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image_nat_nat: ( nat > nat ) > set_nat > set_nat ). 0.19/0.56 0.19/0.56 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_Mt__Com__Ocom_J,type, 0.19/0.56 image_244615942nt_com: ( nat > produc1166363805nt_com ) > set_nat > set_Pr866150653nt_com ). 0.19/0.56 0.19/0.56 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Product____Type__Oprod_It__Com__Ocom_M_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_J,type, 0.19/0.56 image_338722310ar_int: ( nat > produc1260470173ar_int ) > set_nat > set_Pr1148378109ar_int ). 0.19/0.56 0.19/0.56 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_Mt__Com__Ocom_J_001t__Nat__Onat,type, 0.19/0.56 image_596692520om_nat: ( produc1166363805nt_com > nat ) > set_Pr866150653nt_com > set_nat ). 0.19/0.56 0.19/0.56 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_Mt__Com__Ocom_J_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_Mt__Com__Ocom_J,type, 0.19/0.56 image_1874758725nt_com: ( produc1166363805nt_com > produc1166363805nt_com ) > set_Pr866150653nt_com > set_Pr866150653nt_com ). 0.19/0.56 0.19/0.56 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_Mt__Com__Ocom_J_001t__Product____Type__Oprod_It__Com__Ocom_M_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_J,type, 0.19/0.56 image_1968865093ar_int: ( produc1166363805nt_com > produc1260470173ar_int ) > set_Pr866150653nt_com > set_Pr1148378109ar_int ). 0.19/0.56 0.19/0.56 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Com__Ocom_M_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_J_001_Eo,type, 0.19/0.56 image_522938432_int_o: ( produc1260470173ar_int > $o ) > set_Pr1148378109ar_int > set_o ). 0.19/0.56 0.19/0.56 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Com__Ocom_M_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_J_001t__Nat__Onat,type, 0.19/0.56 image_1742782760nt_nat: ( produc1260470173ar_int > nat ) > set_Pr1148378109ar_int > set_nat ). 0.19/0.56 0.19/0.56 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Com__Ocom_M_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_J_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_Mt__Com__Ocom_J,type, 0.19/0.56 image_786684229nt_com: ( produc1260470173ar_int > produc1166363805nt_com ) > set_Pr1148378109ar_int > set_Pr866150653nt_com ). 0.19/0.56 0.19/0.56 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Com__Ocom_M_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_J_001t__Product____Type__Oprod_It__Com__Ocom_M_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_J,type, 0.19/0.56 image_880790597ar_int: ( produc1260470173ar_int > produc1260470173ar_int ) > set_Pr1148378109ar_int > set_Pr1148378109ar_int ). 0.19/0.56 0.19/0.56 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Com__Ocom_M_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_J_001t__Set__Oset_It__Nat__Onat_J,type, 0.19/0.56 image_989727966et_nat: ( produc1260470173ar_int > set_nat ) > set_Pr1148378109ar_int > set_set_nat ). 0.19/0.56 0.19/0.56 thf(sy_c_member_001_Eo,type, 0.19/0.56 member_o: $o > set_o > $o ). 0.19/0.56 0.19/0.56 thf(sy_c_member_001t__Nat__Onat,type, 0.19/0.56 member_nat: nat > set_nat > $o ). 0.19/0.56 0.19/0.56 thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_Mt__Com__Ocom_J,type, 0.19/0.56 member2145628230nt_com: produc1166363805nt_com > set_Pr866150653nt_com > $o ). 0.19/0.56 0.19/0.56 thf(sy_c_member_001t__Product____Type__Oprod_It__Com__Ocom_M_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_J,type, 0.19/0.56 member92250950ar_int: produc1260470173ar_int > set_Pr1148378109ar_int > $o ). 0.19/0.56 0.19/0.56 thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type, 0.19/0.56 member_set_nat: set_nat > set_set_nat > $o ). 0.19/0.56 0.19/0.56 thf(sy_v_P,type, 0.19/0.56 p: ( list_char > int ) > ( list_char > int ) > $o ). 0.19/0.56 0.19/0.56 thf(sy_v_Q,type, 0.19/0.56 q: ( list_char > int ) > ( list_char > int ) > $o ). 0.19/0.56 0.19/0.56 thf(sy_v_c,type, 0.19/0.56 c: com ). 0.19/0.56 0.19/0.56 thf(sy_v_c_H,type, 0.19/0.56 c2: com ). 0.19/0.56 0.19/0.56 thf(fact_126_case__prod__curry,axiom, 0.19/0.56 ! [F2: produc1260470173ar_int > set_nat] : 0.19/0.56 ( ( produc991755120et_nat @ ( produc1791150095et_nat @ F2 ) ) 0.19/0.56 = F2 ) ). 0.19/0.56 0.19/0.56 thf(fact_28_Seq__assoc,axiom, 0.19/0.56 ! [C1: com,C22: com,C32: com,S7: list_char > int,S6: list_char > int] : 0.19/0.56 ( ( big_big_step @ ( produc1193801173ar_int @ ( seq @ ( seq @ C1 @ C22 ) @ C32 ) @ S7 ) @ S6 ) 0.19/0.56 = ( big_big_step @ ( produc1193801173ar_int @ ( seq @ C1 @ ( seq @ C22 @ C32 ) ) @ S7 ) @ S6 ) ) ). 0.19/0.56 0.19/0.56 thf(fact_146_If__True__ir__valid,axiom, 0.19/0.56 ! [P: ( list_char > int ) > ( list_char > int ) > $o,B: bexp,C_1: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,C_2: com] : 0.19/0.56 ( ( relati775585786_valid @ P @ ( if @ B @ C_1 @ C_2 ) @ C2 @ Q ) 0.19/0.56 <= ( relati775585786_valid 0.19/0.56 @ ^ [A5: list_char > int,C3: list_char > int] : 0.19/0.56 ( ( P @ A5 @ C3 ) 0.19/0.56 & ( bval @ B @ A5 ) ) 0.19/0.56 @ C_1 0.19/0.56 @ C2 0.19/0.56 @ Q ) ) ). 0.19/0.56 0.19/0.56 thf(fact_80_sim__while__cong,axiom, 0.19/0.56 ! [C: com,C2: com,B: bexp] : 0.19/0.56 ( ! [S3: list_char > int,T: list_char > int] : 0.19/0.56 ( ( big_big_step @ ( produc1193801173ar_int @ C @ S3 ) @ T ) 0.19/0.56 = ( big_big_step @ ( produc1193801173ar_int @ C2 @ S3 ) @ T ) ) 0.19/0.56 => ! [S8: list_char > int,T7: list_char > int] : 0.19/0.56 ( ( big_big_step @ ( produc1193801173ar_int @ ( while @ B @ C ) @ S8 ) @ T7 ) 0.19/0.56 = ( big_big_step @ ( produc1193801173ar_int @ ( while @ B @ C2 ) @ S8 ) @ T7 ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_135_case__swap,axiom, 0.19/0.56 ! [F2: ( list_char > int ) > com > $o,P4: produc1166363805nt_com] : 0.19/0.56 ( ( produc668584238_int_o 0.19/0.56 @ ^ [Y4: com,X: list_char > int] : ( F2 @ X @ Y4 ) 0.19/0.56 @ ( produc1716235893nt_com @ P4 ) ) 0.19/0.56 = ( produc613711406_com_o @ F2 @ P4 ) ) ). 0.19/0.56 0.19/0.56 thf(fact_104_mem__case__prodI2,axiom, 0.19/0.56 ! [P4: produc1166363805nt_com,Z: produc1260470173ar_int,C: ( list_char > int ) > com > set_Pr1148378109ar_int] : 0.19/0.56 ( ! [A3: list_char > int,B3: com] : 0.19/0.56 ( ( P4 0.19/0.56 = ( produc1139835093nt_com @ A3 @ B3 ) ) 0.19/0.56 => ( member92250950ar_int @ Z @ ( C @ A3 @ B3 ) ) ) 0.19/0.56 => ( member92250950ar_int @ Z @ ( produc1461507731ar_int @ C @ P4 ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_176_case__prodE2,axiom, 0.19/0.56 ! [Q: produc1260470173ar_int > $o,P: com > ( list_char > int ) > produc1260470173ar_int,Z: produc1260470173ar_int] : 0.19/0.56 ( ~ ! [X3: com,Y3: list_char > int] : 0.19/0.56 ( ( Z 0.19/0.56 = ( produc1193801173ar_int @ X3 @ Y3 ) ) 0.19/0.56 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) 0.19/0.56 <= ( Q @ ( produc1288559923ar_int @ P @ Z ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_346_com_Osize_I10_J,axiom, 0.19/0.56 ! [X51: bexp,X52: com] : 0.19/0.56 ( ( size_size_com @ ( while @ X51 @ X52 ) ) 0.19/0.56 = ( plus_plus_nat @ ( size_size_com @ X52 ) @ ( suc @ zero_zero_nat ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_61_triv__if,axiom, 0.19/0.56 ! [B: bexp,C: com,S8: list_char > int,T7: list_char > int] : 0.19/0.56 ( ( big_big_step @ ( produc1193801173ar_int @ ( if @ B @ C @ C ) @ S8 ) @ T7 ) 0.19/0.56 = ( big_big_step @ ( produc1193801173ar_int @ C @ S8 ) @ T7 ) ) ). 0.19/0.56 0.19/0.56 thf(fact_270_image__image,axiom, 0.19/0.56 ! [F2: produc1260470173ar_int > nat,G: nat > produc1260470173ar_int,A4: set_nat] : 0.19/0.56 ( ( image_1742782760nt_nat @ F2 @ ( image_338722310ar_int @ G @ A4 ) ) 0.19/0.56 = ( image_nat_nat 0.19/0.56 @ ^ [X: nat] : ( F2 @ ( G @ X ) ) 0.19/0.56 @ A4 ) ) ). 0.19/0.56 0.19/0.56 thf(fact_93_pair__in__swap__image,axiom, 0.19/0.56 ! [Y: com,X4: list_char > int,A4: set_Pr866150653nt_com] : 0.19/0.56 ( ( member92250950ar_int @ ( produc1193801173ar_int @ Y @ X4 ) @ ( image_1968865093ar_int @ produc1716235893nt_com @ A4 ) ) 0.19/0.56 = ( member2145628230nt_com @ ( produc1139835093nt_com @ X4 @ Y ) @ A4 ) ) ). 0.19/0.56 0.19/0.56 thf(fact_237_image__iff,axiom, 0.19/0.56 ! [Z: nat,F2: produc1260470173ar_int > nat,A4: set_Pr1148378109ar_int] : 0.19/0.56 ( ( member_nat @ Z @ ( image_1742782760nt_nat @ F2 @ A4 ) ) 0.19/0.56 = ( ? [X: produc1260470173ar_int] : 0.19/0.56 ( ( Z 0.19/0.56 = ( F2 @ X ) ) 0.19/0.56 & ( member92250950ar_int @ X @ A4 ) ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_40_old_Oprod_Oinducts,axiom, 0.19/0.56 ! [P: produc1260470173ar_int > $o,Prod: produc1260470173ar_int] : 0.19/0.56 ( ! [A3: com,B3: list_char > int] : ( P @ ( produc1193801173ar_int @ A3 @ B3 ) ) 0.19/0.56 => ( P @ Prod ) ) ). 0.19/0.56 0.19/0.56 thf(fact_144_pair__imageI,axiom, 0.19/0.56 ! [A: com,B: list_char > int,A4: set_Pr1148378109ar_int,F2: com > ( list_char > int ) > produc1260470173ar_int] : 0.19/0.56 ( ( member92250950ar_int @ ( F2 @ A @ B ) @ ( image_880790597ar_int @ ( produc1288559923ar_int @ F2 ) @ A4 ) ) 0.19/0.56 <= ( member92250950ar_int @ ( produc1193801173ar_int @ A @ B ) @ A4 ) ) ). 0.19/0.56 0.19/0.56 thf(fact_343_com_Osize_I8_J,axiom, 0.19/0.56 ! [X31: com,X32: com] : 0.19/0.56 ( ( size_size_com @ ( seq @ X31 @ X32 ) ) 0.19/0.56 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_size_com @ X31 ) @ ( size_size_com @ X32 ) ) @ ( suc @ zero_zero_nat ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_205_image__eqI,axiom, 0.19/0.56 ! [B: nat,F2: produc1260470173ar_int > nat,X4: produc1260470173ar_int,A4: set_Pr1148378109ar_int] : 0.19/0.56 ( ( ( member92250950ar_int @ X4 @ A4 ) 0.19/0.56 => ( member_nat @ B @ ( image_1742782760nt_nat @ F2 @ A4 ) ) ) 0.19/0.56 <= ( B 0.19/0.56 = ( F2 @ X4 ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_336_add__is__1,axiom, 0.19/0.56 ! [M: nat,N3: nat] : 0.19/0.56 ( ( ( plus_plus_nat @ M @ N3 ) 0.19/0.56 = ( suc @ zero_zero_nat ) ) 0.19/0.56 = ( ( ( M = zero_zero_nat ) 0.19/0.56 & ( N3 0.19/0.56 = ( suc @ zero_zero_nat ) ) ) 0.19/0.56 | ( ( N3 = zero_zero_nat ) 0.19/0.56 & ( M 0.19/0.56 = ( suc @ zero_zero_nat ) ) ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_348_zero__notin__Suc__image,axiom, 0.19/0.56 ! [A4: set_nat] : 0.19/0.56 ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A4 ) ) ). 0.19/0.56 0.19/0.56 thf(fact_163_flip__def,axiom, 0.19/0.56 ( relati186416454e_flip 0.19/0.56 = ( ^ [P2: ( list_char > int ) > ( list_char > int ) > $o,S: list_char > int,S2: list_char > int] : ( P2 @ S2 @ S ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_191_ir__If__False,axiom, 0.19/0.56 ! [P: ( list_char > int ) > ( list_char > int ) > $o,B: bexp,C_2: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,C_1: com] : 0.19/0.56 ( ( relati2102071307_hoare 0.19/0.56 @ ^ [S: list_char > int,S2: list_char > int] : 0.19/0.56 ( ~ ( bval @ B @ S ) 0.19/0.56 & ( P @ S @ S2 ) ) 0.19/0.56 @ C_2 0.19/0.56 @ C2 0.19/0.56 @ Q ) 0.19/0.56 => ( relati2102071307_hoare @ P @ ( if @ B @ C_1 @ C_2 ) @ C2 @ Q ) ) ). 0.19/0.56 0.19/0.56 thf(fact_327_Zero__not__Suc,axiom, 0.19/0.56 ! [M: nat] : 0.19/0.56 ( zero_zero_nat 0.19/0.56 != ( suc @ M ) ) ). 0.19/0.56 0.19/0.56 thf(fact_62_curryI,axiom, 0.19/0.56 ! [F2: produc1166363805nt_com > $o,A: list_char > int,B: com] : 0.19/0.56 ( ( produc1803493327_com_o @ F2 @ A @ B ) 0.19/0.56 <= ( F2 @ ( produc1139835093nt_com @ A @ B ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_55_surj__pair,axiom, 0.19/0.56 ! [P4: produc1260470173ar_int] : 0.19/0.56 ? [X3: com,Y3: list_char > int] : 0.19/0.56 ( P4 0.19/0.56 = ( produc1193801173ar_int @ X3 @ Y3 ) ) ). 0.19/0.56 0.19/0.56 thf(fact_22_meh__simp,axiom, 0.19/0.56 ! [S6: list_char > int,T3: list_char > int] : 0.19/0.56 ( ( big_big_step @ ( produc1193801173ar_int @ skip @ S6 ) @ T3 ) 0.19/0.56 = ( S6 = T3 ) ) ). 0.19/0.56 0.19/0.56 thf(fact_280_ab__semigroup__add__class_Oadd__ac_I1_J,axiom, 0.19/0.56 ! [A: nat,B: nat,C: nat] : 0.19/0.56 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C ) 0.19/0.56 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_351_Inf_OINF__identity__eq,axiom, 0.19/0.56 ! [Inf: set_nat > nat,A4: set_nat] : 0.19/0.56 ( ( Inf 0.19/0.56 @ ( image_nat_nat 0.19/0.56 @ ^ [X: nat] : X 0.19/0.56 @ A4 ) ) 0.19/0.56 = ( Inf @ A4 ) ) ). 0.19/0.56 0.19/0.56 thf(fact_6_ir__post,axiom, 0.19/0.56 ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,Q3: ( list_char > int ) > ( list_char > int ) > $o] : 0.19/0.56 ( ( ( relati2102071307_hoare @ P @ C @ C2 @ Q3 ) 0.19/0.56 <= ! [S3: list_char > int,S4: list_char > int] : 0.19/0.56 ( ( Q3 @ S3 @ S4 ) 0.19/0.56 => ( Q @ S3 @ S4 ) ) ) 0.19/0.56 <= ( relati2102071307_hoare @ P @ C @ C2 @ Q ) ) ). 0.19/0.56 0.19/0.56 thf(fact_323_diff__induct,axiom, 0.19/0.56 ! [P: nat > nat > $o,M: nat,N3: nat] : 0.19/0.56 ( ! [X3: nat] : ( P @ X3 @ zero_zero_nat ) 0.19/0.56 => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) ) 0.19/0.56 => ( ( P @ M @ N3 ) 0.19/0.56 <= ! [X3: nat,Y3: nat] : 0.19/0.56 ( ( P @ ( suc @ X3 ) @ ( suc @ Y3 ) ) 0.19/0.56 <= ( P @ X3 @ Y3 ) ) ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_41_old_Oprod_Oexhaust,axiom, 0.19/0.56 ! [Y: produc1166363805nt_com] : 0.19/0.56 ~ ! [A3: list_char > int,B3: com] : 0.19/0.56 ( Y 0.19/0.56 != ( produc1139835093nt_com @ A3 @ B3 ) ) ). 0.19/0.56 0.19/0.56 thf(fact_179_case__prodD,axiom, 0.19/0.56 ! [F2: ( list_char > int ) > com > $o,A: list_char > int,B: com] : 0.19/0.56 ( ( F2 @ A @ B ) 0.19/0.56 <= ( produc613711406_com_o @ F2 @ ( produc1139835093nt_com @ A @ B ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_157_prod_Ocase__distrib,axiom, 0.19/0.56 ! [H: $o > set_nat,F2: com > ( list_char > int ) > $o,Prod: produc1260470173ar_int] : 0.19/0.56 ( ( H @ ( produc668584238_int_o @ F2 @ Prod ) ) 0.19/0.56 = ( produc991755120et_nat 0.19/0.56 @ ^ [X13: com,X24: list_char > int] : ( H @ ( F2 @ X13 @ X24 ) ) 0.19/0.56 @ Prod ) ) ). 0.19/0.56 0.19/0.56 thf(fact_324_zero__induct,axiom, 0.19/0.56 ! [P: nat > $o,K: nat] : 0.19/0.56 ( ( P @ K ) 0.19/0.56 => ( ( P @ zero_zero_nat ) 0.19/0.56 <= ! [N: nat] : 0.19/0.56 ( ( P @ ( suc @ N ) ) 0.19/0.56 => ( P @ N ) ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_23_Skip__ir__valid,axiom, 0.19/0.56 ! [Q: ( list_char > int ) > ( list_char > int ) > $o,P: ( list_char > int ) > ( list_char > int ) > $o,C2: com] : 0.19/0.56 ( ! [T: list_char > int,T2: list_char > int] : 0.19/0.56 ( ( Q @ T @ T2 ) 0.19/0.56 => ? [S5: list_char > int] : 0.19/0.56 ( ( P @ T @ S5 ) 0.19/0.56 & ( big_big_step @ ( produc1193801173ar_int @ C2 @ S5 ) @ T2 ) ) ) 0.19/0.56 => ( relati775585786_valid @ P @ skip @ C2 @ Q ) ) ). 0.19/0.56 0.19/0.56 thf(fact_288_add__right__imp__eq,axiom, 0.19/0.56 ! [B: nat,A: nat,C: nat] : 0.19/0.56 ( ( ( plus_plus_nat @ B @ A ) 0.19/0.56 = ( plus_plus_nat @ C @ A ) ) 0.19/0.56 => ( B = C ) ) ). 0.19/0.56 0.19/0.56 thf(fact_291_ir__Assign,axiom, 0.19/0.56 ! [P: ( list_char > int ) > ( list_char > int ) > $o,X4: list_char,E: aexp,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] : 0.19/0.56 ( ( relati2102071307_hoare 0.19/0.56 @ ^ [T4: list_char > int,T5: list_char > int] : 0.19/0.56 ? [V3: int] : 0.19/0.56 ( ( P @ ( fun_up103088396ar_int @ T4 @ X4 @ V3 ) @ T5 ) 0.19/0.56 & ( ( T4 @ X4 ) 0.19/0.56 = ( aval @ E @ ( fun_up103088396ar_int @ T4 @ X4 @ V3 ) ) ) ) 0.19/0.56 @ skip 0.19/0.56 @ C2 0.19/0.56 @ Q ) 0.19/0.56 => ( relati2102071307_hoare @ P @ ( assign @ X4 @ E ) @ C2 @ Q ) ) ). 0.19/0.56 0.19/0.56 thf(fact_107_mem__case__prodI,axiom, 0.19/0.56 ! [Z: produc1260470173ar_int,C: com > ( list_char > int ) > set_Pr1148378109ar_int,A: com,B: list_char > int] : 0.19/0.56 ( ( member92250950ar_int @ Z @ ( C @ A @ B ) ) 0.19/0.56 => ( member92250950ar_int @ Z @ ( produc128852371ar_int @ C @ ( produc1193801173ar_int @ A @ B ) ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_21_sym__ir__valid,axiom, 0.19/0.56 ! [P: ( list_char > int ) > ( list_char > int ) > $o,C2: com,C: com,Q: ( list_char > int ) > ( list_char > int ) > $o] : 0.19/0.56 ( ( relati775585786_valid @ ( relati186416454e_flip @ P ) @ C2 @ C @ ( relati186416454e_flip @ Q ) ) 0.19/0.56 => ( relati775585786_valid @ P @ C @ C2 @ Q ) ) ). 0.19/0.56 0.19/0.56 thf(fact_127_case__prod__curry,axiom, 0.19/0.56 ! [F2: produc1260470173ar_int > $o] : 0.19/0.56 ( ( produc668584238_int_o @ ( produc1858366159_int_o @ F2 ) ) 0.19/0.56 = F2 ) ). 0.19/0.56 0.19/0.56 thf(fact_339_com_Osize__gen_I1_J,axiom, 0.19/0.56 ( ( size_com @ skip ) 0.19/0.56 = zero_zero_nat ) ). 0.19/0.56 0.19/0.56 thf(fact_198_add__Suc__right,axiom, 0.19/0.56 ! [M: nat,N3: nat] : 0.19/0.56 ( ( plus_plus_nat @ M @ ( suc @ N3 ) ) 0.19/0.56 = ( suc @ ( plus_plus_nat @ M @ N3 ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_70_com_Odistinct_I13_J,axiom, 0.19/0.56 ! [X21: list_char,X22: aexp,X51: bexp,X52: com] : 0.19/0.56 ( ( assign @ X21 @ X22 ) 0.19/0.56 != ( while @ X51 @ X52 ) ) ). 0.19/0.56 0.19/0.56 thf(fact_76_curryE,axiom, 0.19/0.56 ! [F2: produc1166363805nt_com > $o,A: list_char > int,B: com] : 0.19/0.56 ( ( F2 @ ( produc1139835093nt_com @ A @ B ) ) 0.19/0.56 <= ( produc1803493327_com_o @ F2 @ A @ B ) ) ). 0.19/0.56 0.19/0.56 thf(fact_139_pair__imageI,axiom, 0.19/0.56 ! [A: list_char > int,B: com,A4: set_Pr866150653nt_com,F2: ( list_char > int ) > com > nat] : 0.19/0.56 ( ( member_nat @ ( F2 @ A @ B ) @ ( image_596692520om_nat @ ( produc1263502010om_nat @ F2 ) @ A4 ) ) 0.19/0.56 <= ( member2145628230nt_com @ ( produc1139835093nt_com @ A @ B ) @ A4 ) ) ). 0.19/0.56 0.19/0.56 thf(fact_116_case__prodI,axiom, 0.19/0.56 ! [F2: com > ( list_char > int ) > $o,A: com,B: list_char > int] : 0.19/0.56 ( ( produc668584238_int_o @ F2 @ ( produc1193801173ar_int @ A @ B ) ) 0.19/0.56 <= ( F2 @ A @ B ) ) ). 0.19/0.56 0.19/0.56 thf(fact_312_add__eq__0__iff__both__eq__0,axiom, 0.19/0.56 ! [X4: nat,Y: nat] : 0.19/0.56 ( ( ( plus_plus_nat @ X4 @ Y ) 0.19/0.56 = zero_zero_nat ) 0.19/0.56 = ( ( Y = zero_zero_nat ) 0.19/0.56 & ( X4 = zero_zero_nat ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_332_add_Ocomm__neutral,axiom, 0.19/0.56 ! [A: nat] : 0.19/0.56 ( ( plus_plus_nat @ A @ zero_zero_nat ) 0.19/0.56 = A ) ). 0.19/0.56 0.19/0.56 thf(fact_261_Compr__image__eq,axiom, 0.19/0.56 ! [F2: produc1260470173ar_int > produc1166363805nt_com,A4: set_Pr1148378109ar_int,P: produc1166363805nt_com > $o] : 0.19/0.56 ( ( collec676690312nt_com 0.19/0.56 @ ^ [X: produc1166363805nt_com] : 0.19/0.56 ( ( member2145628230nt_com @ X @ ( image_786684229nt_com @ F2 @ A4 ) ) 0.19/0.56 & ( P @ X ) ) ) 0.19/0.56 = ( image_786684229nt_com @ F2 0.19/0.56 @ ( collec770796680ar_int 0.19/0.56 @ ^ [X: produc1260470173ar_int] : 0.19/0.56 ( ( member92250950ar_int @ X @ A4 ) 0.19/0.56 & ( P @ ( F2 @ X ) ) ) ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_53_prod__cases,axiom, 0.19/0.56 ! [P: produc1260470173ar_int > $o,P4: produc1260470173ar_int] : 0.19/0.56 ( ! [A3: com,B3: list_char > int] : ( P @ ( produc1193801173ar_int @ A3 @ B3 ) ) 0.19/0.56 => ( P @ P4 ) ) ). 0.19/0.56 0.19/0.56 thf(fact_282_group__cancel_Oadd1,axiom, 0.19/0.56 ! [A4: nat,K: nat,A: nat,B: nat] : 0.19/0.56 ( ( A4 0.19/0.56 = ( plus_plus_nat @ K @ A ) ) 0.19/0.56 => ( ( plus_plus_nat @ A4 @ B ) 0.19/0.56 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_160_prod_Ocase__distrib,axiom, 0.19/0.56 ! [H: $o > produc1260470173ar_int,F2: com > ( list_char > int ) > $o,Prod: produc1260470173ar_int] : 0.19/0.56 ( ( H @ ( produc668584238_int_o @ F2 @ Prod ) ) 0.19/0.56 = ( produc1288559923ar_int 0.19/0.56 @ ^ [X13: com,X24: list_char > int] : ( H @ ( F2 @ X13 @ X24 ) ) 0.19/0.56 @ Prod ) ) ). 0.19/0.56 0.19/0.56 thf(fact_264_Compr__image__eq,axiom, 0.19/0.56 ! [F2: nat > produc1166363805nt_com,A4: set_nat,P: produc1166363805nt_com > $o] : 0.19/0.56 ( ( collec676690312nt_com 0.19/0.56 @ ^ [X: produc1166363805nt_com] : 0.19/0.56 ( ( member2145628230nt_com @ X @ ( image_244615942nt_com @ F2 @ A4 ) ) 0.19/0.56 & ( P @ X ) ) ) 0.19/0.56 = ( image_244615942nt_com @ F2 0.19/0.56 @ ( collect_nat 0.19/0.56 @ ^ [X: nat] : 0.19/0.56 ( ( P @ ( F2 @ X ) ) 0.19/0.56 & ( member_nat @ X @ A4 ) ) ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_9_ir__valid__decomp2,axiom, 0.19/0.56 ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,R: ( list_char > int ) > ( list_char > int ) > $o,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] : 0.19/0.56 ( ( relati775585786_valid @ P @ C @ C2 @ Q ) 0.19/0.56 <= ( ( relati775585786_valid @ P @ C @ skip @ R ) 0.19/0.56 & ( relati775585786_valid @ R @ skip @ C2 @ Q ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_314_Nat_Oadd__0__right,axiom, 0.19/0.56 ! [M: nat] : 0.19/0.56 ( ( plus_plus_nat @ M @ zero_zero_nat ) 0.19/0.56 = M ) ). 0.19/0.56 0.19/0.56 thf(fact_347_Euclid__induct,axiom, 0.19/0.56 ! [P: nat > nat > $o,A: nat,B: nat] : 0.19/0.56 ( ! [A3: nat,B3: nat] : 0.19/0.56 ( ( P @ A3 @ B3 ) 0.19/0.56 = ( P @ B3 @ A3 ) ) 0.19/0.56 => ( ! [A3: nat] : ( P @ A3 @ zero_zero_nat ) 0.19/0.56 => ( ( P @ A @ B ) 0.19/0.56 <= ! [A3: nat,B3: nat] : 0.19/0.56 ( ( P @ A3 @ ( plus_plus_nat @ A3 @ B3 ) ) 0.19/0.56 <= ( P @ A3 @ B3 ) ) ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_15_ir__Skip__sym,axiom, 0.19/0.56 ! [Q: ( list_char > int ) > ( list_char > int ) > $o,P: ( list_char > int ) > ( list_char > int ) > $o,C2: com] : 0.19/0.56 ( ! [T: list_char > int,T2: list_char > int] : 0.19/0.56 ( ( Q @ T2 @ T ) 0.19/0.56 => ? [S5: list_char > int] : 0.19/0.56 ( ( P @ S5 @ T ) 0.19/0.56 & ( big_big_step @ ( produc1193801173ar_int @ C2 @ S5 ) @ T2 ) ) ) 0.19/0.56 => ( relati2102071307_hoare @ P @ C2 @ skip @ Q ) ) ). 0.19/0.56 0.19/0.56 thf(fact_316_image__add__0,axiom, 0.19/0.56 ! [S9: set_nat] : 0.19/0.56 ( ( image_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ S9 ) 0.19/0.56 = S9 ) ). 0.19/0.56 0.19/0.56 thf(fact_329_old_Onat_Oinducts,axiom, 0.19/0.56 ! [P: nat > $o,Nat: nat] : 0.19/0.56 ( ( ! [Nat3: nat] : 0.19/0.56 ( ( P @ ( suc @ Nat3 ) ) 0.19/0.56 <= ( P @ Nat3 ) ) 0.19/0.56 => ( P @ Nat ) ) 0.19/0.56 <= ( P @ zero_zero_nat ) ) ). 0.19/0.56 0.19/0.56 thf(fact_256_fun__upd__idem,axiom, 0.19/0.56 ! [F2: list_char > int,X4: list_char,Y: int] : 0.19/0.56 ( ( ( fun_up103088396ar_int @ F2 @ X4 @ Y ) 0.19/0.56 = F2 ) 0.19/0.56 <= ( ( F2 @ X4 ) 0.19/0.56 = Y ) ) ). 0.19/0.56 0.19/0.56 thf(fact_308_add__cancel__left__left,axiom, 0.19/0.56 ! [B: nat,A: nat] : 0.19/0.56 ( ( ( plus_plus_nat @ B @ A ) 0.19/0.56 = A ) 0.19/0.56 = ( B = zero_zero_nat ) ) ). 0.19/0.56 0.19/0.56 thf(fact_83_IfTrue,axiom, 0.19/0.56 ! [B: bexp,S7: list_char > int,C_1: com,T6: list_char > int,C_2: com] : 0.19/0.56 ( ( ( big_big_step @ ( produc1193801173ar_int @ ( if @ B @ C_1 @ C_2 ) @ S7 ) @ T6 ) 0.19/0.56 <= ( big_big_step @ ( produc1193801173ar_int @ C_1 @ S7 ) @ T6 ) ) 0.19/0.56 <= ( bval @ B @ S7 ) ) ). 0.19/0.56 0.19/0.56 thf(fact_102_mem__case__prodI2,axiom, 0.19/0.56 ! [P4: produc1260470173ar_int,Z: produc1166363805nt_com,C: com > ( list_char > int ) > set_Pr866150653nt_com] : 0.19/0.56 ( ( member2145628230nt_com @ Z @ ( produc1994108563nt_com @ C @ P4 ) ) 0.19/0.56 <= ! [A3: com,B3: list_char > int] : 0.19/0.56 ( ( P4 0.19/0.56 = ( produc1193801173ar_int @ A3 @ B3 ) ) 0.19/0.56 => ( member2145628230nt_com @ Z @ ( C @ A3 @ B3 ) ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_273_image__image,axiom, 0.19/0.56 ! [F2: nat > nat,G: nat > nat,A4: set_nat] : 0.19/0.56 ( ( image_nat_nat @ F2 @ ( image_nat_nat @ G @ A4 ) ) 0.19/0.56 = ( image_nat_nat 0.19/0.56 @ ^ [X: nat] : ( F2 @ ( G @ X ) ) 0.19/0.56 @ A4 ) ) ). 0.19/0.56 0.19/0.56 thf(fact_63_curryI,axiom, 0.19/0.56 ! [F2: produc1260470173ar_int > $o,A: com,B: list_char > int] : 0.19/0.56 ( ( produc1858366159_int_o @ F2 @ A @ B ) 0.19/0.56 <= ( F2 @ ( produc1193801173ar_int @ A @ B ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_297_decomp__def,axiom, 0.19/0.56 ( relati1310524937decomp 0.19/0.56 = ( ^ [P2: ( list_char > int ) > ( list_char > int ) > $o,C3: com,C4: com,Q2: ( list_char > int ) > ( list_char > int ) > $o,T4: list_char > int,S2: list_char > int] : 0.19/0.56 ? [S: list_char > int,T5: list_char > int] : 0.19/0.56 ( ( P2 @ S @ S2 ) 0.19/0.56 & ( big_big_step @ ( produc1193801173ar_int @ C4 @ S2 ) @ T5 ) 0.19/0.56 & ( Q2 @ T4 @ T5 ) 0.19/0.56 & ( big_big_step @ ( produc1193801173ar_int @ C3 @ S ) @ T4 ) ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_320_old_Onat_Odistinct_I1_J,axiom, 0.19/0.56 ! [Nat2: nat] : 0.19/0.56 ( zero_zero_nat 0.19/0.56 != ( suc @ Nat2 ) ) ). 0.19/0.56 0.19/0.56 thf(fact_328_old_Onat_Oexhaust,axiom, 0.19/0.56 ! [Y: nat] : 0.19/0.56 ( ( Y != zero_zero_nat ) 0.19/0.56 => ~ ! [Nat3: nat] : 0.19/0.56 ( Y 0.19/0.56 != ( suc @ Nat3 ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_236_bex__imageD,axiom, 0.19/0.56 ! [F2: nat > nat,A4: set_nat,P: nat > $o] : 0.19/0.56 ( ? [X3: nat] : 0.19/0.56 ( ( P @ ( F2 @ X3 ) ) 0.19/0.56 & ( member_nat @ X3 @ A4 ) ) 0.19/0.56 <= ? [X5: nat] : 0.19/0.56 ( ( member_nat @ X5 @ ( image_nat_nat @ F2 @ A4 ) ) 0.19/0.56 & ( P @ X5 ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_186_mem__case__prodE,axiom, 0.19/0.56 ! [Z: nat,C: com > ( list_char > int ) > set_nat,P4: produc1260470173ar_int] : 0.19/0.56 ( ~ ! [X3: com,Y3: list_char > int] : 0.19/0.56 ( ( P4 0.19/0.56 = ( produc1193801173ar_int @ X3 @ Y3 ) ) 0.19/0.56 => ~ ( member_nat @ Z @ ( C @ X3 @ Y3 ) ) ) 0.19/0.56 <= ( member_nat @ Z @ ( produc991755120et_nat @ C @ P4 ) ) ) ). 0.19/0.56 0.19/0.56 thf(help_If_3_1_If_001t__Int__Oint_T,axiom, 0.19/0.56 ! [P: $o] : 0.19/0.56 ( ( P = $false ) 0.19/0.56 | ( P = $true ) ) ). 0.19/0.56 0.19/0.56 thf(fact_184_mem__case__prodE,axiom, 0.19/0.56 ! [Z: produc1260470173ar_int,C: ( list_char > int ) > com > set_Pr1148378109ar_int,P4: produc1166363805nt_com] : 0.19/0.56 ( ~ ! [X3: list_char > int,Y3: com] : 0.19/0.56 ( ( P4 0.19/0.56 = ( produc1139835093nt_com @ X3 @ Y3 ) ) 0.19/0.56 => ~ ( member92250950ar_int @ Z @ ( C @ X3 @ Y3 ) ) ) 0.19/0.56 <= ( member92250950ar_int @ Z @ ( produc1461507731ar_int @ C @ P4 ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_274_imageE,axiom, 0.19/0.56 ! [B: nat,F2: nat > nat,A4: set_nat] : 0.19/0.56 ( ( member_nat @ B @ ( image_nat_nat @ F2 @ A4 ) ) 0.19/0.56 => ~ ! [X3: nat] : 0.19/0.56 ( ~ ( member_nat @ X3 @ A4 ) 0.19/0.56 <= ( B 0.19/0.56 = ( F2 @ X3 ) ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_38_sim__trans,axiom, 0.19/0.56 ! [C: com,C2: com,C5: com] : 0.19/0.56 ( ! [S3: list_char > int,T: list_char > int] : 0.19/0.56 ( ( big_big_step @ ( produc1193801173ar_int @ C @ S3 ) @ T ) 0.19/0.56 = ( big_big_step @ ( produc1193801173ar_int @ C2 @ S3 ) @ T ) ) 0.19/0.56 => ( ! [S3: list_char > int,T: list_char > int] : 0.19/0.56 ( ( big_big_step @ ( produc1193801173ar_int @ C2 @ S3 ) @ T ) 0.19/0.56 = ( big_big_step @ ( produc1193801173ar_int @ C5 @ S3 ) @ T ) ) 0.19/0.56 => ! [S8: list_char > int,T7: list_char > int] : 0.19/0.56 ( ( big_big_step @ ( produc1193801173ar_int @ C @ S8 ) @ T7 ) 0.19/0.56 = ( big_big_step @ ( produc1193801173ar_int @ C5 @ S8 ) @ T7 ) ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_17_com_Odistinct_I1_J,axiom, 0.19/0.56 ! [X21: list_char,X22: aexp] : 0.19/0.56 ( skip 0.19/0.56 != ( assign @ X21 @ X22 ) ) ). 0.19/0.56 0.19/0.56 thf(fact_106_mem__case__prodI2,axiom, 0.19/0.56 ! [P4: produc1260470173ar_int,Z: nat,C: com > ( list_char > int ) > set_nat] : 0.19/0.56 ( ! [A3: com,B3: list_char > int] : 0.19/0.56 ( ( member_nat @ Z @ ( C @ A3 @ B3 ) ) 0.19/0.56 <= ( P4 0.19/0.56 = ( produc1193801173ar_int @ A3 @ B3 ) ) ) 0.19/0.56 => ( member_nat @ Z @ ( produc991755120et_nat @ C @ P4 ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_243_imageI,axiom, 0.19/0.56 ! [X4: produc1260470173ar_int,A4: set_Pr1148378109ar_int,F2: produc1260470173ar_int > nat] : 0.19/0.56 ( ( member_nat @ ( F2 @ X4 ) @ ( image_1742782760nt_nat @ F2 @ A4 ) ) 0.19/0.56 <= ( member92250950ar_int @ X4 @ A4 ) ) ). 0.19/0.56 0.19/0.56 thf(fact_35_old_Oprod_Oinject,axiom, 0.19/0.56 ! [A: com,B: list_char > int,A2: com,B2: list_char > int] : 0.19/0.56 ( ( ( produc1193801173ar_int @ A @ B ) 0.19/0.56 = ( produc1193801173ar_int @ A2 @ B2 ) ) 0.19/0.56 = ( ( B = B2 ) 0.19/0.56 & ( A = A2 ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_18_com_Oinject_I2_J,axiom, 0.19/0.56 ! [X31: com,X32: com,Y31: com,Y32: com] : 0.19/0.56 ( ( ( seq @ X31 @ X32 ) 0.19/0.56 = ( seq @ Y31 @ Y32 ) ) 0.19/0.56 = ( ( X32 = Y32 ) 0.19/0.56 & ( X31 = Y31 ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_298_ir__valid__Seq1,axiom, 0.19/0.56 ! [P: ( list_char > int ) > ( list_char > int ) > $o,C1: com,C22: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] : 0.19/0.56 ( ( relati775585786_valid @ P @ ( seq @ C1 @ C22 ) @ C2 @ Q ) 0.19/0.56 => ( relati775585786_valid @ P @ C1 @ C2 0.19/0.56 @ ^ [T4: list_char > int,T5: list_char > int] : 0.19/0.56 ? [S: list_char > int,S2: list_char > int] : 0.19/0.56 ( ? [U2: list_char > int] : 0.19/0.56 ( ( Q @ U2 @ T5 ) 0.19/0.56 & ( big_big_step @ ( produc1193801173ar_int @ C22 @ T4 ) @ U2 ) ) 0.19/0.56 & ( big_big_step @ ( produc1193801173ar_int @ C2 @ S2 ) @ T5 ) 0.19/0.56 & ( big_big_step @ ( produc1193801173ar_int @ C1 @ S ) @ T4 ) 0.19/0.56 & ( P @ S @ S2 ) ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_10_ir__Seq1,axiom, 0.19/0.56 ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,D: com,R: ( list_char > int ) > ( list_char > int ) > $o] : 0.19/0.56 ( ( relati2102071307_hoare @ P @ C @ C2 @ Q ) 0.19/0.56 => ( ( relati2102071307_hoare @ Q @ D @ skip @ R ) 0.19/0.56 => ( relati2102071307_hoare @ P @ ( seq @ C @ D ) @ C2 @ R ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_211_image__eqI,axiom, 0.19/0.56 ! [B: nat,F2: nat > nat,X4: nat,A4: set_nat] : 0.19/0.56 ( ( ( member_nat @ X4 @ A4 ) 0.19/0.56 => ( member_nat @ B @ ( image_nat_nat @ F2 @ A4 ) ) ) 0.19/0.56 <= ( B 0.19/0.56 = ( F2 @ X4 ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_91_swap__swap,axiom, 0.19/0.56 ! [P4: produc1260470173ar_int] : 0.19/0.56 ( ( produc1716235893nt_com @ ( produc1770201973ar_int @ P4 ) ) 0.19/0.56 = P4 ) ). 0.19/0.56 0.19/0.56 thf(fact_141_pair__imageI,axiom, 0.19/0.56 ! [A: list_char > int,B: com,A4: set_Pr866150653nt_com,F2: ( list_char > int ) > com > produc1166363805nt_com] : 0.19/0.56 ( ( member2145628230nt_com @ ( produc1139835093nt_com @ A @ B ) @ A4 ) 0.19/0.56 => ( member2145628230nt_com @ ( F2 @ A @ B ) @ ( image_1874758725nt_com @ ( produc1676975923nt_com @ F2 ) @ A4 ) ) ) ). 0.19/0.56 0.19/0.56 thf(fact_158_prod_Ocase__distrib,axiom, 0.19/0.56 ! [H: nat > set_nat,F2: com > ( list_char > int ) > nat,Prod: produc1260470173ar_int] : 0.19/0.56 ( ( H @ ( produc1311963066nt_nat @ F2 @ Prod ) ) 0.19/0.57 = ( produc991755120et_nat 0.19/0.57 @ ^ [X13: com,X24: list_char > int] : ( H @ ( F2 @ X13 @ X24 ) ) 0.19/0.57 @ Prod ) ) ). 0.19/0.57 0.19/0.57 thf(fact_3_ir__Skip__Skip,axiom, 0.19/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o] : ( relati2102071307_hoare @ P @ skip @ skip @ P ) ). 0.19/0.57 0.19/0.57 thf(fact_117_disj__ir__valid,axiom, 0.19/0.57 ! [P_1: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q_1: ( list_char > int ) > ( list_char > int ) > $o,P_2: ( list_char > int ) > ( list_char > int ) > $o,Q_2: ( list_char > int ) > ( list_char > int ) > $o] : 0.19/0.57 ( ( ( relati775585786_valid @ P_2 @ C @ C2 @ Q_2 ) 0.19/0.57 => ( relati775585786_valid 0.19/0.57 @ ^ [S: list_char > int,S2: list_char > int] : 0.19/0.57 ( ( P_2 @ S @ S2 ) 0.19/0.57 | ( P_1 @ S @ S2 ) ) 0.19/0.57 @ C 0.19/0.57 @ C2 0.19/0.57 @ ^ [T4: list_char > int,T5: list_char > int] : 0.19/0.57 ( ( Q_1 @ T4 @ T5 ) 0.19/0.57 | ( Q_2 @ T4 @ T5 ) ) ) ) 0.19/0.57 <= ( relati775585786_valid @ P_1 @ C @ C2 @ Q_1 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_293_Setcompr__eq__image,axiom, 0.19/0.57 ! [F2: nat > nat,A4: set_nat] : 0.19/0.57 ( ( collect_nat 0.19/0.57 @ ^ [Uu: nat] : 0.19/0.57 ? [X: nat] : 0.19/0.57 ( ( member_nat @ X @ A4 ) 0.19/0.57 & ( Uu 0.19/0.57 = ( F2 @ X ) ) ) ) 0.19/0.57 = ( image_nat_nat @ F2 @ A4 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_124_curry__case__prod,axiom, 0.19/0.57 ! [F2: com > ( list_char > int ) > nat] : 0.19/0.57 ( ( produc763543641nt_nat @ ( produc1311963066nt_nat @ F2 ) ) 0.19/0.57 = F2 ) ). 0.19/0.57 0.19/0.57 thf(fact_96_internal__case__prod__def,axiom, 0.19/0.57 produc641693072nt_nat = produc1311963066nt_nat ). 0.19/0.57 0.19/0.57 thf(fact_24_com_Odistinct_I9_J,axiom, 0.19/0.57 ! [X21: list_char,X22: aexp,X31: com,X32: com] : 0.19/0.57 ( ( assign @ X21 @ X22 ) 0.19/0.57 != ( seq @ X31 @ X32 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_67_com_Odistinct_I19_J,axiom, 0.19/0.57 ! [X41: bexp,X42: com,X43: com,X51: bexp,X52: com] : 0.19/0.57 ( ( if @ X41 @ X42 @ X43 ) 0.19/0.57 != ( while @ X51 @ X52 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_44_mem__Collect__eq,axiom, 0.19/0.57 ! [A: produc1166363805nt_com,P: produc1166363805nt_com > $o] : 0.19/0.57 ( ( member2145628230nt_com @ A @ ( collec676690312nt_com @ P ) ) 0.19/0.57 = ( P @ A ) ) ). 0.19/0.57 0.19/0.57 thf(fact_132_case__swap,axiom, 0.19/0.57 ! [F2: com > ( list_char > int ) > nat,P4: produc1260470173ar_int] : 0.19/0.57 ( ( produc1263502010om_nat 0.19/0.57 @ ^ [Y4: list_char > int,X: com] : ( F2 @ X @ Y4 ) 0.19/0.57 @ ( produc1770201973ar_int @ P4 ) ) 0.19/0.57 = ( produc1311963066nt_nat @ F2 @ P4 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_154_prod_Ocase__distrib,axiom, 0.19/0.57 ! [H: nat > nat,F2: com > ( list_char > int ) > nat,Prod: produc1260470173ar_int] : 0.19/0.57 ( ( H @ ( produc1311963066nt_nat @ F2 @ Prod ) ) 0.19/0.57 = ( produc1311963066nt_nat 0.19/0.57 @ ^ [X13: com,X24: list_char > int] : ( H @ ( F2 @ X13 @ X24 ) ) 0.19/0.57 @ Prod ) ) ). 0.19/0.57 0.19/0.57 thf(fact_87_WhileFalse,axiom, 0.19/0.57 ! [B: bexp,S7: list_char > int,C: com] : 0.19/0.57 ( ( big_big_step @ ( produc1193801173ar_int @ ( while @ B @ C ) @ S7 ) @ S7 ) 0.19/0.57 <= ~ ( bval @ B @ S7 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_20_Seq__ir__valid,axiom, 0.19/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,D: com,D2: com,R: ( list_char > int ) > ( list_char > int ) > $o] : 0.19/0.57 ( ( ( relati775585786_valid @ Q @ D @ D2 @ R ) 0.19/0.57 => ( relati775585786_valid @ P @ ( seq @ C @ D ) @ ( seq @ C2 @ D2 ) @ R ) ) 0.19/0.57 <= ( relati775585786_valid @ P @ C @ C2 @ Q ) ) ). 0.19/0.57 0.19/0.57 thf(fact_304_While__backwards__frontier__ir__valid,axiom, 0.19/0.57 ! [P: nat > ( list_char > int ) > ( list_char > int ) > $o,B: bexp,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] : 0.19/0.57 ( ! [N: nat] : 0.19/0.57 ( relati775585786_valid 0.19/0.57 @ ^ [S: list_char > int,S2: list_char > int] : 0.19/0.57 ( ( P @ N @ S @ S2 ) 0.19/0.57 & ( bval @ B @ S ) ) 0.19/0.57 @ C 0.19/0.57 @ skip 0.19/0.57 @ ( P @ ( suc @ N ) ) ) 0.19/0.57 => ( ( relati775585786_valid @ ( P @ zero_zero_nat ) @ ( while @ B @ C ) @ C2 @ Q ) 0.19/0.57 <= ( relati775585786_valid 0.19/0.57 @ ^ [S: list_char > int,S2: list_char > int] : 0.19/0.57 ? [N5: nat] : ( P @ N5 @ S @ S2 ) 0.19/0.57 @ ( while @ B @ C ) 0.19/0.57 @ C2 0.19/0.57 @ Q ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_325_Suc__neq__Zero,axiom, 0.19/0.57 ! [M: nat] : 0.19/0.57 ( ( suc @ M ) 0.19/0.57 != zero_zero_nat ) ). 0.19/0.57 0.19/0.57 thf(fact_277_add__Suc__shift,axiom, 0.19/0.57 ! [M: nat,N3: nat] : 0.19/0.57 ( ( plus_plus_nat @ ( suc @ M ) @ N3 ) 0.19/0.57 = ( plus_plus_nat @ M @ ( suc @ N3 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_213_nat_Oinject,axiom, 0.19/0.57 ! [X2: nat,Y2: nat] : 0.19/0.57 ( ( ( suc @ X2 ) 0.19/0.57 = ( suc @ Y2 ) ) 0.19/0.57 = ( X2 = Y2 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_100_While__backwards__frontier__ir__valid_H,axiom, 0.19/0.57 ! [P: nat > ( list_char > int ) > ( list_char > int ) > $o,K: nat,B: bexp,C: com,Q: ( list_char > int ) > ( list_char > int ) > $o,C2: com,T6: list_char > int,T3: list_char > int] : 0.19/0.57 ( ( ! [T: list_char > int,T2: list_char > int] : 0.19/0.57 ( ( Q @ T @ T2 ) 0.19/0.57 => ? [S8: list_char > int,S5: list_char > int] : 0.19/0.57 ( ( big_big_step @ ( produc1193801173ar_int @ ( while @ B @ C ) @ S8 ) @ T ) 0.19/0.57 & ( big_big_step @ ( produc1193801173ar_int @ C2 @ S5 ) @ T2 ) 0.19/0.57 & ? [N2: nat] : ( P @ ( plus_plus_nat @ K @ N2 ) @ S8 @ S5 ) ) ) 0.19/0.57 => ( ? [S3: list_char > int,S4: list_char > int] : 0.19/0.57 ( ( P @ K @ S3 @ S4 ) 0.19/0.57 & ( big_big_step @ ( produc1193801173ar_int @ C2 @ S4 ) @ T3 ) 0.19/0.57 & ( big_big_step @ ( produc1193801173ar_int @ ( while @ B @ C ) @ S3 ) @ T6 ) ) 0.19/0.57 <= ( Q @ T6 @ T3 ) ) ) 0.19/0.57 <= ! [N: nat,T: list_char > int,T2: list_char > int] : 0.19/0.57 ( ( P @ ( plus_plus_nat @ K @ ( suc @ N ) ) @ T @ T2 ) 0.19/0.57 => ? [S8: list_char > int] : 0.19/0.57 ( ( P @ ( plus_plus_nat @ K @ N ) @ S8 @ T2 ) 0.19/0.57 & ( bval @ B @ S8 ) 0.19/0.57 & ( big_big_step @ ( produc1193801173ar_int @ C @ S8 ) @ T ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_95_internal__case__prod__def,axiom, 0.19/0.57 produc9062872_int_o = produc668584238_int_o ). 0.19/0.57 0.19/0.57 thf(fact_101_mem__case__prodI2,axiom, 0.19/0.57 ! [P4: produc1260470173ar_int,Z: produc1260470173ar_int,C: com > ( list_char > int ) > set_Pr1148378109ar_int] : 0.19/0.57 ( ( member92250950ar_int @ Z @ ( produc128852371ar_int @ C @ P4 ) ) 0.19/0.57 <= ! [A3: com,B3: list_char > int] : 0.19/0.57 ( ( P4 0.19/0.57 = ( produc1193801173ar_int @ A3 @ B3 ) ) 0.19/0.57 => ( member92250950ar_int @ Z @ ( C @ A3 @ B3 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_333_add__eq__self__zero,axiom, 0.19/0.57 ! [M: nat,N3: nat] : 0.19/0.57 ( ( ( plus_plus_nat @ M @ N3 ) 0.19/0.57 = M ) 0.19/0.57 => ( N3 = zero_zero_nat ) ) ). 0.19/0.57 0.19/0.57 thf(fact_99_While__True__ir__valid,axiom, 0.19/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,B: bexp,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] : 0.19/0.57 ( ( relati775585786_valid 0.19/0.57 @ ^ [S: list_char > int,S2: list_char > int] : 0.19/0.57 ( ( bval @ B @ S ) 0.19/0.57 & ( P @ S @ S2 ) ) 0.19/0.57 @ ( seq @ C @ ( while @ B @ C ) ) 0.19/0.57 @ C2 0.19/0.57 @ Q ) 0.19/0.57 => ( relati775585786_valid @ P @ ( while @ B @ C ) @ C2 @ Q ) ) ). 0.19/0.57 0.19/0.57 thf(fact_108_mem__case__prodI,axiom, 0.19/0.57 ! [Z: produc1166363805nt_com,C: com > ( list_char > int ) > set_Pr866150653nt_com,A: com,B: list_char > int] : 0.19/0.57 ( ( member2145628230nt_com @ Z @ ( produc1994108563nt_com @ C @ ( produc1193801173ar_int @ A @ B ) ) ) 0.19/0.57 <= ( member2145628230nt_com @ Z @ ( C @ A @ B ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_235_bex__imageD,axiom, 0.19/0.57 ! [F2: produc1260470173ar_int > nat,A4: set_Pr1148378109ar_int,P: nat > $o] : 0.19/0.57 ( ? [X3: produc1260470173ar_int] : 0.19/0.57 ( ( P @ ( F2 @ X3 ) ) 0.19/0.57 & ( member92250950ar_int @ X3 @ A4 ) ) 0.19/0.57 <= ? [X5: nat] : 0.19/0.57 ( ( P @ X5 ) 0.19/0.57 & ( member_nat @ X5 @ ( image_1742782760nt_nat @ F2 @ A4 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_247_imageI,axiom, 0.19/0.57 ! [X4: produc1166363805nt_com,A4: set_Pr866150653nt_com,F2: produc1166363805nt_com > produc1260470173ar_int] : 0.19/0.57 ( ( member2145628230nt_com @ X4 @ A4 ) 0.19/0.57 => ( member92250950ar_int @ ( F2 @ X4 ) @ ( image_1968865093ar_int @ F2 @ A4 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_206_image__eqI,axiom, 0.19/0.57 ! [B: produc1260470173ar_int,F2: produc1260470173ar_int > produc1260470173ar_int,X4: produc1260470173ar_int,A4: set_Pr1148378109ar_int] : 0.19/0.57 ( ( ( member92250950ar_int @ X4 @ A4 ) 0.19/0.57 => ( member92250950ar_int @ B @ ( image_880790597ar_int @ F2 @ A4 ) ) ) 0.19/0.57 <= ( B 0.19/0.57 = ( F2 @ X4 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_185_mem__case__prodE,axiom, 0.19/0.57 ! [Z: produc1166363805nt_com,C: ( list_char > int ) > com > set_Pr866150653nt_com,P4: produc1166363805nt_com] : 0.19/0.57 ( ~ ! [X3: list_char > int,Y3: com] : 0.19/0.57 ( ~ ( member2145628230nt_com @ Z @ ( C @ X3 @ Y3 ) ) 0.19/0.57 <= ( P4 0.19/0.57 = ( produc1139835093nt_com @ X3 @ Y3 ) ) ) 0.19/0.57 <= ( member2145628230nt_com @ Z @ ( produc1179280275nt_com @ C @ P4 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_300_get__back_Osimps_I2_J,axiom, 0.19/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,B: bexp,C: com,N3: nat] : 0.19/0.57 ( ( relati23543761ar_int @ P @ B @ C @ ( suc @ N3 ) ) 0.19/0.57 = ( ^ [T4: list_char > int,T5: list_char > int] : 0.19/0.57 ? [S: list_char > int] : 0.19/0.57 ( ( bval @ B @ S ) 0.19/0.57 & ( relati23543761ar_int @ P @ B @ C @ N3 @ S @ T5 ) 0.19/0.57 & ( big_big_step @ ( produc1193801173ar_int @ C @ S ) @ T4 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_178_case__prodE,axiom, 0.19/0.57 ! [C: com > ( list_char > int ) > $o,P4: produc1260470173ar_int] : 0.19/0.57 ( ( produc668584238_int_o @ C @ P4 ) 0.19/0.57 => ~ ! [X3: com,Y3: list_char > int] : 0.19/0.57 ( ( P4 0.19/0.57 = ( produc1193801173ar_int @ X3 @ Y3 ) ) 0.19/0.57 => ~ ( C @ X3 @ Y3 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_0_soundness,axiom, 0.19/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] : 0.19/0.57 ( ( relati775585786_valid @ P @ C @ C2 @ Q ) 0.19/0.57 <= ( relati2102071307_hoare @ P @ C @ C2 @ Q ) ) ). 0.19/0.57 0.19/0.57 thf(fact_207_image__eqI,axiom, 0.19/0.57 ! [B: produc1166363805nt_com,F2: produc1260470173ar_int > produc1166363805nt_com,X4: produc1260470173ar_int,A4: set_Pr1148378109ar_int] : 0.19/0.57 ( ( B 0.19/0.57 = ( F2 @ X4 ) ) 0.19/0.57 => ( ( member92250950ar_int @ X4 @ A4 ) 0.19/0.57 => ( member2145628230nt_com @ B @ ( image_786684229nt_com @ F2 @ A4 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_224_rev__image__eqI,axiom, 0.19/0.57 ! [X4: nat,A4: set_nat,B: nat,F2: nat > nat] : 0.19/0.57 ( ( ( member_nat @ B @ ( image_nat_nat @ F2 @ A4 ) ) 0.19/0.57 <= ( B 0.19/0.57 = ( F2 @ X4 ) ) ) 0.19/0.57 <= ( member_nat @ X4 @ A4 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_335_one__is__add,axiom, 0.19/0.57 ! [M: nat,N3: nat] : 0.19/0.57 ( ( ( suc @ zero_zero_nat ) 0.19/0.57 = ( plus_plus_nat @ M @ N3 ) ) 0.19/0.57 = ( ( ( M = zero_zero_nat ) 0.19/0.57 & ( N3 0.19/0.57 = ( suc @ zero_zero_nat ) ) ) 0.19/0.57 | ( ( N3 = zero_zero_nat ) 0.19/0.57 & ( M 0.19/0.57 = ( suc @ zero_zero_nat ) ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_232_image__cong,axiom, 0.19/0.57 ! [M2: set_nat,N4: set_nat,F2: nat > nat,G: nat > nat] : 0.19/0.57 ( ( M2 = N4 ) 0.19/0.57 => ( ! [X3: nat] : 0.19/0.57 ( ( member_nat @ X3 @ N4 ) 0.19/0.57 => ( ( F2 @ X3 ) 0.19/0.57 = ( G @ X3 ) ) ) 0.19/0.57 => ( ( image_nat_nat @ F2 @ M2 ) 0.19/0.57 = ( image_nat_nat @ G @ N4 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_223_rev__image__eqI,axiom, 0.19/0.57 ! [X4: produc1166363805nt_com,A4: set_Pr866150653nt_com,B: produc1166363805nt_com,F2: produc1166363805nt_com > produc1166363805nt_com] : 0.19/0.57 ( ( member2145628230nt_com @ X4 @ A4 ) 0.19/0.57 => ( ( B 0.19/0.57 = ( F2 @ X4 ) ) 0.19/0.57 => ( member2145628230nt_com @ B @ ( image_1874758725nt_com @ F2 @ A4 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_30_SkipE,axiom, 0.19/0.57 ! [S7: list_char > int,T6: list_char > int] : 0.19/0.57 ( ( T6 = S7 ) 0.19/0.57 <= ( big_big_step @ ( produc1193801173ar_int @ skip @ S7 ) @ T6 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_208_image__eqI,axiom, 0.19/0.57 ! [B: nat,F2: produc1166363805nt_com > nat,X4: produc1166363805nt_com,A4: set_Pr866150653nt_com] : 0.19/0.57 ( ( B 0.19/0.57 = ( F2 @ X4 ) ) 0.19/0.57 => ( ( member_nat @ B @ ( image_596692520om_nat @ F2 @ A4 ) ) 0.19/0.57 <= ( member2145628230nt_com @ X4 @ A4 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_153_prod_Ocase__distrib,axiom, 0.19/0.57 ! [H: nat > $o,F2: com > ( list_char > int ) > nat,Prod: produc1260470173ar_int] : 0.19/0.57 ( ( H @ ( produc1311963066nt_nat @ F2 @ Prod ) ) 0.19/0.57 = ( produc668584238_int_o 0.19/0.57 @ ^ [X13: com,X24: list_char > int] : ( H @ ( F2 @ X13 @ X24 ) ) 0.19/0.57 @ Prod ) ) ). 0.19/0.57 0.19/0.57 thf(fact_19_com_Oinject_I1_J,axiom, 0.19/0.57 ! [X21: list_char,X22: aexp,Y21: list_char,Y22: aexp] : 0.19/0.57 ( ( ( assign @ X21 @ X22 ) 0.19/0.57 = ( assign @ Y21 @ Y22 ) ) 0.19/0.57 = ( ( X21 = Y21 ) 0.19/0.57 & ( X22 = Y22 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_225_ball__imageD,axiom, 0.19/0.57 ! [F2: produc1166363805nt_com > produc1260470173ar_int,A4: set_Pr866150653nt_com,P: produc1260470173ar_int > $o] : 0.19/0.57 ( ! [X5: produc1166363805nt_com] : 0.19/0.57 ( ( P @ ( F2 @ X5 ) ) 0.19/0.57 <= ( member2145628230nt_com @ X5 @ A4 ) ) 0.19/0.57 <= ! [X3: produc1260470173ar_int] : 0.19/0.57 ( ( P @ X3 ) 0.19/0.57 <= ( member92250950ar_int @ X3 @ ( image_1968865093ar_int @ F2 @ A4 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_246_imageI,axiom, 0.19/0.57 ! [X4: produc1166363805nt_com,A4: set_Pr866150653nt_com,F2: produc1166363805nt_com > nat] : 0.19/0.57 ( ( member_nat @ ( F2 @ X4 ) @ ( image_596692520om_nat @ F2 @ A4 ) ) 0.19/0.57 <= ( member2145628230nt_com @ X4 @ A4 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_112_mem__case__prodI,axiom, 0.19/0.57 ! [Z: nat,C: com > ( list_char > int ) > set_nat,A: com,B: list_char > int] : 0.19/0.57 ( ( member_nat @ Z @ ( C @ A @ B ) ) 0.19/0.57 => ( member_nat @ Z @ ( produc991755120et_nat @ C @ ( produc1193801173ar_int @ A @ B ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_217_rev__image__eqI,axiom, 0.19/0.57 ! [X4: nat,A4: set_nat,B: produc1166363805nt_com,F2: nat > produc1166363805nt_com] : 0.19/0.57 ( ( ( B 0.19/0.57 = ( F2 @ X4 ) ) 0.19/0.57 => ( member2145628230nt_com @ B @ ( image_244615942nt_com @ F2 @ A4 ) ) ) 0.19/0.57 <= ( member_nat @ X4 @ A4 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_204_image__eqI,axiom, 0.19/0.57 ! [B: produc1166363805nt_com,F2: nat > produc1166363805nt_com,X4: nat,A4: set_nat] : 0.19/0.57 ( ( ( member2145628230nt_com @ B @ ( image_244615942nt_com @ F2 @ A4 ) ) 0.19/0.57 <= ( member_nat @ X4 @ A4 ) ) 0.19/0.57 <= ( B 0.19/0.57 = ( F2 @ X4 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_266_Compr__image__eq,axiom, 0.19/0.57 ! [F2: produc1166363805nt_com > nat,A4: set_Pr866150653nt_com,P: nat > $o] : 0.19/0.57 ( ( collect_nat 0.19/0.57 @ ^ [X: nat] : 0.19/0.57 ( ( member_nat @ X @ ( image_596692520om_nat @ F2 @ A4 ) ) 0.19/0.57 & ( P @ X ) ) ) 0.19/0.57 = ( image_596692520om_nat @ F2 0.19/0.57 @ ( collec676690312nt_com 0.19/0.57 @ ^ [X: produc1166363805nt_com] : 0.19/0.57 ( ( P @ ( F2 @ X ) ) 0.19/0.57 & ( member2145628230nt_com @ X @ A4 ) ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_149_Assign__blah,axiom, 0.19/0.57 ! [T6: list_char > int,X4: list_char,E: aexp,V2: int] : 0.19/0.57 ( ( big_big_step @ ( produc1193801173ar_int @ ( assign @ X4 @ E ) @ ( fun_up103088396ar_int @ T6 @ X4 @ V2 ) ) @ T6 ) 0.19/0.57 <= ( ( T6 @ X4 ) 0.19/0.57 = ( aval @ E @ ( fun_up103088396ar_int @ T6 @ X4 @ V2 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_42_old_Oprod_Oexhaust,axiom, 0.19/0.57 ! [Y: produc1260470173ar_int] : 0.19/0.57 ~ ! [A3: com,B3: list_char > int] : 0.19/0.57 ( Y 0.19/0.57 != ( produc1193801173ar_int @ A3 @ B3 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_227_ball__imageD,axiom, 0.19/0.57 ! [F2: produc1260470173ar_int > nat,A4: set_Pr1148378109ar_int,P: nat > $o] : 0.19/0.57 ( ! [X3: nat] : 0.19/0.57 ( ( member_nat @ X3 @ ( image_1742782760nt_nat @ F2 @ A4 ) ) 0.19/0.57 => ( P @ X3 ) ) 0.19/0.57 => ! [X5: produc1260470173ar_int] : 0.19/0.57 ( ( member92250950ar_int @ X5 @ A4 ) 0.19/0.57 => ( P @ ( F2 @ X5 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_119_case__prod__conv,axiom, 0.19/0.57 ! [F2: com > ( list_char > int ) > $o,A: com,B: list_char > int] : 0.19/0.57 ( ( produc668584238_int_o @ F2 @ ( produc1193801173ar_int @ A @ B ) ) 0.19/0.57 = ( F2 @ A @ B ) ) ). 0.19/0.57 0.19/0.57 thf(fact_168_cond__case__prod__eta,axiom, 0.19/0.57 ! [F2: com > ( list_char > int ) > produc1260470173ar_int,G: produc1260470173ar_int > produc1260470173ar_int] : 0.19/0.57 ( ( ( produc1288559923ar_int @ F2 ) 0.19/0.57 = G ) 0.19/0.57 <= ! [X3: com,Y3: list_char > int] : 0.19/0.57 ( ( F2 @ X3 @ Y3 ) 0.19/0.57 = ( G @ ( produc1193801173ar_int @ X3 @ Y3 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_1_completeness,axiom, 0.19/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] : 0.19/0.57 ( ( relati775585786_valid @ P @ C @ C2 @ Q ) 0.19/0.57 => ( relati2102071307_hoare @ P @ C @ C2 @ Q ) ) ). 0.19/0.57 0.19/0.57 thf(fact_58_ssubst__Pair__rhs,axiom, 0.19/0.57 ! [R2: com,S7: list_char > int,R: set_Pr1148378109ar_int,S6: list_char > int] : 0.19/0.57 ( ( member92250950ar_int @ ( produc1193801173ar_int @ R2 @ S7 ) @ R ) 0.19/0.57 => ( ( member92250950ar_int @ ( produc1193801173ar_int @ R2 @ S6 ) @ R ) 0.19/0.57 <= ( S6 = S7 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_229_image__cong,axiom, 0.19/0.57 ! [M2: set_Pr1148378109ar_int,N4: set_Pr1148378109ar_int,F2: produc1260470173ar_int > produc1166363805nt_com,G: produc1260470173ar_int > produc1166363805nt_com] : 0.19/0.57 ( ( ! [X3: produc1260470173ar_int] : 0.19/0.57 ( ( ( F2 @ X3 ) 0.19/0.57 = ( G @ X3 ) ) 0.19/0.57 <= ( member92250950ar_int @ X3 @ N4 ) ) 0.19/0.57 => ( ( image_786684229nt_com @ F2 @ M2 ) 0.19/0.57 = ( image_786684229nt_com @ G @ N4 ) ) ) 0.19/0.57 <= ( M2 = N4 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_138_pair__imageI,axiom, 0.19/0.57 ! [A: com,B: list_char > int,A4: set_Pr1148378109ar_int,F2: com > ( list_char > int ) > produc1166363805nt_com] : 0.19/0.57 ( ( member2145628230nt_com @ ( F2 @ A @ B ) @ ( image_786684229nt_com @ ( produc1194453555nt_com @ F2 ) @ A4 ) ) 0.19/0.57 <= ( member92250950ar_int @ ( produc1193801173ar_int @ A @ B ) @ A4 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_54_surj__pair,axiom, 0.19/0.57 ! [P4: produc1166363805nt_com] : 0.19/0.57 ? [X3: list_char > int,Y3: com] : 0.19/0.57 ( P4 0.19/0.57 = ( produc1139835093nt_com @ X3 @ Y3 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_137_case__swap,axiom, 0.19/0.57 ! [F2: ( list_char > int ) > com > produc1260470173ar_int,P4: produc1166363805nt_com] : 0.19/0.57 ( ( produc1288559923ar_int 0.19/0.57 @ ^ [Y4: com,X: list_char > int] : ( F2 @ X @ Y4 ) 0.19/0.57 @ ( produc1716235893nt_com @ P4 ) ) 0.19/0.57 = ( produc1771082291ar_int @ F2 @ P4 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_341_com_Osize__gen_I5_J,axiom, 0.19/0.57 ! [X51: bexp,X52: com] : 0.19/0.57 ( ( size_com @ ( while @ X51 @ X52 ) ) 0.19/0.57 = ( plus_plus_nat @ ( size_com @ X52 ) @ ( suc @ zero_zero_nat ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_197_ir__While__True,axiom, 0.19/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,B: bexp,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] : 0.19/0.57 ( ( relati2102071307_hoare @ P @ ( while @ B @ C ) @ C2 @ Q ) 0.19/0.57 <= ( relati2102071307_hoare 0.19/0.57 @ ^ [S: list_char > int,S2: list_char > int] : 0.19/0.57 ( ( P @ S @ S2 ) 0.19/0.57 & ( bval @ B @ S ) ) 0.19/0.57 @ ( seq @ C @ ( while @ B @ C ) ) 0.19/0.57 @ C2 0.19/0.57 @ Q ) ) ). 0.19/0.57 0.19/0.57 thf(fact_165_cond__case__prod__eta,axiom, 0.19/0.57 ! [F2: com > ( list_char > int ) > set_nat,G: produc1260470173ar_int > set_nat] : 0.19/0.57 ( ( ( produc991755120et_nat @ F2 ) 0.19/0.57 = G ) 0.19/0.57 <= ! [X3: com,Y3: list_char > int] : 0.19/0.57 ( ( F2 @ X3 @ Y3 ) 0.19/0.57 = ( G @ ( produc1193801173ar_int @ X3 @ Y3 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_187_old_Oprod_Ocase,axiom, 0.19/0.57 ! [F2: com > ( list_char > int ) > set_nat,X1: com,X2: list_char > int] : 0.19/0.57 ( ( produc991755120et_nat @ F2 @ ( produc1193801173ar_int @ X1 @ X2 ) ) 0.19/0.57 = ( F2 @ X1 @ X2 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_258_fun__upd__def,axiom, 0.19/0.57 ( fun_up103088396ar_int 0.19/0.57 = ( ^ [F: list_char > int,A5: list_char,B4: int,X: list_char] : ( if_int @ ( X = A5 ) @ B4 @ ( F @ X ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_11_ir__sym,axiom, 0.19/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] : 0.19/0.57 ( ( relati2102071307_hoare @ ( relati186416454e_flip @ P ) @ C @ C2 @ ( relati186416454e_flip @ Q ) ) 0.19/0.57 => ( relati2102071307_hoare @ P @ C2 @ C @ Q ) ) ). 0.19/0.57 0.19/0.57 thf(fact_81_sim__while__cong__aux,axiom, 0.19/0.57 ! [B: bexp,C: com,S7: list_char > int,T6: list_char > int,C2: com] : 0.19/0.57 ( ( ! [S3: list_char > int,T: list_char > int] : 0.19/0.57 ( ( big_big_step @ ( produc1193801173ar_int @ C @ S3 ) @ T ) 0.19/0.57 = ( big_big_step @ ( produc1193801173ar_int @ C2 @ S3 ) @ T ) ) 0.19/0.57 => ( big_big_step @ ( produc1193801173ar_int @ ( while @ B @ C2 ) @ S7 ) @ T6 ) ) 0.19/0.57 <= ( big_big_step @ ( produc1193801173ar_int @ ( while @ B @ C ) @ S7 ) @ T6 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_334_plus__nat_Oadd__0,axiom, 0.19/0.57 ! [N3: nat] : 0.19/0.57 ( ( plus_plus_nat @ zero_zero_nat @ N3 ) 0.19/0.57 = N3 ) ). 0.19/0.57 0.19/0.57 thf(fact_317_get__back_Osimps_I1_J,axiom, 0.19/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,B: bexp,C: com] : 0.19/0.57 ( ( relati23543761ar_int @ P @ B @ C @ zero_zero_nat ) 0.19/0.57 = P ) ). 0.19/0.57 0.19/0.57 thf(fact_340_com_Osize__gen_I2_J,axiom, 0.19/0.57 ! [X21: list_char,X22: aexp] : 0.19/0.57 ( ( size_com @ ( assign @ X21 @ X22 ) ) 0.19/0.57 = zero_zero_nat ) ). 0.19/0.57 0.19/0.57 thf(fact_167_cond__case__prod__eta,axiom, 0.19/0.57 ! [F2: com > ( list_char > int ) > nat,G: produc1260470173ar_int > nat] : 0.19/0.57 ( ( ( produc1311963066nt_nat @ F2 ) 0.19/0.57 = G ) 0.19/0.57 <= ! [X3: com,Y3: list_char > int] : 0.19/0.57 ( ( F2 @ X3 @ Y3 ) 0.19/0.57 = ( G @ ( produc1193801173ar_int @ X3 @ Y3 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_77_curryE,axiom, 0.19/0.57 ! [F2: produc1260470173ar_int > $o,A: com,B: list_char > int] : 0.19/0.57 ( ( produc1858366159_int_o @ F2 @ A @ B ) 0.19/0.57 => ( F2 @ ( produc1193801173ar_int @ A @ B ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_230_image__cong,axiom, 0.19/0.57 ! [M2: set_Pr1148378109ar_int,N4: set_Pr1148378109ar_int,F2: produc1260470173ar_int > nat,G: produc1260470173ar_int > nat] : 0.19/0.57 ( ( M2 = N4 ) 0.19/0.57 => ( ! [X3: produc1260470173ar_int] : 0.19/0.57 ( ( member92250950ar_int @ X3 @ N4 ) 0.19/0.57 => ( ( F2 @ X3 ) 0.19/0.57 = ( G @ X3 ) ) ) 0.19/0.57 => ( ( image_1742782760nt_nat @ F2 @ M2 ) 0.19/0.57 = ( image_1742782760nt_nat @ G @ N4 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_45_mem__Collect__eq,axiom, 0.19/0.57 ! [A: nat,P: nat > $o] : 0.19/0.57 ( ( member_nat @ A @ ( collect_nat @ P ) ) 0.19/0.57 = ( P @ A ) ) ). 0.19/0.57 0.19/0.57 thf(fact_86_WhileTrue,axiom, 0.19/0.57 ! [B: bexp,S_1: list_char > int,C: com,S_22: list_char > int,S_3: list_char > int] : 0.19/0.57 ( ( bval @ B @ S_1 ) 0.19/0.57 => ( ( ( big_big_step @ ( produc1193801173ar_int @ ( while @ B @ C ) @ S_1 ) @ S_3 ) 0.19/0.57 <= ( big_big_step @ ( produc1193801173ar_int @ ( while @ B @ C ) @ S_22 ) @ S_3 ) ) 0.19/0.57 <= ( big_big_step @ ( produc1193801173ar_int @ C @ S_1 ) @ S_22 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_321_nat_OdiscI,axiom, 0.19/0.57 ! [Nat: nat,X2: nat] : 0.19/0.57 ( ( Nat 0.19/0.57 = ( suc @ X2 ) ) 0.19/0.57 => ( Nat != zero_zero_nat ) ) ). 0.19/0.57 0.19/0.57 thf(fact_349_add__0__iff,axiom, 0.19/0.57 ! [B: nat,A: nat] : 0.19/0.57 ( ( B 0.19/0.57 = ( plus_plus_nat @ B @ A ) ) 0.19/0.57 = ( A = zero_zero_nat ) ) ). 0.19/0.57 0.19/0.57 thf(fact_131_case__swap,axiom, 0.19/0.57 ! [F2: com > ( list_char > int ) > $o,P4: produc1260470173ar_int] : 0.19/0.57 ( ( produc613711406_com_o 0.19/0.57 @ ^ [Y4: list_char > int,X: com] : ( F2 @ X @ Y4 ) 0.19/0.57 @ ( produc1770201973ar_int @ P4 ) ) 0.19/0.57 = ( produc668584238_int_o @ F2 @ P4 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_331_comm__monoid__add__class_Oadd__0,axiom, 0.19/0.57 ! [A: nat] : 0.19/0.57 ( ( plus_plus_nat @ zero_zero_nat @ A ) 0.19/0.57 = A ) ). 0.19/0.57 0.19/0.57 thf(fact_200_fun__upd__upd,axiom, 0.19/0.57 ! [F2: list_char > int,X4: list_char,Y: int,Z: int] : 0.19/0.57 ( ( fun_up103088396ar_int @ ( fun_up103088396ar_int @ F2 @ X4 @ Y ) @ X4 @ Z ) 0.19/0.57 = ( fun_up103088396ar_int @ F2 @ X4 @ Z ) ) ). 0.19/0.57 0.19/0.57 thf(fact_294_ir__valid__While2,axiom, 0.19/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,B: bexp,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] : 0.19/0.57 ( ( relati775585786_valid @ P @ ( while @ B @ C ) @ C2 @ Q ) 0.19/0.57 => ( relati775585786_valid 0.19/0.57 @ ^ [S: list_char > int,S2: list_char > int] : 0.19/0.57 ( ( P @ S @ S2 ) 0.19/0.57 & ~ ( bval @ B @ S ) ) 0.19/0.57 @ skip 0.19/0.57 @ C2 0.19/0.57 @ ^ [T4: list_char > int,T5: list_char > int] : 0.19/0.57 ( ( Q @ T4 @ T5 ) 0.19/0.57 & ? [S2: list_char > int] : 0.19/0.57 ( ( big_big_step @ ( produc1193801173ar_int @ C2 @ S2 ) @ T5 ) 0.19/0.57 & ~ ( bval @ B @ T4 ) 0.19/0.57 & ( P @ T4 @ S2 ) ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_134_case__swap,axiom, 0.19/0.57 ! [F2: ( list_char > int ) > com > set_nat,P4: produc1166363805nt_com] : 0.19/0.57 ( ( produc991755120et_nat 0.19/0.57 @ ^ [Y4: com,X: list_char > int] : ( F2 @ X @ Y4 ) 0.19/0.57 @ ( produc1716235893nt_com @ P4 ) ) 0.19/0.57 = ( produc1754105456et_nat @ F2 @ P4 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_192_ir__If__True,axiom, 0.19/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,B: bexp,C_1: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,C_2: com] : 0.19/0.57 ( ( relati2102071307_hoare 0.19/0.57 @ ^ [S: list_char > int,S2: list_char > int] : 0.19/0.57 ( ( bval @ B @ S ) 0.19/0.57 & ( P @ S @ S2 ) ) 0.19/0.57 @ C_1 0.19/0.57 @ C2 0.19/0.57 @ Q ) 0.19/0.57 => ( relati2102071307_hoare @ P @ ( if @ B @ C_1 @ C_2 ) @ C2 @ Q ) ) ). 0.19/0.57 0.19/0.57 thf(fact_65_com_Oinject_I4_J,axiom, 0.19/0.57 ! [X51: bexp,X52: com,Y51: bexp,Y52: com] : 0.19/0.57 ( ( ( while @ X51 @ X52 ) 0.19/0.57 = ( while @ Y51 @ Y52 ) ) 0.19/0.57 = ( ( X51 = Y51 ) 0.19/0.57 & ( X52 = Y52 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_310_add__cancel__right__left,axiom, 0.19/0.57 ! [A: nat,B: nat] : 0.19/0.57 ( ( A 0.19/0.57 = ( plus_plus_nat @ B @ A ) ) 0.19/0.57 = ( B = zero_zero_nat ) ) ). 0.19/0.57 0.19/0.57 thf(fact_169_case__prod__eta,axiom, 0.19/0.57 ! [F2: produc1260470173ar_int > set_nat] : 0.19/0.57 ( ( produc991755120et_nat 0.19/0.57 @ ^ [X: com,Y4: list_char > int] : ( F2 @ ( produc1193801173ar_int @ X @ Y4 ) ) ) 0.19/0.57 = F2 ) ). 0.19/0.57 0.19/0.57 thf(fact_241_imageI,axiom, 0.19/0.57 ! [X4: nat,A4: set_nat,F2: nat > produc1260470173ar_int] : 0.19/0.57 ( ( member_nat @ X4 @ A4 ) 0.19/0.57 => ( member92250950ar_int @ ( F2 @ X4 ) @ ( image_338722310ar_int @ F2 @ A4 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_103_mem__case__prodI2,axiom, 0.19/0.57 ! [P4: produc1166363805nt_com,Z: nat,C: ( list_char > int ) > com > set_nat] : 0.19/0.57 ( ! [A3: list_char > int,B3: com] : 0.19/0.57 ( ( P4 0.19/0.57 = ( produc1139835093nt_com @ A3 @ B3 ) ) 0.19/0.57 => ( member_nat @ Z @ ( C @ A3 @ B3 ) ) ) 0.19/0.57 => ( member_nat @ Z @ ( produc1754105456et_nat @ C @ P4 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_233_bex__imageD,axiom, 0.19/0.57 ! [F2: produc1166363805nt_com > produc1260470173ar_int,A4: set_Pr866150653nt_com,P: produc1260470173ar_int > $o] : 0.19/0.57 ( ? [X5: produc1260470173ar_int] : 0.19/0.57 ( ( member92250950ar_int @ X5 @ ( image_1968865093ar_int @ F2 @ A4 ) ) 0.19/0.57 & ( P @ X5 ) ) 0.19/0.57 => ? [X3: produc1166363805nt_com] : 0.19/0.57 ( ( member2145628230nt_com @ X3 @ A4 ) 0.19/0.57 & ( P @ ( F2 @ X3 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_57_ssubst__Pair__rhs,axiom, 0.19/0.57 ! [R2: list_char > int,S7: com,R: set_Pr866150653nt_com,S6: com] : 0.19/0.57 ( ( ( member2145628230nt_com @ ( produc1139835093nt_com @ R2 @ S6 ) @ R ) 0.19/0.57 <= ( S6 = S7 ) ) 0.19/0.57 <= ( member2145628230nt_com @ ( produc1139835093nt_com @ R2 @ S7 ) @ R ) ) ). 0.19/0.57 0.19/0.57 thf(fact_97_internal__case__prod__def,axiom, 0.19/0.57 produc837840349ar_int = produc1288559923ar_int ). 0.19/0.57 0.19/0.57 thf(fact_292_setcompr__eq__image,axiom, 0.19/0.57 ! [F2: nat > nat,P: nat > $o] : 0.19/0.57 ( ( collect_nat 0.19/0.57 @ ^ [Uu: nat] : 0.19/0.57 ? [X: nat] : 0.19/0.57 ( ( Uu 0.19/0.57 = ( F2 @ X ) ) 0.19/0.57 & ( P @ X ) ) ) 0.19/0.57 = ( image_nat_nat @ F2 @ ( collect_nat @ P ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_4_ir__hoare__Skip__Skip,axiom, 0.19/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,Q: ( list_char > int ) > ( list_char > int ) > $o] : 0.19/0.57 ( ( relati2102071307_hoare @ P @ skip @ skip @ Q ) 0.19/0.57 = ( ! [S: list_char > int,S2: list_char > int] : 0.19/0.57 ( ( Q @ S @ S2 ) 0.19/0.57 => ( P @ S @ S2 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_309_add__cancel__left__right,axiom, 0.19/0.57 ! [A: nat,B: nat] : 0.19/0.57 ( ( ( plus_plus_nat @ A @ B ) 0.19/0.57 = A ) 0.19/0.57 = ( B = zero_zero_nat ) ) ). 0.19/0.57 0.19/0.57 thf(fact_33_prod_Oinject,axiom, 0.19/0.57 ! [X1: com,X2: list_char > int,Y1: com,Y2: list_char > int] : 0.19/0.57 ( ( ( produc1193801173ar_int @ X1 @ X2 ) 0.19/0.57 = ( produc1193801173ar_int @ Y1 @ Y2 ) ) 0.19/0.57 = ( ( X2 = Y2 ) 0.19/0.57 & ( X1 = Y1 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_302_ir__valid__get__back,axiom, 0.19/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,B: bexp,C: com,K: nat,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] : 0.19/0.57 ( ( relati775585786_valid @ ( relati23543761ar_int @ P @ B @ C @ K ) @ ( while @ B @ C ) @ C2 @ Q ) 0.19/0.57 <= ( relati775585786_valid @ ( relati23543761ar_int @ P @ B @ C @ ( suc @ K ) ) @ ( while @ B @ C ) @ C2 @ Q ) ) ). 0.19/0.57 0.19/0.57 thf(fact_311_add__cancel__right__right,axiom, 0.19/0.57 ! [A: nat,B: nat] : 0.19/0.57 ( ( A 0.19/0.57 = ( plus_plus_nat @ A @ B ) ) 0.19/0.57 = ( B = zero_zero_nat ) ) ). 0.19/0.57 0.19/0.57 thf(fact_110_mem__case__prodI,axiom, 0.19/0.57 ! [Z: produc1260470173ar_int,C: ( list_char > int ) > com > set_Pr1148378109ar_int,A: list_char > int,B: com] : 0.19/0.57 ( ( member92250950ar_int @ Z @ ( produc1461507731ar_int @ C @ ( produc1139835093nt_com @ A @ B ) ) ) 0.19/0.57 <= ( member92250950ar_int @ Z @ ( C @ A @ B ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_173_case__prodE2,axiom, 0.19/0.57 ! [Q: set_nat > $o,P: com > ( list_char > int ) > set_nat,Z: produc1260470173ar_int] : 0.19/0.57 ( ( Q @ ( produc991755120et_nat @ P @ Z ) ) 0.19/0.57 => ~ ! [X3: com,Y3: list_char > int] : 0.19/0.57 ( ( Z 0.19/0.57 = ( produc1193801173ar_int @ X3 @ Y3 ) ) 0.19/0.57 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_125_curry__case__prod,axiom, 0.19/0.57 ! [F2: com > ( list_char > int ) > produc1260470173ar_int] : 0.19/0.57 ( ( produc804153044ar_int @ ( produc1288559923ar_int @ F2 ) ) 0.19/0.57 = F2 ) ). 0.19/0.57 0.19/0.57 thf(fact_203_image__eqI,axiom, 0.19/0.57 ! [B: produc1260470173ar_int,F2: nat > produc1260470173ar_int,X4: nat,A4: set_nat] : 0.19/0.57 ( ( B 0.19/0.57 = ( F2 @ X4 ) ) 0.19/0.57 => ( ( member92250950ar_int @ B @ ( image_338722310ar_int @ F2 @ A4 ) ) 0.19/0.57 <= ( member_nat @ X4 @ A4 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_143_pair__imageI,axiom, 0.19/0.57 ! [A: com,B: list_char > int,A4: set_Pr1148378109ar_int,F2: com > ( list_char > int ) > $o] : 0.19/0.57 ( ( member92250950ar_int @ ( produc1193801173ar_int @ A @ B ) @ A4 ) 0.19/0.57 => ( member_o @ ( F2 @ A @ B ) @ ( image_522938432_int_o @ ( produc668584238_int_o @ F2 ) @ A4 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_189_old_Oprod_Ocase,axiom, 0.19/0.57 ! [F2: com > ( list_char > int ) > nat,X1: com,X2: list_char > int] : 0.19/0.57 ( ( produc1311963066nt_nat @ F2 @ ( produc1193801173ar_int @ X1 @ X2 ) ) 0.19/0.57 = ( F2 @ X1 @ X2 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_27_SeqE,axiom, 0.19/0.57 ! [C1: com,C22: com,S1: list_char > int,S32: list_char > int] : 0.19/0.57 ( ( big_big_step @ ( produc1193801173ar_int @ ( seq @ C1 @ C22 ) @ S1 ) @ S32 ) 0.19/0.57 => ~ ! [S_2: list_char > int] : 0.19/0.57 ( ~ ( big_big_step @ ( produc1193801173ar_int @ C22 @ S_2 ) @ S32 ) 0.19/0.57 <= ( big_big_step @ ( produc1193801173ar_int @ C1 @ S1 ) @ S_2 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_13_Seq2__ir__valid,axiom, 0.19/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,Q: ( list_char > int ) > ( list_char > int ) > $o,D: com,C2: com,R: ( list_char > int ) > ( list_char > int ) > $o] : 0.19/0.57 ( ( ( relati775585786_valid @ P @ ( seq @ C @ D ) @ C2 @ R ) 0.19/0.57 <= ( relati775585786_valid @ Q @ D @ C2 @ R ) ) 0.19/0.57 <= ( relati775585786_valid @ P @ C @ skip @ Q ) ) ). 0.19/0.57 0.19/0.57 thf(fact_234_bex__imageD,axiom, 0.19/0.57 ! [F2: produc1260470173ar_int > produc1166363805nt_com,A4: set_Pr1148378109ar_int,P: produc1166363805nt_com > $o] : 0.19/0.57 ( ? [X3: produc1260470173ar_int] : 0.19/0.57 ( ( member92250950ar_int @ X3 @ A4 ) 0.19/0.57 & ( P @ ( F2 @ X3 ) ) ) 0.19/0.57 <= ? [X5: produc1166363805nt_com] : 0.19/0.57 ( ( member2145628230nt_com @ X5 @ ( image_786684229nt_com @ F2 @ A4 ) ) 0.19/0.57 & ( P @ X5 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_48_Collect__mem__eq,axiom, 0.19/0.57 ! [A4: set_nat] : 0.19/0.57 ( ( collect_nat 0.19/0.57 @ ^ [X: nat] : ( member_nat @ X @ A4 ) ) 0.19/0.57 = A4 ) ). 0.19/0.57 0.19/0.57 thf(fact_342_com_Osize_I9_J,axiom, 0.19/0.57 ! [X41: bexp,X42: com,X43: com] : 0.19/0.57 ( ( size_size_com @ ( if @ X41 @ X42 @ X43 ) ) 0.19/0.57 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_size_com @ X42 ) @ ( size_size_com @ X43 ) ) @ ( suc @ zero_zero_nat ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_166_cond__case__prod__eta,axiom, 0.19/0.57 ! [F2: com > ( list_char > int ) > $o,G: produc1260470173ar_int > $o] : 0.19/0.57 ( ( ( produc668584238_int_o @ F2 ) 0.19/0.57 = G ) 0.19/0.57 <= ! [X3: com,Y3: list_char > int] : 0.19/0.57 ( ( F2 @ X3 @ Y3 ) 0.19/0.57 = ( G @ ( produc1193801173ar_int @ X3 @ Y3 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_69_com_Odistinct_I17_J,axiom, 0.19/0.57 ! [X31: com,X32: com,X51: bexp,X52: com] : 0.19/0.57 ( ( seq @ X31 @ X32 ) 0.19/0.57 != ( while @ X51 @ X52 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_249_imageI,axiom, 0.19/0.57 ! [X4: nat,A4: set_nat,F2: nat > nat] : 0.19/0.57 ( ( member_nat @ X4 @ A4 ) 0.19/0.57 => ( member_nat @ ( F2 @ X4 ) @ ( image_nat_nat @ F2 @ A4 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_118_case__prod__conv,axiom, 0.19/0.57 ! [F2: com > ( list_char > int ) > set_nat,A: com,B: list_char > int] : 0.19/0.57 ( ( produc991755120et_nat @ F2 @ ( produc1193801173ar_int @ A @ B ) ) 0.19/0.57 = ( F2 @ A @ B ) ) ). 0.19/0.57 0.19/0.57 thf(fact_59_curry__conv,axiom, 0.19/0.57 ( produc1858366159_int_o 0.19/0.57 = ( ^ [F: produc1260470173ar_int > $o,A5: com,B4: list_char > int] : ( F @ ( produc1193801173ar_int @ A5 @ B4 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_60_commute__if,axiom, 0.19/0.57 ! [B1: bexp,B22: bexp,C11: com,C12: com,C22: com,S8: list_char > int,T7: list_char > int] : 0.19/0.57 ( ( big_big_step @ ( produc1193801173ar_int @ ( if @ B1 @ ( if @ B22 @ C11 @ C12 ) @ C22 ) @ S8 ) @ T7 ) 0.19/0.57 = ( big_big_step @ ( produc1193801173ar_int @ ( if @ B22 @ ( if @ B1 @ C11 @ C22 ) @ ( if @ B1 @ C12 @ C22 ) ) @ S8 ) @ T7 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_219_rev__image__eqI,axiom, 0.19/0.57 ! [X4: produc1260470173ar_int,A4: set_Pr1148378109ar_int,B: produc1260470173ar_int,F2: produc1260470173ar_int > produc1260470173ar_int] : 0.19/0.57 ( ( member92250950ar_int @ X4 @ A4 ) 0.19/0.57 => ( ( member92250950ar_int @ B @ ( image_880790597ar_int @ F2 @ A4 ) ) 0.19/0.57 <= ( B 0.19/0.57 = ( F2 @ X4 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_303_ir__valid__While3,axiom, 0.19/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,B: bexp,C: com,K: nat,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] : 0.19/0.57 ( ( relati775585786_valid @ ( relati23543761ar_int @ P @ B @ C @ K ) @ ( while @ B @ C ) @ C2 @ Q ) 0.19/0.57 => ( relati775585786_valid 0.19/0.57 @ ^ [S: list_char > int,S2: list_char > int] : 0.19/0.57 ( ( relati23543761ar_int @ P @ B @ C @ K @ S @ S2 ) 0.19/0.57 & ( bval @ B @ S ) ) 0.19/0.57 @ C 0.19/0.57 @ C2 0.19/0.57 @ ^ [T4: list_char > int,T5: list_char > int] : 0.19/0.57 ? [S2: list_char > int] : 0.19/0.57 ( ( big_big_step @ ( produc1193801173ar_int @ C2 @ S2 ) @ T5 ) 0.19/0.57 & ( relati23543761ar_int @ P @ B @ C @ ( suc @ K ) @ T4 @ S2 ) 0.19/0.57 & ? [U2: list_char > int] : 0.19/0.57 ( ( big_big_step @ ( produc1193801173ar_int @ ( while @ B @ C ) @ T4 ) @ U2 ) 0.19/0.57 & ( Q @ U2 @ T5 ) ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_52_prod__cases,axiom, 0.19/0.57 ! [P: produc1166363805nt_com > $o,P4: produc1166363805nt_com] : 0.19/0.57 ( ! [A3: list_char > int,B3: com] : ( P @ ( produc1139835093nt_com @ A3 @ B3 ) ) 0.19/0.57 => ( P @ P4 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_272_image__image,axiom, 0.19/0.57 ! [F2: produc1260470173ar_int > nat,G: produc1166363805nt_com > produc1260470173ar_int,A4: set_Pr866150653nt_com] : 0.19/0.57 ( ( image_1742782760nt_nat @ F2 @ ( image_1968865093ar_int @ G @ A4 ) ) 0.19/0.57 = ( image_596692520om_nat 0.19/0.57 @ ^ [X: produc1166363805nt_com] : ( F2 @ ( G @ X ) ) 0.19/0.57 @ A4 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_275_add__Suc,axiom, 0.19/0.57 ! [M: nat,N3: nat] : 0.19/0.57 ( ( plus_plus_nat @ ( suc @ M ) @ N3 ) 0.19/0.57 = ( suc @ ( plus_plus_nat @ M @ N3 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_239_image__iff,axiom, 0.19/0.57 ! [Z: produc1166363805nt_com,F2: produc1260470173ar_int > produc1166363805nt_com,A4: set_Pr1148378109ar_int] : 0.19/0.57 ( ( member2145628230nt_com @ Z @ ( image_786684229nt_com @ F2 @ A4 ) ) 0.19/0.57 = ( ? [X: produc1260470173ar_int] : 0.19/0.57 ( ( member92250950ar_int @ X @ A4 ) 0.19/0.57 & ( Z 0.19/0.57 = ( F2 @ X ) ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_255_fun__upd__same,axiom, 0.19/0.57 ! [F2: list_char > int,X4: list_char,Y: int] : 0.19/0.57 ( ( fun_up103088396ar_int @ F2 @ X4 @ Y @ X4 ) 0.19/0.57 = Y ) ). 0.19/0.57 0.19/0.57 thf(fact_301_ir__valid__While1,axiom, 0.19/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,B: bexp,C: com,K: nat,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] : 0.19/0.57 ( ( relati775585786_valid 0.19/0.57 @ ^ [S: list_char > int,S2: list_char > int] : 0.19/0.57 ( ( relati23543761ar_int @ P @ B @ C @ K @ S @ S2 ) 0.19/0.57 & ( bval @ B @ S ) ) 0.19/0.57 @ C 0.19/0.57 @ skip 0.19/0.57 @ ^ [T4: list_char > int,T5: list_char > int] : 0.19/0.57 ( ( relati23543761ar_int @ P @ B @ C @ ( suc @ K ) @ T4 @ T5 ) 0.19/0.57 & ? [U2: list_char > int,U3: list_char > int] : 0.19/0.57 ( ( big_big_step @ ( produc1193801173ar_int @ ( while @ B @ C ) @ T4 ) @ U2 ) 0.19/0.57 & ( Q @ U2 @ U3 ) 0.19/0.57 & ( big_big_step @ ( produc1193801173ar_int @ C2 @ T5 ) @ U3 ) ) ) ) 0.19/0.57 <= ( relati775585786_valid @ ( relati23543761ar_int @ P @ B @ C @ K ) @ ( while @ B @ C ) @ C2 @ Q ) ) ). 0.19/0.57 0.19/0.57 thf(fact_269_image__image,axiom, 0.19/0.57 ! [F2: produc1260470173ar_int > produc1166363805nt_com,G: produc1166363805nt_com > produc1260470173ar_int,A4: set_Pr866150653nt_com] : 0.19/0.57 ( ( image_786684229nt_com @ F2 @ ( image_1968865093ar_int @ G @ A4 ) ) 0.19/0.57 = ( image_1874758725nt_com 0.19/0.57 @ ^ [X: produc1166363805nt_com] : ( F2 @ ( G @ X ) ) 0.19/0.57 @ A4 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_214_split__part,axiom, 0.19/0.57 ! [P: $o,Q: com > ( list_char > int ) > $o] : 0.19/0.57 ( ( produc668584238_int_o 0.19/0.57 @ ^ [A5: com,B4: list_char > int] : 0.19/0.57 ( ( Q @ A5 @ B4 ) 0.19/0.57 & P ) ) 0.19/0.57 = ( ^ [Ab: produc1260470173ar_int] : 0.19/0.57 ( ( produc668584238_int_o @ Q @ Ab ) 0.19/0.57 & P ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_32_prod_Oinject,axiom, 0.19/0.57 ! [X1: list_char > int,X2: com,Y1: list_char > int,Y2: com] : 0.19/0.57 ( ( ( produc1139835093nt_com @ X1 @ X2 ) 0.19/0.57 = ( produc1139835093nt_com @ Y1 @ Y2 ) ) 0.19/0.57 = ( ( X1 = Y1 ) 0.19/0.57 & ( X2 = Y2 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_164_curry__K,axiom, 0.19/0.57 ! [C: $o] : 0.19/0.57 ( ( produc1858366159_int_o 0.19/0.57 @ ^ [X: produc1260470173ar_int] : C ) 0.19/0.57 = ( ^ [X: com,Y4: list_char > int] : C ) ) ). 0.19/0.57 0.19/0.57 thf(fact_196_ir__While__False,axiom, 0.19/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,B: bexp,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,C: com] : 0.19/0.57 ( ( relati2102071307_hoare @ P @ ( while @ B @ C ) @ C2 @ Q ) 0.19/0.57 <= ( relati2102071307_hoare 0.19/0.57 @ ^ [S: list_char > int,S2: list_char > int] : 0.19/0.57 ( ~ ( bval @ B @ S ) 0.19/0.57 & ( P @ S @ S2 ) ) 0.19/0.57 @ skip 0.19/0.57 @ C2 0.19/0.57 @ Q ) ) ). 0.19/0.57 0.19/0.57 thf(fact_278_add__right__cancel,axiom, 0.19/0.57 ! [B: nat,A: nat,C: nat] : 0.19/0.57 ( ( ( plus_plus_nat @ B @ A ) 0.19/0.57 = ( plus_plus_nat @ C @ A ) ) 0.19/0.57 = ( B = C ) ) ). 0.19/0.57 0.19/0.57 thf(fact_136_case__swap,axiom, 0.19/0.57 ! [F2: ( list_char > int ) > com > nat,P4: produc1166363805nt_com] : 0.19/0.57 ( ( produc1311963066nt_nat 0.19/0.57 @ ^ [Y4: com,X: list_char > int] : ( F2 @ X @ Y4 ) 0.19/0.57 @ ( produc1716235893nt_com @ P4 ) ) 0.19/0.57 = ( produc1263502010om_nat @ F2 @ P4 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_285_add_Ocommute,axiom, 0.19/0.57 ( plus_plus_nat 0.19/0.57 = ( ^ [A5: nat,B4: nat] : ( plus_plus_nat @ B4 @ A5 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_29_Seq,axiom, 0.19/0.57 ! [C_1: com,S_1: list_char > int,S_22: list_char > int,C_2: com,S_3: list_char > int] : 0.19/0.57 ( ( ( big_big_step @ ( produc1193801173ar_int @ C_2 @ S_22 ) @ S_3 ) 0.19/0.57 => ( big_big_step @ ( produc1193801173ar_int @ ( seq @ C_1 @ C_2 ) @ S_1 ) @ S_3 ) ) 0.19/0.57 <= ( big_big_step @ ( produc1193801173ar_int @ C_1 @ S_1 ) @ S_22 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_182_mem__case__prodE,axiom, 0.19/0.57 ! [Z: produc1166363805nt_com,C: com > ( list_char > int ) > set_Pr866150653nt_com,P4: produc1260470173ar_int] : 0.19/0.57 ( ~ ! [X3: com,Y3: list_char > int] : 0.19/0.57 ( ( P4 0.19/0.57 = ( produc1193801173ar_int @ X3 @ Y3 ) ) 0.19/0.57 => ~ ( member2145628230nt_com @ Z @ ( C @ X3 @ Y3 ) ) ) 0.19/0.57 <= ( member2145628230nt_com @ Z @ ( produc1994108563nt_com @ C @ P4 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_222_rev__image__eqI,axiom, 0.19/0.57 ! [X4: produc1166363805nt_com,A4: set_Pr866150653nt_com,B: produc1260470173ar_int,F2: produc1166363805nt_com > produc1260470173ar_int] : 0.19/0.57 ( ( ( member92250950ar_int @ B @ ( image_1968865093ar_int @ F2 @ A4 ) ) 0.19/0.57 <= ( B 0.19/0.57 = ( F2 @ X4 ) ) ) 0.19/0.57 <= ( member2145628230nt_com @ X4 @ A4 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_209_image__eqI,axiom, 0.19/0.57 ! [B: produc1260470173ar_int,F2: produc1166363805nt_com > produc1260470173ar_int,X4: produc1166363805nt_com,A4: set_Pr866150653nt_com] : 0.19/0.57 ( ( B 0.19/0.57 = ( F2 @ X4 ) ) 0.19/0.57 => ( ( member92250950ar_int @ B @ ( image_1968865093ar_int @ F2 @ A4 ) ) 0.19/0.57 <= ( member2145628230nt_com @ X4 @ A4 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_263_Compr__image__eq,axiom, 0.19/0.57 ! [F2: nat > produc1260470173ar_int,A4: set_nat,P: produc1260470173ar_int > $o] : 0.19/0.57 ( ( collec770796680ar_int 0.19/0.57 @ ^ [X: produc1260470173ar_int] : 0.19/0.57 ( ( P @ X ) 0.19/0.57 & ( member92250950ar_int @ X @ ( image_338722310ar_int @ F2 @ A4 ) ) ) ) 0.19/0.57 = ( image_338722310ar_int @ F2 0.19/0.57 @ ( collect_nat 0.19/0.57 @ ^ [X: nat] : 0.19/0.57 ( ( member_nat @ X @ A4 ) 0.19/0.57 & ( P @ ( F2 @ X ) ) ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_181_mem__case__prodE,axiom, 0.19/0.57 ! [Z: produc1260470173ar_int,C: com > ( list_char > int ) > set_Pr1148378109ar_int,P4: produc1260470173ar_int] : 0.19/0.57 ( ~ ! [X3: com,Y3: list_char > int] : 0.19/0.57 ( ~ ( member92250950ar_int @ Z @ ( C @ X3 @ Y3 ) ) 0.19/0.57 <= ( P4 0.19/0.57 = ( produc1193801173ar_int @ X3 @ Y3 ) ) ) 0.19/0.57 <= ( member92250950ar_int @ Z @ ( produc128852371ar_int @ C @ P4 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_242_imageI,axiom, 0.19/0.57 ! [X4: nat,A4: set_nat,F2: nat > produc1166363805nt_com] : 0.19/0.57 ( ( member2145628230nt_com @ ( F2 @ X4 ) @ ( image_244615942nt_com @ F2 @ A4 ) ) 0.19/0.57 <= ( member_nat @ X4 @ A4 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_130_case__swap,axiom, 0.19/0.57 ! [F2: com > ( list_char > int ) > set_nat,P4: produc1260470173ar_int] : 0.19/0.57 ( ( produc1754105456et_nat 0.19/0.57 @ ^ [Y4: list_char > int,X: com] : ( F2 @ X @ Y4 ) 0.19/0.57 @ ( produc1770201973ar_int @ P4 ) ) 0.19/0.57 = ( produc991755120et_nat @ F2 @ P4 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_216_rev__image__eqI,axiom, 0.19/0.57 ! [X4: nat,A4: set_nat,B: produc1260470173ar_int,F2: nat > produc1260470173ar_int] : 0.19/0.57 ( ( ( member92250950ar_int @ B @ ( image_338722310ar_int @ F2 @ A4 ) ) 0.19/0.57 <= ( B 0.19/0.57 = ( F2 @ X4 ) ) ) 0.19/0.57 <= ( member_nat @ X4 @ A4 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_194_assign__simp,axiom, 0.19/0.57 ! [X4: list_char,A: aexp,S7: list_char > int,S6: list_char > int] : 0.19/0.57 ( ( big_big_step @ ( produc1193801173ar_int @ ( assign @ X4 @ A ) @ S7 ) @ S6 ) 0.19/0.57 = ( S6 0.19/0.57 = ( fun_up103088396ar_int @ S7 @ X4 @ ( aval @ A @ S7 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_66_com_Oinject_I3_J,axiom, 0.19/0.57 ! [X41: bexp,X42: com,X43: com,Y41: bexp,Y42: com,Y43: com] : 0.19/0.57 ( ( ( if @ X41 @ X42 @ X43 ) 0.19/0.57 = ( if @ Y41 @ Y42 @ Y43 ) ) 0.19/0.57 = ( ( X43 = Y43 ) 0.19/0.57 & ( X42 = Y42 ) 0.19/0.57 & ( X41 = Y41 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_120_case__prod__conv,axiom, 0.19/0.57 ! [F2: com > ( list_char > int ) > nat,A: com,B: list_char > int] : 0.19/0.57 ( ( produc1311963066nt_nat @ F2 @ ( produc1193801173ar_int @ A @ B ) ) 0.19/0.57 = ( F2 @ A @ B ) ) ). 0.19/0.57 0.19/0.57 thf(fact_72_com_Odistinct_I15_J,axiom, 0.19/0.57 ! [X31: com,X32: com,X41: bexp,X42: com,X43: com] : 0.19/0.57 ( ( seq @ X31 @ X32 ) 0.19/0.57 != ( if @ X41 @ X42 @ X43 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_190_old_Oprod_Ocase,axiom, 0.19/0.57 ! [F2: com > ( list_char > int ) > produc1260470173ar_int,X1: com,X2: list_char > int] : 0.19/0.57 ( ( produc1288559923ar_int @ F2 @ ( produc1193801173ar_int @ X1 @ X2 ) ) 0.19/0.57 = ( F2 @ X1 @ X2 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_71_com_Odistinct_I5_J,axiom, 0.19/0.57 ! [X41: bexp,X42: com,X43: com] : 0.19/0.57 ( skip 0.19/0.57 != ( if @ X41 @ X42 @ X43 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_254_fun__upd__other,axiom, 0.19/0.57 ! [Z: list_char,X4: list_char,F2: list_char > int,Y: int] : 0.19/0.57 ( ( Z != X4 ) 0.19/0.57 => ( ( fun_up103088396ar_int @ F2 @ X4 @ Y @ Z ) 0.19/0.57 = ( F2 @ Z ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_257_fun__upd__eqD,axiom, 0.19/0.57 ! [F2: list_char > int,X4: list_char,Y: int,G: list_char > int,Z: int] : 0.19/0.57 ( ( Y = Z ) 0.19/0.57 <= ( ( fun_up103088396ar_int @ F2 @ X4 @ Y ) 0.19/0.57 = ( fun_up103088396ar_int @ G @ X4 @ Z ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_283_group__cancel_Oadd2,axiom, 0.19/0.57 ! [B5: nat,K: nat,B: nat,A: nat] : 0.19/0.57 ( ( ( plus_plus_nat @ A @ B5 ) 0.19/0.57 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) 0.19/0.57 <= ( B5 0.19/0.57 = ( plus_plus_nat @ K @ B ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_199_image__ident,axiom, 0.19/0.57 ! [Y5: set_nat] : 0.19/0.57 ( ( image_nat_nat 0.19/0.57 @ ^ [X: nat] : X 0.19/0.57 @ Y5 ) 0.19/0.57 = Y5 ) ). 0.19/0.57 0.19/0.57 thf(fact_123_curry__case__prod,axiom, 0.19/0.57 ! [F2: com > ( list_char > int ) > $o] : 0.19/0.57 ( ( produc1858366159_int_o @ ( produc668584238_int_o @ F2 ) ) 0.19/0.57 = F2 ) ). 0.19/0.57 0.19/0.57 thf(fact_79_com_Oexhaust,axiom, 0.19/0.57 ! [Y: com] : 0.19/0.57 ( ( Y != skip ) 0.19/0.57 => ( ! [X212: list_char,X222: aexp] : 0.19/0.57 ( Y 0.19/0.57 != ( assign @ X212 @ X222 ) ) 0.19/0.57 => ( ( ! [X412: bexp,X422: com,X432: com] : 0.19/0.57 ( Y 0.19/0.57 != ( if @ X412 @ X422 @ X432 ) ) 0.19/0.57 => ~ ! [X512: bexp,X522: com] : 0.19/0.57 ( Y 0.19/0.57 != ( while @ X512 @ X522 ) ) ) 0.19/0.57 <= ! [X312: com,X322: com] : 0.19/0.57 ( Y 0.19/0.57 != ( seq @ X312 @ X322 ) ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_147_If__False__ir__valid,axiom, 0.19/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,B: bexp,C_2: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,C_1: com] : 0.19/0.57 ( ( relati775585786_valid @ P @ ( if @ B @ C_1 @ C_2 ) @ C2 @ Q ) 0.19/0.57 <= ( relati775585786_valid 0.19/0.57 @ ^ [A5: list_char > int,C3: list_char > int] : 0.19/0.57 ( ( P @ A5 @ C3 ) 0.19/0.57 & ~ ( bval @ B @ A5 ) ) 0.19/0.57 @ C_2 0.19/0.57 @ C2 0.19/0.57 @ Q ) ) ). 0.19/0.57 0.19/0.57 thf(fact_193_AssignE,axiom, 0.19/0.57 ! [X4: list_char,A: aexp,S7: list_char > int,T6: list_char > int] : 0.19/0.57 ( ( T6 0.19/0.57 = ( fun_up103088396ar_int @ S7 @ X4 @ ( aval @ A @ S7 ) ) ) 0.19/0.57 <= ( big_big_step @ ( produc1193801173ar_int @ ( assign @ X4 @ A ) @ S7 ) @ T6 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_68_com_Odistinct_I7_J,axiom, 0.19/0.57 ! [X51: bexp,X52: com] : 0.19/0.57 ( skip 0.19/0.57 != ( while @ X51 @ X52 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_284_add_Oassoc,axiom, 0.19/0.57 ! [A: nat,B: nat,C: nat] : 0.19/0.57 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C ) 0.19/0.57 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_82_IfE,axiom, 0.19/0.57 ! [B: bexp,C1: com,C22: com,S7: list_char > int,T6: list_char > int] : 0.19/0.57 ( ( ( ~ ( big_big_step @ ( produc1193801173ar_int @ C1 @ S7 ) @ T6 ) 0.19/0.57 <= ( bval @ B @ S7 ) ) 0.19/0.57 => ~ ( ~ ( bval @ B @ S7 ) 0.19/0.57 => ~ ( big_big_step @ ( produc1193801173ar_int @ C22 @ S7 ) @ T6 ) ) ) 0.19/0.57 <= ( big_big_step @ ( produc1193801173ar_int @ ( if @ B @ C1 @ C22 ) @ S7 ) @ T6 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_51_Pair__inject,axiom, 0.19/0.57 ! [A: com,B: list_char > int,A2: com,B2: list_char > int] : 0.19/0.57 ( ( ( produc1193801173ar_int @ A @ B ) 0.19/0.57 = ( produc1193801173ar_int @ A2 @ B2 ) ) 0.19/0.57 => ~ ( ( A = A2 ) 0.19/0.57 => ( B != B2 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_238_image__iff,axiom, 0.19/0.57 ! [Z: produc1260470173ar_int,F2: produc1166363805nt_com > produc1260470173ar_int,A4: set_Pr866150653nt_com] : 0.19/0.57 ( ( member92250950ar_int @ Z @ ( image_1968865093ar_int @ F2 @ A4 ) ) 0.19/0.57 = ( ? [X: produc1166363805nt_com] : 0.19/0.57 ( ( Z 0.19/0.57 = ( F2 @ X ) ) 0.19/0.57 & ( member2145628230nt_com @ X @ A4 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_78_com_Oinduct,axiom, 0.19/0.57 ! [P: com > $o,Com: com] : 0.19/0.57 ( ( P @ skip ) 0.19/0.57 => ( ( ! [X12: com,X23: com] : 0.19/0.57 ( ( ( P @ ( seq @ X12 @ X23 ) ) 0.19/0.57 <= ( P @ X23 ) ) 0.19/0.57 <= ( P @ X12 ) ) 0.19/0.57 => ( ! [X12: bexp,X23: com,X33: com] : 0.19/0.57 ( ( P @ X23 ) 0.19/0.57 => ( ( P @ X33 ) 0.19/0.57 => ( P @ ( if @ X12 @ X23 @ X33 ) ) ) ) 0.19/0.57 => ( ! [X12: bexp,X23: com] : 0.19/0.57 ( ( P @ ( while @ X12 @ X23 ) ) 0.19/0.57 <= ( P @ X23 ) ) 0.19/0.57 => ( P @ Com ) ) ) ) 0.19/0.57 <= ! [X12: list_char,X23: aexp] : ( P @ ( assign @ X12 @ X23 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_188_old_Oprod_Ocase,axiom, 0.19/0.57 ! [F2: com > ( list_char > int ) > $o,X1: com,X2: list_char > int] : 0.19/0.57 ( ( produc668584238_int_o @ F2 @ ( produc1193801173ar_int @ X1 @ X2 ) ) 0.19/0.57 = ( F2 @ X1 @ X2 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_267_Compr__image__eq,axiom, 0.19/0.57 ! [F2: nat > nat,A4: set_nat,P: nat > $o] : 0.19/0.57 ( ( collect_nat 0.19/0.57 @ ^ [X: nat] : 0.19/0.57 ( ( P @ X ) 0.19/0.57 & ( member_nat @ X @ ( image_nat_nat @ F2 @ A4 ) ) ) ) 0.19/0.57 = ( image_nat_nat @ F2 0.19/0.57 @ ( collect_nat 0.19/0.57 @ ^ [X: nat] : 0.19/0.57 ( ( P @ ( F2 @ X ) ) 0.19/0.57 & ( member_nat @ X @ A4 ) ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_281_add__mono__thms__linordered__semiring_I4_J,axiom, 0.19/0.57 ! [I: nat,J: nat,K: nat,L: nat] : 0.19/0.57 ( ( ( K = L ) 0.19/0.57 & ( I = J ) ) 0.19/0.57 => ( ( plus_plus_nat @ I @ K ) 0.19/0.57 = ( plus_plus_nat @ J @ L ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_226_ball__imageD,axiom, 0.19/0.57 ! [F2: produc1260470173ar_int > produc1166363805nt_com,A4: set_Pr1148378109ar_int,P: produc1166363805nt_com > $o] : 0.19/0.57 ( ! [X5: produc1260470173ar_int] : 0.19/0.57 ( ( P @ ( F2 @ X5 ) ) 0.19/0.57 <= ( member92250950ar_int @ X5 @ A4 ) ) 0.19/0.57 <= ! [X3: produc1166363805nt_com] : 0.19/0.57 ( ( P @ X3 ) 0.19/0.57 <= ( member2145628230nt_com @ X3 @ ( image_786684229nt_com @ F2 @ A4 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_174_case__prodE2,axiom, 0.19/0.57 ! [Q: $o > $o,P: com > ( list_char > int ) > $o,Z: produc1260470173ar_int] : 0.19/0.57 ( ( Q @ ( produc668584238_int_o @ P @ Z ) ) 0.19/0.57 => ~ ! [X3: com,Y3: list_char > int] : 0.19/0.57 ( ~ ( Q @ ( P @ X3 @ Y3 ) ) 0.19/0.57 <= ( Z 0.19/0.57 = ( produc1193801173ar_int @ X3 @ Y3 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_50_Pair__inject,axiom, 0.19/0.57 ! [A: list_char > int,B: com,A2: list_char > int,B2: com] : 0.19/0.57 ( ( ( produc1139835093nt_com @ A @ B ) 0.19/0.57 = ( produc1139835093nt_com @ A2 @ B2 ) ) 0.19/0.57 => ~ ( ( B != B2 ) 0.19/0.57 <= ( A = A2 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_121_case__prod__conv,axiom, 0.19/0.57 ! [F2: com > ( list_char > int ) > produc1260470173ar_int,A: com,B: list_char > int] : 0.19/0.57 ( ( produc1288559923ar_int @ F2 @ ( produc1193801173ar_int @ A @ B ) ) 0.19/0.57 = ( F2 @ A @ B ) ) ). 0.19/0.57 0.19/0.57 thf(fact_90_swap__swap,axiom, 0.19/0.57 ! [P4: produc1166363805nt_com] : 0.19/0.57 ( ( produc1770201973ar_int @ ( produc1716235893nt_com @ P4 ) ) 0.19/0.57 = P4 ) ). 0.19/0.57 0.19/0.57 thf(fact_156_prod_Ocase__distrib,axiom, 0.19/0.57 ! [H: set_nat > nat,F2: com > ( list_char > int ) > set_nat,Prod: produc1260470173ar_int] : 0.19/0.57 ( ( H @ ( produc991755120et_nat @ F2 @ Prod ) ) 0.19/0.57 = ( produc1311963066nt_nat 0.19/0.57 @ ^ [X13: com,X24: list_char > int] : ( H @ ( F2 @ X13 @ X24 ) ) 0.19/0.57 @ Prod ) ) ). 0.19/0.57 0.19/0.57 thf(fact_318_nat_Odistinct_I1_J,axiom, 0.19/0.57 ! [X2: nat] : 0.19/0.57 ( zero_zero_nat 0.19/0.57 != ( suc @ X2 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_245_imageI,axiom, 0.19/0.57 ! [X4: produc1260470173ar_int,A4: set_Pr1148378109ar_int,F2: produc1260470173ar_int > produc1166363805nt_com] : 0.19/0.57 ( ( member92250950ar_int @ X4 @ A4 ) 0.19/0.57 => ( member2145628230nt_com @ ( F2 @ X4 ) @ ( image_786684229nt_com @ F2 @ A4 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_201_fun__upd__triv,axiom, 0.19/0.57 ! [F2: list_char > int,X4: list_char] : 0.19/0.57 ( ( fun_up103088396ar_int @ F2 @ X4 @ ( F2 @ X4 ) ) 0.19/0.57 = F2 ) ). 0.19/0.57 0.19/0.57 thf(fact_248_imageI,axiom, 0.19/0.57 ! [X4: produc1166363805nt_com,A4: set_Pr866150653nt_com,F2: produc1166363805nt_com > produc1166363805nt_com] : 0.19/0.57 ( ( member2145628230nt_com @ ( F2 @ X4 ) @ ( image_1874758725nt_com @ F2 @ A4 ) ) 0.19/0.57 <= ( member2145628230nt_com @ X4 @ A4 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_350_verit__sum__simplify,axiom, 0.19/0.57 ! [A: nat] : 0.19/0.57 ( ( plus_plus_nat @ A @ zero_zero_nat ) 0.19/0.57 = A ) ). 0.19/0.57 0.19/0.57 thf(fact_212_old_Onat_Oinject,axiom, 0.19/0.57 ! [Nat: nat,Nat2: nat] : 0.19/0.57 ( ( ( suc @ Nat ) 0.19/0.57 = ( suc @ Nat2 ) ) 0.19/0.57 = ( Nat = Nat2 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_279_add__left__cancel,axiom, 0.19/0.57 ! [A: nat,B: nat,C: nat] : 0.19/0.57 ( ( ( plus_plus_nat @ A @ B ) 0.19/0.57 = ( plus_plus_nat @ A @ C ) ) 0.19/0.57 = ( B = C ) ) ). 0.19/0.57 0.19/0.57 thf(fact_305_ir__While__backwards__frontier,axiom, 0.19/0.57 ! [P: nat > ( list_char > int ) > ( list_char > int ) > $o,B: bexp,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] : 0.19/0.57 ( ( ( relati2102071307_hoare 0.19/0.57 @ ^ [S: list_char > int,S2: list_char > int] : 0.19/0.57 ? [N5: nat] : ( P @ N5 @ S @ S2 ) 0.19/0.57 @ ( while @ B @ C ) 0.19/0.57 @ C2 0.19/0.57 @ Q ) 0.19/0.57 => ( relati2102071307_hoare @ ( P @ zero_zero_nat ) @ ( while @ B @ C ) @ C2 @ Q ) ) 0.19/0.57 <= ! [N: nat] : 0.19/0.57 ( relati2102071307_hoare 0.19/0.57 @ ^ [S: list_char > int,S2: list_char > int] : 0.19/0.57 ( ( bval @ B @ S ) 0.19/0.57 & ( P @ N @ S @ S2 ) ) 0.19/0.57 @ C 0.19/0.57 @ skip 0.19/0.57 @ ( P @ ( suc @ N ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_337_com_Osize__gen_I4_J,axiom, 0.19/0.57 ! [X41: bexp,X42: com,X43: com] : 0.19/0.57 ( ( size_com @ ( if @ X41 @ X42 @ X43 ) ) 0.19/0.57 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_com @ X42 ) @ ( size_com @ X43 ) ) @ ( suc @ zero_zero_nat ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_319_old_Onat_Odistinct_I2_J,axiom, 0.19/0.57 ! [Nat2: nat] : 0.19/0.57 ( ( suc @ Nat2 ) 0.19/0.57 != zero_zero_nat ) ). 0.19/0.57 0.19/0.57 thf(fact_299_ir__valid__If,axiom, 0.19/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,B: bexp,C1: com,C22: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] : 0.19/0.57 ( ( ( relati775585786_valid 0.19/0.57 @ ^ [S: list_char > int,S2: list_char > int] : 0.19/0.57 ( ( P @ S @ S2 ) 0.19/0.57 & ( bval @ B @ S ) ) 0.19/0.57 @ C1 0.19/0.57 @ C2 0.19/0.57 @ ^ [T4: list_char > int,T5: list_char > int] : 0.19/0.57 ( ( Q @ T4 @ T5 ) 0.19/0.57 & ? [S: list_char > int,S2: list_char > int] : 0.19/0.57 ( ( P @ S @ S2 ) 0.19/0.57 & ( bval @ B @ S ) 0.19/0.57 & ( big_big_step @ ( produc1193801173ar_int @ C2 @ S2 ) @ T5 ) 0.19/0.57 & ( big_big_step @ ( produc1193801173ar_int @ C1 @ S ) @ T4 ) ) ) ) 0.19/0.57 & ( relati775585786_valid 0.19/0.57 @ ^ [S: list_char > int,S2: list_char > int] : 0.19/0.57 ( ( P @ S @ S2 ) 0.19/0.57 & ~ ( bval @ B @ S ) ) 0.19/0.57 @ C22 0.19/0.57 @ C2 0.19/0.57 @ ^ [T4: list_char > int,T5: list_char > int] : 0.19/0.57 ( ? [S: list_char > int,S2: list_char > int] : 0.19/0.57 ( ( big_big_step @ ( produc1193801173ar_int @ C22 @ S ) @ T4 ) 0.19/0.57 & ~ ( bval @ B @ S ) 0.19/0.57 & ( big_big_step @ ( produc1193801173ar_int @ C2 @ S2 ) @ T5 ) 0.19/0.57 & ( P @ S @ S2 ) ) 0.19/0.57 & ( Q @ T4 @ T5 ) ) ) ) 0.19/0.57 <= ( relati775585786_valid @ P @ ( if @ B @ C1 @ C22 ) @ C2 @ Q ) ) ). 0.19/0.57 0.19/0.57 thf(fact_175_case__prodE2,axiom, 0.19/0.57 ! [Q: nat > $o,P: com > ( list_char > int ) > nat,Z: produc1260470173ar_int] : 0.19/0.57 ( ( Q @ ( produc1311963066nt_nat @ P @ Z ) ) 0.19/0.57 => ~ ! [X3: com,Y3: list_char > int] : 0.19/0.57 ( ~ ( Q @ ( P @ X3 @ Y3 ) ) 0.19/0.57 <= ( Z 0.19/0.57 = ( produc1193801173ar_int @ X3 @ Y3 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_210_image__eqI,axiom, 0.19/0.57 ! [B: produc1166363805nt_com,F2: produc1166363805nt_com > produc1166363805nt_com,X4: produc1166363805nt_com,A4: set_Pr866150653nt_com] : 0.19/0.57 ( ( ( member2145628230nt_com @ B @ ( image_1874758725nt_com @ F2 @ A4 ) ) 0.19/0.57 <= ( member2145628230nt_com @ X4 @ A4 ) ) 0.19/0.57 <= ( B 0.19/0.57 = ( F2 @ X4 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_8_ir__valid__decomp1,axiom, 0.19/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] : 0.19/0.57 ( ( ( relati775585786_valid @ ( relati1310524937decomp @ P @ C @ C2 @ Q ) @ skip @ C2 @ Q ) 0.19/0.57 & ( relati775585786_valid @ P @ C @ skip @ ( relati1310524937decomp @ P @ C @ C2 @ Q ) ) ) 0.19/0.57 <= ( relati775585786_valid @ P @ C @ C2 @ Q ) ) ). 0.19/0.57 0.19/0.57 thf(fact_265_Compr__image__eq,axiom, 0.19/0.57 ! [F2: produc1260470173ar_int > nat,A4: set_Pr1148378109ar_int,P: nat > $o] : 0.19/0.57 ( ( collect_nat 0.19/0.57 @ ^ [X: nat] : 0.19/0.57 ( ( P @ X ) 0.19/0.57 & ( member_nat @ X @ ( image_1742782760nt_nat @ F2 @ A4 ) ) ) ) 0.19/0.57 = ( image_1742782760nt_nat @ F2 0.19/0.57 @ ( collec770796680ar_int 0.19/0.57 @ ^ [X: produc1260470173ar_int] : 0.19/0.57 ( ( member92250950ar_int @ X @ A4 ) 0.19/0.57 & ( P @ ( F2 @ X ) ) ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_111_mem__case__prodI,axiom, 0.19/0.57 ! [Z: produc1166363805nt_com,C: ( list_char > int ) > com > set_Pr866150653nt_com,A: list_char > int,B: com] : 0.19/0.57 ( ( member2145628230nt_com @ Z @ ( C @ A @ B ) ) 0.19/0.57 => ( member2145628230nt_com @ Z @ ( produc1179280275nt_com @ C @ ( produc1139835093nt_com @ A @ B ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_161_ir__disj,axiom, 0.19/0.57 ! [P_1: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q_1: ( list_char > int ) > ( list_char > int ) > $o,P_2: ( list_char > int ) > ( list_char > int ) > $o,Q_2: ( list_char > int ) > ( list_char > int ) > $o] : 0.19/0.57 ( ( relati2102071307_hoare @ P_1 @ C @ C2 @ Q_1 ) 0.19/0.57 => ( ( relati2102071307_hoare @ P_2 @ C @ C2 @ Q_2 ) 0.19/0.57 => ( relati2102071307_hoare 0.19/0.57 @ ^ [S: list_char > int,S2: list_char > int] : 0.19/0.57 ( ( P_2 @ S @ S2 ) 0.19/0.57 | ( P_1 @ S @ S2 ) ) 0.19/0.57 @ C 0.19/0.57 @ C2 0.19/0.57 @ ^ [T4: list_char > int,T5: list_char > int] : 0.19/0.57 ( ( Q_2 @ T4 @ T5 ) 0.19/0.57 | ( Q_1 @ T4 @ T5 ) ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_253_fun__upd__twist,axiom, 0.19/0.57 ! [A: list_char,C: list_char,M: list_char > int,B: int,D: int] : 0.19/0.57 ( ( ( fun_up103088396ar_int @ ( fun_up103088396ar_int @ M @ A @ B ) @ C @ D ) 0.19/0.57 = ( fun_up103088396ar_int @ ( fun_up103088396ar_int @ M @ C @ D ) @ A @ B ) ) 0.19/0.57 <= ( A != C ) ) ). 0.19/0.57 0.19/0.57 thf(fact_92_pair__in__swap__image,axiom, 0.19/0.57 ! [Y: list_char > int,X4: com,A4: set_Pr1148378109ar_int] : 0.19/0.57 ( ( member2145628230nt_com @ ( produc1139835093nt_com @ Y @ X4 ) @ ( image_786684229nt_com @ produc1770201973ar_int @ A4 ) ) 0.19/0.57 = ( member92250950ar_int @ ( produc1193801173ar_int @ X4 @ Y ) @ A4 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_25_ir__valid__def,axiom, 0.19/0.57 ( relati775585786_valid 0.19/0.57 = ( ^ [P2: ( list_char > int ) > ( list_char > int ) > $o,C3: com,C4: com,Q2: ( list_char > int ) > ( list_char > int ) > $o] : 0.19/0.57 ! [T4: list_char > int,T5: list_char > int] : 0.19/0.57 ( ? [S: list_char > int,S2: list_char > int] : 0.19/0.57 ( ( big_big_step @ ( produc1193801173ar_int @ C4 @ S2 ) @ T5 ) 0.19/0.57 & ( big_big_step @ ( produc1193801173ar_int @ C3 @ S ) @ T4 ) 0.19/0.57 & ( P2 @ S @ S2 ) ) 0.19/0.57 <= ( Q2 @ T4 @ T5 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_276_nat__arith_Osuc1,axiom, 0.19/0.57 ! [A4: nat,K: nat,A: nat] : 0.19/0.57 ( ( ( suc @ A4 ) 0.19/0.57 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) 0.19/0.57 <= ( A4 0.19/0.57 = ( plus_plus_nat @ K @ A ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_306_add_Oleft__neutral,axiom, 0.19/0.57 ! [A: nat] : 0.19/0.57 ( ( plus_plus_nat @ zero_zero_nat @ A ) 0.19/0.57 = A ) ). 0.19/0.57 0.19/0.57 thf(fact_326_Zero__neq__Suc,axiom, 0.19/0.57 ! [M: nat] : 0.19/0.57 ( zero_zero_nat 0.19/0.57 != ( suc @ M ) ) ). 0.19/0.57 0.19/0.57 thf(fact_26_com_Odistinct_I3_J,axiom, 0.19/0.57 ! [X31: com,X32: com] : 0.19/0.57 ( skip 0.19/0.57 != ( seq @ X31 @ X32 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_172_case__prod__eta,axiom, 0.19/0.57 ! [F2: produc1260470173ar_int > produc1260470173ar_int] : 0.19/0.57 ( ( produc1288559923ar_int 0.19/0.57 @ ^ [X: com,Y4: list_char > int] : ( F2 @ ( produc1193801173ar_int @ X @ Y4 ) ) ) 0.19/0.57 = F2 ) ). 0.19/0.57 0.19/0.57 thf(fact_290_Assign__ir__valid,axiom, 0.19/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,X4: list_char,E: aexp,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] : 0.19/0.57 ( ( relati775585786_valid @ P @ ( assign @ X4 @ E ) @ C2 @ Q ) 0.19/0.57 <= ( relati775585786_valid 0.19/0.57 @ ^ [T4: list_char > int,T5: list_char > int] : 0.19/0.57 ? [V3: int] : 0.19/0.57 ( ( P @ ( fun_up103088396ar_int @ T4 @ X4 @ V3 ) @ T5 ) 0.19/0.57 & ( ( T4 @ X4 ) 0.19/0.57 = ( aval @ E @ ( fun_up103088396ar_int @ T4 @ X4 @ V3 ) ) ) ) 0.19/0.57 @ skip 0.19/0.57 @ C2 0.19/0.57 @ Q ) ) ). 0.19/0.57 0.19/0.57 thf(fact_159_prod_Ocase__distrib,axiom, 0.19/0.57 ! [H: set_nat > set_nat,F2: com > ( list_char > int ) > set_nat,Prod: produc1260470173ar_int] : 0.19/0.57 ( ( H @ ( produc991755120et_nat @ F2 @ Prod ) ) 0.19/0.57 = ( produc991755120et_nat 0.19/0.57 @ ^ [X13: com,X24: list_char > int] : ( H @ ( F2 @ X13 @ X24 ) ) 0.19/0.57 @ Prod ) ) ). 0.19/0.57 0.19/0.57 thf(fact_2_ir__valid__decomp,axiom, 0.19/0.57 ( relati775585786_valid 0.19/0.57 = ( ^ [P2: ( list_char > int ) > ( list_char > int ) > $o,C3: com,C4: com,Q2: ( list_char > int ) > ( list_char > int ) > $o] : 0.19/0.57 ( ( relati775585786_valid @ P2 @ C3 @ skip @ ( relati1310524937decomp @ P2 @ C3 @ C4 @ Q2 ) ) 0.19/0.57 & ( relati775585786_valid @ ( relati1310524937decomp @ P2 @ C3 @ C4 @ Q2 ) @ skip @ C4 @ Q2 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_84_IfFalse,axiom, 0.19/0.57 ! [B: bexp,S7: list_char > int,C_2: com,T6: list_char > int,C_1: com] : 0.19/0.57 ( ( ( big_big_step @ ( produc1193801173ar_int @ ( if @ B @ C_1 @ C_2 ) @ S7 ) @ T6 ) 0.19/0.57 <= ( big_big_step @ ( produc1193801173ar_int @ C_2 @ S7 ) @ T6 ) ) 0.19/0.57 <= ~ ( bval @ B @ S7 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_183_mem__case__prodE,axiom, 0.19/0.57 ! [Z: nat,C: ( list_char > int ) > com > set_nat,P4: produc1166363805nt_com] : 0.19/0.57 ( ( member_nat @ Z @ ( produc1754105456et_nat @ C @ P4 ) ) 0.19/0.57 => ~ ! [X3: list_char > int,Y3: com] : 0.19/0.57 ( ( P4 0.19/0.57 = ( produc1139835093nt_com @ X3 @ Y3 ) ) 0.19/0.57 => ~ ( member_nat @ Z @ ( C @ X3 @ Y3 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_338_com_Osize__gen_I3_J,axiom, 0.19/0.57 ! [X31: com,X32: com] : 0.19/0.57 ( ( size_com @ ( seq @ X31 @ X32 ) ) 0.19/0.57 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_com @ X31 ) @ ( size_com @ X32 ) ) @ ( suc @ zero_zero_nat ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_231_image__cong,axiom, 0.19/0.57 ! [M2: set_Pr866150653nt_com,N4: set_Pr866150653nt_com,F2: produc1166363805nt_com > produc1260470173ar_int,G: produc1166363805nt_com > produc1260470173ar_int] : 0.19/0.57 ( ( ! [X3: produc1166363805nt_com] : 0.19/0.57 ( ( member2145628230nt_com @ X3 @ N4 ) 0.19/0.57 => ( ( F2 @ X3 ) 0.19/0.57 = ( G @ X3 ) ) ) 0.19/0.57 => ( ( image_1968865093ar_int @ F2 @ M2 ) 0.19/0.57 = ( image_1968865093ar_int @ G @ N4 ) ) ) 0.19/0.57 <= ( M2 = N4 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_244_imageI,axiom, 0.19/0.57 ! [X4: produc1260470173ar_int,A4: set_Pr1148378109ar_int,F2: produc1260470173ar_int > produc1260470173ar_int] : 0.19/0.57 ( ( member92250950ar_int @ ( F2 @ X4 ) @ ( image_880790597ar_int @ F2 @ A4 ) ) 0.19/0.57 <= ( member92250950ar_int @ X4 @ A4 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_240_image__iff,axiom, 0.19/0.57 ! [Z: nat,F2: nat > nat,A4: set_nat] : 0.19/0.57 ( ( member_nat @ Z @ ( image_nat_nat @ F2 @ A4 ) ) 0.19/0.57 = ( ? [X: nat] : 0.19/0.57 ( ( Z 0.19/0.57 = ( F2 @ X ) ) 0.19/0.57 & ( member_nat @ X @ A4 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(conj_0,conjecture, 0.19/0.57 ( ( relati2102071307_hoare @ p @ c @ c2 @ q ) 0.19/0.57 = ( ( relati2102071307_hoare @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ c2 @ q ) ) 0.19/0.57 & ( relati2102071307_hoare @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ q ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_7_ir__conseq,axiom, 0.19/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,P3: ( list_char > int ) > ( list_char > int ) > $o,Q3: ( list_char > int ) > ( list_char > int ) > $o] : 0.19/0.57 ( ( relati2102071307_hoare @ P @ C @ C2 @ Q ) 0.19/0.57 => ( ! [S3: list_char > int,S4: list_char > int] : 0.19/0.57 ( ( P3 @ S3 @ S4 ) 0.19/0.57 <= ( P @ S3 @ S4 ) ) 0.19/0.57 => ( ! [S3: list_char > int,S4: list_char > int] : 0.19/0.57 ( ( Q @ S3 @ S4 ) 0.19/0.57 <= ( Q3 @ S3 @ S4 ) ) 0.19/0.57 => ( relati2102071307_hoare @ P3 @ C @ C2 @ Q3 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_88_swap__simp,axiom, 0.19/0.57 ! [X4: list_char > int,Y: com] : 0.19/0.57 ( ( produc1716235893nt_com @ ( produc1139835093nt_com @ X4 @ Y ) ) 0.19/0.57 = ( produc1193801173ar_int @ Y @ X4 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_268_image__image,axiom, 0.19/0.57 ! [F2: produc1260470173ar_int > produc1166363805nt_com,G: produc1260470173ar_int > produc1260470173ar_int,A4: set_Pr1148378109ar_int] : 0.19/0.57 ( ( image_786684229nt_com @ F2 @ ( image_880790597ar_int @ G @ A4 ) ) 0.19/0.57 = ( image_786684229nt_com 0.19/0.57 @ ^ [X: produc1260470173ar_int] : ( F2 @ ( G @ X ) ) 0.19/0.57 @ A4 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_289_case__prod__Pair__iden,axiom, 0.19/0.57 ! [P4: produc1260470173ar_int] : 0.19/0.57 ( ( produc1288559923ar_int @ produc1193801173ar_int @ P4 ) 0.19/0.57 = P4 ) ). 0.19/0.57 0.19/0.57 thf(fact_271_image__image,axiom, 0.19/0.57 ! [F2: produc1260470173ar_int > nat,G: produc1260470173ar_int > produc1260470173ar_int,A4: set_Pr1148378109ar_int] : 0.19/0.57 ( ( image_1742782760nt_nat @ F2 @ ( image_880790597ar_int @ G @ A4 ) ) 0.19/0.57 = ( image_1742782760nt_nat 0.19/0.57 @ ^ [X: produc1260470173ar_int] : ( F2 @ ( G @ X ) ) 0.19/0.57 @ A4 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_113_case__prodI2,axiom, 0.19/0.57 ! [P4: produc1166363805nt_com,C: ( list_char > int ) > com > $o] : 0.19/0.57 ( ( produc613711406_com_o @ C @ P4 ) 0.19/0.57 <= ! [A3: list_char > int,B3: com] : 0.19/0.57 ( ( C @ A3 @ B3 ) 0.19/0.57 <= ( P4 0.19/0.57 = ( produc1139835093nt_com @ A3 @ B3 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_287_add__left__imp__eq,axiom, 0.19/0.57 ! [A: nat,B: nat,C: nat] : 0.19/0.57 ( ( ( plus_plus_nat @ A @ B ) 0.19/0.57 = ( plus_plus_nat @ A @ C ) ) 0.19/0.57 => ( B = C ) ) ). 0.19/0.57 0.19/0.57 thf(fact_330_not0__implies__Suc,axiom, 0.19/0.57 ! [N3: nat] : 0.19/0.57 ( ? [M3: nat] : 0.19/0.57 ( N3 0.19/0.57 = ( suc @ M3 ) ) 0.19/0.57 <= ( N3 != zero_zero_nat ) ) ). 0.19/0.57 0.19/0.57 thf(fact_313_zero__eq__add__iff__both__eq__0,axiom, 0.19/0.57 ! [X4: nat,Y: nat] : 0.19/0.57 ( ( zero_zero_nat 0.19/0.57 = ( plus_plus_nat @ X4 @ Y ) ) 0.19/0.57 = ( ( X4 = zero_zero_nat ) 0.19/0.57 & ( Y = zero_zero_nat ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_218_rev__image__eqI,axiom, 0.19/0.57 ! [X4: produc1260470173ar_int,A4: set_Pr1148378109ar_int,B: nat,F2: produc1260470173ar_int > nat] : 0.19/0.57 ( ( ( member_nat @ B @ ( image_1742782760nt_nat @ F2 @ A4 ) ) 0.19/0.57 <= ( B 0.19/0.57 = ( F2 @ X4 ) ) ) 0.19/0.57 <= ( member92250950ar_int @ X4 @ A4 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_315_add__is__0,axiom, 0.19/0.57 ! [M: nat,N3: nat] : 0.19/0.57 ( ( ( plus_plus_nat @ M @ N3 ) 0.19/0.57 = zero_zero_nat ) 0.19/0.57 = ( ( N3 = zero_zero_nat ) 0.19/0.57 & ( M = zero_zero_nat ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_56_big__step__determ,axiom, 0.19/0.57 ! [C: com,S7: list_char > int,T6: list_char > int,U: list_char > int] : 0.19/0.57 ( ( big_big_step @ ( produc1193801173ar_int @ C @ S7 ) @ T6 ) 0.19/0.57 => ( ( U = T6 ) 0.19/0.57 <= ( big_big_step @ ( produc1193801173ar_int @ C @ S7 ) @ U ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_115_case__prodI,axiom, 0.19/0.57 ! [F2: ( list_char > int ) > com > $o,A: list_char > int,B: com] : 0.19/0.57 ( ( F2 @ A @ B ) 0.19/0.57 => ( produc613711406_com_o @ F2 @ ( produc1139835093nt_com @ A @ B ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_322_nat__induct,axiom, 0.19/0.57 ! [P: nat > $o,N3: nat] : 0.19/0.57 ( ( ( P @ N3 ) 0.19/0.57 <= ! [N: nat] : 0.19/0.57 ( ( P @ N ) 0.19/0.57 => ( P @ ( suc @ N ) ) ) ) 0.19/0.57 <= ( P @ zero_zero_nat ) ) ). 0.19/0.57 0.19/0.57 thf(fact_39_old_Oprod_Oinducts,axiom, 0.19/0.57 ! [P: produc1166363805nt_com > $o,Prod: produc1166363805nt_com] : 0.19/0.57 ( ( P @ Prod ) 0.19/0.57 <= ! [A3: list_char > int,B3: com] : ( P @ ( produc1139835093nt_com @ A3 @ B3 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_133_case__swap,axiom, 0.19/0.57 ! [F2: com > ( list_char > int ) > produc1260470173ar_int,P4: produc1260470173ar_int] : 0.19/0.57 ( ( produc1771082291ar_int 0.19/0.57 @ ^ [Y4: list_char > int,X: com] : ( F2 @ X @ Y4 ) 0.19/0.57 @ ( produc1770201973ar_int @ P4 ) ) 0.19/0.57 = ( produc1288559923ar_int @ F2 @ P4 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_250_n__not__Suc__n,axiom, 0.19/0.57 ! [N3: nat] : 0.19/0.57 ( N3 0.19/0.57 != ( suc @ N3 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_140_pair__imageI,axiom, 0.19/0.57 ! [A: list_char > int,B: com,A4: set_Pr866150653nt_com,F2: ( list_char > int ) > com > produc1260470173ar_int] : 0.19/0.57 ( ( member92250950ar_int @ ( F2 @ A @ B ) @ ( image_1968865093ar_int @ ( produc1771082291ar_int @ F2 ) @ A4 ) ) 0.19/0.57 <= ( member2145628230nt_com @ ( produc1139835093nt_com @ A @ B ) @ A4 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_49_Collect__cong,axiom, 0.19/0.57 ! [P: nat > $o,Q: nat > $o] : 0.19/0.57 ( ! [X3: nat] : 0.19/0.57 ( ( P @ X3 ) 0.19/0.57 = ( Q @ X3 ) ) 0.19/0.57 => ( ( collect_nat @ P ) 0.19/0.57 = ( collect_nat @ Q ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_345_com_Osize_I7_J,axiom, 0.19/0.57 ! [X21: list_char,X22: aexp] : 0.19/0.57 ( ( size_size_com @ ( assign @ X21 @ X22 ) ) 0.19/0.57 = zero_zero_nat ) ). 0.19/0.57 0.19/0.57 thf(fact_152_prod_Ocase__distrib,axiom, 0.19/0.57 ! [H: $o > nat,F2: com > ( list_char > int ) > $o,Prod: produc1260470173ar_int] : 0.19/0.57 ( ( H @ ( produc668584238_int_o @ F2 @ Prod ) ) 0.19/0.57 = ( produc1311963066nt_nat 0.19/0.57 @ ^ [X13: com,X24: list_char > int] : ( H @ ( F2 @ X13 @ X24 ) ) 0.19/0.57 @ Prod ) ) ). 0.19/0.57 0.19/0.57 thf(fact_14_conseq__ir__valid,axiom, 0.19/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,P3: ( list_char > int ) > ( list_char > int ) > $o,Q3: ( list_char > int ) > ( list_char > int ) > $o] : 0.19/0.57 ( ( relati775585786_valid @ P @ C @ C2 @ Q ) 0.19/0.57 => ( ! [S3: list_char > int,S4: list_char > int] : 0.19/0.57 ( ( P @ S3 @ S4 ) 0.19/0.57 => ( P3 @ S3 @ S4 ) ) 0.19/0.57 => ( ! [S3: list_char > int,S4: list_char > int] : 0.19/0.57 ( ( Q @ S3 @ S4 ) 0.19/0.57 <= ( Q3 @ S3 @ S4 ) ) 0.19/0.57 => ( relati775585786_valid @ P3 @ C @ C2 @ Q3 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_148_While__False__ir__valid,axiom, 0.19/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,B: bexp,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,C: com] : 0.19/0.57 ( ( relati775585786_valid 0.19/0.57 @ ^ [S: list_char > int,S2: list_char > int] : 0.19/0.57 ( ~ ( bval @ B @ S ) 0.19/0.57 & ( P @ S @ S2 ) ) 0.19/0.57 @ skip 0.19/0.57 @ C2 0.19/0.57 @ Q ) 0.19/0.57 => ( relati775585786_valid @ P @ ( while @ B @ C ) @ C2 @ Q ) ) ). 0.19/0.57 0.19/0.57 thf(fact_16_ir__Skip,axiom, 0.19/0.57 ! [Q: ( list_char > int ) > ( list_char > int ) > $o,P: ( list_char > int ) > ( list_char > int ) > $o,C2: com] : 0.19/0.57 ( ( relati2102071307_hoare @ P @ skip @ C2 @ Q ) 0.19/0.57 <= ! [T: list_char > int,T2: list_char > int] : 0.19/0.57 ( ( Q @ T @ T2 ) 0.19/0.57 => ? [S5: list_char > int] : 0.19/0.57 ( ( big_big_step @ ( produc1193801173ar_int @ C2 @ S5 ) @ T2 ) 0.19/0.57 & ( P @ T @ S5 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(help_If_2_1_If_001t__Int__Oint_T,axiom, 0.19/0.57 ! [X4: int,Y: int] : 0.19/0.57 ( ( if_int @ $false @ X4 @ Y ) 0.19/0.57 = Y ) ). 0.19/0.57 0.19/0.57 thf(fact_295_ir__valid__Seq1_H,axiom, 0.19/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,C1: com,C22: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] : 0.19/0.57 ( ( relati775585786_valid 0.19/0.57 @ ^ [T4: list_char > int,T5: list_char > int] : 0.19/0.57 ? [S: list_char > int,S2: list_char > int] : 0.19/0.57 ( ( P @ S @ S2 ) 0.19/0.57 & ( big_big_step @ ( produc1193801173ar_int @ C2 @ S2 ) @ T5 ) 0.19/0.57 & ? [U2: list_char > int] : 0.19/0.57 ( ( big_big_step @ ( produc1193801173ar_int @ C22 @ T4 ) @ U2 ) 0.19/0.57 & ( Q @ U2 @ T5 ) ) 0.19/0.57 & ( big_big_step @ ( produc1193801173ar_int @ C1 @ S ) @ T4 ) ) 0.19/0.57 @ C22 0.19/0.57 @ skip 0.19/0.57 @ Q ) 0.19/0.57 <= ( relati775585786_valid @ P @ ( seq @ C1 @ C22 ) @ C2 @ Q ) ) ). 0.19/0.57 0.19/0.57 thf(fact_286_add_Oleft__commute,axiom, 0.19/0.57 ! [B: nat,A: nat,C: nat] : 0.19/0.57 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) ) 0.19/0.57 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_129_case__prod__curry,axiom, 0.19/0.57 ! [F2: produc1260470173ar_int > produc1260470173ar_int] : 0.19/0.57 ( ( produc1288559923ar_int @ ( produc804153044ar_int @ F2 ) ) 0.19/0.57 = F2 ) ). 0.19/0.57 0.19/0.57 thf(fact_12_Seq1__ir__valid,axiom, 0.19/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,D: com,R: ( list_char > int ) > ( list_char > int ) > $o] : 0.19/0.57 ( ( relati775585786_valid @ P @ C @ C2 @ Q ) 0.19/0.57 => ( ( relati775585786_valid @ Q @ D @ skip @ R ) 0.19/0.57 => ( relati775585786_valid @ P @ ( seq @ C @ D ) @ C2 @ R ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_85_WhileE,axiom, 0.19/0.57 ! [B: bexp,C: com,S7: list_char > int,T6: list_char > int] : 0.19/0.57 ( ( big_big_step @ ( produc1193801173ar_int @ ( while @ B @ C ) @ S7 ) @ T6 ) 0.19/0.57 => ( ~ ( ! [S_2: list_char > int] : 0.19/0.57 ( ~ ( big_big_step @ ( produc1193801173ar_int @ ( while @ B @ C ) @ S_2 ) @ T6 ) 0.19/0.57 <= ( big_big_step @ ( produc1193801173ar_int @ C @ S7 ) @ S_2 ) ) 0.19/0.57 <= ( bval @ B @ S7 ) ) 0.19/0.57 <= ( ( T6 = S7 ) 0.19/0.57 => ( bval @ B @ S7 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_344_com_Osize_I6_J,axiom, 0.19/0.57 ( ( size_size_com @ skip ) 0.19/0.57 = zero_zero_nat ) ). 0.19/0.57 0.19/0.57 thf(fact_122_curry__case__prod,axiom, 0.19/0.57 ! [F2: com > ( list_char > int ) > set_nat] : 0.19/0.57 ( ( produc1791150095et_nat @ ( produc991755120et_nat @ F2 ) ) 0.19/0.57 = F2 ) ). 0.19/0.57 0.19/0.57 thf(fact_43_mem__Collect__eq,axiom, 0.19/0.57 ! [A: produc1260470173ar_int,P: produc1260470173ar_int > $o] : 0.19/0.57 ( ( member92250950ar_int @ A @ ( collec770796680ar_int @ P ) ) 0.19/0.57 = ( P @ A ) ) ). 0.19/0.57 0.19/0.57 thf(fact_151_prod_Ocase__distrib,axiom, 0.19/0.57 ! [H: $o > $o,F2: com > ( list_char > int ) > $o,Prod: produc1260470173ar_int] : 0.19/0.57 ( ( H @ ( produc668584238_int_o @ F2 @ Prod ) ) 0.19/0.57 = ( produc668584238_int_o 0.19/0.57 @ ^ [X13: com,X24: list_char > int] : ( H @ ( F2 @ X13 @ X24 ) ) 0.19/0.57 @ Prod ) ) ). 0.19/0.57 0.19/0.57 thf(fact_5_ir__pre,axiom, 0.19/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,P3: ( list_char > int ) > ( list_char > int ) > $o] : 0.19/0.57 ( ( relati2102071307_hoare @ P @ C @ C2 @ Q ) 0.19/0.57 => ( ! [S3: list_char > int,S4: list_char > int] : 0.19/0.57 ( ( P @ S3 @ S4 ) 0.19/0.57 => ( P3 @ S3 @ S4 ) ) 0.19/0.57 => ( relati2102071307_hoare @ P3 @ C @ C2 @ Q ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_195_Assign,axiom, 0.19/0.57 ! [X4: list_char,A: aexp,S7: list_char > int] : ( big_big_step @ ( produc1193801173ar_int @ ( assign @ X4 @ A ) @ S7 ) @ ( fun_up103088396ar_int @ S7 @ X4 @ ( aval @ A @ S7 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_170_case__prod__eta,axiom, 0.19/0.57 ! [F2: produc1260470173ar_int > $o] : 0.19/0.57 ( ( produc668584238_int_o 0.19/0.57 @ ^ [X: com,Y4: list_char > int] : ( F2 @ ( produc1193801173ar_int @ X @ Y4 ) ) ) 0.19/0.57 = F2 ) ). 0.19/0.57 0.19/0.57 thf(fact_228_ball__imageD,axiom, 0.19/0.57 ! [F2: nat > nat,A4: set_nat,P: nat > $o] : 0.19/0.57 ( ! [X5: nat] : 0.19/0.57 ( ( P @ ( F2 @ X5 ) ) 0.19/0.57 <= ( member_nat @ X5 @ A4 ) ) 0.19/0.57 <= ! [X3: nat] : 0.19/0.57 ( ( member_nat @ X3 @ ( image_nat_nat @ F2 @ A4 ) ) 0.19/0.57 => ( P @ X3 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_150_curry__def,axiom, 0.19/0.57 ( produc1858366159_int_o 0.19/0.57 = ( ^ [C3: produc1260470173ar_int > $o,X: com,Y4: list_char > int] : ( C3 @ ( produc1193801173ar_int @ X @ Y4 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_36_sim__sym,axiom, 0.19/0.57 ! [C: com,C2: com] : 0.19/0.57 ( ( ! [S: list_char > int,T4: list_char > int] : 0.19/0.57 ( ( big_big_step @ ( produc1193801173ar_int @ C @ S ) @ T4 ) 0.19/0.57 = ( big_big_step @ ( produc1193801173ar_int @ C2 @ S ) @ T4 ) ) ) 0.19/0.57 = ( ! [S: list_char > int,T4: list_char > int] : 0.19/0.57 ( ( big_big_step @ ( produc1193801173ar_int @ C2 @ S ) @ T4 ) 0.19/0.57 = ( big_big_step @ ( produc1193801173ar_int @ C @ S ) @ T4 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_155_prod_Ocase__distrib,axiom, 0.19/0.57 ! [H: set_nat > $o,F2: com > ( list_char > int ) > set_nat,Prod: produc1260470173ar_int] : 0.19/0.57 ( ( H @ ( produc991755120et_nat @ F2 @ Prod ) ) 0.19/0.57 = ( produc668584238_int_o 0.19/0.57 @ ^ [X13: com,X24: list_char > int] : ( H @ ( F2 @ X13 @ X24 ) ) 0.19/0.57 @ Prod ) ) ). 0.19/0.57 0.19/0.57 thf(fact_64_while__unfold,axiom, 0.19/0.57 ! [B: bexp,C: com,S8: list_char > int,T7: list_char > int] : 0.19/0.57 ( ( big_big_step @ ( produc1193801173ar_int @ ( while @ B @ C ) @ S8 ) @ T7 ) 0.19/0.57 = ( big_big_step @ ( produc1193801173ar_int @ ( if @ B @ ( seq @ C @ ( while @ B @ C ) ) @ skip ) @ S8 ) @ T7 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_202_fun__upd__apply,axiom, 0.19/0.57 ( fun_up103088396ar_int 0.19/0.57 = ( ^ [F: list_char > int,X: list_char,Y4: int,Z2: list_char] : ( if_int @ ( Z2 = X ) @ Y4 @ ( F @ Z2 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_262_Compr__image__eq,axiom, 0.19/0.57 ! [F2: produc1166363805nt_com > produc1166363805nt_com,A4: set_Pr866150653nt_com,P: produc1166363805nt_com > $o] : 0.19/0.57 ( ( collec676690312nt_com 0.19/0.57 @ ^ [X: produc1166363805nt_com] : 0.19/0.57 ( ( P @ X ) 0.19/0.57 & ( member2145628230nt_com @ X @ ( image_1874758725nt_com @ F2 @ A4 ) ) ) ) 0.19/0.57 = ( image_1874758725nt_com @ F2 0.19/0.57 @ ( collec676690312nt_com 0.19/0.57 @ ^ [X: produc1166363805nt_com] : 0.19/0.57 ( ( P @ ( F2 @ X ) ) 0.19/0.57 & ( member2145628230nt_com @ X @ A4 ) ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_215_prod_Odisc__eq__case,axiom, 0.19/0.57 ! [Prod: produc1260470173ar_int] : 0.19/0.57 ( produc668584238_int_o 0.19/0.57 @ ^ [Uu: com,Uv: list_char > int] : $true 0.19/0.57 @ Prod ) ). 0.19/0.57 0.19/0.57 thf(fact_73_com_Odistinct_I11_J,axiom, 0.19/0.57 ! [X21: list_char,X22: aexp,X41: bexp,X42: com,X43: com] : 0.19/0.57 ( ( assign @ X21 @ X22 ) 0.19/0.57 != ( if @ X41 @ X42 @ X43 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_145_pair__imageI,axiom, 0.19/0.57 ! [A: com,B: list_char > int,A4: set_Pr1148378109ar_int,F2: com > ( list_char > int ) > nat] : 0.19/0.57 ( ( member92250950ar_int @ ( produc1193801173ar_int @ A @ B ) @ A4 ) 0.19/0.57 => ( member_nat @ ( F2 @ A @ B ) @ ( image_1742782760nt_nat @ ( produc1311963066nt_nat @ F2 ) @ A4 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_180_case__prodD,axiom, 0.19/0.57 ! [F2: com > ( list_char > int ) > $o,A: com,B: list_char > int] : 0.19/0.57 ( ( F2 @ A @ B ) 0.19/0.57 <= ( produc668584238_int_o @ F2 @ ( produc1193801173ar_int @ A @ B ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_260_Compr__image__eq,axiom, 0.19/0.57 ! [F2: produc1166363805nt_com > produc1260470173ar_int,A4: set_Pr866150653nt_com,P: produc1260470173ar_int > $o] : 0.19/0.57 ( ( collec770796680ar_int 0.19/0.57 @ ^ [X: produc1260470173ar_int] : 0.19/0.57 ( ( member92250950ar_int @ X @ ( image_1968865093ar_int @ F2 @ A4 ) ) 0.19/0.57 & ( P @ X ) ) ) 0.19/0.57 = ( image_1968865093ar_int @ F2 0.19/0.57 @ ( collec676690312nt_com 0.19/0.57 @ ^ [X: produc1166363805nt_com] : 0.19/0.57 ( ( member2145628230nt_com @ X @ A4 ) 0.19/0.57 & ( P @ ( F2 @ X ) ) ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_98_Assign__complete,axiom, 0.19/0.57 ! [P: ( list_char > int ) > ( list_char > int ) > $o,X1: list_char,X2: aexp,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,T6: list_char > int,T3: list_char > int] : 0.19/0.57 ( ( relati775585786_valid @ P @ ( assign @ X1 @ X2 ) @ C2 @ Q ) 0.19/0.57 => ( ( Q @ T6 @ T3 ) 0.19/0.57 => ? [S4: list_char > int] : 0.19/0.57 ( ? [V: int] : 0.19/0.57 ( ( P @ ( fun_up103088396ar_int @ T6 @ X1 @ V ) @ S4 ) 0.19/0.57 & ( ( T6 @ X1 ) 0.19/0.57 = ( aval @ X2 @ ( fun_up103088396ar_int @ T6 @ X1 @ V ) ) ) ) 0.19/0.57 & ( big_big_step @ ( produc1193801173ar_int @ C2 @ S4 ) @ T3 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_37_sim__refl,axiom, 0.19/0.57 ! [C: com,S8: list_char > int,T7: list_char > int] : 0.19/0.57 ( ( big_big_step @ ( produc1193801173ar_int @ C @ S8 ) @ T7 ) 0.19/0.57 = ( big_big_step @ ( produc1193801173ar_int @ C @ S8 ) @ T7 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_75_curryD,axiom, 0.19/0.57 ! [F2: produc1260470173ar_int > $o,A: com,B: list_char > int] : 0.19/0.57 ( ( F2 @ ( produc1193801173ar_int @ A @ B ) ) 0.19/0.57 <= ( produc1858366159_int_o @ F2 @ A @ B ) ) ). 0.19/0.57 0.19/0.57 thf(fact_259_Compr__image__eq,axiom, 0.19/0.57 ! [F2: produc1260470173ar_int > produc1260470173ar_int,A4: set_Pr1148378109ar_int,P: produc1260470173ar_int > $o] : 0.19/0.57 ( ( collec770796680ar_int 0.19/0.57 @ ^ [X: produc1260470173ar_int] : 0.19/0.57 ( ( member92250950ar_int @ X @ ( image_880790597ar_int @ F2 @ A4 ) ) 0.19/0.57 & ( P @ X ) ) ) 0.19/0.57 = ( image_880790597ar_int @ F2 0.19/0.57 @ ( collec770796680ar_int 0.19/0.57 @ ^ [X: produc1260470173ar_int] : 0.19/0.57 ( ( P @ ( F2 @ X ) ) 0.19/0.57 & ( member92250950ar_int @ X @ A4 ) ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_74_curryD,axiom, 0.19/0.57 ! [F2: produc1166363805nt_com > $o,A: list_char > int,B: com] : 0.19/0.57 ( ( F2 @ ( produc1139835093nt_com @ A @ B ) ) 0.19/0.57 <= ( produc1803493327_com_o @ F2 @ A @ B ) ) ). 0.19/0.57 0.19/0.57 thf(fact_34_old_Oprod_Oinject,axiom, 0.19/0.57 ! [A: list_char > int,B: com,A2: list_char > int,B2: com] : 0.19/0.57 ( ( ( produc1139835093nt_com @ A @ B ) 0.19/0.57 = ( produc1139835093nt_com @ A2 @ B2 ) ) 0.19/0.57 = ( ( A = A2 ) 0.19/0.57 & ( B = B2 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_89_swap__simp,axiom, 0.19/0.57 ! [X4: com,Y: list_char > int] : 0.19/0.57 ( ( produc1770201973ar_int @ ( produc1193801173ar_int @ X4 @ Y ) ) 0.19/0.57 = ( produc1139835093nt_com @ Y @ X4 ) ) ). 0.19/0.57 0.19/0.57 thf(fact_114_case__prodI2,axiom, 0.19/0.57 ! [P4: produc1260470173ar_int,C: com > ( list_char > int ) > $o] : 0.19/0.57 ( ( produc668584238_int_o @ C @ P4 ) 0.19/0.57 <= ! [A3: com,B3: list_char > int] : 0.19/0.57 ( ( P4 0.19/0.57 = ( produc1193801173ar_int @ A3 @ B3 ) ) 0.19/0.57 => ( C @ A3 @ B3 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_94_internal__case__prod__def,axiom, 0.19/0.57 produc857153862et_nat = produc991755120et_nat ). 0.19/0.57 0.19/0.57 thf(help_If_1_1_If_001t__Int__Oint_T,axiom, 0.19/0.57 ! [X4: int,Y: int] : 0.19/0.57 ( ( if_int @ $true @ X4 @ Y ) 0.19/0.57 = X4 ) ). 0.19/0.57 0.19/0.57 thf(fact_46_Collect__mem__eq,axiom, 0.19/0.57 ! [A4: set_Pr1148378109ar_int] : 0.19/0.57 ( ( collec770796680ar_int 0.19/0.57 @ ^ [X: produc1260470173ar_int] : ( member92250950ar_int @ X @ A4 ) ) 0.19/0.57 = A4 ) ). 0.19/0.57 0.19/0.57 thf(fact_177_case__prodE,axiom, 0.19/0.57 ! [C: ( list_char > int ) > com > $o,P4: produc1166363805nt_com] : 0.19/0.57 ( ( produc613711406_com_o @ C @ P4 ) 0.19/0.57 => ~ ! [X3: list_char > int,Y3: com] : 0.19/0.57 ( ~ ( C @ X3 @ Y3 ) 0.19/0.57 <= ( P4 0.19/0.57 = ( produc1139835093nt_com @ X3 @ Y3 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_109_mem__case__prodI,axiom, 0.19/0.57 ! [Z: nat,C: ( list_char > int ) > com > set_nat,A: list_char > int,B: com] : 0.19/0.57 ( ( member_nat @ Z @ ( produc1754105456et_nat @ C @ ( produc1139835093nt_com @ A @ B ) ) ) 0.19/0.57 <= ( member_nat @ Z @ ( C @ A @ B ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_105_mem__case__prodI2,axiom, 0.19/0.57 ! [P4: produc1166363805nt_com,Z: produc1166363805nt_com,C: ( list_char > int ) > com > set_Pr866150653nt_com] : 0.19/0.57 ( ( member2145628230nt_com @ Z @ ( produc1179280275nt_com @ C @ P4 ) ) 0.19/0.57 <= ! [A3: list_char > int,B3: com] : 0.19/0.57 ( ( member2145628230nt_com @ Z @ ( C @ A3 @ B3 ) ) 0.19/0.57 <= ( P4 0.19/0.57 = ( produc1139835093nt_com @ A3 @ B3 ) ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_251_Suc__inject,axiom, 0.19/0.57 ! [X4: nat,Y: nat] : 0.19/0.57 ( ( X4 = Y ) 0.19/0.57 <= ( ( suc @ X4 ) 0.19/0.57 = ( suc @ Y ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_171_case__prod__eta,axiom, 0.19/0.57 ! [F2: produc1260470173ar_int > nat] : 0.19/0.57 ( ( produc1311963066nt_nat 0.19/0.57 @ ^ [X: com,Y4: list_char > int] : ( F2 @ ( produc1193801173ar_int @ X @ Y4 ) ) ) 0.19/0.57 = F2 ) ). 0.19/0.57 0.19/0.57 thf(fact_142_pair__imageI,axiom, 0.19/0.57 ! [A: com,B: list_char > int,A4: set_Pr1148378109ar_int,F2: com > ( list_char > int ) > set_nat] : 0.19/0.57 ( ( member92250950ar_int @ ( produc1193801173ar_int @ A @ B ) @ A4 ) 0.19/0.57 => ( member_set_nat @ ( F2 @ A @ B ) @ ( image_989727966et_nat @ ( produc991755120et_nat @ F2 ) @ A4 ) ) ) ). 0.19/0.57 0.19/0.57 thf(fact_252_fun__upd__idem__iff,axiom, 0.19/0.57 ! [F2: list_char > int,X4: list_char,Y: int] : 0.19/0.57 ( ( ( fun_up103088396ar_int @ F2 @ X4 @ Y ) 0.19/0.57 = F2 ) 0.19/0.57 = ( ( F2 @ X4 ) 0.19/0.57 = Y ) ) ). 0.19/0.57 0.19/0.57 thf(fact_162_assign__upd__blah,axiom, 0.19/0.57 ! [X1: list_char,S7: list_char > int,X2: aexp] : 0.39/0.65 ( ( ^ [A5: list_char] : ( if_int @ ( A5 = X1 ) @ ( S7 @ X1 ) @ ( fun_up103088396ar_int @ S7 @ X1 @ ( aval @ X2 @ S7 ) @ A5 ) ) ) 0.39/0.65 = S7 ) ). 0.39/0.65 0.39/0.65 thf(fact_128_case__prod__curry,axiom, 0.39/0.65 ! [F2: produc1260470173ar_int > nat] : 0.39/0.65 ( ( produc1311963066nt_nat @ ( produc763543641nt_nat @ F2 ) ) 0.39/0.65 = F2 ) ). 0.39/0.65 0.39/0.65 thf(fact_221_rev__image__eqI,axiom, 0.39/0.65 ! [X4: produc1166363805nt_com,A4: set_Pr866150653nt_com,B: nat,F2: produc1166363805nt_com > nat] : 0.39/0.65 ( ( ( member_nat @ B @ ( image_596692520om_nat @ F2 @ A4 ) ) 0.39/0.65 <= ( B 0.39/0.65 = ( F2 @ X4 ) ) ) 0.39/0.65 <= ( member2145628230nt_com @ X4 @ A4 ) ) ). 0.39/0.65 0.39/0.65 thf(fact_307_add_Oright__neutral,axiom, 0.39/0.65 ! [A: nat] : 0.39/0.65 ( ( plus_plus_nat @ A @ zero_zero_nat ) 0.39/0.65 = A ) ). 0.39/0.65 0.39/0.65 thf(fact_31_Skip,axiom, 0.39/0.65 ! [S7: list_char > int] : ( big_big_step @ ( produc1193801173ar_int @ skip @ S7 ) @ S7 ) ). 0.39/0.65 0.39/0.65 thf(fact_220_rev__image__eqI,axiom, 0.39/0.65 ! [X4: produc1260470173ar_int,A4: set_Pr1148378109ar_int,B: produc1166363805nt_com,F2: produc1260470173ar_int > produc1166363805nt_com] : 0.39/0.65 ( ( member92250950ar_int @ X4 @ A4 ) 0.39/0.65 => ( ( B 0.39/0.65 = ( F2 @ X4 ) ) 0.39/0.65 => ( member2145628230nt_com @ B @ ( image_786684229nt_com @ F2 @ A4 ) ) ) ) ). 0.39/0.65 0.39/0.65 thf(fact_47_Collect__mem__eq,axiom, 0.39/0.65 ! [A4: set_Pr866150653nt_com] : 0.39/0.65 ( ( collec676690312nt_com 0.39/0.65 @ ^ [X: produc1166363805nt_com] : ( member2145628230nt_com @ X @ A4 ) ) 0.39/0.65 = A4 ) ). 0.39/0.65 0.39/0.65 thf(fact_296_ir__valid__track__history,axiom, 0.39/0.65 ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,S7: list_char > int,S6: list_char > int] : 0.39/0.65 ( ( relati775585786_valid @ P @ C @ C2 0.39/0.65 @ ^ [T4: list_char > int,T5: list_char > int] : 0.39/0.65 ( ? [S: list_char > int,S2: list_char > int] : 0.39/0.65 ( ( P @ S @ S2 ) 0.39/0.65 & ( big_big_step @ ( produc1193801173ar_int @ C @ S ) @ T4 ) 0.39/0.65 & ( big_big_step @ ( produc1193801173ar_int @ C2 @ S2 ) @ T5 ) ) 0.39/0.65 & ( Q @ S7 @ S6 ) ) ) 0.39/0.65 <= ( relati775585786_valid @ P @ C @ C2 @ Q ) ) ). 0.39/0.65 0.39/0.65 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.CAwJcuJKWl/cvc5---1.0.5_20735.p... 0.39/0.65 (declare-sort $$unsorted 0) 0.39/0.65 (declare-sort tptp.set_Pr1148378109ar_int 0) 0.39/0.65 (declare-sort tptp.set_Pr866150653nt_com 0) 0.39/0.65 (declare-sort tptp.produc1260470173ar_int 0) 0.39/0.65 (declare-sort tptp.produc1166363805nt_com 0) 0.39/0.65 (declare-sort tptp.set_set_nat 0) 0.39/0.65 (declare-sort tptp.list_char 0) 0.39/0.65 (declare-sort tptp.set_nat 0) 0.39/0.65 (declare-sort tptp.set_o 0) 0.39/0.65 (declare-sort tptp.bexp 0) 0.39/0.65 (declare-sort tptp.aexp 0) 0.39/0.65 (declare-sort tptp.nat 0) 0.39/0.65 (declare-sort tptp.int 0) 0.39/0.65 (declare-sort tptp.com 0) 0.39/0.65 (declare-fun tptp.aval (tptp.aexp (-> tptp.list_char tptp.int)) tptp.int) 0.39/0.65 (declare-fun tptp.bval (tptp.bexp (-> tptp.list_char tptp.int)) Bool) 0.39/0.65 (declare-fun tptp.big_big_step (tptp.produc1260470173ar_int (-> tptp.list_char tptp.int)) Bool) 0.39/0.65 (declare-fun tptp.assign (tptp.list_char tptp.aexp) tptp.com) 0.39/0.65 (declare-fun tptp.if (tptp.bexp tptp.com tptp.com) tptp.com) 0.39/0.65 (declare-fun tptp.skip () tptp.com) 0.39/0.65 (declare-fun tptp.seq (tptp.com tptp.com) tptp.com) 0.39/0.65 (declare-fun tptp.while (tptp.bexp tptp.com) tptp.com) 0.39/0.65 (declare-fun tptp.size_com (tptp.com) tptp.nat) 0.39/0.65 (declare-fun tptp.fun_up103088396ar_int ((-> tptp.list_char tptp.int) tptp.list_char tptp.int tptp.list_char) tptp.int) 0.39/0.65 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat) 0.39/0.65 (declare-fun tptp.zero_zero_nat () tptp.nat) 0.39/0.65 (declare-fun tptp.if_int (Bool tptp.int tptp.int) tptp.int) 0.39/0.65 (declare-fun tptp.suc (tptp.nat) tptp.nat) 0.39/0.65 (declare-fun tptp.size_size_com (tptp.com) tptp.nat) 0.39/0.65 (declare-fun tptp.produc1139835093nt_com ((-> tptp.list_char tptp.int) tptp.com) tptp.produc1166363805nt_com) 0.39/0.65 (declare-fun tptp.produc1193801173ar_int (tptp.com (-> tptp.list_char tptp.int)) tptp.produc1260470173ar_int) 0.39/0.65 (declare-fun tptp.produc1803493327_com_o ((-> tptp.produc1166363805nt_com Bool) (-> tptp.list_char tptp.int) tptp.com) Bool) 0.39/0.65 (declare-fun tptp.produc1858366159_int_o ((-> tptp.produc1260470173ar_int Bool) tptp.com (-> tptp.list_char tptp.int)) Bool) 0.39/0.65 (declare-fun tptp.produc763543641nt_nat ((-> tptp.produc1260470173ar_int tptp.nat) tptp.com (-> tptp.list_char tptp.int)) tptp.nat) 0.39/0.65 (declare-fun tptp.produc804153044ar_int ((-> tptp.produc1260470173ar_int tptp.produc1260470173ar_int) tptp.com (-> tptp.list_char tptp.int)) tptp.produc1260470173ar_int) 0.39/0.65 (declare-fun tptp.produc1791150095et_nat ((-> tptp.produc1260470173ar_int tptp.set_nat) tptp.com (-> tptp.list_char tptp.int)) tptp.set_nat) 0.39/0.65 (declare-fun tptp.produc9062872_int_o ((-> tptp.com (-> tptp.list_char tptp.int) Bool) tptp.produc1260470173ar_int) Bool) 0.39/0.65 (declare-fun tptp.produc641693072nt_nat ((-> tptp.com (-> tptp.list_char tptp.int) tptp.nat) tptp.produc1260470173ar_int) tptp.nat) 0.39/0.65 (declare-fun tptp.produc837840349ar_int ((-> tptp.com (-> tptp.list_char tptp.int) tptp.produc1260470173ar_int) tptp.produc1260470173ar_int) tptp.produc1260470173ar_int) 0.39/0.65 (declare-fun tptp.produc857153862et_nat ((-> tptp.com (-> tptp.list_char tptp.int) tptp.set_nat) tptp.produc1260470173ar_int) tptp.set_nat) 0.39/0.65 (declare-fun tptp.produc613711406_com_o ((-> (-> tptp.list_char tptp.int) tptp.com Bool) tptp.produc1166363805nt_com) Bool) 0.39/0.65 (declare-fun tptp.produc1263502010om_nat ((-> (-> tptp.list_char tptp.int) tptp.com tptp.nat) tptp.produc1166363805nt_com) tptp.nat) 0.39/0.65 (declare-fun tptp.produc1676975923nt_com ((-> (-> tptp.list_char tptp.int) tptp.com tptp.produc1166363805nt_com) tptp.produc1166363805nt_com) tptp.produc1166363805nt_com) 0.39/0.65 (declare-fun tptp.produc1771082291ar_int ((-> (-> tptp.list_char tptp.int) tptp.com tptp.produc1260470173ar_int) tptp.produc1166363805nt_com) tptp.produc1260470173ar_int) 0.39/0.65 (declare-fun tptp.produc1754105456et_nat ((-> (-> tptp.list_char tptp.int) tptp.com tptp.set_nat) tptp.produc1166363805nt_com) tptp.set_nat) 0.39/0.65 (declare-fun tptp.produc1179280275nt_com ((-> (-> tptp.list_char tptp.int) tptp.com tptp.set_Pr866150653nt_com) tptp.produc1166363805nt_com) tptp.set_Pr866150653nt_com) 0.39/0.65 (declare-fun tptp.produc1461507731ar_int ((-> (-> tptp.list_char tptp.int) tptp.com tptp.set_Pr1148378109ar_int) tptp.produc1166363805nt_com) tptp.set_Pr1148378109ar_int) 0.39/0.65 (declare-fun tptp.produc668584238_int_o ((-> tptp.com (-> tptp.list_char tptp.int) Bool) tptp.produc1260470173ar_int) Bool) 0.39/0.65 (declare-fun tptp.produc1311963066nt_nat ((-> tptp.com (-> tptp.list_char tptp.int) tptp.nat) tptp.produc1260470173ar_int) tptp.nat) 0.39/0.65 (declare-fun tptp.produc1194453555nt_com ((-> tptp.com (-> tptp.list_char tptp.int) tptp.produc1166363805nt_com) tptp.produc1260470173ar_int) tptp.produc1166363805nt_com) 0.39/0.65 (declare-fun tptp.produc1288559923ar_int ((-> tptp.com (-> tptp.list_char tptp.int) tptp.produc1260470173ar_int) tptp.produc1260470173ar_int) tptp.produc1260470173ar_int) 0.39/0.65 (declare-fun tptp.produc991755120et_nat ((-> tptp.com (-> tptp.list_char tptp.int) tptp.set_nat) tptp.produc1260470173ar_int) tptp.set_nat) 0.39/0.65 (declare-fun tptp.produc1994108563nt_com ((-> tptp.com (-> tptp.list_char tptp.int) tptp.set_Pr866150653nt_com) tptp.produc1260470173ar_int) tptp.set_Pr866150653nt_com) 0.39/0.65 (declare-fun tptp.produc128852371ar_int ((-> tptp.com (-> tptp.list_char tptp.int) tptp.set_Pr1148378109ar_int) tptp.produc1260470173ar_int) tptp.set_Pr1148378109ar_int) 0.39/0.65 (declare-fun tptp.produc1716235893nt_com (tptp.produc1166363805nt_com) tptp.produc1260470173ar_int) 0.39/0.65 (declare-fun tptp.produc1770201973ar_int (tptp.produc1260470173ar_int) tptp.produc1166363805nt_com) 0.39/0.65 (declare-fun tptp.relati1310524937decomp ((-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool) tptp.com tptp.com (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool) (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int)) Bool) 0.39/0.65 (declare-fun tptp.relati186416454e_flip ((-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool) (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int)) Bool) 0.39/0.65 (declare-fun tptp.relati23543761ar_int ((-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool) tptp.bexp tptp.com tptp.nat (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int)) Bool) 0.39/0.65 (declare-fun tptp.relati2102071307_hoare ((-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool) tptp.com tptp.com (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) Bool) 0.39/0.65 (declare-fun tptp.relati775585786_valid ((-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool) tptp.com tptp.com (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) Bool) 0.39/0.65 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat) 0.39/0.65 (declare-fun tptp.collec676690312nt_com ((-> tptp.produc1166363805nt_com Bool)) tptp.set_Pr866150653nt_com) 0.39/0.65 (declare-fun tptp.collec770796680ar_int ((-> tptp.produc1260470173ar_int Bool)) tptp.set_Pr1148378109ar_int) 0.39/0.65 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat) 0.39/0.65 (declare-fun tptp.image_244615942nt_com ((-> tptp.nat tptp.produc1166363805nt_com) tptp.set_nat) tptp.set_Pr866150653nt_com) 0.39/0.65 (declare-fun tptp.image_338722310ar_int ((-> tptp.nat tptp.produc1260470173ar_int) tptp.set_nat) tptp.set_Pr1148378109ar_int) 0.39/0.65 (declare-fun tptp.image_596692520om_nat ((-> tptp.produc1166363805nt_com tptp.nat) tptp.set_Pr866150653nt_com) tptp.set_nat) 0.39/0.65 (declare-fun tptp.image_1874758725nt_com ((-> tptp.produc1166363805nt_com tptp.produc1166363805nt_com) tptp.set_Pr866150653nt_com) tptp.set_Pr866150653nt_com) 0.39/0.65 (declare-fun tptp.image_1968865093ar_int ((-> tptp.produc1166363805nt_com tptp.produc1260470173ar_int) tptp.set_Pr866150653nt_com) tptp.set_Pr1148378109ar_int) 0.39/0.65 (declare-fun tptp.image_522938432_int_o ((-> tptp.produc1260470173ar_int Bool) tptp.set_Pr1148378109ar_int) tptp.set_o) 0.39/0.65 (declare-fun tptp.image_1742782760nt_nat ((-> tptp.produc1260470173ar_int tptp.nat) tptp.set_Pr1148378109ar_int) tptp.set_nat) 0.39/0.65 (declare-fun tptp.image_786684229nt_com ((-> tptp.produc1260470173ar_int tptp.produc1166363805nt_com) tptp.set_Pr1148378109ar_int) tptp.set_Pr866150653nt_com) 0.39/0.65 (declare-fun tptp.image_880790597ar_int ((-> tptp.produc1260470173ar_int tptp.produc1260470173ar_int) tptp.set_Pr1148378109ar_int) tptp.set_Pr1148378109ar_int) 0.39/0.65 (declare-fun tptp.image_989727966et_nat ((-> tptp.produc1260470173ar_int tptp.set_nat) tptp.set_Pr1148378109ar_int) tptp.set_set_nat) 0.39/0.65 (declare-fun tptp.member_o (Bool tptp.set_o) Bool) 0.39/0.65 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool) 0.39/0.65 (declare-fun tptp.member2145628230nt_com (tptp.produc1166363805nt_com tptp.set_Pr866150653nt_com) Bool) 0.39/0.65 (declare-fun tptp.member92250950ar_int (tptp.produc1260470173ar_int tptp.set_Pr1148378109ar_int) Bool) 0.39/0.65 (declare-fun tptp.member_set_nat (tptp.set_nat tptp.set_set_nat) Bool) 0.39/0.65 (declare-fun tptp.p ((-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int)) Bool) 0.39/0.65 (declare-fun tptp.q ((-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int)) Bool) 0.39/0.65 (declare-fun tptp.c () tptp.com) 0.39/0.65 (declare-fun tptp.c2 () tptp.com) 0.39/0.65 (assert (forall ((F2 (-> tptp.produc1260470173ar_int tptp.set_nat))) (= (@ tptp.produc991755120et_nat (@ tptp.produc1791150095et_nat F2)) F2))) 0.39/0.65 (assert (forall ((C1 tptp.com) (C22 tptp.com) (C32 tptp.com) (S7 (-> tptp.list_char tptp.int)) (S6 (-> tptp.list_char tptp.int))) (let ((_let_1 (@ tptp.seq C1))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.seq (@ _let_1 C22)) C32)) S7)) S6) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ _let_1 (@ (@ tptp.seq C22) C32))) S7)) S6))))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C_1 tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C_2 tptp.com)) (=> (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((A5 (-> tptp.list_char tptp.int)) (C3 (-> tptp.list_char tptp.int))) (and (@ (@ P A5) C3) (@ (@ tptp.bval B) A5)))) C_1) C2) Q) (@ (@ (@ (@ tptp.relati775585786_valid P) (@ (@ (@ tptp.if B) C_1) C_2)) C2) Q)))) 0.39/0.65 (assert (forall ((C tptp.com) (C2 tptp.com) (B tptp.bexp)) (=> (forall ((S3 (-> tptp.list_char tptp.int)) (T (-> tptp.list_char tptp.int))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S3)) T) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S3)) T))) (forall ((S8 (-> tptp.list_char tptp.int)) (T7 (-> tptp.list_char tptp.int))) (let ((_let_1 (@ tptp.while B))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ _let_1 C)) S8)) T7) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ _let_1 C2)) S8)) T7))))))) 0.39/0.65 (assert (forall ((F2 (-> (-> tptp.list_char tptp.int) tptp.com Bool)) (P4 tptp.produc1166363805nt_com)) (= (@ (@ tptp.produc668584238_int_o (lambda ((Y4 tptp.com) (X (-> tptp.list_char tptp.int))) (@ (@ F2 X) Y4))) (@ tptp.produc1716235893nt_com P4)) (@ (@ tptp.produc613711406_com_o F2) P4)))) 0.39/0.65 (assert (forall ((P4 tptp.produc1166363805nt_com) (Z tptp.produc1260470173ar_int) (C (-> (-> tptp.list_char tptp.int) tptp.com tptp.set_Pr1148378109ar_int))) (=> (forall ((A3 (-> tptp.list_char tptp.int)) (B3 tptp.com)) (=> (= P4 (@ (@ tptp.produc1139835093nt_com A3) B3)) (@ (@ tptp.member92250950ar_int Z) (@ (@ C A3) B3)))) (@ (@ tptp.member92250950ar_int Z) (@ (@ tptp.produc1461507731ar_int C) P4))))) 0.39/0.65 (assert (forall ((Q (-> tptp.produc1260470173ar_int Bool)) (P (-> tptp.com (-> tptp.list_char tptp.int) tptp.produc1260470173ar_int)) (Z tptp.produc1260470173ar_int)) (=> (@ Q (@ (@ tptp.produc1288559923ar_int P) Z)) (not (forall ((X3 tptp.com) (Y3 (-> tptp.list_char tptp.int))) (=> (= Z (@ (@ tptp.produc1193801173ar_int X3) Y3)) (not (@ Q (@ (@ P X3) Y3))))))))) 0.39/0.65 (assert (forall ((X51 tptp.bexp) (X52 tptp.com)) (= (@ tptp.size_size_com (@ (@ tptp.while X51) X52)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_com X52)) (@ tptp.suc tptp.zero_zero_nat))))) 0.39/0.65 (assert (forall ((B tptp.bexp) (C tptp.com) (S8 (-> tptp.list_char tptp.int)) (T7 (-> tptp.list_char tptp.int))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ (@ tptp.if B) C) C)) S8)) T7) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S8)) T7)))) 0.39/0.65 (assert (forall ((F2 (-> tptp.produc1260470173ar_int tptp.nat)) (G (-> tptp.nat tptp.produc1260470173ar_int)) (A4 tptp.set_nat)) (= (@ (@ tptp.image_1742782760nt_nat F2) (@ (@ tptp.image_338722310ar_int G) A4)) (@ (@ tptp.image_nat_nat (lambda ((X tptp.nat)) (@ F2 (@ G X)))) A4)))) 0.39/0.65 (assert (forall ((Y tptp.com) (X4 (-> tptp.list_char tptp.int)) (A4 tptp.set_Pr866150653nt_com)) (= (@ (@ tptp.member92250950ar_int (@ (@ tptp.produc1193801173ar_int Y) X4)) (@ (@ tptp.image_1968865093ar_int tptp.produc1716235893nt_com) A4)) (@ (@ tptp.member2145628230nt_com (@ (@ tptp.produc1139835093nt_com X4) Y)) A4)))) 0.39/0.65 (assert (forall ((Z tptp.nat) (F2 (-> tptp.produc1260470173ar_int tptp.nat)) (A4 tptp.set_Pr1148378109ar_int)) (= (@ (@ tptp.member_nat Z) (@ (@ tptp.image_1742782760nt_nat F2) A4)) (exists ((X tptp.produc1260470173ar_int)) (and (= Z (@ F2 X)) (@ (@ tptp.member92250950ar_int X) A4)))))) 0.39/0.65 (assert (forall ((P (-> tptp.produc1260470173ar_int Bool)) (Prod tptp.produc1260470173ar_int)) (=> (forall ((A3 tptp.com) (B3 (-> tptp.list_char tptp.int))) (@ P (@ (@ tptp.produc1193801173ar_int A3) B3))) (@ P Prod)))) 0.39/0.65 (assert (forall ((A tptp.com) (B (-> tptp.list_char tptp.int)) (A4 tptp.set_Pr1148378109ar_int) (F2 (-> tptp.com (-> tptp.list_char tptp.int) tptp.produc1260470173ar_int))) (=> (@ (@ tptp.member92250950ar_int (@ (@ tptp.produc1193801173ar_int A) B)) A4) (@ (@ tptp.member92250950ar_int (@ (@ F2 A) B)) (@ (@ tptp.image_880790597ar_int (@ tptp.produc1288559923ar_int F2)) A4))))) 0.39/0.65 (assert (forall ((X31 tptp.com) (X32 tptp.com)) (= (@ tptp.size_size_com (@ (@ tptp.seq X31) X32)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.size_size_com X31)) (@ tptp.size_size_com X32))) (@ tptp.suc tptp.zero_zero_nat))))) 0.39/0.65 (assert (forall ((B tptp.nat) (F2 (-> tptp.produc1260470173ar_int tptp.nat)) (X4 tptp.produc1260470173ar_int) (A4 tptp.set_Pr1148378109ar_int)) (=> (= B (@ F2 X4)) (=> (@ (@ tptp.member92250950ar_int X4) A4) (@ (@ tptp.member_nat B) (@ (@ tptp.image_1742782760nt_nat F2) A4)))))) 0.39/0.65 (assert (forall ((M tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.plus_plus_nat M) N3) _let_1) (or (and (= M tptp.zero_zero_nat) (= N3 _let_1)) (and (= N3 tptp.zero_zero_nat) (= M _let_1))))))) 0.39/0.65 (assert (forall ((A4 tptp.set_nat)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) A4))))) 0.39/0.65 (assert (= tptp.relati186416454e_flip (lambda ((P2 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (S (-> tptp.list_char tptp.int)) (S2 (-> tptp.list_char tptp.int))) (@ (@ P2 S2) S)))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C_2 tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C_1 tptp.com)) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare (lambda ((S (-> tptp.list_char tptp.int)) (S2 (-> tptp.list_char tptp.int))) (and (not (@ (@ tptp.bval B) S)) (@ (@ P S) S2)))) C_2) C2) Q) (@ (@ (@ (@ tptp.relati2102071307_hoare P) (@ (@ (@ tptp.if B) C_1) C_2)) C2) Q)))) 0.39/0.65 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.produc1166363805nt_com Bool)) (A (-> tptp.list_char tptp.int)) (B tptp.com)) (=> (@ F2 (@ (@ tptp.produc1139835093nt_com A) B)) (@ (@ (@ tptp.produc1803493327_com_o F2) A) B)))) 0.39/0.65 (assert (forall ((P4 tptp.produc1260470173ar_int)) (exists ((X3 tptp.com) (Y3 (-> tptp.list_char tptp.int))) (= P4 (@ (@ tptp.produc1193801173ar_int X3) Y3))))) 0.39/0.65 (assert (forall ((S6 (-> tptp.list_char tptp.int)) (T3 (-> tptp.list_char tptp.int))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int tptp.skip) S6)) T3) (= S6 T3)))) 0.39/0.65 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)))))) 0.39/0.65 (assert (forall ((Inf (-> tptp.set_nat tptp.nat)) (A4 tptp.set_nat)) (= (@ Inf (@ (@ tptp.image_nat_nat (lambda ((X tptp.nat)) X)) A4)) (@ Inf A4)))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (Q3 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ (@ (@ tptp.relati2102071307_hoare P) C) C2))) (=> (@ _let_1 Q) (=> (forall ((S3 (-> tptp.list_char tptp.int)) (S4 (-> tptp.list_char tptp.int))) (=> (@ (@ Q3 S3) S4) (@ (@ Q S3) S4))) (@ _let_1 Q3)))))) 0.39/0.65 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N3 tptp.nat)) (=> (forall ((X3 tptp.nat)) (@ (@ P X3) tptp.zero_zero_nat)) (=> (forall ((Y3 tptp.nat)) (@ (@ P tptp.zero_zero_nat) (@ tptp.suc Y3))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ P X3) Y3) (@ (@ P (@ tptp.suc X3)) (@ tptp.suc Y3)))) (@ (@ P M) N3)))))) 0.39/0.65 (assert (forall ((Y tptp.produc1166363805nt_com)) (not (forall ((A3 (-> tptp.list_char tptp.int)) (B3 tptp.com)) (not (= Y (@ (@ tptp.produc1139835093nt_com A3) B3))))))) 0.39/0.65 (assert (forall ((F2 (-> (-> tptp.list_char tptp.int) tptp.com Bool)) (A (-> tptp.list_char tptp.int)) (B tptp.com)) (=> (@ (@ tptp.produc613711406_com_o F2) (@ (@ tptp.produc1139835093nt_com A) B)) (@ (@ F2 A) B)))) 0.39/0.65 (assert (forall ((H (-> Bool tptp.set_nat)) (F2 (-> tptp.com (-> tptp.list_char tptp.int) Bool)) (Prod tptp.produc1260470173ar_int)) (= (@ H (@ (@ tptp.produc668584238_int_o F2) Prod)) (@ (@ tptp.produc991755120et_nat (lambda ((X13 tptp.com) (X24 (-> tptp.list_char tptp.int))) (@ H (@ (@ F2 X13) X24)))) Prod)))) 0.39/0.65 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P K) (=> (forall ((N tptp.nat)) (=> (@ P (@ tptp.suc N)) (@ P N))) (@ P tptp.zero_zero_nat))))) 0.39/0.65 (assert (forall ((Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C2 tptp.com)) (=> (forall ((T (-> tptp.list_char tptp.int)) (T2 (-> tptp.list_char tptp.int))) (=> (@ (@ Q T) T2) (exists ((S5 (-> tptp.list_char tptp.int))) (and (@ (@ P T) S5) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S5)) T2))))) (@ (@ (@ (@ tptp.relati775585786_valid P) tptp.skip) C2) Q)))) 0.39/0.65 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C) A)) (= B C)))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (X4 tptp.list_char) (E tptp.aexp) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare (lambda ((T4 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (exists ((V3 tptp.int)) (let ((_let_1 (@ (@ (@ tptp.fun_up103088396ar_int T4) X4) V3))) (and (@ (@ P _let_1) T5) (= (@ T4 X4) (@ (@ tptp.aval E) _let_1))))))) tptp.skip) C2) Q) (@ (@ (@ (@ tptp.relati2102071307_hoare P) (@ (@ tptp.assign X4) E)) C2) Q)))) 0.39/0.65 (assert (forall ((Z tptp.produc1260470173ar_int) (C (-> tptp.com (-> tptp.list_char tptp.int) tptp.set_Pr1148378109ar_int)) (A tptp.com) (B (-> tptp.list_char tptp.int))) (let ((_let_1 (@ tptp.member92250950ar_int Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc128852371ar_int C) (@ (@ tptp.produc1193801173ar_int A) B))))))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C2 tptp.com) (C tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati775585786_valid (@ tptp.relati186416454e_flip P)) C2) C) (@ tptp.relati186416454e_flip Q)) (@ (@ (@ (@ tptp.relati775585786_valid P) C) C2) Q)))) 0.39/0.65 (assert (forall ((F2 (-> tptp.produc1260470173ar_int Bool))) (= (@ tptp.produc668584238_int_o (@ tptp.produc1858366159_int_o F2)) F2))) 0.39/0.65 (assert (= (@ tptp.size_com tptp.skip) tptp.zero_zero_nat)) 0.39/0.65 (assert (forall ((M tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ tptp.suc N3)) (@ tptp.suc (@ _let_1 N3)))))) 0.39/0.65 (assert (forall ((X21 tptp.list_char) (X22 tptp.aexp) (X51 tptp.bexp) (X52 tptp.com)) (not (= (@ (@ tptp.assign X21) X22) (@ (@ tptp.while X51) X52))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.produc1166363805nt_com Bool)) (A (-> tptp.list_char tptp.int)) (B tptp.com)) (=> (@ (@ (@ tptp.produc1803493327_com_o F2) A) B) (@ F2 (@ (@ tptp.produc1139835093nt_com A) B))))) 0.39/0.65 (assert (forall ((A (-> tptp.list_char tptp.int)) (B tptp.com) (A4 tptp.set_Pr866150653nt_com) (F2 (-> (-> tptp.list_char tptp.int) tptp.com tptp.nat))) (=> (@ (@ tptp.member2145628230nt_com (@ (@ tptp.produc1139835093nt_com A) B)) A4) (@ (@ tptp.member_nat (@ (@ F2 A) B)) (@ (@ tptp.image_596692520om_nat (@ tptp.produc1263502010om_nat F2)) A4))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.com (-> tptp.list_char tptp.int) Bool)) (A tptp.com) (B (-> tptp.list_char tptp.int))) (=> (@ (@ F2 A) B) (@ (@ tptp.produc668584238_int_o F2) (@ (@ tptp.produc1193801173ar_int A) B))))) 0.39/0.65 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X4) Y) tptp.zero_zero_nat) (and (= Y tptp.zero_zero_nat) (= X4 tptp.zero_zero_nat))))) 0.39/0.65 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A))) 0.39/0.65 (assert (forall ((F2 (-> tptp.produc1260470173ar_int tptp.produc1166363805nt_com)) (A4 tptp.set_Pr1148378109ar_int) (P (-> tptp.produc1166363805nt_com Bool))) (= (@ tptp.collec676690312nt_com (lambda ((X tptp.produc1166363805nt_com)) (and (@ (@ tptp.member2145628230nt_com X) (@ (@ tptp.image_786684229nt_com F2) A4)) (@ P X)))) (@ (@ tptp.image_786684229nt_com F2) (@ tptp.collec770796680ar_int (lambda ((X tptp.produc1260470173ar_int)) (and (@ (@ tptp.member92250950ar_int X) A4) (@ P (@ F2 X))))))))) 0.39/0.65 (assert (forall ((P (-> tptp.produc1260470173ar_int Bool)) (P4 tptp.produc1260470173ar_int)) (=> (forall ((A3 tptp.com) (B3 (-> tptp.list_char tptp.int))) (@ P (@ (@ tptp.produc1193801173ar_int A3) B3))) (@ P P4)))) 0.39/0.65 (assert (forall ((A4 tptp.nat) (K tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_nat A4) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B))))))) 0.39/0.65 (assert (forall ((H (-> Bool tptp.produc1260470173ar_int)) (F2 (-> tptp.com (-> tptp.list_char tptp.int) Bool)) (Prod tptp.produc1260470173ar_int)) (= (@ H (@ (@ tptp.produc668584238_int_o F2) Prod)) (@ (@ tptp.produc1288559923ar_int (lambda ((X13 tptp.com) (X24 (-> tptp.list_char tptp.int))) (@ H (@ (@ F2 X13) X24)))) Prod)))) 0.39/0.65 (assert (forall ((F2 (-> tptp.nat tptp.produc1166363805nt_com)) (A4 tptp.set_nat) (P (-> tptp.produc1166363805nt_com Bool))) (= (@ tptp.collec676690312nt_com (lambda ((X tptp.produc1166363805nt_com)) (and (@ (@ tptp.member2145628230nt_com X) (@ (@ tptp.image_244615942nt_com F2) A4)) (@ P X)))) (@ (@ tptp.image_244615942nt_com F2) (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (@ P (@ F2 X)) (@ (@ tptp.member_nat X) A4)))))))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (R (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ (@ tptp.relati775585786_valid P) C))) (=> (and (@ (@ _let_1 tptp.skip) R) (@ (@ (@ (@ tptp.relati775585786_valid R) tptp.skip) C2) Q)) (@ (@ _let_1 C2) Q))))) 0.39/0.65 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M))) 0.39/0.65 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (= (@ (@ P A3) B3) (@ (@ P B3) A3))) (=> (forall ((A3 tptp.nat)) (@ (@ P A3) tptp.zero_zero_nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ P A3))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.plus_plus_nat A3) B3))))) (@ (@ P A) B)))))) 0.39/0.65 (assert (forall ((Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C2 tptp.com)) (=> (forall ((T (-> tptp.list_char tptp.int)) (T2 (-> tptp.list_char tptp.int))) (=> (@ (@ Q T2) T) (exists ((S5 (-> tptp.list_char tptp.int))) (and (@ (@ P S5) T) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S5)) T2))))) (@ (@ (@ (@ tptp.relati2102071307_hoare P) C2) tptp.skip) Q)))) 0.39/0.65 (assert (forall ((S9 tptp.set_nat)) (= (@ (@ tptp.image_nat_nat (@ tptp.plus_plus_nat tptp.zero_zero_nat)) S9) S9))) 0.39/0.65 (assert (forall ((P (-> tptp.nat Bool)) (Nat tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((Nat3 tptp.nat)) (=> (@ P Nat3) (@ P (@ tptp.suc Nat3)))) (@ P Nat))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.list_char tptp.int)) (X4 tptp.list_char) (Y tptp.int)) (=> (= (@ F2 X4) Y) (= (@ (@ (@ tptp.fun_up103088396ar_int F2) X4) Y) F2)))) 0.39/0.65 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) A) (= B tptp.zero_zero_nat)))) 0.39/0.65 (assert (forall ((B tptp.bexp) (S7 (-> tptp.list_char tptp.int)) (C_1 tptp.com) (T6 (-> tptp.list_char tptp.int)) (C_2 tptp.com)) (=> (@ (@ tptp.bval B) S7) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C_1) S7)) T6) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ (@ tptp.if B) C_1) C_2)) S7)) T6))))) 0.39/0.65 (assert (forall ((P4 tptp.produc1260470173ar_int) (Z tptp.produc1166363805nt_com) (C (-> tptp.com (-> tptp.list_char tptp.int) tptp.set_Pr866150653nt_com))) (=> (forall ((A3 tptp.com) (B3 (-> tptp.list_char tptp.int))) (=> (= P4 (@ (@ tptp.produc1193801173ar_int A3) B3)) (@ (@ tptp.member2145628230nt_com Z) (@ (@ C A3) B3)))) (@ (@ tptp.member2145628230nt_com Z) (@ (@ tptp.produc1994108563nt_com C) P4))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (= (@ (@ tptp.image_nat_nat F2) (@ (@ tptp.image_nat_nat G) A4)) (@ (@ tptp.image_nat_nat (lambda ((X tptp.nat)) (@ F2 (@ G X)))) A4)))) 0.39/0.65 (assert (forall ((F2 (-> tptp.produc1260470173ar_int Bool)) (A tptp.com) (B (-> tptp.list_char tptp.int))) (=> (@ F2 (@ (@ tptp.produc1193801173ar_int A) B)) (@ (@ (@ tptp.produc1858366159_int_o F2) A) B)))) 0.39/0.65 (assert (= tptp.relati1310524937decomp (lambda ((P2 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C3 tptp.com) (C4 tptp.com) (Q2 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (T4 (-> tptp.list_char tptp.int)) (S2 (-> tptp.list_char tptp.int))) (exists ((S (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (and (@ (@ P2 S) S2) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C4) S2)) T5) (@ (@ Q2 T4) T5) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C3) S)) T4)))))) 0.39/0.65 (assert (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2))))) 0.39/0.65 (assert (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y (@ tptp.suc Nat3)))))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (A4 tptp.set_nat) (P (-> tptp.nat Bool))) (=> (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) (@ (@ tptp.image_nat_nat F2) A4)) (@ P X5))) (exists ((X3 tptp.nat)) (and (@ P (@ F2 X3)) (@ (@ tptp.member_nat X3) A4)))))) 0.39/0.65 (assert (forall ((Z tptp.nat) (C (-> tptp.com (-> tptp.list_char tptp.int) tptp.set_nat)) (P4 tptp.produc1260470173ar_int)) (=> (@ (@ tptp.member_nat Z) (@ (@ tptp.produc991755120et_nat C) P4)) (not (forall ((X3 tptp.com) (Y3 (-> tptp.list_char tptp.int))) (=> (= P4 (@ (@ tptp.produc1193801173ar_int X3) Y3)) (not (@ (@ tptp.member_nat Z) (@ (@ C X3) Y3))))))))) 0.39/0.65 (assert (forall ((P Bool)) (or (= P false) (= P true)))) 0.39/0.65 (assert (forall ((Z tptp.produc1260470173ar_int) (C (-> (-> tptp.list_char tptp.int) tptp.com tptp.set_Pr1148378109ar_int)) (P4 tptp.produc1166363805nt_com)) (=> (@ (@ tptp.member92250950ar_int Z) (@ (@ tptp.produc1461507731ar_int C) P4)) (not (forall ((X3 (-> tptp.list_char tptp.int)) (Y3 tptp.com)) (=> (= P4 (@ (@ tptp.produc1139835093nt_com X3) Y3)) (not (@ (@ tptp.member92250950ar_int Z) (@ (@ C X3) Y3))))))))) 0.39/0.65 (assert (forall ((B tptp.nat) (F2 (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (=> (@ (@ tptp.member_nat B) (@ (@ tptp.image_nat_nat F2) A4)) (not (forall ((X3 tptp.nat)) (=> (= B (@ F2 X3)) (not (@ (@ tptp.member_nat X3) A4)))))))) 0.39/0.65 (assert (forall ((C tptp.com) (C2 tptp.com) (C5 tptp.com)) (=> (forall ((S3 (-> tptp.list_char tptp.int)) (T (-> tptp.list_char tptp.int))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S3)) T) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S3)) T))) (=> (forall ((S3 (-> tptp.list_char tptp.int)) (T (-> tptp.list_char tptp.int))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S3)) T) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C5) S3)) T))) (forall ((S8 (-> tptp.list_char tptp.int)) (T7 (-> tptp.list_char tptp.int))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S8)) T7) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C5) S8)) T7))))))) 0.39/0.65 (assert (forall ((X21 tptp.list_char) (X22 tptp.aexp)) (not (= tptp.skip (@ (@ tptp.assign X21) X22))))) 0.39/0.65 (assert (forall ((P4 tptp.produc1260470173ar_int) (Z tptp.nat) (C (-> tptp.com (-> tptp.list_char tptp.int) tptp.set_nat))) (=> (forall ((A3 tptp.com) (B3 (-> tptp.list_char tptp.int))) (=> (= P4 (@ (@ tptp.produc1193801173ar_int A3) B3)) (@ (@ tptp.member_nat Z) (@ (@ C A3) B3)))) (@ (@ tptp.member_nat Z) (@ (@ tptp.produc991755120et_nat C) P4))))) 0.39/0.65 (assert (forall ((X4 tptp.produc1260470173ar_int) (A4 tptp.set_Pr1148378109ar_int) (F2 (-> tptp.produc1260470173ar_int tptp.nat))) (=> (@ (@ tptp.member92250950ar_int X4) A4) (@ (@ tptp.member_nat (@ F2 X4)) (@ (@ tptp.image_1742782760nt_nat F2) A4))))) 0.39/0.65 (assert (forall ((A tptp.com) (B (-> tptp.list_char tptp.int)) (A2 tptp.com) (B2 (-> tptp.list_char tptp.int))) (= (= (@ (@ tptp.produc1193801173ar_int A) B) (@ (@ tptp.produc1193801173ar_int A2) B2)) (and (= B B2) (= A A2))))) 0.39/0.65 (assert (forall ((X31 tptp.com) (X32 tptp.com) (Y31 tptp.com) (Y32 tptp.com)) (= (= (@ (@ tptp.seq X31) X32) (@ (@ tptp.seq Y31) Y32)) (and (= X32 Y32) (= X31 Y31))))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C1 tptp.com) (C22 tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ tptp.relati775585786_valid P))) (=> (@ (@ (@ _let_1 (@ (@ tptp.seq C1) C22)) C2) Q) (@ (@ (@ _let_1 C1) C2) (lambda ((T4 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (exists ((S (-> tptp.list_char tptp.int)) (S2 (-> tptp.list_char tptp.int))) (and (exists ((U2 (-> tptp.list_char tptp.int))) (and (@ (@ Q U2) T5) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C22) T4)) U2))) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S2)) T5) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C1) S)) T4) (@ (@ P S) S2))))))))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (D tptp.com) (R (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ tptp.relati2102071307_hoare P))) (=> (@ (@ (@ _let_1 C) C2) Q) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare Q) D) tptp.skip) R) (@ (@ (@ _let_1 (@ (@ tptp.seq C) D)) C2) R)))))) 0.39/0.65 (assert (forall ((B tptp.nat) (F2 (-> tptp.nat tptp.nat)) (X4 tptp.nat) (A4 tptp.set_nat)) (=> (= B (@ F2 X4)) (=> (@ (@ tptp.member_nat X4) A4) (@ (@ tptp.member_nat B) (@ (@ tptp.image_nat_nat F2) A4)))))) 0.39/0.65 (assert (forall ((P4 tptp.produc1260470173ar_int)) (= (@ tptp.produc1716235893nt_com (@ tptp.produc1770201973ar_int P4)) P4))) 0.39/0.65 (assert (forall ((A (-> tptp.list_char tptp.int)) (B tptp.com) (A4 tptp.set_Pr866150653nt_com) (F2 (-> (-> tptp.list_char tptp.int) tptp.com tptp.produc1166363805nt_com))) (=> (@ (@ tptp.member2145628230nt_com (@ (@ tptp.produc1139835093nt_com A) B)) A4) (@ (@ tptp.member2145628230nt_com (@ (@ F2 A) B)) (@ (@ tptp.image_1874758725nt_com (@ tptp.produc1676975923nt_com F2)) A4))))) 0.39/0.65 (assert (forall ((H (-> tptp.nat tptp.set_nat)) (F2 (-> tptp.com (-> tptp.list_char tptp.int) tptp.nat)) (Prod tptp.produc1260470173ar_int)) (= (@ H (@ (@ tptp.produc1311963066nt_nat F2) Prod)) (@ (@ tptp.produc991755120et_nat (lambda ((X13 tptp.com) (X24 (-> tptp.list_char tptp.int))) (@ H (@ (@ F2 X13) X24)))) Prod)))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (@ (@ (@ (@ tptp.relati2102071307_hoare P) tptp.skip) tptp.skip) P))) 0.39/0.65 (assert (forall ((P_1 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q_1 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (P_2 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (Q_2 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati775585786_valid P_1) C) C2) Q_1) (=> (@ (@ (@ (@ tptp.relati775585786_valid P_2) C) C2) Q_2) (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((S (-> tptp.list_char tptp.int)) (S2 (-> tptp.list_char tptp.int))) (or (@ (@ P_2 S) S2) (@ (@ P_1 S) S2)))) C) C2) (lambda ((T4 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (or (@ (@ Q_1 T4) T5) (@ (@ Q_2 T4) T5)))))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((Uu tptp.nat)) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A4) (= Uu (@ F2 X)))))) (@ (@ tptp.image_nat_nat F2) A4)))) 0.39/0.65 (assert (forall ((F2 (-> tptp.com (-> tptp.list_char tptp.int) tptp.nat))) (= (@ tptp.produc763543641nt_nat (@ tptp.produc1311963066nt_nat F2)) F2))) 0.39/0.65 (assert (= tptp.produc641693072nt_nat tptp.produc1311963066nt_nat)) 0.39/0.65 (assert (forall ((X21 tptp.list_char) (X22 tptp.aexp) (X31 tptp.com) (X32 tptp.com)) (not (= (@ (@ tptp.assign X21) X22) (@ (@ tptp.seq X31) X32))))) 0.39/0.65 (assert (forall ((X41 tptp.bexp) (X42 tptp.com) (X43 tptp.com) (X51 tptp.bexp) (X52 tptp.com)) (not (= (@ (@ (@ tptp.if X41) X42) X43) (@ (@ tptp.while X51) X52))))) 0.39/0.65 (assert (forall ((A tptp.produc1166363805nt_com) (P (-> tptp.produc1166363805nt_com Bool))) (= (@ (@ tptp.member2145628230nt_com A) (@ tptp.collec676690312nt_com P)) (@ P A)))) 0.39/0.65 (assert (forall ((F2 (-> tptp.com (-> tptp.list_char tptp.int) tptp.nat)) (P4 tptp.produc1260470173ar_int)) (= (@ (@ tptp.produc1263502010om_nat (lambda ((Y4 (-> tptp.list_char tptp.int)) (X tptp.com)) (@ (@ F2 X) Y4))) (@ tptp.produc1770201973ar_int P4)) (@ (@ tptp.produc1311963066nt_nat F2) P4)))) 0.39/0.65 (assert (forall ((H (-> tptp.nat tptp.nat)) (F2 (-> tptp.com (-> tptp.list_char tptp.int) tptp.nat)) (Prod tptp.produc1260470173ar_int)) (= (@ H (@ (@ tptp.produc1311963066nt_nat F2) Prod)) (@ (@ tptp.produc1311963066nt_nat (lambda ((X13 tptp.com) (X24 (-> tptp.list_char tptp.int))) (@ H (@ (@ F2 X13) X24)))) Prod)))) 0.39/0.65 (assert (forall ((B tptp.bexp) (S7 (-> tptp.list_char tptp.int)) (C tptp.com)) (=> (not (@ (@ tptp.bval B) S7)) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.while B) C)) S7)) S7)))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (D tptp.com) (D2 tptp.com) (R (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ tptp.relati775585786_valid P))) (=> (@ (@ (@ _let_1 C) C2) Q) (=> (@ (@ (@ (@ tptp.relati775585786_valid Q) D) D2) R) (@ (@ (@ _let_1 (@ (@ tptp.seq C) D)) (@ (@ tptp.seq C2) D2)) R)))))) 0.39/0.65 (assert (forall ((P (-> tptp.nat (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ (@ tptp.while B) C))) (=> (forall ((N tptp.nat)) (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((S (-> tptp.list_char tptp.int)) (S2 (-> tptp.list_char tptp.int))) (and (@ (@ (@ P N) S) S2) (@ (@ tptp.bval B) S)))) C) tptp.skip) (@ P (@ tptp.suc N)))) (=> (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((S (-> tptp.list_char tptp.int)) (S2 (-> tptp.list_char tptp.int))) (exists ((N5 tptp.nat)) (@ (@ (@ P N5) S) S2)))) _let_1) C2) Q) (@ (@ (@ (@ tptp.relati775585786_valid (@ P tptp.zero_zero_nat)) _let_1) C2) Q)))))) 0.39/0.65 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat)))) 0.39/0.65 (assert (forall ((M tptp.nat) (N3 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N3) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N3))))) 0.39/0.65 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (= (@ tptp.suc X2) (@ tptp.suc Y2)) (= X2 Y2)))) 0.39/0.65 (assert (forall ((P (-> tptp.nat (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (K tptp.nat) (B tptp.bexp) (C tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C2 tptp.com) (T6 (-> tptp.list_char tptp.int)) (T3 (-> tptp.list_char tptp.int))) (=> (forall ((N tptp.nat) (T (-> tptp.list_char tptp.int)) (T2 (-> tptp.list_char tptp.int))) (=> (@ (@ (@ P (@ (@ tptp.plus_plus_nat K) (@ tptp.suc N))) T) T2) (exists ((S8 (-> tptp.list_char tptp.int))) (and (@ (@ (@ P (@ (@ tptp.plus_plus_nat K) N)) S8) T2) (@ (@ tptp.bval B) S8) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S8)) T))))) (=> (forall ((T (-> tptp.list_char tptp.int)) (T2 (-> tptp.list_char tptp.int))) (=> (@ (@ Q T) T2) (exists ((S8 (-> tptp.list_char tptp.int)) (S5 (-> tptp.list_char tptp.int))) (and (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.while B) C)) S8)) T) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S5)) T2) (exists ((N2 tptp.nat)) (@ (@ (@ P (@ (@ tptp.plus_plus_nat K) N2)) S8) S5)))))) (=> (@ (@ Q T6) T3) (exists ((S3 (-> tptp.list_char tptp.int)) (S4 (-> tptp.list_char tptp.int))) (and (@ (@ (@ P K) S3) S4) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S4)) T3) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.while B) C)) S3)) T6)))))))) 0.39/0.65 (assert (= tptp.produc9062872_int_o tptp.produc668584238_int_o)) 0.39/0.65 (assert (forall ((P4 tptp.produc1260470173ar_int) (Z tptp.produc1260470173ar_int) (C (-> tptp.com (-> tptp.list_char tptp.int) tptp.set_Pr1148378109ar_int))) (=> (forall ((A3 tptp.com) (B3 (-> tptp.list_char tptp.int))) (=> (= P4 (@ (@ tptp.produc1193801173ar_int A3) B3)) (@ (@ tptp.member92250950ar_int Z) (@ (@ C A3) B3)))) (@ (@ tptp.member92250950ar_int Z) (@ (@ tptp.produc128852371ar_int C) P4))))) 0.39/0.65 (assert (forall ((M tptp.nat) (N3 tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N3) M) (= N3 tptp.zero_zero_nat)))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ (@ tptp.while B) C))) (=> (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((S (-> tptp.list_char tptp.int)) (S2 (-> tptp.list_char tptp.int))) (and (@ (@ tptp.bval B) S) (@ (@ P S) S2)))) (@ (@ tptp.seq C) _let_1)) C2) Q) (@ (@ (@ (@ tptp.relati775585786_valid P) _let_1) C2) Q))))) 0.39/0.65 (assert (forall ((Z tptp.produc1166363805nt_com) (C (-> tptp.com (-> tptp.list_char tptp.int) tptp.set_Pr866150653nt_com)) (A tptp.com) (B (-> tptp.list_char tptp.int))) (let ((_let_1 (@ tptp.member2145628230nt_com Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc1994108563nt_com C) (@ (@ tptp.produc1193801173ar_int A) B))))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.produc1260470173ar_int tptp.nat)) (A4 tptp.set_Pr1148378109ar_int) (P (-> tptp.nat Bool))) (=> (exists ((X5 tptp.nat)) (and (@ P X5) (@ (@ tptp.member_nat X5) (@ (@ tptp.image_1742782760nt_nat F2) A4)))) (exists ((X3 tptp.produc1260470173ar_int)) (and (@ P (@ F2 X3)) (@ (@ tptp.member92250950ar_int X3) A4)))))) 0.39/0.65 (assert (forall ((X4 tptp.produc1166363805nt_com) (A4 tptp.set_Pr866150653nt_com) (F2 (-> tptp.produc1166363805nt_com tptp.produc1260470173ar_int))) (=> (@ (@ tptp.member2145628230nt_com X4) A4) (@ (@ tptp.member92250950ar_int (@ F2 X4)) (@ (@ tptp.image_1968865093ar_int F2) A4))))) 0.39/0.65 (assert (forall ((B tptp.produc1260470173ar_int) (F2 (-> tptp.produc1260470173ar_int tptp.produc1260470173ar_int)) (X4 tptp.produc1260470173ar_int) (A4 tptp.set_Pr1148378109ar_int)) (=> (= B (@ F2 X4)) (=> (@ (@ tptp.member92250950ar_int X4) A4) (@ (@ tptp.member92250950ar_int B) (@ (@ tptp.image_880790597ar_int F2) A4)))))) 0.39/0.65 (assert (forall ((Z tptp.produc1166363805nt_com) (C (-> (-> tptp.list_char tptp.int) tptp.com tptp.set_Pr866150653nt_com)) (P4 tptp.produc1166363805nt_com)) (=> (@ (@ tptp.member2145628230nt_com Z) (@ (@ tptp.produc1179280275nt_com C) P4)) (not (forall ((X3 (-> tptp.list_char tptp.int)) (Y3 tptp.com)) (=> (= P4 (@ (@ tptp.produc1139835093nt_com X3) Y3)) (not (@ (@ tptp.member2145628230nt_com Z) (@ (@ C X3) Y3))))))))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C tptp.com) (N3 tptp.nat)) (= (@ (@ (@ (@ tptp.relati23543761ar_int P) B) C) (@ tptp.suc N3)) (lambda ((T4 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (exists ((S (-> tptp.list_char tptp.int))) (and (@ (@ tptp.bval B) S) (@ (@ (@ (@ (@ (@ tptp.relati23543761ar_int P) B) C) N3) S) T5) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S)) T4))))))) 0.39/0.65 (assert (forall ((C (-> tptp.com (-> tptp.list_char tptp.int) Bool)) (P4 tptp.produc1260470173ar_int)) (=> (@ (@ tptp.produc668584238_int_o C) P4) (not (forall ((X3 tptp.com) (Y3 (-> tptp.list_char tptp.int))) (=> (= P4 (@ (@ tptp.produc1193801173ar_int X3) Y3)) (not (@ (@ C X3) Y3)))))))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare P) C) C2) Q) (@ (@ (@ (@ tptp.relati775585786_valid P) C) C2) Q)))) 0.39/0.65 (assert (forall ((B tptp.produc1166363805nt_com) (F2 (-> tptp.produc1260470173ar_int tptp.produc1166363805nt_com)) (X4 tptp.produc1260470173ar_int) (A4 tptp.set_Pr1148378109ar_int)) (=> (= B (@ F2 X4)) (=> (@ (@ tptp.member92250950ar_int X4) A4) (@ (@ tptp.member2145628230nt_com B) (@ (@ tptp.image_786684229nt_com F2) A4)))))) 0.39/0.65 (assert (forall ((X4 tptp.nat) (A4 tptp.set_nat) (B tptp.nat) (F2 (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.member_nat X4) A4) (=> (= B (@ F2 X4)) (@ (@ tptp.member_nat B) (@ (@ tptp.image_nat_nat F2) A4)))))) 0.39/0.65 (assert (forall ((M tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.plus_plus_nat M) N3)) (or (and (= M tptp.zero_zero_nat) (= N3 _let_1)) (and (= N3 tptp.zero_zero_nat) (= M _let_1))))))) 0.39/0.65 (assert (forall ((M2 tptp.set_nat) (N4 tptp.set_nat) (F2 (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (= M2 N4) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) N4) (= (@ F2 X3) (@ G X3)))) (= (@ (@ tptp.image_nat_nat F2) M2) (@ (@ tptp.image_nat_nat G) N4)))))) 0.39/0.65 (assert (forall ((X4 tptp.produc1166363805nt_com) (A4 tptp.set_Pr866150653nt_com) (B tptp.produc1166363805nt_com) (F2 (-> tptp.produc1166363805nt_com tptp.produc1166363805nt_com))) (=> (@ (@ tptp.member2145628230nt_com X4) A4) (=> (= B (@ F2 X4)) (@ (@ tptp.member2145628230nt_com B) (@ (@ tptp.image_1874758725nt_com F2) A4)))))) 0.39/0.65 (assert (forall ((S7 (-> tptp.list_char tptp.int)) (T6 (-> tptp.list_char tptp.int))) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int tptp.skip) S7)) T6) (= T6 S7)))) 0.39/0.65 (assert (forall ((B tptp.nat) (F2 (-> tptp.produc1166363805nt_com tptp.nat)) (X4 tptp.produc1166363805nt_com) (A4 tptp.set_Pr866150653nt_com)) (=> (= B (@ F2 X4)) (=> (@ (@ tptp.member2145628230nt_com X4) A4) (@ (@ tptp.member_nat B) (@ (@ tptp.image_596692520om_nat F2) A4)))))) 0.39/0.65 (assert (forall ((H (-> tptp.nat Bool)) (F2 (-> tptp.com (-> tptp.list_char tptp.int) tptp.nat)) (Prod tptp.produc1260470173ar_int)) (= (@ H (@ (@ tptp.produc1311963066nt_nat F2) Prod)) (@ (@ tptp.produc668584238_int_o (lambda ((X13 tptp.com) (X24 (-> tptp.list_char tptp.int))) (@ H (@ (@ F2 X13) X24)))) Prod)))) 0.39/0.65 (assert (forall ((X21 tptp.list_char) (X22 tptp.aexp) (Y21 tptp.list_char) (Y22 tptp.aexp)) (= (= (@ (@ tptp.assign X21) X22) (@ (@ tptp.assign Y21) Y22)) (and (= X21 Y21) (= X22 Y22))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.produc1166363805nt_com tptp.produc1260470173ar_int)) (A4 tptp.set_Pr866150653nt_com) (P (-> tptp.produc1260470173ar_int Bool))) (=> (forall ((X3 tptp.produc1260470173ar_int)) (=> (@ (@ tptp.member92250950ar_int X3) (@ (@ tptp.image_1968865093ar_int F2) A4)) (@ P X3))) (forall ((X5 tptp.produc1166363805nt_com)) (=> (@ (@ tptp.member2145628230nt_com X5) A4) (@ P (@ F2 X5))))))) 0.39/0.65 (assert (forall ((X4 tptp.produc1166363805nt_com) (A4 tptp.set_Pr866150653nt_com) (F2 (-> tptp.produc1166363805nt_com tptp.nat))) (=> (@ (@ tptp.member2145628230nt_com X4) A4) (@ (@ tptp.member_nat (@ F2 X4)) (@ (@ tptp.image_596692520om_nat F2) A4))))) 0.39/0.65 (assert (forall ((Z tptp.nat) (C (-> tptp.com (-> tptp.list_char tptp.int) tptp.set_nat)) (A tptp.com) (B (-> tptp.list_char tptp.int))) (let ((_let_1 (@ tptp.member_nat Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc991755120et_nat C) (@ (@ tptp.produc1193801173ar_int A) B))))))) 0.39/0.65 (assert (forall ((X4 tptp.nat) (A4 tptp.set_nat) (B tptp.produc1166363805nt_com) (F2 (-> tptp.nat tptp.produc1166363805nt_com))) (=> (@ (@ tptp.member_nat X4) A4) (=> (= B (@ F2 X4)) (@ (@ tptp.member2145628230nt_com B) (@ (@ tptp.image_244615942nt_com F2) A4)))))) 0.39/0.65 (assert (forall ((B tptp.produc1166363805nt_com) (F2 (-> tptp.nat tptp.produc1166363805nt_com)) (X4 tptp.nat) (A4 tptp.set_nat)) (=> (= B (@ F2 X4)) (=> (@ (@ tptp.member_nat X4) A4) (@ (@ tptp.member2145628230nt_com B) (@ (@ tptp.image_244615942nt_com F2) A4)))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.produc1166363805nt_com tptp.nat)) (A4 tptp.set_Pr866150653nt_com) (P (-> tptp.nat Bool))) (= (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (@ (@ tptp.member_nat X) (@ (@ tptp.image_596692520om_nat F2) A4)) (@ P X)))) (@ (@ tptp.image_596692520om_nat F2) (@ tptp.collec676690312nt_com (lambda ((X tptp.produc1166363805nt_com)) (and (@ P (@ F2 X)) (@ (@ tptp.member2145628230nt_com X) A4)))))))) 0.39/0.65 (assert (forall ((T6 (-> tptp.list_char tptp.int)) (X4 tptp.list_char) (E tptp.aexp) (V2 tptp.int)) (let ((_let_1 (@ (@ (@ tptp.fun_up103088396ar_int T6) X4) V2))) (=> (= (@ T6 X4) (@ (@ tptp.aval E) _let_1)) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.assign X4) E)) _let_1)) T6))))) 0.39/0.65 (assert (forall ((Y tptp.produc1260470173ar_int)) (not (forall ((A3 tptp.com) (B3 (-> tptp.list_char tptp.int))) (not (= Y (@ (@ tptp.produc1193801173ar_int A3) B3))))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.produc1260470173ar_int tptp.nat)) (A4 tptp.set_Pr1148378109ar_int) (P (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.image_1742782760nt_nat F2) A4)) (@ P X3))) (forall ((X5 tptp.produc1260470173ar_int)) (=> (@ (@ tptp.member92250950ar_int X5) A4) (@ P (@ F2 X5))))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.com (-> tptp.list_char tptp.int) Bool)) (A tptp.com) (B (-> tptp.list_char tptp.int))) (= (@ (@ tptp.produc668584238_int_o F2) (@ (@ tptp.produc1193801173ar_int A) B)) (@ (@ F2 A) B)))) 0.39/0.65 (assert (forall ((F2 (-> tptp.com (-> tptp.list_char tptp.int) tptp.produc1260470173ar_int)) (G (-> tptp.produc1260470173ar_int tptp.produc1260470173ar_int))) (=> (forall ((X3 tptp.com) (Y3 (-> tptp.list_char tptp.int))) (= (@ (@ F2 X3) Y3) (@ G (@ (@ tptp.produc1193801173ar_int X3) Y3)))) (= (@ tptp.produc1288559923ar_int F2) G)))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati775585786_valid P) C) C2) Q) (@ (@ (@ (@ tptp.relati2102071307_hoare P) C) C2) Q)))) 0.39/0.65 (assert (forall ((R2 tptp.com) (S7 (-> tptp.list_char tptp.int)) (R tptp.set_Pr1148378109ar_int) (S6 (-> tptp.list_char tptp.int))) (let ((_let_1 (@ tptp.produc1193801173ar_int R2))) (=> (@ (@ tptp.member92250950ar_int (@ _let_1 S7)) R) (=> (= S6 S7) (@ (@ tptp.member92250950ar_int (@ _let_1 S6)) R)))))) 0.39/0.65 (assert (forall ((M2 tptp.set_Pr1148378109ar_int) (N4 tptp.set_Pr1148378109ar_int) (F2 (-> tptp.produc1260470173ar_int tptp.produc1166363805nt_com)) (G (-> tptp.produc1260470173ar_int tptp.produc1166363805nt_com))) (=> (= M2 N4) (=> (forall ((X3 tptp.produc1260470173ar_int)) (=> (@ (@ tptp.member92250950ar_int X3) N4) (= (@ F2 X3) (@ G X3)))) (= (@ (@ tptp.image_786684229nt_com F2) M2) (@ (@ tptp.image_786684229nt_com G) N4)))))) 0.39/0.65 (assert (forall ((A tptp.com) (B (-> tptp.list_char tptp.int)) (A4 tptp.set_Pr1148378109ar_int) (F2 (-> tptp.com (-> tptp.list_char tptp.int) tptp.produc1166363805nt_com))) (=> (@ (@ tptp.member92250950ar_int (@ (@ tptp.produc1193801173ar_int A) B)) A4) (@ (@ tptp.member2145628230nt_com (@ (@ F2 A) B)) (@ (@ tptp.image_786684229nt_com (@ tptp.produc1194453555nt_com F2)) A4))))) 0.39/0.65 (assert (forall ((P4 tptp.produc1166363805nt_com)) (exists ((X3 (-> tptp.list_char tptp.int)) (Y3 tptp.com)) (= P4 (@ (@ tptp.produc1139835093nt_com X3) Y3))))) 0.39/0.65 (assert (forall ((F2 (-> (-> tptp.list_char tptp.int) tptp.com tptp.produc1260470173ar_int)) (P4 tptp.produc1166363805nt_com)) (= (@ (@ tptp.produc1288559923ar_int (lambda ((Y4 tptp.com) (X (-> tptp.list_char tptp.int))) (@ (@ F2 X) Y4))) (@ tptp.produc1716235893nt_com P4)) (@ (@ tptp.produc1771082291ar_int F2) P4)))) 0.39/0.65 (assert (forall ((X51 tptp.bexp) (X52 tptp.com)) (= (@ tptp.size_com (@ (@ tptp.while X51) X52)) (@ (@ tptp.plus_plus_nat (@ tptp.size_com X52)) (@ tptp.suc tptp.zero_zero_nat))))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ (@ tptp.while B) C))) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare (lambda ((S (-> tptp.list_char tptp.int)) (S2 (-> tptp.list_char tptp.int))) (and (@ (@ P S) S2) (@ (@ tptp.bval B) S)))) (@ (@ tptp.seq C) _let_1)) C2) Q) (@ (@ (@ (@ tptp.relati2102071307_hoare P) _let_1) C2) Q))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.com (-> tptp.list_char tptp.int) tptp.set_nat)) (G (-> tptp.produc1260470173ar_int tptp.set_nat))) (=> (forall ((X3 tptp.com) (Y3 (-> tptp.list_char tptp.int))) (= (@ (@ F2 X3) Y3) (@ G (@ (@ tptp.produc1193801173ar_int X3) Y3)))) (= (@ tptp.produc991755120et_nat F2) G)))) 0.39/0.65 (assert (forall ((F2 (-> tptp.com (-> tptp.list_char tptp.int) tptp.set_nat)) (X1 tptp.com) (X2 (-> tptp.list_char tptp.int))) (= (@ (@ tptp.produc991755120et_nat F2) (@ (@ tptp.produc1193801173ar_int X1) X2)) (@ (@ F2 X1) X2)))) 0.39/0.65 (assert (= tptp.fun_up103088396ar_int (lambda ((F (-> tptp.list_char tptp.int)) (A5 tptp.list_char) (B4 tptp.int) (X tptp.list_char)) (@ (@ (@ tptp.if_int (= X A5)) B4) (@ F X))))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare (@ tptp.relati186416454e_flip P)) C) C2) (@ tptp.relati186416454e_flip Q)) (@ (@ (@ (@ tptp.relati2102071307_hoare P) C2) C) Q)))) 0.39/0.65 (assert (forall ((B tptp.bexp) (C tptp.com) (S7 (-> tptp.list_char tptp.int)) (T6 (-> tptp.list_char tptp.int)) (C2 tptp.com)) (let ((_let_1 (@ tptp.while B))) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ _let_1 C)) S7)) T6) (=> (forall ((S3 (-> tptp.list_char tptp.int)) (T (-> tptp.list_char tptp.int))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S3)) T) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S3)) T))) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ _let_1 C2)) S7)) T6)))))) 0.39/0.65 (assert (forall ((N3 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N3) N3))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C tptp.com)) (= (@ (@ (@ (@ tptp.relati23543761ar_int P) B) C) tptp.zero_zero_nat) P))) 0.39/0.65 (assert (forall ((X21 tptp.list_char) (X22 tptp.aexp)) (= (@ tptp.size_com (@ (@ tptp.assign X21) X22)) tptp.zero_zero_nat))) 0.39/0.65 (assert (forall ((F2 (-> tptp.com (-> tptp.list_char tptp.int) tptp.nat)) (G (-> tptp.produc1260470173ar_int tptp.nat))) (=> (forall ((X3 tptp.com) (Y3 (-> tptp.list_char tptp.int))) (= (@ (@ F2 X3) Y3) (@ G (@ (@ tptp.produc1193801173ar_int X3) Y3)))) (= (@ tptp.produc1311963066nt_nat F2) G)))) 0.39/0.65 (assert (forall ((F2 (-> tptp.produc1260470173ar_int Bool)) (A tptp.com) (B (-> tptp.list_char tptp.int))) (=> (@ (@ (@ tptp.produc1858366159_int_o F2) A) B) (@ F2 (@ (@ tptp.produc1193801173ar_int A) B))))) 0.39/0.65 (assert (forall ((M2 tptp.set_Pr1148378109ar_int) (N4 tptp.set_Pr1148378109ar_int) (F2 (-> tptp.produc1260470173ar_int tptp.nat)) (G (-> tptp.produc1260470173ar_int tptp.nat))) (=> (= M2 N4) (=> (forall ((X3 tptp.produc1260470173ar_int)) (=> (@ (@ tptp.member92250950ar_int X3) N4) (= (@ F2 X3) (@ G X3)))) (= (@ (@ tptp.image_1742782760nt_nat F2) M2) (@ (@ tptp.image_1742782760nt_nat G) N4)))))) 0.39/0.65 (assert (forall ((A tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A) (@ tptp.collect_nat P)) (@ P A)))) 0.39/0.65 (assert (forall ((B tptp.bexp) (S_1 (-> tptp.list_char tptp.int)) (C tptp.com) (S_22 (-> tptp.list_char tptp.int)) (S_3 (-> tptp.list_char tptp.int))) (let ((_let_1 (@ tptp.produc1193801173ar_int (@ (@ tptp.while B) C)))) (=> (@ (@ tptp.bval B) S_1) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S_1)) S_22) (=> (@ (@ tptp.big_big_step (@ _let_1 S_22)) S_3) (@ (@ tptp.big_big_step (@ _let_1 S_1)) S_3))))))) 0.39/0.65 (assert (forall ((Nat tptp.nat) (X2 tptp.nat)) (=> (= Nat (@ tptp.suc X2)) (not (= Nat tptp.zero_zero_nat))))) 0.39/0.65 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= B (@ (@ tptp.plus_plus_nat B) A)) (= A tptp.zero_zero_nat)))) 0.39/0.65 (assert (forall ((F2 (-> tptp.com (-> tptp.list_char tptp.int) Bool)) (P4 tptp.produc1260470173ar_int)) (= (@ (@ tptp.produc613711406_com_o (lambda ((Y4 (-> tptp.list_char tptp.int)) (X tptp.com)) (@ (@ F2 X) Y4))) (@ tptp.produc1770201973ar_int P4)) (@ (@ tptp.produc668584238_int_o F2) P4)))) 0.39/0.65 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A))) 0.39/0.65 (assert (forall ((F2 (-> tptp.list_char tptp.int)) (X4 tptp.list_char) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ (@ tptp.fun_up103088396ar_int F2) X4))) (= (@ (@ (@ tptp.fun_up103088396ar_int (@ _let_1 Y)) X4) Z) (@ _let_1 Z))))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati775585786_valid P) (@ (@ tptp.while B) C)) C2) Q) (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((S (-> tptp.list_char tptp.int)) (S2 (-> tptp.list_char tptp.int))) (and (@ (@ P S) S2) (not (@ (@ tptp.bval B) S))))) tptp.skip) C2) (lambda ((T4 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (and (@ (@ Q T4) T5) (exists ((S2 (-> tptp.list_char tptp.int))) (and (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S2)) T5) (not (@ (@ tptp.bval B) T4)) (@ (@ P T4) S2))))))))) 0.39/0.65 (assert (forall ((F2 (-> (-> tptp.list_char tptp.int) tptp.com tptp.set_nat)) (P4 tptp.produc1166363805nt_com)) (= (@ (@ tptp.produc991755120et_nat (lambda ((Y4 tptp.com) (X (-> tptp.list_char tptp.int))) (@ (@ F2 X) Y4))) (@ tptp.produc1716235893nt_com P4)) (@ (@ tptp.produc1754105456et_nat F2) P4)))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C_1 tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C_2 tptp.com)) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare (lambda ((S (-> tptp.list_char tptp.int)) (S2 (-> tptp.list_char tptp.int))) (and (@ (@ tptp.bval B) S) (@ (@ P S) S2)))) C_1) C2) Q) (@ (@ (@ (@ tptp.relati2102071307_hoare P) (@ (@ (@ tptp.if B) C_1) C_2)) C2) Q)))) 0.39/0.65 (assert (forall ((X51 tptp.bexp) (X52 tptp.com) (Y51 tptp.bexp) (Y52 tptp.com)) (= (= (@ (@ tptp.while X51) X52) (@ (@ tptp.while Y51) Y52)) (and (= X51 Y51) (= X52 Y52))))) 0.39/0.65 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat B) A)) (= B tptp.zero_zero_nat)))) 0.39/0.65 (assert (forall ((F2 (-> tptp.produc1260470173ar_int tptp.set_nat))) (= (@ tptp.produc991755120et_nat (lambda ((X tptp.com) (Y4 (-> tptp.list_char tptp.int))) (@ F2 (@ (@ tptp.produc1193801173ar_int X) Y4)))) F2))) 0.39/0.65 (assert (forall ((X4 tptp.nat) (A4 tptp.set_nat) (F2 (-> tptp.nat tptp.produc1260470173ar_int))) (=> (@ (@ tptp.member_nat X4) A4) (@ (@ tptp.member92250950ar_int (@ F2 X4)) (@ (@ tptp.image_338722310ar_int F2) A4))))) 0.39/0.65 (assert (forall ((P4 tptp.produc1166363805nt_com) (Z tptp.nat) (C (-> (-> tptp.list_char tptp.int) tptp.com tptp.set_nat))) (=> (forall ((A3 (-> tptp.list_char tptp.int)) (B3 tptp.com)) (=> (= P4 (@ (@ tptp.produc1139835093nt_com A3) B3)) (@ (@ tptp.member_nat Z) (@ (@ C A3) B3)))) (@ (@ tptp.member_nat Z) (@ (@ tptp.produc1754105456et_nat C) P4))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.produc1166363805nt_com tptp.produc1260470173ar_int)) (A4 tptp.set_Pr866150653nt_com) (P (-> tptp.produc1260470173ar_int Bool))) (=> (exists ((X5 tptp.produc1260470173ar_int)) (and (@ (@ tptp.member92250950ar_int X5) (@ (@ tptp.image_1968865093ar_int F2) A4)) (@ P X5))) (exists ((X3 tptp.produc1166363805nt_com)) (and (@ (@ tptp.member2145628230nt_com X3) A4) (@ P (@ F2 X3))))))) 0.39/0.65 (assert (forall ((R2 (-> tptp.list_char tptp.int)) (S7 tptp.com) (R tptp.set_Pr866150653nt_com) (S6 tptp.com)) (let ((_let_1 (@ tptp.produc1139835093nt_com R2))) (=> (@ (@ tptp.member2145628230nt_com (@ _let_1 S7)) R) (=> (= S6 S7) (@ (@ tptp.member2145628230nt_com (@ _let_1 S6)) R)))))) 0.39/0.65 (assert (= tptp.produc837840349ar_int tptp.produc1288559923ar_int)) 0.39/0.65 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (P (-> tptp.nat Bool))) (= (@ tptp.collect_nat (lambda ((Uu tptp.nat)) (exists ((X tptp.nat)) (and (= Uu (@ F2 X)) (@ P X))))) (@ (@ tptp.image_nat_nat F2) (@ tptp.collect_nat P))))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (= (@ (@ (@ (@ tptp.relati2102071307_hoare P) tptp.skip) tptp.skip) Q) (forall ((S (-> tptp.list_char tptp.int)) (S2 (-> tptp.list_char tptp.int))) (=> (@ (@ Q S) S2) (@ (@ P S) S2)))))) 0.39/0.65 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A) B) A) (= B tptp.zero_zero_nat)))) 0.39/0.65 (assert (forall ((X1 tptp.com) (X2 (-> tptp.list_char tptp.int)) (Y1 tptp.com) (Y2 (-> tptp.list_char tptp.int))) (= (= (@ (@ tptp.produc1193801173ar_int X1) X2) (@ (@ tptp.produc1193801173ar_int Y1) Y2)) (and (= X2 Y2) (= X1 Y1))))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C tptp.com) (K tptp.nat) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ (@ tptp.while B) C))) (let ((_let_2 (@ (@ (@ tptp.relati23543761ar_int P) B) C))) (=> (@ (@ (@ (@ tptp.relati775585786_valid (@ _let_2 (@ tptp.suc K))) _let_1) C2) Q) (@ (@ (@ (@ tptp.relati775585786_valid (@ _let_2 K)) _let_1) C2) Q)))))) 0.39/0.65 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat A) B)) (= B tptp.zero_zero_nat)))) 0.39/0.65 (assert (forall ((Z tptp.produc1260470173ar_int) (C (-> (-> tptp.list_char tptp.int) tptp.com tptp.set_Pr1148378109ar_int)) (A (-> tptp.list_char tptp.int)) (B tptp.com)) (let ((_let_1 (@ tptp.member92250950ar_int Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc1461507731ar_int C) (@ (@ tptp.produc1139835093nt_com A) B))))))) 0.39/0.65 (assert (forall ((Q (-> tptp.set_nat Bool)) (P (-> tptp.com (-> tptp.list_char tptp.int) tptp.set_nat)) (Z tptp.produc1260470173ar_int)) (=> (@ Q (@ (@ tptp.produc991755120et_nat P) Z)) (not (forall ((X3 tptp.com) (Y3 (-> tptp.list_char tptp.int))) (=> (= Z (@ (@ tptp.produc1193801173ar_int X3) Y3)) (not (@ Q (@ (@ P X3) Y3))))))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.com (-> tptp.list_char tptp.int) tptp.produc1260470173ar_int))) (= (@ tptp.produc804153044ar_int (@ tptp.produc1288559923ar_int F2)) F2))) 0.39/0.65 (assert (forall ((B tptp.produc1260470173ar_int) (F2 (-> tptp.nat tptp.produc1260470173ar_int)) (X4 tptp.nat) (A4 tptp.set_nat)) (=> (= B (@ F2 X4)) (=> (@ (@ tptp.member_nat X4) A4) (@ (@ tptp.member92250950ar_int B) (@ (@ tptp.image_338722310ar_int F2) A4)))))) 0.39/0.65 (assert (forall ((A tptp.com) (B (-> tptp.list_char tptp.int)) (A4 tptp.set_Pr1148378109ar_int) (F2 (-> tptp.com (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ tptp.member92250950ar_int (@ (@ tptp.produc1193801173ar_int A) B)) A4) (@ (@ tptp.member_o (@ (@ F2 A) B)) (@ (@ tptp.image_522938432_int_o (@ tptp.produc668584238_int_o F2)) A4))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.com (-> tptp.list_char tptp.int) tptp.nat)) (X1 tptp.com) (X2 (-> tptp.list_char tptp.int))) (= (@ (@ tptp.produc1311963066nt_nat F2) (@ (@ tptp.produc1193801173ar_int X1) X2)) (@ (@ F2 X1) X2)))) 0.39/0.65 (assert (forall ((C1 tptp.com) (C22 tptp.com) (S1 (-> tptp.list_char tptp.int)) (S32 (-> tptp.list_char tptp.int))) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.seq C1) C22)) S1)) S32) (not (forall ((S_2 (-> tptp.list_char tptp.int))) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C1) S1)) S_2) (not (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C22) S_2)) S32)))))))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (D tptp.com) (C2 tptp.com) (R (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ tptp.relati775585786_valid P))) (=> (@ (@ (@ _let_1 C) tptp.skip) Q) (=> (@ (@ (@ (@ tptp.relati775585786_valid Q) D) C2) R) (@ (@ (@ _let_1 (@ (@ tptp.seq C) D)) C2) R)))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.produc1260470173ar_int tptp.produc1166363805nt_com)) (A4 tptp.set_Pr1148378109ar_int) (P (-> tptp.produc1166363805nt_com Bool))) (=> (exists ((X5 tptp.produc1166363805nt_com)) (and (@ (@ tptp.member2145628230nt_com X5) (@ (@ tptp.image_786684229nt_com F2) A4)) (@ P X5))) (exists ((X3 tptp.produc1260470173ar_int)) (and (@ (@ tptp.member92250950ar_int X3) A4) (@ P (@ F2 X3))))))) 0.39/0.65 (assert (forall ((A4 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) A4))) A4))) 0.39/0.65 (assert (forall ((X41 tptp.bexp) (X42 tptp.com) (X43 tptp.com)) (= (@ tptp.size_size_com (@ (@ (@ tptp.if X41) X42) X43)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.size_size_com X42)) (@ tptp.size_size_com X43))) (@ tptp.suc tptp.zero_zero_nat))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.com (-> tptp.list_char tptp.int) Bool)) (G (-> tptp.produc1260470173ar_int Bool))) (=> (forall ((X3 tptp.com) (Y3 (-> tptp.list_char tptp.int))) (= (@ (@ F2 X3) Y3) (@ G (@ (@ tptp.produc1193801173ar_int X3) Y3)))) (= (@ tptp.produc668584238_int_o F2) G)))) 0.39/0.65 (assert (forall ((X31 tptp.com) (X32 tptp.com) (X51 tptp.bexp) (X52 tptp.com)) (not (= (@ (@ tptp.seq X31) X32) (@ (@ tptp.while X51) X52))))) 0.39/0.65 (assert (forall ((X4 tptp.nat) (A4 tptp.set_nat) (F2 (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.member_nat X4) A4) (@ (@ tptp.member_nat (@ F2 X4)) (@ (@ tptp.image_nat_nat F2) A4))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.com (-> tptp.list_char tptp.int) tptp.set_nat)) (A tptp.com) (B (-> tptp.list_char tptp.int))) (= (@ (@ tptp.produc991755120et_nat F2) (@ (@ tptp.produc1193801173ar_int A) B)) (@ (@ F2 A) B)))) 0.39/0.65 (assert (= tptp.produc1858366159_int_o (lambda ((F (-> tptp.produc1260470173ar_int Bool)) (A5 tptp.com) (B4 (-> tptp.list_char tptp.int))) (@ F (@ (@ tptp.produc1193801173ar_int A5) B4))))) 0.39/0.65 (assert (forall ((B1 tptp.bexp) (B22 tptp.bexp) (C11 tptp.com) (C12 tptp.com) (C22 tptp.com) (S8 (-> tptp.list_char tptp.int)) (T7 (-> tptp.list_char tptp.int))) (let ((_let_1 (@ tptp.if B1))) (let ((_let_2 (@ tptp.if B22))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ _let_1 (@ (@ _let_2 C11) C12)) C22)) S8)) T7) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ _let_2 (@ (@ _let_1 C11) C22)) (@ (@ _let_1 C12) C22))) S8)) T7)))))) 0.39/0.65 (assert (forall ((X4 tptp.produc1260470173ar_int) (A4 tptp.set_Pr1148378109ar_int) (B tptp.produc1260470173ar_int) (F2 (-> tptp.produc1260470173ar_int tptp.produc1260470173ar_int))) (=> (@ (@ tptp.member92250950ar_int X4) A4) (=> (= B (@ F2 X4)) (@ (@ tptp.member92250950ar_int B) (@ (@ tptp.image_880790597ar_int F2) A4)))))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C tptp.com) (K tptp.nat) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati775585786_valid (@ (@ (@ (@ tptp.relati23543761ar_int P) B) C) K)) (@ (@ tptp.while B) C)) C2) Q) (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((S (-> tptp.list_char tptp.int)) (S2 (-> tptp.list_char tptp.int))) (and (@ (@ (@ (@ (@ (@ tptp.relati23543761ar_int P) B) C) K) S) S2) (@ (@ tptp.bval B) S)))) C) C2) (lambda ((T4 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (exists ((S2 (-> tptp.list_char tptp.int))) (and (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S2)) T5) (@ (@ (@ (@ (@ (@ tptp.relati23543761ar_int P) B) C) (@ tptp.suc K)) T4) S2) (exists ((U2 (-> tptp.list_char tptp.int))) (and (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.while B) C)) T4)) U2) (@ (@ Q U2) T5)))))))))) 0.39/0.65 (assert (forall ((P (-> tptp.produc1166363805nt_com Bool)) (P4 tptp.produc1166363805nt_com)) (=> (forall ((A3 (-> tptp.list_char tptp.int)) (B3 tptp.com)) (@ P (@ (@ tptp.produc1139835093nt_com A3) B3))) (@ P P4)))) 0.39/0.65 (assert (forall ((F2 (-> tptp.produc1260470173ar_int tptp.nat)) (G (-> tptp.produc1166363805nt_com tptp.produc1260470173ar_int)) (A4 tptp.set_Pr866150653nt_com)) (= (@ (@ tptp.image_1742782760nt_nat F2) (@ (@ tptp.image_1968865093ar_int G) A4)) (@ (@ tptp.image_596692520om_nat (lambda ((X tptp.produc1166363805nt_com)) (@ F2 (@ G X)))) A4)))) 0.39/0.65 (assert (forall ((M tptp.nat) (N3 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N3) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N3))))) 0.39/0.65 (assert (forall ((Z tptp.produc1166363805nt_com) (F2 (-> tptp.produc1260470173ar_int tptp.produc1166363805nt_com)) (A4 tptp.set_Pr1148378109ar_int)) (= (@ (@ tptp.member2145628230nt_com Z) (@ (@ tptp.image_786684229nt_com F2) A4)) (exists ((X tptp.produc1260470173ar_int)) (and (@ (@ tptp.member92250950ar_int X) A4) (= Z (@ F2 X))))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.list_char tptp.int)) (X4 tptp.list_char) (Y tptp.int)) (= (@ (@ (@ (@ tptp.fun_up103088396ar_int F2) X4) Y) X4) Y))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C tptp.com) (K tptp.nat) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati775585786_valid (@ (@ (@ (@ tptp.relati23543761ar_int P) B) C) K)) (@ (@ tptp.while B) C)) C2) Q) (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((S (-> tptp.list_char tptp.int)) (S2 (-> tptp.list_char tptp.int))) (and (@ (@ (@ (@ (@ (@ tptp.relati23543761ar_int P) B) C) K) S) S2) (@ (@ tptp.bval B) S)))) C) tptp.skip) (lambda ((T4 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (and (@ (@ (@ (@ (@ (@ tptp.relati23543761ar_int P) B) C) (@ tptp.suc K)) T4) T5) (exists ((U2 (-> tptp.list_char tptp.int)) (U3 (-> tptp.list_char tptp.int))) (and (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.while B) C)) T4)) U2) (@ (@ Q U2) U3) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) T5)) U3))))))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.produc1260470173ar_int tptp.produc1166363805nt_com)) (G (-> tptp.produc1166363805nt_com tptp.produc1260470173ar_int)) (A4 tptp.set_Pr866150653nt_com)) (= (@ (@ tptp.image_786684229nt_com F2) (@ (@ tptp.image_1968865093ar_int G) A4)) (@ (@ tptp.image_1874758725nt_com (lambda ((X tptp.produc1166363805nt_com)) (@ F2 (@ G X)))) A4)))) 0.39/0.65 (assert (forall ((P Bool) (Q (-> tptp.com (-> tptp.list_char tptp.int) Bool))) (= (@ tptp.produc668584238_int_o (lambda ((A5 tptp.com) (B4 (-> tptp.list_char tptp.int))) (and (@ (@ Q A5) B4) P))) (lambda ((Ab tptp.produc1260470173ar_int)) (and (@ (@ tptp.produc668584238_int_o Q) Ab) P))))) 0.39/0.65 (assert (forall ((X1 (-> tptp.list_char tptp.int)) (X2 tptp.com) (Y1 (-> tptp.list_char tptp.int)) (Y2 tptp.com)) (= (= (@ (@ tptp.produc1139835093nt_com X1) X2) (@ (@ tptp.produc1139835093nt_com Y1) Y2)) (and (= X1 Y1) (= X2 Y2))))) 0.39/0.65 (assert (forall ((C Bool)) (= (@ tptp.produc1858366159_int_o (lambda ((X tptp.produc1260470173ar_int)) C)) (lambda ((X tptp.com) (Y4 (-> tptp.list_char tptp.int))) C)))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com)) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare (lambda ((S (-> tptp.list_char tptp.int)) (S2 (-> tptp.list_char tptp.int))) (and (not (@ (@ tptp.bval B) S)) (@ (@ P S) S2)))) tptp.skip) C2) Q) (@ (@ (@ (@ tptp.relati2102071307_hoare P) (@ (@ tptp.while B) C)) C2) Q)))) 0.39/0.65 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C) A)) (= B C)))) 0.39/0.65 (assert (forall ((F2 (-> (-> tptp.list_char tptp.int) tptp.com tptp.nat)) (P4 tptp.produc1166363805nt_com)) (= (@ (@ tptp.produc1311963066nt_nat (lambda ((Y4 tptp.com) (X (-> tptp.list_char tptp.int))) (@ (@ F2 X) Y4))) (@ tptp.produc1716235893nt_com P4)) (@ (@ tptp.produc1263502010om_nat F2) P4)))) 0.39/0.65 (assert (= tptp.plus_plus_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.plus_plus_nat B4) A5)))) 0.39/0.65 (assert (forall ((C_1 tptp.com) (S_1 (-> tptp.list_char tptp.int)) (S_22 (-> tptp.list_char tptp.int)) (C_2 tptp.com) (S_3 (-> tptp.list_char tptp.int))) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C_1) S_1)) S_22) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C_2) S_22)) S_3) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.seq C_1) C_2)) S_1)) S_3))))) 0.39/0.65 (assert (forall ((Z tptp.produc1166363805nt_com) (C (-> tptp.com (-> tptp.list_char tptp.int) tptp.set_Pr866150653nt_com)) (P4 tptp.produc1260470173ar_int)) (=> (@ (@ tptp.member2145628230nt_com Z) (@ (@ tptp.produc1994108563nt_com C) P4)) (not (forall ((X3 tptp.com) (Y3 (-> tptp.list_char tptp.int))) (=> (= P4 (@ (@ tptp.produc1193801173ar_int X3) Y3)) (not (@ (@ tptp.member2145628230nt_com Z) (@ (@ C X3) Y3))))))))) 0.39/0.65 (assert (forall ((X4 tptp.produc1166363805nt_com) (A4 tptp.set_Pr866150653nt_com) (B tptp.produc1260470173ar_int) (F2 (-> tptp.produc1166363805nt_com tptp.produc1260470173ar_int))) (=> (@ (@ tptp.member2145628230nt_com X4) A4) (=> (= B (@ F2 X4)) (@ (@ tptp.member92250950ar_int B) (@ (@ tptp.image_1968865093ar_int F2) A4)))))) 0.39/0.65 (assert (forall ((B tptp.produc1260470173ar_int) (F2 (-> tptp.produc1166363805nt_com tptp.produc1260470173ar_int)) (X4 tptp.produc1166363805nt_com) (A4 tptp.set_Pr866150653nt_com)) (=> (= B (@ F2 X4)) (=> (@ (@ tptp.member2145628230nt_com X4) A4) (@ (@ tptp.member92250950ar_int B) (@ (@ tptp.image_1968865093ar_int F2) A4)))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.nat tptp.produc1260470173ar_int)) (A4 tptp.set_nat) (P (-> tptp.produc1260470173ar_int Bool))) (= (@ tptp.collec770796680ar_int (lambda ((X tptp.produc1260470173ar_int)) (and (@ P X) (@ (@ tptp.member92250950ar_int X) (@ (@ tptp.image_338722310ar_int F2) A4))))) (@ (@ tptp.image_338722310ar_int F2) (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A4) (@ P (@ F2 X))))))))) 0.39/0.65 (assert (forall ((Z tptp.produc1260470173ar_int) (C (-> tptp.com (-> tptp.list_char tptp.int) tptp.set_Pr1148378109ar_int)) (P4 tptp.produc1260470173ar_int)) (=> (@ (@ tptp.member92250950ar_int Z) (@ (@ tptp.produc128852371ar_int C) P4)) (not (forall ((X3 tptp.com) (Y3 (-> tptp.list_char tptp.int))) (=> (= P4 (@ (@ tptp.produc1193801173ar_int X3) Y3)) (not (@ (@ tptp.member92250950ar_int Z) (@ (@ C X3) Y3))))))))) 0.39/0.65 (assert (forall ((X4 tptp.nat) (A4 tptp.set_nat) (F2 (-> tptp.nat tptp.produc1166363805nt_com))) (=> (@ (@ tptp.member_nat X4) A4) (@ (@ tptp.member2145628230nt_com (@ F2 X4)) (@ (@ tptp.image_244615942nt_com F2) A4))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.com (-> tptp.list_char tptp.int) tptp.set_nat)) (P4 tptp.produc1260470173ar_int)) (= (@ (@ tptp.produc1754105456et_nat (lambda ((Y4 (-> tptp.list_char tptp.int)) (X tptp.com)) (@ (@ F2 X) Y4))) (@ tptp.produc1770201973ar_int P4)) (@ (@ tptp.produc991755120et_nat F2) P4)))) 0.39/0.65 (assert (forall ((X4 tptp.nat) (A4 tptp.set_nat) (B tptp.produc1260470173ar_int) (F2 (-> tptp.nat tptp.produc1260470173ar_int))) (=> (@ (@ tptp.member_nat X4) A4) (=> (= B (@ F2 X4)) (@ (@ tptp.member92250950ar_int B) (@ (@ tptp.image_338722310ar_int F2) A4)))))) 0.39/0.65 (assert (forall ((X4 tptp.list_char) (A tptp.aexp) (S7 (-> tptp.list_char tptp.int)) (S6 (-> tptp.list_char tptp.int))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.assign X4) A)) S7)) S6) (= S6 (@ (@ (@ tptp.fun_up103088396ar_int S7) X4) (@ (@ tptp.aval A) S7)))))) 0.39/0.65 (assert (forall ((X41 tptp.bexp) (X42 tptp.com) (X43 tptp.com) (Y41 tptp.bexp) (Y42 tptp.com) (Y43 tptp.com)) (= (= (@ (@ (@ tptp.if X41) X42) X43) (@ (@ (@ tptp.if Y41) Y42) Y43)) (and (= X43 Y43) (= X42 Y42) (= X41 Y41))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.com (-> tptp.list_char tptp.int) tptp.nat)) (A tptp.com) (B (-> tptp.list_char tptp.int))) (= (@ (@ tptp.produc1311963066nt_nat F2) (@ (@ tptp.produc1193801173ar_int A) B)) (@ (@ F2 A) B)))) 0.39/0.65 (assert (forall ((X31 tptp.com) (X32 tptp.com) (X41 tptp.bexp) (X42 tptp.com) (X43 tptp.com)) (not (= (@ (@ tptp.seq X31) X32) (@ (@ (@ tptp.if X41) X42) X43))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.com (-> tptp.list_char tptp.int) tptp.produc1260470173ar_int)) (X1 tptp.com) (X2 (-> tptp.list_char tptp.int))) (= (@ (@ tptp.produc1288559923ar_int F2) (@ (@ tptp.produc1193801173ar_int X1) X2)) (@ (@ F2 X1) X2)))) 0.39/0.65 (assert (forall ((X41 tptp.bexp) (X42 tptp.com) (X43 tptp.com)) (not (= tptp.skip (@ (@ (@ tptp.if X41) X42) X43))))) 0.39/0.65 (assert (forall ((Z tptp.list_char) (X4 tptp.list_char) (F2 (-> tptp.list_char tptp.int)) (Y tptp.int)) (=> (not (= Z X4)) (= (@ (@ (@ (@ tptp.fun_up103088396ar_int F2) X4) Y) Z) (@ F2 Z))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.list_char tptp.int)) (X4 tptp.list_char) (Y tptp.int) (G (-> tptp.list_char tptp.int)) (Z tptp.int)) (=> (= (@ (@ (@ tptp.fun_up103088396ar_int F2) X4) Y) (@ (@ (@ tptp.fun_up103088396ar_int G) X4) Z)) (= Y Z)))) 0.39/0.65 (assert (forall ((B5 tptp.nat) (K tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (let ((_let_2 (@ tptp.plus_plus_nat K))) (=> (= B5 (@ _let_2 B)) (= (@ _let_1 B5) (@ _let_2 (@ _let_1 B)))))))) 0.39/0.65 (assert (forall ((Y5 tptp.set_nat)) (= (@ (@ tptp.image_nat_nat (lambda ((X tptp.nat)) X)) Y5) Y5))) 0.39/0.65 (assert (forall ((F2 (-> tptp.com (-> tptp.list_char tptp.int) Bool))) (= (@ tptp.produc1858366159_int_o (@ tptp.produc668584238_int_o F2)) F2))) 0.39/0.65 (assert (forall ((Y tptp.com)) (=> (not (= Y tptp.skip)) (=> (forall ((X212 tptp.list_char) (X222 tptp.aexp)) (not (= Y (@ (@ tptp.assign X212) X222)))) (=> (forall ((X312 tptp.com) (X322 tptp.com)) (not (= Y (@ (@ tptp.seq X312) X322)))) (=> (forall ((X412 tptp.bexp) (X422 tptp.com) (X432 tptp.com)) (not (= Y (@ (@ (@ tptp.if X412) X422) X432)))) (not (forall ((X512 tptp.bexp) (X522 tptp.com)) (not (= Y (@ (@ tptp.while X512) X522))))))))))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C_2 tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C_1 tptp.com)) (=> (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((A5 (-> tptp.list_char tptp.int)) (C3 (-> tptp.list_char tptp.int))) (and (@ (@ P A5) C3) (not (@ (@ tptp.bval B) A5))))) C_2) C2) Q) (@ (@ (@ (@ tptp.relati775585786_valid P) (@ (@ (@ tptp.if B) C_1) C_2)) C2) Q)))) 0.39/0.65 (assert (forall ((X4 tptp.list_char) (A tptp.aexp) (S7 (-> tptp.list_char tptp.int)) (T6 (-> tptp.list_char tptp.int))) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.assign X4) A)) S7)) T6) (= T6 (@ (@ (@ tptp.fun_up103088396ar_int S7) X4) (@ (@ tptp.aval A) S7)))))) 0.39/0.65 (assert (forall ((X51 tptp.bexp) (X52 tptp.com)) (not (= tptp.skip (@ (@ tptp.while X51) X52))))) 0.39/0.65 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)))))) 0.39/0.65 (assert (forall ((B tptp.bexp) (C1 tptp.com) (C22 tptp.com) (S7 (-> tptp.list_char tptp.int)) (T6 (-> tptp.list_char tptp.int))) (let ((_let_1 (@ (@ tptp.bval B) S7))) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ (@ tptp.if B) C1) C22)) S7)) T6) (=> (=> _let_1 (not (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C1) S7)) T6))) (not (=> (not _let_1) (not (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C22) S7)) T6))))))))) 0.39/0.65 (assert (forall ((A tptp.com) (B (-> tptp.list_char tptp.int)) (A2 tptp.com) (B2 (-> tptp.list_char tptp.int))) (=> (= (@ (@ tptp.produc1193801173ar_int A) B) (@ (@ tptp.produc1193801173ar_int A2) B2)) (not (=> (= A A2) (not (= B B2))))))) 0.39/0.65 (assert (forall ((Z tptp.produc1260470173ar_int) (F2 (-> tptp.produc1166363805nt_com tptp.produc1260470173ar_int)) (A4 tptp.set_Pr866150653nt_com)) (= (@ (@ tptp.member92250950ar_int Z) (@ (@ tptp.image_1968865093ar_int F2) A4)) (exists ((X tptp.produc1166363805nt_com)) (and (= Z (@ F2 X)) (@ (@ tptp.member2145628230nt_com X) A4)))))) 0.39/0.65 (assert (forall ((P (-> tptp.com Bool)) (Com tptp.com)) (=> (@ P tptp.skip) (=> (forall ((X12 tptp.list_char) (X23 tptp.aexp)) (@ P (@ (@ tptp.assign X12) X23))) (=> (forall ((X12 tptp.com) (X23 tptp.com)) (=> (@ P X12) (=> (@ P X23) (@ P (@ (@ tptp.seq X12) X23))))) (=> (forall ((X12 tptp.bexp) (X23 tptp.com) (X33 tptp.com)) (=> (@ P X23) (=> (@ P X33) (@ P (@ (@ (@ tptp.if X12) X23) X33))))) (=> (forall ((X12 tptp.bexp) (X23 tptp.com)) (=> (@ P X23) (@ P (@ (@ tptp.while X12) X23)))) (@ P Com)))))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.com (-> tptp.list_char tptp.int) Bool)) (X1 tptp.com) (X2 (-> tptp.list_char tptp.int))) (= (@ (@ tptp.produc668584238_int_o F2) (@ (@ tptp.produc1193801173ar_int X1) X2)) (@ (@ F2 X1) X2)))) 0.39/0.65 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (A4 tptp.set_nat) (P (-> tptp.nat Bool))) (= (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (@ P X) (@ (@ tptp.member_nat X) (@ (@ tptp.image_nat_nat F2) A4))))) (@ (@ tptp.image_nat_nat F2) (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (@ P (@ F2 X)) (@ (@ tptp.member_nat X) A4)))))))) 0.39/0.65 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= K L) (= I J)) (= (@ (@ tptp.plus_plus_nat I) K) (@ (@ tptp.plus_plus_nat J) L))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.produc1260470173ar_int tptp.produc1166363805nt_com)) (A4 tptp.set_Pr1148378109ar_int) (P (-> tptp.produc1166363805nt_com Bool))) (=> (forall ((X3 tptp.produc1166363805nt_com)) (=> (@ (@ tptp.member2145628230nt_com X3) (@ (@ tptp.image_786684229nt_com F2) A4)) (@ P X3))) (forall ((X5 tptp.produc1260470173ar_int)) (=> (@ (@ tptp.member92250950ar_int X5) A4) (@ P (@ F2 X5))))))) 0.39/0.65 (assert (forall ((Q (-> Bool Bool)) (P (-> tptp.com (-> tptp.list_char tptp.int) Bool)) (Z tptp.produc1260470173ar_int)) (=> (@ Q (@ (@ tptp.produc668584238_int_o P) Z)) (not (forall ((X3 tptp.com) (Y3 (-> tptp.list_char tptp.int))) (=> (= Z (@ (@ tptp.produc1193801173ar_int X3) Y3)) (not (@ Q (@ (@ P X3) Y3))))))))) 0.39/0.65 (assert (forall ((A (-> tptp.list_char tptp.int)) (B tptp.com) (A2 (-> tptp.list_char tptp.int)) (B2 tptp.com)) (=> (= (@ (@ tptp.produc1139835093nt_com A) B) (@ (@ tptp.produc1139835093nt_com A2) B2)) (not (=> (= A A2) (not (= B B2))))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.com (-> tptp.list_char tptp.int) tptp.produc1260470173ar_int)) (A tptp.com) (B (-> tptp.list_char tptp.int))) (= (@ (@ tptp.produc1288559923ar_int F2) (@ (@ tptp.produc1193801173ar_int A) B)) (@ (@ F2 A) B)))) 0.39/0.65 (assert (forall ((P4 tptp.produc1166363805nt_com)) (= (@ tptp.produc1770201973ar_int (@ tptp.produc1716235893nt_com P4)) P4))) 0.39/0.65 (assert (forall ((H (-> tptp.set_nat tptp.nat)) (F2 (-> tptp.com (-> tptp.list_char tptp.int) tptp.set_nat)) (Prod tptp.produc1260470173ar_int)) (= (@ H (@ (@ tptp.produc991755120et_nat F2) Prod)) (@ (@ tptp.produc1311963066nt_nat (lambda ((X13 tptp.com) (X24 (-> tptp.list_char tptp.int))) (@ H (@ (@ F2 X13) X24)))) Prod)))) 0.39/0.65 (assert (forall ((X2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X2))))) 0.39/0.65 (assert (forall ((X4 tptp.produc1260470173ar_int) (A4 tptp.set_Pr1148378109ar_int) (F2 (-> tptp.produc1260470173ar_int tptp.produc1166363805nt_com))) (=> (@ (@ tptp.member92250950ar_int X4) A4) (@ (@ tptp.member2145628230nt_com (@ F2 X4)) (@ (@ tptp.image_786684229nt_com F2) A4))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.list_char tptp.int)) (X4 tptp.list_char)) (= (@ (@ (@ tptp.fun_up103088396ar_int F2) X4) (@ F2 X4)) F2))) 0.39/0.65 (assert (forall ((X4 tptp.produc1166363805nt_com) (A4 tptp.set_Pr866150653nt_com) (F2 (-> tptp.produc1166363805nt_com tptp.produc1166363805nt_com))) (=> (@ (@ tptp.member2145628230nt_com X4) A4) (@ (@ tptp.member2145628230nt_com (@ F2 X4)) (@ (@ tptp.image_1874758725nt_com F2) A4))))) 0.39/0.65 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A))) 0.39/0.65 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2)))) 0.39/0.65 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))) 0.39/0.65 (assert (forall ((P (-> tptp.nat (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ (@ tptp.while B) C))) (=> (forall ((N tptp.nat)) (@ (@ (@ (@ tptp.relati2102071307_hoare (lambda ((S (-> tptp.list_char tptp.int)) (S2 (-> tptp.list_char tptp.int))) (and (@ (@ tptp.bval B) S) (@ (@ (@ P N) S) S2)))) C) tptp.skip) (@ P (@ tptp.suc N)))) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare (lambda ((S (-> tptp.list_char tptp.int)) (S2 (-> tptp.list_char tptp.int))) (exists ((N5 tptp.nat)) (@ (@ (@ P N5) S) S2)))) _let_1) C2) Q) (@ (@ (@ (@ tptp.relati2102071307_hoare (@ P tptp.zero_zero_nat)) _let_1) C2) Q)))))) 0.39/0.65 (assert (forall ((X41 tptp.bexp) (X42 tptp.com) (X43 tptp.com)) (= (@ tptp.size_com (@ (@ (@ tptp.if X41) X42) X43)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.size_com X42)) (@ tptp.size_com X43))) (@ tptp.suc tptp.zero_zero_nat))))) 0.39/0.65 (assert (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat)))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C1 tptp.com) (C22 tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati775585786_valid P) (@ (@ (@ tptp.if B) C1) C22)) C2) Q) (and (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((S (-> tptp.list_char tptp.int)) (S2 (-> tptp.list_char tptp.int))) (and (@ (@ P S) S2) (@ (@ tptp.bval B) S)))) C1) C2) (lambda ((T4 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (and (@ (@ Q T4) T5) (exists ((S (-> tptp.list_char tptp.int)) (S2 (-> tptp.list_char tptp.int))) (and (@ (@ P S) S2) (@ (@ tptp.bval B) S) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S2)) T5) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C1) S)) T4)))))) (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((S (-> tptp.list_char tptp.int)) (S2 (-> tptp.list_char tptp.int))) (and (@ (@ P S) S2) (not (@ (@ tptp.bval B) S))))) C22) C2) (lambda ((T4 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (and (exists ((S (-> tptp.list_char tptp.int)) (S2 (-> tptp.list_char tptp.int))) (and (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C22) S)) T4) (not (@ (@ tptp.bval B) S)) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S2)) T5) (@ (@ P S) S2))) (@ (@ Q T4) T5)))))))) 0.39/0.65 (assert (forall ((Q (-> tptp.nat Bool)) (P (-> tptp.com (-> tptp.list_char tptp.int) tptp.nat)) (Z tptp.produc1260470173ar_int)) (=> (@ Q (@ (@ tptp.produc1311963066nt_nat P) Z)) (not (forall ((X3 tptp.com) (Y3 (-> tptp.list_char tptp.int))) (=> (= Z (@ (@ tptp.produc1193801173ar_int X3) Y3)) (not (@ Q (@ (@ P X3) Y3))))))))) 0.39/0.65 (assert (forall ((B tptp.produc1166363805nt_com) (F2 (-> tptp.produc1166363805nt_com tptp.produc1166363805nt_com)) (X4 tptp.produc1166363805nt_com) (A4 tptp.set_Pr866150653nt_com)) (=> (= B (@ F2 X4)) (=> (@ (@ tptp.member2145628230nt_com X4) A4) (@ (@ tptp.member2145628230nt_com B) (@ (@ tptp.image_1874758725nt_com F2) A4)))))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ (@ (@ (@ tptp.relati1310524937decomp P) C) C2) Q))) (let ((_let_2 (@ (@ tptp.relati775585786_valid P) C))) (=> (@ (@ _let_2 C2) Q) (and (@ (@ (@ (@ tptp.relati775585786_valid _let_1) tptp.skip) C2) Q) (@ (@ _let_2 tptp.skip) _let_1))))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.produc1260470173ar_int tptp.nat)) (A4 tptp.set_Pr1148378109ar_int) (P (-> tptp.nat Bool))) (= (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (@ P X) (@ (@ tptp.member_nat X) (@ (@ tptp.image_1742782760nt_nat F2) A4))))) (@ (@ tptp.image_1742782760nt_nat F2) (@ tptp.collec770796680ar_int (lambda ((X tptp.produc1260470173ar_int)) (and (@ (@ tptp.member92250950ar_int X) A4) (@ P (@ F2 X))))))))) 0.39/0.65 (assert (forall ((Z tptp.produc1166363805nt_com) (C (-> (-> tptp.list_char tptp.int) tptp.com tptp.set_Pr866150653nt_com)) (A (-> tptp.list_char tptp.int)) (B tptp.com)) (let ((_let_1 (@ tptp.member2145628230nt_com Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc1179280275nt_com C) (@ (@ tptp.produc1139835093nt_com A) B))))))) 0.39/0.65 (assert (forall ((P_1 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q_1 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (P_2 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (Q_2 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare P_1) C) C2) Q_1) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare P_2) C) C2) Q_2) (@ (@ (@ (@ tptp.relati2102071307_hoare (lambda ((S (-> tptp.list_char tptp.int)) (S2 (-> tptp.list_char tptp.int))) (or (@ (@ P_2 S) S2) (@ (@ P_1 S) S2)))) C) C2) (lambda ((T4 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (or (@ (@ Q_2 T4) T5) (@ (@ Q_1 T4) T5)))))))) 0.39/0.65 (assert (forall ((A tptp.list_char) (C tptp.list_char) (M (-> tptp.list_char tptp.int)) (B tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.fun_up103088396ar_int M))) (=> (not (= A C)) (= (@ (@ (@ tptp.fun_up103088396ar_int (@ (@ _let_1 A) B)) C) D) (@ (@ (@ tptp.fun_up103088396ar_int (@ (@ _let_1 C) D)) A) B)))))) 0.39/0.65 (assert (forall ((Y (-> tptp.list_char tptp.int)) (X4 tptp.com) (A4 tptp.set_Pr1148378109ar_int)) (= (@ (@ tptp.member2145628230nt_com (@ (@ tptp.produc1139835093nt_com Y) X4)) (@ (@ tptp.image_786684229nt_com tptp.produc1770201973ar_int) A4)) (@ (@ tptp.member92250950ar_int (@ (@ tptp.produc1193801173ar_int X4) Y)) A4)))) 0.39/0.65 (assert (= tptp.relati775585786_valid (lambda ((P2 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C3 tptp.com) (C4 tptp.com) (Q2 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (forall ((T4 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (=> (@ (@ Q2 T4) T5) (exists ((S (-> tptp.list_char tptp.int)) (S2 (-> tptp.list_char tptp.int))) (and (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C4) S2)) T5) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C3) S)) T4) (@ (@ P2 S) S2)))))))) 0.39/0.65 (assert (forall ((A4 tptp.nat) (K tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A4 (@ _let_1 A)) (= (@ tptp.suc A4) (@ _let_1 (@ tptp.suc A))))))) 0.39/0.65 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A))) 0.39/0.65 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M))))) 0.39/0.65 (assert (forall ((X31 tptp.com) (X32 tptp.com)) (not (= tptp.skip (@ (@ tptp.seq X31) X32))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.produc1260470173ar_int tptp.produc1260470173ar_int))) (= (@ tptp.produc1288559923ar_int (lambda ((X tptp.com) (Y4 (-> tptp.list_char tptp.int))) (@ F2 (@ (@ tptp.produc1193801173ar_int X) Y4)))) F2))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (X4 tptp.list_char) (E tptp.aexp) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((T4 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (exists ((V3 tptp.int)) (let ((_let_1 (@ (@ (@ tptp.fun_up103088396ar_int T4) X4) V3))) (and (@ (@ P _let_1) T5) (= (@ T4 X4) (@ (@ tptp.aval E) _let_1))))))) tptp.skip) C2) Q) (@ (@ (@ (@ tptp.relati775585786_valid P) (@ (@ tptp.assign X4) E)) C2) Q)))) 0.39/0.65 (assert (forall ((H (-> tptp.set_nat tptp.set_nat)) (F2 (-> tptp.com (-> tptp.list_char tptp.int) tptp.set_nat)) (Prod tptp.produc1260470173ar_int)) (= (@ H (@ (@ tptp.produc991755120et_nat F2) Prod)) (@ (@ tptp.produc991755120et_nat (lambda ((X13 tptp.com) (X24 (-> tptp.list_char tptp.int))) (@ H (@ (@ F2 X13) X24)))) Prod)))) 0.39/0.65 (assert (= tptp.relati775585786_valid (lambda ((P2 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C3 tptp.com) (C4 tptp.com) (Q2 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ (@ (@ (@ tptp.relati1310524937decomp P2) C3) C4) Q2))) (and (@ (@ (@ (@ tptp.relati775585786_valid P2) C3) tptp.skip) _let_1) (@ (@ (@ (@ tptp.relati775585786_valid _let_1) tptp.skip) C4) Q2)))))) 0.39/0.65 (assert (forall ((B tptp.bexp) (S7 (-> tptp.list_char tptp.int)) (C_2 tptp.com) (T6 (-> tptp.list_char tptp.int)) (C_1 tptp.com)) (=> (not (@ (@ tptp.bval B) S7)) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C_2) S7)) T6) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ (@ tptp.if B) C_1) C_2)) S7)) T6))))) 0.39/0.65 (assert (forall ((Z tptp.nat) (C (-> (-> tptp.list_char tptp.int) tptp.com tptp.set_nat)) (P4 tptp.produc1166363805nt_com)) (=> (@ (@ tptp.member_nat Z) (@ (@ tptp.produc1754105456et_nat C) P4)) (not (forall ((X3 (-> tptp.list_char tptp.int)) (Y3 tptp.com)) (=> (= P4 (@ (@ tptp.produc1139835093nt_com X3) Y3)) (not (@ (@ tptp.member_nat Z) (@ (@ C X3) Y3))))))))) 0.39/0.65 (assert (forall ((X31 tptp.com) (X32 tptp.com)) (= (@ tptp.size_com (@ (@ tptp.seq X31) X32)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.size_com X31)) (@ tptp.size_com X32))) (@ tptp.suc tptp.zero_zero_nat))))) 0.39/0.65 (assert (forall ((M2 tptp.set_Pr866150653nt_com) (N4 tptp.set_Pr866150653nt_com) (F2 (-> tptp.produc1166363805nt_com tptp.produc1260470173ar_int)) (G (-> tptp.produc1166363805nt_com tptp.produc1260470173ar_int))) (=> (= M2 N4) (=> (forall ((X3 tptp.produc1166363805nt_com)) (=> (@ (@ tptp.member2145628230nt_com X3) N4) (= (@ F2 X3) (@ G X3)))) (= (@ (@ tptp.image_1968865093ar_int F2) M2) (@ (@ tptp.image_1968865093ar_int G) N4)))))) 0.39/0.65 (assert (forall ((X4 tptp.produc1260470173ar_int) (A4 tptp.set_Pr1148378109ar_int) (F2 (-> tptp.produc1260470173ar_int tptp.produc1260470173ar_int))) (=> (@ (@ tptp.member92250950ar_int X4) A4) (@ (@ tptp.member92250950ar_int (@ F2 X4)) (@ (@ tptp.image_880790597ar_int F2) A4))))) 0.39/0.65 (assert (forall ((Z tptp.nat) (F2 (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (= (@ (@ tptp.member_nat Z) (@ (@ tptp.image_nat_nat F2) A4)) (exists ((X tptp.nat)) (and (= Z (@ F2 X)) (@ (@ tptp.member_nat X) A4)))))) 0.39/0.65 (assert (let ((_let_1 (@ (@ (@ (@ tptp.relati1310524937decomp tptp.p) tptp.c) tptp.c2) tptp.q))) (let ((_let_2 (@ (@ tptp.relati2102071307_hoare tptp.p) tptp.c))) (not (= (@ (@ _let_2 tptp.c2) tptp.q) (and (@ (@ _let_2 tptp.skip) _let_1) (@ (@ (@ (@ tptp.relati2102071307_hoare _let_1) tptp.skip) tptp.c2) tptp.q))))))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (P3 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (Q3 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare P) C) C2) Q) (=> (forall ((S3 (-> tptp.list_char tptp.int)) (S4 (-> tptp.list_char tptp.int))) (=> (@ (@ P S3) S4) (@ (@ P3 S3) S4))) (=> (forall ((S3 (-> tptp.list_char tptp.int)) (S4 (-> tptp.list_char tptp.int))) (=> (@ (@ Q3 S3) S4) (@ (@ Q S3) S4))) (@ (@ (@ (@ tptp.relati2102071307_hoare P3) C) C2) Q3)))))) 0.39/0.65 (assert (forall ((X4 (-> tptp.list_char tptp.int)) (Y tptp.com)) (= (@ tptp.produc1716235893nt_com (@ (@ tptp.produc1139835093nt_com X4) Y)) (@ (@ tptp.produc1193801173ar_int Y) X4)))) 0.39/0.65 (assert (forall ((F2 (-> tptp.produc1260470173ar_int tptp.produc1166363805nt_com)) (G (-> tptp.produc1260470173ar_int tptp.produc1260470173ar_int)) (A4 tptp.set_Pr1148378109ar_int)) (= (@ (@ tptp.image_786684229nt_com F2) (@ (@ tptp.image_880790597ar_int G) A4)) (@ (@ tptp.image_786684229nt_com (lambda ((X tptp.produc1260470173ar_int)) (@ F2 (@ G X)))) A4)))) 0.39/0.65 (assert (forall ((P4 tptp.produc1260470173ar_int)) (= (@ (@ tptp.produc1288559923ar_int tptp.produc1193801173ar_int) P4) P4))) 0.39/0.65 (assert (forall ((F2 (-> tptp.produc1260470173ar_int tptp.nat)) (G (-> tptp.produc1260470173ar_int tptp.produc1260470173ar_int)) (A4 tptp.set_Pr1148378109ar_int)) (= (@ (@ tptp.image_1742782760nt_nat F2) (@ (@ tptp.image_880790597ar_int G) A4)) (@ (@ tptp.image_1742782760nt_nat (lambda ((X tptp.produc1260470173ar_int)) (@ F2 (@ G X)))) A4)))) 0.39/0.65 (assert (forall ((P4 tptp.produc1166363805nt_com) (C (-> (-> tptp.list_char tptp.int) tptp.com Bool))) (=> (forall ((A3 (-> tptp.list_char tptp.int)) (B3 tptp.com)) (=> (= P4 (@ (@ tptp.produc1139835093nt_com A3) B3)) (@ (@ C A3) B3))) (@ (@ tptp.produc613711406_com_o C) P4)))) 0.39/0.65 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C))))) 0.39/0.65 (assert (forall ((N3 tptp.nat)) (=> (not (= N3 tptp.zero_zero_nat)) (exists ((M3 tptp.nat)) (= N3 (@ tptp.suc M3)))))) 0.39/0.65 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X4) Y)) (and (= X4 tptp.zero_zero_nat) (= Y tptp.zero_zero_nat))))) 0.39/0.65 (assert (forall ((X4 tptp.produc1260470173ar_int) (A4 tptp.set_Pr1148378109ar_int) (B tptp.nat) (F2 (-> tptp.produc1260470173ar_int tptp.nat))) (=> (@ (@ tptp.member92250950ar_int X4) A4) (=> (= B (@ F2 X4)) (@ (@ tptp.member_nat B) (@ (@ tptp.image_1742782760nt_nat F2) A4)))))) 0.39/0.65 (assert (forall ((M tptp.nat) (N3 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) N3) tptp.zero_zero_nat) (and (= N3 tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))) 0.39/0.65 (assert (forall ((C tptp.com) (S7 (-> tptp.list_char tptp.int)) (T6 (-> tptp.list_char tptp.int)) (U (-> tptp.list_char tptp.int))) (let ((_let_1 (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S7)))) (=> (@ _let_1 T6) (=> (@ _let_1 U) (= U T6)))))) 0.39/0.65 (assert (forall ((F2 (-> (-> tptp.list_char tptp.int) tptp.com Bool)) (A (-> tptp.list_char tptp.int)) (B tptp.com)) (=> (@ (@ F2 A) B) (@ (@ tptp.produc613711406_com_o F2) (@ (@ tptp.produc1139835093nt_com A) B))))) 0.39/0.65 (assert (forall ((P (-> tptp.nat Bool)) (N3 tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N tptp.nat)) (=> (@ P N) (@ P (@ tptp.suc N)))) (@ P N3))))) 0.39/0.65 (assert (forall ((P (-> tptp.produc1166363805nt_com Bool)) (Prod tptp.produc1166363805nt_com)) (=> (forall ((A3 (-> tptp.list_char tptp.int)) (B3 tptp.com)) (@ P (@ (@ tptp.produc1139835093nt_com A3) B3))) (@ P Prod)))) 0.39/0.65 (assert (forall ((F2 (-> tptp.com (-> tptp.list_char tptp.int) tptp.produc1260470173ar_int)) (P4 tptp.produc1260470173ar_int)) (= (@ (@ tptp.produc1771082291ar_int (lambda ((Y4 (-> tptp.list_char tptp.int)) (X tptp.com)) (@ (@ F2 X) Y4))) (@ tptp.produc1770201973ar_int P4)) (@ (@ tptp.produc1288559923ar_int F2) P4)))) 0.39/0.65 (assert (forall ((N3 tptp.nat)) (not (= N3 (@ tptp.suc N3))))) 0.39/0.65 (assert (forall ((A (-> tptp.list_char tptp.int)) (B tptp.com) (A4 tptp.set_Pr866150653nt_com) (F2 (-> (-> tptp.list_char tptp.int) tptp.com tptp.produc1260470173ar_int))) (=> (@ (@ tptp.member2145628230nt_com (@ (@ tptp.produc1139835093nt_com A) B)) A4) (@ (@ tptp.member92250950ar_int (@ (@ F2 A) B)) (@ (@ tptp.image_1968865093ar_int (@ tptp.produc1771082291ar_int F2)) A4))))) 0.39/0.65 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_nat P) (@ tptp.collect_nat Q))))) 0.39/0.65 (assert (forall ((X21 tptp.list_char) (X22 tptp.aexp)) (= (@ tptp.size_size_com (@ (@ tptp.assign X21) X22)) tptp.zero_zero_nat))) 0.39/0.65 (assert (forall ((H (-> Bool tptp.nat)) (F2 (-> tptp.com (-> tptp.list_char tptp.int) Bool)) (Prod tptp.produc1260470173ar_int)) (= (@ H (@ (@ tptp.produc668584238_int_o F2) Prod)) (@ (@ tptp.produc1311963066nt_nat (lambda ((X13 tptp.com) (X24 (-> tptp.list_char tptp.int))) (@ H (@ (@ F2 X13) X24)))) Prod)))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (P3 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (Q3 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati775585786_valid P) C) C2) Q) (=> (forall ((S3 (-> tptp.list_char tptp.int)) (S4 (-> tptp.list_char tptp.int))) (=> (@ (@ P S3) S4) (@ (@ P3 S3) S4))) (=> (forall ((S3 (-> tptp.list_char tptp.int)) (S4 (-> tptp.list_char tptp.int))) (=> (@ (@ Q3 S3) S4) (@ (@ Q S3) S4))) (@ (@ (@ (@ tptp.relati775585786_valid P3) C) C2) Q3)))))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (B tptp.bexp) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com)) (=> (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((S (-> tptp.list_char tptp.int)) (S2 (-> tptp.list_char tptp.int))) (and (not (@ (@ tptp.bval B) S)) (@ (@ P S) S2)))) tptp.skip) C2) Q) (@ (@ (@ (@ tptp.relati775585786_valid P) (@ (@ tptp.while B) C)) C2) Q)))) 0.39/0.65 (assert (forall ((Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C2 tptp.com)) (=> (forall ((T (-> tptp.list_char tptp.int)) (T2 (-> tptp.list_char tptp.int))) (=> (@ (@ Q T) T2) (exists ((S5 (-> tptp.list_char tptp.int))) (and (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S5)) T2) (@ (@ P T) S5))))) (@ (@ (@ (@ tptp.relati2102071307_hoare P) tptp.skip) C2) Q)))) 0.39/0.65 (assert (forall ((X4 tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int false) X4) Y) Y))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C1 tptp.com) (C22 tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati775585786_valid P) (@ (@ tptp.seq C1) C22)) C2) Q) (@ (@ (@ (@ tptp.relati775585786_valid (lambda ((T4 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (exists ((S (-> tptp.list_char tptp.int)) (S2 (-> tptp.list_char tptp.int))) (and (@ (@ P S) S2) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S2)) T5) (exists ((U2 (-> tptp.list_char tptp.int))) (and (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C22) T4)) U2) (@ (@ Q U2) T5))) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C1) S)) T4))))) C22) tptp.skip) Q)))) 0.39/0.65 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat B))) (let ((_let_2 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C))))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.produc1260470173ar_int tptp.produc1260470173ar_int))) (= (@ tptp.produc1288559923ar_int (@ tptp.produc804153044ar_int F2)) F2))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (D tptp.com) (R (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (let ((_let_1 (@ tptp.relati775585786_valid P))) (=> (@ (@ (@ _let_1 C) C2) Q) (=> (@ (@ (@ (@ tptp.relati775585786_valid Q) D) tptp.skip) R) (@ (@ (@ _let_1 (@ (@ tptp.seq C) D)) C2) R)))))) 0.39/0.65 (assert (forall ((B tptp.bexp) (C tptp.com) (S7 (-> tptp.list_char tptp.int)) (T6 (-> tptp.list_char tptp.int))) (let ((_let_1 (@ (@ tptp.bval B) S7))) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.while B) C)) S7)) T6) (=> (=> (= T6 S7) _let_1) (not (=> _let_1 (forall ((S_2 (-> tptp.list_char tptp.int))) (=> (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S7)) S_2) (not (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.while B) C)) S_2)) T6))))))))))) 0.39/0.65 (assert (= (@ tptp.size_size_com tptp.skip) tptp.zero_zero_nat)) 0.39/0.65 (assert (forall ((F2 (-> tptp.com (-> tptp.list_char tptp.int) tptp.set_nat))) (= (@ tptp.produc1791150095et_nat (@ tptp.produc991755120et_nat F2)) F2))) 0.39/0.65 (assert (forall ((A tptp.produc1260470173ar_int) (P (-> tptp.produc1260470173ar_int Bool))) (= (@ (@ tptp.member92250950ar_int A) (@ tptp.collec770796680ar_int P)) (@ P A)))) 0.39/0.65 (assert (forall ((H (-> Bool Bool)) (F2 (-> tptp.com (-> tptp.list_char tptp.int) Bool)) (Prod tptp.produc1260470173ar_int)) (= (@ H (@ (@ tptp.produc668584238_int_o F2) Prod)) (@ (@ tptp.produc668584238_int_o (lambda ((X13 tptp.com) (X24 (-> tptp.list_char tptp.int))) (@ H (@ (@ F2 X13) X24)))) Prod)))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (P3 (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool))) (=> (@ (@ (@ (@ tptp.relati2102071307_hoare P) C) C2) Q) (=> (forall ((S3 (-> tptp.list_char tptp.int)) (S4 (-> tptp.list_char tptp.int))) (=> (@ (@ P S3) S4) (@ (@ P3 S3) S4))) (@ (@ (@ (@ tptp.relati2102071307_hoare P3) C) C2) Q))))) 0.39/0.65 (assert (forall ((X4 tptp.list_char) (A tptp.aexp) (S7 (-> tptp.list_char tptp.int))) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ tptp.assign X4) A)) S7)) (@ (@ (@ tptp.fun_up103088396ar_int S7) X4) (@ (@ tptp.aval A) S7))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.produc1260470173ar_int Bool))) (= (@ tptp.produc668584238_int_o (lambda ((X tptp.com) (Y4 (-> tptp.list_char tptp.int))) (@ F2 (@ (@ tptp.produc1193801173ar_int X) Y4)))) F2))) 0.39/0.65 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (A4 tptp.set_nat) (P (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.image_nat_nat F2) A4)) (@ P X3))) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A4) (@ P (@ F2 X5))))))) 0.39/0.65 (assert (= tptp.produc1858366159_int_o (lambda ((C3 (-> tptp.produc1260470173ar_int Bool)) (X tptp.com) (Y4 (-> tptp.list_char tptp.int))) (@ C3 (@ (@ tptp.produc1193801173ar_int X) Y4))))) 0.39/0.65 (assert (forall ((C tptp.com) (C2 tptp.com)) (= (forall ((S (-> tptp.list_char tptp.int)) (T4 (-> tptp.list_char tptp.int))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S)) T4) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S)) T4))) (forall ((S (-> tptp.list_char tptp.int)) (T4 (-> tptp.list_char tptp.int))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S)) T4) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S)) T4)))))) 0.39/0.65 (assert (forall ((H (-> tptp.set_nat Bool)) (F2 (-> tptp.com (-> tptp.list_char tptp.int) tptp.set_nat)) (Prod tptp.produc1260470173ar_int)) (= (@ H (@ (@ tptp.produc991755120et_nat F2) Prod)) (@ (@ tptp.produc668584238_int_o (lambda ((X13 tptp.com) (X24 (-> tptp.list_char tptp.int))) (@ H (@ (@ F2 X13) X24)))) Prod)))) 0.39/0.65 (assert (forall ((B tptp.bexp) (C tptp.com) (S8 (-> tptp.list_char tptp.int)) (T7 (-> tptp.list_char tptp.int))) (let ((_let_1 (@ (@ tptp.while B) C))) (= (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int _let_1) S8)) T7) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int (@ (@ (@ tptp.if B) (@ (@ tptp.seq C) _let_1)) tptp.skip)) S8)) T7))))) 0.39/0.65 (assert (= tptp.fun_up103088396ar_int (lambda ((F (-> tptp.list_char tptp.int)) (X tptp.list_char) (Y4 tptp.int) (Z2 tptp.list_char)) (@ (@ (@ tptp.if_int (= Z2 X)) Y4) (@ F Z2))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.produc1166363805nt_com tptp.produc1166363805nt_com)) (A4 tptp.set_Pr866150653nt_com) (P (-> tptp.produc1166363805nt_com Bool))) (= (@ tptp.collec676690312nt_com (lambda ((X tptp.produc1166363805nt_com)) (and (@ P X) (@ (@ tptp.member2145628230nt_com X) (@ (@ tptp.image_1874758725nt_com F2) A4))))) (@ (@ tptp.image_1874758725nt_com F2) (@ tptp.collec676690312nt_com (lambda ((X tptp.produc1166363805nt_com)) (and (@ P (@ F2 X)) (@ (@ tptp.member2145628230nt_com X) A4)))))))) 0.39/0.65 (assert (forall ((Prod tptp.produc1260470173ar_int)) (@ (@ tptp.produc668584238_int_o (lambda ((Uu tptp.com) (Uv (-> tptp.list_char tptp.int))) true)) Prod))) 0.39/0.65 (assert (forall ((X21 tptp.list_char) (X22 tptp.aexp) (X41 tptp.bexp) (X42 tptp.com) (X43 tptp.com)) (not (= (@ (@ tptp.assign X21) X22) (@ (@ (@ tptp.if X41) X42) X43))))) 0.39/0.65 (assert (forall ((A tptp.com) (B (-> tptp.list_char tptp.int)) (A4 tptp.set_Pr1148378109ar_int) (F2 (-> tptp.com (-> tptp.list_char tptp.int) tptp.nat))) (=> (@ (@ tptp.member92250950ar_int (@ (@ tptp.produc1193801173ar_int A) B)) A4) (@ (@ tptp.member_nat (@ (@ F2 A) B)) (@ (@ tptp.image_1742782760nt_nat (@ tptp.produc1311963066nt_nat F2)) A4))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.com (-> tptp.list_char tptp.int) Bool)) (A tptp.com) (B (-> tptp.list_char tptp.int))) (=> (@ (@ tptp.produc668584238_int_o F2) (@ (@ tptp.produc1193801173ar_int A) B)) (@ (@ F2 A) B)))) 0.39/0.65 (assert (forall ((F2 (-> tptp.produc1166363805nt_com tptp.produc1260470173ar_int)) (A4 tptp.set_Pr866150653nt_com) (P (-> tptp.produc1260470173ar_int Bool))) (= (@ tptp.collec770796680ar_int (lambda ((X tptp.produc1260470173ar_int)) (and (@ (@ tptp.member92250950ar_int X) (@ (@ tptp.image_1968865093ar_int F2) A4)) (@ P X)))) (@ (@ tptp.image_1968865093ar_int F2) (@ tptp.collec676690312nt_com (lambda ((X tptp.produc1166363805nt_com)) (and (@ (@ tptp.member2145628230nt_com X) A4) (@ P (@ F2 X))))))))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (X1 tptp.list_char) (X2 tptp.aexp) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (T6 (-> tptp.list_char tptp.int)) (T3 (-> tptp.list_char tptp.int))) (=> (@ (@ (@ (@ tptp.relati775585786_valid P) (@ (@ tptp.assign X1) X2)) C2) Q) (=> (@ (@ Q T6) T3) (exists ((S4 (-> tptp.list_char tptp.int))) (and (exists ((V tptp.int)) (let ((_let_1 (@ (@ (@ tptp.fun_up103088396ar_int T6) X1) V))) (and (@ (@ P _let_1) S4) (= (@ T6 X1) (@ (@ tptp.aval X2) _let_1))))) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S4)) T3))))))) 0.39/0.65 (assert (forall ((C tptp.com) (S8 (-> tptp.list_char tptp.int)) (T7 (-> tptp.list_char tptp.int))) (let ((_let_1 (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S8)) T7))) (= _let_1 _let_1)))) 0.39/0.65 (assert (forall ((F2 (-> tptp.produc1260470173ar_int Bool)) (A tptp.com) (B (-> tptp.list_char tptp.int))) (=> (@ (@ (@ tptp.produc1858366159_int_o F2) A) B) (@ F2 (@ (@ tptp.produc1193801173ar_int A) B))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.produc1260470173ar_int tptp.produc1260470173ar_int)) (A4 tptp.set_Pr1148378109ar_int) (P (-> tptp.produc1260470173ar_int Bool))) (= (@ tptp.collec770796680ar_int (lambda ((X tptp.produc1260470173ar_int)) (and (@ (@ tptp.member92250950ar_int X) (@ (@ tptp.image_880790597ar_int F2) A4)) (@ P X)))) (@ (@ tptp.image_880790597ar_int F2) (@ tptp.collec770796680ar_int (lambda ((X tptp.produc1260470173ar_int)) (and (@ P (@ F2 X)) (@ (@ tptp.member92250950ar_int X) A4)))))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.produc1166363805nt_com Bool)) (A (-> tptp.list_char tptp.int)) (B tptp.com)) (=> (@ (@ (@ tptp.produc1803493327_com_o F2) A) B) (@ F2 (@ (@ tptp.produc1139835093nt_com A) B))))) 0.39/0.65 (assert (forall ((A (-> tptp.list_char tptp.int)) (B tptp.com) (A2 (-> tptp.list_char tptp.int)) (B2 tptp.com)) (= (= (@ (@ tptp.produc1139835093nt_com A) B) (@ (@ tptp.produc1139835093nt_com A2) B2)) (and (= A A2) (= B B2))))) 0.39/0.65 (assert (forall ((X4 tptp.com) (Y (-> tptp.list_char tptp.int))) (= (@ tptp.produc1770201973ar_int (@ (@ tptp.produc1193801173ar_int X4) Y)) (@ (@ tptp.produc1139835093nt_com Y) X4)))) 0.39/0.65 (assert (forall ((P4 tptp.produc1260470173ar_int) (C (-> tptp.com (-> tptp.list_char tptp.int) Bool))) (=> (forall ((A3 tptp.com) (B3 (-> tptp.list_char tptp.int))) (=> (= P4 (@ (@ tptp.produc1193801173ar_int A3) B3)) (@ (@ C A3) B3))) (@ (@ tptp.produc668584238_int_o C) P4)))) 0.39/0.65 (assert (= tptp.produc857153862et_nat tptp.produc991755120et_nat)) 0.39/0.65 (assert (forall ((X4 tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int true) X4) Y) X4))) 0.39/0.65 (assert (forall ((A4 tptp.set_Pr1148378109ar_int)) (= (@ tptp.collec770796680ar_int (lambda ((X tptp.produc1260470173ar_int)) (@ (@ tptp.member92250950ar_int X) A4))) A4))) 0.39/0.65 (assert (forall ((C (-> (-> tptp.list_char tptp.int) tptp.com Bool)) (P4 tptp.produc1166363805nt_com)) (=> (@ (@ tptp.produc613711406_com_o C) P4) (not (forall ((X3 (-> tptp.list_char tptp.int)) (Y3 tptp.com)) (=> (= P4 (@ (@ tptp.produc1139835093nt_com X3) Y3)) (not (@ (@ C X3) Y3)))))))) 0.39/0.65 (assert (forall ((Z tptp.nat) (C (-> (-> tptp.list_char tptp.int) tptp.com tptp.set_nat)) (A (-> tptp.list_char tptp.int)) (B tptp.com)) (let ((_let_1 (@ tptp.member_nat Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc1754105456et_nat C) (@ (@ tptp.produc1139835093nt_com A) B))))))) 0.39/0.65 (assert (forall ((P4 tptp.produc1166363805nt_com) (Z tptp.produc1166363805nt_com) (C (-> (-> tptp.list_char tptp.int) tptp.com tptp.set_Pr866150653nt_com))) (=> (forall ((A3 (-> tptp.list_char tptp.int)) (B3 tptp.com)) (=> (= P4 (@ (@ tptp.produc1139835093nt_com A3) B3)) (@ (@ tptp.member2145628230nt_com Z) (@ (@ C A3) B3)))) (@ (@ tptp.member2145628230nt_com Z) (@ (@ tptp.produc1179280275nt_com C) P4))))) 0.39/0.65 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (= (@ tptp.suc X4) (@ tptp.suc Y)) (= X4 Y)))) 0.39/0.65 (assert (forall ((F2 (-> tptp.produc1260470173ar_int tptp.nat))) (= (@ tptp.produc1311963066nt_nat (lambda ((X tptp.com) (Y4 (-> tptp.list_char tptp.int))) (@ F2 (@ (@ tptp.produc1193801173ar_int X) Y4)))) F2))) 0.39/0.65 (assert (forall ((A tptp.com) (B (-> tptp.list_char tptp.int)) (A4 tptp.set_Pr1148378109ar_int) (F2 (-> tptp.com (-> tptp.list_char tptp.int) tptp.set_nat))) (=> (@ (@ tptp.member92250950ar_int (@ (@ tptp.produc1193801173ar_int A) B)) A4) (@ (@ tptp.member_set_nat (@ (@ F2 A) B)) (@ (@ tptp.image_989727966et_nat (@ tptp.produc991755120et_nat F2)) A4))))) 0.39/0.65 (assert (forall ((F2 (-> tptp.list_char tptp.int)) (X4 tptp.list_char) (Y tptp.int)) (= (= (@ (@ (@ tptp.fun_up103088396ar_int F2) X4) Y) F2) (= (@ F2 X4) Y)))) 0.39/0.65 (assert (forall ((X1 tptp.list_char) (S7 (-> tptp.list_char tptp.int)) (X2 tptp.aexp)) (= (lambda ((A5 tptp.list_char)) (@ (@ (@ tptp.if_int (= A5 X1)) (@ S7 X1)) (@ (@ (@ (@ tptp.fun_up103088396ar_int S7) X1) (@ (@ tptp.aval X2) S7)) A5))) S7))) 0.39/0.65 (assert (forall ((F2 (-> tptp.produc1260470173ar_int tptp.nat))) (= (@ tptp.produc1311963066nt_nat (@ tptp.produc763543641nt_nat F2)) F2))) 0.39/0.65 (assert (forall ((X4 tptp.produc1166363805nt_com) (A4 tptp.set_Pr866150653nt_com) (B tptp.nat) (F2 (-> tptp.produc1166363805nt_com tptp.nat))) (=> (@ (@ tptp.member2145628230nt_com X4) A4) (=> (= B (@ F2 X4)) (@ (@ tptp.member_nat B) (@ (@ tptp.image_596692520om_nat F2) A4)))))) 0.39/0.65 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A))) 0.39/0.65 (assert (forall ((S7 (-> tptp.list_char tptp.int))) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int tptp.skip) S7)) S7))) 0.39/0.65 (assert (forall ((X4 tptp.produc1260470173ar_int) (A4 tptp.set_Pr1148378109ar_int) (B tptp.produc1166363805nt_com) (F2 (-> tptp.produc1260470173ar_int tptp.produc1166363805nt_com))) (=> (@ (@ tptp.member92250950ar_int X4) A4) (=> (= B (@ F2 X4)) (@ (@ tptp.member2145628230nt_com B) (@ (@ tptp.image_786684229nt_com F2) A4)))))) 0.39/0.65 (assert (forall ((A4 tptp.set_Pr866150653nt_com)) (= (@ tptp.collec676690312nt_com (lambda ((X tptp.produc1166363805nt_com)) (@ (@ tptp.member2145628230nt_com X) A4))) A4))) 0.39/0.65 (assert (forall ((P (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (C tptp.com) (C2 tptp.com) (Q (-> (-> tptp.list_char tptp.int) (-> tptp.list_char tptp.int) Bool)) (S7 (-> tptp.list_char tptp.int)) (S6 (-> tptp.list_char tptp.int))) (let ((_let_1 (@ (@ (@ tptp.relati775585786_valid P) C) C2))) (=> (@ _let_1 Q) (@ _let_1 (lambda ((T4 (-> tptp.list_char tptp.int)) (T5 (-> tptp.list_char tptp.int))) (and /export/starexec/sandbox2/solver/bin/do_THM_THF: line 35: 20904 Alarm clock ( read result; case "$result" in 179.45/180.04 unsat) 179.45/180.04 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0 179.45/180.04 ;; 179.45/180.04 sat) 179.45/180.04 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0 179.45/180.04 ;; 179.45/180.04 esac; exit 1 ) 179.45/180.05 (exists ((S (-> tptp.list_char tptp.int)) (S2 (-> tptp.list_char tptp.int))) (and (@ (@ P S) S2) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C) S)) T4) (@ (@ tptp.big_big_step (@ (@ tptp.produc1193801173ar_int C2) S2)) T5))) (@ (@ Q S7) S6)))))))) 179.45/180.05 (set-info :filename cvc5---1.0.5_20735) 179.45/180.05 (check-sat-assuming ( true )) 179.45/180.05 ------- get file name : TPTP file name is 179.45/180.05 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_20735.smt2... 179.45/180.05 --- Run --ho-elim --full-saturate-quant at 10... 179.45/180.05 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10... 179.45/180.05 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10... 179.45/180.05 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5... 179.45/180.05 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5... 179.45/180.05 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10... 179.45/180.05 --- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 10... 179.45/180.05 --- Run --ho-elim --full-saturate-quant --enum-inst-interleave at 10... 179.45/180.05 --- Run --no-ho-matching --full-saturate-quant --ho-elim-store-ax at 10... 179.45/180.05 --- Run --ho-elim --no-ho-elim-store-ax --full-saturate-quant... 179.45/180.05 % cvc5---1.0.5 exiting 179.45/180.05 % cvc5---1.0.5 exiting 179.45/180.05 EOF