx4, Xi, Xy) => (|'0'| = Xy)))) & eval_succeeds(Xx5, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx5, Xi, Xy) => (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((((Xa = or(Xx6, Xx7)) & (Xx = |'1'|)) & eval_succeeds(Xx7, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx7, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx8: $i, Xx9: $i] : ((((Xa = or(Xx8, Xx9)) & (Xx = |'1'|)) & eval_succeeds(Xx8, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx8, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx10: $i, Xx11: $i] : ((((Xa = and(Xx10, Xx11)) & (Xx = |'0'|)) & eval_succeeds(Xx11, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx11, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx12: $i, Xx13: $i] : ((((Xa = and(Xx12, Xx13)) & (Xx = |'0'|)) & eval_succeeds(Xx12, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx12, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx14: $i, Xx15: $i] : ((((((Xa = and(Xx14, Xx15)) & (Xx = |'1'|)) & eval_succeeds(Xx14, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx14, Xi, Xy) => (|'1'| = Xy)))) & eval_succeeds(Xx15, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx15, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx16: $i] : ((((Xa = neg(Xx16)) & (Xx = |'0'|)) & eval_succeeds(Xx16, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx16, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx17: $i] : ((((Xa = neg(Xx17)) & (Xx = |'1'|)) & eval_succeeds(Xx17, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx17, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx18: $i] : (((Xa = p(Xx18)) & (Xx = |'0'|)) & member_succeeds(neg(p(Xx18)), Xi))) <=> ((?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx16: $i] : ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx17: $i] : ((Xa = neg(Xx17)) & (Xx = |'1'|) & eval_succeeds(Xx17, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy))))) | ?[Xx18: $i] : ((Xa = p(Xx18)) & (Xx = |'0'|) & member_succeeds(neg(p(Xx18)), Xi))))), rewrite(((?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx16: $i] : ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx17: $i] : ((Xa = neg(Xx17)) & (Xx = |'1'|) & eval_succeeds(Xx17, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy))))) | ?[Xx18: $i] : ((Xa = p(Xx18)) & (Xx = |'0'|) & member_succeeds(neg(p(Xx18)), Xi))) <=> (?[Xx18: $i] : ((Xa = p(Xx18)) & (Xx = |'0'|) & member_succeeds(neg(p(Xx18)), Xi)) | ?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx16: $i] : ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx17: $i] : ((Xa = neg(Xx17)) & (Xx = |'1'|) & eval_succeeds(Xx17, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy)))))), (((((((((?[Xx4: $i, Xx5: $i] : ((((((Xa = or(Xx4, Xx5)) & (Xx = |'0'|)) & eval_succeeds(Xx4, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx4, Xi, Xy) => (|'0'| = Xy)))) & eval_succeeds(Xx5, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx5, Xi, Xy) => (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((((Xa = or(Xx6, Xx7)) & (Xx = |'1'|)) & eval_succeeds(Xx7, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx7, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx8: $i, Xx9: $i] : ((((Xa = or(Xx8, Xx9)) & (Xx = |'1'|)) & eval_succeeds(Xx8, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx8, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx10: $i, Xx11: $i] : ((((Xa = and(Xx10, Xx11)) & (Xx = |'0'|)) & eval_succeeds(Xx11, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx11, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx12: $i, Xx13: $i] : ((((Xa = and(Xx12, Xx13)) & (Xx = |'0'|)) & eval_succeeds(Xx12, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx12, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx14: $i, Xx15: $i] : ((((((Xa = and(Xx14, Xx15)) & (Xx = |'1'|)) & eval_succeeds(Xx14, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx14, Xi, Xy) => (|'1'| = Xy)))) & eval_succeeds(Xx15, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx15, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx16: $i] : ((((Xa = neg(Xx16)) & (Xx = |'0'|)) & eval_succeeds(Xx16, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx16, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx17: $i] : ((((Xa = neg(Xx17)) & (Xx = |'1'|)) & eval_succeeds(Xx17, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx17, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx18: $i] : (((Xa = p(Xx18)) & (Xx = |'0'|)) & member_succeeds(neg(p(Xx18)), Xi))) <=> (?[Xx18: $i] : ((Xa = p(Xx18)) & (Xx = |'0'|) & member_succeeds(neg(p(Xx18)), Xi)) | ?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx16: $i] : ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx17: $i] : ((Xa = neg(Xx17)) & (Xx = |'1'|) & eval_succeeds(Xx17, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy))))))), quant_intro(proof_bind(^[Xx19: $i] : rewrite((((Xa = p(Xx19)) & (Xx = |'1'|)) & member_succeeds(p(Xx19), Xi)) <=> ((Xa = p(Xx19)) & (Xx = |'1'|) & member_succeeds(p(Xx19), Xi)))), (?[Xx19: $i] : (((Xa = p(Xx19)) & (Xx = |'1'|)) & member_succeeds(p(Xx19), Xi)) <=> ?[Xx19: $i] : ((Xa = p(Xx19)) & (Xx = |'1'|) & member_succeeds(p(Xx19), Xi)))), ((((((((((?[Xx4: $i, Xx5: $i] : ((((((Xa = or(Xx4, Xx5)) & (Xx = |'0'|)) & eval_succeeds(Xx4, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx4, Xi, Xy) => (|'0'| = Xy)))) & eval_succeeds(Xx5, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx5, Xi, Xy) => (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((((Xa = or(Xx6, Xx7)) & (Xx = |'1'|)) & eval_succeeds(Xx7, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx7, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx8: $i, Xx9: $i] : ((((Xa = or(Xx8, Xx9)) & (Xx = |'1'|)) & eval_succeeds(Xx8, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx8, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx10: $i, Xx11: $i] : ((((Xa = and(Xx10, Xx11)) & (Xx = |'0'|)) & eval_succeeds(Xx11, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx11, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx12: $i, Xx13: $i] : ((((Xa = and(Xx12, Xx13)) & (Xx = |'0'|)) & eval_succeeds(Xx12, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx12, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx14: $i, Xx15: $i] : ((((((Xa = and(Xx14, Xx15)) & (Xx = |'1'|)) & eval_succeeds(Xx14, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx14, Xi, Xy) => (|'1'| = Xy)))) & eval_succeeds(Xx15, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx15, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx16: $i] : ((((Xa = neg(Xx16)) & (Xx = |'0'|)) & eval_succeeds(Xx16, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx16, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx17: $i] : ((((Xa = neg(Xx17)) & (Xx = |'1'|)) & eval_succeeds(Xx17, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx17, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx18: $i] : (((Xa = p(Xx18)) & (Xx = |'0'|)) & member_succeeds(neg(p(Xx18)), Xi))) | ?[Xx19: $i] : (((Xa = p(Xx19)) & (Xx = |'1'|)) & member_succeeds(p(Xx19), Xi))) <=> ((?[Xx18: $i] : ((Xa = p(Xx18)) & (Xx = |'0'|) & member_succeeds(neg(p(Xx18)), Xi)) | ?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx16: $i] : ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx17: $i] : ((Xa = neg(Xx17)) & (Xx = |'1'|) & eval_succeeds(Xx17, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy))))) | ?[Xx19: $i] : ((Xa = p(Xx19)) & (Xx = |'1'|) & member_succeeds(p(Xx19), Xi))))), rewrite(((?[Xx18: $i] : ((Xa = p(Xx18)) & (Xx = |'0'|) & member_succeeds(neg(p(Xx18)), Xi)) | ?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx16: $i] : ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx17: $i] : ((Xa = neg(Xx17)) & (Xx = |'1'|) & eval_succeeds(Xx17, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy))))) | ?[Xx19: $i] : ((Xa = p(Xx19)) & (Xx = |'1'|) & member_succeeds(p(Xx19), Xi))) <=> (?[Xx18: $i] : ((Xa = p(Xx18)) & (Xx = |'0'|) & member_succeeds(neg(p(Xx18)), Xi)) | ?[Xx19: $i] : ((Xa = p(Xx19)) & (Xx = |'1'|) & member_succeeds(p(Xx19), Xi)) | ?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx16: $i] : ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx17: $i] : ((Xa = neg(Xx17)) & (Xx = |'1'|) & eval_succeeds(Xx17, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy)))))), ((((((((((?[Xx4: $i, Xx5: $i] : ((((((Xa = or(Xx4, Xx5)) & (Xx = |'0'|)) & eval_succeeds(Xx4, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx4, Xi, Xy) => (|'0'| = Xy)))) & eval_succeeds(Xx5, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx5, Xi, Xy) => (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((((Xa = or(Xx6, Xx7)) & (Xx = |'1'|)) & eval_succeeds(Xx7, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx7, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx8: $i, Xx9: $i] : ((((Xa = or(Xx8, Xx9)) & (Xx = |'1'|)) & eval_succeeds(Xx8, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx8, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx10: $i, Xx11: $i] : ((((Xa = and(Xx10, Xx11)) & (Xx = |'0'|)) & eval_succeeds(Xx11, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx11, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx12: $i, Xx13: $i] : ((((Xa = and(Xx12, Xx13)) & (Xx = |'0'|)) & eval_succeeds(Xx12, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx12, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx14: $i, Xx15: $i] : ((((((Xa = and(Xx14, Xx15)) & (Xx = |'1'|)) & eval_succeeds(Xx14, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx14, Xi, Xy) => (|'1'| = Xy)))) & eval_succeeds(Xx15, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx15, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx16: $i] : ((((Xa = neg(Xx16)) & (Xx = |'0'|)) & eval_succeeds(Xx16, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx16, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx17: $i] : ((((Xa = neg(Xx17)) & (Xx = |'1'|)) & eval_succeeds(Xx17, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx17, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx18: $i] : (((Xa = p(Xx18)) & (Xx = |'0'|)) & member_succeeds(neg(p(Xx18)), Xi))) | ?[Xx19: $i] : (((Xa = p(Xx19)) & (Xx = |'1'|)) & member_succeeds(p(Xx19), Xi))) <=> (?[Xx18: $i] : ((Xa = p(Xx18)) & (Xx = |'0'|) & member_succeeds(neg(p(Xx18)), Xi)) | ?[Xx19: $i] : ((Xa = p(Xx19)) & (Xx = |'1'|) & member_succeeds(p(Xx19), Xi)) | ?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx16: $i] : ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx17: $i] : ((Xa = neg(Xx17)) & (Xx = |'1'|) & eval_succeeds(Xx17, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy))))))), trans(monotonicity(quant_intro(proof_bind(^[Xy: $i] : rewrite((eval_succeeds(Xa, Xi, Xy) => (Xx = Xy)) <=> ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)))), (![Xy: $i] : (eval_succeeds(Xa, Xi, Xy) => (Xx = Xy)) <=> ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)))), ((interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xa, Xi, Xy) => (Xx = Xy))) <=> (interpretation_succeeds(Xi) => ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy))))), rewrite((interpretation_succeeds(Xi) => ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy))) <=> ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)))), ((interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xa, Xi, Xy) => (Xx = Xy))) <=> ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy))))), (((((((((((?[Xx4: $i, Xx5: $i] : ((((((Xa = or(Xx4, Xx5)) & (Xx = |'0'|)) & eval_succeeds(Xx4, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx4, Xi, Xy) => (|'0'| = Xy)))) & eval_succeeds(Xx5, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx5, Xi, Xy) => (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((((Xa = or(Xx6, Xx7)) & (Xx = |'1'|)) & eval_succeeds(Xx7, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx7, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx8: $i, Xx9: $i] : ((((Xa = or(Xx8, Xx9)) & (Xx = |'1'|)) & eval_succeeds(Xx8, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx8, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx10: $i, Xx11: $i] : ((((Xa = and(Xx10, Xx11)) & (Xx = |'0'|)) & eval_succeeds(Xx11, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx11, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx12: $i, Xx13: $i] : ((((Xa = and(Xx12, Xx13)) & (Xx = |'0'|)) & eval_succeeds(Xx12, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx12, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx14: $i, Xx15: $i] : ((((((Xa = and(Xx14, Xx15)) & (Xx = |'1'|)) & eval_succeeds(Xx14, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx14, Xi, Xy) => (|'1'| = Xy)))) & eval_succeeds(Xx15, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx15, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx16: $i] : ((((Xa = neg(Xx16)) & (Xx = |'0'|)) & eval_succeeds(Xx16, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx16, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx17: $i] : ((((Xa = neg(Xx17)) & (Xx = |'1'|)) & eval_succeeds(Xx17, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx17, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx18: $i] : (((Xa = p(Xx18)) & (Xx = |'0'|)) & member_succeeds(neg(p(Xx18)), Xi))) | ?[Xx19: $i] : (((Xa = p(Xx19)) & (Xx = |'1'|)) & member_succeeds(p(Xx19), Xi))) => (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xa, Xi, Xy) => (Xx = Xy)))) <=> ((?[Xx18: $i] : ((Xa = p(Xx18)) & (Xx = |'0'|) & member_succeeds(neg(p(Xx18)), Xi)) | ?[Xx19: $i] : ((Xa = p(Xx19)) & (Xx = |'1'|) & member_succeeds(p(Xx19), Xi)) | ?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx16: $i] : ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx17: $i] : ((Xa = neg(Xx17)) & (Xx = |'1'|) & eval_succeeds(Xx17, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy))))) => ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)))))), rewrite(((?[Xx18: $i] : ((Xa = p(Xx18)) & (Xx = |'0'|) & member_succeeds(neg(p(Xx18)), Xi)) | ?[Xx19: $i] : ((Xa = p(Xx19)) & (Xx = |'1'|) & member_succeeds(p(Xx19), Xi)) | ?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx16: $i] : ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx17: $i] : ((Xa = neg(Xx17)) & (Xx = |'1'|) & eval_succeeds(Xx17, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy))))) => ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)))) <=> ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)) | (~(?[Xx18: $i] : ((Xa = p(Xx18)) & (Xx = |'0'|) & member_succeeds(neg(p(Xx18)), Xi)) | ?[Xx19: $i] : ((Xa = p(Xx19)) & (Xx = |'1'|) & member_succeeds(p(Xx19), Xi)) | ?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx16: $i] : ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx17: $i] : ((Xa = neg(Xx17)) & (Xx = |'1'|) & eval_succeeds(Xx17, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy)))))))), (((((((((((?[Xx4: $i, Xx5: $i] : ((((((Xa = or(Xx4, Xx5)) & (Xx = |'0'|)) & eval_succeeds(Xx4, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx4, Xi, Xy) => (|'0'| = Xy)))) & eval_succeeds(Xx5, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx5, Xi, Xy) => (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((((Xa = or(Xx6, Xx7)) & (Xx = |'1'|)) & eval_succeeds(Xx7, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx7, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx8: $i, Xx9: $i] : ((((Xa = or(Xx8, Xx9)) & (Xx = |'1'|)) & eval_succeeds(Xx8, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx8, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx10: $i, Xx11: $i] : ((((Xa = and(Xx10, Xx11)) & (Xx = |'0'|)) & eval_succeeds(Xx11, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx11, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx12: $i, Xx13: $i] : ((((Xa = and(Xx12, Xx13)) & (Xx = |'0'|)) & eval_succeeds(Xx12, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx12, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx14: $i, Xx15: $i] : ((((((Xa = and(Xx14, Xx15)) & (Xx = |'1'|)) & eval_succeeds(Xx14, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx14, Xi, Xy) => (|'1'| = Xy)))) & eval_succeeds(Xx15, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx15, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx16: $i] : ((((Xa = neg(Xx16)) & (Xx = |'0'|)) & eval_succeeds(Xx16, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx16, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx17: $i] : ((((Xa = neg(Xx17)) & (Xx = |'1'|)) & eval_succeeds(Xx17, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx17, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx18: $i] : (((Xa = p(Xx18)) & (Xx = |'0'|)) & member_succeeds(neg(p(Xx18)), Xi))) | ?[Xx19: $i] : (((Xa = p(Xx19)) & (Xx = |'1'|)) & member_succeeds(p(Xx19), Xi))) => (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xa, Xi, Xy) => (Xx = Xy)))) <=> ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)) | (~(?[Xx18: $i] : ((Xa = p(Xx18)) & (Xx = |'0'|) & member_succeeds(neg(p(Xx18)), Xi)) | ?[Xx19: $i] : ((Xa = p(Xx19)) & (Xx = |'1'|) & member_succeeds(p(Xx19), Xi)) | ?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx16: $i] : ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx17: $i] : ((Xa = neg(Xx17)) & (Xx = |'1'|) & eval_succeeds(Xx17, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy)))))))))),
% 0.64/0.78 inference(bind,[status(th)],[])).
% 0.64/0.78 tff(74,plain,
% 0.64/0.78 (![Xa: $i, Xi: $i, Xx: $i] : ((((((((((?[Xx4: $i, Xx5: $i] : ((((((Xa = or(Xx4, Xx5)) & (Xx = |'0'|)) & eval_succeeds(Xx4, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx4, Xi, Xy) => (|'0'| = Xy)))) & eval_succeeds(Xx5, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx5, Xi, Xy) => (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((((Xa = or(Xx6, Xx7)) & (Xx = |'1'|)) & eval_succeeds(Xx7, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx7, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx8: $i, Xx9: $i] : ((((Xa = or(Xx8, Xx9)) & (Xx = |'1'|)) & eval_succeeds(Xx8, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx8, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx10: $i, Xx11: $i] : ((((Xa = and(Xx10, Xx11)) & (Xx = |'0'|)) & eval_succeeds(Xx11, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx11, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx12: $i, Xx13: $i] : ((((Xa = and(Xx12, Xx13)) & (Xx = |'0'|)) & eval_succeeds(Xx12, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx12, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx14: $i, Xx15: $i] : ((((((Xa = and(Xx14, Xx15)) & (Xx = |'1'|)) & eval_succeeds(Xx14, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx14, Xi, Xy) => (|'1'| = Xy)))) & eval_succeeds(Xx15, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx15, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx16: $i] : ((((Xa = neg(Xx16)) & (Xx = |'0'|)) & eval_succeeds(Xx16, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx16, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx17: $i] : ((((Xa = neg(Xx17)) & (Xx = |'1'|)) & eval_succeeds(Xx17, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx17, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx18: $i] : (((Xa = p(Xx18)) & (Xx = |'0'|)) & member_succeeds(neg(p(Xx18)), Xi))) | ?[Xx19: $i] : (((Xa = p(Xx19)) & (Xx = |'1'|)) & member_succeeds(p(Xx19), Xi))) => (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xa, Xi, Xy) => (Xx = Xy)))) <=> ![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)) | (~(?[Xx18: $i] : ((Xa = p(Xx18)) & (Xx = |'0'|) & member_succeeds(neg(p(Xx18)), Xi)) | ?[Xx19: $i] : ((Xa = p(Xx19)) & (Xx = |'1'|) & member_succeeds(p(Xx19), Xi)) | ?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx16: $i] : ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx17: $i] : ((Xa = neg(Xx17)) & (Xx = |'1'|) & eval_succeeds(Xx17, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy)))))))),
% 0.64/0.79 inference(quant_intro,[status(thm)],[73])).
% 0.64/0.79 tff(75,plain,
% 0.64/0.79 ((![Xa: $i, Xi: $i, Xx: $i] : ((((((((((?[Xx4: $i, Xx5: $i] : ((((((Xa = or(Xx4, Xx5)) & (Xx = |'0'|)) & eval_succeeds(Xx4, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx4, Xi, Xy) => (|'0'| = Xy)))) & eval_succeeds(Xx5, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx5, Xi, Xy) => (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((((Xa = or(Xx6, Xx7)) & (Xx = |'1'|)) & eval_succeeds(Xx7, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx7, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx8: $i, Xx9: $i] : ((((Xa = or(Xx8, Xx9)) & (Xx = |'1'|)) & eval_succeeds(Xx8, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx8, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx10: $i, Xx11: $i] : ((((Xa = and(Xx10, Xx11)) & (Xx = |'0'|)) & eval_succeeds(Xx11, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx11, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx12: $i, Xx13: $i] : ((((Xa = and(Xx12, Xx13)) & (Xx = |'0'|)) & eval_succeeds(Xx12, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx12, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx14: $i, Xx15: $i] : ((((((Xa = and(Xx14, Xx15)) & (Xx = |'1'|)) & eval_succeeds(Xx14, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx14, Xi, Xy) => (|'1'| = Xy)))) & eval_succeeds(Xx15, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx15, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx16: $i] : ((((Xa = neg(Xx16)) & (Xx = |'0'|)) & eval_succeeds(Xx16, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx16, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx17: $i] : ((((Xa = neg(Xx17)) & (Xx = |'1'|)) & eval_succeeds(Xx17, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx17, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx18: $i] : (((Xa = p(Xx18)) & (Xx = |'0'|)) & member_succeeds(neg(p(Xx18)), Xi))) | ?[Xx19: $i] : (((Xa = p(Xx19)) & (Xx = |'1'|)) & member_succeeds(p(Xx19), Xi))) => (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xa, Xi, Xy) => (Xx = Xy)))) => ![Xa: $i, Xi: $i, Xx: $i] : (eval_succeeds(Xa, Xi, Xx) => (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xa, Xi, Xy) => (Xx = Xy))))) <=> (![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)) | (~(?[Xx18: $i] : ((Xa = p(Xx18)) & (Xx = |'0'|) & member_succeeds(neg(p(Xx18)), Xi)) | ?[Xx19: $i] : ((Xa = p(Xx19)) & (Xx = |'1'|) & member_succeeds(p(Xx19), Xi)) | ?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx16: $i] : ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx17: $i] : ((Xa = neg(Xx17)) & (Xx = |'1'|) & eval_succeeds(Xx17, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy))))))) => ![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | (~eval_succeeds(Xa, Xi, Xx)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy))))),
% 0.64/0.79 inference(monotonicity,[status(thm)],[74, 72])).
% 0.64/0.79 tff(76,plain,
% 0.64/0.79 ((![Xa: $i, Xi: $i, Xx: $i] : ((((((((((?[Xx4: $i, Xx5: $i] : ((((((Xa = or(Xx4, Xx5)) & (Xx = |'0'|)) & eval_succeeds(Xx4, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx4, Xi, Xy) => (|'0'| = Xy)))) & eval_succeeds(Xx5, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx5, Xi, Xy) => (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((((Xa = or(Xx6, Xx7)) & (Xx = |'1'|)) & eval_succeeds(Xx7, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx7, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx8: $i, Xx9: $i] : ((((Xa = or(Xx8, Xx9)) & (Xx = |'1'|)) & eval_succeeds(Xx8, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx8, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx10: $i, Xx11: $i] : ((((Xa = and(Xx10, Xx11)) & (Xx = |'0'|)) & eval_succeeds(Xx11, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx11, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx12: $i, Xx13: $i] : ((((Xa = and(Xx12, Xx13)) & (Xx = |'0'|)) & eval_succeeds(Xx12, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx12, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx14: $i, Xx15: $i] : ((((((Xa = and(Xx14, Xx15)) & (Xx = |'1'|)) & eval_succeeds(Xx14, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx14, Xi, Xy) => (|'1'| = Xy)))) & eval_succeeds(Xx15, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx15, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx16: $i] : ((((Xa = neg(Xx16)) & (Xx = |'0'|)) & eval_succeeds(Xx16, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx16, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx17: $i] : ((((Xa = neg(Xx17)) & (Xx = |'1'|)) & eval_succeeds(Xx17, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx17, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx18: $i] : (((Xa = p(Xx18)) & (Xx = |'0'|)) & member_succeeds(neg(p(Xx18)), Xi))) | ?[Xx19: $i] : (((Xa = p(Xx19)) & (Xx = |'1'|)) & member_succeeds(p(Xx19), Xi))) => (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xa, Xi, Xy) => (Xx = Xy)))) => ![Xa: $i, Xi: $i, Xx: $i] : (eval_succeeds(Xa, Xi, Xx) => (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xa, Xi, Xy) => (Xx = Xy))))) <=> ((~![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)) | (~(?[Xx18: $i] : ((Xa = p(Xx18)) & (Xx = |'0'|) & member_succeeds(neg(p(Xx18)), Xi)) | ?[Xx19: $i] : ((Xa = p(Xx19)) & (Xx = |'1'|) & member_succeeds(p(Xx19), Xi)) | ?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx16: $i] : ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx17: $i] : ((Xa = neg(Xx17)) & (Xx = |'1'|) & eval_succeeds(Xx17, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy)))))))) | ![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | (~eval_succeeds(Xa, Xi, Xx)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy))))),
% 0.64/0.79 inference(transitivity,[status(thm)],[75, 70])).
% 0.64/0.79 tff(77,axiom,(![Xa: $i, Xi: $i, Xx: $i] : ((((((((((?[Xx4: $i, Xx5: $i] : ((((((Xa = or(Xx4, Xx5)) & (Xx = |'0'|)) & eval_succeeds(Xx4, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx4, Xi, Xy) => (|'0'| = Xy)))) & eval_succeeds(Xx5, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx5, Xi, Xy) => (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((((Xa = or(Xx6, Xx7)) & (Xx = |'1'|)) & eval_succeeds(Xx7, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx7, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx8: $i, Xx9: $i] : ((((Xa = or(Xx8, Xx9)) & (Xx = |'1'|)) & eval_succeeds(Xx8, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx8, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx10: $i, Xx11: $i] : ((((Xa = and(Xx10, Xx11)) & (Xx = |'0'|)) & eval_succeeds(Xx11, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx11, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx12: $i, Xx13: $i] : ((((Xa = and(Xx12, Xx13)) & (Xx = |'0'|)) & eval_succeeds(Xx12, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx12, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx14: $i, Xx15: $i] : ((((((Xa = and(Xx14, Xx15)) & (Xx = |'1'|)) & eval_succeeds(Xx14, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx14, Xi, Xy) => (|'1'| = Xy)))) & eval_succeeds(Xx15, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx15, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx16: $i] : ((((Xa = neg(Xx16)) & (Xx = |'0'|)) & eval_succeeds(Xx16, Xi, |'1'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx16, Xi, Xy) => (|'1'| = Xy))))) | ?[Xx17: $i] : ((((Xa = neg(Xx17)) & (Xx = |'1'|)) & eval_succeeds(Xx17, Xi, |'0'|)) & (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xx17, Xi, Xy) => (|'0'| = Xy))))) | ?[Xx18: $i] : (((Xa = p(Xx18)) & (Xx = |'0'|)) & member_succeeds(neg(p(Xx18)), Xi))) | ?[Xx19: $i] : (((Xa = p(Xx19)) & (Xx = |'1'|)) & member_succeeds(p(Xx19), Xi))) => (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xa, Xi, Xy) => (Xx = Xy)))) => ![Xa: $i, Xi: $i, Xx: $i] : (eval_succeeds(Xa, Xi, Xx) => (interpretation_succeeds(Xi) => ![Xy: $i] : (eval_succeeds(Xa, Xi, Xy) => (Xx = Xy))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','induction')).
% 0.64/0.79 tff(78,plain,
% 0.64/0.79 ((~![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)) | (~(?[Xx18: $i] : ((Xa = p(Xx18)) & (Xx = |'0'|) & member_succeeds(neg(p(Xx18)), Xi)) | ?[Xx19: $i] : ((Xa = p(Xx19)) & (Xx = |'1'|) & member_succeeds(p(Xx19), Xi)) | ?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx16: $i] : ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx17: $i] : ((Xa = neg(Xx17)) & (Xx = |'1'|) & eval_succeeds(Xx17, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy)))))))) | ![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | (~eval_succeeds(Xa, Xi, Xx)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)))),
% 0.64/0.79 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.64/0.79 tff(79,plain,
% 0.64/0.79 ((~![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)) | (~(?[Xx18: $i] : ((Xa = p(Xx18)) & (Xx = |'0'|) & member_succeeds(neg(p(Xx18)), Xi)) | ?[Xx19: $i] : ((Xa = p(Xx19)) & (Xx = |'1'|) & member_succeeds(p(Xx19), Xi)) | ?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx16: $i] : ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx17: $i] : ((Xa = neg(Xx17)) & (Xx = |'1'|) & eval_succeeds(Xx17, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy)))))))) | ![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | (~eval_succeeds(Xa, Xi, Xx)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)))),
% 0.64/0.79 inference(modus_ponens,[status(thm)],[78, 69])).
% 0.64/0.79 tff(80,plain,
% 0.64/0.79 ((~![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)) | (~(?[Xx18: $i] : ((Xa = p(Xx18)) & (Xx = |'0'|) & member_succeeds(neg(p(Xx18)), Xi)) | ?[Xx19: $i] : ((Xa = p(Xx19)) & (Xx = |'1'|) & member_succeeds(p(Xx19), Xi)) | ?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx16: $i] : ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx17: $i] : ((Xa = neg(Xx17)) & (Xx = |'1'|) & eval_succeeds(Xx17, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy)))))))) | ![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | (~eval_succeeds(Xa, Xi, Xx)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)))),
% 0.64/0.79 inference(modus_ponens,[status(thm)],[79, 69])).
% 0.64/0.79 tff(81,plain,
% 0.64/0.79 ((~![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)) | (~(?[Xx18: $i] : ((Xa = p(Xx18)) & (Xx = |'0'|) & member_succeeds(neg(p(Xx18)), Xi)) | ?[Xx19: $i] : ((Xa = p(Xx19)) & (Xx = |'1'|) & member_succeeds(p(Xx19), Xi)) | ?[Xx8: $i, Xx9: $i] : ((Xa = or(Xx8, Xx9)) & (Xx = |'1'|) & eval_succeeds(Xx8, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx8, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx10: $i, Xx11: $i] : ((Xa = and(Xx10, Xx11)) & (Xx = |'0'|) & eval_succeeds(Xx11, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx11, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx4: $i, Xx5: $i] : ((Xa = or(Xx4, Xx5)) & (Xx = |'0'|) & eval_succeeds(Xx4, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx4, Xi, Xy)) | (|'0'| = Xy))) & eval_succeeds(Xx5, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx5, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx6: $i, Xx7: $i] : ((Xa = or(Xx6, Xx7)) & (Xx = |'1'|) & eval_succeeds(Xx7, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx7, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx12: $i, Xx13: $i] : ((Xa = and(Xx12, Xx13)) & (Xx = |'0'|) & eval_succeeds(Xx12, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx12, Xi, Xy)) | (|'0'| = Xy)))) | ?[Xx14: $i, Xx15: $i] : ((Xa = and(Xx14, Xx15)) & (Xx = |'1'|) & eval_succeeds(Xx14, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx14, Xi, Xy)) | (|'1'| = Xy))) & eval_succeeds(Xx15, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx15, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx16: $i] : ((Xa = neg(Xx16)) & (Xx = |'0'|) & eval_succeeds(Xx16, Xi, |'1'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx16, Xi, Xy)) | (|'1'| = Xy)))) | ?[Xx17: $i] : ((Xa = neg(Xx17)) & (Xx = |'1'|) & eval_succeeds(Xx17, Xi, |'0'|) & ((~interpretation_succeeds(Xi)) | ![Xy: $i] : ((~eval_succeeds(Xx17, Xi, Xy)) | (|'0'| = Xy)))))))) | ![Xa: $i, Xi: $i, Xx: $i] : ((~interpretation_succeeds(Xi)) | (~eval_succeeds(Xa, Xi, Xx)) | ![Xy: $i] : ((~eval_succeeds(Xa, Xi, Xy)) | (Xx = Xy)))),
% 0.64/0.79 inference(modus_ponens,[status(thm)],[80, 69])).
% 0.64/0.79 Proof display could not be completed: monotonicity rule is not handled
% 0.64/0.80 % E exiting
%------------------------------------------------------------------------------