0.00/0.00 % Leo-III: Strategy 1 (for '60') 61.78/33.05 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 61.78/33.05 % [INFO] Parsing done (312ms). 61.78/33.05 % [INFO] Running in sequential loop mode. 61.78/33.05 % [CONFIG] Using configuration: timeout(60) with strategy 61.78/33.05 % [INFO] eprover registered as external prover. 61.78/33.05 % [INFO] cvc4 registered as external prover. 61.78/33.05 % [INFO] Parsing finished. Scanning for conjecture ... 61.78/33.05 % [INFO] Found a conjecture and 355 axioms. Running axiom selection ... 61.78/33.05 % [INFO] Axiom selection finished. Selected 169 axioms (removed 186 axioms). 61.78/33.05 % [INFO] Problem is higher-order (TPTP THF). 61.78/33.05 % [INFO] Type checking passed. Searching for refutation ... 61.78/33.05 % External prover 'cvc4' found a proof! 61.78/33.05 % [INFO] Killing All external provers ... 61.78/33.05 % Time passed: 32609ms (effective reasoning time: 31918ms) 61.78/33.05 % Solved by strategy 61.78/33.05 % Axioms used in derivation (169): fact_10_ir__Seq1, fact_87_WhileFalse, fact_305_ir__While__backwards__frontier, fact_306_add_Oleft__neutral, fact_299_ir__valid__If, fact_15_ir__Skip__sym, fact_279_add__left__cancel, fact_28_Seq__assoc, fact_349_add__0__iff, fact_42_old_Oprod_Oexhaust, fact_324_zero__induct, fact_0_soundness, fact_80_sim__while__cong, fact_283_group__cancel_Oadd2, fact_2_ir__valid__decomp, fact_17_com_Odistinct_I1_J, fact_16_ir__Skip, fact_30_SkipE, fact_333_add__eq__self__zero, fact_18_com_Oinject_I2_J, fact_284_add_Oassoc, fact_304_While__backwards__frontier__ir__valid, fact_295_ir__valid__Seq1_H, fact_252_fun__upd__idem__iff, fact_276_nat__arith_Osuc1, fact_31_Skip, fact_64_while__unfold, fact_5_ir__pre, fact_24_com_Odistinct_I9_J, fact_193_AssignE, fact_319_old_Onat_Odistinct_I2_J, fact_98_Assign__complete, fact_286_add_Oleft__commute, fact_320_old_Onat_Odistinct_I1_J, fact_38_sim__trans, fact_314_Nat_Oadd__0__right, fact_302_ir__valid__get__back, fact_201_fun__upd__triv, fact_72_com_Odistinct_I15_J, fact_309_add__cancel__left__right, fact_84_IfFalse, fact_323_diff__induct, fact_285_add_Ocommute, fact_307_add_Oright__neutral, fact_73_com_Odistinct_I11_J, fact_296_ir__valid__track__history, fact_61_triv__if, fact_55_surj__pair, fact_53_prod__cases, fact_66_com_Oinject_I3_J, fact_258_fun__upd__def, fact_67_com_Odistinct_I19_J, fact_197_ir__While__True, fact_20_Seq__ir__valid, fact_256_fun__upd__idem, fact_313_zero__eq__add__iff__both__eq__0, fact_25_ir__valid__def, fact_281_add__mono__thms__linordered__semiring_I4_J, fact_147_If__False__ir__valid, fact_290_Assign__ir__valid, fact_312_add__eq__0__iff__both__eq__0, fact_23_Skip__ir__valid, fact_22_meh__simp, fact_350_verit__sum__simplify, fact_297_decomp__def, fact_148_While__False__ir__valid, fact_117_disj__ir__valid, fact_327_Zero__not__Suc, fact_14_conseq__ir__valid, fact_27_SeqE, fact_11_ir__sym, fact_65_com_Oinject_I4_J, fact_192_ir__If__True, fact_26_com_Odistinct_I3_J, fact_250_n__not__Suc__n, fact_19_com_Oinject_I1_J, fact_278_add__right__cancel, fact_202_fun__upd__apply, fact_196_ir__While__False, fact_329_old_Onat_Oinducts, fact_347_Euclid__induct, fact_82_IfE, fact_341_com_Osize__gen_I5_J, fact_343_com_Osize_I8_J, fact_334_plus__nat_Oadd__0, fact_6_ir__post, fact_291_ir__Assign, fact_81_sim__while__cong__aux, fact_146_If__True__ir__valid, fact_339_com_Osize__gen_I1_J, fact_83_IfTrue, fact_257_fun__upd__eqD, fact_254_fun__upd__other, fact_277_add__Suc__shift, fact_13_Seq2__ir__valid, fact_35_old_Oprod_Oinject, fact_321_nat_OdiscI, fact_338_com_Osize__gen_I3_J, fact_161_ir__disj, fact_301_ir__valid__While1, fact_70_com_Odistinct_I13_J, fact_280_ab__semigroup__add__class_Oadd__ac_I1_J, fact_317_get__back_Osimps_I1_J, fact_308_add__cancel__left__left, fact_253_fun__upd__twist, fact_346_com_Osize_I10_J, fact_69_com_Odistinct_I17_J, fact_56_big__step__determ, fact_340_com_Osize__gen_I2_J, fact_326_Zero__neq__Suc, fact_162_assign__upd__blah, fact_1_completeness, fact_287_add__left__imp__eq, fact_325_Suc__neq__Zero, fact_275_add__Suc, fact_315_add__is__0, fact_36_sim__sym, fact_200_fun__upd__upd, fact_7_ir__conseq, fact_163_flip__def, fact_322_nat__induct, fact_51_Pair__inject, fact_318_nat_Odistinct_I1_J, fact_300_get__back_Osimps_I2_J, fact_344_com_Osize_I6_J, fact_99_While__True__ir__valid, fact_68_com_Odistinct_I7_J, fact_335_one__is__add, fact_29_Seq, fact_213_nat_Oinject, fact_328_old_Onat_Oexhaust, fact_8_ir__valid__decomp1, fact_311_add__cancel__right__right, fact_79_com_Oexhaust, fact_195_Assign, fact_337_com_Osize__gen_I4_J, fact_310_add__cancel__right__left, fact_298_ir__valid__Seq1, fact_40_old_Oprod_Oinducts, fact_255_fun__upd__same, fact_345_com_Osize_I7_J, fact_33_prod_Oinject, fact_100_While__backwards__frontier__ir__valid_H, fact_37_sim__refl, fact_282_group__cancel_Oadd1, fact_251_Suc__inject, fact_331_comm__monoid__add__class_Oadd__0, fact_85_WhileE, fact_303_ir__valid__While3, fact_332_add_Ocomm__neutral, fact_60_commute__if, fact_212_old_Onat_Oinject, fact_21_sym__ir__valid, fact_4_ir__hoare__Skip__Skip, fact_294_ir__valid__While2, fact_194_assign__simp, fact_330_not0__implies__Suc, fact_3_ir__Skip__Skip, fact_198_add__Suc__right, fact_288_add__right__imp__eq, fact_86_WhileTrue, fact_12_Seq1__ir__valid, fact_78_com_Oinduct, fact_191_ir__If__False, fact_336_add__is__1, fact_342_com_Osize_I9_J, fact_149_Assign__blah, fact_9_ir__valid__decomp2, fact_71_com_Odistinct_I5_J 61.78/33.05 % No. of inferences in proof: 342 61.78/33.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 32609 ms resp. 31918 ms w/o parsing 61.78/33.05 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 61.78/33.05 thf(set_Pr1148378109ar_int_type, type, set_Pr1148378109ar_int: $tType). 61.78/33.05 thf(set_Pr866150653nt_com_type, type, set_Pr866150653nt_com: $tType). 61.78/33.05 thf(produc1260470173ar_int_type, type, produc1260470173ar_int: $tType). 61.78/33.05 thf(produc1166363805nt_com_type, type, produc1166363805nt_com: $tType). 61.78/33.05 thf(set_set_nat_type, type, set_set_nat: $tType). 61.78/33.05 thf(list_char_type, type, list_char: $tType). 61.78/33.05 thf(set_nat_type, type, set_nat: $tType). 61.78/33.05 thf(set_o_type, type, set_o: $tType). 61.78/33.05 thf(bexp_type, type, bexp: $tType). 61.78/33.05 thf(aexp_type, type, aexp: $tType). 61.78/33.05 thf(nat_type, type, nat: $tType). 61.78/33.05 thf(int_type, type, int: $tType). 61.78/33.05 thf(com_type, type, com: $tType). 61.78/33.05 thf(aval_type, type, aval: (aexp > ((list_char > int) > int))). 61.78/33.05 thf(bval_type, type, bval: (bexp > ((list_char > int) > $o))). 61.78/33.05 thf(big_big_step_type, type, big_big_step: (produc1260470173ar_int > ((list_char > int) > $o))). 61.78/33.05 thf(assign_type, type, assign: (list_char > (aexp > com))). 61.78/33.05 thf(if_type, type, if: (bexp > (com > (com > com)))). 61.78/33.05 thf(skip_type, type, skip: com). 61.78/33.05 thf(seq_type, type, seq: (com > (com > com))). 61.78/33.05 thf(while_type, type, while: (bexp > (com > com))). 61.78/33.05 thf(size_com_type, type, size_com: (com > nat)). 61.78/33.05 thf(fun_up103088396ar_int_type, type, fun_up103088396ar_int: ((list_char > int) > (list_char > (int > (list_char > int))))). 61.78/33.05 thf(plus_plus_nat_type, type, plus_plus_nat: (nat > (nat > nat))). 61.78/33.05 thf(zero_zero_nat_type, type, zero_zero_nat: nat). 61.78/33.05 thf(if_int_type, type, if_int: ($o > (int > (int > int)))). 61.78/33.05 thf(suc_type, type, suc: (nat > nat)). 61.78/33.05 thf(size_size_com_type, type, size_size_com: (com > nat)). 61.78/33.05 thf(produc1193801173ar_int_type, type, produc1193801173ar_int: (com > ((list_char > int) > produc1260470173ar_int))). 61.78/33.05 thf(relati1310524937decomp_type, type, relati1310524937decomp: (((list_char > int) > ((list_char > int) > $o)) > (com > (com > (((list_char > int) > ((list_char > int) > $o)) > ((list_char > int) > ((list_char > int) > $o))))))). 61.78/33.05 thf(relati186416454e_flip_type, type, relati186416454e_flip: (((list_char > int) > ((list_char > int) > $o)) > ((list_char > int) > ((list_char > int) > $o)))). 61.78/33.05 thf(relati23543761ar_int_type, type, relati23543761ar_int: (((list_char > int) > ((list_char > int) > $o)) > (bexp > (com > (nat > ((list_char > int) > ((list_char > int) > $o))))))). 61.78/33.05 thf(relati2102071307_hoare_type, type, relati2102071307_hoare: (((list_char > int) > ((list_char > int) > $o)) > (com > (com > (((list_char > int) > ((list_char > int) > $o)) > $o))))). 61.78/33.05 thf(relati775585786_valid_type, type, relati775585786_valid: (((list_char > int) > ((list_char > int) > $o)) > (com > (com > (((list_char > int) > ((list_char > int) > $o)) > $o))))). 61.78/33.05 thf(p_type, type, p: ((list_char > int) > ((list_char > int) > $o))). 61.78/33.05 thf(q_type, type, q: ((list_char > int) > ((list_char > int) > $o))). 61.78/33.05 thf(c_type, type, c: com). 61.78/33.05 thf(c2_type, type, c2: com). 61.78/33.05 thf(92,axiom,((! [A:(nat > $o),B:nat]: ((A @ B) => ((A @ zero_zero_nat) <= (! [C:nat]: ((A @ (suc @ C)) => (A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_zero__induct)). 61.78/33.05 thf(485,plain,((! [A:(nat > $o),B:nat]: ((A @ B) => ((A @ zero_zero_nat) | ~ (! [C:nat]: ((A @ (suc @ C)) => (A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 61.78/33.05 thf(134,axiom,((! [A:(nat > ((list_char > int) > ((list_char > int) > $o))),B:bexp,C:com,D:com,E:((list_char > int) > ((list_char > int) > $o))]: ((! [F:nat]: (relati2102071307_hoare @ (^ [G:(list_char > int),H:(list_char > int)]: ((bval @ B @ G) & (A @ F @ G @ H))) @ C @ skip @ (A @ (suc @ F)))) => ((relati2102071307_hoare @ (A @ zero_zero_nat) @ (while @ B @ C) @ D @ E) <= (relati2102071307_hoare @ (^ [F:(list_char > int),G:(list_char > int)]: ? [H:nat]: (A @ H @ F @ G)) @ (while @ B @ C) @ D @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_ir__While__backwards__frontier)). 61.78/33.05 thf(637,plain,((! [A:(nat > ((list_char > int) > ((list_char > int) > $o))),B:bexp,C:com,D:com,E:((list_char > int) > ((list_char > int) > $o))]: ((! [F:nat]: (relati2102071307_hoare @ (^ [G:(list_char > int),H:(list_char > int)]: ((bval @ B @ G) & (A @ F @ G @ H))) @ C @ skip @ (A @ (suc @ F)))) => ((relati2102071307_hoare @ (A @ zero_zero_nat) @ (while @ B @ C) @ D @ (E)) | ~ (relati2102071307_hoare @ (^ [F:(list_char > int),G:(list_char > int)]: ? [H:nat]: (A @ H @ F @ G)) @ (while @ B @ C) @ D @ (E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 61.78/33.05 thf(131,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o)),E:com,F:((list_char > int) > ((list_char > int) > $o))]: ((relati2102071307_hoare @ A @ B @ C @ D) => ((relati2102071307_hoare @ D @ E @ skip @ F) => (relati2102071307_hoare @ A @ (seq @ B @ E) @ C @ F))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_ir__Seq1)). 61.78/33.05 thf(629,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o)),E:com,F:((list_char > int) > ((list_char > int) > $o))]: ((relati2102071307_hoare @ (A) @ B @ C @ (D)) => ((relati2102071307_hoare @ (D) @ E @ skip @ (F)) => (relati2102071307_hoare @ (A) @ (seq @ B @ E) @ C @ (F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])). 61.78/33.05 thf(167,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:bexp,C:com,D:((list_char > int) > ((list_char > int) > $o)),E:com]: ((relati2102071307_hoare @ A @ (while @ B @ E) @ C @ D) <= (relati2102071307_hoare @ (^ [F:(list_char > int),G:(list_char > int)]: (~ (bval @ B @ F) & (A @ F @ G))) @ skip @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_ir__While__False)). 61.78/33.05 thf(760,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:bexp,C:com,D:((list_char > int) > ((list_char > int) > $o)),E:com]: ((relati2102071307_hoare @ (A) @ (while @ B @ E) @ C @ (D)) | ~ (relati2102071307_hoare @ (^ [F:(list_char > int),G:(list_char > int)]: (~ (bval @ B @ F) & (A @ F @ G))) @ skip @ C @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])). 61.78/33.05 thf(53,axiom,((! [A:com,B:(list_char > int),C:(list_char > int),D:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ A @ B) @ C) => ((big_big_step @ (produc1193801173ar_int @ A @ B) @ D) => (D = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_big__step__determ)). 61.78/33.05 thf(347,plain,((! [A:com,B:(list_char > int),C:(list_char > int),D:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ A @ (B)) @ (C)) => ((big_big_step @ (produc1193801173ar_int @ A @ (B)) @ (D)) => ((D) = (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 61.78/33.05 thf(21,axiom,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_add__0__iff)). 61.78/33.05 thf(234,plain,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 61.78/33.05 thf(111,axiom,((! [A:nat,B:nat]: ((A != zero_zero_nat) <= (A = (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_nat_OdiscI)). 61.78/33.05 thf(555,plain,((! [A:nat,B:nat]: (~ (A = zero_zero_nat) | ~ (A = (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 61.78/33.05 thf(91,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((((! [D:nat,E:nat]: ((A @ (suc @ D) @ (suc @ E)) <= (A @ D @ E))) => (A @ B @ C)) <= (! [D:nat]: (A @ zero_zero_nat @ (suc @ D)))) <= (! [D:nat]: (A @ D @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_diff__induct)). 61.78/33.05 thf(481,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: (((! [D:nat,E:nat]: ((A @ (suc @ D) @ (suc @ E)) | ~ (A @ D @ E))) => (A @ B @ C)) | ~ (! [D:nat]: (A @ zero_zero_nat @ (suc @ D))) | ~ (! [D:nat]: (A @ D @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 61.78/33.05 thf(49,axiom,((! [A:com,B:com,C:com,D:com]: (((seq @ A @ B) = (seq @ C @ D)) = ((A = C) & (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_com_Oinject_I2_J)). 61.78/33.05 thf(333,plain,((! [A:com,B:com,C:com,D:com]: (((seq @ A @ B) = (seq @ C @ D)) = ((A = C) & (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 61.78/33.05 thf(26,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = A) = (B = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_add__cancel__left__right)). 61.78/33.05 thf(249,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = A) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 61.78/33.05 thf(71,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_Zero__neq__Suc)). 61.78/33.05 thf(408,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 61.78/33.05 thf(161,axiom,((! [A:bexp,B:com,C:com]: (skip != (if @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_com_Odistinct_I5_J)). 61.78/33.05 thf(741,plain,((! [A:bexp,B:com,C:com]: ~ (skip = (if @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])). 61.78/33.05 thf(79,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o))]: ((relati775585786_valid @ (relati186416454e_flip @ A) @ B @ C @ (relati186416454e_flip @ D)) => (relati775585786_valid @ A @ C @ B @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_sym__ir__valid)). 61.78/33.05 thf(440,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o))]: ((relati775585786_valid @ (relati186416454e_flip @ A) @ B @ C @ (relati186416454e_flip @ D)) => (relati775585786_valid @ (A) @ C @ B @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 61.78/33.05 thf(12,axiom,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_plus__nat_Oadd__0)). 61.78/33.05 thf(202,plain,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 61.78/33.05 thf(157,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:list_char,C:aexp,D:com,E:((list_char > int) > ((list_char > int) > $o))]: ((relati2102071307_hoare @ (^ [F:(list_char > int),G:(list_char > int)]: ? [H:int]: (((F @ B) = (aval @ C @ (fun_up103088396ar_int @ F @ B @ H))) & (A @ (fun_up103088396ar_int @ F @ B @ H) @ G))) @ skip @ D @ E) => (relati2102071307_hoare @ A @ (assign @ B @ C) @ D @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_ir__Assign)). 61.78/33.05 thf(730,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:list_char,C:aexp,D:com,E:((list_char > int) > ((list_char > int) > $o))]: ((relati2102071307_hoare @ (^ [F:(list_char > int),G:(list_char > int)]: ? [H:int]: (((F @ B) = (aval @ C @ (fun_up103088396ar_int @ F @ B @ H))) & (A @ (fun_up103088396ar_int @ F @ B @ H) @ G))) @ skip @ D @ (E)) => (relati2102071307_hoare @ (A) @ (assign @ B @ C) @ D @ (E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])). 61.78/33.05 thf(16,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_Nat_Oadd__0__right)). 61.78/33.05 thf(217,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 61.78/33.05 thf(63,axiom,((! [A:com,B:com,C:(list_char > int),D:(list_char > int)]: ((~ (! [E:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ A @ C) @ E) => (~ (big_big_step @ (produc1193801173ar_int @ B @ E) @ D))))) <= (big_big_step @ (produc1193801173ar_int @ (seq @ A @ B) @ C) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_SeqE)). 61.78/33.05 thf(385,plain,((! [A:com,B:com,C:(list_char > int),D:(list_char > int)]: (~ (! [E:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ A @ (C)) @ (E)) => (~ (big_big_step @ (produc1193801173ar_int @ B @ (E)) @ (D))))) | ~ (big_big_step @ (produc1193801173ar_int @ (seq @ A @ B) @ (C)) @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])). 61.78/33.05 thf(51,axiom,((! [A:nat]: ((suc @ A) != zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_old_Onat_Odistinct_I2_J)). 61.78/33.05 thf(340,plain,((! [A:nat]: ~ ((suc @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 61.78/33.05 thf(107,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:bexp,C:com,D:com,E:((list_char > int) > ((list_char > int) > $o)),F:com]: ((relati775585786_valid @ (^ [G:(list_char > int),H:(list_char > int)]: (~ (bval @ B @ G) & (A @ G @ H))) @ C @ D @ E) => (relati775585786_valid @ A @ (if @ B @ F @ C) @ D @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_If__False__ir__valid)). 61.78/33.05 thf(538,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:bexp,C:com,D:com,E:((list_char > int) > ((list_char > int) > $o)),F:com]: ((relati775585786_valid @ (^ [G:(list_char > int),H:(list_char > int)]: (~ (bval @ B @ G) & (A @ G @ H))) @ C @ D @ (E)) => (relati775585786_valid @ (A) @ (if @ B @ F @ C) @ D @ (E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 61.78/33.05 thf(3,axiom,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_add_Oleft__neutral)). 61.78/33.05 thf(174,plain,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 61.78/33.05 thf(151,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o)),E:com,F:((list_char > int) > ((list_char > int) > $o))]: ((relati775585786_valid @ A @ B @ C @ D) => ((relati775585786_valid @ A @ (seq @ B @ E) @ C @ F) <= (relati775585786_valid @ D @ E @ skip @ F))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_Seq1__ir__valid)). 61.78/33.05 thf(709,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o)),E:com,F:((list_char > int) > ((list_char > int) > $o))]: ((relati775585786_valid @ (A) @ B @ C @ (D)) => ((relati775585786_valid @ (A) @ (seq @ B @ E) @ C @ (F)) | ~ (relati775585786_valid @ (D) @ E @ skip @ (F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])). 61.78/33.05 thf(38,axiom,((! [A:com,B:com,C:bexp]: ((! [D:(list_char > int),E:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ (while @ C @ A) @ D) @ E) = (big_big_step @ (produc1193801173ar_int @ (while @ C @ B) @ D) @ E))) <= (! [D:(list_char > int),E:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ A @ D) @ E) = (big_big_step @ (produc1193801173ar_int @ B @ D) @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_sim__while__cong)). 61.78/33.05 thf(288,plain,((! [A:com,B:com,C:bexp]: (! [D:(list_char > int),E:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ (while @ C @ A) @ (D)) @ (E)) = (big_big_step @ (produc1193801173ar_int @ (while @ C @ B) @ (D)) @ (E))) | ~ (! [D:(list_char > int),E:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ A @ (D)) @ (E)) = (big_big_step @ (produc1193801173ar_int @ B @ (D)) @ (E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 61.78/33.05 thf(78,axiom,((! [A:list_char,B:aexp,C:bexp,D:com,E:com]: ((assign @ A @ B) != (if @ C @ D @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_com_Odistinct_I11_J)). 61.78/33.05 thf(436,plain,((! [A:list_char,B:aexp,C:bexp,D:com,E:com]: ~ ((assign @ A @ B) = (if @ C @ D @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 61.78/33.05 thf(139,axiom,(((size_com @ skip) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_com_Osize__gen_I1_J)). 61.78/33.05 thf(651,plain,(((size_com @ skip) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 61.78/33.05 thf(155,axiom,((! [A:com,B:com]: (skip != (seq @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_com_Odistinct_I3_J)). 61.78/33.05 thf(724,plain,((! [A:com,B:com]: ~ (skip = (seq @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])). 61.78/33.05 thf(115,axiom,((! [A:bexp,B:com,C:com,D:bexp,E:com,F:com]: (((if @ A @ B @ C) = (if @ D @ E @ F)) = ((A = D) & (C = F) & (B = E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_com_Oinject_I3_J)). 61.78/33.05 thf(570,plain,((! [A:bexp,B:com,C:com,D:bexp,E:com,F:com]: (((if @ A @ B @ C) = (if @ D @ E @ F)) = ((A = D) & (C = F) & (B = E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 61.78/33.05 thf(61,axiom,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((A @ B) <= (! [C:nat]: ((A @ C) => (A @ (suc @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_nat__induct)). 61.78/33.05 thf(372,plain,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((A @ B) | ~ (! [C:nat]: ((A @ C) => (A @ (suc @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 61.78/33.05 thf(96,axiom,((! [A:produc1260470173ar_int]: ? [B:com,C:(list_char > int)]: (A = (produc1193801173ar_int @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_surj__pair)). 61.78/33.05 thf(504,plain,((! [A:produc1260470173ar_int]: ? [B:com,C:(list_char > int)]: (A = (produc1193801173ar_int @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 61.78/33.05 thf(120,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o)),E:((list_char > int) > ((list_char > int) > $o)),F:((list_char > int) > ((list_char > int) > $o))]: ((((relati775585786_valid @ E @ B @ C @ F) <= (! [G:(list_char > int),H:(list_char > int)]: ((D @ G @ H) <= (F @ G @ H)))) <= (! [G:(list_char > int),H:(list_char > int)]: ((E @ G @ H) <= (A @ G @ H)))) <= (relati775585786_valid @ A @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_conseq__ir__valid)). 61.78/33.05 thf(587,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o)),E:((list_char > int) > ((list_char > int) > $o)),F:((list_char > int) > ((list_char > int) > $o))]: ((relati775585786_valid @ (E) @ B @ C @ (F)) | ~ (! [G:(list_char > int),H:(list_char > int)]: ((D @ (G) @ (H)) | ~ (F @ (G) @ (H)))) | ~ (! [G:(list_char > int),H:(list_char > int)]: ((E @ (G) @ (H)) | ~ (A @ (G) @ (H)))) | ~ (relati775585786_valid @ (A) @ B @ C @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 61.78/33.05 thf(164,axiom,((! [A:list_char,B:aexp]: (skip != (assign @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_com_Odistinct_I1_J)). 61.78/33.05 thf(751,plain,((! [A:list_char,B:aexp]: ~ (skip = (assign @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])). 61.78/33.05 thf(52,axiom,((! [A:com,B:com,C:com,D:(list_char > int),E:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ (seq @ (seq @ A @ B) @ C) @ D) @ E) = (big_big_step @ (produc1193801173ar_int @ (seq @ A @ (seq @ B @ C)) @ D) @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_Seq__assoc)). 61.78/33.05 thf(344,plain,((! [A:com,B:com,C:com,D:(list_char > int),E:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ (seq @ (seq @ A @ B) @ C) @ (D)) @ (E)) = (big_big_step @ (produc1193801173ar_int @ (seq @ A @ (seq @ B @ C)) @ (D)) @ (E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 61.78/33.05 thf(56,axiom,((! [A:list_char,B:aexp,C:list_char,D:aexp]: (((assign @ A @ B) = (assign @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_com_Oinject_I1_J)). 61.78/33.05 thf(357,plain,((! [A:list_char,B:aexp,C:list_char,D:aexp]: (((assign @ A @ B) = (assign @ C @ D)) = ((B = D) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 61.78/33.05 thf(8,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ A @ (suc @ B)) = (suc @ (plus_plus_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_add__Suc__right)). 61.78/33.05 thf(189,plain,((! [A:nat,B:nat]: ((plus_plus_nat @ A @ (suc @ B)) = (suc @ (plus_plus_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 61.78/33.05 thf(125,axiom,((relati775585786_valid = (^ [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o))]: ! [E:(list_char > int),F:(list_char > int)]: ((? [G:(list_char > int),H:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ B @ G) @ E) & (big_big_step @ (produc1193801173ar_int @ C @ H) @ F) & (A @ G @ H))) <= (D @ E @ F))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_ir__valid__def)). 61.78/33.05 thf(606,plain,(((relati775585786_valid) = (^ [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o))]: ! [E:(list_char > int),F:(list_char > int)]: (? [G:(list_char > int),H:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ B @ G) @ E) & (big_big_step @ (produc1193801173ar_int @ C @ H) @ F) & (A @ G @ H)) | ~ (D @ E @ F))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 61.78/33.05 thf(81,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = (suc @ zero_zero_nat)) = (((B = (suc @ zero_zero_nat)) & (A = zero_zero_nat)) | ((B = zero_zero_nat) & (A = (suc @ zero_zero_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_add__is__1)). 61.78/33.05 thf(448,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = (suc @ zero_zero_nat)) = (((B = (suc @ zero_zero_nat)) & (A = zero_zero_nat)) | ((B = zero_zero_nat) & (A = (suc @ zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 61.78/33.05 thf(35,axiom,((! [A:(list_char > int),B:list_char,C:int,D:int]: ((fun_up103088396ar_int @ (fun_up103088396ar_int @ A @ B @ C) @ B @ D) = (fun_up103088396ar_int @ A @ B @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_fun__upd__upd)). 61.78/33.05 thf(280,plain,((! [A:(list_char > int),B:list_char,C:int,D:int]: ((fun_up103088396ar_int @ (fun_up103088396ar_int @ A @ B @ C) @ B @ D) = (fun_up103088396ar_int @ A @ B @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 61.78/33.05 thf(133,axiom,((! [A:(nat > ((list_char > int) > ((list_char > int) > $o))),B:bexp,C:com,D:com,E:((list_char > int) > ((list_char > int) > $o))]: ((! [F:nat]: (relati775585786_valid @ (^ [G:(list_char > int),H:(list_char > int)]: ((bval @ B @ G) & (A @ F @ G @ H))) @ C @ skip @ (A @ (suc @ F)))) => ((relati775585786_valid @ (^ [F:(list_char > int),G:(list_char > int)]: ? [H:nat]: (A @ H @ F @ G)) @ (while @ B @ C) @ D @ E) => (relati775585786_valid @ (A @ zero_zero_nat) @ (while @ B @ C) @ D @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_While__backwards__frontier__ir__valid)). 61.78/33.05 thf(634,plain,((! [A:(nat > ((list_char > int) > ((list_char > int) > $o))),B:bexp,C:com,D:com,E:((list_char > int) > ((list_char > int) > $o))]: ((! [F:nat]: (relati775585786_valid @ (^ [G:(list_char > int),H:(list_char > int)]: ((bval @ B @ G) & (A @ F @ G @ H))) @ C @ skip @ (A @ (suc @ F)))) => ((relati775585786_valid @ (^ [F:(list_char > int),G:(list_char > int)]: ? [H:nat]: (A @ H @ F @ G)) @ (while @ B @ C) @ D @ (E)) => (relati775585786_valid @ (A @ zero_zero_nat) @ (while @ B @ C) @ D @ (E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])). 61.78/33.05 thf(145,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o)),E:((list_char > int) > ((list_char > int) > $o))]: ((relati2102071307_hoare @ A @ B @ C @ D) => ((relati2102071307_hoare @ A @ B @ C @ E) <= (! [F:(list_char > int),G:(list_char > int)]: ((D @ F @ G) <= (E @ F @ G))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_ir__post)). 61.78/33.05 thf(692,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o)),E:((list_char > int) > ((list_char > int) > $o))]: ((relati2102071307_hoare @ (A) @ B @ C @ (D)) => ((relati2102071307_hoare @ (A) @ B @ C @ (E)) | ~ (! [F:(list_char > int),G:(list_char > int)]: ((D @ (F) @ (G)) | ~ (E @ (F) @ (G)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])). 61.78/33.05 thf(83,axiom,((! [A:list_char,B:aexp,C:bexp,D:com]: ((assign @ A @ B) != (while @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_com_Odistinct_I13_J)). 61.78/33.05 thf(453,plain,((! [A:list_char,B:aexp,C:bexp,D:com]: ~ ((assign @ A @ B) = (while @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 61.78/33.05 thf(76,axiom,((! [A:bexp,B:com,C:com]: ((size_com @ (if @ A @ B @ C)) = (plus_plus_nat @ (plus_plus_nat @ (size_com @ B) @ (size_com @ C)) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_com_Osize__gen_I4_J)). 61.78/33.05 thf(428,plain,((! [A:bexp,B:com,C:com]: ((size_com @ (if @ A @ B @ C)) = (plus_plus_nat @ (plus_plus_nat @ (size_com @ B) @ (size_com @ C)) @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 61.78/33.05 thf(31,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((A = (plus_plus_nat @ B @ C)) => ((plus_plus_nat @ D @ A) = (plus_plus_nat @ B @ (plus_plus_nat @ D @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_group__cancel_Oadd2)). 61.78/33.05 thf(265,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((A = (plus_plus_nat @ B @ C)) => ((plus_plus_nat @ D @ A) = (plus_plus_nat @ B @ (plus_plus_nat @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 61.78/33.05 thf(97,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:com,E:((list_char > int) > ((list_char > int) > $o))]: ((relati775585786_valid @ A @ (seq @ B @ C) @ D @ E) => (relati775585786_valid @ A @ B @ D @ (^ [F:(list_char > int),G:(list_char > int)]: ? [H:(list_char > int),I:(list_char > int)]: ((A @ H @ I) & ? [J:(list_char > int)]: ((E @ J @ G) & (big_big_step @ (produc1193801173ar_int @ C @ F) @ J)) & (big_big_step @ (produc1193801173ar_int @ D @ I) @ G) & (big_big_step @ (produc1193801173ar_int @ B @ H) @ F))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_ir__valid__Seq1)). 61.78/33.05 thf(507,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:com,E:((list_char > int) > ((list_char > int) > $o))]: ((relati775585786_valid @ (A) @ (seq @ B @ C) @ D @ (E)) => (relati775585786_valid @ (A) @ B @ D @ (^ [F:(list_char > int),G:(list_char > int)]: ? [H:(list_char > int),I:(list_char > int)]: ((A @ H @ I) & ? [J:(list_char > int)]: ((E @ J @ G) & (big_big_step @ (produc1193801173ar_int @ C @ F) @ J)) & (big_big_step @ (produc1193801173ar_int @ D @ I) @ G) & (big_big_step @ (produc1193801173ar_int @ B @ H) @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 61.78/33.05 thf(45,axiom,((! [A:(nat > ((list_char > int) > ((list_char > int) > $o))),B:nat,C:bexp,D:com,E:((list_char > int) > ((list_char > int) > $o)),F:com,G:(list_char > int),H:(list_char > int)]: ((! [I:nat,J:(list_char > int),K:(list_char > int)]: ((? [L:(list_char > int)]: ((A @ (plus_plus_nat @ B @ I) @ L @ K) & (bval @ C @ L) & (big_big_step @ (produc1193801173ar_int @ D @ L) @ J))) <= (A @ (plus_plus_nat @ B @ (suc @ I)) @ J @ K))) => (((E @ G @ H) => (? [I:(list_char > int),J:(list_char > int)]: ((A @ B @ I @ J) & (big_big_step @ (produc1193801173ar_int @ F @ J) @ H) & (big_big_step @ (produc1193801173ar_int @ (while @ C @ D) @ I) @ G)))) <= (! [I:(list_char > int),J:(list_char > int)]: ((E @ I @ J) => (? [K:(list_char > int),L:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ F @ L) @ J) & (big_big_step @ (produc1193801173ar_int @ (while @ C @ D) @ K) @ I) & ? [M:nat]: (A @ (plus_plus_nat @ B @ M) @ K @ L))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_While__backwards__frontier__ir__valid_H)). 61.78/33.05 thf(312,plain,((! [A:(nat > ((list_char > int) > ((list_char > int) > $o))),B:nat,C:bexp,D:com,E:((list_char > int) > ((list_char > int) > $o)),F:com,G:(list_char > int),H:(list_char > int)]: ((! [I:nat,J:(list_char > int),K:(list_char > int)]: (? [L:(list_char > int)]: ((A @ (plus_plus_nat @ B @ I) @ (L) @ (K)) & (bval @ C @ (L)) & (big_big_step @ (produc1193801173ar_int @ D @ (L)) @ (J))) | ~ (A @ (plus_plus_nat @ B @ (suc @ I)) @ (J) @ (K)))) => (((E @ (G) @ (H)) => (? [I:(list_char > int),J:(list_char > int)]: ((A @ B @ (I) @ (J)) & (big_big_step @ (produc1193801173ar_int @ F @ (J)) @ (H)) & (big_big_step @ (produc1193801173ar_int @ (while @ C @ D) @ (I)) @ (G))))) | ~ (! [I:(list_char > int),J:(list_char > int)]: ((E @ (I) @ (J)) => (? [K:(list_char > int),L:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ F @ (L)) @ (J)) & (big_big_step @ (produc1193801173ar_int @ (while @ C @ D) @ (K)) @ (I)) & ? [M:nat]: (A @ (plus_plus_nat @ B @ M) @ (K) @ (L)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 61.78/33.05 thf(67,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_old_Onat_Oinject)). 61.78/33.05 thf(397,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 61.78/33.05 thf(143,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o))]: ((relati2102071307_hoare @ A @ B @ C @ D) <= (relati775585786_valid @ A @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_completeness)). 61.78/33.05 thf(687,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o))]: ((relati2102071307_hoare @ (A) @ B @ C @ (D)) | ~ (relati775585786_valid @ (A) @ B @ C @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])). 61.78/33.05 thf(39,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:bexp,C:com,D:nat]: ((relati23543761ar_int @ A @ B @ C @ (suc @ D)) = (^ [E:(list_char > int),F:(list_char > int)]: ? [G:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ C @ G) @ E) & (relati23543761ar_int @ A @ B @ C @ D @ G @ F) & (bval @ B @ G)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_get__back_Osimps_I2_J)). 61.78/33.05 thf(292,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:bexp,C:com,D:nat]: ((relati23543761ar_int @ A @ B @ C @ (suc @ D)) = (^ [E:(list_char > int),F:(list_char > int)]: ? [G:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ C @ G) @ E) & (relati23543761ar_int @ A @ B @ C @ D @ G @ F) & (bval @ B @ G)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 61.78/33.05 thf(99,axiom,((! [A:(list_char > int),B:list_char,C:int]: (((fun_up103088396ar_int @ A @ B @ C) = A) <= ((A @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_fun__upd__idem)). 61.78/33.05 thf(512,plain,((! [A:(list_char > int),B:list_char,C:int]: (((fun_up103088396ar_int @ A @ B @ C) = (A)) | ~ ((A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 61.78/33.05 thf(32,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) => (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_add__right__imp__eq)). 61.78/33.05 thf(270,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) => (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 61.78/33.05 thf(106,axiom,((! [A:nat]: (A != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_n__not__Suc__n)). 61.78/33.05 thf(534,plain,((! [A:nat]: ~ (A = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 61.78/33.05 thf(17,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_verit__sum__simplify)). 61.78/33.05 thf(220,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 61.78/33.05 thf(59,axiom,((! [A:list_char,B:aexp,C:(list_char > int),D:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ (assign @ A @ B) @ C) @ D) = (D = (fun_up103088396ar_int @ C @ A @ (aval @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_assign__simp)). 61.78/33.05 thf(366,plain,((! [A:list_char,B:aexp,C:(list_char > int),D:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ (assign @ A @ B) @ (C)) @ (D)) = ((D) = (fun_up103088396ar_int @ C @ A @ (aval @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 61.78/33.05 thf(42,axiom,((! [A:bexp,B:(list_char > int),C:com,D:(list_char > int),E:(list_char > int)]: ((bval @ A @ B) => (((big_big_step @ (produc1193801173ar_int @ (while @ A @ C) @ D) @ E) => (big_big_step @ (produc1193801173ar_int @ (while @ A @ C) @ B) @ E)) <= (big_big_step @ (produc1193801173ar_int @ C @ B) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_WhileTrue)). 61.78/33.05 thf(302,plain,((! [A:bexp,B:(list_char > int),C:com,D:(list_char > int),E:(list_char > int)]: ((bval @ A @ (B)) => (((big_big_step @ (produc1193801173ar_int @ (while @ A @ C) @ (D)) @ (E)) => (big_big_step @ (produc1193801173ar_int @ (while @ A @ C) @ (B)) @ (E))) | ~ (big_big_step @ (produc1193801173ar_int @ C @ (B)) @ (D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 61.78/33.05 thf(9,axiom,((! [A:nat,B:nat]: ((zero_zero_nat = (plus_plus_nat @ A @ B)) = ((B = zero_zero_nat) & (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_zero__eq__add__iff__both__eq__0)). 61.78/33.05 thf(192,plain,((! [A:nat,B:nat]: ((zero_zero_nat = (plus_plus_nat @ A @ B)) = ((B = zero_zero_nat) & (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 61.78/33.05 thf(27,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_add__left__cancel)). 61.78/33.05 thf(252,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 61.78/33.05 thf(47,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:bexp,C:com,D:nat,E:com,F:((list_char > int) > ((list_char > int) > $o))]: ((relati775585786_valid @ (relati23543761ar_int @ A @ B @ C @ D) @ (while @ B @ C) @ E @ F) => (relati775585786_valid @ (^ [G:(list_char > int),H:(list_char > int)]: ((bval @ B @ G) & (relati23543761ar_int @ A @ B @ C @ D @ G @ H))) @ C @ E @ (^ [G:(list_char > int),H:(list_char > int)]: ? [I:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ E @ I) @ H) & (relati23543761ar_int @ A @ B @ C @ (suc @ D) @ G @ I) & ? [J:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ (while @ B @ C) @ G) @ J) & (F @ J @ H)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_ir__valid__While3)). 61.78/33.05 thf(329,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:bexp,C:com,D:nat,E:com,F:((list_char > int) > ((list_char > int) > $o))]: ((relati775585786_valid @ (relati23543761ar_int @ A @ B @ C @ D) @ (while @ B @ C) @ E @ (F)) => (relati775585786_valid @ (^ [G:(list_char > int),H:(list_char > int)]: ((bval @ B @ G) & (relati23543761ar_int @ A @ B @ C @ D @ G @ H))) @ C @ E @ (^ [G:(list_char > int),H:(list_char > int)]: ? [I:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ E @ I) @ H) & (relati23543761ar_int @ A @ B @ C @ (suc @ D) @ G @ I) & ? [J:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ (while @ B @ C) @ G) @ J) & (F @ J @ H)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 61.78/33.05 thf(85,axiom,((! [A:nat]: ((suc @ A) != zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_Suc__neq__Zero)). 61.78/33.05 thf(461,plain,((! [A:nat]: ~ ((suc @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 61.78/33.05 thf(141,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:bexp,C:com,D:com,E:((list_char > int) > ((list_char > int) > $o))]: ((relati2102071307_hoare @ A @ (while @ B @ C) @ D @ E) <= (relati2102071307_hoare @ (^ [F:(list_char > int),G:(list_char > int)]: ((A @ F @ G) & (bval @ B @ F))) @ (seq @ C @ (while @ B @ C)) @ D @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_ir__While__True)). 61.78/33.05 thf(682,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:bexp,C:com,D:com,E:((list_char > int) > ((list_char > int) > $o))]: ((relati2102071307_hoare @ (A) @ (while @ B @ C) @ D @ (E)) | ~ (relati2102071307_hoare @ (^ [F:(list_char > int),G:(list_char > int)]: ((A @ F @ G) & (bval @ B @ F))) @ (seq @ C @ (while @ B @ C)) @ D @ (E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])). 61.78/33.05 thf(110,axiom,((! [A:list_char,B:list_char,C:(list_char > int),D:int]: (((fun_up103088396ar_int @ C @ B @ D @ A) = (C @ A)) <= (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_fun__upd__other)). 61.78/33.05 thf(551,plain,((! [A:list_char,B:list_char,C:(list_char > int),D:int]: (((fun_up103088396ar_int @ (C) @ B @ D @ A) = (C @ A)) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 61.78/33.05 thf(37,axiom,((! [A:bexp,B:(list_char > int),C:com,D:(list_char > int),E:com]: ((bval @ A @ B) => ((big_big_step @ (produc1193801173ar_int @ (if @ A @ C @ E) @ B) @ D) <= (big_big_step @ (produc1193801173ar_int @ C @ B) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_IfTrue)). 61.78/33.05 thf(285,plain,((! [A:bexp,B:(list_char > int),C:com,D:(list_char > int),E:com]: ((bval @ A @ (B)) => ((big_big_step @ (produc1193801173ar_int @ (if @ A @ C @ E) @ (B)) @ (D)) | ~ (big_big_step @ (produc1193801173ar_int @ C @ (B)) @ (D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 61.78/33.05 thf(119,axiom,((! [A:com,B:com,C:bexp,D:com]: ((seq @ A @ B) != (while @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_com_Odistinct_I17_J)). 61.78/33.05 thf(583,plain,((! [A:com,B:com,C:bexp,D:com]: ~ ((seq @ A @ B) = (while @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 61.78/33.05 thf(102,axiom,((! [A:list_char,B:aexp,C:(list_char > int)]: (big_big_step @ (produc1193801173ar_int @ (assign @ A @ B) @ C) @ (fun_up103088396ar_int @ C @ A @ (aval @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_Assign)). 61.78/33.05 thf(522,plain,((! [A:list_char,B:aexp,C:(list_char > int)]: (big_big_step @ (produc1193801173ar_int @ (assign @ A @ B) @ (C)) @ (fun_up103088396ar_int @ C @ A @ (aval @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 61.78/33.05 thf(64,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:bexp,C:com,D:com,E:((list_char > int) > ((list_char > int) > $o)),F:com]: ((relati775585786_valid @ A @ (if @ B @ C @ F) @ D @ E) <= (relati775585786_valid @ (^ [G:(list_char > int),H:(list_char > int)]: ((A @ G @ H) & (bval @ B @ G))) @ C @ D @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_If__True__ir__valid)). 61.78/33.05 thf(388,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:bexp,C:com,D:com,E:((list_char > int) > ((list_char > int) > $o)),F:com]: ((relati775585786_valid @ (A) @ (if @ B @ C @ F) @ D @ (E)) | ~ (relati775585786_valid @ (^ [G:(list_char > int),H:(list_char > int)]: ((A @ G @ H) & (bval @ B @ G))) @ C @ D @ (E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 61.78/33.05 thf(121,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o)),E:((list_char > int) > ((list_char > int) > $o)),F:((list_char > int) > ((list_char > int) > $o))]: ((relati775585786_valid @ A @ B @ C @ D) => ((relati775585786_valid @ E @ B @ C @ F) => (relati775585786_valid @ (^ [G:(list_char > int),H:(list_char > int)]: ((A @ G @ H) | (E @ G @ H))) @ B @ C @ (^ [G:(list_char > int),H:(list_char > int)]: ((D @ G @ H) | (F @ G @ H)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_disj__ir__valid)). 61.78/33.05 thf(593,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o)),E:((list_char > int) > ((list_char > int) > $o)),F:((list_char > int) > ((list_char > int) > $o))]: ((relati775585786_valid @ (A) @ B @ C @ (D)) => ((relati775585786_valid @ (E) @ B @ C @ (F)) => (relati775585786_valid @ (^ [G:(list_char > int),H:(list_char > int)]: ((A @ G @ H) | (E @ G @ H))) @ B @ C @ (^ [G:(list_char > int),H:(list_char > int)]: ((D @ G @ H) | (F @ G @ H)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 61.78/33.05 thf(137,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:bexp,C:com,D:nat,E:com,F:((list_char > int) > ((list_char > int) > $o))]: ((relati775585786_valid @ (^ [G:(list_char > int),H:(list_char > int)]: ((relati23543761ar_int @ A @ B @ C @ D @ G @ H) & (bval @ B @ G))) @ C @ skip @ (^ [G:(list_char > int),H:(list_char > int)]: ((relati23543761ar_int @ A @ B @ C @ (suc @ D) @ G @ H) & ? [I:(list_char > int),J:(list_char > int)]: ((F @ I @ J) & (big_big_step @ (produc1193801173ar_int @ E @ H) @ J) & (big_big_step @ (produc1193801173ar_int @ (while @ B @ C) @ G) @ I))))) <= (relati775585786_valid @ (relati23543761ar_int @ A @ B @ C @ D) @ (while @ B @ C) @ E @ F)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_ir__valid__While1)). 61.78/33.05 thf(647,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:bexp,C:com,D:nat,E:com,F:((list_char > int) > ((list_char > int) > $o))]: ((relati775585786_valid @ (^ [G:(list_char > int),H:(list_char > int)]: ((relati23543761ar_int @ A @ B @ C @ D @ G @ H) & (bval @ B @ G))) @ C @ skip @ (^ [G:(list_char > int),H:(list_char > int)]: ((relati23543761ar_int @ A @ B @ C @ (suc @ D) @ G @ H) & ? [I:(list_char > int),J:(list_char > int)]: ((F @ I @ J) & (big_big_step @ (produc1193801173ar_int @ E @ H) @ J) & (big_big_step @ (produc1193801173ar_int @ (while @ B @ C) @ G) @ I))))) | ~ (relati775585786_valid @ (relati23543761ar_int @ A @ B @ C @ D) @ (while @ B @ C) @ E @ (F))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])). 61.78/33.05 thf(160,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:bexp,C:com,D:((list_char > int) > ((list_char > int) > $o)),E:com]: ((relati775585786_valid @ (^ [F:(list_char > int),G:(list_char > int)]: (~ (bval @ B @ F) & (A @ F @ G))) @ skip @ C @ D) => (relati775585786_valid @ A @ (while @ B @ E) @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_While__False__ir__valid)). 61.78/33.05 thf(738,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:bexp,C:com,D:((list_char > int) > ((list_char > int) > $o)),E:com]: ((relati775585786_valid @ (^ [F:(list_char > int),G:(list_char > int)]: (~ (bval @ B @ F) & (A @ F @ G))) @ skip @ C @ (D)) => (relati775585786_valid @ (A) @ (while @ B @ E) @ C @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 61.78/33.05 thf(84,axiom,((! [A:nat,B:nat]: ((A = B) <= ((suc @ A) = (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_Suc__inject)). 61.78/33.05 thf(457,plain,((! [A:nat,B:nat]: ((A = B) | ~ ((suc @ A) = (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 61.78/33.05 thf(22,axiom,((plus_plus_nat = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_add_Ocommute)). 61.78/33.05 thf(237,plain,(((plus_plus_nat) = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 61.78/33.05 thf(57,axiom,((! [A:bexp,B:com,C:com]: ((size_size_com @ (if @ A @ B @ C)) = (plus_plus_nat @ (plus_plus_nat @ (size_size_com @ B) @ (size_size_com @ C)) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_com_Osize_I9_J)). 61.78/33.05 thf(360,plain,((! [A:bexp,B:com,C:com]: ((size_size_com @ (if @ A @ B @ C)) = (plus_plus_nat @ (plus_plus_nat @ (size_size_com @ B) @ (size_size_com @ C)) @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 61.78/33.05 thf(13,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = B) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_add__cancel__left__left)). 61.78/33.05 thf(205,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = B) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 61.78/33.05 thf(108,axiom,((! [A:(produc1260470173ar_int > $o),B:produc1260470173ar_int]: ((! [C:com,D:(list_char > int)]: (A @ (produc1193801173ar_int @ C @ D))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_prod__cases)). 61.78/33.05 thf(541,plain,((! [A:(produc1260470173ar_int > $o),B:produc1260470173ar_int]: ((! [C:com,D:(list_char > int)]: (A @ (produc1193801173ar_int @ C @ (D)))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 61.78/33.05 thf(169,axiom,((! [A:(list_char > int),B:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ skip @ A) @ B) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_meh__simp)). 61.78/33.05 thf(765,plain,((! [A:(list_char > int),B:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ skip @ (A)) @ (B)) = ((A) = (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])). 61.78/33.05 thf(153,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:bexp,C:com,D:com,E:((list_char > int) > ((list_char > int) > $o))]: ((relati775585786_valid @ (^ [F:(list_char > int),G:(list_char > int)]: ((A @ F @ G) & ~ (bval @ B @ F))) @ skip @ D @ (^ [F:(list_char > int),G:(list_char > int)]: ((E @ F @ G) & ? [H:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ D @ H) @ G) & (A @ F @ H) & ~ (bval @ B @ F))))) <= (relati775585786_valid @ A @ (while @ B @ C) @ D @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_ir__valid__While2)). 61.78/33.05 thf(718,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:bexp,C:com,D:com,E:((list_char > int) > ((list_char > int) > $o))]: ((relati775585786_valid @ (^ [F:(list_char > int),G:(list_char > int)]: ((A @ F @ G) & ~ (bval @ B @ F))) @ skip @ D @ (^ [F:(list_char > int),G:(list_char > int)]: ((E @ F @ G) & ? [H:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ D @ H) @ G) & (A @ F @ H) & ~ (bval @ B @ F))))) | ~ (relati775585786_valid @ (A) @ (while @ B @ C) @ D @ (E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 61.78/33.05 thf(72,axiom,((! [A:bexp,B:com,C:(list_char > int),D:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ (while @ A @ B) @ C) @ D) => ((~ ((! [E:(list_char > int)]: ((~ (big_big_step @ (produc1193801173ar_int @ (while @ A @ B) @ E) @ D)) <= (big_big_step @ (produc1193801173ar_int @ B @ C) @ E))) <= (bval @ A @ C))) <= ((bval @ A @ C) <= (D = C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_WhileE)). 61.78/33.05 thf(412,plain,((! [A:bexp,B:com,C:(list_char > int),D:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ (while @ A @ B) @ (C)) @ (D)) => (~ (! [E:(list_char > int)]: (~ (big_big_step @ (produc1193801173ar_int @ (while @ A @ B) @ (E)) @ (D)) | ~ (big_big_step @ (produc1193801173ar_int @ B @ (C)) @ (E))) | ~ (bval @ A @ (C))) | ~ ((bval @ A @ (C)) | ~ ((D) = (C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 61.78/33.05 thf(127,axiom,((! [A:nat]: ((? [B:nat]: (A = (suc @ B))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_not0__implies__Suc)). 61.78/33.05 thf(618,plain,((! [A:nat]: (? [B:nat]: (A = (suc @ B)) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 61.78/33.05 thf(75,axiom,((! [A:list_char,B:aexp]: ((size_size_com @ (assign @ A @ B)) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_com_Osize_I7_J)). 61.78/33.05 thf(425,plain,((! [A:list_char,B:aexp]: ((size_size_com @ (assign @ A @ B)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 61.78/33.05 thf(162,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o))]: ((relati775585786_valid @ A @ B @ C @ D) => ((relati775585786_valid @ (relati1310524937decomp @ A @ B @ C @ D) @ skip @ C @ D) & (relati775585786_valid @ A @ B @ skip @ (relati1310524937decomp @ A @ B @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_ir__valid__decomp1)). 61.78/33.05 thf(745,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o))]: ((relati775585786_valid @ (A) @ B @ C @ (D)) => ((relati775585786_valid @ (relati1310524937decomp @ A @ B @ C @ D) @ skip @ C @ (D)) & (relati775585786_valid @ (A) @ B @ skip @ (relati1310524937decomp @ A @ B @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])). 61.78/33.05 thf(116,axiom,((! [A:nat,B:nat]: (((suc @ zero_zero_nat) = (plus_plus_nat @ A @ B)) = (((B = zero_zero_nat) & (A = (suc @ zero_zero_nat))) | ((A = zero_zero_nat) & (B = (suc @ zero_zero_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_one__is__add)). 61.78/33.05 thf(573,plain,((! [A:nat,B:nat]: (((suc @ zero_zero_nat) = (plus_plus_nat @ A @ B)) = (((B = zero_zero_nat) & (A = (suc @ zero_zero_nat))) | ((A = zero_zero_nat) & (B = (suc @ zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 61.78/33.05 thf(5,axiom,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ B @ A)) = (B = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_add__cancel__right__left)). 61.78/33.05 thf(180,plain,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ B @ A)) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 61.78/33.05 thf(144,axiom,((! [A:bexp,B:com,C:(list_char > int),D:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ (while @ A @ B) @ C) @ D) = (big_big_step @ (produc1193801173ar_int @ (if @ A @ (seq @ B @ (while @ A @ B)) @ skip) @ C) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_while__unfold)). 61.78/33.05 thf(689,plain,((! [A:bexp,B:com,C:(list_char > int),D:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ (while @ A @ B) @ (C)) @ (D)) = (big_big_step @ (produc1193801173ar_int @ (if @ A @ (seq @ B @ (while @ A @ B)) @ skip) @ (C)) @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])). 61.78/33.05 thf(69,axiom,((! [A:list_char,B:aexp,C:(list_char > int),D:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ (assign @ A @ B) @ C) @ D) => (D = (fun_up103088396ar_int @ C @ A @ (aval @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_AssignE)). 61.78/33.05 thf(402,plain,((! [A:list_char,B:aexp,C:(list_char > int),D:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ (assign @ A @ B) @ (C)) @ (D)) => ((D) = (fun_up103088396ar_int @ C @ A @ (aval @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 61.78/33.05 thf(158,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:bexp,C:com,D:com,E:((list_char > int) > ((list_char > int) > $o)),F:com]: ((relati2102071307_hoare @ (^ [G:(list_char > int),H:(list_char > int)]: ((A @ G @ H) & (bval @ B @ G))) @ C @ D @ E) => (relati2102071307_hoare @ A @ (if @ B @ C @ F) @ D @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_ir__If__True)). 61.78/33.05 thf(732,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:bexp,C:com,D:com,E:((list_char > int) > ((list_char > int) > $o)),F:com]: ((relati2102071307_hoare @ (^ [G:(list_char > int),H:(list_char > int)]: ((A @ G @ H) & (bval @ B @ G))) @ C @ D @ (E)) => (relati2102071307_hoare @ (A) @ (if @ B @ C @ F) @ D @ (E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])). 61.78/33.05 thf(29,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) = (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_add__right__cancel)). 61.78/33.05 thf(259,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) = (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 61.78/33.05 thf(65,axiom,((! [A:(list_char > int),B:list_char]: ((fun_up103088396ar_int @ A @ B @ (A @ B)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_fun__upd__triv)). 61.78/33.05 thf(391,plain,((! [A:(list_char > int),B:list_char]: ((fun_up103088396ar_int @ A @ B @ (A @ B)) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 61.78/33.05 thf(62,axiom,((! [A:bexp,B:com,C:(list_char > int),D:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ (if @ A @ B @ B) @ C) @ D) = (big_big_step @ (produc1193801173ar_int @ B @ C) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_triv__if)). 61.78/33.05 thf(382,plain,((! [A:bexp,B:com,C:(list_char > int),D:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ (if @ A @ B @ B) @ (C)) @ (D)) = (big_big_step @ (produc1193801173ar_int @ B @ (C)) @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 61.78/33.05 thf(94,axiom,((! [A:list_char,B:aexp]: ((size_com @ (assign @ A @ B)) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_com_Osize__gen_I2_J)). 61.78/33.05 thf(498,plain,((! [A:list_char,B:aexp]: ((size_com @ (assign @ A @ B)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 61.78/33.05 thf(1,conjecture,(((relati2102071307_hoare @ p @ c @ c2 @ q) = ((relati2102071307_hoare @ p @ c @ skip @ (relati1310524937decomp @ p @ c @ c2 @ q)) & (relati2102071307_hoare @ (relati1310524937decomp @ p @ c @ c2 @ q) @ skip @ c2 @ q)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)). 61.78/33.05 thf(2,negated_conjecture,((~ ((relati2102071307_hoare @ p @ c @ c2 @ q) = ((relati2102071307_hoare @ p @ c @ skip @ (relati1310524937decomp @ p @ c @ c2 @ q)) & (relati2102071307_hoare @ (relati1310524937decomp @ p @ c @ c2 @ q) @ skip @ c2 @ q))))),inference(neg_conjecture,[status(cth)],[1])). 61.78/33.05 thf(172,plain,((~ ((relati2102071307_hoare @ (p) @ c @ c2 @ (q)) = ((relati2102071307_hoare @ (p) @ c @ skip @ (relati1310524937decomp @ p @ c @ c2 @ q)) & (relati2102071307_hoare @ (relati1310524937decomp @ p @ c @ c2 @ q) @ skip @ c2 @ (q)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 61.78/33.05 thf(33,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ (suc @ A) @ B) = (plus_plus_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_add__Suc__shift)). 61.78/33.05 thf(274,plain,((! [A:nat,B:nat]: ((plus_plus_nat @ (suc @ A) @ B) = (plus_plus_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 61.78/33.05 thf(73,axiom,((! [A:bexp,B:(list_char > int),C:com]: ((~ (bval @ A @ B)) => (big_big_step @ (produc1193801173ar_int @ (while @ A @ C) @ B) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_WhileFalse)). 61.78/33.05 thf(419,plain,((! [A:bexp,B:(list_char > int),C:com]: ((~ (bval @ A @ (B))) => (big_big_step @ (produc1193801173ar_int @ (while @ A @ C) @ (B)) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 61.78/33.05 thf(25,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((A = B) & (C = D)) => ((plus_plus_nat @ A @ C) = (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_add__mono__thms__linordered__semiring_I4_J)). 61.78/33.05 thf(245,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((A = B) & (C = D)) => ((plus_plus_nat @ A @ C) = (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 61.78/33.05 thf(14,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((A @ D @ E) = (A @ E @ D))) => (((A @ B @ C) <= (! [D:nat,E:nat]: ((A @ D @ (plus_plus_nat @ D @ E)) <= (A @ D @ E)))) <= (! [D:nat]: (A @ D @ zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_Euclid__induct)). 61.78/33.05 thf(208,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((A @ D @ E) = (A @ E @ D))) => ((A @ B @ C) | ~ (! [D:nat,E:nat]: ((A @ D @ (plus_plus_nat @ D @ E)) | ~ (A @ D @ E))) | ~ (! [D:nat]: (A @ D @ zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 61.78/33.05 thf(123,axiom,((! [A:bexp,B:com,C:com,D:bexp,E:com]: ((if @ A @ B @ C) != (while @ D @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_com_Odistinct_I19_J)). 61.78/33.05 thf(599,plain,((! [A:bexp,B:com,C:com,D:bexp,E:com]: ~ ((if @ A @ B @ C) = (while @ D @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 61.78/33.05 thf(82,axiom,((relati186416454e_flip = (^ [A:((list_char > int) > ((list_char > int) > $o)),B:(list_char > int),C:(list_char > int)]: (A @ C @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_flip__def)). 61.78/33.05 thf(451,plain,(((relati186416454e_flip) = (^ [A:((list_char > int) > ((list_char > int) > $o)),B:(list_char > int),C:(list_char > int)]: (A @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 61.78/33.05 thf(114,axiom,((! [A:(list_char > int),B:list_char,C:int]: ((fun_up103088396ar_int @ A @ B @ C @ B) = C))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_fun__upd__same)). 61.78/33.05 thf(567,plain,((! [A:(list_char > int),B:list_char,C:int]: ((fun_up103088396ar_int @ (A) @ B @ C @ B) = C))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 61.78/33.05 thf(98,axiom,((! [A:com,B:(list_char > int),C:com,D:(list_char > int)]: (((produc1193801173ar_int @ A @ B) = (produc1193801173ar_int @ C @ D)) = ((A = C) & (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_old_Oprod_Oinject)). 61.78/33.05 thf(509,plain,((! [A:com,B:(list_char > int),C:com,D:(list_char > int)]: (((produc1193801173ar_int @ A @ (B)) = (produc1193801173ar_int @ C @ (D))) = ((A = C) & ((B) = (D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])). 61.78/33.05 thf(138,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o))]: ((relati775585786_valid @ A @ B @ C @ D) <= (relati2102071307_hoare @ A @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_soundness)). 61.78/33.05 thf(649,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o))]: ((relati775585786_valid @ (A) @ B @ C @ (D)) | ~ (relati2102071307_hoare @ (A) @ B @ C @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 61.78/33.05 thf(90,axiom,((! [A:list_char,B:aexp,C:com,D:com]: ((assign @ A @ B) != (seq @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_com_Odistinct_I9_J)). 61.78/33.05 thf(477,plain,((! [A:list_char,B:aexp,C:com,D:com]: ~ ((assign @ A @ B) = (seq @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 61.78/33.05 thf(166,axiom,((relati775585786_valid = (^ [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o))]: ((relati775585786_valid @ A @ B @ skip @ (relati1310524937decomp @ A @ B @ C @ D)) & (relati775585786_valid @ (relati1310524937decomp @ A @ B @ C @ D) @ skip @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_ir__valid__decomp)). 61.78/33.05 thf(758,plain,(((relati775585786_valid) = (^ [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o))]: ((relati775585786_valid @ A @ B @ skip @ (relati1310524937decomp @ A @ B @ C @ D)) & (relati775585786_valid @ (relati1310524937decomp @ A @ B @ C @ D) @ skip @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])). 61.78/33.05 thf(128,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o)),E:com,F:com,G:((list_char > int) > ((list_char > int) > $o))]: (((relati775585786_valid @ D @ E @ F @ G) => (relati775585786_valid @ A @ (seq @ B @ E) @ (seq @ C @ F) @ G)) <= (relati775585786_valid @ A @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_Seq__ir__valid)). 61.78/33.05 thf(621,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o)),E:com,F:com,G:((list_char > int) > ((list_char > int) > $o))]: (((relati775585786_valid @ (D) @ E @ F @ (G)) => (relati775585786_valid @ (A) @ (seq @ B @ E) @ (seq @ C @ F) @ (G))) | ~ (relati775585786_valid @ (A) @ B @ C @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 61.78/33.05 thf(101,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:bexp,C:com,D:nat,E:com,F:((list_char > int) > ((list_char > int) > $o))]: ((relati775585786_valid @ (relati23543761ar_int @ A @ B @ C @ (suc @ D)) @ (while @ B @ C) @ E @ F) => (relati775585786_valid @ (relati23543761ar_int @ A @ B @ C @ D) @ (while @ B @ C) @ E @ F)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_ir__valid__get__back)). 61.78/33.05 thf(520,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:bexp,C:com,D:nat,E:com,F:((list_char > int) > ((list_char > int) > $o))]: ((relati775585786_valid @ (relati23543761ar_int @ A @ B @ C @ (suc @ D)) @ (while @ B @ C) @ E @ (F)) => (relati775585786_valid @ (relati23543761ar_int @ A @ B @ C @ D) @ (while @ B @ C) @ E @ (F))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 61.78/33.05 thf(11,axiom,((! [A:nat,B:nat,C:nat]: (((suc @ A) = (plus_plus_nat @ B @ (suc @ C))) <= (A = (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_nat__arith_Osuc1)). 61.78/33.05 thf(198,plain,((! [A:nat,B:nat,C:nat]: (((suc @ A) = (plus_plus_nat @ B @ (suc @ C))) | ~ (A = (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 61.78/33.05 thf(170,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:((list_char > int) > ((list_char > int) > $o))]: ((relati2102071307_hoare @ A @ skip @ skip @ B) = (! [C:(list_char > int),D:(list_char > int)]: ((B @ C @ D) => (A @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_ir__hoare__Skip__Skip)). 61.78/33.05 thf(768,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:((list_char > int) > ((list_char > int) > $o))]: ((relati2102071307_hoare @ (A) @ skip @ skip @ (B)) = (! [C:(list_char > int),D:(list_char > int)]: ((B @ (C) @ (D)) => (A @ (C) @ (D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])). 61.78/33.05 thf(66,axiom,((! [A:list_char,B:(list_char > int),C:aexp]: ((^ [D:list_char]: (if_int @ (D = A) @ (B @ A) @ (fun_up103088396ar_int @ B @ A @ (aval @ C @ B) @ D))) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_assign__upd__blah)). 61.78/33.05 thf(394,plain,((! [A:list_char,B:(list_char > int),C:aexp]: ((^ [D:list_char]: (if_int @ (D = A) @ (B @ A) @ (fun_up103088396ar_int @ B @ A @ (aval @ C @ B) @ D))) = (B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 61.78/33.05 thf(41,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:bexp,C:com]: ((relati23543761ar_int @ A @ B @ C @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_get__back_Osimps_I1_J)). 61.78/33.05 thf(299,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:bexp,C:com]: ((relati23543761ar_int @ A @ B @ C @ zero_zero_nat) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 61.78/33.05 thf(19,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((A = (plus_plus_nat @ B @ C)) => ((plus_plus_nat @ A @ D) = (plus_plus_nat @ B @ (plus_plus_nat @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_group__cancel_Oadd1)). 61.78/33.05 thf(226,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((A = (plus_plus_nat @ B @ C)) => ((plus_plus_nat @ A @ D) = (plus_plus_nat @ B @ (plus_plus_nat @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 61.78/33.05 thf(77,axiom,((! [A:bexp,B:com,C:com,D:(list_char > int),E:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ (if @ A @ B @ C) @ D) @ E) => ((~ ((~ (bval @ A @ D)) => (~ (big_big_step @ (produc1193801173ar_int @ C @ D) @ E)))) <= ((~ (big_big_step @ (produc1193801173ar_int @ B @ D) @ E)) <= (bval @ A @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_IfE)). 61.78/33.05 thf(431,plain,((! [A:bexp,B:com,C:com,D:(list_char > int),E:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ (if @ A @ B @ C) @ (D)) @ (E)) => (~ ((~ (bval @ A @ (D))) => (~ (big_big_step @ (produc1193801173ar_int @ C @ (D)) @ (E)))) | ~ (~ (big_big_step @ (produc1193801173ar_int @ B @ (D)) @ (E)) | ~ (bval @ A @ (D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 61.78/33.05 thf(140,axiom,((! [A:(com > $o),B:com]: ((A @ skip) => ((((! [C:bexp,D:com,E:com]: ((A @ D) => ((A @ E) => (A @ (if @ C @ D @ E))))) => ((! [C:bexp,D:com]: ((A @ D) => (A @ (while @ C @ D)))) => (A @ B))) <= (! [C:com,D:com]: (((A @ (seq @ C @ D)) <= (A @ D)) <= (A @ C)))) <= (! [C:list_char,D:aexp]: (A @ (assign @ C @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_com_Oinduct)). 61.78/33.05 thf(653,plain,((! [A:(com > $o),B:com]: ((A @ skip) => (((! [C:bexp,D:com,E:com]: ((A @ D) => ((A @ E) => (A @ (if @ C @ D @ E))))) => ((! [C:bexp,D:com]: ((A @ D) => (A @ (while @ C @ D)))) => (A @ B))) | ~ (! [C:com,D:com]: ((A @ (seq @ C @ D)) | ~ (A @ D) | ~ (A @ C))) | ~ (! [C:list_char,D:aexp]: (A @ (assign @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 61.78/33.05 thf(18,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_add__is__0)). 61.78/33.05 thf(223,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 61.78/33.05 thf(126,axiom,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((! [C:nat]: ((A @ C) => (A @ (suc @ C)))) => (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_old_Onat_Oinducts)). 61.78/33.05 thf(608,plain,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((! [C:nat]: ((A @ C) => (A @ (suc @ C)))) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 61.78/33.05 thf(89,axiom,((! [A:produc1260470173ar_int]: ~ (! [B:com,C:(list_char > int)]: (A != (produc1193801173ar_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_old_Oprod_Oexhaust)). 61.78/33.05 thf(473,plain,((! [A:produc1260470173ar_int]: ~ (! [B:com,C:(list_char > int)]: ~ (A = (produc1193801173ar_int @ B @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 61.78/33.05 thf(105,axiom,((! [A:(list_char > int),B:list_char,C:int,D:(list_char > int),E:int]: (((fun_up103088396ar_int @ A @ B @ C) = (fun_up103088396ar_int @ D @ B @ E)) => (C = E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_fun__upd__eqD)). 61.78/33.05 thf(531,plain,((! [A:(list_char > int),B:list_char,C:int,D:(list_char > int),E:int]: (((fun_up103088396ar_int @ A @ B @ C) = (fun_up103088396ar_int @ D @ B @ E)) => (C = E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])). 61.78/33.05 thf(28,axiom,((! [A:nat,B:nat,C:nat]: ((B = C) <= ((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_add__left__imp__eq)). 61.78/33.05 thf(255,plain,((! [A:nat,B:nat,C:nat]: ((B = C) | ~ ((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 61.78/33.05 thf(100,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_old_Onat_Odistinct_I1_J)). 61.78/33.05 thf(516,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 61.78/33.05 thf(152,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o)),E:((list_char > int) > ((list_char > int) > $o)),F:((list_char > int) > ((list_char > int) > $o))]: ((relati2102071307_hoare @ A @ B @ C @ D) => (((relati2102071307_hoare @ E @ B @ C @ F) <= (! [G:(list_char > int),H:(list_char > int)]: ((F @ G @ H) => (D @ G @ H)))) <= (! [G:(list_char > int),H:(list_char > int)]: ((E @ G @ H) <= (A @ G @ H))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_ir__conseq)). 61.78/33.05 thf(712,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o)),E:((list_char > int) > ((list_char > int) > $o)),F:((list_char > int) > ((list_char > int) > $o))]: ((relati2102071307_hoare @ (A) @ B @ C @ (D)) => ((relati2102071307_hoare @ (E) @ B @ C @ (F)) | ~ (! [G:(list_char > int),H:(list_char > int)]: ((F @ (G) @ (H)) => (D @ (G) @ (H)))) | ~ (! [G:(list_char > int),H:(list_char > int)]: ((E @ (G) @ (H)) | ~ (A @ (G) @ (H)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])). 61.78/33.05 thf(118,axiom,((! [A:(list_char > int),B:list_char,C:aexp,D:int]: (((A @ B) = (aval @ C @ (fun_up103088396ar_int @ A @ B @ D))) => (big_big_step @ (produc1193801173ar_int @ (assign @ B @ C) @ (fun_up103088396ar_int @ A @ B @ D)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_Assign__blah)). 61.78/33.05 thf(580,plain,((! [A:(list_char > int),B:list_char,C:aexp,D:int]: (((A @ B) = (aval @ C @ (fun_up103088396ar_int @ A @ B @ D))) => (big_big_step @ (produc1193801173ar_int @ (assign @ B @ C) @ (fun_up103088396ar_int @ A @ B @ D)) @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 61.78/33.05 thf(135,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o)),E:((list_char > int) > ((list_char > int) > $o))]: ((relati2102071307_hoare @ A @ B @ C @ D) => ((relati2102071307_hoare @ E @ B @ C @ D) <= (! [F:(list_char > int),G:(list_char > int)]: ((A @ F @ G) => (E @ F @ G))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_ir__pre)). 61.78/33.05 thf(640,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o)),E:((list_char > int) > ((list_char > int) > $o))]: ((relati2102071307_hoare @ (A) @ B @ C @ (D)) => ((relati2102071307_hoare @ (E) @ B @ C @ (D)) | ~ (! [F:(list_char > int),G:(list_char > int)]: ((A @ (F) @ (G)) => (E @ (F) @ (G)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 61.78/33.05 thf(40,axiom,((! [A:nat]: ((A != zero_zero_nat) => (~ (! [B:nat]: (A != (suc @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_old_Onat_Oexhaust)). 61.78/33.05 thf(295,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) => (~ (! [B:nat]: ~ (A = (suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 61.78/33.05 thf(149,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:com,E:((list_char > int) > ((list_char > int) > $o))]: ((relati775585786_valid @ A @ (seq @ B @ C) @ D @ E) => (relati775585786_valid @ (^ [F:(list_char > int),G:(list_char > int)]: ? [H:(list_char > int),I:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ B @ H) @ F) & ? [J:(list_char > int)]: ((E @ J @ G) & (big_big_step @ (produc1193801173ar_int @ C @ F) @ J)) & (big_big_step @ (produc1193801173ar_int @ D @ I) @ G) & (A @ H @ I))) @ C @ skip @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_ir__valid__Seq1_H)). 61.78/33.05 thf(705,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:com,E:((list_char > int) > ((list_char > int) > $o))]: ((relati775585786_valid @ (A) @ (seq @ B @ C) @ D @ (E)) => (relati775585786_valid @ (^ [F:(list_char > int),G:(list_char > int)]: ? [H:(list_char > int),I:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ B @ H) @ F) & ? [J:(list_char > int)]: ((E @ J @ G) & (big_big_step @ (produc1193801173ar_int @ C @ F) @ J)) & (big_big_step @ (produc1193801173ar_int @ D @ I) @ G) & (A @ H @ I))) @ C @ skip @ (E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])). 61.78/33.05 thf(150,axiom,((relati1310524937decomp = (^ [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o)),E:(list_char > int),F:(list_char > int)]: ? [G:(list_char > int),H:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ B @ G) @ E) & (D @ E @ H) & (big_big_step @ (produc1193801173ar_int @ C @ F) @ H) & (A @ G @ F))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_decomp__def)). 61.78/33.05 thf(707,plain,(((relati1310524937decomp) = (^ [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o)),E:(list_char > int),F:(list_char > int)]: ? [G:(list_char > int),H:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ B @ G) @ E) & (D @ E @ H) & (big_big_step @ (produc1193801173ar_int @ C @ F) @ H) & (A @ G @ F))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 61.78/33.05 thf(4,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_add_Oright__neutral)). 61.78/33.05 thf(177,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 61.78/33.05 thf(48,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:bexp,C:com,D:com,E:((list_char > int) > ((list_char > int) > $o))]: ((relati775585786_valid @ (^ [F:(list_char > int),G:(list_char > int)]: ((A @ F @ G) & (bval @ B @ F))) @ (seq @ C @ (while @ B @ C)) @ D @ E) => (relati775585786_valid @ A @ (while @ B @ C) @ D @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_While__True__ir__valid)). 61.78/33.05 thf(331,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:bexp,C:com,D:com,E:((list_char > int) > ((list_char > int) > $o))]: ((relati775585786_valid @ (^ [F:(list_char > int),G:(list_char > int)]: ((A @ F @ G) & (bval @ B @ F))) @ (seq @ C @ (while @ B @ C)) @ D @ (E)) => (relati775585786_valid @ (A) @ (while @ B @ C) @ D @ (E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 61.78/33.05 thf(109,axiom,((! [A:com,B:(list_char > int),C:com,D:(list_char > int)]: (((produc1193801173ar_int @ A @ B) = (produc1193801173ar_int @ C @ D)) => (~ ((B != D) <= (A = C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_Pair__inject)). 61.78/33.05 thf(544,plain,((! [A:com,B:(list_char > int),C:com,D:(list_char > int)]: (((produc1193801173ar_int @ A @ (B)) = (produc1193801173ar_int @ C @ (D))) => (~ (~ ((B) = (D)) | ~ (A = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 61.78/33.05 thf(88,axiom,((! [A:bexp,B:com]: ((size_com @ (while @ A @ B)) = (plus_plus_nat @ (size_com @ B) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_com_Osize__gen_I5_J)). 61.78/33.05 thf(470,plain,((! [A:bexp,B:com]: ((size_com @ (while @ A @ B)) = (plus_plus_nat @ (size_com @ B) @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 61.78/33.05 thf(117,axiom,((! [A:list_char,B:list_char,C:(list_char > int),D:int,E:int]: (((fun_up103088396ar_int @ (fun_up103088396ar_int @ C @ A @ D) @ B @ E) = (fun_up103088396ar_int @ (fun_up103088396ar_int @ C @ B @ E) @ A @ D)) <= (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_fun__upd__twist)). 61.78/33.05 thf(576,plain,((! [A:list_char,B:list_char,C:(list_char > int),D:int,E:int]: (((fun_up103088396ar_int @ (fun_up103088396ar_int @ C @ A @ D) @ B @ E) = (fun_up103088396ar_int @ (fun_up103088396ar_int @ C @ B @ E) @ A @ D)) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 61.78/33.05 thf(50,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_Zero__not__Suc)). 61.78/33.05 thf(336,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 61.78/33.05 thf(148,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o))]: ((relati2102071307_hoare @ (relati186416454e_flip @ A) @ B @ C @ (relati186416454e_flip @ D)) => (relati2102071307_hoare @ A @ C @ B @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_ir__sym)). 61.78/33.05 thf(703,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o))]: ((relati2102071307_hoare @ (relati186416454e_flip @ A) @ B @ C @ (relati186416454e_flip @ D)) => (relati2102071307_hoare @ (A) @ C @ B @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])). 61.78/33.05 thf(130,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:((list_char > int) > ((list_char > int) > $o)),D:com,E:((list_char > int) > ((list_char > int) > $o))]: ((relati775585786_valid @ A @ B @ D @ E) <= ((relati775585786_valid @ A @ B @ skip @ C) & (relati775585786_valid @ C @ skip @ D @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_ir__valid__decomp2)). 61.78/33.05 thf(627,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:((list_char > int) > ((list_char > int) > $o)),D:com,E:((list_char > int) > ((list_char > int) > $o))]: ((relati775585786_valid @ (A) @ B @ D @ (E)) | ~ ((relati775585786_valid @ (A) @ B @ skip @ (C)) & (relati775585786_valid @ (C) @ skip @ D @ (E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 61.78/33.05 thf(58,axiom,((! [A:(produc1260470173ar_int > $o),B:produc1260470173ar_int]: ((! [C:com,D:(list_char > int)]: (A @ (produc1193801173ar_int @ C @ D))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_old_Oprod_Oinducts)). 61.78/33.05 thf(363,plain,((! [A:(produc1260470173ar_int > $o),B:produc1260470173ar_int]: ((! [C:com,D:(list_char > int)]: (A @ (produc1193801173ar_int @ C @ (D)))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 61.78/33.05 thf(103,axiom,((! [A:com,B:com,C:bexp,D:com,E:com]: ((seq @ A @ B) != (if @ C @ D @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_com_Odistinct_I15_J)). 61.78/33.05 thf(524,plain,((! [A:com,B:com,C:bexp,D:com,E:com]: ~ ((seq @ A @ B) = (if @ C @ D @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 61.78/33.05 thf(93,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:bexp,C:com,D:com,E:com,F:((list_char > int) > ((list_char > int) > $o))]: (((relati775585786_valid @ (^ [G:(list_char > int),H:(list_char > int)]: (~ (bval @ B @ G) & (A @ G @ H))) @ D @ E @ (^ [G:(list_char > int),H:(list_char > int)]: (? [I:(list_char > int),J:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ E @ J) @ H) & ~ (bval @ B @ I) & (big_big_step @ (produc1193801173ar_int @ D @ I) @ G) & (A @ I @ J)) & (F @ G @ H)))) & (relati775585786_valid @ (^ [G:(list_char > int),H:(list_char > int)]: ((bval @ B @ G) & (A @ G @ H))) @ C @ E @ (^ [G:(list_char > int),H:(list_char > int)]: (? [I:(list_char > int),J:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ E @ J) @ H) & (bval @ B @ I) & (big_big_step @ (produc1193801173ar_int @ C @ I) @ G) & (A @ I @ J)) & (F @ G @ H))))) <= (relati775585786_valid @ A @ (if @ B @ C @ D) @ E @ F)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_ir__valid__If)). 61.78/33.05 thf(495,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:bexp,C:com,D:com,E:com,F:((list_char > int) > ((list_char > int) > $o))]: (((relati775585786_valid @ (^ [G:(list_char > int),H:(list_char > int)]: (~ (bval @ B @ G) & (A @ G @ H))) @ D @ E @ (^ [G:(list_char > int),H:(list_char > int)]: (? [I:(list_char > int),J:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ E @ J) @ H) & ~ (bval @ B @ I) & (big_big_step @ (produc1193801173ar_int @ D @ I) @ G) & (A @ I @ J)) & (F @ G @ H)))) & (relati775585786_valid @ (^ [G:(list_char > int),H:(list_char > int)]: ((bval @ B @ G) & (A @ G @ H))) @ C @ E @ (^ [G:(list_char > int),H:(list_char > int)]: (? [I:(list_char > int),J:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ E @ J) @ H) & (bval @ B @ I) & (big_big_step @ (produc1193801173ar_int @ C @ I) @ G) & (A @ I @ J)) & (F @ G @ H))))) | ~ (relati775585786_valid @ (A) @ (if @ B @ C @ D) @ E @ (F))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 61.78/33.05 thf(171,axiom,((! [A:(list_char > int)]: (big_big_step @ (produc1193801173ar_int @ skip @ A) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_Skip)). 61.78/33.05 thf(771,plain,((! [A:(list_char > int)]: (big_big_step @ (produc1193801173ar_int @ skip @ (A)) @ (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])). 61.78/33.05 thf(86,axiom,((! [A:com,B:com,C:com]: ((! [D:(list_char > int),E:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ A @ D) @ E) = (big_big_step @ (produc1193801173ar_int @ B @ D) @ E))) => ((! [D:(list_char > int),E:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ B @ D) @ E) = (big_big_step @ (produc1193801173ar_int @ C @ D) @ E))) => (! [D:(list_char > int),E:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ A @ D) @ E) = (big_big_step @ (produc1193801173ar_int @ C @ D) @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_sim__trans)). 61.78/33.05 thf(465,plain,((! [A:com,B:com,C:com]: ((! [D:(list_char > int),E:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ A @ (D)) @ (E)) = (big_big_step @ (produc1193801173ar_int @ B @ (D)) @ (E)))) => ((! [D:(list_char > int),E:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ B @ (D)) @ (E)) = (big_big_step @ (produc1193801173ar_int @ C @ (D)) @ (E)))) => (! [D:(list_char > int),E:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ A @ (D)) @ (E)) = (big_big_step @ (produc1193801173ar_int @ C @ (D)) @ (E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 61.78/33.05 thf(20,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ B @ (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_add_Oleft__commute)). 61.78/33.05 thf(231,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ B @ (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 61.78/33.05 thf(147,axiom,((! [A:bexp,B:com]: (skip != (while @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_com_Odistinct_I7_J)). 61.78/33.05 thf(699,plain,((! [A:bexp,B:com]: ~ (skip = (while @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])). 61.78/33.05 thf(163,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:bexp,C:com,D:com,E:((list_char > int) > ((list_char > int) > $o)),F:com]: ((relati2102071307_hoare @ (^ [G:(list_char > int),H:(list_char > int)]: ((A @ G @ H) & ~ (bval @ B @ G))) @ C @ D @ E) => (relati2102071307_hoare @ A @ (if @ B @ F @ C) @ D @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_ir__If__False)). 61.78/33.05 thf(748,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:bexp,C:com,D:com,E:((list_char > int) > ((list_char > int) > $o)),F:com]: ((relati2102071307_hoare @ (^ [G:(list_char > int),H:(list_char > int)]: ((A @ G @ H) & ~ (bval @ B @ G))) @ C @ D @ (E)) => (relati2102071307_hoare @ (A) @ (if @ B @ F @ C) @ D @ (E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])). 61.78/33.05 thf(54,axiom,((! [A:bexp,B:com]: ((size_size_com @ (while @ A @ B)) = (plus_plus_nat @ (size_size_com @ B) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_com_Osize_I10_J)). 61.78/33.05 thf(351,plain,((! [A:bexp,B:com]: ((size_size_com @ (while @ A @ B)) = (plus_plus_nat @ (size_size_com @ B) @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 61.78/33.05 thf(7,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ (suc @ A) @ B) = (suc @ (plus_plus_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_add__Suc)). 61.78/33.05 thf(186,plain,((! [A:nat,B:nat]: ((plus_plus_nat @ (suc @ A) @ B) = (suc @ (plus_plus_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 61.78/33.05 thf(132,axiom,((! [A:((list_char > int) > ((list_char > int) > $o))]: (relati2102071307_hoare @ A @ skip @ skip @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_ir__Skip__Skip)). 61.78/33.05 thf(632,plain,((! [A:((list_char > int) > ((list_char > int) > $o))]: (relati2102071307_hoare @ (A) @ skip @ skip @ (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 61.78/33.05 thf(168,axiom,(((size_size_com @ skip) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_com_Osize_I6_J)). 61.78/33.05 thf(763,plain,(((size_size_com @ skip) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])). 61.78/33.05 thf(142,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o)),E:((list_char > int) > ((list_char > int) > $o)),F:((list_char > int) > ((list_char > int) > $o))]: ((relati2102071307_hoare @ A @ B @ C @ D) => ((relati2102071307_hoare @ (^ [G:(list_char > int),H:(list_char > int)]: ((E @ G @ H) | (A @ G @ H))) @ B @ C @ (^ [G:(list_char > int),H:(list_char > int)]: ((D @ G @ H) | (F @ G @ H)))) <= (relati2102071307_hoare @ E @ B @ C @ F))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_ir__disj)). 61.78/33.05 thf(684,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o)),E:((list_char > int) > ((list_char > int) > $o)),F:((list_char > int) > ((list_char > int) > $o))]: ((relati2102071307_hoare @ (A) @ B @ C @ (D)) => ((relati2102071307_hoare @ (^ [G:(list_char > int),H:(list_char > int)]: ((E @ G @ H) | (A @ G @ H))) @ B @ C @ (^ [G:(list_char > int),H:(list_char > int)]: ((D @ G @ H) | (F @ G @ H)))) | ~ (relati2102071307_hoare @ (E) @ B @ C @ (F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 61.78/33.05 thf(15,axiom,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_comm__monoid__add__class_Oadd__0)). 61.78/33.05 thf(214,plain,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 61.78/33.05 thf(30,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_add_Ocomm__neutral)). 61.78/33.05 thf(262,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 61.78/33.05 thf(70,axiom,((! [A:com,B:com]: ((size_size_com @ (seq @ A @ B)) = (plus_plus_nat @ (plus_plus_nat @ (size_size_com @ A) @ (size_size_com @ B)) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_com_Osize_I8_J)). 61.78/33.05 thf(405,plain,((! [A:com,B:com]: ((size_size_com @ (seq @ A @ B)) = (plus_plus_nat @ (plus_plus_nat @ (size_size_com @ A) @ (size_size_com @ B)) @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 61.78/33.05 thf(6,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = A) => (B = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_add__eq__self__zero)). 61.78/33.05 thf(183,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = A) => (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 61.78/33.05 thf(74,axiom,((! [A:bexp,B:(list_char > int),C:com,D:(list_char > int),E:com]: (((big_big_step @ (produc1193801173ar_int @ C @ B) @ D) => (big_big_step @ (produc1193801173ar_int @ (if @ A @ E @ C) @ B) @ D)) <= (~ (bval @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_IfFalse)). 61.78/33.05 thf(422,plain,((! [A:bexp,B:(list_char > int),C:com,D:(list_char > int),E:com]: (((big_big_step @ (produc1193801173ar_int @ C @ (B)) @ (D)) => (big_big_step @ (produc1193801173ar_int @ (if @ A @ E @ C) @ (B)) @ (D))) | (bval @ A @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 61.78/33.05 thf(124,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_nat_Oinject)). 61.78/33.05 thf(603,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 61.78/33.05 thf(159,axiom,((! [A:(list_char > int),B:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ skip @ A) @ B) => (B = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_SkipE)). 61.78/33.05 thf(735,plain,((! [A:(list_char > int),B:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ skip @ (A)) @ (B)) => ((B) = (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])). 61.78/33.05 thf(113,axiom,((! [A:com,B:(list_char > int),C:(list_char > int),D:com,E:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ A @ B) @ C) => ((big_big_step @ (produc1193801173ar_int @ D @ C) @ E) => (big_big_step @ (produc1193801173ar_int @ (seq @ A @ D) @ B) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_Seq)). 61.78/33.05 thf(564,plain,((! [A:com,B:(list_char > int),C:(list_char > int),D:com,E:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ A @ (B)) @ (C)) => ((big_big_step @ (produc1193801173ar_int @ D @ (C)) @ (E)) => (big_big_step @ (produc1193801173ar_int @ (seq @ A @ D) @ (B)) @ (E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 61.78/33.05 thf(43,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_nat_Odistinct_I1_J)). 61.78/33.05 thf(305,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 61.78/33.05 thf(46,axiom,((! [A:bexp,B:bexp,C:com,D:com,E:com,F:(list_char > int),G:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ (if @ A @ (if @ B @ C @ D) @ E) @ F) @ G) = (big_big_step @ (produc1193801173ar_int @ (if @ B @ (if @ A @ C @ E) @ (if @ A @ D @ E)) @ F) @ G)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_commute__if)). 61.78/33.05 thf(326,plain,((! [A:bexp,B:bexp,C:com,D:com,E:com,F:(list_char > int),G:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ (if @ A @ (if @ B @ C @ D) @ E) @ (F)) @ (G)) = (big_big_step @ (produc1193801173ar_int @ (if @ B @ (if @ A @ C @ E) @ (if @ A @ D @ E)) @ (F)) @ (G))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 61.78/33.05 thf(10,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_ab__semigroup__add__class_Oadd__ac_I1_J)). 61.78/33.05 thf(195,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 61.78/33.05 thf(68,axiom,((fun_up103088396ar_int = (^ [A:(list_char > int),B:list_char,C:int,D:list_char]: (if_int @ (D = B) @ C @ (A @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_fun__upd__def)). 61.78/33.05 thf(400,plain,(((fun_up103088396ar_int) = (^ [A:(list_char > int),B:list_char,C:int,D:list_char]: (if_int @ (D = B) @ C @ (A @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 61.78/33.05 thf(146,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:((list_char > int) > ((list_char > int) > $o)),D:com,E:com,F:((list_char > int) > ((list_char > int) > $o))]: (((relati775585786_valid @ C @ D @ E @ F) => (relati775585786_valid @ A @ (seq @ B @ D) @ E @ F)) <= (relati775585786_valid @ A @ B @ skip @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_Seq2__ir__valid)). 61.78/33.05 thf(696,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:((list_char > int) > ((list_char > int) > $o)),D:com,E:com,F:((list_char > int) > ((list_char > int) > $o))]: (((relati775585786_valid @ (C) @ D @ E @ (F)) => (relati775585786_valid @ (A) @ (seq @ B @ D) @ E @ (F))) | ~ (relati775585786_valid @ (A) @ B @ skip @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 61.78/33.05 thf(154,axiom,((! [A:com]: ((A != skip) => ((! [B:list_char,C:aexp]: (A != (assign @ B @ C))) => (((~ (! [B:bexp,C:com]: (A != (while @ B @ C)))) <= (! [B:bexp,C:com,D:com]: (A != (if @ B @ C @ D)))) <= (! [B:com,C:com]: (A != (seq @ B @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_com_Oexhaust)). 61.78/33.05 thf(720,plain,((! [A:com]: ((~ (A = skip)) => ((! [B:list_char,C:aexp]: ~ (A = (assign @ B @ C))) => (~ (! [B:bexp,C:com]: ~ (A = (while @ B @ C))) | ~ (! [B:bexp,C:com,D:com]: ~ (A = (if @ B @ C @ D))) | ~ (! [B:com,C:com]: ~ (A = (seq @ B @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])). 61.78/33.05 thf(36,axiom,((fun_up103088396ar_int = (^ [A:(list_char > int),B:list_char,C:int,D:list_char]: (if_int @ (D = B) @ C @ (A @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_fun__upd__apply)). 61.78/33.05 thf(283,plain,(((fun_up103088396ar_int) = (^ [A:(list_char > int),B:list_char,C:int,D:list_char]: (if_int @ (D = B) @ C @ (A @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 61.78/33.05 thf(23,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) & (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_add__eq__0__iff__both__eq__0)). 61.78/33.05 thf(239,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) & (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 61.78/33.05 thf(24,axiom,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_add__cancel__right__right)). 61.78/33.05 thf(242,plain,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 61.78/33.05 thf(129,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:((list_char > int) > ((list_char > int) > $o)),C:com]: ((relati2102071307_hoare @ B @ C @ skip @ A) <= (! [D:(list_char > int),E:(list_char > int)]: ((A @ E @ D) => (? [F:(list_char > int)]: ((B @ F @ D) & (big_big_step @ (produc1193801173ar_int @ C @ F) @ E)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_ir__Skip__sym)). 61.78/33.05 thf(624,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:((list_char > int) > ((list_char > int) > $o)),C:com]: ((relati2102071307_hoare @ (B) @ C @ skip @ (A)) | ~ (! [D:(list_char > int),E:(list_char > int)]: ((A @ (E) @ (D)) => (? [F:(list_char > int)]: ((B @ (F) @ (D)) & (big_big_step @ (produc1193801173ar_int @ C @ (F)) @ (E))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])). 61.78/33.05 thf(156,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:list_char,C:aexp,D:com,E:((list_char > int) > ((list_char > int) > $o))]: ((relati775585786_valid @ (^ [F:(list_char > int),G:(list_char > int)]: ? [H:int]: (((F @ B) = (aval @ C @ (fun_up103088396ar_int @ F @ B @ H))) & (A @ (fun_up103088396ar_int @ F @ B @ H) @ G))) @ skip @ D @ E) => (relati775585786_valid @ A @ (assign @ B @ C) @ D @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_Assign__ir__valid)). 61.78/33.05 thf(728,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:list_char,C:aexp,D:com,E:((list_char > int) > ((list_char > int) > $o))]: ((relati775585786_valid @ (^ [F:(list_char > int),G:(list_char > int)]: ? [H:int]: (((F @ B) = (aval @ C @ (fun_up103088396ar_int @ F @ B @ H))) & (A @ (fun_up103088396ar_int @ F @ B @ H) @ G))) @ skip @ D @ (E)) => (relati775585786_valid @ (A) @ (assign @ B @ C) @ D @ (E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 61.78/33.05 thf(122,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o)),E:(list_char > int),F:(list_char > int)]: ((relati775585786_valid @ A @ B @ C @ (^ [G:(list_char > int),H:(list_char > int)]: (? [I:(list_char > int),J:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ B @ I) @ G) & (big_big_step @ (produc1193801173ar_int @ C @ J) @ H) & (A @ I @ J)) & (D @ E @ F)))) <= (relati775585786_valid @ A @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_ir__valid__track__history)). 61.78/33.05 thf(596,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:com,C:com,D:((list_char > int) > ((list_char > int) > $o)),E:(list_char > int),F:(list_char > int)]: ((relati775585786_valid @ (A) @ B @ C @ (^ [G:(list_char > int),H:(list_char > int)]: (? [I:(list_char > int),J:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ B @ I) @ G) & (big_big_step @ (produc1193801173ar_int @ C @ J) @ H) & (A @ I @ J)) & (D @ E @ F)))) | ~ (relati775585786_valid @ (A) @ B @ C @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 61.78/33.05 thf(104,axiom,((! [A:bexp,B:com,C:bexp,D:com]: (((while @ A @ B) = (while @ C @ D)) = ((A = C) & (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_com_Oinject_I4_J)). 61.78/33.05 thf(528,plain,((! [A:bexp,B:com,C:bexp,D:com]: (((while @ A @ B) = (while @ C @ D)) = ((A = C) & (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 61.78/33.05 thf(136,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:((list_char > int) > ((list_char > int) > $o)),C:com]: ((relati2102071307_hoare @ B @ skip @ C @ A) <= (! [D:(list_char > int),E:(list_char > int)]: ((A @ D @ E) => (? [F:(list_char > int)]: ((B @ D @ F) & (big_big_step @ (produc1193801173ar_int @ C @ F) @ E)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_ir__Skip)). 61.78/33.05 thf(644,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:((list_char > int) > ((list_char > int) > $o)),C:com]: ((relati2102071307_hoare @ (B) @ skip @ C @ (A)) | ~ (! [D:(list_char > int),E:(list_char > int)]: ((A @ (D) @ (E)) => (? [F:(list_char > int)]: ((B @ (D) @ (F)) & (big_big_step @ (produc1193801173ar_int @ C @ (F)) @ (E))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 61.78/33.05 thf(34,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_add_Oassoc)). 61.78/33.05 thf(277,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 61.78/33.05 thf(80,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:list_char,C:aexp,D:com,E:((list_char > int) > ((list_char > int) > $o)),F:(list_char > int),G:(list_char > int)]: ((relati775585786_valid @ A @ (assign @ B @ C) @ D @ E) => ((E @ F @ G) => (? [H:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ D @ H) @ G) & ? [I:int]: (((F @ B) = (aval @ C @ (fun_up103088396ar_int @ F @ B @ I))) & (A @ (fun_up103088396ar_int @ F @ B @ I) @ H)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_Assign__complete)). 61.78/33.05 thf(442,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:list_char,C:aexp,D:com,E:((list_char > int) > ((list_char > int) > $o)),F:(list_char > int),G:(list_char > int)]: ((relati775585786_valid @ (A) @ (assign @ B @ C) @ D @ (E)) => ((E @ (F) @ (G)) => (? [H:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ D @ (H)) @ (G)) & ? [I:int]: (((F @ B) = (aval @ C @ (fun_up103088396ar_int @ F @ B @ I))) & (A @ (fun_up103088396ar_int @ F @ B @ I) @ (H))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 61.78/33.05 thf(95,axiom,((! [A:(list_char > int),B:list_char,C:int]: (((fun_up103088396ar_int @ A @ B @ C) = A) = ((A @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_fun__upd__idem__iff)). 61.78/33.05 thf(501,plain,((! [A:(list_char > int),B:list_char,C:int]: (((fun_up103088396ar_int @ A @ B @ C) = (A)) = ((A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 61.78/33.05 thf(60,axiom,((! [A:com,B:com]: ((! [C:(list_char > int),D:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ A @ C) @ D) = (big_big_step @ (produc1193801173ar_int @ B @ C) @ D))) = (! [C:(list_char > int),D:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ B @ C) @ D) = (big_big_step @ (produc1193801173ar_int @ A @ C) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_sim__sym)). 61.78/33.05 thf(369,plain,((! [A:com,B:com]: ((! [C:(list_char > int),D:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ A @ (C)) @ (D)) = (big_big_step @ (produc1193801173ar_int @ B @ (C)) @ (D)))) = (! [C:(list_char > int),D:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ B @ (C)) @ (D)) = (big_big_step @ (produc1193801173ar_int @ A @ (C)) @ (D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 61.78/33.05 thf(87,axiom,((! [A:com,B:(list_char > int),C:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ A @ B) @ C) = (big_big_step @ (produc1193801173ar_int @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_sim__refl)). 61.78/33.05 thf(469,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 61.78/33.05 thf(55,axiom,((! [A:com,B:com]: ((size_com @ (seq @ A @ B)) = (plus_plus_nat @ (plus_plus_nat @ (size_com @ A) @ (size_com @ B)) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_com_Osize__gen_I3_J)). 61.78/33.05 thf(354,plain,((! [A:com,B:com]: ((size_com @ (seq @ A @ B)) = (plus_plus_nat @ (plus_plus_nat @ (size_com @ A) @ (size_com @ B)) @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 61.78/33.05 thf(44,axiom,((! [A:com,B:(list_char > int),C:com,D:(list_char > int)]: (((produc1193801173ar_int @ A @ B) = (produc1193801173ar_int @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_prod_Oinject)). 61.78/33.05 thf(309,plain,((! [A:com,B:(list_char > int),C:com,D:(list_char > int)]: (((produc1193801173ar_int @ A @ (B)) = (produc1193801173ar_int @ C @ (D))) = (((B) = (D)) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 61.78/33.05 thf(112,axiom,((! [A:bexp,B:com,C:(list_char > int),D:(list_char > int),E:com]: (((! [F:(list_char > int),G:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ B @ F) @ G) = (big_big_step @ (produc1193801173ar_int @ E @ F) @ G))) => (big_big_step @ (produc1193801173ar_int @ (while @ A @ E) @ C) @ D)) <= (big_big_step @ (produc1193801173ar_int @ (while @ A @ B) @ C) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_sim__while__cong__aux)). 61.78/33.05 thf(560,plain,((! [A:bexp,B:com,C:(list_char > int),D:(list_char > int),E:com]: (((! [F:(list_char > int),G:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ B @ (F)) @ (G)) = (big_big_step @ (produc1193801173ar_int @ E @ (F)) @ (G)))) => (big_big_step @ (produc1193801173ar_int @ (while @ A @ E) @ (C)) @ (D))) | ~ (big_big_step @ (produc1193801173ar_int @ (while @ A @ B) @ (C)) @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 61.78/33.05 thf(165,axiom,((! [A:((list_char > int) > ((list_char > int) > $o)),B:((list_char > int) > ((list_char > int) > $o)),C:com]: ((! [D:(list_char > int),E:(list_char > int)]: ((A @ D @ E) => (? [F:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ C @ F) @ E) & (B @ D @ F))))) => (relati775585786_valid @ B @ skip @ C @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_Skip__ir__valid)). 61.78/33.05 thf(755,plain,((! [A:((list_char > int) > ((list_char > int) > $o)),B:((list_char > int) > ((list_char > int) > $o)),C:com]: ((! [D:(list_char > int),E:(list_char > int)]: ((A @ (D) @ (E)) => (? [F:(list_char > int)]: ((big_big_step @ (produc1193801173ar_int @ C @ (F)) @ (E)) & (B @ (D) @ (F)))))) => (relati775585786_valid @ (B) @ skip @ C @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])). 61.78/33.05 thf(1769,plain,($false),inference(cvc4,[status(thm)],[485,637,629,760,347,234,555,481,333,249,408,741,440,202,730,217,385,340,538,174,709,288,436,651,724,570,372,504,587,751,344,357,189,606,448,280,634,692,453,428,265,507,312,397,687,292,512,270,534,220,366,302,192,252,329,461,682,551,285,583,522,388,593,647,738,457,237,360,205,541,765,718,412,618,425,745,573,180,689,402,732,259,391,382,498,172,274,419,245,208,599,451,567,509,649,477,758,621,520,198,768,394,299,226,431,653,223,608,473,531,255,516,712,580,640,295,705,707,177,331,544,470,576,336,703,627,363,524,495,771,465,231,699,748,351,186,632,763,684,214,262,405,183,422,603,735,564,305,326,195,400,696,720,283,239,242,624,728,596,528,644,277,442,501,369,469,354,309,560,755])). 61.78/33.05 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 61.78/33.05 % [INFO] Killing All external provers ... 61.78/33.05 FINAL WATCH: 61.2 CPU 33.0 WC 61.78/33.05 EOF