TSTP Solution File: ITP141^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP141^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 03:18:35 EDT 2023
% Result : Theorem 1.15s 1.45s
% Output : Proof 1.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.18 % Problem : ITP141^1 : TPTP v8.1.2. Released v7.5.0.
% 0.09/0.18 % Command : do_cvc5 %s %d
% 0.14/0.38 % Computer : n005.cluster.edu
% 0.14/0.38 % Model : x86_64 x86_64
% 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38 % Memory : 8042.1875MB
% 0.14/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.38 % CPULimit : 300
% 0.14/0.38 % WCLimit : 300
% 0.14/0.38 % DateTime : Sun Aug 27 15:50:23 EDT 2023
% 0.14/0.38 % CPUTime :
% 0.20/0.53 %----Proving TH0
% 0.20/0.53 %------------------------------------------------------------------------------
% 0.20/0.53 % File : ITP141^1 : TPTP v8.1.2. Released v7.5.0.
% 0.20/0.53 % Domain : Interactive Theorem Proving
% 0.20/0.53 % Problem : Sledgehammer PHoareTotal problem prob_135__3259094_1
% 0.20/0.53 % Version : Especial.
% 0.20/0.53 % English :
% 0.20/0.53
% 0.20/0.53 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.20/0.53 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.20/0.53 % Source : [Des21]
% 0.20/0.53 % Names : PHoareTotal/prob_135__3259094_1 [Des21]
% 0.20/0.53
% 0.20/0.53 % Status : Theorem
% 0.20/0.53 % Rating : 0.62 v8.1.0, 0.55 v7.5.0
% 0.20/0.53 % Syntax : Number of formulae : 486 ( 197 unt; 129 typ; 0 def)
% 0.20/0.53 % Number of atoms : 965 ( 395 equ; 0 cnn)
% 0.20/0.53 % Maximal formula atoms : 21 ( 2 avg)
% 0.20/0.53 % Number of connectives : 2845 ( 189 ~; 21 |; 103 &;2146 @)
% 0.20/0.53 % ( 0 <=>; 386 =>; 0 <=; 0 <~>)
% 0.20/0.53 % Maximal formula depth : 22 ( 7 avg)
% 0.20/0.53 % Number of types : 21 ( 20 usr)
% 0.20/0.53 % Number of type conns : 488 ( 488 >; 0 *; 0 +; 0 <<)
% 0.20/0.53 % Number of symbols : 112 ( 109 usr; 17 con; 0-4 aty)
% 0.20/0.53 % Number of variables : 1075 ( 140 ^; 895 !; 40 ?;1075 :)
% 0.20/0.53 % SPC : TH0_THM_EQU_NAR
% 0.20/0.53
% 0.20/0.53 % Comments : This file was generated by Sledgehammer 2021-02-23 15:32:35.907
% 0.20/0.53 %------------------------------------------------------------------------------
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% 0.20/0.53 % Explicit typings (109)
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% 0.20/0.54
% 0.20/0.54 % thoare.Asm
% 0.20/0.54 thf(fact_1_weaken__post,axiom,
% 0.20/0.54 ! [C: set_Pr1590995257tate_o,P: a > state > $o,C2: com,Q: a > state > $o,Q2: a > state > $o] :
% 0.20/0.54 ( ( pHoare382919414oare_a @ C @ P @ C2 @ Q )
% 0.20/0.54 => ( ! [Z: a,S: state] :
% 0.20/0.54 ( ( Q @ Z @ S )
% 0.20/0.54 => ( Q2 @ Z @ S ) )
% 0.20/0.54 => ( pHoare382919414oare_a @ C @ P @ C2 @ Q2 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % weaken_post
% 0.20/0.54 thf(fact_2_thoare_OConseq,axiom,
% 0.20/0.54 ! [C: set_Pr1590995257tate_o,P2: a > state > $o,C2: com,Q2: a > state > $o,P: a > state > $o,Q: a > state > $o] :
% 0.20/0.54 ( ( pHoare382919414oare_a @ C @ P2 @ C2 @ Q2 )
% 0.20/0.54 => ( ( ! [S: state,T: state] :
% 0.20/0.54 ( ! [Z2: a] :
% 0.20/0.54 ( ( P2 @ Z2 @ S )
% 0.20/0.54 => ( Q2 @ Z2 @ T ) )
% 0.20/0.54 => ! [Z: a] :
% 0.20/0.54 ( ( P @ Z @ S )
% 0.20/0.54 => ( Q @ Z @ T ) ) )
% 0.20/0.54 & ! [S: state] :
% 0.20/0.54 ( ? [Z: a] : ( P @ Z @ S )
% 0.20/0.54 => ? [Z2: a] : ( P2 @ Z2 @ S ) ) )
% 0.20/0.54 => ( pHoare382919414oare_a @ C @ P @ C2 @ Q ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % thoare.Conseq
% 0.20/0.54 thf(fact_3_PHoareTotal__Mirabelle__ynemugpbor_Ostrengthen__pre,axiom,
% 0.20/0.54 ! [P2: a > state > $o,P: a > state > $o,C: set_Pr1590995257tate_o,C2: com,Q: a > state > $o] :
% 0.20/0.54 ( ! [Z: a,S: state] :
% 0.20/0.54 ( ( P2 @ Z @ S )
% 0.20/0.54 => ( P @ Z @ S ) )
% 0.20/0.54 => ( ( pHoare382919414oare_a @ C @ P @ C2 @ Q )
% 0.20/0.54 => ( pHoare382919414oare_a @ C @ P2 @ C2 @ Q ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % PHoareTotal_Mirabelle_ynemugpbor.strengthen_pre
% 0.20/0.54 thf(fact_4_singleton__conv,axiom,
% 0.20/0.54 ! [A: produc1115495963_state] :
% 0.20/0.54 ( ( collec496201222_state
% 0.20/0.54 @ ^ [X: produc1115495963_state] : ( X = A ) )
% 0.20/0.54 = ( insert311944171_state @ A @ bot_bo1625160935_state ) ) ).
% 0.20/0.54
% 0.20/0.54 % singleton_conv
% 0.20/0.54 thf(fact_5_singleton__conv,axiom,
% 0.20/0.54 ! [A: product_prod_nat_nat] :
% 0.20/0.54 ( ( collec7649004at_nat
% 0.20/0.54 @ ^ [X: product_prod_nat_nat] : ( X = A ) )
% 0.20/0.54 = ( insert271595217at_nat @ A @ bot_bo2130386637at_nat ) ) ).
% 0.20/0.54
% 0.20/0.54 % singleton_conv
% 0.20/0.54 thf(fact_6_singleton__conv,axiom,
% 0.20/0.54 ! [A: produc696469763tate_o] :
% 0.20/0.54 ( ( collec1499596504tate_o
% 0.20/0.54 @ ^ [X: produc696469763tate_o] : ( X = A ) )
% 0.20/0.54 = ( insert2053719859tate_o @ A @ bot_bo170732493tate_o ) ) ).
% 0.20/0.54
% 0.20/0.54 % singleton_conv
% 0.20/0.54 thf(fact_7_singleton__conv2,axiom,
% 0.20/0.54 ! [A: produc1115495963_state] :
% 0.20/0.54 ( ( collec496201222_state
% 0.20/0.54 @ ( ^ [Y: produc1115495963_state,Z3: produc1115495963_state] : ( Y = Z3 )
% 0.20/0.54 @ A ) )
% 0.20/0.54 = ( insert311944171_state @ A @ bot_bo1625160935_state ) ) ).
% 0.20/0.54
% 0.20/0.54 % singleton_conv2
% 0.20/0.54 thf(fact_8_singleton__conv2,axiom,
% 0.20/0.54 ! [A: product_prod_nat_nat] :
% 0.20/0.54 ( ( collec7649004at_nat
% 0.20/0.54 @ ( ^ [Y: product_prod_nat_nat,Z3: product_prod_nat_nat] : ( Y = Z3 )
% 0.20/0.54 @ A ) )
% 0.20/0.54 = ( insert271595217at_nat @ A @ bot_bo2130386637at_nat ) ) ).
% 0.20/0.54
% 0.20/0.54 % singleton_conv2
% 0.20/0.54 thf(fact_9_singleton__conv2,axiom,
% 0.20/0.54 ! [A: produc696469763tate_o] :
% 0.20/0.54 ( ( collec1499596504tate_o
% 0.20/0.54 @ ( ^ [Y: produc696469763tate_o,Z3: produc696469763tate_o] : ( Y = Z3 )
% 0.20/0.54 @ A ) )
% 0.20/0.54 = ( insert2053719859tate_o @ A @ bot_bo170732493tate_o ) ) ).
% 0.20/0.54
% 0.20/0.54 % singleton_conv2
% 0.20/0.54 thf(fact_10_singletonI,axiom,
% 0.20/0.54 ! [A: produc1115495963_state] : ( member1389040324_state @ A @ ( insert311944171_state @ A @ bot_bo1625160935_state ) ) ).
% 0.20/0.54
% 0.20/0.54 % singletonI
% 0.20/0.54 thf(fact_11_singletonI,axiom,
% 0.20/0.54 ! [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( insert271595217at_nat @ A @ bot_bo2130386637at_nat ) ) ).
% 0.20/0.54
% 0.20/0.54 % singletonI
% 0.20/0.54 thf(fact_12_singletonI,axiom,
% 0.20/0.54 ! [A: produc696469763tate_o] : ( member1838112666tate_o @ A @ ( insert2053719859tate_o @ A @ bot_bo170732493tate_o ) ) ).
% 0.20/0.54
% 0.20/0.54 % singletonI
% 0.20/0.54 thf(fact_13_termi_Ointros_I7_J,axiom,
% 0.20/0.54 ! [S2: state] :
% 0.20/0.54 ( ( termi @ body @ S2 )
% 0.20/0.54 => ( termi @ call @ S2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % termi.intros(7)
% 0.20/0.54 thf(fact_14_exec_Ointros_I7_J,axiom,
% 0.20/0.54 ! [S2: state,T2: state] :
% 0.20/0.54 ( ( exec @ S2 @ body @ T2 )
% 0.20/0.54 => ( exec @ S2 @ call @ T2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % exec.intros(7)
% 0.20/0.54 thf(fact_15_thoare_OCall,axiom,
% 0.20/0.54 ! [R: set_Pr795498619_state,P: a > state > $o,Q: a > state > $o] :
% 0.20/0.54 ( ( wf_state @ R )
% 0.20/0.54 => ( ! [S3: state] :
% 0.20/0.54 ( pHoare382919414oare_a
% 0.20/0.54 @ ( insert2053719859tate_o
% 0.20/0.54 @ ( produc33908149tate_o
% 0.20/0.54 @ ^ [Z4: a,S4: state] :
% 0.20/0.54 ( ( P @ Z4 @ S4 )
% 0.20/0.54 & ( member1389040324_state @ ( produc64584659_state @ S4 @ S3 ) @ R ) )
% 0.20/0.54 @ ( produc1948644831tate_o @ call @ Q ) )
% 0.20/0.54 @ bot_bo170732493tate_o )
% 0.20/0.54 @ ^ [Z4: a,S4: state] :
% 0.20/0.54 ( ( P @ Z4 @ S4 )
% 0.20/0.54 & ( S4 = S3 ) )
% 0.20/0.54 @ body
% 0.20/0.54 @ Q )
% 0.20/0.54 => ( pHoare382919414oare_a @ bot_bo170732493tate_o @ P @ call @ Q ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % thoare.Call
% 0.20/0.54 thf(fact_16_insertCI,axiom,
% 0.20/0.54 ! [A: produc1115495963_state,B: set_Pr795498619_state,B2: produc1115495963_state] :
% 0.20/0.54 ( ( ~ ( member1389040324_state @ A @ B )
% 0.20/0.54 => ( A = B2 ) )
% 0.20/0.54 => ( member1389040324_state @ A @ ( insert311944171_state @ B2 @ B ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % insertCI
% 0.20/0.54 thf(fact_17_insertCI,axiom,
% 0.20/0.54 ! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat,B2: product_prod_nat_nat] :
% 0.20/0.54 ( ( ~ ( member701585322at_nat @ A @ B )
% 0.20/0.54 => ( A = B2 ) )
% 0.20/0.54 => ( member701585322at_nat @ A @ ( insert271595217at_nat @ B2 @ B ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % insertCI
% 0.20/0.54 thf(fact_18_insertCI,axiom,
% 0.20/0.54 ! [A: produc696469763tate_o,B: set_Pr1590995257tate_o,B2: produc696469763tate_o] :
% 0.20/0.54 ( ( ~ ( member1838112666tate_o @ A @ B )
% 0.20/0.54 => ( A = B2 ) )
% 0.20/0.54 => ( member1838112666tate_o @ A @ ( insert2053719859tate_o @ B2 @ B ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % insertCI
% 0.20/0.54 thf(fact_19_insert__iff,axiom,
% 0.20/0.54 ! [A: produc1115495963_state,B2: produc1115495963_state,A2: set_Pr795498619_state] :
% 0.20/0.54 ( ( member1389040324_state @ A @ ( insert311944171_state @ B2 @ A2 ) )
% 0.20/0.54 = ( ( A = B2 )
% 0.20/0.54 | ( member1389040324_state @ A @ A2 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % insert_iff
% 0.20/0.54 thf(fact_20_insert__iff,axiom,
% 0.20/0.54 ! [A: product_prod_nat_nat,B2: product_prod_nat_nat,A2: set_Pr1986765409at_nat] :
% 0.20/0.54 ( ( member701585322at_nat @ A @ ( insert271595217at_nat @ B2 @ A2 ) )
% 0.20/0.54 = ( ( A = B2 )
% 0.20/0.54 | ( member701585322at_nat @ A @ A2 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % insert_iff
% 0.20/0.54 thf(fact_21_insert__iff,axiom,
% 0.20/0.54 ! [A: produc696469763tate_o,B2: produc696469763tate_o,A2: set_Pr1590995257tate_o] :
% 0.20/0.54 ( ( member1838112666tate_o @ A @ ( insert2053719859tate_o @ B2 @ A2 ) )
% 0.20/0.54 = ( ( A = B2 )
% 0.20/0.54 | ( member1838112666tate_o @ A @ A2 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % insert_iff
% 0.20/0.54 thf(fact_22_insert__absorb2,axiom,
% 0.20/0.54 ! [X2: produc696469763tate_o,A2: set_Pr1590995257tate_o] :
% 0.20/0.54 ( ( insert2053719859tate_o @ X2 @ ( insert2053719859tate_o @ X2 @ A2 ) )
% 0.20/0.54 = ( insert2053719859tate_o @ X2 @ A2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % insert_absorb2
% 0.20/0.54 thf(fact_23_insert__absorb2,axiom,
% 0.20/0.54 ! [X2: product_prod_nat_nat,A2: set_Pr1986765409at_nat] :
% 0.20/0.54 ( ( insert271595217at_nat @ X2 @ ( insert271595217at_nat @ X2 @ A2 ) )
% 0.20/0.54 = ( insert271595217at_nat @ X2 @ A2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % insert_absorb2
% 0.20/0.54 thf(fact_24_insert__absorb2,axiom,
% 0.20/0.54 ! [X2: produc1115495963_state,A2: set_Pr795498619_state] :
% 0.20/0.54 ( ( insert311944171_state @ X2 @ ( insert311944171_state @ X2 @ A2 ) )
% 0.20/0.54 = ( insert311944171_state @ X2 @ A2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % insert_absorb2
% 0.20/0.54 thf(fact_25_hoare_OCall,axiom,
% 0.20/0.54 ! [P: a > state > $o,Q: a > state > $o] :
% 0.20/0.54 ( ( hoare_a @ ( insert2053719859tate_o @ ( produc33908149tate_o @ P @ ( produc1948644831tate_o @ call @ Q ) ) @ bot_bo170732493tate_o ) @ P @ body @ Q )
% 0.20/0.54 => ( hoare_a @ bot_bo170732493tate_o @ P @ call @ Q ) ) ).
% 0.20/0.54
% 0.20/0.54 % hoare.Call
% 0.20/0.54 thf(fact_26_empty__iff,axiom,
% 0.20/0.54 ! [C2: produc696469763tate_o] :
% 0.20/0.54 ~ ( member1838112666tate_o @ C2 @ bot_bo170732493tate_o ) ).
% 0.20/0.54
% 0.20/0.54 % empty_iff
% 0.20/0.54 thf(fact_27_empty__iff,axiom,
% 0.20/0.54 ! [C2: product_prod_nat_nat] :
% 0.20/0.54 ~ ( member701585322at_nat @ C2 @ bot_bo2130386637at_nat ) ).
% 0.20/0.54
% 0.20/0.54 % empty_iff
% 0.20/0.54 thf(fact_28_empty__iff,axiom,
% 0.20/0.54 ! [C2: produc1115495963_state] :
% 0.20/0.54 ~ ( member1389040324_state @ C2 @ bot_bo1625160935_state ) ).
% 0.20/0.54
% 0.20/0.54 % empty_iff
% 0.20/0.54 thf(fact_29_all__not__in__conv,axiom,
% 0.20/0.54 ! [A2: set_Pr1590995257tate_o] :
% 0.20/0.54 ( ( ! [X: produc696469763tate_o] :
% 0.20/0.54 ~ ( member1838112666tate_o @ X @ A2 ) )
% 0.20/0.54 = ( A2 = bot_bo170732493tate_o ) ) ).
% 0.20/0.54
% 0.20/0.54 % all_not_in_conv
% 0.20/0.54 thf(fact_30_all__not__in__conv,axiom,
% 0.20/0.54 ! [A2: set_Pr1986765409at_nat] :
% 0.20/0.54 ( ( ! [X: product_prod_nat_nat] :
% 0.20/0.54 ~ ( member701585322at_nat @ X @ A2 ) )
% 0.20/0.54 = ( A2 = bot_bo2130386637at_nat ) ) ).
% 0.20/0.54
% 0.20/0.54 % all_not_in_conv
% 0.20/0.54 thf(fact_31_all__not__in__conv,axiom,
% 0.20/0.54 ! [A2: set_Pr795498619_state] :
% 0.20/0.54 ( ( ! [X: produc1115495963_state] :
% 0.20/0.54 ~ ( member1389040324_state @ X @ A2 ) )
% 0.20/0.54 = ( A2 = bot_bo1625160935_state ) ) ).
% 0.20/0.54
% 0.20/0.54 % all_not_in_conv
% 0.20/0.54 thf(fact_32_empty__Collect__eq,axiom,
% 0.20/0.54 ! [P: produc696469763tate_o > $o] :
% 0.20/0.54 ( ( bot_bo170732493tate_o
% 0.20/0.54 = ( collec1499596504tate_o @ P ) )
% 0.20/0.54 = ( ! [X: produc696469763tate_o] :
% 0.20/0.54 ~ ( P @ X ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % empty_Collect_eq
% 0.20/0.54 thf(fact_33_empty__Collect__eq,axiom,
% 0.20/0.54 ! [P: product_prod_nat_nat > $o] :
% 0.20/0.54 ( ( bot_bo2130386637at_nat
% 0.20/0.54 = ( collec7649004at_nat @ P ) )
% 0.20/0.54 = ( ! [X: product_prod_nat_nat] :
% 0.20/0.54 ~ ( P @ X ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % empty_Collect_eq
% 0.20/0.54 thf(fact_34_empty__Collect__eq,axiom,
% 0.20/0.54 ! [P: produc1115495963_state > $o] :
% 0.20/0.54 ( ( bot_bo1625160935_state
% 0.20/0.54 = ( collec496201222_state @ P ) )
% 0.20/0.54 = ( ! [X: produc1115495963_state] :
% 0.20/0.54 ~ ( P @ X ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % empty_Collect_eq
% 0.20/0.54 thf(fact_35_Collect__empty__eq,axiom,
% 0.20/0.54 ! [P: produc696469763tate_o > $o] :
% 0.20/0.54 ( ( ( collec1499596504tate_o @ P )
% 0.20/0.54 = bot_bo170732493tate_o )
% 0.20/0.54 = ( ! [X: produc696469763tate_o] :
% 0.20/0.54 ~ ( P @ X ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % Collect_empty_eq
% 0.20/0.54 thf(fact_36_Collect__empty__eq,axiom,
% 0.20/0.54 ! [P: product_prod_nat_nat > $o] :
% 0.20/0.54 ( ( ( collec7649004at_nat @ P )
% 0.20/0.54 = bot_bo2130386637at_nat )
% 0.20/0.54 = ( ! [X: product_prod_nat_nat] :
% 0.20/0.54 ~ ( P @ X ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % Collect_empty_eq
% 0.20/0.54 thf(fact_37_Collect__empty__eq,axiom,
% 0.20/0.54 ! [P: produc1115495963_state > $o] :
% 0.20/0.54 ( ( ( collec496201222_state @ P )
% 0.20/0.54 = bot_bo1625160935_state )
% 0.20/0.54 = ( ! [X: produc1115495963_state] :
% 0.20/0.54 ~ ( P @ X ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % Collect_empty_eq
% 0.20/0.54 thf(fact_38_ex__in__conv,axiom,
% 0.20/0.54 ! [A2: set_Pr1590995257tate_o] :
% 0.20/0.54 ( ( ? [X: produc696469763tate_o] : ( member1838112666tate_o @ X @ A2 ) )
% 0.20/0.54 = ( A2 != bot_bo170732493tate_o ) ) ).
% 0.20/0.54
% 0.20/0.54 % ex_in_conv
% 0.20/0.54 thf(fact_39_ex__in__conv,axiom,
% 0.20/0.54 ! [A2: set_Pr1986765409at_nat] :
% 0.20/0.54 ( ( ? [X: product_prod_nat_nat] : ( member701585322at_nat @ X @ A2 ) )
% 0.20/0.54 = ( A2 != bot_bo2130386637at_nat ) ) ).
% 0.20/0.54
% 0.20/0.54 % ex_in_conv
% 0.20/0.54 thf(fact_40_ex__in__conv,axiom,
% 0.20/0.54 ! [A2: set_Pr795498619_state] :
% 0.20/0.54 ( ( ? [X: produc1115495963_state] : ( member1389040324_state @ X @ A2 ) )
% 0.20/0.54 = ( A2 != bot_bo1625160935_state ) ) ).
% 0.20/0.54
% 0.20/0.54 % ex_in_conv
% 0.20/0.54 thf(fact_41_equals0I,axiom,
% 0.20/0.54 ! [A2: set_Pr1590995257tate_o] :
% 0.20/0.54 ( ! [Y2: produc696469763tate_o] :
% 0.20/0.54 ~ ( member1838112666tate_o @ Y2 @ A2 )
% 0.20/0.54 => ( A2 = bot_bo170732493tate_o ) ) ).
% 0.20/0.54
% 0.20/0.54 % equals0I
% 0.20/0.54 thf(fact_42_equals0I,axiom,
% 0.20/0.54 ! [A2: set_Pr1986765409at_nat] :
% 0.20/0.54 ( ! [Y2: product_prod_nat_nat] :
% 0.20/0.54 ~ ( member701585322at_nat @ Y2 @ A2 )
% 0.20/0.54 => ( A2 = bot_bo2130386637at_nat ) ) ).
% 0.20/0.54
% 0.20/0.54 % equals0I
% 0.20/0.54 thf(fact_43_equals0I,axiom,
% 0.20/0.54 ! [A2: set_Pr795498619_state] :
% 0.20/0.54 ( ! [Y2: produc1115495963_state] :
% 0.20/0.54 ~ ( member1389040324_state @ Y2 @ A2 )
% 0.20/0.54 => ( A2 = bot_bo1625160935_state ) ) ).
% 0.20/0.54
% 0.20/0.54 % equals0I
% 0.20/0.54 thf(fact_44_equals0D,axiom,
% 0.20/0.54 ! [A2: set_Pr1590995257tate_o,A: produc696469763tate_o] :
% 0.20/0.54 ( ( A2 = bot_bo170732493tate_o )
% 0.20/0.54 => ~ ( member1838112666tate_o @ A @ A2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % equals0D
% 0.20/0.54 thf(fact_45_equals0D,axiom,
% 0.20/0.54 ! [A2: set_Pr1986765409at_nat,A: product_prod_nat_nat] :
% 0.20/0.54 ( ( A2 = bot_bo2130386637at_nat )
% 0.20/0.54 => ~ ( member701585322at_nat @ A @ A2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % equals0D
% 0.20/0.54 thf(fact_46_equals0D,axiom,
% 0.20/0.54 ! [A2: set_Pr795498619_state,A: produc1115495963_state] :
% 0.20/0.54 ( ( A2 = bot_bo1625160935_state )
% 0.20/0.54 => ~ ( member1389040324_state @ A @ A2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % equals0D
% 0.20/0.54 thf(fact_47_emptyE,axiom,
% 0.20/0.54 ! [A: produc696469763tate_o] :
% 0.20/0.54 ~ ( member1838112666tate_o @ A @ bot_bo170732493tate_o ) ).
% 0.20/0.54
% 0.20/0.54 % emptyE
% 0.20/0.54 thf(fact_48_emptyE,axiom,
% 0.20/0.54 ! [A: product_prod_nat_nat] :
% 0.20/0.54 ~ ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) ).
% 0.20/0.54
% 0.20/0.54 % emptyE
% 0.20/0.54 thf(fact_49_emptyE,axiom,
% 0.20/0.54 ! [A: produc1115495963_state] :
% 0.20/0.54 ~ ( member1389040324_state @ A @ bot_bo1625160935_state ) ).
% 0.20/0.54
% 0.20/0.54 % emptyE
% 0.20/0.54 thf(fact_50_mk__disjoint__insert,axiom,
% 0.20/0.54 ! [A: produc1115495963_state,A2: set_Pr795498619_state] :
% 0.20/0.54 ( ( member1389040324_state @ A @ A2 )
% 0.20/0.54 => ? [B3: set_Pr795498619_state] :
% 0.20/0.54 ( ( A2
% 0.20/0.54 = ( insert311944171_state @ A @ B3 ) )
% 0.20/0.54 & ~ ( member1389040324_state @ A @ B3 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % mk_disjoint_insert
% 0.20/0.54 thf(fact_51_mk__disjoint__insert,axiom,
% 0.20/0.54 ! [A: product_prod_nat_nat,A2: set_Pr1986765409at_nat] :
% 0.20/0.54 ( ( member701585322at_nat @ A @ A2 )
% 0.20/0.54 => ? [B3: set_Pr1986765409at_nat] :
% 0.20/0.54 ( ( A2
% 0.20/0.54 = ( insert271595217at_nat @ A @ B3 ) )
% 0.20/0.54 & ~ ( member701585322at_nat @ A @ B3 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % mk_disjoint_insert
% 0.20/0.54 thf(fact_52_mk__disjoint__insert,axiom,
% 0.20/0.54 ! [A: produc696469763tate_o,A2: set_Pr1590995257tate_o] :
% 0.20/0.54 ( ( member1838112666tate_o @ A @ A2 )
% 0.20/0.54 => ? [B3: set_Pr1590995257tate_o] :
% 0.20/0.54 ( ( A2
% 0.20/0.54 = ( insert2053719859tate_o @ A @ B3 ) )
% 0.20/0.54 & ~ ( member1838112666tate_o @ A @ B3 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % mk_disjoint_insert
% 0.20/0.54 thf(fact_53_insert__commute,axiom,
% 0.20/0.54 ! [X2: produc696469763tate_o,Y3: produc696469763tate_o,A2: set_Pr1590995257tate_o] :
% 0.20/0.54 ( ( insert2053719859tate_o @ X2 @ ( insert2053719859tate_o @ Y3 @ A2 ) )
% 0.20/0.54 = ( insert2053719859tate_o @ Y3 @ ( insert2053719859tate_o @ X2 @ A2 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % insert_commute
% 0.20/0.54 thf(fact_54_insert__commute,axiom,
% 0.20/0.54 ! [X2: product_prod_nat_nat,Y3: product_prod_nat_nat,A2: set_Pr1986765409at_nat] :
% 0.20/0.54 ( ( insert271595217at_nat @ X2 @ ( insert271595217at_nat @ Y3 @ A2 ) )
% 0.20/0.54 = ( insert271595217at_nat @ Y3 @ ( insert271595217at_nat @ X2 @ A2 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % insert_commute
% 0.20/0.54 thf(fact_55_insert__commute,axiom,
% 0.20/0.54 ! [X2: produc1115495963_state,Y3: produc1115495963_state,A2: set_Pr795498619_state] :
% 0.20/0.54 ( ( insert311944171_state @ X2 @ ( insert311944171_state @ Y3 @ A2 ) )
% 0.20/0.54 = ( insert311944171_state @ Y3 @ ( insert311944171_state @ X2 @ A2 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % insert_commute
% 0.20/0.54 thf(fact_56_insert__eq__iff,axiom,
% 0.20/0.54 ! [A: produc1115495963_state,A2: set_Pr795498619_state,B2: produc1115495963_state,B: set_Pr795498619_state] :
% 0.20/0.54 ( ~ ( member1389040324_state @ A @ A2 )
% 0.20/0.54 => ( ~ ( member1389040324_state @ B2 @ B )
% 0.20/0.54 => ( ( ( insert311944171_state @ A @ A2 )
% 0.20/0.54 = ( insert311944171_state @ B2 @ B ) )
% 0.20/0.54 = ( ( ( A = B2 )
% 0.20/0.54 => ( A2 = B ) )
% 0.20/0.54 & ( ( A != B2 )
% 0.20/0.54 => ? [C3: set_Pr795498619_state] :
% 0.20/0.54 ( ( A2
% 0.20/0.54 = ( insert311944171_state @ B2 @ C3 ) )
% 0.20/0.54 & ~ ( member1389040324_state @ B2 @ C3 )
% 0.20/0.54 & ( B
% 0.20/0.54 = ( insert311944171_state @ A @ C3 ) )
% 0.20/0.54 & ~ ( member1389040324_state @ A @ C3 ) ) ) ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % insert_eq_iff
% 0.20/0.54 thf(fact_57_insert__eq__iff,axiom,
% 0.20/0.54 ! [A: product_prod_nat_nat,A2: set_Pr1986765409at_nat,B2: product_prod_nat_nat,B: set_Pr1986765409at_nat] :
% 0.20/0.54 ( ~ ( member701585322at_nat @ A @ A2 )
% 0.20/0.54 => ( ~ ( member701585322at_nat @ B2 @ B )
% 0.20/0.54 => ( ( ( insert271595217at_nat @ A @ A2 )
% 0.20/0.54 = ( insert271595217at_nat @ B2 @ B ) )
% 0.20/0.54 = ( ( ( A = B2 )
% 0.20/0.54 => ( A2 = B ) )
% 0.20/0.54 & ( ( A != B2 )
% 0.20/0.54 => ? [C3: set_Pr1986765409at_nat] :
% 0.20/0.54 ( ( A2
% 0.20/0.54 = ( insert271595217at_nat @ B2 @ C3 ) )
% 0.20/0.54 & ~ ( member701585322at_nat @ B2 @ C3 )
% 0.20/0.54 & ( B
% 0.20/0.54 = ( insert271595217at_nat @ A @ C3 ) )
% 0.20/0.54 & ~ ( member701585322at_nat @ A @ C3 ) ) ) ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % insert_eq_iff
% 0.20/0.54 thf(fact_58_insert__eq__iff,axiom,
% 0.20/0.54 ! [A: produc696469763tate_o,A2: set_Pr1590995257tate_o,B2: produc696469763tate_o,B: set_Pr1590995257tate_o] :
% 0.20/0.54 ( ~ ( member1838112666tate_o @ A @ A2 )
% 0.20/0.54 => ( ~ ( member1838112666tate_o @ B2 @ B )
% 0.20/0.54 => ( ( ( insert2053719859tate_o @ A @ A2 )
% 0.20/0.54 = ( insert2053719859tate_o @ B2 @ B ) )
% 0.20/0.54 = ( ( ( A = B2 )
% 0.20/0.54 => ( A2 = B ) )
% 0.20/0.54 & ( ( A != B2 )
% 0.20/0.54 => ? [C3: set_Pr1590995257tate_o] :
% 0.20/0.54 ( ( A2
% 0.20/0.54 = ( insert2053719859tate_o @ B2 @ C3 ) )
% 0.20/0.54 & ~ ( member1838112666tate_o @ B2 @ C3 )
% 0.20/0.54 & ( B
% 0.20/0.54 = ( insert2053719859tate_o @ A @ C3 ) )
% 0.20/0.54 & ~ ( member1838112666tate_o @ A @ C3 ) ) ) ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % insert_eq_iff
% 0.20/0.54 thf(fact_59_insert__absorb,axiom,
% 0.20/0.54 ! [A: produc1115495963_state,A2: set_Pr795498619_state] :
% 0.20/0.54 ( ( member1389040324_state @ A @ A2 )
% 0.20/0.54 => ( ( insert311944171_state @ A @ A2 )
% 0.20/0.54 = A2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % insert_absorb
% 0.20/0.54 thf(fact_60_insert__absorb,axiom,
% 0.20/0.54 ! [A: product_prod_nat_nat,A2: set_Pr1986765409at_nat] :
% 0.20/0.54 ( ( member701585322at_nat @ A @ A2 )
% 0.20/0.54 => ( ( insert271595217at_nat @ A @ A2 )
% 0.20/0.54 = A2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % insert_absorb
% 0.20/0.54 thf(fact_61_insert__absorb,axiom,
% 0.20/0.54 ! [A: produc696469763tate_o,A2: set_Pr1590995257tate_o] :
% 0.20/0.54 ( ( member1838112666tate_o @ A @ A2 )
% 0.20/0.54 => ( ( insert2053719859tate_o @ A @ A2 )
% 0.20/0.54 = A2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % insert_absorb
% 0.20/0.54 thf(fact_62_insert__ident,axiom,
% 0.20/0.54 ! [X2: produc1115495963_state,A2: set_Pr795498619_state,B: set_Pr795498619_state] :
% 0.20/0.54 ( ~ ( member1389040324_state @ X2 @ A2 )
% 0.20/0.54 => ( ~ ( member1389040324_state @ X2 @ B )
% 0.20/0.54 => ( ( ( insert311944171_state @ X2 @ A2 )
% 0.20/0.54 = ( insert311944171_state @ X2 @ B ) )
% 0.20/0.54 = ( A2 = B ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % insert_ident
% 0.20/0.54 thf(fact_63_insert__ident,axiom,
% 0.20/0.54 ! [X2: product_prod_nat_nat,A2: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.20/0.54 ( ~ ( member701585322at_nat @ X2 @ A2 )
% 0.20/0.54 => ( ~ ( member701585322at_nat @ X2 @ B )
% 0.20/0.54 => ( ( ( insert271595217at_nat @ X2 @ A2 )
% 0.20/0.54 = ( insert271595217at_nat @ X2 @ B ) )
% 0.20/0.54 = ( A2 = B ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % insert_ident
% 0.20/0.54 thf(fact_64_insert__ident,axiom,
% 0.20/0.54 ! [X2: produc696469763tate_o,A2: set_Pr1590995257tate_o,B: set_Pr1590995257tate_o] :
% 0.20/0.54 ( ~ ( member1838112666tate_o @ X2 @ A2 )
% 0.20/0.54 => ( ~ ( member1838112666tate_o @ X2 @ B )
% 0.20/0.54 => ( ( ( insert2053719859tate_o @ X2 @ A2 )
% 0.20/0.54 = ( insert2053719859tate_o @ X2 @ B ) )
% 0.20/0.54 = ( A2 = B ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % insert_ident
% 0.20/0.54 thf(fact_65_Set_Oset__insert,axiom,
% 0.20/0.54 ! [X2: produc1115495963_state,A2: set_Pr795498619_state] :
% 0.20/0.54 ( ( member1389040324_state @ X2 @ A2 )
% 0.20/0.54 => ~ ! [B3: set_Pr795498619_state] :
% 0.20/0.54 ( ( A2
% 0.20/0.54 = ( insert311944171_state @ X2 @ B3 ) )
% 0.20/0.54 => ( member1389040324_state @ X2 @ B3 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % Set.set_insert
% 0.20/0.54 thf(fact_66_Set_Oset__insert,axiom,
% 0.20/0.54 ! [X2: product_prod_nat_nat,A2: set_Pr1986765409at_nat] :
% 0.20/0.54 ( ( member701585322at_nat @ X2 @ A2 )
% 0.20/0.54 => ~ ! [B3: set_Pr1986765409at_nat] :
% 0.20/0.54 ( ( A2
% 0.20/0.54 = ( insert271595217at_nat @ X2 @ B3 ) )
% 0.20/0.54 => ( member701585322at_nat @ X2 @ B3 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % Set.set_insert
% 0.20/0.54 thf(fact_67_Set_Oset__insert,axiom,
% 0.20/0.54 ! [X2: produc696469763tate_o,A2: set_Pr1590995257tate_o] :
% 0.20/0.54 ( ( member1838112666tate_o @ X2 @ A2 )
% 0.20/0.54 => ~ ! [B3: set_Pr1590995257tate_o] :
% 0.20/0.54 ( ( A2
% 0.20/0.54 = ( insert2053719859tate_o @ X2 @ B3 ) )
% 0.20/0.54 => ( member1838112666tate_o @ X2 @ B3 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % Set.set_insert
% 0.20/0.54 thf(fact_68_insertI2,axiom,
% 0.20/0.54 ! [A: produc1115495963_state,B: set_Pr795498619_state,B2: produc1115495963_state] :
% 0.20/0.54 ( ( member1389040324_state @ A @ B )
% 0.20/0.54 => ( member1389040324_state @ A @ ( insert311944171_state @ B2 @ B ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % insertI2
% 0.20/0.54 thf(fact_69_insertI2,axiom,
% 0.20/0.54 ! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat,B2: product_prod_nat_nat] :
% 0.20/0.54 ( ( member701585322at_nat @ A @ B )
% 0.20/0.54 => ( member701585322at_nat @ A @ ( insert271595217at_nat @ B2 @ B ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % insertI2
% 0.20/0.54 thf(fact_70_insertI2,axiom,
% 0.20/0.54 ! [A: produc696469763tate_o,B: set_Pr1590995257tate_o,B2: produc696469763tate_o] :
% 0.20/0.54 ( ( member1838112666tate_o @ A @ B )
% 0.20/0.54 => ( member1838112666tate_o @ A @ ( insert2053719859tate_o @ B2 @ B ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % insertI2
% 0.20/0.54 thf(fact_71_insertI1,axiom,
% 0.20/0.54 ! [A: produc1115495963_state,B: set_Pr795498619_state] : ( member1389040324_state @ A @ ( insert311944171_state @ A @ B ) ) ).
% 0.20/0.54
% 0.20/0.54 % insertI1
% 0.20/0.54 thf(fact_72_insertI1,axiom,
% 0.20/0.54 ! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat] : ( member701585322at_nat @ A @ ( insert271595217at_nat @ A @ B ) ) ).
% 0.20/0.54
% 0.20/0.54 % insertI1
% 0.20/0.54 thf(fact_73_insertI1,axiom,
% 0.20/0.54 ! [A: produc696469763tate_o,B: set_Pr1590995257tate_o] : ( member1838112666tate_o @ A @ ( insert2053719859tate_o @ A @ B ) ) ).
% 0.20/0.54
% 0.20/0.54 % insertI1
% 0.20/0.54 thf(fact_74_insertE,axiom,
% 0.20/0.54 ! [A: produc1115495963_state,B2: produc1115495963_state,A2: set_Pr795498619_state] :
% 0.20/0.54 ( ( member1389040324_state @ A @ ( insert311944171_state @ B2 @ A2 ) )
% 0.20/0.54 => ( ( A != B2 )
% 0.20/0.54 => ( member1389040324_state @ A @ A2 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % insertE
% 0.20/0.54 thf(fact_75_insertE,axiom,
% 0.20/0.54 ! [A: product_prod_nat_nat,B2: product_prod_nat_nat,A2: set_Pr1986765409at_nat] :
% 0.20/0.54 ( ( member701585322at_nat @ A @ ( insert271595217at_nat @ B2 @ A2 ) )
% 0.20/0.54 => ( ( A != B2 )
% 0.20/0.54 => ( member701585322at_nat @ A @ A2 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % insertE
% 0.20/0.54 thf(fact_76_insertE,axiom,
% 0.20/0.54 ! [A: produc696469763tate_o,B2: produc696469763tate_o,A2: set_Pr1590995257tate_o] :
% 0.20/0.54 ( ( member1838112666tate_o @ A @ ( insert2053719859tate_o @ B2 @ A2 ) )
% 0.20/0.54 => ( ( A != B2 )
% 0.20/0.54 => ( member1838112666tate_o @ A @ A2 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % insertE
% 0.20/0.54 thf(fact_77_empty__def,axiom,
% 0.20/0.54 ( bot_bo170732493tate_o
% 0.20/0.54 = ( collec1499596504tate_o
% 0.20/0.54 @ ^ [X: produc696469763tate_o] : $false ) ) ).
% 0.20/0.54
% 0.20/0.54 % empty_def
% 0.20/0.54 thf(fact_78_empty__def,axiom,
% 0.20/0.54 ( bot_bo2130386637at_nat
% 0.20/0.54 = ( collec7649004at_nat
% 0.20/0.54 @ ^ [X: product_prod_nat_nat] : $false ) ) ).
% 0.20/0.54
% 0.20/0.54 % empty_def
% 0.20/0.54 thf(fact_79_empty__def,axiom,
% 0.20/0.54 ( bot_bo1625160935_state
% 0.20/0.54 = ( collec496201222_state
% 0.20/0.54 @ ^ [X: produc1115495963_state] : $false ) ) ).
% 0.20/0.54
% 0.20/0.54 % empty_def
% 0.20/0.54 thf(fact_80_insert__Collect,axiom,
% 0.20/0.54 ! [A: produc1115495963_state,P: produc1115495963_state > $o] :
% 0.20/0.54 ( ( insert311944171_state @ A @ ( collec496201222_state @ P ) )
% 0.20/0.54 = ( collec496201222_state
% 0.20/0.54 @ ^ [U: produc1115495963_state] :
% 0.20/0.54 ( ( U != A )
% 0.20/0.54 => ( P @ U ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % insert_Collect
% 0.20/0.54 thf(fact_81_insert__Collect,axiom,
% 0.20/0.54 ! [A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 0.20/0.54 ( ( insert271595217at_nat @ A @ ( collec7649004at_nat @ P ) )
% 0.20/0.54 = ( collec7649004at_nat
% 0.20/0.54 @ ^ [U: product_prod_nat_nat] :
% 0.20/0.54 ( ( U != A )
% 0.20/0.54 => ( P @ U ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % insert_Collect
% 0.20/0.54 thf(fact_82_insert__Collect,axiom,
% 0.20/0.54 ! [A: produc696469763tate_o,P: produc696469763tate_o > $o] :
% 0.20/0.54 ( ( insert2053719859tate_o @ A @ ( collec1499596504tate_o @ P ) )
% 0.20/0.54 = ( collec1499596504tate_o
% 0.20/0.54 @ ^ [U: produc696469763tate_o] :
% 0.20/0.54 ( ( U != A )
% 0.20/0.54 => ( P @ U ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % insert_Collect
% 0.20/0.54 thf(fact_83_insert__compr,axiom,
% 0.20/0.54 ( insert311944171_state
% 0.20/0.54 = ( ^ [A3: produc1115495963_state,B4: set_Pr795498619_state] :
% 0.20/0.54 ( collec496201222_state
% 0.20/0.54 @ ^ [X: produc1115495963_state] :
% 0.20/0.54 ( ( X = A3 )
% 0.20/0.54 | ( member1389040324_state @ X @ B4 ) ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % insert_compr
% 0.20/0.54 thf(fact_84_insert__compr,axiom,
% 0.20/0.54 ( insert271595217at_nat
% 0.20/0.54 = ( ^ [A3: product_prod_nat_nat,B4: set_Pr1986765409at_nat] :
% 0.20/0.54 ( collec7649004at_nat
% 0.20/0.54 @ ^ [X: product_prod_nat_nat] :
% 0.20/0.54 ( ( X = A3 )
% 0.20/0.54 | ( member701585322at_nat @ X @ B4 ) ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % insert_compr
% 0.20/0.54 thf(fact_85_insert__compr,axiom,
% 0.20/0.54 ( insert2053719859tate_o
% 0.20/0.54 = ( ^ [A3: produc696469763tate_o,B4: set_Pr1590995257tate_o] :
% 0.20/0.54 ( collec1499596504tate_o
% 0.20/0.54 @ ^ [X: produc696469763tate_o] :
% 0.20/0.54 ( ( X = A3 )
% 0.20/0.54 | ( member1838112666tate_o @ X @ B4 ) ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % insert_compr
% 0.20/0.54 thf(fact_86_singleton__inject,axiom,
% 0.20/0.54 ! [A: produc696469763tate_o,B2: produc696469763tate_o] :
% 0.20/0.54 ( ( ( insert2053719859tate_o @ A @ bot_bo170732493tate_o )
% 0.20/0.54 = ( insert2053719859tate_o @ B2 @ bot_bo170732493tate_o ) )
% 0.20/0.54 => ( A = B2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % singleton_inject
% 0.20/0.54 thf(fact_87_singleton__inject,axiom,
% 0.20/0.54 ! [A: product_prod_nat_nat,B2: product_prod_nat_nat] :
% 0.20/0.54 ( ( ( insert271595217at_nat @ A @ bot_bo2130386637at_nat )
% 0.20/0.54 = ( insert271595217at_nat @ B2 @ bot_bo2130386637at_nat ) )
% 0.20/0.54 => ( A = B2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % singleton_inject
% 0.20/0.54 thf(fact_88_singleton__inject,axiom,
% 0.20/0.54 ! [A: produc1115495963_state,B2: produc1115495963_state] :
% 0.20/0.54 ( ( ( insert311944171_state @ A @ bot_bo1625160935_state )
% 0.20/0.54 = ( insert311944171_state @ B2 @ bot_bo1625160935_state ) )
% 0.20/0.54 => ( A = B2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % singleton_inject
% 0.20/0.54 thf(fact_89_insert__not__empty,axiom,
% 0.20/0.54 ! [A: produc696469763tate_o,A2: set_Pr1590995257tate_o] :
% 0.20/0.54 ( ( insert2053719859tate_o @ A @ A2 )
% 0.20/0.54 != bot_bo170732493tate_o ) ).
% 0.20/0.54
% 0.20/0.54 % insert_not_empty
% 0.20/0.54 thf(fact_90_insert__not__empty,axiom,
% 0.20/0.54 ! [A: product_prod_nat_nat,A2: set_Pr1986765409at_nat] :
% 0.20/0.54 ( ( insert271595217at_nat @ A @ A2 )
% 0.20/0.54 != bot_bo2130386637at_nat ) ).
% 0.20/0.54
% 0.20/0.54 % insert_not_empty
% 0.20/0.54 thf(fact_91_insert__not__empty,axiom,
% 0.20/0.54 ! [A: produc1115495963_state,A2: set_Pr795498619_state] :
% 0.20/0.54 ( ( insert311944171_state @ A @ A2 )
% 0.20/0.54 != bot_bo1625160935_state ) ).
% 0.20/0.54
% 0.20/0.54 % insert_not_empty
% 0.20/0.54 thf(fact_92_doubleton__eq__iff,axiom,
% 0.20/0.54 ! [A: produc696469763tate_o,B2: produc696469763tate_o,C2: produc696469763tate_o,D: produc696469763tate_o] :
% 0.20/0.54 ( ( ( insert2053719859tate_o @ A @ ( insert2053719859tate_o @ B2 @ bot_bo170732493tate_o ) )
% 0.20/0.54 = ( insert2053719859tate_o @ C2 @ ( insert2053719859tate_o @ D @ bot_bo170732493tate_o ) ) )
% 0.20/0.54 = ( ( ( A = C2 )
% 0.20/0.54 & ( B2 = D ) )
% 0.20/0.54 | ( ( A = D )
% 0.20/0.54 & ( B2 = C2 ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % doubleton_eq_iff
% 0.20/0.54 thf(fact_93_doubleton__eq__iff,axiom,
% 0.20/0.54 ! [A: product_prod_nat_nat,B2: product_prod_nat_nat,C2: product_prod_nat_nat,D: product_prod_nat_nat] :
% 0.20/0.54 ( ( ( insert271595217at_nat @ A @ ( insert271595217at_nat @ B2 @ bot_bo2130386637at_nat ) )
% 0.20/0.54 = ( insert271595217at_nat @ C2 @ ( insert271595217at_nat @ D @ bot_bo2130386637at_nat ) ) )
% 0.20/0.54 = ( ( ( A = C2 )
% 0.20/0.54 & ( B2 = D ) )
% 0.20/0.54 | ( ( A = D )
% 0.20/0.54 & ( B2 = C2 ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % doubleton_eq_iff
% 0.20/0.54 thf(fact_94_doubleton__eq__iff,axiom,
% 0.20/0.54 ! [A: produc1115495963_state,B2: produc1115495963_state,C2: produc1115495963_state,D: produc1115495963_state] :
% 0.20/0.54 ( ( ( insert311944171_state @ A @ ( insert311944171_state @ B2 @ bot_bo1625160935_state ) )
% 0.20/0.54 = ( insert311944171_state @ C2 @ ( insert311944171_state @ D @ bot_bo1625160935_state ) ) )
% 0.20/0.54 = ( ( ( A = C2 )
% 0.20/0.54 & ( B2 = D ) )
% 0.20/0.54 | ( ( A = D )
% 0.20/0.54 & ( B2 = C2 ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % doubleton_eq_iff
% 0.20/0.54 thf(fact_95_singleton__iff,axiom,
% 0.20/0.54 ! [B2: produc696469763tate_o,A: produc696469763tate_o] :
% 0.20/0.54 ( ( member1838112666tate_o @ B2 @ ( insert2053719859tate_o @ A @ bot_bo170732493tate_o ) )
% 0.20/0.54 = ( B2 = A ) ) ).
% 0.20/0.54
% 0.20/0.54 % singleton_iff
% 0.20/0.54 thf(fact_96_singleton__iff,axiom,
% 0.20/0.54 ! [B2: product_prod_nat_nat,A: product_prod_nat_nat] :
% 0.20/0.54 ( ( member701585322at_nat @ B2 @ ( insert271595217at_nat @ A @ bot_bo2130386637at_nat ) )
% 0.20/0.54 = ( B2 = A ) ) ).
% 0.20/0.54
% 0.20/0.54 % singleton_iff
% 0.20/0.54 thf(fact_97_singleton__iff,axiom,
% 0.20/0.54 ! [B2: produc1115495963_state,A: produc1115495963_state] :
% 0.20/0.54 ( ( member1389040324_state @ B2 @ ( insert311944171_state @ A @ bot_bo1625160935_state ) )
% 0.20/0.54 = ( B2 = A ) ) ).
% 0.20/0.54
% 0.20/0.54 % singleton_iff
% 0.20/0.54 thf(fact_98_singletonD,axiom,
% 0.20/0.54 ! [B2: produc696469763tate_o,A: produc696469763tate_o] :
% 0.20/0.54 ( ( member1838112666tate_o @ B2 @ ( insert2053719859tate_o @ A @ bot_bo170732493tate_o ) )
% 0.20/0.54 => ( B2 = A ) ) ).
% 0.20/0.54
% 0.20/0.54 % singletonD
% 0.20/0.54 thf(fact_99_singletonD,axiom,
% 0.20/0.54 ! [B2: product_prod_nat_nat,A: product_prod_nat_nat] :
% 0.20/0.54 ( ( member701585322at_nat @ B2 @ ( insert271595217at_nat @ A @ bot_bo2130386637at_nat ) )
% 0.20/0.54 => ( B2 = A ) ) ).
% 0.20/0.54
% 0.20/0.54 % singletonD
% 0.20/0.54 thf(fact_100_singletonD,axiom,
% 0.20/0.54 ! [B2: produc1115495963_state,A: produc1115495963_state] :
% 0.20/0.54 ( ( member1389040324_state @ B2 @ ( insert311944171_state @ A @ bot_bo1625160935_state ) )
% 0.20/0.54 => ( B2 = A ) ) ).
% 0.20/0.54
% 0.20/0.54 % singletonD
% 0.20/0.54 thf(fact_101_hoare_OAsm,axiom,
% 0.20/0.54 ! [P: a > state > $o,Q: a > state > $o] : ( hoare_a @ ( insert2053719859tate_o @ ( produc33908149tate_o @ P @ ( produc1948644831tate_o @ call @ Q ) ) @ bot_bo170732493tate_o ) @ P @ call @ Q ) ).
% 0.20/0.54
% 0.20/0.54 % hoare.Asm
% 0.20/0.54 thf(fact_102_Collect__conv__if2,axiom,
% 0.20/0.54 ! [P: produc696469763tate_o > $o,A: produc696469763tate_o] :
% 0.20/0.54 ( ( ( P @ A )
% 0.20/0.54 => ( ( collec1499596504tate_o
% 0.20/0.54 @ ^ [X: produc696469763tate_o] :
% 0.20/0.54 ( ( A = X )
% 0.20/0.54 & ( P @ X ) ) )
% 0.20/0.54 = ( insert2053719859tate_o @ A @ bot_bo170732493tate_o ) ) )
% 0.20/0.54 & ( ~ ( P @ A )
% 0.20/0.54 => ( ( collec1499596504tate_o
% 0.20/0.54 @ ^ [X: produc696469763tate_o] :
% 0.20/0.54 ( ( A = X )
% 0.20/0.54 & ( P @ X ) ) )
% 0.20/0.54 = bot_bo170732493tate_o ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % Collect_conv_if2
% 0.20/0.54 thf(fact_103_Collect__conv__if2,axiom,
% 0.20/0.54 ! [P: product_prod_nat_nat > $o,A: product_prod_nat_nat] :
% 0.20/0.54 ( ( ( P @ A )
% 0.20/0.54 => ( ( collec7649004at_nat
% 0.20/0.54 @ ^ [X: product_prod_nat_nat] :
% 0.20/0.54 ( ( A = X )
% 0.20/0.54 & ( P @ X ) ) )
% 0.20/0.54 = ( insert271595217at_nat @ A @ bot_bo2130386637at_nat ) ) )
% 0.20/0.54 & ( ~ ( P @ A )
% 0.20/0.54 => ( ( collec7649004at_nat
% 0.20/0.54 @ ^ [X: product_prod_nat_nat] :
% 0.20/0.54 ( ( A = X )
% 0.20/0.54 & ( P @ X ) ) )
% 0.20/0.54 = bot_bo2130386637at_nat ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % Collect_conv_if2
% 0.20/0.54 thf(fact_104_Collect__conv__if2,axiom,
% 0.20/0.54 ! [P: produc1115495963_state > $o,A: produc1115495963_state] :
% 0.20/0.54 ( ( ( P @ A )
% 0.20/0.54 => ( ( collec496201222_state
% 0.20/0.54 @ ^ [X: produc1115495963_state] :
% 0.20/0.54 ( ( A = X )
% 0.20/0.54 & ( P @ X ) ) )
% 0.20/0.54 = ( insert311944171_state @ A @ bot_bo1625160935_state ) ) )
% 0.20/0.54 & ( ~ ( P @ A )
% 0.20/0.54 => ( ( collec496201222_state
% 0.20/0.54 @ ^ [X: produc1115495963_state] :
% 0.20/0.54 ( ( A = X )
% 0.20/0.54 & ( P @ X ) ) )
% 0.20/0.54 = bot_bo1625160935_state ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % Collect_conv_if2
% 0.20/0.54 thf(fact_105_Collect__conv__if,axiom,
% 0.20/0.54 ! [P: produc696469763tate_o > $o,A: produc696469763tate_o] :
% 0.20/0.54 ( ( ( P @ A )
% 0.20/0.54 => ( ( collec1499596504tate_o
% 0.20/0.54 @ ^ [X: produc696469763tate_o] :
% 0.20/0.54 ( ( X = A )
% 0.20/0.54 & ( P @ X ) ) )
% 0.20/0.54 = ( insert2053719859tate_o @ A @ bot_bo170732493tate_o ) ) )
% 0.20/0.54 & ( ~ ( P @ A )
% 0.20/0.54 => ( ( collec1499596504tate_o
% 0.20/0.54 @ ^ [X: produc696469763tate_o] :
% 0.20/0.54 ( ( X = A )
% 0.20/0.54 & ( P @ X ) ) )
% 0.20/0.54 = bot_bo170732493tate_o ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % Collect_conv_if
% 0.20/0.54 thf(fact_106_Collect__conv__if,axiom,
% 0.20/0.54 ! [P: product_prod_nat_nat > $o,A: product_prod_nat_nat] :
% 0.20/0.54 ( ( ( P @ A )
% 0.20/0.54 => ( ( collec7649004at_nat
% 0.20/0.54 @ ^ [X: product_prod_nat_nat] :
% 0.20/0.54 ( ( X = A )
% 0.20/0.54 & ( P @ X ) ) )
% 0.20/0.54 = ( insert271595217at_nat @ A @ bot_bo2130386637at_nat ) ) )
% 0.20/0.54 & ( ~ ( P @ A )
% 0.20/0.54 => ( ( collec7649004at_nat
% 0.20/0.54 @ ^ [X: product_prod_nat_nat] :
% 0.20/0.54 ( ( X = A )
% 0.20/0.54 & ( P @ X ) ) )
% 0.20/0.54 = bot_bo2130386637at_nat ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % Collect_conv_if
% 0.20/0.54 thf(fact_107_Collect__conv__if,axiom,
% 0.20/0.54 ! [P: produc1115495963_state > $o,A: produc1115495963_state] :
% 0.20/0.54 ( ( ( P @ A )
% 0.20/0.54 => ( ( collec496201222_state
% 0.20/0.54 @ ^ [X: produc1115495963_state] :
% 0.20/0.54 ( ( X = A )
% 0.20/0.54 & ( P @ X ) ) )
% 0.20/0.54 = ( insert311944171_state @ A @ bot_bo1625160935_state ) ) )
% 0.20/0.54 & ( ~ ( P @ A )
% 0.20/0.54 => ( ( collec496201222_state
% 0.20/0.54 @ ^ [X: produc1115495963_state] :
% 0.20/0.54 ( ( X = A )
% 0.20/0.54 & ( P @ X ) ) )
% 0.20/0.54 = bot_bo1625160935_state ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % Collect_conv_if
% 0.20/0.54 thf(fact_108_wf__empty,axiom,
% 0.20/0.54 wf_nat @ bot_bo2130386637at_nat ).
% 0.20/0.54
% 0.20/0.54 % wf_empty
% 0.20/0.54 thf(fact_109_wf__empty,axiom,
% 0.20/0.54 wf_state @ bot_bo1625160935_state ).
% 0.20/0.54
% 0.20/0.54 % wf_empty
% 0.20/0.54 thf(fact_110_mem__Collect__eq,axiom,
% 0.20/0.54 ! [A: produc1115495963_state,P: produc1115495963_state > $o] :
% 0.20/0.54 ( ( member1389040324_state @ A @ ( collec496201222_state @ P ) )
% 0.20/0.54 = ( P @ A ) ) ).
% 0.20/0.54
% 0.20/0.54 % mem_Collect_eq
% 0.20/0.54 thf(fact_111_mem__Collect__eq,axiom,
% 0.20/0.54 ! [A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 0.20/0.54 ( ( member701585322at_nat @ A @ ( collec7649004at_nat @ P ) )
% 0.20/0.54 = ( P @ A ) ) ).
% 0.20/0.54
% 0.20/0.54 % mem_Collect_eq
% 0.20/0.54 thf(fact_112_mem__Collect__eq,axiom,
% 0.20/0.54 ! [A: produc696469763tate_o,P: produc696469763tate_o > $o] :
% 0.20/0.54 ( ( member1838112666tate_o @ A @ ( collec1499596504tate_o @ P ) )
% 0.20/0.54 = ( P @ A ) ) ).
% 0.20/0.54
% 0.20/0.54 % mem_Collect_eq
% 0.20/0.54 thf(fact_113_Collect__mem__eq,axiom,
% 0.20/0.54 ! [A2: set_Pr795498619_state] :
% 0.20/0.54 ( ( collec496201222_state
% 0.20/0.54 @ ^ [X: produc1115495963_state] : ( member1389040324_state @ X @ A2 ) )
% 0.20/0.54 = A2 ) ).
% 0.20/0.54
% 0.20/0.54 % Collect_mem_eq
% 0.20/0.54 thf(fact_114_Collect__mem__eq,axiom,
% 0.20/0.54 ! [A2: set_Pr1986765409at_nat] :
% 0.20/0.54 ( ( collec7649004at_nat
% 0.20/0.54 @ ^ [X: product_prod_nat_nat] : ( member701585322at_nat @ X @ A2 ) )
% 0.20/0.54 = A2 ) ).
% 0.20/0.54
% 0.20/0.54 % Collect_mem_eq
% 0.20/0.54 thf(fact_115_Collect__mem__eq,axiom,
% 0.20/0.54 ! [A2: set_Pr1590995257tate_o] :
% 0.20/0.54 ( ( collec1499596504tate_o
% 0.20/0.54 @ ^ [X: produc696469763tate_o] : ( member1838112666tate_o @ X @ A2 ) )
% 0.20/0.54 = A2 ) ).
% 0.20/0.54
% 0.20/0.54 % Collect_mem_eq
% 0.20/0.54 thf(fact_116_Collect__cong,axiom,
% 0.20/0.54 ! [P: produc1115495963_state > $o,Q: produc1115495963_state > $o] :
% 0.20/0.54 ( ! [X3: produc1115495963_state] :
% 0.20/0.54 ( ( P @ X3 )
% 0.20/0.54 = ( Q @ X3 ) )
% 0.20/0.54 => ( ( collec496201222_state @ P )
% 0.20/0.54 = ( collec496201222_state @ Q ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % Collect_cong
% 0.20/0.54 thf(fact_117_Collect__cong,axiom,
% 0.20/0.54 ! [P: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 0.20/0.54 ( ! [X3: product_prod_nat_nat] :
% 0.20/0.54 ( ( P @ X3 )
% 0.20/0.54 = ( Q @ X3 ) )
% 0.20/0.54 => ( ( collec7649004at_nat @ P )
% 0.20/0.54 = ( collec7649004at_nat @ Q ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % Collect_cong
% 0.20/0.54 thf(fact_118_Collect__cong,axiom,
% 0.20/0.54 ! [P: produc696469763tate_o > $o,Q: produc696469763tate_o > $o] :
% 0.20/0.54 ( ! [X3: produc696469763tate_o] :
% 0.20/0.54 ( ( P @ X3 )
% 0.20/0.54 = ( Q @ X3 ) )
% 0.20/0.54 => ( ( collec1499596504tate_o @ P )
% 0.20/0.54 = ( collec1499596504tate_o @ Q ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % Collect_cong
% 0.20/0.54 thf(fact_119_wfE__min_H,axiom,
% 0.20/0.54 ! [R2: set_Pr795498619_state,Q: set_state] :
% 0.20/0.54 ( ( wf_state @ R2 )
% 0.20/0.54 => ( ( Q != bot_bot_set_state )
% 0.20/0.54 => ~ ! [Z: state] :
% 0.20/0.54 ( ( member_state @ Z @ Q )
% 0.20/0.54 => ~ ! [Y4: state] :
% 0.20/0.54 ( ( member1389040324_state @ ( produc64584659_state @ Y4 @ Z ) @ R2 )
% 0.20/0.54 => ~ ( member_state @ Y4 @ Q ) ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % wfE_min'
% 0.20/0.54 thf(fact_120_wfE__min_H,axiom,
% 0.20/0.54 ! [R2: set_Pr1986765409at_nat,Q: set_nat] :
% 0.20/0.54 ( ( wf_nat @ R2 )
% 0.20/0.54 => ( ( Q != bot_bot_set_nat )
% 0.20/0.54 => ~ ! [Z: nat] :
% 0.20/0.54 ( ( member_nat @ Z @ Q )
% 0.20/0.54 => ~ ! [Y4: nat] :
% 0.20/0.54 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Y4 @ Z ) @ R2 )
% 0.20/0.54 => ~ ( member_nat @ Y4 @ Q ) ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % wfE_min'
% 0.20/0.54 thf(fact_121_wfE__min_H,axiom,
% 0.20/0.54 ! [R2: set_Pr1702239303tate_o,Q: set_Pr1590995257tate_o] :
% 0.20/0.54 ( ( wf_Pro309705690tate_o @ R2 )
% 0.20/0.54 => ( ( Q != bot_bo170732493tate_o )
% 0.20/0.54 => ~ ! [Z: produc696469763tate_o] :
% 0.20/0.54 ( ( member1838112666tate_o @ Z @ Q )
% 0.20/0.54 => ~ ! [Y4: produc696469763tate_o] :
% 0.20/0.54 ( ( member1629320336tate_o @ ( produc1684562079tate_o @ Y4 @ Z ) @ R2 )
% 0.20/0.54 => ~ ( member1838112666tate_o @ Y4 @ Q ) ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % wfE_min'
% 0.20/0.54 thf(fact_122_wfE__min_H,axiom,
% 0.20/0.54 ! [R2: set_Pr1490359111at_nat,Q: set_Pr1986765409at_nat] :
% 0.20/0.54 ( ( wf_Pro745352042at_nat @ R2 )
% 0.20/0.54 => ( ( Q != bot_bo2130386637at_nat )
% 0.20/0.54 => ~ ! [Z: product_prod_nat_nat] :
% 0.20/0.54 ( ( member701585322at_nat @ Z @ Q )
% 0.20/0.54 => ~ ! [Y4: product_prod_nat_nat] :
% 0.20/0.54 ( ( member2027625872at_nat @ ( produc1168807639at_nat @ Y4 @ Z ) @ R2 )
% 0.20/0.54 => ~ ( member701585322at_nat @ Y4 @ Q ) ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % wfE_min'
% 0.20/0.54 thf(fact_123_wfE__min_H,axiom,
% 0.20/0.54 ! [R2: set_Pr778812871_state,Q: set_Pr795498619_state] :
% 0.20/0.54 ( ( wf_Pro1783588484_state @ R2 )
% 0.20/0.54 => ( ( Q != bot_bo1625160935_state )
% 0.20/0.54 => ~ ! [Z: produc1115495963_state] :
% 0.20/0.54 ( ( member1389040324_state @ Z @ Q )
% 0.20/0.54 => ~ ! [Y4: produc1115495963_state] :
% 0.20/0.54 ( ( member768948240_state @ ( produc1964772951_state @ Y4 @ Z ) @ R2 )
% 0.20/0.54 => ~ ( member1389040324_state @ Y4 @ Q ) ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % wfE_min'
% 0.20/0.54 thf(fact_124_the__elem__eq,axiom,
% 0.20/0.54 ! [X2: produc696469763tate_o] :
% 0.20/0.54 ( ( the_el1569055182tate_o @ ( insert2053719859tate_o @ X2 @ bot_bo170732493tate_o ) )
% 0.20/0.54 = X2 ) ).
% 0.20/0.54
% 0.20/0.54 % the_elem_eq
% 0.20/0.54 thf(fact_125_the__elem__eq,axiom,
% 0.20/0.54 ! [X2: product_prod_nat_nat] :
% 0.20/0.54 ( ( the_el1949240438at_nat @ ( insert271595217at_nat @ X2 @ bot_bo2130386637at_nat ) )
% 0.20/0.54 = X2 ) ).
% 0.20/0.54
% 0.20/0.54 % the_elem_eq
% 0.20/0.54 thf(fact_126_the__elem__eq,axiom,
% 0.20/0.54 ! [X2: produc1115495963_state] :
% 0.20/0.54 ( ( the_el1967402896_state @ ( insert311944171_state @ X2 @ bot_bo1625160935_state ) )
% 0.20/0.54 = X2 ) ).
% 0.20/0.54
% 0.20/0.54 % the_elem_eq
% 0.20/0.54 thf(fact_127_old_Oprod_Oinject,axiom,
% 0.20/0.54 ! [A: a > state > $o,B2: produc204914599tate_o,A4: a > state > $o,B5: produc204914599tate_o] :
% 0.20/0.54 ( ( ( produc33908149tate_o @ A @ B2 )
% 0.20/0.54 = ( produc33908149tate_o @ A4 @ B5 ) )
% 0.20/0.54 = ( ( A = A4 )
% 0.20/0.54 & ( B2 = B5 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % old.prod.inject
% 0.20/0.54 thf(fact_128_old_Oprod_Oinject,axiom,
% 0.20/0.54 ! [A: state,B2: state,A4: state,B5: state] :
% 0.20/0.54 ( ( ( produc64584659_state @ A @ B2 )
% 0.20/0.54 = ( produc64584659_state @ A4 @ B5 ) )
% 0.20/0.54 = ( ( A = A4 )
% 0.20/0.54 & ( B2 = B5 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % old.prod.inject
% 0.20/0.54 thf(fact_129_old_Oprod_Oinject,axiom,
% 0.20/0.54 ! [A: com,B2: a > state > $o,A4: com,B5: a > state > $o] :
% 0.20/0.54 ( ( ( produc1948644831tate_o @ A @ B2 )
% 0.20/0.54 = ( produc1948644831tate_o @ A4 @ B5 ) )
% 0.20/0.54 = ( ( A = A4 )
% 0.20/0.54 & ( B2 = B5 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % old.prod.inject
% 0.20/0.54 thf(fact_130_old_Oprod_Oinject,axiom,
% 0.20/0.54 ! [A: nat,B2: nat,A4: nat,B5: nat] :
% 0.20/0.54 ( ( ( product_Pair_nat_nat @ A @ B2 )
% 0.20/0.54 = ( product_Pair_nat_nat @ A4 @ B5 ) )
% 0.20/0.54 = ( ( A = A4 )
% 0.20/0.54 & ( B2 = B5 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % old.prod.inject
% 0.20/0.54 thf(fact_131_prod_Oinject,axiom,
% 0.20/0.54 ! [X1: a > state > $o,X22: produc204914599tate_o,Y1: a > state > $o,Y22: produc204914599tate_o] :
% 0.20/0.54 ( ( ( produc33908149tate_o @ X1 @ X22 )
% 0.20/0.54 = ( produc33908149tate_o @ Y1 @ Y22 ) )
% 0.20/0.54 = ( ( X1 = Y1 )
% 0.20/0.54 & ( X22 = Y22 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % prod.inject
% 0.20/0.54 thf(fact_132_prod_Oinject,axiom,
% 0.20/0.54 ! [X1: state,X22: state,Y1: state,Y22: state] :
% 0.20/0.54 ( ( ( produc64584659_state @ X1 @ X22 )
% 0.20/0.54 = ( produc64584659_state @ Y1 @ Y22 ) )
% 0.20/0.54 = ( ( X1 = Y1 )
% 0.20/0.54 & ( X22 = Y22 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % prod.inject
% 0.20/0.54 thf(fact_133_prod_Oinject,axiom,
% 0.20/0.54 ! [X1: com,X22: a > state > $o,Y1: com,Y22: a > state > $o] :
% 0.20/0.54 ( ( ( produc1948644831tate_o @ X1 @ X22 )
% 0.20/0.54 = ( produc1948644831tate_o @ Y1 @ Y22 ) )
% 0.20/0.54 = ( ( X1 = Y1 )
% 0.20/0.54 & ( X22 = Y22 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % prod.inject
% 0.20/0.54 thf(fact_134_prod_Oinject,axiom,
% 0.20/0.54 ! [X1: nat,X22: nat,Y1: nat,Y22: nat] :
% 0.20/0.54 ( ( ( product_Pair_nat_nat @ X1 @ X22 )
% 0.20/0.54 = ( product_Pair_nat_nat @ Y1 @ Y22 ) )
% 0.20/0.54 = ( ( X1 = Y1 )
% 0.20/0.54 & ( X22 = Y22 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % prod.inject
% 0.20/0.54 thf(fact_135_is__singletonI,axiom,
% 0.20/0.54 ! [X2: produc696469763tate_o] : ( is_sin1547905295tate_o @ ( insert2053719859tate_o @ X2 @ bot_bo170732493tate_o ) ) ).
% 0.20/0.54
% 0.20/0.54 % is_singletonI
% 0.20/0.54 thf(fact_136_is__singletonI,axiom,
% 0.20/0.54 ! [X2: product_prod_nat_nat] : ( is_sin1352690165at_nat @ ( insert271595217at_nat @ X2 @ bot_bo2130386637at_nat ) ) ).
% 0.20/0.54
% 0.20/0.54 % is_singletonI
% 0.20/0.54 thf(fact_137_is__singletonI,axiom,
% 0.20/0.54 ! [X2: produc1115495963_state] : ( is_sin1132515087_state @ ( insert311944171_state @ X2 @ bot_bo1625160935_state ) ) ).
% 0.20/0.54
% 0.20/0.54 % is_singletonI
% 0.20/0.54 thf(fact_138_bot__set__def,axiom,
% 0.20/0.54 ( bot_bo170732493tate_o
% 0.20/0.54 = ( collec1499596504tate_o @ bot_bo250281208te_o_o ) ) ).
% 0.20/0.54
% 0.20/0.54 % bot_set_def
% 0.20/0.54 thf(fact_139_bot__set__def,axiom,
% 0.20/0.54 ( bot_bo2130386637at_nat
% 0.20/0.54 = ( collec7649004at_nat @ bot_bo513358416_nat_o ) ) ).
% 0.20/0.54
% 0.20/0.54 % bot_set_def
% 0.20/0.54 thf(fact_140_bot__set__def,axiom,
% 0.20/0.54 ( bot_bo1625160935_state
% 0.20/0.54 = ( collec496201222_state @ bot_bo446391478tate_o ) ) ).
% 0.20/0.54
% 0.20/0.54 % bot_set_def
% 0.20/0.54 thf(fact_141_is__singleton__the__elem,axiom,
% 0.20/0.54 ( is_sin1547905295tate_o
% 0.20/0.54 = ( ^ [A5: set_Pr1590995257tate_o] :
% 0.20/0.54 ( A5
% 0.20/0.54 = ( insert2053719859tate_o @ ( the_el1569055182tate_o @ A5 ) @ bot_bo170732493tate_o ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % is_singleton_the_elem
% 0.20/0.54 thf(fact_142_is__singleton__the__elem,axiom,
% 0.20/0.54 ( is_sin1352690165at_nat
% 0.20/0.54 = ( ^ [A5: set_Pr1986765409at_nat] :
% 0.20/0.54 ( A5
% 0.20/0.54 = ( insert271595217at_nat @ ( the_el1949240438at_nat @ A5 ) @ bot_bo2130386637at_nat ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % is_singleton_the_elem
% 0.20/0.54 thf(fact_143_is__singleton__the__elem,axiom,
% 0.20/0.54 ( is_sin1132515087_state
% 0.20/0.54 = ( ^ [A5: set_Pr795498619_state] :
% 0.20/0.54 ( A5
% 0.20/0.54 = ( insert311944171_state @ ( the_el1967402896_state @ A5 ) @ bot_bo1625160935_state ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % is_singleton_the_elem
% 0.20/0.54 thf(fact_144_is__singletonI_H,axiom,
% 0.20/0.54 ! [A2: set_Pr1590995257tate_o] :
% 0.20/0.54 ( ( A2 != bot_bo170732493tate_o )
% 0.20/0.54 => ( ! [X3: produc696469763tate_o,Y2: produc696469763tate_o] :
% 0.20/0.54 ( ( member1838112666tate_o @ X3 @ A2 )
% 0.20/0.54 => ( ( member1838112666tate_o @ Y2 @ A2 )
% 0.20/0.54 => ( X3 = Y2 ) ) )
% 0.20/0.54 => ( is_sin1547905295tate_o @ A2 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % is_singletonI'
% 0.20/0.54 thf(fact_145_is__singletonI_H,axiom,
% 0.20/0.54 ! [A2: set_Pr1986765409at_nat] :
% 0.20/0.54 ( ( A2 != bot_bo2130386637at_nat )
% 0.20/0.54 => ( ! [X3: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 0.20/0.54 ( ( member701585322at_nat @ X3 @ A2 )
% 0.20/0.54 => ( ( member701585322at_nat @ Y2 @ A2 )
% 0.20/0.54 => ( X3 = Y2 ) ) )
% 0.20/0.54 => ( is_sin1352690165at_nat @ A2 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % is_singletonI'
% 0.20/0.54 thf(fact_146_is__singletonI_H,axiom,
% 0.20/0.54 ! [A2: set_Pr795498619_state] :
% 0.20/0.54 ( ( A2 != bot_bo1625160935_state )
% 0.20/0.54 => ( ! [X3: produc1115495963_state,Y2: produc1115495963_state] :
% 0.20/0.54 ( ( member1389040324_state @ X3 @ A2 )
% 0.20/0.54 => ( ( member1389040324_state @ Y2 @ A2 )
% 0.20/0.54 => ( X3 = Y2 ) ) )
% 0.20/0.54 => ( is_sin1132515087_state @ A2 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % is_singletonI'
% 0.20/0.54 thf(fact_147_surj__pair,axiom,
% 0.20/0.54 ! [P3: produc696469763tate_o] :
% 0.20/0.54 ? [X3: a > state > $o,Y2: produc204914599tate_o] :
% 0.20/0.54 ( P3
% 0.20/0.54 = ( produc33908149tate_o @ X3 @ Y2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % surj_pair
% 0.20/0.54 thf(fact_148_surj__pair,axiom,
% 0.20/0.54 ! [P3: produc1115495963_state] :
% 0.20/0.54 ? [X3: state,Y2: state] :
% 0.20/0.54 ( P3
% 0.20/0.54 = ( produc64584659_state @ X3 @ Y2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % surj_pair
% 0.20/0.54 thf(fact_149_surj__pair,axiom,
% 0.20/0.54 ! [P3: produc204914599tate_o] :
% 0.20/0.54 ? [X3: com,Y2: a > state > $o] :
% 0.20/0.54 ( P3
% 0.20/0.54 = ( produc1948644831tate_o @ X3 @ Y2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % surj_pair
% 0.20/0.54 thf(fact_150_surj__pair,axiom,
% 0.20/0.54 ! [P3: product_prod_nat_nat] :
% 0.20/0.54 ? [X3: nat,Y2: nat] :
% 0.20/0.54 ( P3
% 0.20/0.54 = ( product_Pair_nat_nat @ X3 @ Y2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % surj_pair
% 0.20/0.54 thf(fact_151_prod__cases,axiom,
% 0.20/0.54 ! [P: produc696469763tate_o > $o,P3: produc696469763tate_o] :
% 0.20/0.54 ( ! [A6: a > state > $o,B6: produc204914599tate_o] : ( P @ ( produc33908149tate_o @ A6 @ B6 ) )
% 0.20/0.54 => ( P @ P3 ) ) ).
% 0.20/0.54
% 0.20/0.54 % prod_cases
% 0.20/0.54 thf(fact_152_prod__cases,axiom,
% 0.20/0.54 ! [P: produc1115495963_state > $o,P3: produc1115495963_state] :
% 0.20/0.54 ( ! [A6: state,B6: state] : ( P @ ( produc64584659_state @ A6 @ B6 ) )
% 0.20/0.54 => ( P @ P3 ) ) ).
% 0.20/0.54
% 0.20/0.54 % prod_cases
% 0.20/0.54 thf(fact_153_prod__cases,axiom,
% 0.20/0.54 ! [P: produc204914599tate_o > $o,P3: produc204914599tate_o] :
% 0.20/0.54 ( ! [A6: com,B6: a > state > $o] : ( P @ ( produc1948644831tate_o @ A6 @ B6 ) )
% 0.20/0.54 => ( P @ P3 ) ) ).
% 0.20/0.54
% 0.20/0.54 % prod_cases
% 0.20/0.54 thf(fact_154_prod__cases,axiom,
% 0.20/0.54 ! [P: product_prod_nat_nat > $o,P3: product_prod_nat_nat] :
% 0.20/0.54 ( ! [A6: nat,B6: nat] : ( P @ ( product_Pair_nat_nat @ A6 @ B6 ) )
% 0.20/0.54 => ( P @ P3 ) ) ).
% 0.20/0.54
% 0.20/0.54 % prod_cases
% 0.20/0.54 thf(fact_155_Pair__inject,axiom,
% 0.20/0.54 ! [A: a > state > $o,B2: produc204914599tate_o,A4: a > state > $o,B5: produc204914599tate_o] :
% 0.20/0.54 ( ( ( produc33908149tate_o @ A @ B2 )
% 0.20/0.54 = ( produc33908149tate_o @ A4 @ B5 ) )
% 0.20/0.54 => ~ ( ( A = A4 )
% 0.20/0.54 => ( B2 != B5 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % Pair_inject
% 0.20/0.54 thf(fact_156_Pair__inject,axiom,
% 0.20/0.54 ! [A: state,B2: state,A4: state,B5: state] :
% 0.20/0.54 ( ( ( produc64584659_state @ A @ B2 )
% 0.20/0.54 = ( produc64584659_state @ A4 @ B5 ) )
% 0.20/0.54 => ~ ( ( A = A4 )
% 0.20/0.54 => ( B2 != B5 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % Pair_inject
% 0.20/0.54 thf(fact_157_Pair__inject,axiom,
% 0.20/0.54 ! [A: com,B2: a > state > $o,A4: com,B5: a > state > $o] :
% 0.20/0.54 ( ( ( produc1948644831tate_o @ A @ B2 )
% 0.20/0.54 = ( produc1948644831tate_o @ A4 @ B5 ) )
% 0.20/0.54 => ~ ( ( A = A4 )
% 0.20/0.54 => ( B2 != B5 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % Pair_inject
% 0.20/0.54 thf(fact_158_Pair__inject,axiom,
% 0.20/0.54 ! [A: nat,B2: nat,A4: nat,B5: nat] :
% 0.20/0.54 ( ( ( product_Pair_nat_nat @ A @ B2 )
% 0.20/0.54 = ( product_Pair_nat_nat @ A4 @ B5 ) )
% 0.20/0.54 => ~ ( ( A = A4 )
% 0.20/0.54 => ( B2 != B5 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % Pair_inject
% 0.20/0.54 thf(fact_159_old_Oprod_Oexhaust,axiom,
% 0.20/0.54 ! [Y3: produc696469763tate_o] :
% 0.20/0.54 ~ ! [A6: a > state > $o,B6: produc204914599tate_o] :
% 0.20/0.54 ( Y3
% 0.20/0.54 != ( produc33908149tate_o @ A6 @ B6 ) ) ).
% 0.20/0.54
% 0.20/0.54 % old.prod.exhaust
% 0.20/0.54 thf(fact_160_old_Oprod_Oexhaust,axiom,
% 0.20/0.54 ! [Y3: produc1115495963_state] :
% 0.20/0.54 ~ ! [A6: state,B6: state] :
% 0.20/0.54 ( Y3
% 0.20/0.54 != ( produc64584659_state @ A6 @ B6 ) ) ).
% 0.20/0.54
% 0.20/0.54 % old.prod.exhaust
% 0.20/0.54 thf(fact_161_old_Oprod_Oexhaust,axiom,
% 0.20/0.54 ! [Y3: produc204914599tate_o] :
% 0.20/0.54 ~ ! [A6: com,B6: a > state > $o] :
% 0.20/0.54 ( Y3
% 0.20/0.54 != ( produc1948644831tate_o @ A6 @ B6 ) ) ).
% 0.20/0.54
% 0.20/0.54 % old.prod.exhaust
% 0.20/0.54 thf(fact_162_old_Oprod_Oexhaust,axiom,
% 0.20/0.54 ! [Y3: product_prod_nat_nat] :
% 0.20/0.54 ~ ! [A6: nat,B6: nat] :
% 0.20/0.54 ( Y3
% 0.20/0.54 != ( product_Pair_nat_nat @ A6 @ B6 ) ) ).
% 0.20/0.54
% 0.20/0.54 % old.prod.exhaust
% 0.20/0.54 thf(fact_163_old_Oprod_Oinducts,axiom,
% 0.20/0.54 ! [P: produc696469763tate_o > $o,Prod: produc696469763tate_o] :
% 0.20/0.54 ( ! [A6: a > state > $o,B6: produc204914599tate_o] : ( P @ ( produc33908149tate_o @ A6 @ B6 ) )
% 0.20/0.54 => ( P @ Prod ) ) ).
% 0.20/0.54
% 0.20/0.54 % old.prod.inducts
% 0.20/0.54 thf(fact_164_old_Oprod_Oinducts,axiom,
% 0.20/0.54 ! [P: produc1115495963_state > $o,Prod: produc1115495963_state] :
% 0.20/0.54 ( ! [A6: state,B6: state] : ( P @ ( produc64584659_state @ A6 @ B6 ) )
% 0.20/0.54 => ( P @ Prod ) ) ).
% 0.20/0.54
% 0.20/0.54 % old.prod.inducts
% 0.20/0.54 thf(fact_165_old_Oprod_Oinducts,axiom,
% 0.20/0.54 ! [P: produc204914599tate_o > $o,Prod: produc204914599tate_o] :
% 0.20/0.54 ( ! [A6: com,B6: a > state > $o] : ( P @ ( produc1948644831tate_o @ A6 @ B6 ) )
% 0.20/0.54 => ( P @ Prod ) ) ).
% 0.20/0.54
% 0.20/0.54 % old.prod.inducts
% 0.20/0.54 thf(fact_166_old_Oprod_Oinducts,axiom,
% 0.20/0.54 ! [P: product_prod_nat_nat > $o,Prod: product_prod_nat_nat] :
% 0.20/0.54 ( ! [A6: nat,B6: nat] : ( P @ ( product_Pair_nat_nat @ A6 @ B6 ) )
% 0.20/0.54 => ( P @ Prod ) ) ).
% 0.20/0.54
% 0.20/0.54 % old.prod.inducts
% 0.20/0.54 thf(fact_167_is__singletonE,axiom,
% 0.20/0.54 ! [A2: set_Pr1590995257tate_o] :
% 0.20/0.54 ( ( is_sin1547905295tate_o @ A2 )
% 0.20/0.54 => ~ ! [X3: produc696469763tate_o] :
% 0.20/0.54 ( A2
% 0.20/0.54 != ( insert2053719859tate_o @ X3 @ bot_bo170732493tate_o ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % is_singletonE
% 0.20/0.54 thf(fact_168_is__singletonE,axiom,
% 0.20/0.54 ! [A2: set_Pr1986765409at_nat] :
% 0.20/0.54 ( ( is_sin1352690165at_nat @ A2 )
% 0.20/0.54 => ~ ! [X3: product_prod_nat_nat] :
% 0.20/0.54 ( A2
% 0.20/0.54 != ( insert271595217at_nat @ X3 @ bot_bo2130386637at_nat ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % is_singletonE
% 0.20/0.54 thf(fact_169_is__singletonE,axiom,
% 0.20/0.54 ! [A2: set_Pr795498619_state] :
% 0.20/0.54 ( ( is_sin1132515087_state @ A2 )
% 0.20/0.54 => ~ ! [X3: produc1115495963_state] :
% 0.20/0.54 ( A2
% 0.20/0.54 != ( insert311944171_state @ X3 @ bot_bo1625160935_state ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % is_singletonE
% 0.20/0.54 thf(fact_170_is__singleton__def,axiom,
% 0.20/0.54 ( is_sin1547905295tate_o
% 0.20/0.54 = ( ^ [A5: set_Pr1590995257tate_o] :
% 0.20/0.54 ? [X: produc696469763tate_o] :
% 0.20/0.54 ( A5
% 0.20/0.54 = ( insert2053719859tate_o @ X @ bot_bo170732493tate_o ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % is_singleton_def
% 0.20/0.54 thf(fact_171_is__singleton__def,axiom,
% 0.20/0.54 ( is_sin1352690165at_nat
% 0.20/0.54 = ( ^ [A5: set_Pr1986765409at_nat] :
% 0.20/0.54 ? [X: product_prod_nat_nat] :
% 0.20/0.54 ( A5
% 0.20/0.54 = ( insert271595217at_nat @ X @ bot_bo2130386637at_nat ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % is_singleton_def
% 0.20/0.54 thf(fact_172_is__singleton__def,axiom,
% 0.20/0.54 ( is_sin1132515087_state
% 0.20/0.54 = ( ^ [A5: set_Pr795498619_state] :
% 0.20/0.54 ? [X: produc1115495963_state] :
% 0.20/0.54 ( A5
% 0.20/0.54 = ( insert311944171_state @ X @ bot_bo1625160935_state ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % is_singleton_def
% 0.20/0.54 thf(fact_173_wf__def,axiom,
% 0.20/0.54 ( wf_state
% 0.20/0.54 = ( ^ [R3: set_Pr795498619_state] :
% 0.20/0.54 ! [P4: state > $o] :
% 0.20/0.54 ( ! [X: state] :
% 0.20/0.54 ( ! [Y5: state] :
% 0.20/0.54 ( ( member1389040324_state @ ( produc64584659_state @ Y5 @ X ) @ R3 )
% 0.20/0.54 => ( P4 @ Y5 ) )
% 0.20/0.54 => ( P4 @ X ) )
% 0.20/0.54 => ! [X4: state] : ( P4 @ X4 ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % wf_def
% 0.20/0.54 thf(fact_174_wf__def,axiom,
% 0.20/0.54 ( wf_nat
% 0.20/0.54 = ( ^ [R3: set_Pr1986765409at_nat] :
% 0.20/0.54 ! [P4: nat > $o] :
% 0.20/0.54 ( ! [X: nat] :
% 0.20/0.54 ( ! [Y5: nat] :
% 0.20/0.54 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Y5 @ X ) @ R3 )
% 0.20/0.54 => ( P4 @ Y5 ) )
% 0.20/0.54 => ( P4 @ X ) )
% 0.20/0.54 => ! [X4: nat] : ( P4 @ X4 ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % wf_def
% 0.20/0.54 thf(fact_175_wfE__min,axiom,
% 0.20/0.54 ! [R2: set_Pr778812871_state,X2: produc1115495963_state,Q: set_Pr795498619_state] :
% 0.20/0.54 ( ( wf_Pro1783588484_state @ R2 )
% 0.20/0.54 => ( ( member1389040324_state @ X2 @ Q )
% 0.20/0.54 => ~ ! [Z: produc1115495963_state] :
% 0.20/0.54 ( ( member1389040324_state @ Z @ Q )
% 0.20/0.54 => ~ ! [Y4: produc1115495963_state] :
% 0.20/0.54 ( ( member768948240_state @ ( produc1964772951_state @ Y4 @ Z ) @ R2 )
% 0.20/0.54 => ~ ( member1389040324_state @ Y4 @ Q ) ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % wfE_min
% 0.20/0.54 thf(fact_176_wfE__min,axiom,
% 0.20/0.54 ! [R2: set_Pr1490359111at_nat,X2: product_prod_nat_nat,Q: set_Pr1986765409at_nat] :
% 0.20/0.54 ( ( wf_Pro745352042at_nat @ R2 )
% 0.20/0.54 => ( ( member701585322at_nat @ X2 @ Q )
% 0.20/0.54 => ~ ! [Z: product_prod_nat_nat] :
% 0.20/0.54 ( ( member701585322at_nat @ Z @ Q )
% 0.20/0.54 => ~ ! [Y4: product_prod_nat_nat] :
% 0.20/0.54 ( ( member2027625872at_nat @ ( produc1168807639at_nat @ Y4 @ Z ) @ R2 )
% 0.20/0.54 => ~ ( member701585322at_nat @ Y4 @ Q ) ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % wfE_min
% 0.20/0.54 thf(fact_177_wfE__min,axiom,
% 0.20/0.54 ! [R2: set_Pr1702239303tate_o,X2: produc696469763tate_o,Q: set_Pr1590995257tate_o] :
% 0.20/0.54 ( ( wf_Pro309705690tate_o @ R2 )
% 0.20/0.54 => ( ( member1838112666tate_o @ X2 @ Q )
% 0.20/0.54 => ~ ! [Z: produc696469763tate_o] :
% 0.20/0.54 ( ( member1838112666tate_o @ Z @ Q )
% 0.20/0.54 => ~ ! [Y4: produc696469763tate_o] :
% 0.20/0.54 ( ( member1629320336tate_o @ ( produc1684562079tate_o @ Y4 @ Z ) @ R2 )
% 0.20/0.54 => ~ ( member1838112666tate_o @ Y4 @ Q ) ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % wfE_min
% 0.20/0.54 thf(fact_178_wfE__min,axiom,
% 0.20/0.54 ! [R2: set_Pr795498619_state,X2: state,Q: set_state] :
% 0.20/0.54 ( ( wf_state @ R2 )
% 0.20/0.54 => ( ( member_state @ X2 @ Q )
% 0.20/0.54 => ~ ! [Z: state] :
% 0.20/0.54 ( ( member_state @ Z @ Q )
% 0.20/0.54 => ~ ! [Y4: state] :
% 0.20/0.54 ( ( member1389040324_state @ ( produc64584659_state @ Y4 @ Z ) @ R2 )
% 0.20/0.54 => ~ ( member_state @ Y4 @ Q ) ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % wfE_min
% 0.20/0.54 thf(fact_179_wfE__min,axiom,
% 0.20/0.54 ! [R2: set_Pr1986765409at_nat,X2: nat,Q: set_nat] :
% 0.20/0.54 ( ( wf_nat @ R2 )
% 0.20/0.54 => ( ( member_nat @ X2 @ Q )
% 0.20/0.54 => ~ ! [Z: nat] :
% 0.20/0.54 ( ( member_nat @ Z @ Q )
% 0.20/0.54 => ~ ! [Y4: nat] :
% 0.20/0.54 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Y4 @ Z ) @ R2 )
% 0.20/0.54 => ~ ( member_nat @ Y4 @ Q ) ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % wfE_min
% 0.20/0.54 thf(fact_180_wfI__min,axiom,
% 0.20/0.54 ! [R2: set_Pr778812871_state] :
% 0.20/0.54 ( ! [X3: produc1115495963_state,Q3: set_Pr795498619_state] :
% 0.20/0.54 ( ( member1389040324_state @ X3 @ Q3 )
% 0.20/0.54 => ? [Xa: produc1115495963_state] :
% 0.20/0.54 ( ( member1389040324_state @ Xa @ Q3 )
% 0.20/0.54 & ! [Y2: produc1115495963_state] :
% 0.20/0.54 ( ( member768948240_state @ ( produc1964772951_state @ Y2 @ Xa ) @ R2 )
% 0.20/0.54 => ~ ( member1389040324_state @ Y2 @ Q3 ) ) ) )
% 0.20/0.54 => ( wf_Pro1783588484_state @ R2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % wfI_min
% 0.20/0.54 thf(fact_181_wfI__min,axiom,
% 0.20/0.54 ! [R2: set_Pr1490359111at_nat] :
% 0.20/0.54 ( ! [X3: product_prod_nat_nat,Q3: set_Pr1986765409at_nat] :
% 0.20/0.54 ( ( member701585322at_nat @ X3 @ Q3 )
% 0.20/0.54 => ? [Xa: product_prod_nat_nat] :
% 0.20/0.54 ( ( member701585322at_nat @ Xa @ Q3 )
% 0.20/0.54 & ! [Y2: product_prod_nat_nat] :
% 0.20/0.54 ( ( member2027625872at_nat @ ( produc1168807639at_nat @ Y2 @ Xa ) @ R2 )
% 0.20/0.54 => ~ ( member701585322at_nat @ Y2 @ Q3 ) ) ) )
% 0.20/0.54 => ( wf_Pro745352042at_nat @ R2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % wfI_min
% 0.20/0.54 thf(fact_182_wfI__min,axiom,
% 0.20/0.54 ! [R2: set_Pr1702239303tate_o] :
% 0.20/0.54 ( ! [X3: produc696469763tate_o,Q3: set_Pr1590995257tate_o] :
% 0.20/0.54 ( ( member1838112666tate_o @ X3 @ Q3 )
% 0.20/0.54 => ? [Xa: produc696469763tate_o] :
% 0.20/0.54 ( ( member1838112666tate_o @ Xa @ Q3 )
% 0.20/0.54 & ! [Y2: produc696469763tate_o] :
% 0.20/0.54 ( ( member1629320336tate_o @ ( produc1684562079tate_o @ Y2 @ Xa ) @ R2 )
% 0.20/0.54 => ~ ( member1838112666tate_o @ Y2 @ Q3 ) ) ) )
% 0.20/0.54 => ( wf_Pro309705690tate_o @ R2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % wfI_min
% 0.20/0.54 thf(fact_183_wfI__min,axiom,
% 0.20/0.54 ! [R2: set_Pr795498619_state] :
% 0.20/0.54 ( ! [X3: state,Q3: set_state] :
% 0.20/0.54 ( ( member_state @ X3 @ Q3 )
% 0.20/0.54 => ? [Xa: state] :
% 0.20/0.54 ( ( member_state @ Xa @ Q3 )
% 0.20/0.54 & ! [Y2: state] :
% 0.20/0.54 ( ( member1389040324_state @ ( produc64584659_state @ Y2 @ Xa ) @ R2 )
% 0.20/0.54 => ~ ( member_state @ Y2 @ Q3 ) ) ) )
% 0.20/0.54 => ( wf_state @ R2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % wfI_min
% 0.20/0.54 thf(fact_184_wfI__min,axiom,
% 0.20/0.54 ! [R2: set_Pr1986765409at_nat] :
% 0.20/0.54 ( ! [X3: nat,Q3: set_nat] :
% 0.20/0.54 ( ( member_nat @ X3 @ Q3 )
% 0.20/0.54 => ? [Xa: nat] :
% 0.20/0.54 ( ( member_nat @ Xa @ Q3 )
% 0.20/0.54 & ! [Y2: nat] :
% 0.20/0.54 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Y2 @ Xa ) @ R2 )
% 0.20/0.54 => ~ ( member_nat @ Y2 @ Q3 ) ) ) )
% 0.20/0.54 => ( wf_nat @ R2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % wfI_min
% 0.20/0.54 thf(fact_185_wfUNIVI,axiom,
% 0.20/0.54 ! [R: set_Pr795498619_state] :
% 0.20/0.54 ( ! [P5: state > $o,X3: state] :
% 0.20/0.54 ( ! [Xa: state] :
% 0.20/0.54 ( ! [Y2: state] :
% 0.20/0.54 ( ( member1389040324_state @ ( produc64584659_state @ Y2 @ Xa ) @ R )
% 0.20/0.54 => ( P5 @ Y2 ) )
% 0.20/0.54 => ( P5 @ Xa ) )
% 0.20/0.54 => ( P5 @ X3 ) )
% 0.20/0.54 => ( wf_state @ R ) ) ).
% 0.20/0.54
% 0.20/0.54 % wfUNIVI
% 0.20/0.54 thf(fact_186_wfUNIVI,axiom,
% 0.20/0.54 ! [R: set_Pr1986765409at_nat] :
% 0.20/0.54 ( ! [P5: nat > $o,X3: nat] :
% 0.20/0.54 ( ! [Xa: nat] :
% 0.20/0.54 ( ! [Y2: nat] :
% 0.20/0.54 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Y2 @ Xa ) @ R )
% 0.20/0.54 => ( P5 @ Y2 ) )
% 0.20/0.54 => ( P5 @ Xa ) )
% 0.20/0.54 => ( P5 @ X3 ) )
% 0.20/0.54 => ( wf_nat @ R ) ) ).
% 0.20/0.54
% 0.20/0.54 % wfUNIVI
% 0.20/0.54 thf(fact_187_wf__asym,axiom,
% 0.20/0.54 ! [R: set_Pr795498619_state,A: state,X2: state] :
% 0.20/0.54 ( ( wf_state @ R )
% 0.20/0.54 => ( ( member1389040324_state @ ( produc64584659_state @ A @ X2 ) @ R )
% 0.20/0.54 => ~ ( member1389040324_state @ ( produc64584659_state @ X2 @ A ) @ R ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % wf_asym
% 0.20/0.54 thf(fact_188_wf__asym,axiom,
% 0.20/0.54 ! [R: set_Pr1986765409at_nat,A: nat,X2: nat] :
% 0.20/0.54 ( ( wf_nat @ R )
% 0.20/0.54 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ X2 ) @ R )
% 0.20/0.54 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ X2 @ A ) @ R ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % wf_asym
% 0.20/0.54 thf(fact_189_wf__induct,axiom,
% 0.20/0.54 ! [R: set_Pr795498619_state,P: state > $o,A: state] :
% 0.20/0.54 ( ( wf_state @ R )
% 0.20/0.54 => ( ! [X3: state] :
% 0.20/0.54 ( ! [Y4: state] :
% 0.20/0.54 ( ( member1389040324_state @ ( produc64584659_state @ Y4 @ X3 ) @ R )
% 0.20/0.54 => ( P @ Y4 ) )
% 0.20/0.54 => ( P @ X3 ) )
% 0.20/0.54 => ( P @ A ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % wf_induct
% 0.20/0.54 thf(fact_190_wf__induct,axiom,
% 0.20/0.54 ! [R: set_Pr1986765409at_nat,P: nat > $o,A: nat] :
% 0.20/0.54 ( ( wf_nat @ R )
% 0.20/0.54 => ( ! [X3: nat] :
% 0.20/0.54 ( ! [Y4: nat] :
% 0.20/0.54 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Y4 @ X3 ) @ R )
% 0.20/0.54 => ( P @ Y4 ) )
% 0.20/0.54 => ( P @ X3 ) )
% 0.20/0.54 => ( P @ A ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % wf_induct
% 0.20/0.54 thf(fact_191_wf__irrefl,axiom,
% 0.20/0.54 ! [R: set_Pr795498619_state,A: state] :
% 0.20/0.54 ( ( wf_state @ R )
% 0.20/0.54 => ~ ( member1389040324_state @ ( produc64584659_state @ A @ A ) @ R ) ) ).
% 0.20/0.54
% 0.20/0.54 % wf_irrefl
% 0.20/0.54 thf(fact_192_wf__irrefl,axiom,
% 0.20/0.54 ! [R: set_Pr1986765409at_nat,A: nat] :
% 0.20/0.54 ( ( wf_nat @ R )
% 0.20/0.54 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ A ) @ R ) ) ).
% 0.20/0.54
% 0.20/0.54 % wf_irrefl
% 0.20/0.54 thf(fact_193_wf__not__sym,axiom,
% 0.20/0.54 ! [R: set_Pr795498619_state,A: state,X2: state] :
% 0.20/0.54 ( ( wf_state @ R )
% 0.20/0.54 => ( ( member1389040324_state @ ( produc64584659_state @ A @ X2 ) @ R )
% 0.20/0.54 => ~ ( member1389040324_state @ ( produc64584659_state @ X2 @ A ) @ R ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % wf_not_sym
% 0.20/0.54 thf(fact_194_wf__not__sym,axiom,
% 0.20/0.54 ! [R: set_Pr1986765409at_nat,A: nat,X2: nat] :
% 0.20/0.54 ( ( wf_nat @ R )
% 0.20/0.54 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ X2 ) @ R )
% 0.20/0.54 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ X2 @ A ) @ R ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % wf_not_sym
% 0.20/0.54 thf(fact_195_wf__not__refl,axiom,
% 0.20/0.54 ! [R: set_Pr795498619_state,A: state] :
% 0.20/0.54 ( ( wf_state @ R )
% 0.20/0.54 => ~ ( member1389040324_state @ ( produc64584659_state @ A @ A ) @ R ) ) ).
% 0.20/0.54
% 0.20/0.54 % wf_not_refl
% 0.20/0.54 thf(fact_196_wf__not__refl,axiom,
% 0.20/0.54 ! [R: set_Pr1986765409at_nat,A: nat] :
% 0.20/0.54 ( ( wf_nat @ R )
% 0.20/0.54 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ A ) @ R ) ) ).
% 0.20/0.54
% 0.20/0.54 % wf_not_refl
% 0.20/0.54 thf(fact_197_wf__eq__minimal,axiom,
% 0.20/0.54 ( wf_Pro1783588484_state
% 0.20/0.54 = ( ^ [R3: set_Pr778812871_state] :
% 0.20/0.54 ! [Q4: set_Pr795498619_state] :
% 0.20/0.54 ( ? [X: produc1115495963_state] : ( member1389040324_state @ X @ Q4 )
% 0.20/0.54 => ? [X: produc1115495963_state] :
% 0.20/0.54 ( ( member1389040324_state @ X @ Q4 )
% 0.20/0.54 & ! [Y5: produc1115495963_state] :
% 0.20/0.54 ( ( member768948240_state @ ( produc1964772951_state @ Y5 @ X ) @ R3 )
% 0.20/0.54 => ~ ( member1389040324_state @ Y5 @ Q4 ) ) ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % wf_eq_minimal
% 0.20/0.54 thf(fact_198_wf__eq__minimal,axiom,
% 0.20/0.54 ( wf_Pro745352042at_nat
% 0.20/0.54 = ( ^ [R3: set_Pr1490359111at_nat] :
% 0.20/0.54 ! [Q4: set_Pr1986765409at_nat] :
% 0.20/0.54 ( ? [X: product_prod_nat_nat] : ( member701585322at_nat @ X @ Q4 )
% 0.20/0.54 => ? [X: product_prod_nat_nat] :
% 0.20/0.54 ( ( member701585322at_nat @ X @ Q4 )
% 0.20/0.54 & ! [Y5: product_prod_nat_nat] :
% 0.20/0.54 ( ( member2027625872at_nat @ ( produc1168807639at_nat @ Y5 @ X ) @ R3 )
% 0.20/0.54 => ~ ( member701585322at_nat @ Y5 @ Q4 ) ) ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % wf_eq_minimal
% 0.20/0.54 thf(fact_199_wf__eq__minimal,axiom,
% 0.20/0.54 ( wf_Pro309705690tate_o
% 0.20/0.54 = ( ^ [R3: set_Pr1702239303tate_o] :
% 0.20/0.54 ! [Q4: set_Pr1590995257tate_o] :
% 0.20/0.54 ( ? [X: produc696469763tate_o] : ( member1838112666tate_o @ X @ Q4 )
% 0.20/0.54 => ? [X: produc696469763tate_o] :
% 0.20/0.54 ( ( member1838112666tate_o @ X @ Q4 )
% 0.20/0.54 & ! [Y5: produc696469763tate_o] :
% 0.20/0.54 ( ( member1629320336tate_o @ ( produc1684562079tate_o @ Y5 @ X ) @ R3 )
% 0.20/0.54 => ~ ( member1838112666tate_o @ Y5 @ Q4 ) ) ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % wf_eq_minimal
% 0.20/0.54 thf(fact_200_wf__eq__minimal,axiom,
% 0.20/0.54 ( wf_state
% 0.20/0.54 = ( ^ [R3: set_Pr795498619_state] :
% 0.20/0.54 ! [Q4: set_state] :
% 0.20/0.54 ( ? [X: state] : ( member_state @ X @ Q4 )
% 0.20/0.54 => ? [X: state] :
% 0.20/0.54 ( ( member_state @ X @ Q4 )
% 0.20/0.54 & ! [Y5: state] :
% 0.20/0.54 ( ( member1389040324_state @ ( produc64584659_state @ Y5 @ X ) @ R3 )
% 0.20/0.54 => ~ ( member_state @ Y5 @ Q4 ) ) ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % wf_eq_minimal
% 0.20/0.54 thf(fact_201_wf__eq__minimal,axiom,
% 0.20/0.54 ( wf_nat
% 0.20/0.54 = ( ^ [R3: set_Pr1986765409at_nat] :
% 0.20/0.54 ! [Q4: set_nat] :
% 0.20/0.54 ( ? [X: nat] : ( member_nat @ X @ Q4 )
% 0.20/0.54 => ? [X: nat] :
% 0.20/0.54 ( ( member_nat @ X @ Q4 )
% 0.20/0.54 & ! [Y5: nat] :
% 0.20/0.54 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Y5 @ X ) @ R3 )
% 0.20/0.54 => ~ ( member_nat @ Y5 @ Q4 ) ) ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % wf_eq_minimal
% 0.20/0.54 thf(fact_202_wf__induct__rule,axiom,
% 0.20/0.54 ! [R: set_Pr795498619_state,P: state > $o,A: state] :
% 0.20/0.54 ( ( wf_state @ R )
% 0.20/0.54 => ( ! [X3: state] :
% 0.20/0.54 ( ! [Y4: state] :
% 0.20/0.54 ( ( member1389040324_state @ ( produc64584659_state @ Y4 @ X3 ) @ R )
% 0.20/0.54 => ( P @ Y4 ) )
% 0.20/0.54 => ( P @ X3 ) )
% 0.20/0.54 => ( P @ A ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % wf_induct_rule
% 0.20/0.54 thf(fact_203_wf__induct__rule,axiom,
% 0.20/0.54 ! [R: set_Pr1986765409at_nat,P: nat > $o,A: nat] :
% 0.20/0.54 ( ( wf_nat @ R )
% 0.20/0.54 => ( ! [X3: nat] :
% 0.20/0.54 ( ! [Y4: nat] :
% 0.20/0.54 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Y4 @ X3 ) @ R )
% 0.20/0.54 => ( P @ Y4 ) )
% 0.20/0.54 => ( P @ X3 ) )
% 0.20/0.54 => ( P @ A ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % wf_induct_rule
% 0.20/0.54 thf(fact_204_prod__cases3,axiom,
% 0.20/0.54 ! [Y3: produc696469763tate_o] :
% 0.20/0.54 ~ ! [A6: a > state > $o,B6: com,C4: a > state > $o] :
% 0.20/0.54 ( Y3
% 0.20/0.54 != ( produc33908149tate_o @ A6 @ ( produc1948644831tate_o @ B6 @ C4 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % prod_cases3
% 0.20/0.54 thf(fact_205_prod__induct3,axiom,
% 0.20/0.54 ! [P: produc696469763tate_o > $o,X2: produc696469763tate_o] :
% 0.20/0.54 ( ! [A6: a > state > $o,B6: com,C4: a > state > $o] : ( P @ ( produc33908149tate_o @ A6 @ ( produc1948644831tate_o @ B6 @ C4 ) ) )
% 0.20/0.54 => ( P @ X2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % prod_induct3
% 0.20/0.54 thf(fact_206_bot__empty__eq2,axiom,
% 0.20/0.54 ( bot_bo935656620te_o_o
% 0.20/0.54 = ( ^ [X: com,Y5: a > state > $o] : ( member221067728tate_o @ ( produc1948644831tate_o @ X @ Y5 ) @ bot_bo1692783091tate_o ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % bot_empty_eq2
% 0.20/0.54 thf(fact_207_bot__empty__eq2,axiom,
% 0.20/0.54 ( bot_bo2130564770te_o_o
% 0.20/0.54 = ( ^ [X: a > state > $o,Y5: produc204914599tate_o] : ( member1838112666tate_o @ ( produc33908149tate_o @ X @ Y5 ) @ bot_bo170732493tate_o ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % bot_empty_eq2
% 0.20/0.54 thf(fact_208_bot__empty__eq2,axiom,
% 0.20/0.54 ( bot_bot_nat_nat_o
% 0.20/0.54 = ( ^ [X: nat,Y5: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Y5 ) @ bot_bo2130386637at_nat ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % bot_empty_eq2
% 0.20/0.54 thf(fact_209_bot__empty__eq2,axiom,
% 0.20/0.54 ( bot_bo51534648tate_o
% 0.20/0.54 = ( ^ [X: state,Y5: state] : ( member1389040324_state @ ( produc64584659_state @ X @ Y5 ) @ bot_bo1625160935_state ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % bot_empty_eq2
% 0.20/0.54 thf(fact_210_wf__measure,axiom,
% 0.20/0.54 ! [F: state > nat] : ( wf_state @ ( measure_state @ F ) ) ).
% 0.20/0.54
% 0.20/0.54 % wf_measure
% 0.20/0.54 thf(fact_211_wf__measure,axiom,
% 0.20/0.54 ! [F: nat > nat] : ( wf_nat @ ( measure_nat @ F ) ) ).
% 0.20/0.54
% 0.20/0.54 % wf_measure
% 0.20/0.54 thf(fact_212_thoare_OWhile,axiom,
% 0.20/0.54 ! [R: set_Pr795498619_state,C: set_Pr1590995257tate_o,P: a > state > $o,B2: state > $o,C2: com] :
% 0.20/0.54 ( ( wf_state @ R )
% 0.20/0.54 => ( ! [S3: state] :
% 0.20/0.54 ( pHoare382919414oare_a @ C
% 0.20/0.54 @ ^ [Z4: a,S4: state] :
% 0.20/0.54 ( ( P @ Z4 @ S4 )
% 0.20/0.54 & ( B2 @ S4 )
% 0.20/0.54 & ( S3 = S4 ) )
% 0.20/0.54 @ C2
% 0.20/0.54 @ ^ [Z4: a,S4: state] :
% 0.20/0.54 ( ( P @ Z4 @ S4 )
% 0.20/0.54 & ( member1389040324_state @ ( produc64584659_state @ S4 @ S3 ) @ R ) ) )
% 0.20/0.54 => ( pHoare382919414oare_a @ C @ P @ ( while @ B2 @ C2 )
% 0.20/0.54 @ ^ [Z4: a,S4: state] :
% 0.20/0.54 ( ( P @ Z4 @ S4 )
% 0.20/0.54 & ~ ( B2 @ S4 ) ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % thoare.While
% 0.20/0.54 thf(fact_213_Set_Ois__empty__def,axiom,
% 0.20/0.54 ( is_emp807847857tate_o
% 0.20/0.54 = ( ^ [A5: set_Pr1590995257tate_o] : ( A5 = bot_bo170732493tate_o ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % Set.is_empty_def
% 0.20/0.54 thf(fact_214_Set_Ois__empty__def,axiom,
% 0.20/0.54 ( is_emp825011411at_nat
% 0.20/0.54 = ( ^ [A5: set_Pr1986765409at_nat] : ( A5 = bot_bo2130386637at_nat ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % Set.is_empty_def
% 0.20/0.54 thf(fact_215_Set_Ois__empty__def,axiom,
% 0.20/0.54 ( is_emp1062983149_state
% 0.20/0.54 = ( ^ [A5: set_Pr795498619_state] : ( A5 = bot_bo1625160935_state ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % Set.is_empty_def
% 0.20/0.54 thf(fact_216_com_Oinject_I4_J,axiom,
% 0.20/0.54 ! [X41: state > $o,X42: com,Y41: state > $o,Y42: com] :
% 0.20/0.54 ( ( ( while @ X41 @ X42 )
% 0.20/0.54 = ( while @ Y41 @ Y42 ) )
% 0.20/0.54 = ( ( X41 = Y41 )
% 0.20/0.54 & ( X42 = Y42 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % com.inject(4)
% 0.20/0.54 thf(fact_217_com_Odistinct_I25_J,axiom,
% 0.20/0.54 ! [X41: state > $o,X42: com] :
% 0.20/0.54 ( ( while @ X41 @ X42 )
% 0.20/0.54 != call ) ).
% 0.20/0.54
% 0.20/0.54 % com.distinct(25)
% 0.20/0.54 thf(fact_218_exec_OWhileFalse,axiom,
% 0.20/0.54 ! [B2: state > $o,S2: state,C2: com] :
% 0.20/0.54 ( ~ ( B2 @ S2 )
% 0.20/0.54 => ( exec @ S2 @ ( while @ B2 @ C2 ) @ S2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % exec.WhileFalse
% 0.20/0.54 thf(fact_219_exec_OWhileTrue,axiom,
% 0.20/0.54 ! [B2: state > $o,S2: state,C2: com,T2: state,U2: state] :
% 0.20/0.54 ( ( B2 @ S2 )
% 0.20/0.54 => ( ( exec @ S2 @ C2 @ T2 )
% 0.20/0.54 => ( ( exec @ T2 @ ( while @ B2 @ C2 ) @ U2 )
% 0.20/0.54 => ( exec @ S2 @ ( while @ B2 @ C2 ) @ U2 ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % exec.WhileTrue
% 0.20/0.54 thf(fact_220_termi_OWhileFalse,axiom,
% 0.20/0.54 ! [B2: state > $o,S2: state,C2: com] :
% 0.20/0.54 ( ~ ( B2 @ S2 )
% 0.20/0.54 => ( termi @ ( while @ B2 @ C2 ) @ S2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % termi.WhileFalse
% 0.20/0.54 thf(fact_221_termi_OWhileTrue,axiom,
% 0.20/0.54 ! [B2: state > $o,S2: state,C2: com] :
% 0.20/0.54 ( ( B2 @ S2 )
% 0.20/0.54 => ( ( termi @ C2 @ S2 )
% 0.20/0.54 => ( ! [T: state] :
% 0.20/0.54 ( ( exec @ S2 @ C2 @ T )
% 0.20/0.54 => ( termi @ ( while @ B2 @ C2 ) @ T ) )
% 0.20/0.54 => ( termi @ ( while @ B2 @ C2 ) @ S2 ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % termi.WhileTrue
% 0.20/0.54 thf(fact_222_bot__empty__eq,axiom,
% 0.20/0.54 ( bot_bo250281208te_o_o
% 0.20/0.54 = ( ^ [X: produc696469763tate_o] : ( member1838112666tate_o @ X @ bot_bo170732493tate_o ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % bot_empty_eq
% 0.20/0.54 thf(fact_223_bot__empty__eq,axiom,
% 0.20/0.54 ( bot_bo513358416_nat_o
% 0.20/0.54 = ( ^ [X: product_prod_nat_nat] : ( member701585322at_nat @ X @ bot_bo2130386637at_nat ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % bot_empty_eq
% 0.20/0.54 thf(fact_224_bot__empty__eq,axiom,
% 0.20/0.54 ( bot_bo446391478tate_o
% 0.20/0.54 = ( ^ [X: produc1115495963_state] : ( member1389040324_state @ X @ bot_bo1625160935_state ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % bot_empty_eq
% 0.20/0.54 thf(fact_225_pred__equals__eq2,axiom,
% 0.20/0.54 ! [R2: set_Pr1590995257tate_o,S5: set_Pr1590995257tate_o] :
% 0.20/0.54 ( ( ( ^ [X: a > state > $o,Y5: produc204914599tate_o] : ( member1838112666tate_o @ ( produc33908149tate_o @ X @ Y5 ) @ R2 ) )
% 0.20/0.54 = ( ^ [X: a > state > $o,Y5: produc204914599tate_o] : ( member1838112666tate_o @ ( produc33908149tate_o @ X @ Y5 ) @ S5 ) ) )
% 0.20/0.54 = ( R2 = S5 ) ) ).
% 0.20/0.54
% 0.20/0.54 % pred_equals_eq2
% 0.20/0.54 thf(fact_226_pred__equals__eq2,axiom,
% 0.20/0.54 ! [R2: set_Pr795498619_state,S5: set_Pr795498619_state] :
% 0.20/0.54 ( ( ( ^ [X: state,Y5: state] : ( member1389040324_state @ ( produc64584659_state @ X @ Y5 ) @ R2 ) )
% 0.20/0.54 = ( ^ [X: state,Y5: state] : ( member1389040324_state @ ( produc64584659_state @ X @ Y5 ) @ S5 ) ) )
% 0.20/0.54 = ( R2 = S5 ) ) ).
% 0.20/0.54
% 0.20/0.54 % pred_equals_eq2
% 0.20/0.54 thf(fact_227_pred__equals__eq2,axiom,
% 0.20/0.54 ! [R2: set_Pr1740974983tate_o,S5: set_Pr1740974983tate_o] :
% 0.20/0.54 ( ( ( ^ [X: com,Y5: a > state > $o] : ( member221067728tate_o @ ( produc1948644831tate_o @ X @ Y5 ) @ R2 ) )
% 0.20/0.54 = ( ^ [X: com,Y5: a > state > $o] : ( member221067728tate_o @ ( produc1948644831tate_o @ X @ Y5 ) @ S5 ) ) )
% 0.20/0.54 = ( R2 = S5 ) ) ).
% 0.20/0.54
% 0.20/0.54 % pred_equals_eq2
% 0.20/0.54 thf(fact_228_pred__equals__eq2,axiom,
% 0.20/0.54 ! [R2: set_Pr1986765409at_nat,S5: set_Pr1986765409at_nat] :
% 0.20/0.54 ( ( ( ^ [X: nat,Y5: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Y5 ) @ R2 ) )
% 0.20/0.54 = ( ^ [X: nat,Y5: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Y5 ) @ S5 ) ) )
% 0.20/0.54 = ( R2 = S5 ) ) ).
% 0.20/0.54
% 0.20/0.54 % pred_equals_eq2
% 0.20/0.54 thf(fact_229_Collect__empty__eq__bot,axiom,
% 0.20/0.54 ! [P: produc696469763tate_o > $o] :
% 0.20/0.54 ( ( ( collec1499596504tate_o @ P )
% 0.20/0.54 = bot_bo170732493tate_o )
% 0.20/0.54 = ( P = bot_bo250281208te_o_o ) ) ).
% 0.20/0.54
% 0.20/0.54 % Collect_empty_eq_bot
% 0.20/0.54 thf(fact_230_Collect__empty__eq__bot,axiom,
% 0.20/0.54 ! [P: product_prod_nat_nat > $o] :
% 0.20/0.54 ( ( ( collec7649004at_nat @ P )
% 0.20/0.54 = bot_bo2130386637at_nat )
% 0.20/0.54 = ( P = bot_bo513358416_nat_o ) ) ).
% 0.20/0.54
% 0.20/0.54 % Collect_empty_eq_bot
% 0.20/0.54 thf(fact_231_Collect__empty__eq__bot,axiom,
% 0.20/0.54 ! [P: produc1115495963_state > $o] :
% 0.20/0.54 ( ( ( collec496201222_state @ P )
% 0.20/0.54 = bot_bo1625160935_state )
% 0.20/0.54 = ( P = bot_bo446391478tate_o ) ) ).
% 0.20/0.54
% 0.20/0.54 % Collect_empty_eq_bot
% 0.20/0.54 thf(fact_232_total__on__singleton,axiom,
% 0.20/0.54 ! [X2: nat] : ( total_on_nat @ ( insert_nat @ X2 @ bot_bot_set_nat ) @ ( insert271595217at_nat @ ( product_Pair_nat_nat @ X2 @ X2 ) @ bot_bo2130386637at_nat ) ) ).
% 0.20/0.54
% 0.20/0.54 % total_on_singleton
% 0.20/0.54 thf(fact_233_total__on__singleton,axiom,
% 0.20/0.54 ! [X2: state] : ( total_on_state @ ( insert_state @ X2 @ bot_bot_set_state ) @ ( insert311944171_state @ ( produc64584659_state @ X2 @ X2 ) @ bot_bo1625160935_state ) ) ).
% 0.20/0.54
% 0.20/0.54 % total_on_singleton
% 0.20/0.54 thf(fact_234_total__on__singleton,axiom,
% 0.20/0.54 ! [X2: produc696469763tate_o] : ( total_795385983tate_o @ ( insert2053719859tate_o @ X2 @ bot_bo170732493tate_o ) @ ( insert1597128631tate_o @ ( produc1684562079tate_o @ X2 @ X2 ) @ bot_bo1714653363tate_o ) ) ).
% 0.20/0.54
% 0.20/0.54 % total_on_singleton
% 0.20/0.54 thf(fact_235_total__on__singleton,axiom,
% 0.20/0.54 ! [X2: product_prod_nat_nat] : ( total_1775715973at_nat @ ( insert271595217at_nat @ X2 @ bot_bo2130386637at_nat ) @ ( insert584009271at_nat @ ( produc1168807639at_nat @ X2 @ X2 ) @ bot_bo34127283at_nat ) ) ).
% 0.20/0.54
% 0.20/0.54 % total_on_singleton
% 0.20/0.54 thf(fact_236_total__on__singleton,axiom,
% 0.20/0.54 ! [X2: produc1115495963_state] : ( total_1316653983_state @ ( insert311944171_state @ X2 @ bot_bo1625160935_state ) @ ( insert1616594103_state @ ( produc1964772951_state @ X2 @ X2 ) @ bot_bo1331673139_state ) ) ).
% 0.20/0.54
% 0.20/0.54 % total_on_singleton
% 0.20/0.54 thf(fact_237_refl__on__singleton,axiom,
% 0.20/0.54 ! [X2: nat] : ( refl_on_nat @ ( insert_nat @ X2 @ bot_bot_set_nat ) @ ( insert271595217at_nat @ ( product_Pair_nat_nat @ X2 @ X2 ) @ bot_bo2130386637at_nat ) ) ).
% 0.20/0.54
% 0.20/0.54 % refl_on_singleton
% 0.20/0.54 thf(fact_238_refl__on__singleton,axiom,
% 0.20/0.54 ! [X2: state] : ( refl_on_state @ ( insert_state @ X2 @ bot_bot_set_state ) @ ( insert311944171_state @ ( produc64584659_state @ X2 @ X2 ) @ bot_bo1625160935_state ) ) ).
% 0.20/0.54
% 0.20/0.54 % refl_on_singleton
% 0.20/0.54 thf(fact_239_refl__on__singleton,axiom,
% 0.20/0.54 ! [X2: produc696469763tate_o] : ( refl_o489021252tate_o @ ( insert2053719859tate_o @ X2 @ bot_bo170732493tate_o ) @ ( insert1597128631tate_o @ ( produc1684562079tate_o @ X2 @ X2 ) @ bot_bo1714653363tate_o ) ) ).
% 0.20/0.54
% 0.20/0.54 % refl_on_singleton
% 0.20/0.54 thf(fact_240_refl__on__singleton,axiom,
% 0.20/0.54 ! [X2: product_prod_nat_nat] : ( refl_o1619599232at_nat @ ( insert271595217at_nat @ X2 @ bot_bo2130386637at_nat ) @ ( insert584009271at_nat @ ( produc1168807639at_nat @ X2 @ X2 ) @ bot_bo34127283at_nat ) ) ).
% 0.20/0.54
% 0.20/0.54 % refl_on_singleton
% 0.20/0.54 thf(fact_241_refl__on__singleton,axiom,
% 0.20/0.54 ! [X2: produc1115495963_state] : ( refl_o1438232218_state @ ( insert311944171_state @ X2 @ bot_bo1625160935_state ) @ ( insert1616594103_state @ ( produc1964772951_state @ X2 @ X2 ) @ bot_bo1331673139_state ) ) ).
% 0.20/0.54
% 0.20/0.54 % refl_on_singleton
% 0.20/0.54 thf(fact_242_wf__termi,axiom,
% 0.20/0.54 ! [B2: state > $o,C2: com] :
% 0.20/0.54 ( wf_state
% 0.20/0.54 @ ( collec496201222_state
% 0.20/0.54 @ ( produc789892016tate_o
% 0.20/0.54 @ ^ [T3: state,S4: state] :
% 0.20/0.54 ( ( termi @ ( while @ B2 @ C2 ) @ S4 )
% 0.20/0.54 & ( B2 @ S4 )
% 0.20/0.54 & ( exec @ S4 @ C2 @ T3 ) ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % wf_termi
% 0.20/0.54 thf(fact_243_linear__order__on__singleton,axiom,
% 0.20/0.54 ! [X2: nat] : ( order_130026331on_nat @ ( insert_nat @ X2 @ bot_bot_set_nat ) @ ( insert271595217at_nat @ ( product_Pair_nat_nat @ X2 @ X2 ) @ bot_bo2130386637at_nat ) ) ).
% 0.20/0.54
% 0.20/0.54 % linear_order_on_singleton
% 0.20/0.54 thf(fact_244_linear__order__on__singleton,axiom,
% 0.20/0.54 ! [X2: state] : ( order_286167592_state @ ( insert_state @ X2 @ bot_bot_set_state ) @ ( insert311944171_state @ ( produc64584659_state @ X2 @ X2 ) @ bot_bo1625160935_state ) ) ).
% 0.20/0.54
% 0.20/0.54 % linear_order_on_singleton
% 0.20/0.54 thf(fact_245_linear__order__on__singleton,axiom,
% 0.20/0.54 ! [X2: produc696469763tate_o] : ( order_50454158tate_o @ ( insert2053719859tate_o @ X2 @ bot_bo170732493tate_o ) @ ( insert1597128631tate_o @ ( produc1684562079tate_o @ X2 @ X2 ) @ bot_bo1714653363tate_o ) ) ).
% 0.20/0.54
% 0.20/0.54 % linear_order_on_singleton
% 0.20/0.54 thf(fact_246_linear__order__on__singleton,axiom,
% 0.20/0.54 ! [X2: product_prod_nat_nat] : ( order_721919926at_nat @ ( insert271595217at_nat @ X2 @ bot_bo2130386637at_nat ) @ ( insert584009271at_nat @ ( produc1168807639at_nat @ X2 @ X2 ) @ bot_bo34127283at_nat ) ) ).
% 0.20/0.54
% 0.20/0.54 % linear_order_on_singleton
% 0.20/0.54 thf(fact_247_linear__order__on__singleton,axiom,
% 0.20/0.54 ! [X2: produc1115495963_state] : ( order_178668240_state @ ( insert311944171_state @ X2 @ bot_bo1625160935_state ) @ ( insert1616594103_state @ ( produc1964772951_state @ X2 @ X2 ) @ bot_bo1331673139_state ) ) ).
% 0.20/0.54
% 0.20/0.54 % linear_order_on_singleton
% 0.20/0.54 thf(fact_248_split__part,axiom,
% 0.20/0.54 ! [P: $o,Q: state > state > $o] :
% 0.20/0.54 ( ( produc789892016tate_o
% 0.20/0.54 @ ^ [A3: state,B7: state] :
% 0.20/0.54 ( P
% 0.20/0.54 & ( Q @ A3 @ B7 ) ) )
% 0.20/0.54 = ( ^ [Ab: produc1115495963_state] :
% 0.20/0.54 ( P
% 0.20/0.54 & ( produc789892016tate_o @ Q @ Ab ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % split_part
% 0.20/0.54 thf(fact_249_split__part,axiom,
% 0.20/0.54 ! [P: $o,Q: nat > nat > $o] :
% 0.20/0.54 ( ( produc949581770_nat_o
% 0.20/0.54 @ ^ [A3: nat,B7: nat] :
% 0.20/0.54 ( P
% 0.20/0.54 & ( Q @ A3 @ B7 ) ) )
% 0.20/0.54 = ( ^ [Ab: product_prod_nat_nat] :
% 0.20/0.54 ( P
% 0.20/0.54 & ( produc949581770_nat_o @ Q @ Ab ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % split_part
% 0.20/0.54 thf(fact_250_case__prod__conv,axiom,
% 0.20/0.54 ! [F: state > state > $o,A: state,B2: state] :
% 0.20/0.54 ( ( produc789892016tate_o @ F @ ( produc64584659_state @ A @ B2 ) )
% 0.20/0.54 = ( F @ A @ B2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % case_prod_conv
% 0.20/0.54 thf(fact_251_case__prod__conv,axiom,
% 0.20/0.54 ! [F: nat > nat > $o,A: nat,B2: nat] :
% 0.20/0.54 ( ( produc949581770_nat_o @ F @ ( product_Pair_nat_nat @ A @ B2 ) )
% 0.20/0.54 = ( F @ A @ B2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % case_prod_conv
% 0.20/0.54 thf(fact_252_case__prodI,axiom,
% 0.20/0.54 ! [F: ( a > state > $o ) > produc204914599tate_o > $o,A: a > state > $o,B2: produc204914599tate_o] :
% 0.20/0.54 ( ( F @ A @ B2 )
% 0.20/0.54 => ( produc1271576886te_o_o @ F @ ( produc33908149tate_o @ A @ B2 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % case_prodI
% 0.20/0.54 thf(fact_253_case__prodI,axiom,
% 0.20/0.54 ! [F: com > ( a > state > $o ) > $o,A: com,B2: a > state > $o] :
% 0.20/0.54 ( ( F @ A @ B2 )
% 0.20/0.54 => ( produc281270436te_o_o @ F @ ( produc1948644831tate_o @ A @ B2 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % case_prodI
% 0.20/0.54 thf(fact_254_case__prodI,axiom,
% 0.20/0.54 ! [F: state > state > $o,A: state,B2: state] :
% 0.20/0.54 ( ( F @ A @ B2 )
% 0.20/0.54 => ( produc789892016tate_o @ F @ ( produc64584659_state @ A @ B2 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % case_prodI
% 0.20/0.54 thf(fact_255_case__prodI,axiom,
% 0.20/0.54 ! [F: nat > nat > $o,A: nat,B2: nat] :
% 0.20/0.54 ( ( F @ A @ B2 )
% 0.20/0.54 => ( produc949581770_nat_o @ F @ ( product_Pair_nat_nat @ A @ B2 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % case_prodI
% 0.20/0.54 thf(fact_256_case__prodI2,axiom,
% 0.20/0.54 ! [P3: produc696469763tate_o,C2: ( a > state > $o ) > produc204914599tate_o > $o] :
% 0.20/0.54 ( ! [A6: a > state > $o,B6: produc204914599tate_o] :
% 0.20/0.54 ( ( P3
% 0.20/0.54 = ( produc33908149tate_o @ A6 @ B6 ) )
% 0.20/0.54 => ( C2 @ A6 @ B6 ) )
% 0.20/0.54 => ( produc1271576886te_o_o @ C2 @ P3 ) ) ).
% 0.20/0.54
% 0.20/0.54 % case_prodI2
% 0.20/0.54 thf(fact_257_case__prodI2,axiom,
% 0.20/0.54 ! [P3: produc204914599tate_o,C2: com > ( a > state > $o ) > $o] :
% 0.20/0.54 ( ! [A6: com,B6: a > state > $o] :
% 0.20/0.54 ( ( P3
% 0.20/0.54 = ( produc1948644831tate_o @ A6 @ B6 ) )
% 0.20/0.54 => ( C2 @ A6 @ B6 ) )
% 0.20/0.54 => ( produc281270436te_o_o @ C2 @ P3 ) ) ).
% 0.20/0.54
% 0.20/0.54 % case_prodI2
% 0.20/0.54 thf(fact_258_case__prodI2,axiom,
% 0.20/0.54 ! [P3: produc1115495963_state,C2: state > state > $o] :
% 0.20/0.54 ( ! [A6: state,B6: state] :
% 0.20/0.54 ( ( P3
% 0.20/0.54 = ( produc64584659_state @ A6 @ B6 ) )
% 0.20/0.54 => ( C2 @ A6 @ B6 ) )
% 0.20/0.54 => ( produc789892016tate_o @ C2 @ P3 ) ) ).
% 0.20/0.54
% 0.20/0.54 % case_prodI2
% 0.20/0.54 thf(fact_259_case__prodI2,axiom,
% 0.20/0.54 ! [P3: product_prod_nat_nat,C2: nat > nat > $o] :
% 0.20/0.54 ( ! [A6: nat,B6: nat] :
% 0.20/0.54 ( ( P3
% 0.20/0.54 = ( product_Pair_nat_nat @ A6 @ B6 ) )
% 0.20/0.54 => ( C2 @ A6 @ B6 ) )
% 0.20/0.54 => ( produc949581770_nat_o @ C2 @ P3 ) ) ).
% 0.20/0.54
% 0.20/0.54 % case_prodI2
% 0.20/0.54 thf(fact_260_refl__on__domain,axiom,
% 0.20/0.54 ! [A2: set_Pr795498619_state,R: set_Pr778812871_state,A: produc1115495963_state,B2: produc1115495963_state] :
% 0.20/0.54 ( ( refl_o1438232218_state @ A2 @ R )
% 0.20/0.54 => ( ( member768948240_state @ ( produc1964772951_state @ A @ B2 ) @ R )
% 0.20/0.54 => ( ( member1389040324_state @ A @ A2 )
% 0.20/0.54 & ( member1389040324_state @ B2 @ A2 ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % refl_on_domain
% 0.20/0.54 thf(fact_261_refl__on__domain,axiom,
% 0.20/0.54 ! [A2: set_Pr1986765409at_nat,R: set_Pr1490359111at_nat,A: product_prod_nat_nat,B2: product_prod_nat_nat] :
% 0.20/0.54 ( ( refl_o1619599232at_nat @ A2 @ R )
% 0.20/0.54 => ( ( member2027625872at_nat @ ( produc1168807639at_nat @ A @ B2 ) @ R )
% 0.20/0.54 => ( ( member701585322at_nat @ A @ A2 )
% 0.20/0.54 & ( member701585322at_nat @ B2 @ A2 ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % refl_on_domain
% 0.20/0.54 thf(fact_262_refl__on__domain,axiom,
% 0.20/0.54 ! [A2: set_Pr1590995257tate_o,R: set_Pr1702239303tate_o,A: produc696469763tate_o,B2: produc696469763tate_o] :
% 0.20/0.54 ( ( refl_o489021252tate_o @ A2 @ R )
% 0.20/0.54 => ( ( member1629320336tate_o @ ( produc1684562079tate_o @ A @ B2 ) @ R )
% 0.20/0.54 => ( ( member1838112666tate_o @ A @ A2 )
% 0.20/0.54 & ( member1838112666tate_o @ B2 @ A2 ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % refl_on_domain
% 0.20/0.54 thf(fact_263_refl__on__domain,axiom,
% 0.20/0.54 ! [A2: set_state,R: set_Pr795498619_state,A: state,B2: state] :
% 0.20/0.54 ( ( refl_on_state @ A2 @ R )
% 0.20/0.54 => ( ( member1389040324_state @ ( produc64584659_state @ A @ B2 ) @ R )
% 0.20/0.54 => ( ( member_state @ A @ A2 )
% 0.20/0.54 & ( member_state @ B2 @ A2 ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % refl_on_domain
% 0.20/0.54 thf(fact_264_refl__on__domain,axiom,
% 0.20/0.54 ! [A2: set_nat,R: set_Pr1986765409at_nat,A: nat,B2: nat] :
% 0.20/0.54 ( ( refl_on_nat @ A2 @ R )
% 0.20/0.54 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B2 ) @ R )
% 0.20/0.54 => ( ( member_nat @ A @ A2 )
% 0.20/0.54 & ( member_nat @ B2 @ A2 ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % refl_on_domain
% 0.20/0.54 thf(fact_265_prod_Ocase__distrib,axiom,
% 0.20/0.54 ! [H: $o > $o,F: state > state > $o,Prod: produc1115495963_state] :
% 0.20/0.54 ( ( H @ ( produc789892016tate_o @ F @ Prod ) )
% 0.20/0.54 = ( produc789892016tate_o
% 0.20/0.54 @ ^ [X12: state,X23: state] : ( H @ ( F @ X12 @ X23 ) )
% 0.20/0.54 @ Prod ) ) ).
% 0.20/0.54
% 0.20/0.54 % prod.case_distrib
% 0.20/0.54 thf(fact_266_prod_Ocase__distrib,axiom,
% 0.20/0.54 ! [H: $o > $o,F: nat > nat > $o,Prod: product_prod_nat_nat] :
% 0.20/0.54 ( ( H @ ( produc949581770_nat_o @ F @ Prod ) )
% 0.20/0.54 = ( produc949581770_nat_o
% 0.20/0.54 @ ^ [X12: nat,X23: nat] : ( H @ ( F @ X12 @ X23 ) )
% 0.20/0.54 @ Prod ) ) ).
% 0.20/0.54
% 0.20/0.54 % prod.case_distrib
% 0.20/0.54 thf(fact_267_prod_Odisc__eq__case,axiom,
% 0.20/0.54 ! [Prod: produc1115495963_state] :
% 0.20/0.54 ( produc789892016tate_o
% 0.20/0.54 @ ^ [Uu: state,Uv: state] : $true
% 0.20/0.54 @ Prod ) ).
% 0.20/0.54
% 0.20/0.54 % prod.disc_eq_case
% 0.20/0.54 thf(fact_268_prod_Odisc__eq__case,axiom,
% 0.20/0.54 ! [Prod: product_prod_nat_nat] :
% 0.20/0.54 ( produc949581770_nat_o
% 0.20/0.54 @ ^ [Uu: nat,Uv: nat] : $true
% 0.20/0.54 @ Prod ) ).
% 0.20/0.54
% 0.20/0.54 % prod.disc_eq_case
% 0.20/0.54 thf(fact_269_old_Oprod_Ocase,axiom,
% 0.20/0.54 ! [F: state > state > $o,X1: state,X22: state] :
% 0.20/0.54 ( ( produc789892016tate_o @ F @ ( produc64584659_state @ X1 @ X22 ) )
% 0.20/0.54 = ( F @ X1 @ X22 ) ) ).
% 0.20/0.54
% 0.20/0.54 % old.prod.case
% 0.20/0.54 thf(fact_270_old_Oprod_Ocase,axiom,
% 0.20/0.54 ! [F: nat > nat > $o,X1: nat,X22: nat] :
% 0.20/0.54 ( ( produc949581770_nat_o @ F @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 0.20/0.54 = ( F @ X1 @ X22 ) ) ).
% 0.20/0.54
% 0.20/0.54 % old.prod.case
% 0.20/0.54 thf(fact_271_refl__onD2,axiom,
% 0.20/0.54 ! [A2: set_Pr795498619_state,R: set_Pr778812871_state,X2: produc1115495963_state,Y3: produc1115495963_state] :
% 0.20/0.54 ( ( refl_o1438232218_state @ A2 @ R )
% 0.20/0.54 => ( ( member768948240_state @ ( produc1964772951_state @ X2 @ Y3 ) @ R )
% 0.20/0.54 => ( member1389040324_state @ Y3 @ A2 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % refl_onD2
% 0.20/0.54 thf(fact_272_refl__onD2,axiom,
% 0.20/0.54 ! [A2: set_Pr1986765409at_nat,R: set_Pr1490359111at_nat,X2: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 0.20/0.54 ( ( refl_o1619599232at_nat @ A2 @ R )
% 0.20/0.54 => ( ( member2027625872at_nat @ ( produc1168807639at_nat @ X2 @ Y3 ) @ R )
% 0.20/0.54 => ( member701585322at_nat @ Y3 @ A2 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % refl_onD2
% 0.20/0.54 thf(fact_273_refl__onD2,axiom,
% 0.20/0.54 ! [A2: set_Pr1590995257tate_o,R: set_Pr1702239303tate_o,X2: produc696469763tate_o,Y3: produc696469763tate_o] :
% 0.20/0.54 ( ( refl_o489021252tate_o @ A2 @ R )
% 0.20/0.54 => ( ( member1629320336tate_o @ ( produc1684562079tate_o @ X2 @ Y3 ) @ R )
% 0.20/0.54 => ( member1838112666tate_o @ Y3 @ A2 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % refl_onD2
% 0.20/0.54 thf(fact_274_refl__onD2,axiom,
% 0.20/0.54 ! [A2: set_state,R: set_Pr795498619_state,X2: state,Y3: state] :
% 0.20/0.54 ( ( refl_on_state @ A2 @ R )
% 0.20/0.54 => ( ( member1389040324_state @ ( produc64584659_state @ X2 @ Y3 ) @ R )
% 0.20/0.54 => ( member_state @ Y3 @ A2 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % refl_onD2
% 0.20/0.54 thf(fact_275_refl__onD2,axiom,
% 0.20/0.54 ! [A2: set_nat,R: set_Pr1986765409at_nat,X2: nat,Y3: nat] :
% 0.20/0.54 ( ( refl_on_nat @ A2 @ R )
% 0.20/0.54 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ R )
% 0.20/0.54 => ( member_nat @ Y3 @ A2 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % refl_onD2
% 0.20/0.54 thf(fact_276_refl__onD1,axiom,
% 0.20/0.54 ! [A2: set_Pr795498619_state,R: set_Pr778812871_state,X2: produc1115495963_state,Y3: produc1115495963_state] :
% 0.20/0.54 ( ( refl_o1438232218_state @ A2 @ R )
% 0.20/0.54 => ( ( member768948240_state @ ( produc1964772951_state @ X2 @ Y3 ) @ R )
% 0.20/0.54 => ( member1389040324_state @ X2 @ A2 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % refl_onD1
% 0.20/0.54 thf(fact_277_refl__onD1,axiom,
% 0.20/0.54 ! [A2: set_Pr1986765409at_nat,R: set_Pr1490359111at_nat,X2: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 0.20/0.54 ( ( refl_o1619599232at_nat @ A2 @ R )
% 0.20/0.54 => ( ( member2027625872at_nat @ ( produc1168807639at_nat @ X2 @ Y3 ) @ R )
% 0.20/0.54 => ( member701585322at_nat @ X2 @ A2 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % refl_onD1
% 0.20/0.54 thf(fact_278_refl__onD1,axiom,
% 0.20/0.54 ! [A2: set_Pr1590995257tate_o,R: set_Pr1702239303tate_o,X2: produc696469763tate_o,Y3: produc696469763tate_o] :
% 0.20/0.54 ( ( refl_o489021252tate_o @ A2 @ R )
% 0.20/0.54 => ( ( member1629320336tate_o @ ( produc1684562079tate_o @ X2 @ Y3 ) @ R )
% 0.20/0.54 => ( member1838112666tate_o @ X2 @ A2 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % refl_onD1
% 0.20/0.54 thf(fact_279_refl__onD1,axiom,
% 0.20/0.54 ! [A2: set_state,R: set_Pr795498619_state,X2: state,Y3: state] :
% 0.20/0.54 ( ( refl_on_state @ A2 @ R )
% 0.20/0.54 => ( ( member1389040324_state @ ( produc64584659_state @ X2 @ Y3 ) @ R )
% 0.20/0.54 => ( member_state @ X2 @ A2 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % refl_onD1
% 0.20/0.54 thf(fact_280_refl__onD1,axiom,
% 0.20/0.54 ! [A2: set_nat,R: set_Pr1986765409at_nat,X2: nat,Y3: nat] :
% 0.20/0.54 ( ( refl_on_nat @ A2 @ R )
% 0.20/0.54 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ R )
% 0.20/0.54 => ( member_nat @ X2 @ A2 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % refl_onD1
% 0.20/0.54 thf(fact_281_refl__onD,axiom,
% 0.20/0.54 ! [A2: set_Pr795498619_state,R: set_Pr778812871_state,A: produc1115495963_state] :
% 0.20/0.54 ( ( refl_o1438232218_state @ A2 @ R )
% 0.20/0.54 => ( ( member1389040324_state @ A @ A2 )
% 0.20/0.54 => ( member768948240_state @ ( produc1964772951_state @ A @ A ) @ R ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % refl_onD
% 0.20/0.54 thf(fact_282_refl__onD,axiom,
% 0.20/0.54 ! [A2: set_Pr1986765409at_nat,R: set_Pr1490359111at_nat,A: product_prod_nat_nat] :
% 0.20/0.54 ( ( refl_o1619599232at_nat @ A2 @ R )
% 0.20/0.54 => ( ( member701585322at_nat @ A @ A2 )
% 0.20/0.54 => ( member2027625872at_nat @ ( produc1168807639at_nat @ A @ A ) @ R ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % refl_onD
% 0.20/0.54 thf(fact_283_refl__onD,axiom,
% 0.20/0.54 ! [A2: set_Pr1590995257tate_o,R: set_Pr1702239303tate_o,A: produc696469763tate_o] :
% 0.20/0.54 ( ( refl_o489021252tate_o @ A2 @ R )
% 0.20/0.54 => ( ( member1838112666tate_o @ A @ A2 )
% 0.20/0.54 => ( member1629320336tate_o @ ( produc1684562079tate_o @ A @ A ) @ R ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % refl_onD
% 0.20/0.54 thf(fact_284_refl__onD,axiom,
% 0.20/0.54 ! [A2: set_state,R: set_Pr795498619_state,A: state] :
% 0.20/0.54 ( ( refl_on_state @ A2 @ R )
% 0.20/0.54 => ( ( member_state @ A @ A2 )
% 0.20/0.54 => ( member1389040324_state @ ( produc64584659_state @ A @ A ) @ R ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % refl_onD
% 0.20/0.54 thf(fact_285_refl__onD,axiom,
% 0.20/0.54 ! [A2: set_nat,R: set_Pr1986765409at_nat,A: nat] :
% 0.20/0.54 ( ( refl_on_nat @ A2 @ R )
% 0.20/0.54 => ( ( member_nat @ A @ A2 )
% 0.20/0.54 => ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ A ) @ R ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % refl_onD
% 0.20/0.54 thf(fact_286_case__prodD,axiom,
% 0.20/0.54 ! [F: ( a > state > $o ) > produc204914599tate_o > $o,A: a > state > $o,B2: produc204914599tate_o] :
% 0.20/0.54 ( ( produc1271576886te_o_o @ F @ ( produc33908149tate_o @ A @ B2 ) )
% 0.20/0.54 => ( F @ A @ B2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % case_prodD
% 0.20/0.54 thf(fact_287_case__prodD,axiom,
% 0.20/0.54 ! [F: com > ( a > state > $o ) > $o,A: com,B2: a > state > $o] :
% 0.20/0.54 ( ( produc281270436te_o_o @ F @ ( produc1948644831tate_o @ A @ B2 ) )
% 0.20/0.54 => ( F @ A @ B2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % case_prodD
% 0.20/0.54 thf(fact_288_case__prodD,axiom,
% 0.20/0.54 ! [F: state > state > $o,A: state,B2: state] :
% 0.20/0.54 ( ( produc789892016tate_o @ F @ ( produc64584659_state @ A @ B2 ) )
% 0.20/0.54 => ( F @ A @ B2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % case_prodD
% 0.20/0.54 thf(fact_289_case__prodD,axiom,
% 0.20/0.54 ! [F: nat > nat > $o,A: nat,B2: nat] :
% 0.20/0.54 ( ( produc949581770_nat_o @ F @ ( product_Pair_nat_nat @ A @ B2 ) )
% 0.20/0.54 => ( F @ A @ B2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % case_prodD
% 0.20/0.54 thf(fact_290_case__prodE,axiom,
% 0.20/0.54 ! [C2: ( a > state > $o ) > produc204914599tate_o > $o,P3: produc696469763tate_o] :
% 0.20/0.54 ( ( produc1271576886te_o_o @ C2 @ P3 )
% 0.20/0.54 => ~ ! [X3: a > state > $o,Y2: produc204914599tate_o] :
% 0.20/0.54 ( ( P3
% 0.20/0.54 = ( produc33908149tate_o @ X3 @ Y2 ) )
% 0.20/0.54 => ~ ( C2 @ X3 @ Y2 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % case_prodE
% 0.20/0.54 thf(fact_291_case__prodE,axiom,
% 0.20/0.54 ! [C2: com > ( a > state > $o ) > $o,P3: produc204914599tate_o] :
% 0.20/0.54 ( ( produc281270436te_o_o @ C2 @ P3 )
% 0.20/0.54 => ~ ! [X3: com,Y2: a > state > $o] :
% 0.20/0.54 ( ( P3
% 0.20/0.54 = ( produc1948644831tate_o @ X3 @ Y2 ) )
% 0.20/0.54 => ~ ( C2 @ X3 @ Y2 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % case_prodE
% 0.20/0.54 thf(fact_292_case__prodE,axiom,
% 0.20/0.54 ! [C2: state > state > $o,P3: produc1115495963_state] :
% 0.20/0.54 ( ( produc789892016tate_o @ C2 @ P3 )
% 0.20/0.54 => ~ ! [X3: state,Y2: state] :
% 0.20/0.54 ( ( P3
% 0.20/0.54 = ( produc64584659_state @ X3 @ Y2 ) )
% 0.20/0.54 => ~ ( C2 @ X3 @ Y2 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % case_prodE
% 0.20/0.54 thf(fact_293_case__prodE,axiom,
% 0.20/0.54 ! [C2: nat > nat > $o,P3: product_prod_nat_nat] :
% 0.20/0.54 ( ( produc949581770_nat_o @ C2 @ P3 )
% 0.20/0.54 => ~ ! [X3: nat,Y2: nat] :
% 0.20/0.54 ( ( P3
% 0.20/0.54 = ( product_Pair_nat_nat @ X3 @ Y2 ) )
% 0.20/0.54 => ~ ( C2 @ X3 @ Y2 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % case_prodE
% 0.20/0.54 thf(fact_294_total__on__def,axiom,
% 0.20/0.54 ( total_on_state
% 0.20/0.54 = ( ^ [A5: set_state,R3: set_Pr795498619_state] :
% 0.20/0.54 ! [X: state] :
% 0.20/0.54 ( ( member_state @ X @ A5 )
% 0.20/0.54 => ! [Y5: state] :
% 0.20/0.54 ( ( member_state @ Y5 @ A5 )
% 0.20/0.54 => ( ( X != Y5 )
% 0.20/0.54 => ( ( member1389040324_state @ ( produc64584659_state @ X @ Y5 ) @ R3 )
% 0.20/0.54 | ( member1389040324_state @ ( produc64584659_state @ Y5 @ X ) @ R3 ) ) ) ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % total_on_def
% 0.20/0.54 thf(fact_295_total__on__def,axiom,
% 0.20/0.54 ( total_on_nat
% 0.20/0.54 = ( ^ [A5: set_nat,R3: set_Pr1986765409at_nat] :
% 0.20/0.54 ! [X: nat] :
% 0.20/0.54 ( ( member_nat @ X @ A5 )
% 0.20/0.54 => ! [Y5: nat] :
% 0.20/0.54 ( ( member_nat @ Y5 @ A5 )
% 0.20/0.54 => ( ( X != Y5 )
% 0.20/0.54 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Y5 ) @ R3 )
% 0.20/0.54 | ( member701585322at_nat @ ( product_Pair_nat_nat @ Y5 @ X ) @ R3 ) ) ) ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % total_on_def
% 0.20/0.54 thf(fact_296_total__onI,axiom,
% 0.20/0.54 ! [A2: set_Pr795498619_state,R: set_Pr778812871_state] :
% 0.20/0.54 ( ! [X3: produc1115495963_state,Y2: produc1115495963_state] :
% 0.20/0.54 ( ( member1389040324_state @ X3 @ A2 )
% 0.20/0.54 => ( ( member1389040324_state @ Y2 @ A2 )
% 0.20/0.54 => ( ( X3 != Y2 )
% 0.20/0.54 => ( ( member768948240_state @ ( produc1964772951_state @ X3 @ Y2 ) @ R )
% 0.20/0.54 | ( member768948240_state @ ( produc1964772951_state @ Y2 @ X3 ) @ R ) ) ) ) )
% 0.20/0.54 => ( total_1316653983_state @ A2 @ R ) ) ).
% 0.20/0.54
% 0.20/0.54 % total_onI
% 0.20/0.54 thf(fact_297_total__onI,axiom,
% 0.20/0.54 ! [A2: set_Pr1986765409at_nat,R: set_Pr1490359111at_nat] :
% 0.20/0.54 ( ! [X3: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 0.20/0.54 ( ( member701585322at_nat @ X3 @ A2 )
% 0.20/0.54 => ( ( member701585322at_nat @ Y2 @ A2 )
% 0.20/0.54 => ( ( X3 != Y2 )
% 0.20/0.54 => ( ( member2027625872at_nat @ ( produc1168807639at_nat @ X3 @ Y2 ) @ R )
% 0.20/0.54 | ( member2027625872at_nat @ ( produc1168807639at_nat @ Y2 @ X3 ) @ R ) ) ) ) )
% 0.20/0.54 => ( total_1775715973at_nat @ A2 @ R ) ) ).
% 0.20/0.54
% 0.20/0.54 % total_onI
% 0.20/0.54 thf(fact_298_total__onI,axiom,
% 0.20/0.54 ! [A2: set_Pr1590995257tate_o,R: set_Pr1702239303tate_o] :
% 0.20/0.54 ( ! [X3: produc696469763tate_o,Y2: produc696469763tate_o] :
% 0.20/0.54 ( ( member1838112666tate_o @ X3 @ A2 )
% 0.20/0.54 => ( ( member1838112666tate_o @ Y2 @ A2 )
% 0.20/0.54 => ( ( X3 != Y2 )
% 0.20/0.54 => ( ( member1629320336tate_o @ ( produc1684562079tate_o @ X3 @ Y2 ) @ R )
% 0.20/0.54 | ( member1629320336tate_o @ ( produc1684562079tate_o @ Y2 @ X3 ) @ R ) ) ) ) )
% 0.20/0.54 => ( total_795385983tate_o @ A2 @ R ) ) ).
% 0.20/0.54
% 0.20/0.54 % total_onI
% 0.20/0.54 thf(fact_299_total__onI,axiom,
% 0.20/0.54 ! [A2: set_state,R: set_Pr795498619_state] :
% 0.20/0.54 ( ! [X3: state,Y2: state] :
% 0.20/0.54 ( ( member_state @ X3 @ A2 )
% 0.20/0.54 => ( ( member_state @ Y2 @ A2 )
% 0.20/0.54 => ( ( X3 != Y2 )
% 0.20/0.54 => ( ( member1389040324_state @ ( produc64584659_state @ X3 @ Y2 ) @ R )
% 0.20/0.54 | ( member1389040324_state @ ( produc64584659_state @ Y2 @ X3 ) @ R ) ) ) ) )
% 0.20/0.54 => ( total_on_state @ A2 @ R ) ) ).
% 0.20/0.54
% 0.20/0.54 % total_onI
% 0.20/0.54 thf(fact_300_total__onI,axiom,
% 0.20/0.54 ! [A2: set_nat,R: set_Pr1986765409at_nat] :
% 0.20/0.54 ( ! [X3: nat,Y2: nat] :
% 0.20/0.54 ( ( member_nat @ X3 @ A2 )
% 0.20/0.54 => ( ( member_nat @ Y2 @ A2 )
% 0.20/0.54 => ( ( X3 != Y2 )
% 0.20/0.54 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X3 @ Y2 ) @ R )
% 0.20/0.54 | ( member701585322at_nat @ ( product_Pair_nat_nat @ Y2 @ X3 ) @ R ) ) ) ) )
% 0.20/0.54 => ( total_on_nat @ A2 @ R ) ) ).
% 0.20/0.54
% 0.20/0.54 % total_onI
% 0.20/0.54 thf(fact_301_total__on__empty,axiom,
% 0.20/0.54 ! [R: set_Pr1986765409at_nat] : ( total_on_nat @ bot_bot_set_nat @ R ) ).
% 0.20/0.54
% 0.20/0.54 % total_on_empty
% 0.20/0.54 thf(fact_302_total__on__empty,axiom,
% 0.20/0.54 ! [R: set_Pr1702239303tate_o] : ( total_795385983tate_o @ bot_bo170732493tate_o @ R ) ).
% 0.20/0.54
% 0.20/0.54 % total_on_empty
% 0.20/0.54 thf(fact_303_total__on__empty,axiom,
% 0.20/0.54 ! [R: set_Pr1490359111at_nat] : ( total_1775715973at_nat @ bot_bo2130386637at_nat @ R ) ).
% 0.20/0.54
% 0.20/0.54 % total_on_empty
% 0.20/0.54 thf(fact_304_total__on__empty,axiom,
% 0.20/0.54 ! [R: set_Pr778812871_state] : ( total_1316653983_state @ bot_bo1625160935_state @ R ) ).
% 0.20/0.54
% 0.20/0.54 % total_on_empty
% 0.20/0.54 thf(fact_305_case__prodE2,axiom,
% 0.20/0.54 ! [Q: $o > $o,P: state > state > $o,Z5: produc1115495963_state] :
% 0.20/0.54 ( ( Q @ ( produc789892016tate_o @ P @ Z5 ) )
% 0.20/0.54 => ~ ! [X3: state,Y2: state] :
% 0.20/0.54 ( ( Z5
% 0.20/0.54 = ( produc64584659_state @ X3 @ Y2 ) )
% 0.20/0.54 => ~ ( Q @ ( P @ X3 @ Y2 ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % case_prodE2
% 0.20/0.54 thf(fact_306_case__prodE2,axiom,
% 0.20/0.54 ! [Q: $o > $o,P: nat > nat > $o,Z5: product_prod_nat_nat] :
% 0.20/0.54 ( ( Q @ ( produc949581770_nat_o @ P @ Z5 ) )
% 0.20/0.54 => ~ ! [X3: nat,Y2: nat] :
% 0.20/0.54 ( ( Z5
% 0.20/0.54 = ( product_Pair_nat_nat @ X3 @ Y2 ) )
% 0.20/0.54 => ~ ( Q @ ( P @ X3 @ Y2 ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % case_prodE2
% 0.20/0.54 thf(fact_307_case__prod__eta,axiom,
% 0.20/0.54 ! [F: produc1115495963_state > $o] :
% 0.20/0.54 ( ( produc789892016tate_o
% 0.20/0.54 @ ^ [X: state,Y5: state] : ( F @ ( produc64584659_state @ X @ Y5 ) ) )
% 0.20/0.54 = F ) ).
% 0.20/0.54
% 0.20/0.54 % case_prod_eta
% 0.20/0.54 thf(fact_308_case__prod__eta,axiom,
% 0.20/0.54 ! [F: product_prod_nat_nat > $o] :
% 0.20/0.54 ( ( produc949581770_nat_o
% 0.20/0.54 @ ^ [X: nat,Y5: nat] : ( F @ ( product_Pair_nat_nat @ X @ Y5 ) ) )
% 0.20/0.54 = F ) ).
% 0.20/0.54
% 0.20/0.54 % case_prod_eta
% 0.20/0.54 thf(fact_309_cond__case__prod__eta,axiom,
% 0.20/0.54 ! [F: state > state > $o,G: produc1115495963_state > $o] :
% 0.20/0.54 ( ! [X3: state,Y2: state] :
% 0.20/0.54 ( ( F @ X3 @ Y2 )
% 0.20/0.54 = ( G @ ( produc64584659_state @ X3 @ Y2 ) ) )
% 0.20/0.54 => ( ( produc789892016tate_o @ F )
% 0.20/0.54 = G ) ) ).
% 0.20/0.54
% 0.20/0.54 % cond_case_prod_eta
% 0.20/0.54 thf(fact_310_cond__case__prod__eta,axiom,
% 0.20/0.54 ! [F: nat > nat > $o,G: product_prod_nat_nat > $o] :
% 0.20/0.54 ( ! [X3: nat,Y2: nat] :
% 0.20/0.54 ( ( F @ X3 @ Y2 )
% 0.20/0.54 = ( G @ ( product_Pair_nat_nat @ X3 @ Y2 ) ) )
% 0.20/0.54 => ( ( produc949581770_nat_o @ F )
% 0.20/0.54 = G ) ) ).
% 0.20/0.54
% 0.20/0.54 % cond_case_prod_eta
% 0.20/0.54 thf(fact_311_lnear__order__on__empty,axiom,
% 0.20/0.54 order_130026331on_nat @ bot_bot_set_nat @ bot_bo2130386637at_nat ).
% 0.20/0.54
% 0.20/0.54 % lnear_order_on_empty
% 0.20/0.54 thf(fact_312_lnear__order__on__empty,axiom,
% 0.20/0.54 order_286167592_state @ bot_bot_set_state @ bot_bo1625160935_state ).
% 0.20/0.54
% 0.20/0.54 % lnear_order_on_empty
% 0.20/0.54 thf(fact_313_lnear__order__on__empty,axiom,
% 0.20/0.54 order_50454158tate_o @ bot_bo170732493tate_o @ bot_bo1714653363tate_o ).
% 0.20/0.54
% 0.20/0.54 % lnear_order_on_empty
% 0.20/0.54 thf(fact_314_lnear__order__on__empty,axiom,
% 0.20/0.54 order_721919926at_nat @ bot_bo2130386637at_nat @ bot_bo34127283at_nat ).
% 0.20/0.54
% 0.20/0.54 % lnear_order_on_empty
% 0.20/0.54 thf(fact_315_lnear__order__on__empty,axiom,
% 0.20/0.54 order_178668240_state @ bot_bo1625160935_state @ bot_bo1331673139_state ).
% 0.20/0.54
% 0.20/0.54 % lnear_order_on_empty
% 0.20/0.54 thf(fact_316_refl__on__empty,axiom,
% 0.20/0.54 refl_on_nat @ bot_bot_set_nat @ bot_bo2130386637at_nat ).
% 0.20/0.54
% 0.20/0.54 % refl_on_empty
% 0.20/0.54 thf(fact_317_refl__on__empty,axiom,
% 0.20/0.54 refl_on_state @ bot_bot_set_state @ bot_bo1625160935_state ).
% 0.20/0.54
% 0.20/0.54 % refl_on_empty
% 0.20/0.54 thf(fact_318_refl__on__empty,axiom,
% 0.20/0.54 refl_o489021252tate_o @ bot_bo170732493tate_o @ bot_bo1714653363tate_o ).
% 0.20/0.54
% 0.20/0.54 % refl_on_empty
% 0.20/0.54 thf(fact_319_refl__on__empty,axiom,
% 0.20/0.54 refl_o1619599232at_nat @ bot_bo2130386637at_nat @ bot_bo34127283at_nat ).
% 0.20/0.54
% 0.20/0.54 % refl_on_empty
% 0.20/0.54 thf(fact_320_refl__on__empty,axiom,
% 0.20/0.54 refl_o1438232218_state @ bot_bo1625160935_state @ bot_bo1331673139_state ).
% 0.20/0.54
% 0.20/0.54 % refl_on_empty
% 0.20/0.54 thf(fact_321_split__cong,axiom,
% 0.20/0.54 ! [Q5: produc1115495963_state,F: state > state > $o,G: state > state > $o,P3: produc1115495963_state] :
% 0.20/0.54 ( ! [X3: state,Y2: state] :
% 0.20/0.54 ( ( ( produc64584659_state @ X3 @ Y2 )
% 0.20/0.54 = Q5 )
% 0.20/0.54 => ( ( F @ X3 @ Y2 )
% 0.20/0.54 = ( G @ X3 @ Y2 ) ) )
% 0.20/0.54 => ( ( P3 = Q5 )
% 0.20/0.54 => ( ( produc789892016tate_o @ F @ P3 )
% 0.20/0.54 = ( produc789892016tate_o @ G @ Q5 ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % split_cong
% 0.20/0.54 thf(fact_322_split__cong,axiom,
% 0.20/0.54 ! [Q5: product_prod_nat_nat,F: nat > nat > $o,G: nat > nat > $o,P3: product_prod_nat_nat] :
% 0.20/0.54 ( ! [X3: nat,Y2: nat] :
% 0.20/0.54 ( ( ( product_Pair_nat_nat @ X3 @ Y2 )
% 0.20/0.54 = Q5 )
% 0.20/0.54 => ( ( F @ X3 @ Y2 )
% 0.20/0.54 = ( G @ X3 @ Y2 ) ) )
% 0.20/0.54 => ( ( P3 = Q5 )
% 0.20/0.54 => ( ( produc949581770_nat_o @ F @ P3 )
% 0.20/0.54 = ( produc949581770_nat_o @ G @ Q5 ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % split_cong
% 0.20/0.54 thf(fact_323_aboveS__def,axiom,
% 0.20/0.54 ( order_2027321734_state
% 0.20/0.54 = ( ^ [R3: set_Pr778812871_state,A3: produc1115495963_state] :
% 0.20/0.54 ( collec496201222_state
% 0.20/0.54 @ ^ [B7: produc1115495963_state] :
% 0.20/0.54 ( ( B7 != A3 )
% 0.20/0.54 & ( member768948240_state @ ( produc1964772951_state @ A3 @ B7 ) @ R3 ) ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % aboveS_def
% 0.20/0.54 thf(fact_324_aboveS__def,axiom,
% 0.20/0.54 ( order_665764460at_nat
% 0.20/0.54 = ( ^ [R3: set_Pr1490359111at_nat,A3: product_prod_nat_nat] :
% 0.20/0.54 ( collec7649004at_nat
% 0.20/0.54 @ ^ [B7: product_prod_nat_nat] :
% 0.20/0.54 ( ( B7 != A3 )
% 0.20/0.54 & ( member2027625872at_nat @ ( produc1168807639at_nat @ A3 @ B7 ) @ R3 ) ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % aboveS_def
% 0.20/0.54 thf(fact_325_aboveS__def,axiom,
% 0.20/0.54 ( order_1121016664tate_o
% 0.20/0.54 = ( ^ [R3: set_Pr1702239303tate_o,A3: produc696469763tate_o] :
% 0.20/0.54 ( collec1499596504tate_o
% 0.20/0.54 @ ^ [B7: produc696469763tate_o] :
% 0.20/0.54 ( ( B7 != A3 )
% 0.20/0.54 & ( member1629320336tate_o @ ( produc1684562079tate_o @ A3 @ B7 ) @ R3 ) ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % aboveS_def
% 0.20/0.54 thf(fact_326_aboveS__def,axiom,
% 0.20/0.54 ( order_aboveS_state
% 0.20/0.54 = ( ^ [R3: set_Pr795498619_state,A3: state] :
% 0.20/0.54 ( collect_state
% 0.20/0.54 @ ^ [B7: state] :
% 0.20/0.54 ( ( B7 != A3 )
% 0.20/0.54 & ( member1389040324_state @ ( produc64584659_state @ A3 @ B7 ) @ R3 ) ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % aboveS_def
% 0.20/0.54 thf(fact_327_aboveS__def,axiom,
% 0.20/0.54 ( order_aboveS_nat
% 0.20/0.54 = ( ^ [R3: set_Pr1986765409at_nat,A3: nat] :
% 0.20/0.54 ( collect_nat
% 0.20/0.54 @ ^ [B7: nat] :
% 0.20/0.54 ( ( B7 != A3 )
% 0.20/0.54 & ( member701585322at_nat @ ( product_Pair_nat_nat @ A3 @ B7 ) @ R3 ) ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % aboveS_def
% 0.20/0.54 thf(fact_328_internal__case__prod__def,axiom,
% 0.20/0.54 produc938968666tate_o = produc789892016tate_o ).
% 0.20/0.54
% 0.20/0.54 % internal_case_prod_def
% 0.20/0.54 thf(fact_329_internal__case__prod__def,axiom,
% 0.20/0.54 produc385877620_nat_o = produc949581770_nat_o ).
% 0.20/0.54
% 0.20/0.54 % internal_case_prod_def
% 0.20/0.54 thf(fact_330_mem__case__prodI2,axiom,
% 0.20/0.54 ! [P3: product_prod_nat_nat,Z5: produc1115495963_state,C2: nat > nat > set_Pr795498619_state] :
% 0.20/0.54 ( ! [A6: nat,B6: nat] :
% 0.20/0.54 ( ( P3
% 0.20/0.54 = ( product_Pair_nat_nat @ A6 @ B6 ) )
% 0.20/0.54 => ( member1389040324_state @ Z5 @ ( C2 @ A6 @ B6 ) ) )
% 0.20/0.54 => ( member1389040324_state @ Z5 @ ( produc1654445_state @ C2 @ P3 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % mem_case_prodI2
% 0.20/0.54 thf(fact_331_mem__case__prodI2,axiom,
% 0.20/0.54 ! [P3: product_prod_nat_nat,Z5: product_prod_nat_nat,C2: nat > nat > set_Pr1986765409at_nat] :
% 0.20/0.54 ( ! [A6: nat,B6: nat] :
% 0.20/0.54 ( ( P3
% 0.20/0.54 = ( product_Pair_nat_nat @ A6 @ B6 ) )
% 0.20/0.54 => ( member701585322at_nat @ Z5 @ ( C2 @ A6 @ B6 ) ) )
% 0.20/0.54 => ( member701585322at_nat @ Z5 @ ( produc1915186323at_nat @ C2 @ P3 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % mem_case_prodI2
% 0.20/0.54 thf(fact_332_mem__case__prodI2,axiom,
% 0.20/0.54 ! [P3: product_prod_nat_nat,Z5: produc696469763tate_o,C2: nat > nat > set_Pr1590995257tate_o] :
% 0.20/0.54 ( ! [A6: nat,B6: nat] :
% 0.20/0.54 ( ( P3
% 0.20/0.54 = ( product_Pair_nat_nat @ A6 @ B6 ) )
% 0.20/0.54 => ( member1838112666tate_o @ Z5 @ ( C2 @ A6 @ B6 ) ) )
% 0.20/0.54 => ( member1838112666tate_o @ Z5 @ ( produc1610543495tate_o @ C2 @ P3 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % mem_case_prodI2
% 0.20/0.54 thf(fact_333_termi__while,axiom,
% 0.20/0.54 ! [B2: state > $o,C2: com,F: nat > state,K: nat] :
% 0.20/0.54 ( ( termi @ ( while @ B2 @ C2 ) @ ( F @ K ) )
% 0.20/0.54 => ( ! [I: nat] : ( exec @ ( F @ I ) @ C2 @ ( F @ ( suc @ I ) ) )
% 0.20/0.54 => ? [I: nat] :
% 0.20/0.54 ~ ( B2 @ ( F @ I ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % termi_while
% 0.20/0.54 thf(fact_334_termi__while__lemma,axiom,
% 0.20/0.54 ! [W: com,Fk: state,F: nat > state,K: nat,B2: state > $o,C2: com] :
% 0.20/0.54 ( ( termi @ W @ Fk )
% 0.20/0.54 => ( ( ( Fk
% 0.20/0.54 = ( F @ K ) )
% 0.20/0.54 & ( W
% 0.20/0.54 = ( while @ B2 @ C2 ) )
% 0.20/0.54 & ! [I: nat] : ( exec @ ( F @ I ) @ C2 @ ( F @ ( suc @ I ) ) ) )
% 0.20/0.54 => ? [I: nat] :
% 0.20/0.54 ~ ( B2 @ ( F @ I ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % termi_while_lemma
% 0.20/0.54 thf(fact_335_execn_Ointros_I7_J,axiom,
% 0.20/0.54 ! [S2: state,N: nat,T2: state] :
% 0.20/0.54 ( ( execn @ S2 @ body @ N @ T2 )
% 0.20/0.54 => ( execn @ S2 @ call @ ( suc @ N ) @ T2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % execn.intros(7)
% 0.20/0.54 thf(fact_336_pred__nat__def,axiom,
% 0.20/0.54 ( pred_nat
% 0.20/0.54 = ( collec7649004at_nat
% 0.20/0.54 @ ( produc949581770_nat_o
% 0.20/0.54 @ ^ [M: nat,N2: nat] :
% 0.20/0.54 ( N2
% 0.20/0.54 = ( suc @ M ) ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % pred_nat_def
% 0.20/0.54 thf(fact_337_while__rule,axiom,
% 0.20/0.54 ! [S2: state,B2: state > $o,C2: com,N: nat,T2: state,P: state > $o] :
% 0.20/0.54 ( ( execn @ S2 @ ( while @ B2 @ C2 ) @ N @ T2 )
% 0.20/0.54 => ( ( P @ S2 )
% 0.20/0.54 => ( ! [S: state,S3: state] :
% 0.20/0.54 ( ( P @ S )
% 0.20/0.54 => ( ( B2 @ S )
% 0.20/0.54 => ( ( execn @ S @ C2 @ N @ S3 )
% 0.20/0.54 => ( P @ S3 ) ) ) )
% 0.20/0.54 => ( ( P @ T2 )
% 0.20/0.54 & ~ ( B2 @ T2 ) ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % while_rule
% 0.20/0.54 thf(fact_338_while__lemma,axiom,
% 0.20/0.54 ! [S2: state,W: com,N: nat,T2: state,B2: state > $o,C2: com,P: state > $o] :
% 0.20/0.54 ( ( execn @ S2 @ W @ N @ T2 )
% 0.20/0.54 => ( ( ( W
% 0.20/0.54 = ( while @ B2 @ C2 ) )
% 0.20/0.54 & ( P @ S2 )
% 0.20/0.54 & ! [S: state,S3: state] :
% 0.20/0.54 ( ( ( P @ S )
% 0.20/0.54 & ( B2 @ S )
% 0.20/0.54 & ( execn @ S @ C2 @ N @ S3 ) )
% 0.20/0.54 => ( P @ S3 ) ) )
% 0.20/0.54 => ( ( P @ T2 )
% 0.20/0.54 & ~ ( B2 @ T2 ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % while_lemma
% 0.20/0.54 thf(fact_339_execn_OWhileTrue,axiom,
% 0.20/0.54 ! [B2: state > $o,S2: state,C2: com,N: nat,T2: state,U2: state] :
% 0.20/0.54 ( ( B2 @ S2 )
% 0.20/0.54 => ( ( execn @ S2 @ C2 @ N @ T2 )
% 0.20/0.54 => ( ( execn @ T2 @ ( while @ B2 @ C2 ) @ N @ U2 )
% 0.20/0.54 => ( execn @ S2 @ ( while @ B2 @ C2 ) @ N @ U2 ) ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % execn.WhileTrue
% 0.20/0.54 thf(fact_340_execn_OWhileFalse,axiom,
% 0.20/0.54 ! [B2: state > $o,S2: state,C2: com,N: nat] :
% 0.20/0.54 ( ~ ( B2 @ S2 )
% 0.20/0.54 => ( execn @ S2 @ ( while @ B2 @ C2 ) @ N @ S2 ) ) ).
% 0.20/0.54
% 0.20/0.54 % execn.WhileFalse
% 0.20/0.54 thf(fact_341_exec__iff__execn,axiom,
% 0.20/0.54 ( exec
% 0.20/0.54 = ( ^ [S4: state,C5: com,T3: state] :
% 0.20/0.54 ? [N2: nat] : ( execn @ S4 @ C5 @ N2 @ T3 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % exec_iff_execn
% 0.20/0.54 thf(fact_342_wf__pred__nat,axiom,
% 0.20/0.54 wf_nat @ pred_nat ).
% 0.20/0.54
% 0.20/0.54 % wf_pred_nat
% 0.20/0.54 thf(fact_343_termi_OSemi,axiom,
% 0.20/0.54 ! [C1: com,S0: state,C22: com] :
% 0.20/0.54 ( ( termi @ C1 @ S0 )
% 0.20/0.54 => ( ! [S1: state] :
% 0.20/0.54 ( ( exec @ S0 @ C1 @ S1 )
% 0.20/0.54 => ( termi @ C22 @ S1 ) )
% 0.20/0.54 => ( termi @ ( semi @ C1 @ C22 ) @ S0 ) ) ) ).
% 0.20/0.54
% 0.20/0.54 % termi.Semi
% 0.20/0.54 thf(fact_344_com_Oinject_I2_J,axiom,
% 0.20/0.54 ! [X21: com,X222: com,Y21: com,Y222: com] :
% 0.20/0.54 ( ( ( semi @ X21 @ X222 )
% 0.20/0.54 = ( semi @ Y21 @ Y222 ) )
% 0.20/0.58 = ( ( X21 = Y21 )
% 0.20/0.58 & ( X222 = Y222 ) ) ) ).
% 0.20/0.58
% 0.20/0.58 % com.inject(2)
% 0.20/0.58 thf(fact_345_execn_Ointros_I2_J,axiom,
% 0.20/0.58 ! [S0: state,C1: com,N: nat,S12: state,C22: com,S22: state] :
% 0.20/0.58 ( ( execn @ S0 @ C1 @ N @ S12 )
% 0.20/0.58 => ( ( execn @ S12 @ C22 @ N @ S22 )
% 0.20/0.58 => ( execn @ S0 @ ( semi @ C1 @ C22 ) @ N @ S22 ) ) ) ).
% 0.20/0.58
% 0.20/0.58 % execn.intros(2)
% 0.20/0.58 thf(fact_346_com_Odistinct_I13_J,axiom,
% 0.20/0.58 ! [X21: com,X222: com,X41: state > $o,X42: com] :
% 0.20/0.58 ( ( semi @ X21 @ X222 )
% 0.20/0.58 != ( while @ X41 @ X42 ) ) ).
% 0.20/0.58
% 0.20/0.58 % com.distinct(13)
% 0.20/0.58 thf(fact_347_com_Odistinct_I15_J,axiom,
% 0.20/0.58 ! [X21: com,X222: com] :
% 0.20/0.58 ( ( semi @ X21 @ X222 )
% 0.20/0.58 != call ) ).
% 0.20/0.58
% 0.20/0.58 % com.distinct(15)
% 0.20/0.58 thf(fact_348_exec_OSemi,axiom,
% 0.20/0.58 ! [S0: state,C1: com,S12: state,C22: com,S22: state] :
% 0.20/0.58 ( ( exec @ S0 @ C1 @ S12 )
% 0.20/0.58 => ( ( exec @ S12 @ C22 @ S22 )
% 0.20/0.58 => ( exec @ S0 @ ( semi @ C1 @ C22 ) @ S22 ) ) ) ).
% 0.20/0.58
% 0.20/0.58 % exec.Semi
% 0.20/0.58 thf(fact_349_wf__less__than,axiom,
% 0.20/0.58 wf_nat @ less_than ).
% 0.20/0.58
% 0.20/0.58 % wf_less_than
% 0.20/0.58 thf(fact_350_total__on__less__than,axiom,
% 0.20/0.58 ! [A2: set_nat] : ( total_on_nat @ A2 @ less_than ) ).
% 0.20/0.58
% 0.20/0.58 % total_on_less_than
% 0.20/0.58 thf(fact_351_irrefl__less__than,axiom,
% 0.20/0.58 irrefl_nat @ less_than ).
% 0.20/0.58
% 0.20/0.58 % irrefl_less_than
% 0.20/0.58 thf(fact_352_trans__less__than,axiom,
% 0.20/0.58 trans_nat @ less_than ).
% 0.20/0.58
% 0.20/0.58 % trans_less_than
% 0.20/0.58 thf(fact_353_less__than__iff,axiom,
% 0.20/0.58 ! [X2: nat,Y3: nat] :
% 0.20/0.58 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ less_than )
% 0.20/0.58 = ( ord_less_nat @ X2 @ Y3 ) ) ).
% 0.20/0.58
% 0.20/0.58 % less_than_iff
% 0.20/0.58
% 0.20/0.58 % Conjectures (3)
% 0.20/0.58 thf(conj_0,hypothesis,
% 0.20/0.58 ! [S6: state] :
% 0.20/0.58 ( ( pHoare382919414oare_a
% 0.20/0.58 @ ( insert2053719859tate_o
% 0.20/0.58 @ ( produc33908149tate_o
% 0.20/0.58 @ ^ [Z4: a,S4: state] :
% 0.20/0.58 ( ( pa @ Z4 @ S4 )
% 0.20/0.58 & ( member1389040324_state @ ( produc64584659_state @ S4 @ S6 ) @ r ) )
% 0.20/0.58 @ ( produc1948644831tate_o @ call @ qa ) )
% 0.20/0.58 @ bot_bo170732493tate_o )
% 0.20/0.58 @ ^ [Z4: a,S4: state] :
% 0.20/0.58 ( ( pa @ Z4 @ S4 )
% 0.20/0.58 & ( S4 = S6 ) )
% 0.20/0.58 @ body
% 0.20/0.58 @ qa )
% 0.20/0.58 & ( ( ! [S: state,T: state] :
% 0.20/0.58 ( ( exec @ S @ body @ T )
% 0.20/0.58 => ! [Z: a] :
% 0.20/0.58 ( ( ( pa @ Z @ S )
% 0.20/0.58 & ( member1389040324_state @ ( produc64584659_state @ S @ S6 ) @ r ) )
% 0.20/0.58 => ( qa @ Z @ T ) ) )
% 0.20/0.58 & ! [Z: a,S: state] :
% 0.20/0.58 ( ( ( pa @ Z @ S )
% 0.20/0.58 & ( member1389040324_state @ ( produc64584659_state @ S @ S6 ) @ r ) )
% 0.20/0.58 => ( termi @ body @ S ) ) )
% 0.20/0.58 => ( ! [S7: state,T4: state] :
% 0.20/0.58 ( ( exec @ S7 @ body @ T4 )
% 0.20/0.58 => ! [Z2: a] :
% 0.20/0.58 ( ( ( pa @ Z2 @ S7 )
% 0.20/0.58 & ( S7 = S6 ) )
% 0.20/0.58 => ( qa @ Z2 @ T4 ) ) )
% 0.20/0.58 & ! [Z2: a,S7: state] :
% 0.20/0.58 ( ( ( pa @ Z2 @ S7 )
% 0.20/0.58 & ( S7 = S6 ) )
% 0.20/0.58 => ( termi @ body @ S7 ) ) ) ) ) ).
% 0.20/0.58
% 0.20/0.58 thf(conj_1,hypothesis,
% 0.20/0.58 ! [Y4: state] :
% 0.20/0.58 ( ( member1389040324_state @ ( produc64584659_state @ Y4 @ x ) @ r )
% 0.20/0.58 => ( ! [S7: state,T4: state] :
% 0.20/0.58 ( ( exec @ S7 @ body @ T4 )
% 0.20/0.58 => ! [Z2: a] :
% 0.20/0.58 ( ( ( pa @ Z2 @ S7 )
% 0.20/0.59 & ( S7 = Y4 ) )
% 0.20/0.59 => ( qa @ Z2 @ T4 ) ) )
% 0.20/0.59 & ! [Z2: a,S7: state] :
% 0.20/0.59 ( ( ( pa @ Z2 @ S7 )
% 0.20/0.59 & ( S7 = Y4 ) )
% 0.20/0.59 => ( termi @ body @ S7 ) ) ) ) ).
% 0.20/0.59
% 0.20/0.59 thf(conj_2,conjecture,
% 0.20/0.59 ( ! [S: state,T: state] :
% 0.20/0.59 ( ~ ( exec @ S @ body @ T )
% 0.20/0.59 | ! [Z: a] :
% 0.20/0.59 ( ~ ( pa @ Z @ S )
% 0.20/0.59 | ( S != x )
% 0.20/0.59 | ( qa @ Z @ T ) ) )
% 0.20/0.59 & ! [Z: a,S: state] :
% 0.20/0.59 ( ~ ( pa @ Z @ S )
% 0.20/0.59 | ( S != x )
% 0.20/0.59 | ( termi @ body @ S ) ) ) ).
% 0.20/0.59
% 0.20/0.59 %------------------------------------------------------------------------------
% 0.20/0.59 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.dN4uzIvVWe/cvc5---1.0.5_17700.p...
% 0.20/0.59 (declare-sort $$unsorted 0)
% 0.20/0.59 (declare-sort tptp.set_Pr1702239303tate_o 0)
% 0.20/0.59 (declare-sort tptp.produc1307154919tate_o 0)
% 0.20/0.59 (declare-sort tptp.set_Pr1590995257tate_o 0)
% 0.20/0.59 (declare-sort tptp.set_Pr778812871_state 0)
% 0.20/0.59 (declare-sort tptp.produc696469763tate_o 0)
% 0.20/0.59 (declare-sort tptp.set_Pr1490359111at_nat 0)
% 0.20/0.59 (declare-sort tptp.produc1390548711_state 0)
% 0.20/0.59 (declare-sort tptp.produc842455143at_nat 0)
% 0.20/0.59 (declare-sort tptp.set_Pr1740974983tate_o 0)
% 0.20/0.59 (declare-sort tptp.produc204914599tate_o 0)
% 0.20/0.59 (declare-sort tptp.set_Pr795498619_state 0)
% 0.20/0.59 (declare-sort tptp.set_Pr1986765409at_nat 0)
% 0.20/0.59 (declare-sort tptp.produc1115495963_state 0)
% 0.20/0.59 (declare-sort tptp.product_prod_nat_nat 0)
% 0.20/0.59 (declare-sort tptp.set_state 0)
% 0.20/0.59 (declare-sort tptp.set_nat 0)
% 0.20/0.59 (declare-sort tptp.state 0)
% 0.20/0.59 (declare-sort tptp.com 0)
% 0.20/0.59 (declare-sort tptp.nat 0)
% 0.20/0.59 (declare-sort tptp.a 0)
% 0.20/0.59 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 0.20/0.59 (declare-fun tptp.order_aboveS_nat (tptp.set_Pr1986765409at_nat tptp.nat) tptp.set_nat)
% 0.20/0.59 (declare-fun tptp.order_aboveS_state (tptp.set_Pr795498619_state tptp.state) tptp.set_state)
% 0.20/0.59 (declare-fun tptp.order_1121016664tate_o (tptp.set_Pr1702239303tate_o tptp.produc696469763tate_o) tptp.set_Pr1590995257tate_o)
% 0.20/0.59 (declare-fun tptp.order_665764460at_nat (tptp.set_Pr1490359111at_nat tptp.product_prod_nat_nat) tptp.set_Pr1986765409at_nat)
% 0.20/0.59 (declare-fun tptp.order_2027321734_state (tptp.set_Pr778812871_state tptp.produc1115495963_state) tptp.set_Pr795498619_state)
% 0.20/0.59 (declare-fun tptp.order_130026331on_nat (tptp.set_nat tptp.set_Pr1986765409at_nat) Bool)
% 0.20/0.59 (declare-fun tptp.order_286167592_state (tptp.set_state tptp.set_Pr795498619_state) Bool)
% 0.20/0.59 (declare-fun tptp.order_50454158tate_o (tptp.set_Pr1590995257tate_o tptp.set_Pr1702239303tate_o) Bool)
% 0.20/0.59 (declare-fun tptp.order_721919926at_nat (tptp.set_Pr1986765409at_nat tptp.set_Pr1490359111at_nat) Bool)
% 0.20/0.59 (declare-fun tptp.order_178668240_state (tptp.set_Pr795498619_state tptp.set_Pr778812871_state) Bool)
% 0.20/0.59 (declare-fun tptp.bot_bo2130564770te_o_o ((-> tptp.a tptp.state Bool) tptp.produc204914599tate_o) Bool)
% 0.20/0.59 (declare-fun tptp.bot_bot_nat_nat_o (tptp.nat tptp.nat) Bool)
% 0.20/0.59 (declare-fun tptp.bot_bo935656620te_o_o (tptp.com (-> tptp.a tptp.state Bool)) Bool)
% 0.20/0.59 (declare-fun tptp.bot_bo51534648tate_o (tptp.state tptp.state) Bool)
% 0.20/0.59 (declare-fun tptp.bot_bo250281208te_o_o (tptp.produc696469763tate_o) Bool)
% 0.20/0.59 (declare-fun tptp.bot_bo513358416_nat_o (tptp.product_prod_nat_nat) Bool)
% 0.20/0.59 (declare-fun tptp.bot_bo446391478tate_o (tptp.produc1115495963_state) Bool)
% 0.20/0.59 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 0.20/0.59 (declare-fun tptp.bot_bot_set_state () tptp.set_state)
% 0.20/0.59 (declare-fun tptp.bot_bo170732493tate_o () tptp.set_Pr1590995257tate_o)
% 0.20/0.59 (declare-fun tptp.bot_bo2130386637at_nat () tptp.set_Pr1986765409at_nat)
% 0.20/0.59 (declare-fun tptp.bot_bo1692783091tate_o () tptp.set_Pr1740974983tate_o)
% 0.20/0.59 (declare-fun tptp.bot_bo1625160935_state () tptp.set_Pr795498619_state)
% 0.20/0.59 (declare-fun tptp.bot_bo1714653363tate_o () tptp.set_Pr1702239303tate_o)
% 0.20/0.59 (declare-fun tptp.bot_bo34127283at_nat () tptp.set_Pr1490359111at_nat)
% 0.20/0.59 (declare-fun tptp.bot_bo1331673139_state () tptp.set_Pr778812871_state)
% 0.20/0.59 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 0.20/0.59 (declare-fun tptp.pHoare382919414oare_a (tptp.set_Pr1590995257tate_o (-> tptp.a tptp.state Bool) tptp.com (-> tptp.a tptp.state Bool)) Bool)
% 0.20/0.59 (declare-fun tptp.hoare_a (tptp.set_Pr1590995257tate_o (-> tptp.a tptp.state Bool) tptp.com (-> tptp.a tptp.state Bool)) Bool)
% 0.20/0.59 (declare-fun tptp.body () tptp.com)
% 0.20/0.59 (declare-fun tptp.call () tptp.com)
% 0.20/0.59 (declare-fun tptp.semi (tptp.com tptp.com) tptp.com)
% 0.20/0.59 (declare-fun tptp.while ((-> tptp.state Bool) tptp.com) tptp.com)
% 0.20/0.59 (declare-fun tptp.exec (tptp.state tptp.com tptp.state) Bool)
% 0.20/0.59 (declare-fun tptp.execn (tptp.state tptp.com tptp.nat tptp.state) Bool)
% 0.20/0.59 (declare-fun tptp.termi (tptp.com tptp.state) Bool)
% 0.20/0.59 (declare-fun tptp.produc33908149tate_o ((-> tptp.a tptp.state Bool) tptp.produc204914599tate_o) tptp.produc696469763tate_o)
% 0.20/0.59 (declare-fun tptp.product_Pair_nat_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 0.20/0.59 (declare-fun tptp.produc1948644831tate_o (tptp.com (-> tptp.a tptp.state Bool)) tptp.produc204914599tate_o)
% 0.20/0.59 (declare-fun tptp.produc64584659_state (tptp.state tptp.state) tptp.produc1115495963_state)
% 0.20/0.59 (declare-fun tptp.produc1684562079tate_o (tptp.produc696469763tate_o tptp.produc696469763tate_o) tptp.produc1307154919tate_o)
% 0.20/0.59 (declare-fun tptp.produc1168807639at_nat (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.produc842455143at_nat)
% 0.20/0.59 (declare-fun tptp.produc1964772951_state (tptp.produc1115495963_state tptp.produc1115495963_state) tptp.produc1390548711_state)
% 0.20/0.59 (declare-fun tptp.produc385877620_nat_o ((-> tptp.nat tptp.nat Bool) tptp.product_prod_nat_nat) Bool)
% 0.20/0.59 (declare-fun tptp.produc938968666tate_o ((-> tptp.state tptp.state Bool) tptp.produc1115495963_state) Bool)
% 0.20/0.59 (declare-fun tptp.produc1271576886te_o_o ((-> (-> tptp.a tptp.state Bool) tptp.produc204914599tate_o Bool) tptp.produc696469763tate_o) Bool)
% 0.20/0.59 (declare-fun tptp.produc949581770_nat_o ((-> tptp.nat tptp.nat Bool) tptp.product_prod_nat_nat) Bool)
% 0.20/0.59 (declare-fun tptp.produc1610543495tate_o ((-> tptp.nat tptp.nat tptp.set_Pr1590995257tate_o) tptp.product_prod_nat_nat) tptp.set_Pr1590995257tate_o)
% 0.20/0.59 (declare-fun tptp.produc1915186323at_nat ((-> tptp.nat tptp.nat tptp.set_Pr1986765409at_nat) tptp.product_prod_nat_nat) tptp.set_Pr1986765409at_nat)
% 0.20/0.59 (declare-fun tptp.produc1654445_state ((-> tptp.nat tptp.nat tptp.set_Pr795498619_state) tptp.product_prod_nat_nat) tptp.set_Pr795498619_state)
% 0.20/0.59 (declare-fun tptp.produc281270436te_o_o ((-> tptp.com (-> tptp.a tptp.state Bool) Bool) tptp.produc204914599tate_o) Bool)
% 0.20/0.59 (declare-fun tptp.produc789892016tate_o ((-> tptp.state tptp.state Bool) tptp.produc1115495963_state) Bool)
% 0.20/0.59 (declare-fun tptp.irrefl_nat (tptp.set_Pr1986765409at_nat) Bool)
% 0.20/0.59 (declare-fun tptp.refl_on_nat (tptp.set_nat tptp.set_Pr1986765409at_nat) Bool)
% 0.20/0.59 (declare-fun tptp.refl_on_state (tptp.set_state tptp.set_Pr795498619_state) Bool)
% 0.20/0.59 (declare-fun tptp.refl_o489021252tate_o (tptp.set_Pr1590995257tate_o tptp.set_Pr1702239303tate_o) Bool)
% 0.20/0.59 (declare-fun tptp.refl_o1619599232at_nat (tptp.set_Pr1986765409at_nat tptp.set_Pr1490359111at_nat) Bool)
% 0.20/0.59 (declare-fun tptp.refl_o1438232218_state (tptp.set_Pr795498619_state tptp.set_Pr778812871_state) Bool)
% 0.20/0.59 (declare-fun tptp.total_on_nat (tptp.set_nat tptp.set_Pr1986765409at_nat) Bool)
% 0.20/0.59 (declare-fun tptp.total_on_state (tptp.set_state tptp.set_Pr795498619_state) Bool)
% 0.20/0.59 (declare-fun tptp.total_795385983tate_o (tptp.set_Pr1590995257tate_o tptp.set_Pr1702239303tate_o) Bool)
% 0.20/0.59 (declare-fun tptp.total_1775715973at_nat (tptp.set_Pr1986765409at_nat tptp.set_Pr1490359111at_nat) Bool)
% 0.20/0.59 (declare-fun tptp.total_1316653983_state (tptp.set_Pr795498619_state tptp.set_Pr778812871_state) Bool)
% 0.20/0.59 (declare-fun tptp.trans_nat (tptp.set_Pr1986765409at_nat) Bool)
% 0.20/0.59 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 0.20/0.59 (declare-fun tptp.collect_state ((-> tptp.state Bool)) tptp.set_state)
% 0.20/0.59 (declare-fun tptp.collec1499596504tate_o ((-> tptp.produc696469763tate_o Bool)) tptp.set_Pr1590995257tate_o)
% 0.20/0.59 (declare-fun tptp.collec7649004at_nat ((-> tptp.product_prod_nat_nat Bool)) tptp.set_Pr1986765409at_nat)
% 0.20/0.59 (declare-fun tptp.collec496201222_state ((-> tptp.produc1115495963_state Bool)) tptp.set_Pr795498619_state)
% 0.20/0.59 (declare-fun tptp.insert_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 0.20/0.59 (declare-fun tptp.insert_state (tptp.state tptp.set_state) tptp.set_state)
% 0.20/0.59 (declare-fun tptp.insert2053719859tate_o (tptp.produc696469763tate_o tptp.set_Pr1590995257tate_o) tptp.set_Pr1590995257tate_o)
% 0.20/0.59 (declare-fun tptp.insert271595217at_nat (tptp.product_prod_nat_nat tptp.set_Pr1986765409at_nat) tptp.set_Pr1986765409at_nat)
% 0.20/0.59 (declare-fun tptp.insert311944171_state (tptp.produc1115495963_state tptp.set_Pr795498619_state) tptp.set_Pr795498619_state)
% 0.20/0.59 (declare-fun tptp.insert1597128631tate_o (tptp.produc1307154919tate_o tptp.set_Pr1702239303tate_o) tptp.set_Pr1702239303tate_o)
% 0.20/0.59 (declare-fun tptp.insert584009271at_nat (tptp.produc842455143at_nat tptp.set_Pr1490359111at_nat) tptp.set_Pr1490359111at_nat)
% 0.20/0.59 (declare-fun tptp.insert1616594103_state (tptp.produc1390548711_state tptp.set_Pr778812871_state) tptp.set_Pr778812871_state)
% 0.20/0.59 (declare-fun tptp.is_emp807847857tate_o (tptp.set_Pr1590995257tate_o) Bool)
% 0.20/0.59 (declare-fun tptp.is_emp825011411at_nat (tptp.set_Pr1986765409at_nat) Bool)
% 0.20/0.59 (declare-fun tptp.is_emp1062983149_state (tptp.set_Pr795498619_state) Bool)
% 0.20/0.59 (declare-fun tptp.is_sin1547905295tate_o (tptp.set_Pr1590995257tate_o) Bool)
% 0.20/0.59 (declare-fun tptp.is_sin1352690165at_nat (tptp.set_Pr1986765409at_nat) Bool)
% 0.20/0.59 (declare-fun tptp.is_sin1132515087_state (tptp.set_Pr795498619_state) Bool)
% 0.20/0.59 (declare-fun tptp.the_el1569055182tate_o (tptp.set_Pr1590995257tate_o) tptp.produc696469763tate_o)
% 0.20/0.59 (declare-fun tptp.the_el1949240438at_nat (tptp.set_Pr1986765409at_nat) tptp.product_prod_nat_nat)
% 0.20/0.59 (declare-fun tptp.the_el1967402896_state (tptp.set_Pr795498619_state) tptp.produc1115495963_state)
% 0.20/0.59 (declare-fun tptp.less_than () tptp.set_Pr1986765409at_nat)
% 0.20/0.59 (declare-fun tptp.measure_nat ((-> tptp.nat tptp.nat)) tptp.set_Pr1986765409at_nat)
% 0.20/0.59 (declare-fun tptp.measure_state ((-> tptp.state tptp.nat)) tptp.set_Pr795498619_state)
% 0.20/0.59 (declare-fun tptp.pred_nat () tptp.set_Pr1986765409at_nat)
% 0.20/0.59 (declare-fun tptp.wf_nat (tptp.set_Pr1986765409at_nat) Bool)
% 0.20/0.59 (declare-fun tptp.wf_state (tptp.set_Pr795498619_state) Bool)
% 0.20/0.59 (declare-fun tptp.wf_Pro309705690tate_o (tptp.set_Pr1702239303tate_o) Bool)
% 0.20/0.59 (declare-fun tptp.wf_Pro745352042at_nat (tptp.set_Pr1490359111at_nat) Bool)
% 0.20/0.59 (declare-fun tptp.wf_Pro1783588484_state (tptp.set_Pr778812871_state) Bool)
% 0.20/0.59 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 0.20/0.59 (declare-fun tptp.member_state (tptp.state tptp.set_state) Bool)
% 0.20/0.59 (declare-fun tptp.member1838112666tate_o (tptp.produc696469763tate_o tptp.set_Pr1590995257tate_o) Bool)
% 0.20/0.59 (declare-fun tptp.member701585322at_nat (tptp.product_prod_nat_nat tptp.set_Pr1986765409at_nat) Bool)
% 0.20/0.59 (declare-fun tptp.member221067728tate_o (tptp.produc204914599tate_o tptp.set_Pr1740974983tate_o) Bool)
% 0.20/0.59 (declare-fun tptp.member1389040324_state (tptp.produc1115495963_state tptp.set_Pr795498619_state) Bool)
% 0.20/0.59 (declare-fun tptp.member1629320336tate_o (tptp.produc1307154919tate_o tptp.set_Pr1702239303tate_o) Bool)
% 0.20/0.59 (declare-fun tptp.member2027625872at_nat (tptp.produc842455143at_nat tptp.set_Pr1490359111at_nat) Bool)
% 0.20/0.59 (declare-fun tptp.member768948240_state (tptp.produc1390548711_state tptp.set_Pr778812871_state) Bool)
% 0.20/0.59 (declare-fun tptp.pa (tptp.a tptp.state) Bool)
% 0.20/0.59 (declare-fun tptp.qa (tptp.a tptp.state) Bool)
% 0.20/0.59 (declare-fun tptp.r () tptp.set_Pr795498619_state)
% 0.20/0.59 (declare-fun tptp.x () tptp.state)
% 0.20/0.59 (assert (forall ((P (-> tptp.a tptp.state Bool)) (Q (-> tptp.a tptp.state Bool))) (@ (@ (@ (@ tptp.pHoare382919414oare_a (@ (@ tptp.insert2053719859tate_o (@ (@ tptp.produc33908149tate_o P) (@ (@ tptp.produc1948644831tate_o tptp.call) Q))) tptp.bot_bo170732493tate_o)) P) tptp.call) Q)))
% 0.20/0.59 (assert (forall ((C tptp.set_Pr1590995257tate_o) (P (-> tptp.a tptp.state Bool)) (C2 tptp.com) (Q (-> tptp.a tptp.state Bool)) (Q2 (-> tptp.a tptp.state Bool))) (let ((_let_1 (@ (@ (@ tptp.pHoare382919414oare_a C) P) C2))) (=> (@ _let_1 Q) (=> (forall ((Z tptp.a) (S tptp.state)) (=> (@ (@ Q Z) S) (@ (@ Q2 Z) S))) (@ _let_1 Q2))))))
% 0.20/0.59 (assert (forall ((C tptp.set_Pr1590995257tate_o) (P2 (-> tptp.a tptp.state Bool)) (C2 tptp.com) (Q2 (-> tptp.a tptp.state Bool)) (P (-> tptp.a tptp.state Bool)) (Q (-> tptp.a tptp.state Bool))) (let ((_let_1 (@ tptp.pHoare382919414oare_a C))) (=> (@ (@ (@ _let_1 P2) C2) Q2) (=> (and (forall ((S tptp.state) (T tptp.state)) (=> (forall ((Z2 tptp.a)) (=> (@ (@ P2 Z2) S) (@ (@ Q2 Z2) T))) (forall ((Z tptp.a)) (=> (@ (@ P Z) S) (@ (@ Q Z) T))))) (forall ((S tptp.state)) (=> (exists ((Z tptp.a)) (@ (@ P Z) S)) (exists ((Z2 tptp.a)) (@ (@ P2 Z2) S))))) (@ (@ (@ _let_1 P) C2) Q))))))
% 0.20/0.59 (assert (forall ((P2 (-> tptp.a tptp.state Bool)) (P (-> tptp.a tptp.state Bool)) (C tptp.set_Pr1590995257tate_o) (C2 tptp.com) (Q (-> tptp.a tptp.state Bool))) (let ((_let_1 (@ tptp.pHoare382919414oare_a C))) (=> (forall ((Z tptp.a) (S tptp.state)) (=> (@ (@ P2 Z) S) (@ (@ P Z) S))) (=> (@ (@ (@ _let_1 P) C2) Q) (@ (@ (@ _let_1 P2) C2) Q))))))
% 0.20/0.59 (assert (forall ((A tptp.produc1115495963_state)) (= (@ tptp.collec496201222_state (lambda ((X tptp.produc1115495963_state)) (= X A))) (@ (@ tptp.insert311944171_state A) tptp.bot_bo1625160935_state))))
% 0.20/0.59 (assert (forall ((A tptp.product_prod_nat_nat)) (= (@ tptp.collec7649004at_nat (lambda ((X tptp.product_prod_nat_nat)) (= X A))) (@ (@ tptp.insert271595217at_nat A) tptp.bot_bo2130386637at_nat))))
% 0.20/0.59 (assert (forall ((A tptp.produc696469763tate_o)) (= (@ tptp.collec1499596504tate_o (lambda ((X tptp.produc696469763tate_o)) (= X A))) (@ (@ tptp.insert2053719859tate_o A) tptp.bot_bo170732493tate_o))))
% 0.20/0.59 (assert (forall ((A tptp.produc1115495963_state)) (= (@ tptp.collec496201222_state (@ (lambda ((Y tptp.produc1115495963_state) (Z3 tptp.produc1115495963_state)) (= Y Z3)) A)) (@ (@ tptp.insert311944171_state A) tptp.bot_bo1625160935_state))))
% 0.20/0.59 (assert (forall ((A tptp.product_prod_nat_nat)) (= (@ tptp.collec7649004at_nat (@ (lambda ((Y tptp.product_prod_nat_nat) (Z3 tptp.product_prod_nat_nat)) (= Y Z3)) A)) (@ (@ tptp.insert271595217at_nat A) tptp.bot_bo2130386637at_nat))))
% 0.20/0.59 (assert (forall ((A tptp.produc696469763tate_o)) (= (@ tptp.collec1499596504tate_o (@ (lambda ((Y tptp.produc696469763tate_o) (Z3 tptp.produc696469763tate_o)) (= Y Z3)) A)) (@ (@ tptp.insert2053719859tate_o A) tptp.bot_bo170732493tate_o))))
% 0.20/0.59 (assert (forall ((A tptp.produc1115495963_state)) (@ (@ tptp.member1389040324_state A) (@ (@ tptp.insert311944171_state A) tptp.bot_bo1625160935_state))))
% 0.20/0.59 (assert (forall ((A tptp.product_prod_nat_nat)) (@ (@ tptp.member701585322at_nat A) (@ (@ tptp.insert271595217at_nat A) tptp.bot_bo2130386637at_nat))))
% 0.20/0.59 (assert (forall ((A tptp.produc696469763tate_o)) (@ (@ tptp.member1838112666tate_o A) (@ (@ tptp.insert2053719859tate_o A) tptp.bot_bo170732493tate_o))))
% 0.20/0.59 (assert (forall ((S2 tptp.state)) (=> (@ (@ tptp.termi tptp.body) S2) (@ (@ tptp.termi tptp.call) S2))))
% 0.20/0.59 (assert (forall ((S2 tptp.state) (T2 tptp.state)) (let ((_let_1 (@ tptp.exec S2))) (=> (@ (@ _let_1 tptp.body) T2) (@ (@ _let_1 tptp.call) T2)))))
% 0.20/0.59 (assert (forall ((R tptp.set_Pr795498619_state) (P (-> tptp.a tptp.state Bool)) (Q (-> tptp.a tptp.state Bool))) (=> (@ tptp.wf_state R) (=> (forall ((S3 tptp.state)) (@ (@ (@ (@ tptp.pHoare382919414oare_a (@ (@ tptp.insert2053719859tate_o (@ (@ tptp.produc33908149tate_o (lambda ((Z4 tptp.a) (S4 tptp.state)) (and (@ (@ P Z4) S4) (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state S4) S3)) R)))) (@ (@ tptp.produc1948644831tate_o tptp.call) Q))) tptp.bot_bo170732493tate_o)) (lambda ((Z4 tptp.a) (S4 tptp.state)) (and (@ (@ P Z4) S4) (= S4 S3)))) tptp.body) Q)) (@ (@ (@ (@ tptp.pHoare382919414oare_a tptp.bot_bo170732493tate_o) P) tptp.call) Q)))))
% 0.20/0.59 (assert (forall ((A tptp.produc1115495963_state) (B tptp.set_Pr795498619_state) (B2 tptp.produc1115495963_state)) (let ((_let_1 (@ tptp.member1389040324_state A))) (=> (=> (not (@ _let_1 B)) (= A B2)) (@ _let_1 (@ (@ tptp.insert311944171_state B2) B))))))
% 0.20/0.59 (assert (forall ((A tptp.product_prod_nat_nat) (B tptp.set_Pr1986765409at_nat) (B2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member701585322at_nat A))) (=> (=> (not (@ _let_1 B)) (= A B2)) (@ _let_1 (@ (@ tptp.insert271595217at_nat B2) B))))))
% 0.20/0.59 (assert (forall ((A tptp.produc696469763tate_o) (B tptp.set_Pr1590995257tate_o) (B2 tptp.produc696469763tate_o)) (let ((_let_1 (@ tptp.member1838112666tate_o A))) (=> (=> (not (@ _let_1 B)) (= A B2)) (@ _let_1 (@ (@ tptp.insert2053719859tate_o B2) B))))))
% 0.20/0.59 (assert (forall ((A tptp.produc1115495963_state) (B2 tptp.produc1115495963_state) (A2 tptp.set_Pr795498619_state)) (let ((_let_1 (@ tptp.member1389040324_state A))) (= (@ _let_1 (@ (@ tptp.insert311944171_state B2) A2)) (or (= A B2) (@ _let_1 A2))))))
% 0.20/0.59 (assert (forall ((A tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat) (A2 tptp.set_Pr1986765409at_nat)) (let ((_let_1 (@ tptp.member701585322at_nat A))) (= (@ _let_1 (@ (@ tptp.insert271595217at_nat B2) A2)) (or (= A B2) (@ _let_1 A2))))))
% 0.20/0.59 (assert (forall ((A tptp.produc696469763tate_o) (B2 tptp.produc696469763tate_o) (A2 tptp.set_Pr1590995257tate_o)) (let ((_let_1 (@ tptp.member1838112666tate_o A))) (= (@ _let_1 (@ (@ tptp.insert2053719859tate_o B2) A2)) (or (= A B2) (@ _let_1 A2))))))
% 0.20/0.59 (assert (forall ((X2 tptp.produc696469763tate_o) (A2 tptp.set_Pr1590995257tate_o)) (let ((_let_1 (@ tptp.insert2053719859tate_o X2))) (let ((_let_2 (@ _let_1 A2))) (= (@ _let_1 _let_2) _let_2)))))
% 0.20/0.59 (assert (forall ((X2 tptp.product_prod_nat_nat) (A2 tptp.set_Pr1986765409at_nat)) (let ((_let_1 (@ tptp.insert271595217at_nat X2))) (let ((_let_2 (@ _let_1 A2))) (= (@ _let_1 _let_2) _let_2)))))
% 0.20/0.59 (assert (forall ((X2 tptp.produc1115495963_state) (A2 tptp.set_Pr795498619_state)) (let ((_let_1 (@ tptp.insert311944171_state X2))) (let ((_let_2 (@ _let_1 A2))) (= (@ _let_1 _let_2) _let_2)))))
% 0.20/0.59 (assert (forall ((P (-> tptp.a tptp.state Bool)) (Q (-> tptp.a tptp.state Bool))) (=> (@ (@ (@ (@ tptp.hoare_a (@ (@ tptp.insert2053719859tate_o (@ (@ tptp.produc33908149tate_o P) (@ (@ tptp.produc1948644831tate_o tptp.call) Q))) tptp.bot_bo170732493tate_o)) P) tptp.body) Q) (@ (@ (@ (@ tptp.hoare_a tptp.bot_bo170732493tate_o) P) tptp.call) Q))))
% 0.20/0.59 (assert (forall ((C2 tptp.produc696469763tate_o)) (not (@ (@ tptp.member1838112666tate_o C2) tptp.bot_bo170732493tate_o))))
% 0.20/0.59 (assert (forall ((C2 tptp.product_prod_nat_nat)) (not (@ (@ tptp.member701585322at_nat C2) tptp.bot_bo2130386637at_nat))))
% 0.20/0.59 (assert (forall ((C2 tptp.produc1115495963_state)) (not (@ (@ tptp.member1389040324_state C2) tptp.bot_bo1625160935_state))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr1590995257tate_o)) (= (forall ((X tptp.produc696469763tate_o)) (not (@ (@ tptp.member1838112666tate_o X) A2))) (= A2 tptp.bot_bo170732493tate_o))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr1986765409at_nat)) (= (forall ((X tptp.product_prod_nat_nat)) (not (@ (@ tptp.member701585322at_nat X) A2))) (= A2 tptp.bot_bo2130386637at_nat))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr795498619_state)) (= (forall ((X tptp.produc1115495963_state)) (not (@ (@ tptp.member1389040324_state X) A2))) (= A2 tptp.bot_bo1625160935_state))))
% 0.20/0.59 (assert (forall ((P (-> tptp.produc696469763tate_o Bool))) (= (= tptp.bot_bo170732493tate_o (@ tptp.collec1499596504tate_o P)) (forall ((X tptp.produc696469763tate_o)) (not (@ P X))))))
% 0.20/0.59 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool))) (= (= tptp.bot_bo2130386637at_nat (@ tptp.collec7649004at_nat P)) (forall ((X tptp.product_prod_nat_nat)) (not (@ P X))))))
% 0.20/0.59 (assert (forall ((P (-> tptp.produc1115495963_state Bool))) (= (= tptp.bot_bo1625160935_state (@ tptp.collec496201222_state P)) (forall ((X tptp.produc1115495963_state)) (not (@ P X))))))
% 0.20/0.59 (assert (forall ((P (-> tptp.produc696469763tate_o Bool))) (= (= (@ tptp.collec1499596504tate_o P) tptp.bot_bo170732493tate_o) (forall ((X tptp.produc696469763tate_o)) (not (@ P X))))))
% 0.20/0.59 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool))) (= (= (@ tptp.collec7649004at_nat P) tptp.bot_bo2130386637at_nat) (forall ((X tptp.product_prod_nat_nat)) (not (@ P X))))))
% 0.20/0.59 (assert (forall ((P (-> tptp.produc1115495963_state Bool))) (= (= (@ tptp.collec496201222_state P) tptp.bot_bo1625160935_state) (forall ((X tptp.produc1115495963_state)) (not (@ P X))))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr1590995257tate_o)) (= (exists ((X tptp.produc696469763tate_o)) (@ (@ tptp.member1838112666tate_o X) A2)) (not (= A2 tptp.bot_bo170732493tate_o)))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr1986765409at_nat)) (= (exists ((X tptp.product_prod_nat_nat)) (@ (@ tptp.member701585322at_nat X) A2)) (not (= A2 tptp.bot_bo2130386637at_nat)))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr795498619_state)) (= (exists ((X tptp.produc1115495963_state)) (@ (@ tptp.member1389040324_state X) A2)) (not (= A2 tptp.bot_bo1625160935_state)))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr1590995257tate_o)) (=> (forall ((Y2 tptp.produc696469763tate_o)) (not (@ (@ tptp.member1838112666tate_o Y2) A2))) (= A2 tptp.bot_bo170732493tate_o))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr1986765409at_nat)) (=> (forall ((Y2 tptp.product_prod_nat_nat)) (not (@ (@ tptp.member701585322at_nat Y2) A2))) (= A2 tptp.bot_bo2130386637at_nat))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr795498619_state)) (=> (forall ((Y2 tptp.produc1115495963_state)) (not (@ (@ tptp.member1389040324_state Y2) A2))) (= A2 tptp.bot_bo1625160935_state))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr1590995257tate_o) (A tptp.produc696469763tate_o)) (=> (= A2 tptp.bot_bo170732493tate_o) (not (@ (@ tptp.member1838112666tate_o A) A2)))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr1986765409at_nat) (A tptp.product_prod_nat_nat)) (=> (= A2 tptp.bot_bo2130386637at_nat) (not (@ (@ tptp.member701585322at_nat A) A2)))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr795498619_state) (A tptp.produc1115495963_state)) (=> (= A2 tptp.bot_bo1625160935_state) (not (@ (@ tptp.member1389040324_state A) A2)))))
% 0.20/0.59 (assert (forall ((A tptp.produc696469763tate_o)) (not (@ (@ tptp.member1838112666tate_o A) tptp.bot_bo170732493tate_o))))
% 0.20/0.59 (assert (forall ((A tptp.product_prod_nat_nat)) (not (@ (@ tptp.member701585322at_nat A) tptp.bot_bo2130386637at_nat))))
% 0.20/0.59 (assert (forall ((A tptp.produc1115495963_state)) (not (@ (@ tptp.member1389040324_state A) tptp.bot_bo1625160935_state))))
% 0.20/0.59 (assert (forall ((A tptp.produc1115495963_state) (A2 tptp.set_Pr795498619_state)) (=> (@ (@ tptp.member1389040324_state A) A2) (exists ((B3 tptp.set_Pr795498619_state)) (and (= A2 (@ (@ tptp.insert311944171_state A) B3)) (not (@ (@ tptp.member1389040324_state A) B3)))))))
% 0.20/0.59 (assert (forall ((A tptp.product_prod_nat_nat) (A2 tptp.set_Pr1986765409at_nat)) (=> (@ (@ tptp.member701585322at_nat A) A2) (exists ((B3 tptp.set_Pr1986765409at_nat)) (and (= A2 (@ (@ tptp.insert271595217at_nat A) B3)) (not (@ (@ tptp.member701585322at_nat A) B3)))))))
% 0.20/0.59 (assert (forall ((A tptp.produc696469763tate_o) (A2 tptp.set_Pr1590995257tate_o)) (=> (@ (@ tptp.member1838112666tate_o A) A2) (exists ((B3 tptp.set_Pr1590995257tate_o)) (and (= A2 (@ (@ tptp.insert2053719859tate_o A) B3)) (not (@ (@ tptp.member1838112666tate_o A) B3)))))))
% 0.20/0.59 (assert (forall ((X2 tptp.produc696469763tate_o) (Y3 tptp.produc696469763tate_o) (A2 tptp.set_Pr1590995257tate_o)) (let ((_let_1 (@ tptp.insert2053719859tate_o X2))) (let ((_let_2 (@ tptp.insert2053719859tate_o Y3))) (= (@ _let_1 (@ _let_2 A2)) (@ _let_2 (@ _let_1 A2)))))))
% 0.20/0.59 (assert (forall ((X2 tptp.product_prod_nat_nat) (Y3 tptp.product_prod_nat_nat) (A2 tptp.set_Pr1986765409at_nat)) (let ((_let_1 (@ tptp.insert271595217at_nat X2))) (let ((_let_2 (@ tptp.insert271595217at_nat Y3))) (= (@ _let_1 (@ _let_2 A2)) (@ _let_2 (@ _let_1 A2)))))))
% 0.20/0.59 (assert (forall ((X2 tptp.produc1115495963_state) (Y3 tptp.produc1115495963_state) (A2 tptp.set_Pr795498619_state)) (let ((_let_1 (@ tptp.insert311944171_state X2))) (let ((_let_2 (@ tptp.insert311944171_state Y3))) (= (@ _let_1 (@ _let_2 A2)) (@ _let_2 (@ _let_1 A2)))))))
% 0.20/0.59 (assert (forall ((A tptp.produc1115495963_state) (A2 tptp.set_Pr795498619_state) (B2 tptp.produc1115495963_state) (B tptp.set_Pr795498619_state)) (let ((_let_1 (= A B2))) (=> (not (@ (@ tptp.member1389040324_state A) A2)) (=> (not (@ (@ tptp.member1389040324_state B2) B)) (= (= (@ (@ tptp.insert311944171_state A) A2) (@ (@ tptp.insert311944171_state B2) B)) (and (=> _let_1 (= A2 B)) (=> (not _let_1) (exists ((C3 tptp.set_Pr795498619_state)) (and (= A2 (@ (@ tptp.insert311944171_state B2) C3)) (not (@ (@ tptp.member1389040324_state B2) C3)) (= B (@ (@ tptp.insert311944171_state A) C3)) (not (@ (@ tptp.member1389040324_state A) C3))))))))))))
% 0.20/0.59 (assert (forall ((A tptp.product_prod_nat_nat) (A2 tptp.set_Pr1986765409at_nat) (B2 tptp.product_prod_nat_nat) (B tptp.set_Pr1986765409at_nat)) (let ((_let_1 (= A B2))) (=> (not (@ (@ tptp.member701585322at_nat A) A2)) (=> (not (@ (@ tptp.member701585322at_nat B2) B)) (= (= (@ (@ tptp.insert271595217at_nat A) A2) (@ (@ tptp.insert271595217at_nat B2) B)) (and (=> _let_1 (= A2 B)) (=> (not _let_1) (exists ((C3 tptp.set_Pr1986765409at_nat)) (and (= A2 (@ (@ tptp.insert271595217at_nat B2) C3)) (not (@ (@ tptp.member701585322at_nat B2) C3)) (= B (@ (@ tptp.insert271595217at_nat A) C3)) (not (@ (@ tptp.member701585322at_nat A) C3))))))))))))
% 0.20/0.59 (assert (forall ((A tptp.produc696469763tate_o) (A2 tptp.set_Pr1590995257tate_o) (B2 tptp.produc696469763tate_o) (B tptp.set_Pr1590995257tate_o)) (let ((_let_1 (= A B2))) (=> (not (@ (@ tptp.member1838112666tate_o A) A2)) (=> (not (@ (@ tptp.member1838112666tate_o B2) B)) (= (= (@ (@ tptp.insert2053719859tate_o A) A2) (@ (@ tptp.insert2053719859tate_o B2) B)) (and (=> _let_1 (= A2 B)) (=> (not _let_1) (exists ((C3 tptp.set_Pr1590995257tate_o)) (and (= A2 (@ (@ tptp.insert2053719859tate_o B2) C3)) (not (@ (@ tptp.member1838112666tate_o B2) C3)) (= B (@ (@ tptp.insert2053719859tate_o A) C3)) (not (@ (@ tptp.member1838112666tate_o A) C3))))))))))))
% 0.20/0.59 (assert (forall ((A tptp.produc1115495963_state) (A2 tptp.set_Pr795498619_state)) (=> (@ (@ tptp.member1389040324_state A) A2) (= (@ (@ tptp.insert311944171_state A) A2) A2))))
% 0.20/0.59 (assert (forall ((A tptp.product_prod_nat_nat) (A2 tptp.set_Pr1986765409at_nat)) (=> (@ (@ tptp.member701585322at_nat A) A2) (= (@ (@ tptp.insert271595217at_nat A) A2) A2))))
% 0.20/0.59 (assert (forall ((A tptp.produc696469763tate_o) (A2 tptp.set_Pr1590995257tate_o)) (=> (@ (@ tptp.member1838112666tate_o A) A2) (= (@ (@ tptp.insert2053719859tate_o A) A2) A2))))
% 0.20/0.59 (assert (forall ((X2 tptp.produc1115495963_state) (A2 tptp.set_Pr795498619_state) (B tptp.set_Pr795498619_state)) (let ((_let_1 (@ tptp.insert311944171_state X2))) (let ((_let_2 (@ tptp.member1389040324_state X2))) (=> (not (@ _let_2 A2)) (=> (not (@ _let_2 B)) (= (= (@ _let_1 A2) (@ _let_1 B)) (= A2 B))))))))
% 0.20/0.59 (assert (forall ((X2 tptp.product_prod_nat_nat) (A2 tptp.set_Pr1986765409at_nat) (B tptp.set_Pr1986765409at_nat)) (let ((_let_1 (@ tptp.insert271595217at_nat X2))) (let ((_let_2 (@ tptp.member701585322at_nat X2))) (=> (not (@ _let_2 A2)) (=> (not (@ _let_2 B)) (= (= (@ _let_1 A2) (@ _let_1 B)) (= A2 B))))))))
% 0.20/0.59 (assert (forall ((X2 tptp.produc696469763tate_o) (A2 tptp.set_Pr1590995257tate_o) (B tptp.set_Pr1590995257tate_o)) (let ((_let_1 (@ tptp.insert2053719859tate_o X2))) (let ((_let_2 (@ tptp.member1838112666tate_o X2))) (=> (not (@ _let_2 A2)) (=> (not (@ _let_2 B)) (= (= (@ _let_1 A2) (@ _let_1 B)) (= A2 B))))))))
% 0.20/0.59 (assert (forall ((X2 tptp.produc1115495963_state) (A2 tptp.set_Pr795498619_state)) (=> (@ (@ tptp.member1389040324_state X2) A2) (not (forall ((B3 tptp.set_Pr795498619_state)) (=> (= A2 (@ (@ tptp.insert311944171_state X2) B3)) (@ (@ tptp.member1389040324_state X2) B3)))))))
% 0.20/0.59 (assert (forall ((X2 tptp.product_prod_nat_nat) (A2 tptp.set_Pr1986765409at_nat)) (=> (@ (@ tptp.member701585322at_nat X2) A2) (not (forall ((B3 tptp.set_Pr1986765409at_nat)) (=> (= A2 (@ (@ tptp.insert271595217at_nat X2) B3)) (@ (@ tptp.member701585322at_nat X2) B3)))))))
% 0.20/0.59 (assert (forall ((X2 tptp.produc696469763tate_o) (A2 tptp.set_Pr1590995257tate_o)) (=> (@ (@ tptp.member1838112666tate_o X2) A2) (not (forall ((B3 tptp.set_Pr1590995257tate_o)) (=> (= A2 (@ (@ tptp.insert2053719859tate_o X2) B3)) (@ (@ tptp.member1838112666tate_o X2) B3)))))))
% 0.20/0.59 (assert (forall ((A tptp.produc1115495963_state) (B tptp.set_Pr795498619_state) (B2 tptp.produc1115495963_state)) (let ((_let_1 (@ tptp.member1389040324_state A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert311944171_state B2) B))))))
% 0.20/0.59 (assert (forall ((A tptp.product_prod_nat_nat) (B tptp.set_Pr1986765409at_nat) (B2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member701585322at_nat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert271595217at_nat B2) B))))))
% 0.20/0.59 (assert (forall ((A tptp.produc696469763tate_o) (B tptp.set_Pr1590995257tate_o) (B2 tptp.produc696469763tate_o)) (let ((_let_1 (@ tptp.member1838112666tate_o A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert2053719859tate_o B2) B))))))
% 0.20/0.59 (assert (forall ((A tptp.produc1115495963_state) (B tptp.set_Pr795498619_state)) (@ (@ tptp.member1389040324_state A) (@ (@ tptp.insert311944171_state A) B))))
% 0.20/0.59 (assert (forall ((A tptp.product_prod_nat_nat) (B tptp.set_Pr1986765409at_nat)) (@ (@ tptp.member701585322at_nat A) (@ (@ tptp.insert271595217at_nat A) B))))
% 0.20/0.59 (assert (forall ((A tptp.produc696469763tate_o) (B tptp.set_Pr1590995257tate_o)) (@ (@ tptp.member1838112666tate_o A) (@ (@ tptp.insert2053719859tate_o A) B))))
% 0.20/0.59 (assert (forall ((A tptp.produc1115495963_state) (B2 tptp.produc1115495963_state) (A2 tptp.set_Pr795498619_state)) (let ((_let_1 (@ tptp.member1389040324_state A))) (=> (@ _let_1 (@ (@ tptp.insert311944171_state B2) A2)) (=> (not (= A B2)) (@ _let_1 A2))))))
% 0.20/0.59 (assert (forall ((A tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat) (A2 tptp.set_Pr1986765409at_nat)) (let ((_let_1 (@ tptp.member701585322at_nat A))) (=> (@ _let_1 (@ (@ tptp.insert271595217at_nat B2) A2)) (=> (not (= A B2)) (@ _let_1 A2))))))
% 0.20/0.59 (assert (forall ((A tptp.produc696469763tate_o) (B2 tptp.produc696469763tate_o) (A2 tptp.set_Pr1590995257tate_o)) (let ((_let_1 (@ tptp.member1838112666tate_o A))) (=> (@ _let_1 (@ (@ tptp.insert2053719859tate_o B2) A2)) (=> (not (= A B2)) (@ _let_1 A2))))))
% 0.20/0.59 (assert (= tptp.bot_bo170732493tate_o (@ tptp.collec1499596504tate_o (lambda ((X tptp.produc696469763tate_o)) false))))
% 0.20/0.59 (assert (= tptp.bot_bo2130386637at_nat (@ tptp.collec7649004at_nat (lambda ((X tptp.product_prod_nat_nat)) false))))
% 0.20/0.59 (assert (= tptp.bot_bo1625160935_state (@ tptp.collec496201222_state (lambda ((X tptp.produc1115495963_state)) false))))
% 0.20/0.59 (assert (forall ((A tptp.produc1115495963_state) (P (-> tptp.produc1115495963_state Bool))) (= (@ (@ tptp.insert311944171_state A) (@ tptp.collec496201222_state P)) (@ tptp.collec496201222_state (lambda ((U tptp.produc1115495963_state)) (=> (not (= U A)) (@ P U)))))))
% 0.20/0.59 (assert (forall ((A tptp.product_prod_nat_nat) (P (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.insert271595217at_nat A) (@ tptp.collec7649004at_nat P)) (@ tptp.collec7649004at_nat (lambda ((U tptp.product_prod_nat_nat)) (=> (not (= U A)) (@ P U)))))))
% 0.20/0.59 (assert (forall ((A tptp.produc696469763tate_o) (P (-> tptp.produc696469763tate_o Bool))) (= (@ (@ tptp.insert2053719859tate_o A) (@ tptp.collec1499596504tate_o P)) (@ tptp.collec1499596504tate_o (lambda ((U tptp.produc696469763tate_o)) (=> (not (= U A)) (@ P U)))))))
% 0.20/0.59 (assert (= tptp.insert311944171_state (lambda ((A3 tptp.produc1115495963_state) (B4 tptp.set_Pr795498619_state)) (@ tptp.collec496201222_state (lambda ((X tptp.produc1115495963_state)) (or (= X A3) (@ (@ tptp.member1389040324_state X) B4)))))))
% 0.20/0.59 (assert (= tptp.insert271595217at_nat (lambda ((A3 tptp.product_prod_nat_nat) (B4 tptp.set_Pr1986765409at_nat)) (@ tptp.collec7649004at_nat (lambda ((X tptp.product_prod_nat_nat)) (or (= X A3) (@ (@ tptp.member701585322at_nat X) B4)))))))
% 0.20/0.59 (assert (= tptp.insert2053719859tate_o (lambda ((A3 tptp.produc696469763tate_o) (B4 tptp.set_Pr1590995257tate_o)) (@ tptp.collec1499596504tate_o (lambda ((X tptp.produc696469763tate_o)) (or (= X A3) (@ (@ tptp.member1838112666tate_o X) B4)))))))
% 0.20/0.59 (assert (forall ((A tptp.produc696469763tate_o) (B2 tptp.produc696469763tate_o)) (=> (= (@ (@ tptp.insert2053719859tate_o A) tptp.bot_bo170732493tate_o) (@ (@ tptp.insert2053719859tate_o B2) tptp.bot_bo170732493tate_o)) (= A B2))))
% 0.20/0.59 (assert (forall ((A tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat)) (=> (= (@ (@ tptp.insert271595217at_nat A) tptp.bot_bo2130386637at_nat) (@ (@ tptp.insert271595217at_nat B2) tptp.bot_bo2130386637at_nat)) (= A B2))))
% 0.20/0.59 (assert (forall ((A tptp.produc1115495963_state) (B2 tptp.produc1115495963_state)) (=> (= (@ (@ tptp.insert311944171_state A) tptp.bot_bo1625160935_state) (@ (@ tptp.insert311944171_state B2) tptp.bot_bo1625160935_state)) (= A B2))))
% 0.20/0.59 (assert (forall ((A tptp.produc696469763tate_o) (A2 tptp.set_Pr1590995257tate_o)) (not (= (@ (@ tptp.insert2053719859tate_o A) A2) tptp.bot_bo170732493tate_o))))
% 0.20/0.59 (assert (forall ((A tptp.product_prod_nat_nat) (A2 tptp.set_Pr1986765409at_nat)) (not (= (@ (@ tptp.insert271595217at_nat A) A2) tptp.bot_bo2130386637at_nat))))
% 0.20/0.59 (assert (forall ((A tptp.produc1115495963_state) (A2 tptp.set_Pr795498619_state)) (not (= (@ (@ tptp.insert311944171_state A) A2) tptp.bot_bo1625160935_state))))
% 0.20/0.59 (assert (forall ((A tptp.produc696469763tate_o) (B2 tptp.produc696469763tate_o) (C2 tptp.produc696469763tate_o) (D tptp.produc696469763tate_o)) (= (= (@ (@ tptp.insert2053719859tate_o A) (@ (@ tptp.insert2053719859tate_o B2) tptp.bot_bo170732493tate_o)) (@ (@ tptp.insert2053719859tate_o C2) (@ (@ tptp.insert2053719859tate_o D) tptp.bot_bo170732493tate_o))) (or (and (= A C2) (= B2 D)) (and (= A D) (= B2 C2))))))
% 0.20/0.59 (assert (forall ((A tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat) (C2 tptp.product_prod_nat_nat) (D tptp.product_prod_nat_nat)) (= (= (@ (@ tptp.insert271595217at_nat A) (@ (@ tptp.insert271595217at_nat B2) tptp.bot_bo2130386637at_nat)) (@ (@ tptp.insert271595217at_nat C2) (@ (@ tptp.insert271595217at_nat D) tptp.bot_bo2130386637at_nat))) (or (and (= A C2) (= B2 D)) (and (= A D) (= B2 C2))))))
% 0.20/0.59 (assert (forall ((A tptp.produc1115495963_state) (B2 tptp.produc1115495963_state) (C2 tptp.produc1115495963_state) (D tptp.produc1115495963_state)) (= (= (@ (@ tptp.insert311944171_state A) (@ (@ tptp.insert311944171_state B2) tptp.bot_bo1625160935_state)) (@ (@ tptp.insert311944171_state C2) (@ (@ tptp.insert311944171_state D) tptp.bot_bo1625160935_state))) (or (and (= A C2) (= B2 D)) (and (= A D) (= B2 C2))))))
% 0.20/0.59 (assert (forall ((B2 tptp.produc696469763tate_o) (A tptp.produc696469763tate_o)) (= (@ (@ tptp.member1838112666tate_o B2) (@ (@ tptp.insert2053719859tate_o A) tptp.bot_bo170732493tate_o)) (= B2 A))))
% 0.20/0.59 (assert (forall ((B2 tptp.product_prod_nat_nat) (A tptp.product_prod_nat_nat)) (= (@ (@ tptp.member701585322at_nat B2) (@ (@ tptp.insert271595217at_nat A) tptp.bot_bo2130386637at_nat)) (= B2 A))))
% 0.20/0.59 (assert (forall ((B2 tptp.produc1115495963_state) (A tptp.produc1115495963_state)) (= (@ (@ tptp.member1389040324_state B2) (@ (@ tptp.insert311944171_state A) tptp.bot_bo1625160935_state)) (= B2 A))))
% 0.20/0.59 (assert (forall ((B2 tptp.produc696469763tate_o) (A tptp.produc696469763tate_o)) (=> (@ (@ tptp.member1838112666tate_o B2) (@ (@ tptp.insert2053719859tate_o A) tptp.bot_bo170732493tate_o)) (= B2 A))))
% 0.20/0.59 (assert (forall ((B2 tptp.product_prod_nat_nat) (A tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member701585322at_nat B2) (@ (@ tptp.insert271595217at_nat A) tptp.bot_bo2130386637at_nat)) (= B2 A))))
% 0.20/0.59 (assert (forall ((B2 tptp.produc1115495963_state) (A tptp.produc1115495963_state)) (=> (@ (@ tptp.member1389040324_state B2) (@ (@ tptp.insert311944171_state A) tptp.bot_bo1625160935_state)) (= B2 A))))
% 0.20/0.59 (assert (forall ((P (-> tptp.a tptp.state Bool)) (Q (-> tptp.a tptp.state Bool))) (@ (@ (@ (@ tptp.hoare_a (@ (@ tptp.insert2053719859tate_o (@ (@ tptp.produc33908149tate_o P) (@ (@ tptp.produc1948644831tate_o tptp.call) Q))) tptp.bot_bo170732493tate_o)) P) tptp.call) Q)))
% 0.20/0.59 (assert (forall ((P (-> tptp.produc696469763tate_o Bool)) (A tptp.produc696469763tate_o)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collec1499596504tate_o (lambda ((X tptp.produc696469763tate_o)) (and (= A X) (@ P X)))) (@ (@ tptp.insert2053719859tate_o A) tptp.bot_bo170732493tate_o))) (=> (not _let_1) (= (@ tptp.collec1499596504tate_o (lambda ((X tptp.produc696469763tate_o)) (and (= A X) (@ P X)))) tptp.bot_bo170732493tate_o))))))
% 0.20/0.59 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (A tptp.product_prod_nat_nat)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collec7649004at_nat (lambda ((X tptp.product_prod_nat_nat)) (and (= A X) (@ P X)))) (@ (@ tptp.insert271595217at_nat A) tptp.bot_bo2130386637at_nat))) (=> (not _let_1) (= (@ tptp.collec7649004at_nat (lambda ((X tptp.product_prod_nat_nat)) (and (= A X) (@ P X)))) tptp.bot_bo2130386637at_nat))))))
% 0.20/0.59 (assert (forall ((P (-> tptp.produc1115495963_state Bool)) (A tptp.produc1115495963_state)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collec496201222_state (lambda ((X tptp.produc1115495963_state)) (and (= A X) (@ P X)))) (@ (@ tptp.insert311944171_state A) tptp.bot_bo1625160935_state))) (=> (not _let_1) (= (@ tptp.collec496201222_state (lambda ((X tptp.produc1115495963_state)) (and (= A X) (@ P X)))) tptp.bot_bo1625160935_state))))))
% 0.20/0.59 (assert (forall ((P (-> tptp.produc696469763tate_o Bool)) (A tptp.produc696469763tate_o)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collec1499596504tate_o (lambda ((X tptp.produc696469763tate_o)) (and (= X A) (@ P X)))) (@ (@ tptp.insert2053719859tate_o A) tptp.bot_bo170732493tate_o))) (=> (not _let_1) (= (@ tptp.collec1499596504tate_o (lambda ((X tptp.produc696469763tate_o)) (and (= X A) (@ P X)))) tptp.bot_bo170732493tate_o))))))
% 0.20/0.59 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (A tptp.product_prod_nat_nat)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collec7649004at_nat (lambda ((X tptp.product_prod_nat_nat)) (and (= X A) (@ P X)))) (@ (@ tptp.insert271595217at_nat A) tptp.bot_bo2130386637at_nat))) (=> (not _let_1) (= (@ tptp.collec7649004at_nat (lambda ((X tptp.product_prod_nat_nat)) (and (= X A) (@ P X)))) tptp.bot_bo2130386637at_nat))))))
% 0.20/0.59 (assert (forall ((P (-> tptp.produc1115495963_state Bool)) (A tptp.produc1115495963_state)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collec496201222_state (lambda ((X tptp.produc1115495963_state)) (and (= X A) (@ P X)))) (@ (@ tptp.insert311944171_state A) tptp.bot_bo1625160935_state))) (=> (not _let_1) (= (@ tptp.collec496201222_state (lambda ((X tptp.produc1115495963_state)) (and (= X A) (@ P X)))) tptp.bot_bo1625160935_state))))))
% 0.20/0.59 (assert (@ tptp.wf_nat tptp.bot_bo2130386637at_nat))
% 0.20/0.59 (assert (@ tptp.wf_state tptp.bot_bo1625160935_state))
% 0.20/0.59 (assert (forall ((A tptp.produc1115495963_state) (P (-> tptp.produc1115495963_state Bool))) (= (@ (@ tptp.member1389040324_state A) (@ tptp.collec496201222_state P)) (@ P A))))
% 0.20/0.59 (assert (forall ((A tptp.product_prod_nat_nat) (P (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.member701585322at_nat A) (@ tptp.collec7649004at_nat P)) (@ P A))))
% 0.20/0.59 (assert (forall ((A tptp.produc696469763tate_o) (P (-> tptp.produc696469763tate_o Bool))) (= (@ (@ tptp.member1838112666tate_o A) (@ tptp.collec1499596504tate_o P)) (@ P A))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr795498619_state)) (= (@ tptp.collec496201222_state (lambda ((X tptp.produc1115495963_state)) (@ (@ tptp.member1389040324_state X) A2))) A2)))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr1986765409at_nat)) (= (@ tptp.collec7649004at_nat (lambda ((X tptp.product_prod_nat_nat)) (@ (@ tptp.member701585322at_nat X) A2))) A2)))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr1590995257tate_o)) (= (@ tptp.collec1499596504tate_o (lambda ((X tptp.produc696469763tate_o)) (@ (@ tptp.member1838112666tate_o X) A2))) A2)))
% 0.20/0.59 (assert (forall ((P (-> tptp.produc1115495963_state Bool)) (Q (-> tptp.produc1115495963_state Bool))) (=> (forall ((X3 tptp.produc1115495963_state)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collec496201222_state P) (@ tptp.collec496201222_state Q)))))
% 0.20/0.59 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Q (-> tptp.product_prod_nat_nat Bool))) (=> (forall ((X3 tptp.product_prod_nat_nat)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collec7649004at_nat P) (@ tptp.collec7649004at_nat Q)))))
% 0.20/0.59 (assert (forall ((P (-> tptp.produc696469763tate_o Bool)) (Q (-> tptp.produc696469763tate_o Bool))) (=> (forall ((X3 tptp.produc696469763tate_o)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collec1499596504tate_o P) (@ tptp.collec1499596504tate_o Q)))))
% 0.20/0.59 (assert (forall ((R2 tptp.set_Pr795498619_state) (Q tptp.set_state)) (=> (@ tptp.wf_state R2) (=> (not (= Q tptp.bot_bot_set_state)) (not (forall ((Z tptp.state)) (=> (@ (@ tptp.member_state Z) Q) (not (forall ((Y4 tptp.state)) (=> (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state Y4) Z)) R2) (not (@ (@ tptp.member_state Y4) Q))))))))))))
% 0.20/0.59 (assert (forall ((R2 tptp.set_Pr1986765409at_nat) (Q tptp.set_nat)) (=> (@ tptp.wf_nat R2) (=> (not (= Q tptp.bot_bot_set_nat)) (not (forall ((Z tptp.nat)) (=> (@ (@ tptp.member_nat Z) Q) (not (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat Y4) Z)) R2) (not (@ (@ tptp.member_nat Y4) Q))))))))))))
% 0.20/0.59 (assert (forall ((R2 tptp.set_Pr1702239303tate_o) (Q tptp.set_Pr1590995257tate_o)) (=> (@ tptp.wf_Pro309705690tate_o R2) (=> (not (= Q tptp.bot_bo170732493tate_o)) (not (forall ((Z tptp.produc696469763tate_o)) (=> (@ (@ tptp.member1838112666tate_o Z) Q) (not (forall ((Y4 tptp.produc696469763tate_o)) (=> (@ (@ tptp.member1629320336tate_o (@ (@ tptp.produc1684562079tate_o Y4) Z)) R2) (not (@ (@ tptp.member1838112666tate_o Y4) Q))))))))))))
% 0.20/0.59 (assert (forall ((R2 tptp.set_Pr1490359111at_nat) (Q tptp.set_Pr1986765409at_nat)) (=> (@ tptp.wf_Pro745352042at_nat R2) (=> (not (= Q tptp.bot_bo2130386637at_nat)) (not (forall ((Z tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member701585322at_nat Z) Q) (not (forall ((Y4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member2027625872at_nat (@ (@ tptp.produc1168807639at_nat Y4) Z)) R2) (not (@ (@ tptp.member701585322at_nat Y4) Q))))))))))))
% 0.20/0.59 (assert (forall ((R2 tptp.set_Pr778812871_state) (Q tptp.set_Pr795498619_state)) (=> (@ tptp.wf_Pro1783588484_state R2) (=> (not (= Q tptp.bot_bo1625160935_state)) (not (forall ((Z tptp.produc1115495963_state)) (=> (@ (@ tptp.member1389040324_state Z) Q) (not (forall ((Y4 tptp.produc1115495963_state)) (=> (@ (@ tptp.member768948240_state (@ (@ tptp.produc1964772951_state Y4) Z)) R2) (not (@ (@ tptp.member1389040324_state Y4) Q))))))))))))
% 0.20/0.59 (assert (forall ((X2 tptp.produc696469763tate_o)) (= (@ tptp.the_el1569055182tate_o (@ (@ tptp.insert2053719859tate_o X2) tptp.bot_bo170732493tate_o)) X2)))
% 0.20/0.59 (assert (forall ((X2 tptp.product_prod_nat_nat)) (= (@ tptp.the_el1949240438at_nat (@ (@ tptp.insert271595217at_nat X2) tptp.bot_bo2130386637at_nat)) X2)))
% 0.20/0.59 (assert (forall ((X2 tptp.produc1115495963_state)) (= (@ tptp.the_el1967402896_state (@ (@ tptp.insert311944171_state X2) tptp.bot_bo1625160935_state)) X2)))
% 0.20/0.59 (assert (forall ((A (-> tptp.a tptp.state Bool)) (B2 tptp.produc204914599tate_o) (A4 (-> tptp.a tptp.state Bool)) (B5 tptp.produc204914599tate_o)) (= (= (@ (@ tptp.produc33908149tate_o A) B2) (@ (@ tptp.produc33908149tate_o A4) B5)) (and (= A A4) (= B2 B5)))))
% 0.20/0.59 (assert (forall ((A tptp.state) (B2 tptp.state) (A4 tptp.state) (B5 tptp.state)) (= (= (@ (@ tptp.produc64584659_state A) B2) (@ (@ tptp.produc64584659_state A4) B5)) (and (= A A4) (= B2 B5)))))
% 0.20/0.59 (assert (forall ((A tptp.com) (B2 (-> tptp.a tptp.state Bool)) (A4 tptp.com) (B5 (-> tptp.a tptp.state Bool))) (= (= (@ (@ tptp.produc1948644831tate_o A) B2) (@ (@ tptp.produc1948644831tate_o A4) B5)) (and (= A A4) (= B2 B5)))))
% 0.20/0.59 (assert (forall ((A tptp.nat) (B2 tptp.nat) (A4 tptp.nat) (B5 tptp.nat)) (= (= (@ (@ tptp.product_Pair_nat_nat A) B2) (@ (@ tptp.product_Pair_nat_nat A4) B5)) (and (= A A4) (= B2 B5)))))
% 0.20/0.59 (assert (forall ((X1 (-> tptp.a tptp.state Bool)) (X22 tptp.produc204914599tate_o) (Y1 (-> tptp.a tptp.state Bool)) (Y22 tptp.produc204914599tate_o)) (= (= (@ (@ tptp.produc33908149tate_o X1) X22) (@ (@ tptp.produc33908149tate_o Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 0.20/0.59 (assert (forall ((X1 tptp.state) (X22 tptp.state) (Y1 tptp.state) (Y22 tptp.state)) (= (= (@ (@ tptp.produc64584659_state X1) X22) (@ (@ tptp.produc64584659_state Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 0.20/0.59 (assert (forall ((X1 tptp.com) (X22 (-> tptp.a tptp.state Bool)) (Y1 tptp.com) (Y22 (-> tptp.a tptp.state Bool))) (= (= (@ (@ tptp.produc1948644831tate_o X1) X22) (@ (@ tptp.produc1948644831tate_o Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 0.20/0.59 (assert (forall ((X1 tptp.nat) (X22 tptp.nat) (Y1 tptp.nat) (Y22 tptp.nat)) (= (= (@ (@ tptp.product_Pair_nat_nat X1) X22) (@ (@ tptp.product_Pair_nat_nat Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 0.20/0.59 (assert (forall ((X2 tptp.produc696469763tate_o)) (@ tptp.is_sin1547905295tate_o (@ (@ tptp.insert2053719859tate_o X2) tptp.bot_bo170732493tate_o))))
% 0.20/0.59 (assert (forall ((X2 tptp.product_prod_nat_nat)) (@ tptp.is_sin1352690165at_nat (@ (@ tptp.insert271595217at_nat X2) tptp.bot_bo2130386637at_nat))))
% 0.20/0.59 (assert (forall ((X2 tptp.produc1115495963_state)) (@ tptp.is_sin1132515087_state (@ (@ tptp.insert311944171_state X2) tptp.bot_bo1625160935_state))))
% 0.20/0.59 (assert (= tptp.bot_bo170732493tate_o (@ tptp.collec1499596504tate_o tptp.bot_bo250281208te_o_o)))
% 0.20/0.59 (assert (= tptp.bot_bo2130386637at_nat (@ tptp.collec7649004at_nat tptp.bot_bo513358416_nat_o)))
% 0.20/0.59 (assert (= tptp.bot_bo1625160935_state (@ tptp.collec496201222_state tptp.bot_bo446391478tate_o)))
% 0.20/0.59 (assert (= tptp.is_sin1547905295tate_o (lambda ((A5 tptp.set_Pr1590995257tate_o)) (= A5 (@ (@ tptp.insert2053719859tate_o (@ tptp.the_el1569055182tate_o A5)) tptp.bot_bo170732493tate_o)))))
% 0.20/0.59 (assert (= tptp.is_sin1352690165at_nat (lambda ((A5 tptp.set_Pr1986765409at_nat)) (= A5 (@ (@ tptp.insert271595217at_nat (@ tptp.the_el1949240438at_nat A5)) tptp.bot_bo2130386637at_nat)))))
% 0.20/0.59 (assert (= tptp.is_sin1132515087_state (lambda ((A5 tptp.set_Pr795498619_state)) (= A5 (@ (@ tptp.insert311944171_state (@ tptp.the_el1967402896_state A5)) tptp.bot_bo1625160935_state)))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr1590995257tate_o)) (=> (not (= A2 tptp.bot_bo170732493tate_o)) (=> (forall ((X3 tptp.produc696469763tate_o) (Y2 tptp.produc696469763tate_o)) (=> (@ (@ tptp.member1838112666tate_o X3) A2) (=> (@ (@ tptp.member1838112666tate_o Y2) A2) (= X3 Y2)))) (@ tptp.is_sin1547905295tate_o A2)))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr1986765409at_nat)) (=> (not (= A2 tptp.bot_bo2130386637at_nat)) (=> (forall ((X3 tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member701585322at_nat X3) A2) (=> (@ (@ tptp.member701585322at_nat Y2) A2) (= X3 Y2)))) (@ tptp.is_sin1352690165at_nat A2)))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr795498619_state)) (=> (not (= A2 tptp.bot_bo1625160935_state)) (=> (forall ((X3 tptp.produc1115495963_state) (Y2 tptp.produc1115495963_state)) (=> (@ (@ tptp.member1389040324_state X3) A2) (=> (@ (@ tptp.member1389040324_state Y2) A2) (= X3 Y2)))) (@ tptp.is_sin1132515087_state A2)))))
% 0.20/0.59 (assert (forall ((P3 tptp.produc696469763tate_o)) (exists ((X3 (-> tptp.a tptp.state Bool)) (Y2 tptp.produc204914599tate_o)) (= P3 (@ (@ tptp.produc33908149tate_o X3) Y2)))))
% 0.20/0.59 (assert (forall ((P3 tptp.produc1115495963_state)) (exists ((X3 tptp.state) (Y2 tptp.state)) (= P3 (@ (@ tptp.produc64584659_state X3) Y2)))))
% 0.20/0.59 (assert (forall ((P3 tptp.produc204914599tate_o)) (exists ((X3 tptp.com) (Y2 (-> tptp.a tptp.state Bool))) (= P3 (@ (@ tptp.produc1948644831tate_o X3) Y2)))))
% 0.20/0.59 (assert (forall ((P3 tptp.product_prod_nat_nat)) (exists ((X3 tptp.nat) (Y2 tptp.nat)) (= P3 (@ (@ tptp.product_Pair_nat_nat X3) Y2)))))
% 0.20/0.59 (assert (forall ((P (-> tptp.produc696469763tate_o Bool)) (P3 tptp.produc696469763tate_o)) (=> (forall ((A6 (-> tptp.a tptp.state Bool)) (B6 tptp.produc204914599tate_o)) (@ P (@ (@ tptp.produc33908149tate_o A6) B6))) (@ P P3))))
% 0.20/0.59 (assert (forall ((P (-> tptp.produc1115495963_state Bool)) (P3 tptp.produc1115495963_state)) (=> (forall ((A6 tptp.state) (B6 tptp.state)) (@ P (@ (@ tptp.produc64584659_state A6) B6))) (@ P P3))))
% 0.20/0.59 (assert (forall ((P (-> tptp.produc204914599tate_o Bool)) (P3 tptp.produc204914599tate_o)) (=> (forall ((A6 tptp.com) (B6 (-> tptp.a tptp.state Bool))) (@ P (@ (@ tptp.produc1948644831tate_o A6) B6))) (@ P P3))))
% 0.20/0.59 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (P3 tptp.product_prod_nat_nat)) (=> (forall ((A6 tptp.nat) (B6 tptp.nat)) (@ P (@ (@ tptp.product_Pair_nat_nat A6) B6))) (@ P P3))))
% 0.20/0.59 (assert (forall ((A (-> tptp.a tptp.state Bool)) (B2 tptp.produc204914599tate_o) (A4 (-> tptp.a tptp.state Bool)) (B5 tptp.produc204914599tate_o)) (=> (= (@ (@ tptp.produc33908149tate_o A) B2) (@ (@ tptp.produc33908149tate_o A4) B5)) (not (=> (= A A4) (not (= B2 B5)))))))
% 0.20/0.59 (assert (forall ((A tptp.state) (B2 tptp.state) (A4 tptp.state) (B5 tptp.state)) (=> (= (@ (@ tptp.produc64584659_state A) B2) (@ (@ tptp.produc64584659_state A4) B5)) (not (=> (= A A4) (not (= B2 B5)))))))
% 0.20/0.59 (assert (forall ((A tptp.com) (B2 (-> tptp.a tptp.state Bool)) (A4 tptp.com) (B5 (-> tptp.a tptp.state Bool))) (=> (= (@ (@ tptp.produc1948644831tate_o A) B2) (@ (@ tptp.produc1948644831tate_o A4) B5)) (not (=> (= A A4) (not (= B2 B5)))))))
% 0.20/0.59 (assert (forall ((A tptp.nat) (B2 tptp.nat) (A4 tptp.nat) (B5 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat A) B2) (@ (@ tptp.product_Pair_nat_nat A4) B5)) (not (=> (= A A4) (not (= B2 B5)))))))
% 0.20/0.59 (assert (forall ((Y3 tptp.produc696469763tate_o)) (not (forall ((A6 (-> tptp.a tptp.state Bool)) (B6 tptp.produc204914599tate_o)) (not (= Y3 (@ (@ tptp.produc33908149tate_o A6) B6)))))))
% 0.20/0.59 (assert (forall ((Y3 tptp.produc1115495963_state)) (not (forall ((A6 tptp.state) (B6 tptp.state)) (not (= Y3 (@ (@ tptp.produc64584659_state A6) B6)))))))
% 0.20/0.59 (assert (forall ((Y3 tptp.produc204914599tate_o)) (not (forall ((A6 tptp.com) (B6 (-> tptp.a tptp.state Bool))) (not (= Y3 (@ (@ tptp.produc1948644831tate_o A6) B6)))))))
% 0.20/0.59 (assert (forall ((Y3 tptp.product_prod_nat_nat)) (not (forall ((A6 tptp.nat) (B6 tptp.nat)) (not (= Y3 (@ (@ tptp.product_Pair_nat_nat A6) B6)))))))
% 0.20/0.59 (assert (forall ((P (-> tptp.produc696469763tate_o Bool)) (Prod tptp.produc696469763tate_o)) (=> (forall ((A6 (-> tptp.a tptp.state Bool)) (B6 tptp.produc204914599tate_o)) (@ P (@ (@ tptp.produc33908149tate_o A6) B6))) (@ P Prod))))
% 0.20/0.59 (assert (forall ((P (-> tptp.produc1115495963_state Bool)) (Prod tptp.produc1115495963_state)) (=> (forall ((A6 tptp.state) (B6 tptp.state)) (@ P (@ (@ tptp.produc64584659_state A6) B6))) (@ P Prod))))
% 0.20/0.59 (assert (forall ((P (-> tptp.produc204914599tate_o Bool)) (Prod tptp.produc204914599tate_o)) (=> (forall ((A6 tptp.com) (B6 (-> tptp.a tptp.state Bool))) (@ P (@ (@ tptp.produc1948644831tate_o A6) B6))) (@ P Prod))))
% 0.20/0.59 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Prod tptp.product_prod_nat_nat)) (=> (forall ((A6 tptp.nat) (B6 tptp.nat)) (@ P (@ (@ tptp.product_Pair_nat_nat A6) B6))) (@ P Prod))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr1590995257tate_o)) (=> (@ tptp.is_sin1547905295tate_o A2) (not (forall ((X3 tptp.produc696469763tate_o)) (not (= A2 (@ (@ tptp.insert2053719859tate_o X3) tptp.bot_bo170732493tate_o))))))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr1986765409at_nat)) (=> (@ tptp.is_sin1352690165at_nat A2) (not (forall ((X3 tptp.product_prod_nat_nat)) (not (= A2 (@ (@ tptp.insert271595217at_nat X3) tptp.bot_bo2130386637at_nat))))))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr795498619_state)) (=> (@ tptp.is_sin1132515087_state A2) (not (forall ((X3 tptp.produc1115495963_state)) (not (= A2 (@ (@ tptp.insert311944171_state X3) tptp.bot_bo1625160935_state))))))))
% 0.20/0.59 (assert (= tptp.is_sin1547905295tate_o (lambda ((A5 tptp.set_Pr1590995257tate_o)) (exists ((X tptp.produc696469763tate_o)) (= A5 (@ (@ tptp.insert2053719859tate_o X) tptp.bot_bo170732493tate_o))))))
% 0.20/0.59 (assert (= tptp.is_sin1352690165at_nat (lambda ((A5 tptp.set_Pr1986765409at_nat)) (exists ((X tptp.product_prod_nat_nat)) (= A5 (@ (@ tptp.insert271595217at_nat X) tptp.bot_bo2130386637at_nat))))))
% 0.20/0.59 (assert (= tptp.is_sin1132515087_state (lambda ((A5 tptp.set_Pr795498619_state)) (exists ((X tptp.produc1115495963_state)) (= A5 (@ (@ tptp.insert311944171_state X) tptp.bot_bo1625160935_state))))))
% 0.20/0.59 (assert (= tptp.wf_state (lambda ((R3 tptp.set_Pr795498619_state)) (forall ((P4 (-> tptp.state Bool))) (=> (forall ((X tptp.state)) (=> (forall ((Y5 tptp.state)) (=> (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state Y5) X)) R3) (@ P4 Y5))) (@ P4 X))) (forall ((X4 tptp.state)) (@ P4 X4)))))))
% 0.20/0.59 (assert (= tptp.wf_nat (lambda ((R3 tptp.set_Pr1986765409at_nat)) (forall ((P4 (-> tptp.nat Bool))) (=> (forall ((X tptp.nat)) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat Y5) X)) R3) (@ P4 Y5))) (@ P4 X))) (forall ((X4 tptp.nat)) (@ P4 X4)))))))
% 0.20/0.59 (assert (forall ((R2 tptp.set_Pr778812871_state) (X2 tptp.produc1115495963_state) (Q tptp.set_Pr795498619_state)) (=> (@ tptp.wf_Pro1783588484_state R2) (=> (@ (@ tptp.member1389040324_state X2) Q) (not (forall ((Z tptp.produc1115495963_state)) (=> (@ (@ tptp.member1389040324_state Z) Q) (not (forall ((Y4 tptp.produc1115495963_state)) (=> (@ (@ tptp.member768948240_state (@ (@ tptp.produc1964772951_state Y4) Z)) R2) (not (@ (@ tptp.member1389040324_state Y4) Q))))))))))))
% 0.20/0.59 (assert (forall ((R2 tptp.set_Pr1490359111at_nat) (X2 tptp.product_prod_nat_nat) (Q tptp.set_Pr1986765409at_nat)) (=> (@ tptp.wf_Pro745352042at_nat R2) (=> (@ (@ tptp.member701585322at_nat X2) Q) (not (forall ((Z tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member701585322at_nat Z) Q) (not (forall ((Y4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member2027625872at_nat (@ (@ tptp.produc1168807639at_nat Y4) Z)) R2) (not (@ (@ tptp.member701585322at_nat Y4) Q))))))))))))
% 0.20/0.59 (assert (forall ((R2 tptp.set_Pr1702239303tate_o) (X2 tptp.produc696469763tate_o) (Q tptp.set_Pr1590995257tate_o)) (=> (@ tptp.wf_Pro309705690tate_o R2) (=> (@ (@ tptp.member1838112666tate_o X2) Q) (not (forall ((Z tptp.produc696469763tate_o)) (=> (@ (@ tptp.member1838112666tate_o Z) Q) (not (forall ((Y4 tptp.produc696469763tate_o)) (=> (@ (@ tptp.member1629320336tate_o (@ (@ tptp.produc1684562079tate_o Y4) Z)) R2) (not (@ (@ tptp.member1838112666tate_o Y4) Q))))))))))))
% 0.20/0.59 (assert (forall ((R2 tptp.set_Pr795498619_state) (X2 tptp.state) (Q tptp.set_state)) (=> (@ tptp.wf_state R2) (=> (@ (@ tptp.member_state X2) Q) (not (forall ((Z tptp.state)) (=> (@ (@ tptp.member_state Z) Q) (not (forall ((Y4 tptp.state)) (=> (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state Y4) Z)) R2) (not (@ (@ tptp.member_state Y4) Q))))))))))))
% 0.20/0.59 (assert (forall ((R2 tptp.set_Pr1986765409at_nat) (X2 tptp.nat) (Q tptp.set_nat)) (=> (@ tptp.wf_nat R2) (=> (@ (@ tptp.member_nat X2) Q) (not (forall ((Z tptp.nat)) (=> (@ (@ tptp.member_nat Z) Q) (not (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat Y4) Z)) R2) (not (@ (@ tptp.member_nat Y4) Q))))))))))))
% 0.20/0.59 (assert (forall ((R2 tptp.set_Pr778812871_state)) (=> (forall ((X3 tptp.produc1115495963_state) (Q3 tptp.set_Pr795498619_state)) (=> (@ (@ tptp.member1389040324_state X3) Q3) (exists ((Xa tptp.produc1115495963_state)) (and (@ (@ tptp.member1389040324_state Xa) Q3) (forall ((Y2 tptp.produc1115495963_state)) (=> (@ (@ tptp.member768948240_state (@ (@ tptp.produc1964772951_state Y2) Xa)) R2) (not (@ (@ tptp.member1389040324_state Y2) Q3)))))))) (@ tptp.wf_Pro1783588484_state R2))))
% 0.20/0.59 (assert (forall ((R2 tptp.set_Pr1490359111at_nat)) (=> (forall ((X3 tptp.product_prod_nat_nat) (Q3 tptp.set_Pr1986765409at_nat)) (=> (@ (@ tptp.member701585322at_nat X3) Q3) (exists ((Xa tptp.product_prod_nat_nat)) (and (@ (@ tptp.member701585322at_nat Xa) Q3) (forall ((Y2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member2027625872at_nat (@ (@ tptp.produc1168807639at_nat Y2) Xa)) R2) (not (@ (@ tptp.member701585322at_nat Y2) Q3)))))))) (@ tptp.wf_Pro745352042at_nat R2))))
% 0.20/0.59 (assert (forall ((R2 tptp.set_Pr1702239303tate_o)) (=> (forall ((X3 tptp.produc696469763tate_o) (Q3 tptp.set_Pr1590995257tate_o)) (=> (@ (@ tptp.member1838112666tate_o X3) Q3) (exists ((Xa tptp.produc696469763tate_o)) (and (@ (@ tptp.member1838112666tate_o Xa) Q3) (forall ((Y2 tptp.produc696469763tate_o)) (=> (@ (@ tptp.member1629320336tate_o (@ (@ tptp.produc1684562079tate_o Y2) Xa)) R2) (not (@ (@ tptp.member1838112666tate_o Y2) Q3)))))))) (@ tptp.wf_Pro309705690tate_o R2))))
% 0.20/0.59 (assert (forall ((R2 tptp.set_Pr795498619_state)) (=> (forall ((X3 tptp.state) (Q3 tptp.set_state)) (=> (@ (@ tptp.member_state X3) Q3) (exists ((Xa tptp.state)) (and (@ (@ tptp.member_state Xa) Q3) (forall ((Y2 tptp.state)) (=> (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state Y2) Xa)) R2) (not (@ (@ tptp.member_state Y2) Q3)))))))) (@ tptp.wf_state R2))))
% 0.20/0.59 (assert (forall ((R2 tptp.set_Pr1986765409at_nat)) (=> (forall ((X3 tptp.nat) (Q3 tptp.set_nat)) (=> (@ (@ tptp.member_nat X3) Q3) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) Q3) (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat Y2) Xa)) R2) (not (@ (@ tptp.member_nat Y2) Q3)))))))) (@ tptp.wf_nat R2))))
% 0.20/0.59 (assert (forall ((R tptp.set_Pr795498619_state)) (=> (forall ((P5 (-> tptp.state Bool)) (X3 tptp.state)) (=> (forall ((Xa tptp.state)) (=> (forall ((Y2 tptp.state)) (=> (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state Y2) Xa)) R) (@ P5 Y2))) (@ P5 Xa))) (@ P5 X3))) (@ tptp.wf_state R))))
% 0.20/0.59 (assert (forall ((R tptp.set_Pr1986765409at_nat)) (=> (forall ((P5 (-> tptp.nat Bool)) (X3 tptp.nat)) (=> (forall ((Xa tptp.nat)) (=> (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat Y2) Xa)) R) (@ P5 Y2))) (@ P5 Xa))) (@ P5 X3))) (@ tptp.wf_nat R))))
% 0.20/0.59 (assert (forall ((R tptp.set_Pr795498619_state) (A tptp.state) (X2 tptp.state)) (=> (@ tptp.wf_state R) (=> (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state A) X2)) R) (not (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state X2) A)) R))))))
% 0.20/0.59 (assert (forall ((R tptp.set_Pr1986765409at_nat) (A tptp.nat) (X2 tptp.nat)) (=> (@ tptp.wf_nat R) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A) X2)) R) (not (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X2) A)) R))))))
% 0.20/0.59 (assert (forall ((R tptp.set_Pr795498619_state) (P (-> tptp.state Bool)) (A tptp.state)) (=> (@ tptp.wf_state R) (=> (forall ((X3 tptp.state)) (=> (forall ((Y4 tptp.state)) (=> (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state Y4) X3)) R) (@ P Y4))) (@ P X3))) (@ P A)))))
% 0.20/0.59 (assert (forall ((R tptp.set_Pr1986765409at_nat) (P (-> tptp.nat Bool)) (A tptp.nat)) (=> (@ tptp.wf_nat R) (=> (forall ((X3 tptp.nat)) (=> (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat Y4) X3)) R) (@ P Y4))) (@ P X3))) (@ P A)))))
% 0.20/0.59 (assert (forall ((R tptp.set_Pr795498619_state) (A tptp.state)) (=> (@ tptp.wf_state R) (not (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state A) A)) R)))))
% 0.20/0.59 (assert (forall ((R tptp.set_Pr1986765409at_nat) (A tptp.nat)) (=> (@ tptp.wf_nat R) (not (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A) A)) R)))))
% 0.20/0.59 (assert (forall ((R tptp.set_Pr795498619_state) (A tptp.state) (X2 tptp.state)) (=> (@ tptp.wf_state R) (=> (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state A) X2)) R) (not (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state X2) A)) R))))))
% 0.20/0.59 (assert (forall ((R tptp.set_Pr1986765409at_nat) (A tptp.nat) (X2 tptp.nat)) (=> (@ tptp.wf_nat R) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A) X2)) R) (not (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X2) A)) R))))))
% 0.20/0.59 (assert (forall ((R tptp.set_Pr795498619_state) (A tptp.state)) (=> (@ tptp.wf_state R) (not (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state A) A)) R)))))
% 0.20/0.59 (assert (forall ((R tptp.set_Pr1986765409at_nat) (A tptp.nat)) (=> (@ tptp.wf_nat R) (not (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A) A)) R)))))
% 0.20/0.59 (assert (= tptp.wf_Pro1783588484_state (lambda ((R3 tptp.set_Pr778812871_state)) (forall ((Q4 tptp.set_Pr795498619_state)) (=> (exists ((X tptp.produc1115495963_state)) (@ (@ tptp.member1389040324_state X) Q4)) (exists ((X tptp.produc1115495963_state)) (and (@ (@ tptp.member1389040324_state X) Q4) (forall ((Y5 tptp.produc1115495963_state)) (=> (@ (@ tptp.member768948240_state (@ (@ tptp.produc1964772951_state Y5) X)) R3) (not (@ (@ tptp.member1389040324_state Y5) Q4)))))))))))
% 0.20/0.59 (assert (= tptp.wf_Pro745352042at_nat (lambda ((R3 tptp.set_Pr1490359111at_nat)) (forall ((Q4 tptp.set_Pr1986765409at_nat)) (=> (exists ((X tptp.product_prod_nat_nat)) (@ (@ tptp.member701585322at_nat X) Q4)) (exists ((X tptp.product_prod_nat_nat)) (and (@ (@ tptp.member701585322at_nat X) Q4) (forall ((Y5 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member2027625872at_nat (@ (@ tptp.produc1168807639at_nat Y5) X)) R3) (not (@ (@ tptp.member701585322at_nat Y5) Q4)))))))))))
% 0.20/0.59 (assert (= tptp.wf_Pro309705690tate_o (lambda ((R3 tptp.set_Pr1702239303tate_o)) (forall ((Q4 tptp.set_Pr1590995257tate_o)) (=> (exists ((X tptp.produc696469763tate_o)) (@ (@ tptp.member1838112666tate_o X) Q4)) (exists ((X tptp.produc696469763tate_o)) (and (@ (@ tptp.member1838112666tate_o X) Q4) (forall ((Y5 tptp.produc696469763tate_o)) (=> (@ (@ tptp.member1629320336tate_o (@ (@ tptp.produc1684562079tate_o Y5) X)) R3) (not (@ (@ tptp.member1838112666tate_o Y5) Q4)))))))))))
% 0.20/0.59 (assert (= tptp.wf_state (lambda ((R3 tptp.set_Pr795498619_state)) (forall ((Q4 tptp.set_state)) (=> (exists ((X tptp.state)) (@ (@ tptp.member_state X) Q4)) (exists ((X tptp.state)) (and (@ (@ tptp.member_state X) Q4) (forall ((Y5 tptp.state)) (=> (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state Y5) X)) R3) (not (@ (@ tptp.member_state Y5) Q4)))))))))))
% 0.20/0.59 (assert (= tptp.wf_nat (lambda ((R3 tptp.set_Pr1986765409at_nat)) (forall ((Q4 tptp.set_nat)) (=> (exists ((X tptp.nat)) (@ (@ tptp.member_nat X) Q4)) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) Q4) (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat Y5) X)) R3) (not (@ (@ tptp.member_nat Y5) Q4)))))))))))
% 0.20/0.59 (assert (forall ((R tptp.set_Pr795498619_state) (P (-> tptp.state Bool)) (A tptp.state)) (=> (@ tptp.wf_state R) (=> (forall ((X3 tptp.state)) (=> (forall ((Y4 tptp.state)) (=> (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state Y4) X3)) R) (@ P Y4))) (@ P X3))) (@ P A)))))
% 0.20/0.59 (assert (forall ((R tptp.set_Pr1986765409at_nat) (P (-> tptp.nat Bool)) (A tptp.nat)) (=> (@ tptp.wf_nat R) (=> (forall ((X3 tptp.nat)) (=> (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat Y4) X3)) R) (@ P Y4))) (@ P X3))) (@ P A)))))
% 0.20/0.59 (assert (forall ((Y3 tptp.produc696469763tate_o)) (not (forall ((A6 (-> tptp.a tptp.state Bool)) (B6 tptp.com) (C4 (-> tptp.a tptp.state Bool))) (not (= Y3 (@ (@ tptp.produc33908149tate_o A6) (@ (@ tptp.produc1948644831tate_o B6) C4))))))))
% 0.20/0.59 (assert (forall ((P (-> tptp.produc696469763tate_o Bool)) (X2 tptp.produc696469763tate_o)) (=> (forall ((A6 (-> tptp.a tptp.state Bool)) (B6 tptp.com) (C4 (-> tptp.a tptp.state Bool))) (@ P (@ (@ tptp.produc33908149tate_o A6) (@ (@ tptp.produc1948644831tate_o B6) C4)))) (@ P X2))))
% 0.20/0.59 (assert (= tptp.bot_bo935656620te_o_o (lambda ((X tptp.com) (Y5 (-> tptp.a tptp.state Bool))) (@ (@ tptp.member221067728tate_o (@ (@ tptp.produc1948644831tate_o X) Y5)) tptp.bot_bo1692783091tate_o))))
% 0.20/0.59 (assert (= tptp.bot_bo2130564770te_o_o (lambda ((X (-> tptp.a tptp.state Bool)) (Y5 tptp.produc204914599tate_o)) (@ (@ tptp.member1838112666tate_o (@ (@ tptp.produc33908149tate_o X) Y5)) tptp.bot_bo170732493tate_o))))
% 0.20/0.59 (assert (= tptp.bot_bot_nat_nat_o (lambda ((X tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X) Y5)) tptp.bot_bo2130386637at_nat))))
% 0.20/0.59 (assert (= tptp.bot_bo51534648tate_o (lambda ((X tptp.state) (Y5 tptp.state)) (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state X) Y5)) tptp.bot_bo1625160935_state))))
% 0.20/0.59 (assert (forall ((F (-> tptp.state tptp.nat))) (@ tptp.wf_state (@ tptp.measure_state F))))
% 0.20/0.59 (assert (forall ((F (-> tptp.nat tptp.nat))) (@ tptp.wf_nat (@ tptp.measure_nat F))))
% 0.20/0.59 (assert (forall ((R tptp.set_Pr795498619_state) (C tptp.set_Pr1590995257tate_o) (P (-> tptp.a tptp.state Bool)) (B2 (-> tptp.state Bool)) (C2 tptp.com)) (=> (@ tptp.wf_state R) (=> (forall ((S3 tptp.state)) (@ (@ (@ (@ tptp.pHoare382919414oare_a C) (lambda ((Z4 tptp.a) (S4 tptp.state)) (and (@ (@ P Z4) S4) (@ B2 S4) (= S3 S4)))) C2) (lambda ((Z4 tptp.a) (S4 tptp.state)) (and (@ (@ P Z4) S4) (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state S4) S3)) R))))) (@ (@ (@ (@ tptp.pHoare382919414oare_a C) P) (@ (@ tptp.while B2) C2)) (lambda ((Z4 tptp.a) (S4 tptp.state)) (and (@ (@ P Z4) S4) (not (@ B2 S4)))))))))
% 0.20/0.59 (assert (= tptp.is_emp807847857tate_o (lambda ((A5 tptp.set_Pr1590995257tate_o)) (= A5 tptp.bot_bo170732493tate_o))))
% 0.20/0.59 (assert (= tptp.is_emp825011411at_nat (lambda ((A5 tptp.set_Pr1986765409at_nat)) (= A5 tptp.bot_bo2130386637at_nat))))
% 0.20/0.59 (assert (= tptp.is_emp1062983149_state (lambda ((A5 tptp.set_Pr795498619_state)) (= A5 tptp.bot_bo1625160935_state))))
% 0.20/0.59 (assert (forall ((X41 (-> tptp.state Bool)) (X42 tptp.com) (Y41 (-> tptp.state Bool)) (Y42 tptp.com)) (= (= (@ (@ tptp.while X41) X42) (@ (@ tptp.while Y41) Y42)) (and (= X41 Y41) (= X42 Y42)))))
% 0.20/0.59 (assert (forall ((X41 (-> tptp.state Bool)) (X42 tptp.com)) (not (= (@ (@ tptp.while X41) X42) tptp.call))))
% 0.20/0.59 (assert (forall ((B2 (-> tptp.state Bool)) (S2 tptp.state) (C2 tptp.com)) (=> (not (@ B2 S2)) (@ (@ (@ tptp.exec S2) (@ (@ tptp.while B2) C2)) S2))))
% 0.20/0.59 (assert (forall ((B2 (-> tptp.state Bool)) (S2 tptp.state) (C2 tptp.com) (T2 tptp.state) (U2 tptp.state)) (let ((_let_1 (@ (@ tptp.while B2) C2))) (let ((_let_2 (@ tptp.exec S2))) (=> (@ B2 S2) (=> (@ (@ _let_2 C2) T2) (=> (@ (@ (@ tptp.exec T2) _let_1) U2) (@ (@ _let_2 _let_1) U2))))))))
% 0.20/0.59 (assert (forall ((B2 (-> tptp.state Bool)) (S2 tptp.state) (C2 tptp.com)) (=> (not (@ B2 S2)) (@ (@ tptp.termi (@ (@ tptp.while B2) C2)) S2))))
% 0.20/0.59 (assert (forall ((B2 (-> tptp.state Bool)) (S2 tptp.state) (C2 tptp.com)) (=> (@ B2 S2) (=> (@ (@ tptp.termi C2) S2) (=> (forall ((T tptp.state)) (=> (@ (@ (@ tptp.exec S2) C2) T) (@ (@ tptp.termi (@ (@ tptp.while B2) C2)) T))) (@ (@ tptp.termi (@ (@ tptp.while B2) C2)) S2))))))
% 0.20/0.59 (assert (= tptp.bot_bo250281208te_o_o (lambda ((X tptp.produc696469763tate_o)) (@ (@ tptp.member1838112666tate_o X) tptp.bot_bo170732493tate_o))))
% 0.20/0.59 (assert (= tptp.bot_bo513358416_nat_o (lambda ((X tptp.product_prod_nat_nat)) (@ (@ tptp.member701585322at_nat X) tptp.bot_bo2130386637at_nat))))
% 0.20/0.59 (assert (= tptp.bot_bo446391478tate_o (lambda ((X tptp.produc1115495963_state)) (@ (@ tptp.member1389040324_state X) tptp.bot_bo1625160935_state))))
% 0.20/0.59 (assert (forall ((R2 tptp.set_Pr1590995257tate_o) (S5 tptp.set_Pr1590995257tate_o)) (= (= (lambda ((X (-> tptp.a tptp.state Bool)) (Y5 tptp.produc204914599tate_o)) (@ (@ tptp.member1838112666tate_o (@ (@ tptp.produc33908149tate_o X) Y5)) R2)) (lambda ((X (-> tptp.a tptp.state Bool)) (Y5 tptp.produc204914599tate_o)) (@ (@ tptp.member1838112666tate_o (@ (@ tptp.produc33908149tate_o X) Y5)) S5))) (= R2 S5))))
% 0.20/0.59 (assert (forall ((R2 tptp.set_Pr795498619_state) (S5 tptp.set_Pr795498619_state)) (= (= (lambda ((X tptp.state) (Y5 tptp.state)) (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state X) Y5)) R2)) (lambda ((X tptp.state) (Y5 tptp.state)) (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state X) Y5)) S5))) (= R2 S5))))
% 0.20/0.59 (assert (forall ((R2 tptp.set_Pr1740974983tate_o) (S5 tptp.set_Pr1740974983tate_o)) (= (= (lambda ((X tptp.com) (Y5 (-> tptp.a tptp.state Bool))) (@ (@ tptp.member221067728tate_o (@ (@ tptp.produc1948644831tate_o X) Y5)) R2)) (lambda ((X tptp.com) (Y5 (-> tptp.a tptp.state Bool))) (@ (@ tptp.member221067728tate_o (@ (@ tptp.produc1948644831tate_o X) Y5)) S5))) (= R2 S5))))
% 0.20/0.59 (assert (forall ((R2 tptp.set_Pr1986765409at_nat) (S5 tptp.set_Pr1986765409at_nat)) (= (= (lambda ((X tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X) Y5)) R2)) (lambda ((X tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X) Y5)) S5))) (= R2 S5))))
% 0.20/0.59 (assert (forall ((P (-> tptp.produc696469763tate_o Bool))) (= (= (@ tptp.collec1499596504tate_o P) tptp.bot_bo170732493tate_o) (= P tptp.bot_bo250281208te_o_o))))
% 0.20/0.59 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool))) (= (= (@ tptp.collec7649004at_nat P) tptp.bot_bo2130386637at_nat) (= P tptp.bot_bo513358416_nat_o))))
% 0.20/0.59 (assert (forall ((P (-> tptp.produc1115495963_state Bool))) (= (= (@ tptp.collec496201222_state P) tptp.bot_bo1625160935_state) (= P tptp.bot_bo446391478tate_o))))
% 0.20/0.59 (assert (forall ((X2 tptp.nat)) (@ (@ tptp.total_on_nat (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat)) (@ (@ tptp.insert271595217at_nat (@ (@ tptp.product_Pair_nat_nat X2) X2)) tptp.bot_bo2130386637at_nat))))
% 0.20/0.59 (assert (forall ((X2 tptp.state)) (@ (@ tptp.total_on_state (@ (@ tptp.insert_state X2) tptp.bot_bot_set_state)) (@ (@ tptp.insert311944171_state (@ (@ tptp.produc64584659_state X2) X2)) tptp.bot_bo1625160935_state))))
% 0.20/0.59 (assert (forall ((X2 tptp.produc696469763tate_o)) (@ (@ tptp.total_795385983tate_o (@ (@ tptp.insert2053719859tate_o X2) tptp.bot_bo170732493tate_o)) (@ (@ tptp.insert1597128631tate_o (@ (@ tptp.produc1684562079tate_o X2) X2)) tptp.bot_bo1714653363tate_o))))
% 0.20/0.59 (assert (forall ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.total_1775715973at_nat (@ (@ tptp.insert271595217at_nat X2) tptp.bot_bo2130386637at_nat)) (@ (@ tptp.insert584009271at_nat (@ (@ tptp.produc1168807639at_nat X2) X2)) tptp.bot_bo34127283at_nat))))
% 0.20/0.59 (assert (forall ((X2 tptp.produc1115495963_state)) (@ (@ tptp.total_1316653983_state (@ (@ tptp.insert311944171_state X2) tptp.bot_bo1625160935_state)) (@ (@ tptp.insert1616594103_state (@ (@ tptp.produc1964772951_state X2) X2)) tptp.bot_bo1331673139_state))))
% 0.20/0.59 (assert (forall ((X2 tptp.nat)) (@ (@ tptp.refl_on_nat (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat)) (@ (@ tptp.insert271595217at_nat (@ (@ tptp.product_Pair_nat_nat X2) X2)) tptp.bot_bo2130386637at_nat))))
% 0.20/0.59 (assert (forall ((X2 tptp.state)) (@ (@ tptp.refl_on_state (@ (@ tptp.insert_state X2) tptp.bot_bot_set_state)) (@ (@ tptp.insert311944171_state (@ (@ tptp.produc64584659_state X2) X2)) tptp.bot_bo1625160935_state))))
% 0.20/0.59 (assert (forall ((X2 tptp.produc696469763tate_o)) (@ (@ tptp.refl_o489021252tate_o (@ (@ tptp.insert2053719859tate_o X2) tptp.bot_bo170732493tate_o)) (@ (@ tptp.insert1597128631tate_o (@ (@ tptp.produc1684562079tate_o X2) X2)) tptp.bot_bo1714653363tate_o))))
% 0.20/0.59 (assert (forall ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.refl_o1619599232at_nat (@ (@ tptp.insert271595217at_nat X2) tptp.bot_bo2130386637at_nat)) (@ (@ tptp.insert584009271at_nat (@ (@ tptp.produc1168807639at_nat X2) X2)) tptp.bot_bo34127283at_nat))))
% 0.20/0.59 (assert (forall ((X2 tptp.produc1115495963_state)) (@ (@ tptp.refl_o1438232218_state (@ (@ tptp.insert311944171_state X2) tptp.bot_bo1625160935_state)) (@ (@ tptp.insert1616594103_state (@ (@ tptp.produc1964772951_state X2) X2)) tptp.bot_bo1331673139_state))))
% 0.20/0.59 (assert (forall ((B2 (-> tptp.state Bool)) (C2 tptp.com)) (@ tptp.wf_state (@ tptp.collec496201222_state (@ tptp.produc789892016tate_o (lambda ((T3 tptp.state) (S4 tptp.state)) (and (@ (@ tptp.termi (@ (@ tptp.while B2) C2)) S4) (@ B2 S4) (@ (@ (@ tptp.exec S4) C2) T3))))))))
% 0.20/0.59 (assert (forall ((X2 tptp.nat)) (@ (@ tptp.order_130026331on_nat (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat)) (@ (@ tptp.insert271595217at_nat (@ (@ tptp.product_Pair_nat_nat X2) X2)) tptp.bot_bo2130386637at_nat))))
% 0.20/0.59 (assert (forall ((X2 tptp.state)) (@ (@ tptp.order_286167592_state (@ (@ tptp.insert_state X2) tptp.bot_bot_set_state)) (@ (@ tptp.insert311944171_state (@ (@ tptp.produc64584659_state X2) X2)) tptp.bot_bo1625160935_state))))
% 0.20/0.59 (assert (forall ((X2 tptp.produc696469763tate_o)) (@ (@ tptp.order_50454158tate_o (@ (@ tptp.insert2053719859tate_o X2) tptp.bot_bo170732493tate_o)) (@ (@ tptp.insert1597128631tate_o (@ (@ tptp.produc1684562079tate_o X2) X2)) tptp.bot_bo1714653363tate_o))))
% 0.20/0.59 (assert (forall ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.order_721919926at_nat (@ (@ tptp.insert271595217at_nat X2) tptp.bot_bo2130386637at_nat)) (@ (@ tptp.insert584009271at_nat (@ (@ tptp.produc1168807639at_nat X2) X2)) tptp.bot_bo34127283at_nat))))
% 0.20/0.59 (assert (forall ((X2 tptp.produc1115495963_state)) (@ (@ tptp.order_178668240_state (@ (@ tptp.insert311944171_state X2) tptp.bot_bo1625160935_state)) (@ (@ tptp.insert1616594103_state (@ (@ tptp.produc1964772951_state X2) X2)) tptp.bot_bo1331673139_state))))
% 0.20/0.59 (assert (forall ((P Bool) (Q (-> tptp.state tptp.state Bool))) (= (@ tptp.produc789892016tate_o (lambda ((A3 tptp.state) (B7 tptp.state)) (and P (@ (@ Q A3) B7)))) (lambda ((Ab tptp.produc1115495963_state)) (and P (@ (@ tptp.produc789892016tate_o Q) Ab))))))
% 0.20/0.59 (assert (forall ((P Bool) (Q (-> tptp.nat tptp.nat Bool))) (= (@ tptp.produc949581770_nat_o (lambda ((A3 tptp.nat) (B7 tptp.nat)) (and P (@ (@ Q A3) B7)))) (lambda ((Ab tptp.product_prod_nat_nat)) (and P (@ (@ tptp.produc949581770_nat_o Q) Ab))))))
% 0.20/0.59 (assert (forall ((F (-> tptp.state tptp.state Bool)) (A tptp.state) (B2 tptp.state)) (= (@ (@ tptp.produc789892016tate_o F) (@ (@ tptp.produc64584659_state A) B2)) (@ (@ F A) B2))))
% 0.20/0.59 (assert (forall ((F (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.produc949581770_nat_o F) (@ (@ tptp.product_Pair_nat_nat A) B2)) (@ (@ F A) B2))))
% 0.20/0.59 (assert (forall ((F (-> (-> tptp.a tptp.state Bool) tptp.produc204914599tate_o Bool)) (A (-> tptp.a tptp.state Bool)) (B2 tptp.produc204914599tate_o)) (=> (@ (@ F A) B2) (@ (@ tptp.produc1271576886te_o_o F) (@ (@ tptp.produc33908149tate_o A) B2)))))
% 0.20/0.59 (assert (forall ((F (-> tptp.com (-> tptp.a tptp.state Bool) Bool)) (A tptp.com) (B2 (-> tptp.a tptp.state Bool))) (=> (@ (@ F A) B2) (@ (@ tptp.produc281270436te_o_o F) (@ (@ tptp.produc1948644831tate_o A) B2)))))
% 0.20/0.59 (assert (forall ((F (-> tptp.state tptp.state Bool)) (A tptp.state) (B2 tptp.state)) (=> (@ (@ F A) B2) (@ (@ tptp.produc789892016tate_o F) (@ (@ tptp.produc64584659_state A) B2)))))
% 0.20/0.59 (assert (forall ((F (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B2 tptp.nat)) (=> (@ (@ F A) B2) (@ (@ tptp.produc949581770_nat_o F) (@ (@ tptp.product_Pair_nat_nat A) B2)))))
% 0.20/0.59 (assert (forall ((P3 tptp.produc696469763tate_o) (C2 (-> (-> tptp.a tptp.state Bool) tptp.produc204914599tate_o Bool))) (=> (forall ((A6 (-> tptp.a tptp.state Bool)) (B6 tptp.produc204914599tate_o)) (=> (= P3 (@ (@ tptp.produc33908149tate_o A6) B6)) (@ (@ C2 A6) B6))) (@ (@ tptp.produc1271576886te_o_o C2) P3))))
% 0.20/0.59 (assert (forall ((P3 tptp.produc204914599tate_o) (C2 (-> tptp.com (-> tptp.a tptp.state Bool) Bool))) (=> (forall ((A6 tptp.com) (B6 (-> tptp.a tptp.state Bool))) (=> (= P3 (@ (@ tptp.produc1948644831tate_o A6) B6)) (@ (@ C2 A6) B6))) (@ (@ tptp.produc281270436te_o_o C2) P3))))
% 0.20/0.59 (assert (forall ((P3 tptp.produc1115495963_state) (C2 (-> tptp.state tptp.state Bool))) (=> (forall ((A6 tptp.state) (B6 tptp.state)) (=> (= P3 (@ (@ tptp.produc64584659_state A6) B6)) (@ (@ C2 A6) B6))) (@ (@ tptp.produc789892016tate_o C2) P3))))
% 0.20/0.59 (assert (forall ((P3 tptp.product_prod_nat_nat) (C2 (-> tptp.nat tptp.nat Bool))) (=> (forall ((A6 tptp.nat) (B6 tptp.nat)) (=> (= P3 (@ (@ tptp.product_Pair_nat_nat A6) B6)) (@ (@ C2 A6) B6))) (@ (@ tptp.produc949581770_nat_o C2) P3))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr795498619_state) (R tptp.set_Pr778812871_state) (A tptp.produc1115495963_state) (B2 tptp.produc1115495963_state)) (=> (@ (@ tptp.refl_o1438232218_state A2) R) (=> (@ (@ tptp.member768948240_state (@ (@ tptp.produc1964772951_state A) B2)) R) (and (@ (@ tptp.member1389040324_state A) A2) (@ (@ tptp.member1389040324_state B2) A2))))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr1986765409at_nat) (R tptp.set_Pr1490359111at_nat) (A tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.refl_o1619599232at_nat A2) R) (=> (@ (@ tptp.member2027625872at_nat (@ (@ tptp.produc1168807639at_nat A) B2)) R) (and (@ (@ tptp.member701585322at_nat A) A2) (@ (@ tptp.member701585322at_nat B2) A2))))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr1590995257tate_o) (R tptp.set_Pr1702239303tate_o) (A tptp.produc696469763tate_o) (B2 tptp.produc696469763tate_o)) (=> (@ (@ tptp.refl_o489021252tate_o A2) R) (=> (@ (@ tptp.member1629320336tate_o (@ (@ tptp.produc1684562079tate_o A) B2)) R) (and (@ (@ tptp.member1838112666tate_o A) A2) (@ (@ tptp.member1838112666tate_o B2) A2))))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_state) (R tptp.set_Pr795498619_state) (A tptp.state) (B2 tptp.state)) (=> (@ (@ tptp.refl_on_state A2) R) (=> (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state A) B2)) R) (and (@ (@ tptp.member_state A) A2) (@ (@ tptp.member_state B2) A2))))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_nat) (R tptp.set_Pr1986765409at_nat) (A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.refl_on_nat A2) R) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A) B2)) R) (and (@ (@ tptp.member_nat A) A2) (@ (@ tptp.member_nat B2) A2))))))
% 0.20/0.59 (assert (forall ((H (-> Bool Bool)) (F (-> tptp.state tptp.state Bool)) (Prod tptp.produc1115495963_state)) (= (@ H (@ (@ tptp.produc789892016tate_o F) Prod)) (@ (@ tptp.produc789892016tate_o (lambda ((X12 tptp.state) (X23 tptp.state)) (@ H (@ (@ F X12) X23)))) Prod))))
% 0.20/0.59 (assert (forall ((H (-> Bool Bool)) (F (-> tptp.nat tptp.nat Bool)) (Prod tptp.product_prod_nat_nat)) (= (@ H (@ (@ tptp.produc949581770_nat_o F) Prod)) (@ (@ tptp.produc949581770_nat_o (lambda ((X12 tptp.nat) (X23 tptp.nat)) (@ H (@ (@ F X12) X23)))) Prod))))
% 0.20/0.59 (assert (forall ((Prod tptp.produc1115495963_state)) (@ (@ tptp.produc789892016tate_o (lambda ((Uu tptp.state) (Uv tptp.state)) true)) Prod)))
% 0.20/0.59 (assert (forall ((Prod tptp.product_prod_nat_nat)) (@ (@ tptp.produc949581770_nat_o (lambda ((Uu tptp.nat) (Uv tptp.nat)) true)) Prod)))
% 0.20/0.59 (assert (forall ((F (-> tptp.state tptp.state Bool)) (X1 tptp.state) (X22 tptp.state)) (= (@ (@ tptp.produc789892016tate_o F) (@ (@ tptp.produc64584659_state X1) X22)) (@ (@ F X1) X22))))
% 0.20/0.59 (assert (forall ((F (-> tptp.nat tptp.nat Bool)) (X1 tptp.nat) (X22 tptp.nat)) (= (@ (@ tptp.produc949581770_nat_o F) (@ (@ tptp.product_Pair_nat_nat X1) X22)) (@ (@ F X1) X22))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr795498619_state) (R tptp.set_Pr778812871_state) (X2 tptp.produc1115495963_state) (Y3 tptp.produc1115495963_state)) (=> (@ (@ tptp.refl_o1438232218_state A2) R) (=> (@ (@ tptp.member768948240_state (@ (@ tptp.produc1964772951_state X2) Y3)) R) (@ (@ tptp.member1389040324_state Y3) A2)))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr1986765409at_nat) (R tptp.set_Pr1490359111at_nat) (X2 tptp.product_prod_nat_nat) (Y3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.refl_o1619599232at_nat A2) R) (=> (@ (@ tptp.member2027625872at_nat (@ (@ tptp.produc1168807639at_nat X2) Y3)) R) (@ (@ tptp.member701585322at_nat Y3) A2)))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr1590995257tate_o) (R tptp.set_Pr1702239303tate_o) (X2 tptp.produc696469763tate_o) (Y3 tptp.produc696469763tate_o)) (=> (@ (@ tptp.refl_o489021252tate_o A2) R) (=> (@ (@ tptp.member1629320336tate_o (@ (@ tptp.produc1684562079tate_o X2) Y3)) R) (@ (@ tptp.member1838112666tate_o Y3) A2)))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_state) (R tptp.set_Pr795498619_state) (X2 tptp.state) (Y3 tptp.state)) (=> (@ (@ tptp.refl_on_state A2) R) (=> (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state X2) Y3)) R) (@ (@ tptp.member_state Y3) A2)))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_nat) (R tptp.set_Pr1986765409at_nat) (X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.refl_on_nat A2) R) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X2) Y3)) R) (@ (@ tptp.member_nat Y3) A2)))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr795498619_state) (R tptp.set_Pr778812871_state) (X2 tptp.produc1115495963_state) (Y3 tptp.produc1115495963_state)) (=> (@ (@ tptp.refl_o1438232218_state A2) R) (=> (@ (@ tptp.member768948240_state (@ (@ tptp.produc1964772951_state X2) Y3)) R) (@ (@ tptp.member1389040324_state X2) A2)))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr1986765409at_nat) (R tptp.set_Pr1490359111at_nat) (X2 tptp.product_prod_nat_nat) (Y3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.refl_o1619599232at_nat A2) R) (=> (@ (@ tptp.member2027625872at_nat (@ (@ tptp.produc1168807639at_nat X2) Y3)) R) (@ (@ tptp.member701585322at_nat X2) A2)))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr1590995257tate_o) (R tptp.set_Pr1702239303tate_o) (X2 tptp.produc696469763tate_o) (Y3 tptp.produc696469763tate_o)) (=> (@ (@ tptp.refl_o489021252tate_o A2) R) (=> (@ (@ tptp.member1629320336tate_o (@ (@ tptp.produc1684562079tate_o X2) Y3)) R) (@ (@ tptp.member1838112666tate_o X2) A2)))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_state) (R tptp.set_Pr795498619_state) (X2 tptp.state) (Y3 tptp.state)) (=> (@ (@ tptp.refl_on_state A2) R) (=> (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state X2) Y3)) R) (@ (@ tptp.member_state X2) A2)))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_nat) (R tptp.set_Pr1986765409at_nat) (X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.refl_on_nat A2) R) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X2) Y3)) R) (@ (@ tptp.member_nat X2) A2)))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr795498619_state) (R tptp.set_Pr778812871_state) (A tptp.produc1115495963_state)) (=> (@ (@ tptp.refl_o1438232218_state A2) R) (=> (@ (@ tptp.member1389040324_state A) A2) (@ (@ tptp.member768948240_state (@ (@ tptp.produc1964772951_state A) A)) R)))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr1986765409at_nat) (R tptp.set_Pr1490359111at_nat) (A tptp.product_prod_nat_nat)) (=> (@ (@ tptp.refl_o1619599232at_nat A2) R) (=> (@ (@ tptp.member701585322at_nat A) A2) (@ (@ tptp.member2027625872at_nat (@ (@ tptp.produc1168807639at_nat A) A)) R)))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr1590995257tate_o) (R tptp.set_Pr1702239303tate_o) (A tptp.produc696469763tate_o)) (=> (@ (@ tptp.refl_o489021252tate_o A2) R) (=> (@ (@ tptp.member1838112666tate_o A) A2) (@ (@ tptp.member1629320336tate_o (@ (@ tptp.produc1684562079tate_o A) A)) R)))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_state) (R tptp.set_Pr795498619_state) (A tptp.state)) (=> (@ (@ tptp.refl_on_state A2) R) (=> (@ (@ tptp.member_state A) A2) (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state A) A)) R)))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_nat) (R tptp.set_Pr1986765409at_nat) (A tptp.nat)) (=> (@ (@ tptp.refl_on_nat A2) R) (=> (@ (@ tptp.member_nat A) A2) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A) A)) R)))))
% 0.20/0.59 (assert (forall ((F (-> (-> tptp.a tptp.state Bool) tptp.produc204914599tate_o Bool)) (A (-> tptp.a tptp.state Bool)) (B2 tptp.produc204914599tate_o)) (=> (@ (@ tptp.produc1271576886te_o_o F) (@ (@ tptp.produc33908149tate_o A) B2)) (@ (@ F A) B2))))
% 0.20/0.59 (assert (forall ((F (-> tptp.com (-> tptp.a tptp.state Bool) Bool)) (A tptp.com) (B2 (-> tptp.a tptp.state Bool))) (=> (@ (@ tptp.produc281270436te_o_o F) (@ (@ tptp.produc1948644831tate_o A) B2)) (@ (@ F A) B2))))
% 0.20/0.59 (assert (forall ((F (-> tptp.state tptp.state Bool)) (A tptp.state) (B2 tptp.state)) (=> (@ (@ tptp.produc789892016tate_o F) (@ (@ tptp.produc64584659_state A) B2)) (@ (@ F A) B2))))
% 0.20/0.59 (assert (forall ((F (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.produc949581770_nat_o F) (@ (@ tptp.product_Pair_nat_nat A) B2)) (@ (@ F A) B2))))
% 0.20/0.59 (assert (forall ((C2 (-> (-> tptp.a tptp.state Bool) tptp.produc204914599tate_o Bool)) (P3 tptp.produc696469763tate_o)) (=> (@ (@ tptp.produc1271576886te_o_o C2) P3) (not (forall ((X3 (-> tptp.a tptp.state Bool)) (Y2 tptp.produc204914599tate_o)) (=> (= P3 (@ (@ tptp.produc33908149tate_o X3) Y2)) (not (@ (@ C2 X3) Y2))))))))
% 0.20/0.59 (assert (forall ((C2 (-> tptp.com (-> tptp.a tptp.state Bool) Bool)) (P3 tptp.produc204914599tate_o)) (=> (@ (@ tptp.produc281270436te_o_o C2) P3) (not (forall ((X3 tptp.com) (Y2 (-> tptp.a tptp.state Bool))) (=> (= P3 (@ (@ tptp.produc1948644831tate_o X3) Y2)) (not (@ (@ C2 X3) Y2))))))))
% 0.20/0.59 (assert (forall ((C2 (-> tptp.state tptp.state Bool)) (P3 tptp.produc1115495963_state)) (=> (@ (@ tptp.produc789892016tate_o C2) P3) (not (forall ((X3 tptp.state) (Y2 tptp.state)) (=> (= P3 (@ (@ tptp.produc64584659_state X3) Y2)) (not (@ (@ C2 X3) Y2))))))))
% 0.20/0.59 (assert (forall ((C2 (-> tptp.nat tptp.nat Bool)) (P3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.produc949581770_nat_o C2) P3) (not (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (= P3 (@ (@ tptp.product_Pair_nat_nat X3) Y2)) (not (@ (@ C2 X3) Y2))))))))
% 0.20/0.59 (assert (= tptp.total_on_state (lambda ((A5 tptp.set_state) (R3 tptp.set_Pr795498619_state)) (forall ((X tptp.state)) (=> (@ (@ tptp.member_state X) A5) (forall ((Y5 tptp.state)) (=> (@ (@ tptp.member_state Y5) A5) (=> (not (= X Y5)) (or (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state X) Y5)) R3) (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state Y5) X)) R3))))))))))
% 0.20/0.59 (assert (= tptp.total_on_nat (lambda ((A5 tptp.set_nat) (R3 tptp.set_Pr1986765409at_nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) A5) (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member_nat Y5) A5) (=> (not (= X Y5)) (or (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X) Y5)) R3) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat Y5) X)) R3))))))))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr795498619_state) (R tptp.set_Pr778812871_state)) (=> (forall ((X3 tptp.produc1115495963_state) (Y2 tptp.produc1115495963_state)) (=> (@ (@ tptp.member1389040324_state X3) A2) (=> (@ (@ tptp.member1389040324_state Y2) A2) (=> (not (= X3 Y2)) (or (@ (@ tptp.member768948240_state (@ (@ tptp.produc1964772951_state X3) Y2)) R) (@ (@ tptp.member768948240_state (@ (@ tptp.produc1964772951_state Y2) X3)) R)))))) (@ (@ tptp.total_1316653983_state A2) R))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr1986765409at_nat) (R tptp.set_Pr1490359111at_nat)) (=> (forall ((X3 tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member701585322at_nat X3) A2) (=> (@ (@ tptp.member701585322at_nat Y2) A2) (=> (not (= X3 Y2)) (or (@ (@ tptp.member2027625872at_nat (@ (@ tptp.produc1168807639at_nat X3) Y2)) R) (@ (@ tptp.member2027625872at_nat (@ (@ tptp.produc1168807639at_nat Y2) X3)) R)))))) (@ (@ tptp.total_1775715973at_nat A2) R))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_Pr1590995257tate_o) (R tptp.set_Pr1702239303tate_o)) (=> (forall ((X3 tptp.produc696469763tate_o) (Y2 tptp.produc696469763tate_o)) (=> (@ (@ tptp.member1838112666tate_o X3) A2) (=> (@ (@ tptp.member1838112666tate_o Y2) A2) (=> (not (= X3 Y2)) (or (@ (@ tptp.member1629320336tate_o (@ (@ tptp.produc1684562079tate_o X3) Y2)) R) (@ (@ tptp.member1629320336tate_o (@ (@ tptp.produc1684562079tate_o Y2) X3)) R)))))) (@ (@ tptp.total_795385983tate_o A2) R))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_state) (R tptp.set_Pr795498619_state)) (=> (forall ((X3 tptp.state) (Y2 tptp.state)) (=> (@ (@ tptp.member_state X3) A2) (=> (@ (@ tptp.member_state Y2) A2) (=> (not (= X3 Y2)) (or (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state X3) Y2)) R) (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state Y2) X3)) R)))))) (@ (@ tptp.total_on_state A2) R))))
% 0.20/0.59 (assert (forall ((A2 tptp.set_nat) (R tptp.set_Pr1986765409at_nat)) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (=> (@ (@ tptp.member_nat Y2) A2) (=> (not (= X3 Y2)) (or (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y2)) R) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat Y2) X3)) R)))))) (@ (@ tptp.total_on_nat A2) R))))
% 0.20/0.59 (assert (forall ((R tptp.set_Pr1986765409at_nat)) (@ (@ tptp.total_on_nat tptp.bot_bot_set_nat) R)))
% 0.20/0.59 (assert (forall ((R tptp.set_Pr1702239303tate_o)) (@ (@ tptp.total_795385983tate_o tptp.bot_bo170732493tate_o) R)))
% 0.20/0.59 (assert (forall ((R tptp.set_Pr1490359111at_nat)) (@ (@ tptp.total_1775715973at_nat tptp.bot_bo2130386637at_nat) R)))
% 0.20/0.59 (assert (forall ((R tptp.set_Pr778812871_state)) (@ (@ tptp.total_1316653983_state tptp.bot_bo1625160935_state) R)))
% 0.20/0.59 (assert (forall ((Q (-> Bool Bool)) (P (-> tptp.state tptp.state Bool)) (Z5 tptp.produc1115495963_state)) (=> (@ Q (@ (@ tptp.produc789892016tate_o P) Z5)) (not (forall ((X3 tptp.state) (Y2 tptp.state)) (=> (= Z5 (@ (@ tptp.produc64584659_state X3) Y2)) (not (@ Q (@ (@ P X3) Y2)))))))))
% 0.20/0.59 (assert (forall ((Q (-> Bool Bool)) (P (-> tptp.nat tptp.nat Bool)) (Z5 tptp.product_prod_nat_nat)) (=> (@ Q (@ (@ tptp.produc949581770_nat_o P) Z5)) (not (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (= Z5 (@ (@ tptp.product_Pair_nat_nat X3) Y2)) (not (@ Q (@ (@ P X3) Y2)))))))))
% 0.20/0.59 (assert (forall ((F (-> tptp.produc1115495963_state Bool))) (= (@ tptp.produc789892016tate_o (lambda ((X tptp.state) (Y5 tptp.state)) (@ F (@ (@ tptp.produc64584659_state X) Y5)))) F)))
% 0.20/0.59 (assert (forall ((F (-> tptp.product_prod_nat_nat Bool))) (= (@ tptp.produc949581770_nat_o (lambda ((X tptp.nat) (Y5 tptp.nat)) (@ F (@ (@ tptp.product_Pair_nat_nat X) Y5)))) F)))
% 0.20/0.59 (assert (forall ((F (-> tptp.state tptp.state Bool)) (G (-> tptp.produc1115495963_state Bool))) (=> (forall ((X3 tptp.state) (Y2 tptp.state)) (= (@ (@ F X3) Y2) (@ G (@ (@ tptp.produc64584659_state X3) Y2)))) (= (@ tptp.produc789892016tate_o F) G))))
% 0.20/0.59 (assert (forall ((F (-> tptp.nat tptp.nat Bool)) (G (-> tptp.product_prod_nat_nat Bool))) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (= (@ (@ F X3) Y2) (@ G (@ (@ tptp.product_Pair_nat_nat X3) Y2)))) (= (@ tptp.produc949581770_nat_o F) G))))
% 0.20/0.59 (assert (@ (@ tptp.order_130026331on_nat tptp.bot_bot_set_nat) tptp.bot_bo2130386637at_nat))
% 0.20/0.59 (assert (@ (@ tptp.order_286167592_state tptp.bot_bot_set_state) tptp.bot_bo1625160935_state))
% 0.20/0.59 (assert (@ (@ tptp.order_50454158tate_o tptp.bot_bo170732493tate_o) tptp.bot_bo1714653363tate_o))
% 0.20/0.59 (assert (@ (@ tptp.order_721919926at_nat tptp.bot_bo2130386637at_nat) tptp.bot_bo34127283at_nat))
% 0.20/0.59 (assert (@ (@ tptp.order_178668240_state tptp.bot_bo1625160935_state) tptp.bot_bo1331673139_state))
% 0.20/0.59 (assert (@ (@ tptp.refl_on_nat tptp.bot_bot_set_nat) tptp.bot_bo2130386637at_nat))
% 0.20/0.59 (assert (@ (@ tptp.refl_on_state tptp.bot_bot_set_state) tptp.bot_bo1625160935_state))
% 0.20/0.59 (assert (@ (@ tptp.refl_o489021252tate_o tptp.bot_bo170732493tate_o) tptp.bot_bo1714653363tate_o))
% 0.20/0.59 (assert (@ (@ tptp.refl_o1619599232at_nat tptp.bot_bo2130386637at_nat) tptp.bot_bo34127283at_nat))
% 0.20/0.59 (assert (@ (@ tptp.refl_o1438232218_state tptp.bot_bo1625160935_state) tptp.bot_bo1331673139_state))
% 0.20/0.59 (assert (forall ((Q5 tptp.produc1115495963_state) (F (-> tptp.state tptp.state Bool)) (G (-> tptp.state tptp.state Bool)) (P3 tptp.produc1115495963_state)) (=> (forall ((X3 tptp.state) (Y2 tptp.state)) (=> (= (@ (@ tptp.produc64584659_state X3) Y2) Q5) (= (@ (@ F X3) Y2) (@ (@ G X3) Y2)))) (=> (= P3 Q5) (= (@ (@ tptp.produc789892016tate_o F) P3) (@ (@ tptp.produc789892016tate_o G) Q5))))))
% 0.20/0.59 (assert (forall ((Q5 tptp.product_prod_nat_nat) (F (-> tptp.nat tptp.nat Bool)) (G (-> tptp.nat tptp.nat Bool)) (P3 tptp.product_prod_nat_nat)) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat X3) Y2) Q5) (= (@ (@ F X3) Y2) (@ (@ G X3) Y2)))) (=> (= P3 Q5) (= (@ (@ tptp.produc949581770_nat_o F) P3) (@ (@ tptp.produc949581770_nat_o G) Q5))))))
% 0.20/0.59 (assert (= tptp.order_2027321734_state (lambda ((R3 tptp.set_Pr778812871_state) (A3 tptp.produc1115495963_state)) (@ tptp.collec496201222_state (lambda ((B7 tptp.produc1115495963_state)) (and (not (= B7 A3)) (@ (@ tptp.member768948240_state (@ (@ tptp.produc1964772951_state A3) B7)) R3)))))))
% 0.20/0.59 (assert (= tptp.order_665764460at_nat (lambda ((R3 tptp.set_Pr1490359111at_nat) (A3 tptp.product_prod_nat_nat)) (@ tptp.collec7649004at_nat (lambda ((B7 tptp.product_prod_nat_nat)) (and (not (= B7 A3)) (@ (@ tptp.member2027625872at_nat (@ (@ tptp.produc1168807639at_nat A3) B7)) R3)))))))
% 0.20/0.59 (assert (= tptp.order_1121016664tate_o (lambda ((R3 tptp.set_Pr1702239303tate_o) (A3 tptp.produc696469763tate_o)) (@ tptp.collec1499596504tate_o (lambda ((B7 tptp.produc696469763tate_o)) (and (not (= B7 A3)) (@ (@ tptp.member1629320336tate_o (@ (@ tptp.produc1684562079tate_o A3) B7)) R3)))))))
% 0.20/0.59 (assert (= tptp.order_aboveS_state (lambda ((R3 tptp.set_Pr795498619_state) (A3 tptp.state)) (@ tptp.collect_state (lambda ((B7 tptp.state)) (and (not (= B7 A3)) (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state A3) B7)) R3)))))))
% 0.20/0.59 (assert (= tptp.order_aboveS_nat (lambda ((R3 tptp.set_Pr1986765409at_nat) (A3 tptp.nat)) (@ tptp.collect_nat (lambda ((B7 tptp.nat)) (and (not (= B7 A3)) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A3) B7)) R3)))))))
% 0.20/0.59 (assert (= tptp.produc938968666tate_o tptp.produc789892016tate_o))
% 0.20/0.59 (assert (= tptp.produc385877620_nat_o tptp.produc949581770_nat_o))
% 0.20/0.59 (assert (forall ((P3 tptp.product_prod_nat_nat) (Z5 tptp.produc1115495963_state) (C2 (-> tptp.nat tptp.nat tptp.set_Pr795498619_state))) (=> (forall ((A6 tptp.nat) (B6 tptp.nat)) (=> (= P3 (@ (@ tptp.product_Pair_nat_nat A6) B6)) (@ (@ tptp.member1389040324_state Z5) (@ (@ C2 A6) B6)))) (@ (@ tptp.member1389040324_state Z5) (@ (@ tptp.produc1654445_state C2) P3)))))
% 0.20/0.59 (assert (forall ((P3 tptp.product_prod_nat_nat) (Z5 tptp.product_prod_nat_nat) (C2 (-> tptp.nat tptp.nat tptp.set_Pr1986765409at_nat))) (=> (forall ((A6 tptp.nat) (B6 tptp.nat)) (=> (= P3 (@ (@ tptp.product_Pair_nat_nat A6) B6)) (@ (@ tptp.member701585322at_nat Z5) (@ (@ C2 A6) B6)))) (@ (@ tptp.member701585322at_nat Z5) (@ (@ tptp.produc1915186323at_nat C2) P3)))))
% 0.20/0.59 (assert (forall ((P3 tptp.product_prod_nat_nat) (Z5 tptp.produc696469763tate_o) (C2 (-> tptp.nat tptp.nat tptp.set_Pr1590995257tate_o))) (=> (forall ((A6 tptp.nat) (B6 tptp.nat)) (=> (= P3 (@ (@ tptp.product_Pair_nat_nat A6) B6)) (@ (@ tptp.member1838112666tate_o Z5) (@ (@ C2 A6) B6)))) (@ (@ tptp.member1838112666tate_o Z5) (@ (@ tptp.produc1610543495tate_o C2) P3)))))
% 0.20/0.59 (assert (forall ((B2 (-> tptp.state Bool)) (C2 tptp.com) (F (-> tptp.nat tptp.state)) (K tptp.nat)) (=> (@ (@ tptp.termi (@ (@ tptp.while B2) C2)) (@ F K)) (=> (forall ((I tptp.nat)) (@ (@ (@ tptp.exec (@ F I)) C2) (@ F (@ tptp.suc I)))) (exists ((I tptp.nat)) (not (@ B2 (@ F I))))))))
% 0.20/0.59 (assert (forall ((W tptp.com) (Fk tptp.state) (F (-> tptp.nat tptp.state)) (K tptp.nat) (B2 (-> tptp.state Bool)) (C2 tptp.com)) (=> (@ (@ tptp.termi W) Fk) (=> (and (= Fk (@ F K)) (= W (@ (@ tptp.while B2) C2)) (forall ((I tptp.nat)) (@ (@ (@ tptp.exec (@ F I)) C2) (@ F (@ tptp.suc I))))) (exists ((I tptp.nat)) (not (@ B2 (@ F I))))))))
% 0.20/0.59 (assert (forall ((S2 tptp.state) (N tptp.nat) (T2 tptp.state)) (let ((_let_1 (@ tptp.execn S2))) (=> (@ (@ (@ _let_1 tptp.body) N) T2) (@ (@ (@ _let_1 tptp.call) (@ tptp.suc N)) T2)))))
% 0.20/0.59 (assert (= tptp.pred_nat (@ tptp.collec7649004at_nat (@ tptp.produc949581770_nat_o (lambda ((M tptp.nat) (N2 tptp.nat)) (= N2 (@ tptp.suc M)))))))
% 0.20/0.59 (assert (forall ((S2 tptp.state) (B2 (-> tptp.state Bool)) (C2 tptp.com) (N tptp.nat) (T2 tptp.state) (P (-> tptp.state Bool))) (=> (@ (@ (@ (@ tptp.execn S2) (@ (@ tptp.while B2) C2)) N) T2) (=> (@ P S2) (=> (forall ((S tptp.state) (S3 tptp.state)) (=> (@ P S) (=> (@ B2 S) (=> (@ (@ (@ (@ tptp.execn S) C2) N) S3) (@ P S3))))) (and (@ P T2) (not (@ B2 T2))))))))
% 0.20/0.59 (assert (forall ((S2 tptp.state) (W tptp.com) (N tptp.nat) (T2 tptp.state) (B2 (-> tptp.state Bool)) (C2 tptp.com) (P (-> tptp.state Bool))) (=> (@ (@ (@ (@ tptp.execn S2) W) N) T2) (=> (and (= W (@ (@ tptp.while B2) C2)) (@ P S2) (forall ((S tptp.state) (S3 tptp.state)) (=> (and (@ P S) (@ B2 S) (@ (@ (@ (@ tptp.execn S) C2) N) S3)) (@ P S3)))) (and (@ P T2) (not (@ B2 T2)))))))
% 0.20/0.59 (assert (forall ((B2 (-> tptp.state Bool)) (S2 tptp.state) (C2 tptp.com) (N tptp.nat) (T2 tptp.state) (U2 tptp.state)) (let ((_let_1 (@ (@ tptp.while B2) C2))) (let ((_let_2 (@ tptp.execn S2))) (=> (@ B2 S2) (=> (@ (@ (@ _let_2 C2) N) T2) (=> (@ (@ (@ (@ tptp.execn T2) _let_1) N) U2) (@ (@ (@ _let_2 _let_1) N) U2))))))))
% 0.20/0.59 (assert (forall ((B2 (-> tptp.state Bool)) (S2 tptp.state) (C2 tptp.com) (N tptp.nat)) (=> (not (@ B2 S2)) (@ (@ (@ (@ tptp.execn S2) (@ (@ tptp.while B2) C2)) N) S2))))
% 0.20/0.59 (assert (= tptp.exec (lambda ((S4 tptp.state) (C5 tptp.com) (T3 tptp.state)) (exists ((N2 tptp.nat)) (@ (@ (@ (@ tptp.execn S4) C5) N2) T3)))))
% 0.20/0.59 (assert (@ tptp.wf_nat tptp.pred_nat))
% 0.20/0.59 (assert (forall ((C1 tptp.com) (S0 tptp.state) (C22 tptp.com)) (=> (@ (@ tptp.termi C1) S0) (=> (forall ((S1 tptp.state)) (=> (@ (@ (@ tptp.exec S0) C1) S1) (@ (@ tptp.termi C22) S1))) (@ (@ tptp.termi (@ (@ tptp.semi C1) C22)) S0)))))
% 0.20/0.59 (assert (forall ((X21 tptp.com) (X222 tptp.com) (Y21 tptp.com) (Y222 tptp.com)) (= (= (@ (@ tptp.semi X21) X222) (@ (@ tptp.semi Y21) Y222)) (and (= X21 Y21) (= X222 Y222)))))
% 0.20/0.59 (assert (forall ((S0 tptp.state) (C1 tptp.com) (N tptp.nat) (S12 tptp.state) (C22 tptp.com) (S22 tptp.state)) (let ((_let_1 (@ tptp.execn S0))) (=> (@ (@ (@ _let_1 C1) N) S12) (=> (@ (@ (@ (@ tptp.execn S12) C22) N) S22) (@ (@ (@ _let_1 (@ (@ tptp.semi C1) C22)) N) S22))))))
% 0.20/0.59 (assert (forall ((X21 tptp.com) (X222 tptp.com) (X41 (-> tptp.state Bool)) (X42 tptp.com)) (not (= (@ (@ tptp.semi X21) X222) (@ (@ tptp.while X41) X42)))))
% 0.20/0.59 (assert (forall ((X21 tptp.com) (X222 tptp.com)) (not (= (@ (@ tptp.semi X21) X222) tptp.call))))
% 0.20/0.59 (assert (forall ((S0 tptp.state) (C1 tptp.com) (S12 tptp.state) (C22 tptp.com) (S22 tptp.state)) (let ((_let_1 (@ tptp.exec S0))) (=> (@ (@ _let_1 C1) S12) (=> (@ (@ (@ tptp.exec S12) C22) S22) (@ (@ _let_1 (@ (@ tptp.semi C1) C22)) S22))))))
% 0.20/0.59 (assert (@ tptp.wf_nat tptp.less_than))
% 0.20/0.59 (assert (forall ((A2 tptp.set_nat)) (@ (@ tptp.total_on_nat A2) tptp.less_than)))
% 0.20/0.59 (assert (@ tptp.irrefl_nat tptp.less_than))
% 0.20/0.59 (assert (@ tptp.trans_nat tptp.less_than))
% 0.20/0.59 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (= (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X2) Y3)) tptp.less_than) (@ (@ tptp.ord_less_nat X2) Y3))))
% 0.20/0.59 (assert (forall ((S6 tptp.state)) (and (@ (@ (@ (@ tptp.pHoare382919414oare_a (@ (@ tptp.insert2053719859tate_o (@ (@ tptp.produc33908149tate_o (lambda ((Z4 tptp.a) (S4 tptp.state)) (and (@ (@ tptp.pa Z4) S4) (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state S4) S6)) tptp.r)))) (@ (@ tptp.produc1948644831tate_o tptp.call) tptp.qa))) tptp.bot_bo170732493tate_o)) (lambda ((Z4 tptp.a) (S4 tptp.state)) (and (@ (@ tptp.pa Z4) S4) (= S4 S6)))) tptp.body) tptp.qa) (=> (and (forall ((S tptp.state) (T tptp.state)) (=> (@ (@ (@ tptp.exec S) tptp.body) T) (forall ((Z tptp.a)) (=> (and (@ (@ tptp.pa Z) S) (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state S) S6)) tptp.r)) (@ (@ tptp.qa Z) T))))) (forall ((Z tptp.a) (S tptp.state)) (=> (and (@ (@ tptp.pa Z) S) (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state S) S6)) tptp.r)) (@ (@ tptp.termi tptp.body) S)))) (and (forall ((S7 tptp.state) (T4 tptp.state)) (=> (@ (@ (@ tptp.exec S7) tptp.body) T4) (forall ((Z2 tptp.a)) (=> (and (@ (@ tptp.pa Z2) S7) (= S7 S6)) (@ (@ tptp.qa Z2) T4))))) (forall ((Z2 tptp.a) (S7 tptp.state)) (=> (and (@ (@ tptp.pa Z2) S7) (= S7 S6)) (@ (@ tptp.termi tptp.body) S7))))))))
% 0.20/0.59 (assert (forall ((Y4 tptp.state)) (=> (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state Y4) tptp.x)) tptp.r) (and (forall ((S7 tptp.state) (T4 tptp.state)) (=> (@ (@ (@ tptp.exec S7) tptp.body) T4) (forall ((Z2 tptp.a)) (=> (and (@ (@ tptp.pa Z2) S7) (= S7 Y4)) (@ (@ tptp.qa Z2) T4))))) (forall ((Z2 tptp.a) (S7 tptp.state)) (=> (and (@ (@ tptp.pa Z2) S7) (= S7 Y4)) (@ (@ tptp.termi tptp.body) S7)))))))
% 0.20/0.59 (assert (not (and (forall ((S tptp.state) (T tptp.state)) (or (not (@ (@ (@ tptp.exec S) tptp.body) T)) (forall ((Z tptp.a)) (or (not (@ (@ tptp.pa Z) S)) (not (= S tptp.x)) (@ (@ tptp.qa Z) T))))) (forall ((Z tptp.a) (S tptp.state)) (or (not (@ (@ tptp.pa Z) S)) (not (= S tptp.x)) (@ (@ tptp.termi tptp.body) S))))))
% 0.20/0.59 (set-info :filename cvc5---1.0.5_17700)
% 0.20/0.59 (check-sat-assuming ( true ))
% 1.15/1.45 ------- get file name : TPTP file name is ITP141^1
% 1.15/1.45 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_17700.smt2...
% 1.15/1.45 --- Run --ho-elim --full-saturate-quant at 10...
% 1.15/1.45 % SZS status Theorem for ITP141^1
% 1.15/1.45 % SZS output start Proof for ITP141^1
% 1.15/1.45 (
% 1.15/1.45 (let ((_let_1 (not (and (forall ((S tptp.state) (T tptp.state)) (or (not (@ (@ (@ tptp.exec S) tptp.body) T)) (forall ((Z tptp.a)) (or (not (@ (@ tptp.pa Z) S)) (not (= S tptp.x)) (@ (@ tptp.qa Z) T))))) (forall ((Z tptp.a) (S tptp.state)) (or (not (@ (@ tptp.pa Z) S)) (not (= S tptp.x)) (@ (@ tptp.termi tptp.body) S))))))) (let ((_let_2 (forall ((Y4 tptp.state)) (=> (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state Y4) tptp.x)) tptp.r) (and (forall ((S7 tptp.state) (T4 tptp.state)) (=> (@ (@ (@ tptp.exec S7) tptp.body) T4) (forall ((Z2 tptp.a)) (=> (and (@ (@ tptp.pa Z2) S7) (= S7 Y4)) (@ (@ tptp.qa Z2) T4))))) (forall ((Z2 tptp.a) (S7 tptp.state)) (=> (and (@ (@ tptp.pa Z2) S7) (= S7 Y4)) (@ (@ tptp.termi tptp.body) S7)))))))) (let ((_let_3 (forall ((S6 tptp.state)) (and (@ (@ (@ (@ tptp.pHoare382919414oare_a (@ (@ tptp.insert2053719859tate_o (@ (@ tptp.produc33908149tate_o (lambda ((Z4 tptp.a) (S4 tptp.state)) (and (@ (@ tptp.pa Z4) S4) (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state S4) S6)) tptp.r)))) (@ (@ tptp.produc1948644831tate_o tptp.call) tptp.qa))) tptp.bot_bo170732493tate_o)) (lambda ((Z4 tptp.a) (S4 tptp.state)) (and (@ (@ tptp.pa Z4) S4) (= S4 S6)))) tptp.body) tptp.qa) (=> (and (forall ((S tptp.state) (T tptp.state)) (=> (@ (@ (@ tptp.exec S) tptp.body) T) (forall ((Z tptp.a)) (=> (and (@ (@ tptp.pa Z) S) (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state S) S6)) tptp.r)) (@ (@ tptp.qa Z) T))))) (forall ((Z tptp.a) (S tptp.state)) (=> (and (@ (@ tptp.pa Z) S) (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state S) S6)) tptp.r)) (@ (@ tptp.termi tptp.body) S)))) (and (forall ((S7 tptp.state) (T4 tptp.state)) (=> (@ (@ (@ tptp.exec S7) tptp.body) T4) (forall ((Z2 tptp.a)) (=> (and (@ (@ tptp.pa Z2) S7) (= S7 S6)) (@ (@ tptp.qa Z2) T4))))) (forall ((Z2 tptp.a) (S7 tptp.state)) (=> (and (@ (@ tptp.pa Z2) S7) (= S7 S6)) (@ (@ tptp.termi tptp.body) S7))))))))) (let ((_let_4 (= tptp.exec (lambda ((S4 tptp.state) (C5 tptp.com) (T3 tptp.state)) (exists ((N2 tptp.nat)) (@ (@ (@ (@ tptp.execn S4) C5) N2) T3)))))) (let ((_let_5 (= tptp.pred_nat (@ tptp.collec7649004at_nat (@ tptp.produc949581770_nat_o (lambda ((M tptp.nat) (N2 tptp.nat)) (= N2 (@ tptp.suc M)))))))) (let ((_let_6 (= tptp.produc385877620_nat_o tptp.produc949581770_nat_o))) (let ((_let_7 (= tptp.produc938968666tate_o tptp.produc789892016tate_o))) (let ((_let_8 (= tptp.order_aboveS_nat (lambda ((R3 tptp.set_Pr1986765409at_nat) (A3 tptp.nat)) (@ tptp.collect_nat (lambda ((B7 tptp.nat)) (and (not (= B7 A3)) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A3) B7)) R3)))))))) (let ((_let_9 (= tptp.order_aboveS_state (lambda ((R3 tptp.set_Pr795498619_state) (A3 tptp.state)) (@ tptp.collect_state (lambda ((B7 tptp.state)) (and (not (= B7 A3)) (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state A3) B7)) R3)))))))) (let ((_let_10 (= tptp.order_1121016664tate_o (lambda ((R3 tptp.set_Pr1702239303tate_o) (A3 tptp.produc696469763tate_o)) (@ tptp.collec1499596504tate_o (lambda ((B7 tptp.produc696469763tate_o)) (and (not (= B7 A3)) (@ (@ tptp.member1629320336tate_o (@ (@ tptp.produc1684562079tate_o A3) B7)) R3)))))))) (let ((_let_11 (= tptp.order_665764460at_nat (lambda ((R3 tptp.set_Pr1490359111at_nat) (A3 tptp.product_prod_nat_nat)) (@ tptp.collec7649004at_nat (lambda ((B7 tptp.product_prod_nat_nat)) (and (not (= B7 A3)) (@ (@ tptp.member2027625872at_nat (@ (@ tptp.produc1168807639at_nat A3) B7)) R3)))))))) (let ((_let_12 (= tptp.order_2027321734_state (lambda ((R3 tptp.set_Pr778812871_state) (A3 tptp.produc1115495963_state)) (@ tptp.collec496201222_state (lambda ((B7 tptp.produc1115495963_state)) (and (not (= B7 A3)) (@ (@ tptp.member768948240_state (@ (@ tptp.produc1964772951_state A3) B7)) R3)))))))) (let ((_let_13 (= tptp.total_on_nat (lambda ((A5 tptp.set_nat) (R3 tptp.set_Pr1986765409at_nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) A5) (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member_nat Y5) A5) (=> (not (= X Y5)) (or (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X) Y5)) R3) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat Y5) X)) R3))))))))))) (let ((_let_14 (= tptp.total_on_state (lambda ((A5 tptp.set_state) (R3 tptp.set_Pr795498619_state)) (forall ((X tptp.state)) (=> (@ (@ tptp.member_state X) A5) (forall ((Y5 tptp.state)) (=> (@ (@ tptp.member_state Y5) A5) (=> (not (= X Y5)) (or (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state X) Y5)) R3) (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state Y5) X)) R3))))))))))) (let ((_let_15 (= tptp.bot_bo446391478tate_o (lambda ((X tptp.produc1115495963_state)) (@ (@ tptp.member1389040324_state X) tptp.bot_bo1625160935_state))))) (let ((_let_16 (= tptp.bot_bo513358416_nat_o (lambda ((X tptp.product_prod_nat_nat)) (@ (@ tptp.member701585322at_nat X) tptp.bot_bo2130386637at_nat))))) (let ((_let_17 (= tptp.bot_bo250281208te_o_o (lambda ((X tptp.produc696469763tate_o)) (@ (@ tptp.member1838112666tate_o X) tptp.bot_bo170732493tate_o))))) (let ((_let_18 (= tptp.is_emp1062983149_state (lambda ((A5 tptp.set_Pr795498619_state)) (= A5 tptp.bot_bo1625160935_state))))) (let ((_let_19 (= tptp.is_emp825011411at_nat (lambda ((A5 tptp.set_Pr1986765409at_nat)) (= A5 tptp.bot_bo2130386637at_nat))))) (let ((_let_20 (= tptp.is_emp807847857tate_o (lambda ((A5 tptp.set_Pr1590995257tate_o)) (= A5 tptp.bot_bo170732493tate_o))))) (let ((_let_21 (= tptp.bot_bo51534648tate_o (lambda ((X tptp.state) (Y5 tptp.state)) (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state X) Y5)) tptp.bot_bo1625160935_state))))) (let ((_let_22 (= tptp.bot_bot_nat_nat_o (lambda ((X tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X) Y5)) tptp.bot_bo2130386637at_nat))))) (let ((_let_23 (= tptp.bot_bo2130564770te_o_o (lambda ((X (-> tptp.a tptp.state Bool)) (Y5 tptp.produc204914599tate_o)) (@ (@ tptp.member1838112666tate_o (@ (@ tptp.produc33908149tate_o X) Y5)) tptp.bot_bo170732493tate_o))))) (let ((_let_24 (= tptp.bot_bo935656620te_o_o (lambda ((X tptp.com) (Y5 (-> tptp.a tptp.state Bool))) (@ (@ tptp.member221067728tate_o (@ (@ tptp.produc1948644831tate_o X) Y5)) tptp.bot_bo1692783091tate_o))))) (let ((_let_25 (= tptp.wf_Pro309705690tate_o (lambda ((R3 tptp.set_Pr1702239303tate_o)) (forall ((Q4 tptp.set_Pr1590995257tate_o)) (=> (exists ((X tptp.produc696469763tate_o)) (@ (@ tptp.member1838112666tate_o X) Q4)) (exists ((X tptp.produc696469763tate_o)) (and (@ (@ tptp.member1838112666tate_o X) Q4) (forall ((Y5 tptp.produc696469763tate_o)) (=> (@ (@ tptp.member1629320336tate_o (@ (@ tptp.produc1684562079tate_o Y5) X)) R3) (not (@ (@ tptp.member1838112666tate_o Y5) Q4)))))))))))) (let ((_let_26 (= tptp.wf_Pro745352042at_nat (lambda ((R3 tptp.set_Pr1490359111at_nat)) (forall ((Q4 tptp.set_Pr1986765409at_nat)) (=> (exists ((X tptp.product_prod_nat_nat)) (@ (@ tptp.member701585322at_nat X) Q4)) (exists ((X tptp.product_prod_nat_nat)) (and (@ (@ tptp.member701585322at_nat X) Q4) (forall ((Y5 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member2027625872at_nat (@ (@ tptp.produc1168807639at_nat Y5) X)) R3) (not (@ (@ tptp.member701585322at_nat Y5) Q4)))))))))))) (let ((_let_27 (= tptp.wf_Pro1783588484_state (lambda ((R3 tptp.set_Pr778812871_state)) (forall ((Q4 tptp.set_Pr795498619_state)) (=> (exists ((X tptp.produc1115495963_state)) (@ (@ tptp.member1389040324_state X) Q4)) (exists ((X tptp.produc1115495963_state)) (and (@ (@ tptp.member1389040324_state X) Q4) (forall ((Y5 tptp.produc1115495963_state)) (=> (@ (@ tptp.member768948240_state (@ (@ tptp.produc1964772951_state Y5) X)) R3) (not (@ (@ tptp.member1389040324_state Y5) Q4)))))))))))) (let ((_let_28 (= tptp.wf_nat (lambda ((R3 tptp.set_Pr1986765409at_nat)) (forall ((P4 (-> tptp.nat Bool))) (=> (forall ((X tptp.nat)) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat Y5) X)) R3) (@ P4 Y5))) (@ P4 X))) (forall ((X4 tptp.nat)) (@ P4 X4)))))))) (let ((_let_29 (= tptp.wf_state (lambda ((R3 tptp.set_Pr795498619_state)) (forall ((P4 (-> tptp.state Bool))) (=> (forall ((X tptp.state)) (=> (forall ((Y5 tptp.state)) (=> (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state Y5) X)) R3) (@ P4 Y5))) (@ P4 X))) (forall ((X4 tptp.state)) (@ P4 X4)))))))) (let ((_let_30 (= tptp.is_sin1132515087_state (lambda ((A5 tptp.set_Pr795498619_state)) (= A5 (@ (@ tptp.insert311944171_state (@ tptp.the_el1967402896_state A5)) tptp.bot_bo1625160935_state)))))) (let ((_let_31 (= tptp.is_sin1352690165at_nat (lambda ((A5 tptp.set_Pr1986765409at_nat)) (= A5 (@ (@ tptp.insert271595217at_nat (@ tptp.the_el1949240438at_nat A5)) tptp.bot_bo2130386637at_nat)))))) (let ((_let_32 (= tptp.is_sin1547905295tate_o (lambda ((A5 tptp.set_Pr1590995257tate_o)) (= A5 (@ (@ tptp.insert2053719859tate_o (@ tptp.the_el1569055182tate_o A5)) tptp.bot_bo170732493tate_o)))))) (let ((_let_33 (= tptp.insert2053719859tate_o (lambda ((A3 tptp.produc696469763tate_o) (B4 tptp.set_Pr1590995257tate_o)) (@ tptp.collec1499596504tate_o (lambda ((X tptp.produc696469763tate_o)) (or (= X A3) (@ (@ tptp.member1838112666tate_o X) B4)))))))) (let ((_let_34 (= tptp.insert271595217at_nat (lambda ((A3 tptp.product_prod_nat_nat) (B4 tptp.set_Pr1986765409at_nat)) (@ tptp.collec7649004at_nat (lambda ((X tptp.product_prod_nat_nat)) (or (= X A3) (@ (@ tptp.member701585322at_nat X) B4)))))))) (let ((_let_35 (= tptp.insert311944171_state (lambda ((A3 tptp.produc1115495963_state) (B4 tptp.set_Pr795498619_state)) (@ tptp.collec496201222_state (lambda ((X tptp.produc1115495963_state)) (or (= X A3) (@ (@ tptp.member1389040324_state X) B4)))))))) (let ((_let_36 (= tptp.bot_bo1625160935_state (@ tptp.collec496201222_state (lambda ((X tptp.produc1115495963_state)) false))))) (let ((_let_37 (= tptp.bot_bo2130386637at_nat (@ tptp.collec7649004at_nat (lambda ((X tptp.product_prod_nat_nat)) false))))) (let ((_let_38 (= tptp.bot_bo170732493tate_o (@ tptp.collec1499596504tate_o (lambda ((X tptp.produc696469763tate_o)) false))))) (let ((_let_39 (forall ((S tptp.state) (T tptp.state) (BOUND_VARIABLE_8983 tptp.a) (BOUND_VARIABLE_11938 tptp.nat)) (or (not (ho_230 (ho_356 (ho_355 (ho_354 k_353 S) tptp.body) BOUND_VARIABLE_11938) T)) (not (ho_236 (ho_235 k_234 (ho_233 (ho_232 k_231 S) tptp.x)) tptp.r)) (not (ho_230 (ho_229 k_237 BOUND_VARIABLE_8983) S)) (ho_230 (ho_229 k_299 BOUND_VARIABLE_8983) T))))) (let ((_let_40 (forall ((Z tptp.a) (S tptp.state)) (or (not (ho_230 (ho_229 k_237 Z) S)) (not (ho_236 (ho_235 k_234 (ho_233 (ho_232 k_231 S) tptp.x)) tptp.r)) (ho_230 (ho_361 k_360 tptp.body) S))))) (let ((_let_41 (ho_230 (ho_229 k_237 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_684) tptp.x))) (let ((_let_42 (not _let_41))) (let ((_let_43 (ho_361 k_360 tptp.body))) (let ((_let_44 (ho_230 _let_43 tptp.x))) (let ((_let_45 (or _let_44 _let_42))) (let ((_let_46 (ho_230 (ho_229 k_299 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_680) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_679))) (let ((_let_47 (ho_229 k_237 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_680))) (let ((_let_48 (ho_355 (ho_354 k_353 tptp.x) tptp.body))) (let ((_let_49 (and (or (not (ho_230 (ho_356 _let_48 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_681) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_679)) (not (ho_230 _let_47 tptp.x)) _let_46) _let_45))) (let ((_let_50 (not _let_40))) (let ((_let_51 (not _let_39))) (let ((_let_52 (or _let_51 _let_50 _let_49))) (let ((_let_53 (ho_230 _let_47 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_678))) (let ((_let_54 (not _let_53))) (let ((_let_55 (ho_236 (ho_235 k_234 (ho_233 (ho_232 k_231 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_678) tptp.x)) tptp.r))) (let ((_let_56 (not _let_55))) (let ((_let_57 (ho_230 (ho_356 (ho_355 (ho_354 k_353 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_678) tptp.body) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_681) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_679))) (let ((_let_58 (not _let_57))) (let ((_let_59 (or _let_58 _let_56 _let_54 _let_46))) (let ((_let_60 (ho_229 k_237 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_664))) (let ((_let_61 (or _let_58 _let_54 _let_46))) (let ((_let_62 (and _let_61 (or (ho_230 _let_43 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_678) (not (ho_230 _let_60 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_678)))))) (let ((_let_63 (or _let_56 _let_62))) (let ((_let_64 (or))) (let ((_let_65 (REFL :args (_let_59)))) (let ((_let_66 (forall ((Y4 tptp.state) (BOUND_VARIABLE_9249 tptp.a) (BOUND_VARIABLE_9239 tptp.a) (BOUND_VARIABLE_9237 tptp.state) (BOUND_VARIABLE_12020 tptp.nat)) (or (not (ho_236 (ho_235 k_234 (ho_233 (ho_232 k_231 Y4) tptp.x)) tptp.r)) (and (or (not (ho_230 (ho_356 (ho_355 (ho_354 k_353 Y4) tptp.body) BOUND_VARIABLE_12020) BOUND_VARIABLE_9237)) (not (ho_230 (ho_229 k_237 BOUND_VARIABLE_9239) Y4)) (ho_230 (ho_229 k_299 BOUND_VARIABLE_9239) BOUND_VARIABLE_9237)) (or (ho_230 (ho_361 k_360 tptp.body) Y4) (not (ho_230 (ho_229 k_237 BOUND_VARIABLE_9249) Y4)))))))) (let ((_let_67 (EQ_RESOLVE (ASSUME :args (_let_38)) (MACRO_SR_EQ_INTRO :args (_let_38 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_68 (EQ_RESOLVE (ASSUME :args (_let_37)) (MACRO_SR_EQ_INTRO :args (_let_37 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_36)) (MACRO_SR_EQ_INTRO :args (_let_36 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_35)) (MACRO_SR_EQ_INTRO :args (_let_35 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_34)) (MACRO_SR_EQ_INTRO :args (_let_34 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_33)) (MACRO_SR_EQ_INTRO :args (_let_33 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (EQ_RESOLVE (ASSUME :args (_let_32)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_72 _let_71 _let_70 _let_69 _let_68 _let_67) :args (_let_32 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_74 (EQ_RESOLVE (ASSUME :args (_let_31)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67) :args (_let_31 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_75 (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67) :args (_let_30 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_76 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_77 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_81 (ASSUME :args (_let_24)))) (let ((_let_82 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67) :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_83 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67) :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_84 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67) :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67) :args ((= tptp.is_emp807847857tate_o (lambda ((A5 tptp.set_Pr1590995257tate_o)) (= tptp.bot_bo170732493tate_o A5))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_86 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67) :args ((= tptp.is_emp825011411at_nat (lambda ((A5 tptp.set_Pr1986765409at_nat)) (= tptp.bot_bo2130386637at_nat A5))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_87 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67) :args ((= tptp.is_emp1062983149_state (lambda ((A5 tptp.set_Pr795498619_state)) (= tptp.bot_bo1625160935_state A5))) SB_DEFAULT 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(MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_103 1)) :args ((or _let_101 (not _let_103)))) (REORDERING (CNF_OR_POS :args (_let_101)) :args ((or _let_99 _let_95 (not _let_101)))) (REORDERING (CNF_OR_POS :args (_let_104)) :args ((or _let_97 _let_103 (not _let_104)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_91 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_683 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_682 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_664 tptp.x SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_665 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_92)) _let_91 :args (_let_104 false _let_66)) (CNF_OR_NEG :args (_let_100 2)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_100 1)) (CONG _let_105 (MACRO_SR_PRED_INTRO :args ((= (not _let_97) _let_96))) :args _let_64)) :args ((or _let_96 _let_100))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_100 0)) (CONG _let_105 (MACRO_SR_PRED_INTRO :args ((= (not _let_99) _let_98))) :args _let_64)) :args ((or _let_98 _let_100))) :args (_let_100 true 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tptp.produc696469763tate_o) (A2 tptp.set_Pr1590995257tate_o)) (let ((_let_1 (@ tptp.insert2053719859tate_o X2))) (let ((_let_2 (@ tptp.insert2053719859tate_o Y3))) (= (@ _let_1 (@ _let_2 A2)) (@ _let_2 (@ _let_1 A2)))))) (forall ((X2 tptp.product_prod_nat_nat) (Y3 tptp.product_prod_nat_nat) (A2 tptp.set_Pr1986765409at_nat)) (let ((_let_1 (@ tptp.insert271595217at_nat X2))) (let ((_let_2 (@ tptp.insert271595217at_nat Y3))) (= (@ _let_1 (@ _let_2 A2)) (@ _let_2 (@ _let_1 A2)))))) (forall ((X2 tptp.produc1115495963_state) (Y3 tptp.produc1115495963_state) (A2 tptp.set_Pr795498619_state)) (let ((_let_1 (@ tptp.insert311944171_state X2))) (let ((_let_2 (@ tptp.insert311944171_state Y3))) (= (@ _let_1 (@ _let_2 A2)) (@ _let_2 (@ _let_1 A2)))))) (forall ((A tptp.produc1115495963_state) (A2 tptp.set_Pr795498619_state) (B2 tptp.produc1115495963_state) (B tptp.set_Pr795498619_state)) (let ((_let_1 (= A B2))) (=> (not (@ (@ tptp.member1389040324_state A) A2)) (=> (not (@ (@ 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(@ tptp.member701585322at_nat A) C3))))))))))) (forall ((A tptp.produc696469763tate_o) (A2 tptp.set_Pr1590995257tate_o) (B2 tptp.produc696469763tate_o) (B tptp.set_Pr1590995257tate_o)) (let ((_let_1 (= A B2))) (=> (not (@ (@ tptp.member1838112666tate_o A) A2)) (=> (not (@ (@ tptp.member1838112666tate_o B2) B)) (= (= (@ (@ tptp.insert2053719859tate_o A) A2) (@ (@ tptp.insert2053719859tate_o B2) B)) (and (=> _let_1 (= A2 B)) (=> (not _let_1) (exists ((C3 tptp.set_Pr1590995257tate_o)) (and (= A2 (@ (@ tptp.insert2053719859tate_o B2) C3)) (not (@ (@ tptp.member1838112666tate_o B2) C3)) (= B (@ (@ tptp.insert2053719859tate_o A) C3)) (not (@ (@ tptp.member1838112666tate_o A) C3))))))))))) (forall ((A tptp.produc1115495963_state) (A2 tptp.set_Pr795498619_state)) (=> (@ (@ tptp.member1389040324_state A) A2) (= (@ (@ tptp.insert311944171_state A) A2) A2))) (forall ((A tptp.product_prod_nat_nat) (A2 tptp.set_Pr1986765409at_nat)) (=> (@ (@ tptp.member701585322at_nat A) A2) (= (@ (@ 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tptp.member1838112666tate_o X2))) (=> (not (@ _let_2 A2)) (=> (not (@ _let_2 B)) (= (= (@ _let_1 A2) (@ _let_1 B)) (= A2 B))))))) (forall ((X2 tptp.produc1115495963_state) (A2 tptp.set_Pr795498619_state)) (=> (@ (@ tptp.member1389040324_state X2) A2) (not (forall ((B3 tptp.set_Pr795498619_state)) (=> (= A2 (@ (@ tptp.insert311944171_state X2) B3)) (@ (@ tptp.member1389040324_state X2) B3)))))) (forall ((X2 tptp.product_prod_nat_nat) (A2 tptp.set_Pr1986765409at_nat)) (=> (@ (@ tptp.member701585322at_nat X2) A2) (not (forall ((B3 tptp.set_Pr1986765409at_nat)) (=> (= A2 (@ (@ tptp.insert271595217at_nat X2) B3)) (@ (@ tptp.member701585322at_nat X2) B3)))))) (forall ((X2 tptp.produc696469763tate_o) (A2 tptp.set_Pr1590995257tate_o)) (=> (@ (@ tptp.member1838112666tate_o X2) A2) (not (forall ((B3 tptp.set_Pr1590995257tate_o)) (=> (= A2 (@ (@ tptp.insert2053719859tate_o X2) B3)) (@ (@ tptp.member1838112666tate_o X2) B3)))))) (forall ((A tptp.produc1115495963_state) (B tptp.set_Pr795498619_state) (B2 tptp.produc1115495963_state)) (let ((_let_1 (@ tptp.member1389040324_state A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert311944171_state B2) B))))) (forall ((A tptp.product_prod_nat_nat) (B tptp.set_Pr1986765409at_nat) (B2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member701585322at_nat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert271595217at_nat B2) B))))) (forall ((A tptp.produc696469763tate_o) (B tptp.set_Pr1590995257tate_o) (B2 tptp.produc696469763tate_o)) (let ((_let_1 (@ tptp.member1838112666tate_o A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert2053719859tate_o B2) B))))) (forall ((A tptp.produc1115495963_state) (B tptp.set_Pr795498619_state)) (@ (@ tptp.member1389040324_state A) (@ (@ tptp.insert311944171_state A) B))) (forall ((A tptp.product_prod_nat_nat) (B tptp.set_Pr1986765409at_nat)) (@ (@ tptp.member701585322at_nat A) (@ (@ tptp.insert271595217at_nat A) B))) (forall ((A tptp.produc696469763tate_o) (B tptp.set_Pr1590995257tate_o)) (@ (@ tptp.member1838112666tate_o A) (@ (@ tptp.insert2053719859tate_o A) B))) (forall ((A tptp.produc1115495963_state) (B2 tptp.produc1115495963_state) (A2 tptp.set_Pr795498619_state)) (let ((_let_1 (@ tptp.member1389040324_state A))) (=> (@ _let_1 (@ (@ tptp.insert311944171_state B2) A2)) (=> (not (= A B2)) (@ _let_1 A2))))) (forall ((A tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat) (A2 tptp.set_Pr1986765409at_nat)) (let ((_let_1 (@ tptp.member701585322at_nat A))) (=> (@ _let_1 (@ (@ tptp.insert271595217at_nat B2) A2)) (=> (not (= A B2)) (@ _let_1 A2))))) (forall ((A tptp.produc696469763tate_o) (B2 tptp.produc696469763tate_o) (A2 tptp.set_Pr1590995257tate_o)) (let ((_let_1 (@ tptp.member1838112666tate_o A))) (=> (@ _let_1 (@ (@ tptp.insert2053719859tate_o B2) A2)) (=> (not (= A B2)) (@ _let_1 A2))))) _let_38 _let_37 _let_36 (forall ((A tptp.produc1115495963_state) (P (-> tptp.produc1115495963_state Bool))) (= (@ (@ tptp.insert311944171_state A) (@ tptp.collec496201222_state P)) (@ tptp.collec496201222_state (lambda ((U tptp.produc1115495963_state)) (=> (not (= U A)) (@ P U)))))) (forall ((A tptp.product_prod_nat_nat) (P (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.insert271595217at_nat A) (@ tptp.collec7649004at_nat P)) (@ tptp.collec7649004at_nat (lambda ((U tptp.product_prod_nat_nat)) (=> (not (= U A)) (@ P U)))))) (forall ((A tptp.produc696469763tate_o) (P (-> tptp.produc696469763tate_o Bool))) (= (@ (@ tptp.insert2053719859tate_o A) (@ tptp.collec1499596504tate_o P)) (@ tptp.collec1499596504tate_o (lambda ((U tptp.produc696469763tate_o)) (=> (not (= U A)) (@ P U)))))) _let_35 _let_34 _let_33 (forall ((A tptp.produc696469763tate_o) (B2 tptp.produc696469763tate_o)) (=> (= (@ (@ tptp.insert2053719859tate_o A) tptp.bot_bo170732493tate_o) (@ (@ tptp.insert2053719859tate_o B2) tptp.bot_bo170732493tate_o)) (= A B2))) (forall ((A tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat)) (=> (= (@ (@ tptp.insert271595217at_nat A) tptp.bot_bo2130386637at_nat) (@ (@ tptp.insert271595217at_nat B2) tptp.bot_bo2130386637at_nat)) (= A B2))) (forall ((A tptp.produc1115495963_state) (B2 tptp.produc1115495963_state)) (=> (= (@ (@ tptp.insert311944171_state A) tptp.bot_bo1625160935_state) (@ (@ tptp.insert311944171_state B2) tptp.bot_bo1625160935_state)) (= A B2))) (forall ((A tptp.produc696469763tate_o) (A2 tptp.set_Pr1590995257tate_o)) (not (= (@ (@ tptp.insert2053719859tate_o A) A2) tptp.bot_bo170732493tate_o))) (forall ((A tptp.product_prod_nat_nat) (A2 tptp.set_Pr1986765409at_nat)) (not (= (@ (@ tptp.insert271595217at_nat A) A2) tptp.bot_bo2130386637at_nat))) (forall ((A tptp.produc1115495963_state) (A2 tptp.set_Pr795498619_state)) (not (= (@ (@ tptp.insert311944171_state A) A2) tptp.bot_bo1625160935_state))) (forall ((A tptp.produc696469763tate_o) (B2 tptp.produc696469763tate_o) (C2 tptp.produc696469763tate_o) (D tptp.produc696469763tate_o)) (= (= (@ (@ tptp.insert2053719859tate_o A) (@ (@ tptp.insert2053719859tate_o B2) tptp.bot_bo170732493tate_o)) (@ (@ tptp.insert2053719859tate_o C2) (@ (@ tptp.insert2053719859tate_o D) tptp.bot_bo170732493tate_o))) (or (and (= A C2) (= B2 D)) (and (= A D) (= B2 C2))))) (forall ((A tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat) (C2 tptp.product_prod_nat_nat) (D tptp.product_prod_nat_nat)) (= (= (@ (@ tptp.insert271595217at_nat A) (@ (@ tptp.insert271595217at_nat B2) tptp.bot_bo2130386637at_nat)) (@ (@ tptp.insert271595217at_nat C2) (@ (@ tptp.insert271595217at_nat D) tptp.bot_bo2130386637at_nat))) (or (and (= A C2) (= B2 D)) (and (= A D) (= B2 C2))))) (forall ((A tptp.produc1115495963_state) (B2 tptp.produc1115495963_state) (C2 tptp.produc1115495963_state) (D tptp.produc1115495963_state)) (= (= (@ (@ tptp.insert311944171_state A) (@ (@ tptp.insert311944171_state B2) tptp.bot_bo1625160935_state)) (@ (@ tptp.insert311944171_state C2) (@ (@ tptp.insert311944171_state D) tptp.bot_bo1625160935_state))) (or (and (= A C2) (= B2 D)) (and (= A D) (= B2 C2))))) (forall ((B2 tptp.produc696469763tate_o) (A tptp.produc696469763tate_o)) (= (@ (@ tptp.member1838112666tate_o B2) (@ (@ tptp.insert2053719859tate_o A) tptp.bot_bo170732493tate_o)) (= B2 A))) (forall ((B2 tptp.product_prod_nat_nat) (A tptp.product_prod_nat_nat)) (= (@ (@ tptp.member701585322at_nat B2) (@ (@ tptp.insert271595217at_nat A) tptp.bot_bo2130386637at_nat)) (= B2 A))) (forall ((B2 tptp.produc1115495963_state) (A tptp.produc1115495963_state)) (= (@ (@ tptp.member1389040324_state B2) (@ (@ tptp.insert311944171_state A) tptp.bot_bo1625160935_state)) (= B2 A))) (forall ((B2 tptp.produc696469763tate_o) (A tptp.produc696469763tate_o)) (=> (@ (@ tptp.member1838112666tate_o B2) (@ (@ tptp.insert2053719859tate_o A) tptp.bot_bo170732493tate_o)) (= B2 A))) (forall ((B2 tptp.product_prod_nat_nat) (A tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member701585322at_nat B2) (@ (@ tptp.insert271595217at_nat A) tptp.bot_bo2130386637at_nat)) (= B2 A))) (forall ((B2 tptp.produc1115495963_state) (A tptp.produc1115495963_state)) (=> (@ (@ tptp.member1389040324_state B2) (@ (@ tptp.insert311944171_state A) tptp.bot_bo1625160935_state)) (= B2 A))) (forall ((P (-> tptp.a tptp.state Bool)) (Q (-> tptp.a tptp.state Bool))) (@ (@ (@ (@ tptp.hoare_a (@ (@ tptp.insert2053719859tate_o (@ (@ tptp.produc33908149tate_o P) (@ (@ tptp.produc1948644831tate_o tptp.call) Q))) tptp.bot_bo170732493tate_o)) P) tptp.call) Q)) (forall ((P (-> tptp.produc696469763tate_o Bool)) (A tptp.produc696469763tate_o)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collec1499596504tate_o (lambda ((X tptp.produc696469763tate_o)) (and (= A X) (@ P X)))) (@ (@ tptp.insert2053719859tate_o A) tptp.bot_bo170732493tate_o))) (=> (not _let_1) (= (@ tptp.collec1499596504tate_o (lambda ((X tptp.produc696469763tate_o)) (and (= A X) (@ P X)))) tptp.bot_bo170732493tate_o))))) (forall ((P (-> tptp.product_prod_nat_nat Bool)) (A tptp.product_prod_nat_nat)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collec7649004at_nat (lambda ((X tptp.product_prod_nat_nat)) (and (= A X) (@ P X)))) (@ (@ tptp.insert271595217at_nat A) tptp.bot_bo2130386637at_nat))) (=> (not _let_1) (= (@ tptp.collec7649004at_nat (lambda ((X tptp.product_prod_nat_nat)) (and (= A X) (@ P X)))) tptp.bot_bo2130386637at_nat))))) (forall ((P (-> tptp.produc1115495963_state Bool)) (A tptp.produc1115495963_state)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collec496201222_state (lambda ((X tptp.produc1115495963_state)) (and (= A X) (@ P X)))) (@ (@ tptp.insert311944171_state A) tptp.bot_bo1625160935_state))) (=> (not _let_1) (= (@ tptp.collec496201222_state (lambda ((X tptp.produc1115495963_state)) (and (= A X) (@ P X)))) tptp.bot_bo1625160935_state))))) (forall ((P (-> tptp.produc696469763tate_o Bool)) (A tptp.produc696469763tate_o)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collec1499596504tate_o (lambda ((X tptp.produc696469763tate_o)) (and (= X A) (@ P X)))) (@ (@ 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(forall ((A2 tptp.set_Pr1590995257tate_o)) (= (@ tptp.collec1499596504tate_o (lambda ((X tptp.produc696469763tate_o)) (@ (@ tptp.member1838112666tate_o X) A2))) A2)) (forall ((P (-> tptp.produc1115495963_state Bool)) (Q (-> tptp.produc1115495963_state Bool))) (=> (forall ((X3 tptp.produc1115495963_state)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collec496201222_state P) (@ tptp.collec496201222_state Q)))) (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Q (-> tptp.product_prod_nat_nat Bool))) (=> (forall ((X3 tptp.product_prod_nat_nat)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collec7649004at_nat P) (@ tptp.collec7649004at_nat Q)))) (forall ((P (-> tptp.produc696469763tate_o Bool)) (Q (-> tptp.produc696469763tate_o Bool))) (=> (forall ((X3 tptp.produc696469763tate_o)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collec1499596504tate_o P) (@ tptp.collec1499596504tate_o Q)))) (forall ((R2 tptp.set_Pr795498619_state) (Q tptp.set_state)) (=> (@ tptp.wf_state R2) (=> (not (= Q tptp.bot_bot_set_state)) (not (forall ((Z tptp.state)) (=> (@ (@ tptp.member_state Z) Q) (not (forall ((Y4 tptp.state)) (=> (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state Y4) Z)) R2) (not (@ (@ tptp.member_state Y4) Q))))))))))) (forall ((R2 tptp.set_Pr1986765409at_nat) (Q tptp.set_nat)) (=> (@ tptp.wf_nat R2) (=> (not (= Q tptp.bot_bot_set_nat)) (not (forall ((Z tptp.nat)) (=> (@ (@ tptp.member_nat Z) Q) (not (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat Y4) Z)) R2) (not (@ (@ tptp.member_nat Y4) Q))))))))))) (forall ((R2 tptp.set_Pr1702239303tate_o) (Q tptp.set_Pr1590995257tate_o)) (=> (@ tptp.wf_Pro309705690tate_o R2) (=> (not (= Q tptp.bot_bo170732493tate_o)) (not (forall ((Z tptp.produc696469763tate_o)) (=> (@ (@ tptp.member1838112666tate_o Z) Q) (not (forall ((Y4 tptp.produc696469763tate_o)) (=> (@ (@ tptp.member1629320336tate_o (@ (@ tptp.produc1684562079tate_o Y4) Z)) R2) (not (@ (@ tptp.member1838112666tate_o Y4) Q))))))))))) (forall ((R2 tptp.set_Pr1490359111at_nat) (Q tptp.set_Pr1986765409at_nat)) (=> (@ tptp.wf_Pro745352042at_nat R2) (=> (not (= Q tptp.bot_bo2130386637at_nat)) (not (forall ((Z tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member701585322at_nat Z) Q) (not (forall ((Y4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member2027625872at_nat (@ (@ tptp.produc1168807639at_nat Y4) Z)) R2) (not (@ (@ tptp.member701585322at_nat Y4) Q))))))))))) (forall ((R2 tptp.set_Pr778812871_state) (Q tptp.set_Pr795498619_state)) (=> (@ tptp.wf_Pro1783588484_state R2) (=> (not (= Q tptp.bot_bo1625160935_state)) (not (forall ((Z tptp.produc1115495963_state)) (=> (@ (@ tptp.member1389040324_state Z) Q) (not (forall ((Y4 tptp.produc1115495963_state)) (=> (@ (@ tptp.member768948240_state (@ (@ tptp.produc1964772951_state Y4) Z)) R2) (not (@ (@ tptp.member1389040324_state Y4) Q))))))))))) (forall ((X2 tptp.produc696469763tate_o)) (= (@ tptp.the_el1569055182tate_o (@ (@ tptp.insert2053719859tate_o X2) tptp.bot_bo170732493tate_o)) X2)) (forall ((X2 tptp.product_prod_nat_nat)) (= (@ tptp.the_el1949240438at_nat (@ (@ tptp.insert271595217at_nat X2) tptp.bot_bo2130386637at_nat)) X2)) (forall ((X2 tptp.produc1115495963_state)) (= (@ tptp.the_el1967402896_state (@ (@ tptp.insert311944171_state X2) tptp.bot_bo1625160935_state)) X2)) (forall ((A (-> tptp.a tptp.state Bool)) (B2 tptp.produc204914599tate_o) (A4 (-> tptp.a tptp.state Bool)) (B5 tptp.produc204914599tate_o)) (= (= (@ (@ tptp.produc33908149tate_o A) B2) (@ (@ tptp.produc33908149tate_o A4) B5)) (and (= A A4) (= B2 B5)))) (forall ((A tptp.state) (B2 tptp.state) (A4 tptp.state) (B5 tptp.state)) (= (= (@ (@ tptp.produc64584659_state A) B2) (@ (@ tptp.produc64584659_state A4) B5)) (and (= A A4) (= B2 B5)))) (forall ((A tptp.com) (B2 (-> tptp.a tptp.state Bool)) (A4 tptp.com) (B5 (-> tptp.a tptp.state Bool))) (= (= (@ (@ tptp.produc1948644831tate_o A) B2) (@ (@ tptp.produc1948644831tate_o A4) B5)) (and (= A A4) (= B2 B5)))) (forall ((A tptp.nat) (B2 tptp.nat) (A4 tptp.nat) (B5 tptp.nat)) (= (= (@ (@ tptp.product_Pair_nat_nat A) B2) (@ (@ tptp.product_Pair_nat_nat A4) B5)) (and (= A A4) (= B2 B5)))) (forall ((X1 (-> tptp.a tptp.state Bool)) (X22 tptp.produc204914599tate_o) (Y1 (-> tptp.a tptp.state Bool)) (Y22 tptp.produc204914599tate_o)) (= (= (@ (@ tptp.produc33908149tate_o X1) X22) (@ (@ tptp.produc33908149tate_o Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))) (forall ((X1 tptp.state) (X22 tptp.state) (Y1 tptp.state) (Y22 tptp.state)) (= (= (@ (@ tptp.produc64584659_state X1) X22) (@ (@ tptp.produc64584659_state Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))) (forall ((X1 tptp.com) (X22 (-> tptp.a tptp.state Bool)) (Y1 tptp.com) (Y22 (-> tptp.a tptp.state Bool))) (= (= (@ (@ tptp.produc1948644831tate_o X1) X22) (@ (@ tptp.produc1948644831tate_o Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))) (forall ((X1 tptp.nat) (X22 tptp.nat) (Y1 tptp.nat) (Y22 tptp.nat)) (= (= (@ (@ tptp.product_Pair_nat_nat X1) X22) (@ (@ tptp.product_Pair_nat_nat Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))) (forall ((X2 tptp.produc696469763tate_o)) (@ tptp.is_sin1547905295tate_o (@ (@ tptp.insert2053719859tate_o X2) tptp.bot_bo170732493tate_o))) (forall ((X2 tptp.product_prod_nat_nat)) (@ tptp.is_sin1352690165at_nat (@ (@ tptp.insert271595217at_nat X2) tptp.bot_bo2130386637at_nat))) (forall ((X2 tptp.produc1115495963_state)) (@ tptp.is_sin1132515087_state (@ (@ tptp.insert311944171_state X2) tptp.bot_bo1625160935_state))) (= tptp.bot_bo170732493tate_o (@ tptp.collec1499596504tate_o tptp.bot_bo250281208te_o_o)) (= tptp.bot_bo2130386637at_nat (@ tptp.collec7649004at_nat tptp.bot_bo513358416_nat_o)) (= tptp.bot_bo1625160935_state (@ tptp.collec496201222_state tptp.bot_bo446391478tate_o)) _let_32 _let_31 _let_30 (forall ((A2 tptp.set_Pr1590995257tate_o)) (=> (not (= A2 tptp.bot_bo170732493tate_o)) (=> (forall ((X3 tptp.produc696469763tate_o) (Y2 tptp.produc696469763tate_o)) (=> (@ (@ tptp.member1838112666tate_o X3) A2) (=> (@ (@ tptp.member1838112666tate_o Y2) A2) (= X3 Y2)))) (@ tptp.is_sin1547905295tate_o A2)))) (forall ((A2 tptp.set_Pr1986765409at_nat)) (=> (not (= A2 tptp.bot_bo2130386637at_nat)) (=> (forall ((X3 tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member701585322at_nat X3) A2) (=> (@ (@ tptp.member701585322at_nat Y2) A2) (= X3 Y2)))) (@ tptp.is_sin1352690165at_nat A2)))) (forall ((A2 tptp.set_Pr795498619_state)) (=> (not (= A2 tptp.bot_bo1625160935_state)) (=> (forall ((X3 tptp.produc1115495963_state) (Y2 tptp.produc1115495963_state)) (=> (@ (@ tptp.member1389040324_state X3) A2) (=> (@ (@ tptp.member1389040324_state Y2) A2) (= X3 Y2)))) (@ tptp.is_sin1132515087_state A2)))) (forall ((P3 tptp.produc696469763tate_o)) (exists ((X3 (-> tptp.a tptp.state Bool)) (Y2 tptp.produc204914599tate_o)) (= P3 (@ (@ tptp.produc33908149tate_o X3) Y2)))) (forall ((P3 tptp.produc1115495963_state)) (exists ((X3 tptp.state) (Y2 tptp.state)) (= P3 (@ (@ tptp.produc64584659_state X3) Y2)))) (forall ((P3 tptp.produc204914599tate_o)) (exists ((X3 tptp.com) (Y2 (-> tptp.a tptp.state Bool))) (= P3 (@ (@ tptp.produc1948644831tate_o X3) Y2)))) (forall ((P3 tptp.product_prod_nat_nat)) (exists ((X3 tptp.nat) (Y2 tptp.nat)) (= P3 (@ (@ tptp.product_Pair_nat_nat X3) Y2)))) (forall ((P (-> tptp.produc696469763tate_o Bool)) (P3 tptp.produc696469763tate_o)) (=> (forall ((A6 (-> tptp.a tptp.state Bool)) (B6 tptp.produc204914599tate_o)) (@ P (@ (@ tptp.produc33908149tate_o A6) B6))) (@ P P3))) (forall ((P (-> tptp.produc1115495963_state Bool)) (P3 tptp.produc1115495963_state)) (=> (forall ((A6 tptp.state) (B6 tptp.state)) (@ P (@ (@ tptp.produc64584659_state A6) B6))) (@ P P3))) (forall ((P (-> tptp.produc204914599tate_o Bool)) (P3 tptp.produc204914599tate_o)) (=> (forall ((A6 tptp.com) (B6 (-> tptp.a tptp.state Bool))) (@ P (@ (@ tptp.produc1948644831tate_o A6) B6))) (@ P P3))) (forall ((P (-> tptp.product_prod_nat_nat Bool)) (P3 tptp.product_prod_nat_nat)) (=> (forall ((A6 tptp.nat) (B6 tptp.nat)) (@ P (@ (@ tptp.product_Pair_nat_nat A6) B6))) (@ P P3))) (forall ((A (-> tptp.a tptp.state Bool)) (B2 tptp.produc204914599tate_o) (A4 (-> tptp.a tptp.state Bool)) (B5 tptp.produc204914599tate_o)) (=> (= (@ (@ tptp.produc33908149tate_o A) B2) (@ (@ tptp.produc33908149tate_o A4) B5)) (not (=> (= A A4) (not (= B2 B5)))))) (forall ((A tptp.state) (B2 tptp.state) (A4 tptp.state) (B5 tptp.state)) (=> (= (@ (@ tptp.produc64584659_state A) B2) (@ (@ tptp.produc64584659_state A4) B5)) (not (=> (= A A4) (not (= B2 B5)))))) (forall ((A tptp.com) (B2 (-> tptp.a tptp.state Bool)) (A4 tptp.com) (B5 (-> tptp.a tptp.state Bool))) (=> (= (@ (@ tptp.produc1948644831tate_o A) B2) (@ (@ tptp.produc1948644831tate_o A4) B5)) (not (=> (= A A4) (not (= B2 B5)))))) (forall ((A tptp.nat) (B2 tptp.nat) (A4 tptp.nat) (B5 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat A) B2) (@ (@ tptp.product_Pair_nat_nat A4) B5)) (not (=> (= A A4) (not (= B2 B5)))))) (forall ((Y3 tptp.produc696469763tate_o)) (not (forall ((A6 (-> tptp.a tptp.state Bool)) (B6 tptp.produc204914599tate_o)) (not (= Y3 (@ (@ tptp.produc33908149tate_o A6) B6)))))) (forall ((Y3 tptp.produc1115495963_state)) (not (forall ((A6 tptp.state) (B6 tptp.state)) (not (= Y3 (@ (@ tptp.produc64584659_state A6) B6)))))) (forall ((Y3 tptp.produc204914599tate_o)) (not (forall ((A6 tptp.com) (B6 (-> tptp.a tptp.state Bool))) (not (= Y3 (@ (@ tptp.produc1948644831tate_o A6) B6)))))) (forall ((Y3 tptp.product_prod_nat_nat)) (not (forall ((A6 tptp.nat) (B6 tptp.nat)) (not (= Y3 (@ (@ tptp.product_Pair_nat_nat A6) B6)))))) (forall ((P (-> tptp.produc696469763tate_o Bool)) (Prod tptp.produc696469763tate_o)) (=> (forall ((A6 (-> tptp.a tptp.state Bool)) (B6 tptp.produc204914599tate_o)) (@ P (@ (@ tptp.produc33908149tate_o A6) B6))) (@ P Prod))) (forall ((P (-> tptp.produc1115495963_state Bool)) (Prod tptp.produc1115495963_state)) (=> (forall ((A6 tptp.state) (B6 tptp.state)) (@ P (@ (@ tptp.produc64584659_state A6) B6))) (@ P Prod))) (forall ((P (-> tptp.produc204914599tate_o Bool)) (Prod tptp.produc204914599tate_o)) (=> (forall ((A6 tptp.com) (B6 (-> tptp.a tptp.state Bool))) (@ P (@ (@ tptp.produc1948644831tate_o A6) B6))) (@ P Prod))) (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Prod tptp.product_prod_nat_nat)) (=> (forall ((A6 tptp.nat) (B6 tptp.nat)) (@ P (@ (@ tptp.product_Pair_nat_nat A6) B6))) (@ P Prod))) (forall ((A2 tptp.set_Pr1590995257tate_o)) (=> (@ tptp.is_sin1547905295tate_o A2) (not (forall ((X3 tptp.produc696469763tate_o)) (not (= A2 (@ (@ tptp.insert2053719859tate_o X3) tptp.bot_bo170732493tate_o))))))) (forall ((A2 tptp.set_Pr1986765409at_nat)) (=> (@ tptp.is_sin1352690165at_nat A2) (not (forall ((X3 tptp.product_prod_nat_nat)) (not (= A2 (@ (@ tptp.insert271595217at_nat X3) tptp.bot_bo2130386637at_nat))))))) (forall ((A2 tptp.set_Pr795498619_state)) (=> (@ tptp.is_sin1132515087_state A2) (not (forall ((X3 tptp.produc1115495963_state)) (not (= A2 (@ (@ tptp.insert311944171_state X3) tptp.bot_bo1625160935_state))))))) (= tptp.is_sin1547905295tate_o (lambda ((A5 tptp.set_Pr1590995257tate_o)) (exists ((X tptp.produc696469763tate_o)) (= A5 (@ (@ tptp.insert2053719859tate_o X) tptp.bot_bo170732493tate_o))))) (= tptp.is_sin1352690165at_nat (lambda ((A5 tptp.set_Pr1986765409at_nat)) (exists ((X tptp.product_prod_nat_nat)) (= A5 (@ (@ tptp.insert271595217at_nat X) tptp.bot_bo2130386637at_nat))))) (= tptp.is_sin1132515087_state (lambda ((A5 tptp.set_Pr795498619_state)) (exists ((X tptp.produc1115495963_state)) (= A5 (@ (@ tptp.insert311944171_state X) tptp.bot_bo1625160935_state))))) _let_29 _let_28 (forall ((R2 tptp.set_Pr778812871_state) (X2 tptp.produc1115495963_state) (Q tptp.set_Pr795498619_state)) (=> (@ tptp.wf_Pro1783588484_state R2) (=> (@ (@ tptp.member1389040324_state X2) Q) (not (forall ((Z tptp.produc1115495963_state)) (=> (@ (@ tptp.member1389040324_state Z) Q) (not (forall ((Y4 tptp.produc1115495963_state)) (=> (@ (@ tptp.member768948240_state (@ (@ tptp.produc1964772951_state Y4) Z)) R2) (not (@ (@ tptp.member1389040324_state Y4) Q))))))))))) (forall ((R2 tptp.set_Pr1490359111at_nat) (X2 tptp.product_prod_nat_nat) (Q tptp.set_Pr1986765409at_nat)) (=> (@ tptp.wf_Pro745352042at_nat R2) (=> (@ (@ tptp.member701585322at_nat X2) Q) (not (forall ((Z tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member701585322at_nat Z) Q) (not (forall ((Y4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member2027625872at_nat (@ (@ tptp.produc1168807639at_nat Y4) Z)) R2) (not (@ (@ tptp.member701585322at_nat Y4) Q))))))))))) (forall ((R2 tptp.set_Pr1702239303tate_o) (X2 tptp.produc696469763tate_o) (Q tptp.set_Pr1590995257tate_o)) (=> (@ tptp.wf_Pro309705690tate_o R2) (=> (@ (@ tptp.member1838112666tate_o X2) Q) (not (forall ((Z tptp.produc696469763tate_o)) (=> (@ (@ tptp.member1838112666tate_o Z) Q) (not (forall ((Y4 tptp.produc696469763tate_o)) (=> (@ (@ tptp.member1629320336tate_o (@ (@ tptp.produc1684562079tate_o Y4) Z)) R2) (not (@ (@ tptp.member1838112666tate_o Y4) Q))))))))))) (forall ((R2 tptp.set_Pr795498619_state) (X2 tptp.state) (Q tptp.set_state)) (=> (@ tptp.wf_state R2) (=> (@ (@ tptp.member_state X2) Q) (not (forall ((Z tptp.state)) (=> (@ (@ tptp.member_state Z) Q) (not (forall ((Y4 tptp.state)) (=> (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state Y4) Z)) R2) (not (@ (@ tptp.member_state Y4) Q))))))))))) (forall ((R2 tptp.set_Pr1986765409at_nat) (X2 tptp.nat) (Q tptp.set_nat)) (=> (@ tptp.wf_nat R2) (=> (@ (@ tptp.member_nat X2) Q) (not (forall ((Z tptp.nat)) (=> (@ (@ tptp.member_nat Z) Q) (not (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat Y4) Z)) R2) (not (@ (@ tptp.member_nat Y4) Q))))))))))) (forall ((R2 tptp.set_Pr778812871_state)) (=> (forall ((X3 tptp.produc1115495963_state) (Q3 tptp.set_Pr795498619_state)) (=> (@ (@ tptp.member1389040324_state X3) Q3) (exists ((Xa tptp.produc1115495963_state)) (and (@ (@ tptp.member1389040324_state Xa) Q3) (forall ((Y2 tptp.produc1115495963_state)) (=> (@ (@ tptp.member768948240_state (@ (@ tptp.produc1964772951_state Y2) Xa)) R2) (not (@ (@ tptp.member1389040324_state Y2) Q3)))))))) (@ tptp.wf_Pro1783588484_state R2))) (forall ((R2 tptp.set_Pr1490359111at_nat)) (=> (forall ((X3 tptp.product_prod_nat_nat) (Q3 tptp.set_Pr1986765409at_nat)) (=> (@ (@ tptp.member701585322at_nat X3) Q3) (exists ((Xa tptp.product_prod_nat_nat)) (and (@ (@ tptp.member701585322at_nat Xa) Q3) (forall ((Y2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member2027625872at_nat (@ (@ tptp.produc1168807639at_nat Y2) Xa)) R2) (not (@ (@ tptp.member701585322at_nat Y2) Q3)))))))) (@ tptp.wf_Pro745352042at_nat R2))) (forall ((R2 tptp.set_Pr1702239303tate_o)) (=> (forall ((X3 tptp.produc696469763tate_o) (Q3 tptp.set_Pr1590995257tate_o)) (=> (@ (@ tptp.member1838112666tate_o X3) Q3) (exists ((Xa tptp.produc696469763tate_o)) (and (@ (@ tptp.member1838112666tate_o Xa) Q3) (forall ((Y2 tptp.produc696469763tate_o)) (=> (@ (@ tptp.member1629320336tate_o (@ (@ tptp.produc1684562079tate_o Y2) Xa)) R2) (not (@ (@ tptp.member1838112666tate_o Y2) Q3)))))))) (@ tptp.wf_Pro309705690tate_o R2))) (forall ((R2 tptp.set_Pr795498619_state)) (=> (forall ((X3 tptp.state) (Q3 tptp.set_state)) (=> (@ (@ tptp.member_state X3) Q3) (exists ((Xa tptp.state)) (and (@ (@ tptp.member_state Xa) Q3) (forall ((Y2 tptp.state)) (=> (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state Y2) Xa)) R2) (not (@ (@ tptp.member_state Y2) Q3)))))))) (@ tptp.wf_state R2))) (forall ((R2 tptp.set_Pr1986765409at_nat)) (=> (forall ((X3 tptp.nat) (Q3 tptp.set_nat)) (=> (@ (@ tptp.member_nat X3) Q3) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) Q3) (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat Y2) Xa)) R2) (not (@ (@ tptp.member_nat Y2) Q3)))))))) (@ tptp.wf_nat R2))) (forall ((R tptp.set_Pr795498619_state)) (=> (forall ((P5 (-> tptp.state Bool)) (X3 tptp.state)) (=> (forall ((Xa tptp.state)) (=> (forall ((Y2 tptp.state)) (=> (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state Y2) Xa)) R) (@ P5 Y2))) (@ P5 Xa))) (@ P5 X3))) (@ tptp.wf_state R))) (forall ((R tptp.set_Pr1986765409at_nat)) (=> (forall ((P5 (-> tptp.nat Bool)) (X3 tptp.nat)) (=> (forall ((Xa tptp.nat)) (=> (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat Y2) Xa)) R) (@ P5 Y2))) (@ P5 Xa))) (@ P5 X3))) (@ tptp.wf_nat R))) (forall ((R tptp.set_Pr795498619_state) (A tptp.state) (X2 tptp.state)) (=> (@ tptp.wf_state R) (=> (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state A) X2)) R) (not (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state X2) A)) R))))) (forall ((R tptp.set_Pr1986765409at_nat) (A tptp.nat) (X2 tptp.nat)) (=> (@ tptp.wf_nat R) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A) X2)) R) (not (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X2) A)) R))))) (forall ((R tptp.set_Pr795498619_state) (P (-> tptp.state Bool)) (A tptp.state)) (=> (@ tptp.wf_state R) (=> (forall ((X3 tptp.state)) (=> (forall ((Y4 tptp.state)) (=> (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state Y4) X3)) R) (@ P Y4))) (@ P X3))) (@ P A)))) (forall ((R tptp.set_Pr1986765409at_nat) (P (-> tptp.nat Bool)) (A tptp.nat)) (=> (@ tptp.wf_nat R) (=> (forall ((X3 tptp.nat)) (=> (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat Y4) X3)) R) (@ P Y4))) (@ P X3))) (@ P A)))) (forall ((R tptp.set_Pr795498619_state) (A tptp.state)) (=> (@ tptp.wf_state R) (not (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state A) A)) R)))) (forall ((R tptp.set_Pr1986765409at_nat) (A tptp.nat)) (=> (@ tptp.wf_nat R) (not (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A) A)) R)))) (forall ((R tptp.set_Pr795498619_state) (A tptp.state) (X2 tptp.state)) (=> (@ tptp.wf_state R) (=> (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state A) X2)) R) (not (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state X2) A)) R))))) (forall ((R tptp.set_Pr1986765409at_nat) (A tptp.nat) (X2 tptp.nat)) (=> (@ tptp.wf_nat R) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A) X2)) R) (not (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X2) A)) R))))) (forall ((R tptp.set_Pr795498619_state) (A tptp.state)) (=> (@ tptp.wf_state R) (not (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state A) A)) R)))) (forall ((R tptp.set_Pr1986765409at_nat) (A tptp.nat)) (=> (@ tptp.wf_nat R) (not (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A) A)) R)))) _let_27 _let_26 _let_25 (= tptp.wf_state (lambda ((R3 tptp.set_Pr795498619_state)) (forall ((Q4 tptp.set_state)) (=> (exists ((X tptp.state)) (@ (@ tptp.member_state X) Q4)) (exists ((X tptp.state)) (and (@ (@ tptp.member_state X) Q4) (forall ((Y5 tptp.state)) (=> (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state Y5) X)) R3) (not (@ (@ tptp.member_state Y5) Q4)))))))))) (= tptp.wf_nat (lambda ((R3 tptp.set_Pr1986765409at_nat)) (forall ((Q4 tptp.set_nat)) (=> (exists ((X tptp.nat)) (@ (@ tptp.member_nat X) Q4)) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) Q4) (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat Y5) X)) R3) (not (@ (@ tptp.member_nat Y5) Q4)))))))))) (forall ((R tptp.set_Pr795498619_state) (P (-> tptp.state Bool)) (A tptp.state)) (=> (@ tptp.wf_state R) (=> (forall ((X3 tptp.state)) (=> (forall ((Y4 tptp.state)) (=> (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state Y4) X3)) R) (@ P Y4))) (@ P X3))) (@ P A)))) (forall ((R tptp.set_Pr1986765409at_nat) (P (-> tptp.nat Bool)) (A tptp.nat)) (=> (@ tptp.wf_nat R) (=> (forall ((X3 tptp.nat)) (=> (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat Y4) X3)) R) (@ P Y4))) (@ P X3))) (@ P A)))) (forall ((Y3 tptp.produc696469763tate_o)) (not (forall ((A6 (-> tptp.a tptp.state Bool)) (B6 tptp.com) (C4 (-> tptp.a tptp.state Bool))) (not (= Y3 (@ (@ tptp.produc33908149tate_o A6) (@ (@ tptp.produc1948644831tate_o B6) C4))))))) (forall ((P (-> tptp.produc696469763tate_o Bool)) (X2 tptp.produc696469763tate_o)) (=> (forall ((A6 (-> tptp.a tptp.state Bool)) (B6 tptp.com) (C4 (-> tptp.a tptp.state Bool))) (@ P (@ (@ tptp.produc33908149tate_o A6) (@ (@ tptp.produc1948644831tate_o B6) C4)))) (@ P X2))) _let_24 _let_23 _let_22 _let_21 (forall ((F (-> tptp.state tptp.nat))) (@ tptp.wf_state (@ tptp.measure_state F))) (forall ((F (-> tptp.nat tptp.nat))) (@ tptp.wf_nat (@ tptp.measure_nat F))) (forall ((R tptp.set_Pr795498619_state) (C tptp.set_Pr1590995257tate_o) (P (-> tptp.a tptp.state Bool)) (B2 (-> tptp.state Bool)) (C2 tptp.com)) (=> (@ tptp.wf_state R) (=> (forall ((S3 tptp.state)) (@ (@ (@ (@ tptp.pHoare382919414oare_a C) (lambda ((Z4 tptp.a) (S4 tptp.state)) (and (@ (@ P Z4) S4) (@ B2 S4) (= S3 S4)))) C2) (lambda ((Z4 tptp.a) (S4 tptp.state)) (and (@ (@ P Z4) S4) (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state S4) S3)) R))))) (@ (@ (@ (@ tptp.pHoare382919414oare_a C) P) (@ (@ tptp.while B2) C2)) (lambda ((Z4 tptp.a) (S4 tptp.state)) (and (@ (@ P Z4) S4) (not (@ B2 S4)))))))) _let_20 _let_19 _let_18 (forall ((X41 (-> tptp.state Bool)) (X42 tptp.com) (Y41 (-> tptp.state Bool)) (Y42 tptp.com)) (= (= (@ (@ tptp.while X41) X42) (@ (@ tptp.while Y41) Y42)) (and (= X41 Y41) (= X42 Y42)))) (forall ((X41 (-> tptp.state Bool)) (X42 tptp.com)) (not (= (@ (@ tptp.while X41) X42) tptp.call))) (forall ((B2 (-> tptp.state Bool)) (S2 tptp.state) (C2 tptp.com)) (=> (not (@ B2 S2)) (@ (@ (@ tptp.exec S2) (@ (@ tptp.while B2) C2)) S2))) (forall ((B2 (-> tptp.state Bool)) (S2 tptp.state) (C2 tptp.com) (T2 tptp.state) (U2 tptp.state)) (let ((_let_1 (@ (@ tptp.while B2) C2))) (let ((_let_2 (@ tptp.exec S2))) (=> (@ B2 S2) (=> (@ (@ _let_2 C2) T2) (=> (@ (@ (@ tptp.exec T2) _let_1) U2) (@ (@ _let_2 _let_1) U2))))))) (forall ((B2 (-> tptp.state Bool)) (S2 tptp.state) (C2 tptp.com)) (=> (not (@ B2 S2)) (@ (@ tptp.termi (@ (@ tptp.while B2) C2)) S2))) (forall ((B2 (-> tptp.state Bool)) (S2 tptp.state) (C2 tptp.com)) (=> (@ B2 S2) (=> (@ (@ tptp.termi C2) S2) (=> (forall ((T tptp.state)) (=> (@ (@ (@ tptp.exec S2) C2) T) (@ (@ tptp.termi (@ (@ tptp.while B2) C2)) T))) (@ (@ tptp.termi (@ (@ tptp.while B2) C2)) S2))))) _let_17 _let_16 _let_15 (forall ((R2 tptp.set_Pr1590995257tate_o) (S5 tptp.set_Pr1590995257tate_o)) (= (= (lambda ((X (-> tptp.a tptp.state Bool)) (Y5 tptp.produc204914599tate_o)) (@ (@ tptp.member1838112666tate_o (@ (@ tptp.produc33908149tate_o X) Y5)) R2)) (lambda ((X (-> tptp.a tptp.state Bool)) (Y5 tptp.produc204914599tate_o)) (@ (@ tptp.member1838112666tate_o (@ (@ tptp.produc33908149tate_o X) Y5)) S5))) (= R2 S5))) (forall ((R2 tptp.set_Pr795498619_state) (S5 tptp.set_Pr795498619_state)) (= (= (lambda ((X tptp.state) (Y5 tptp.state)) (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state X) Y5)) R2)) (lambda ((X tptp.state) (Y5 tptp.state)) (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state X) Y5)) S5))) (= R2 S5))) (forall ((R2 tptp.set_Pr1740974983tate_o) (S5 tptp.set_Pr1740974983tate_o)) (= (= (lambda ((X tptp.com) (Y5 (-> tptp.a tptp.state Bool))) (@ (@ tptp.member221067728tate_o (@ (@ tptp.produc1948644831tate_o X) Y5)) R2)) (lambda ((X tptp.com) (Y5 (-> tptp.a tptp.state Bool))) (@ (@ tptp.member221067728tate_o (@ (@ tptp.produc1948644831tate_o X) Y5)) S5))) (= R2 S5))) (forall ((R2 tptp.set_Pr1986765409at_nat) (S5 tptp.set_Pr1986765409at_nat)) (= (= (lambda ((X tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X) Y5)) R2)) (lambda ((X tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X) Y5)) S5))) (= R2 S5))) (forall ((P (-> tptp.produc696469763tate_o Bool))) (= (= (@ tptp.collec1499596504tate_o P) tptp.bot_bo170732493tate_o) (= P tptp.bot_bo250281208te_o_o))) (forall ((P (-> tptp.product_prod_nat_nat Bool))) (= (= (@ tptp.collec7649004at_nat P) tptp.bot_bo2130386637at_nat) (= P tptp.bot_bo513358416_nat_o))) (forall ((P (-> tptp.produc1115495963_state Bool))) (= (= (@ tptp.collec496201222_state P) tptp.bot_bo1625160935_state) (= P tptp.bot_bo446391478tate_o))) (forall ((X2 tptp.nat)) (@ (@ tptp.total_on_nat (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat)) (@ (@ tptp.insert271595217at_nat (@ (@ tptp.product_Pair_nat_nat X2) X2)) tptp.bot_bo2130386637at_nat))) (forall ((X2 tptp.state)) (@ (@ tptp.total_on_state (@ (@ tptp.insert_state X2) tptp.bot_bot_set_state)) (@ (@ tptp.insert311944171_state (@ (@ tptp.produc64584659_state X2) X2)) tptp.bot_bo1625160935_state))) (forall ((X2 tptp.produc696469763tate_o)) (@ (@ tptp.total_795385983tate_o (@ (@ tptp.insert2053719859tate_o X2) tptp.bot_bo170732493tate_o)) (@ (@ tptp.insert1597128631tate_o (@ (@ tptp.produc1684562079tate_o X2) X2)) tptp.bot_bo1714653363tate_o))) (forall ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.total_1775715973at_nat (@ (@ tptp.insert271595217at_nat X2) tptp.bot_bo2130386637at_nat)) (@ (@ tptp.insert584009271at_nat (@ (@ tptp.produc1168807639at_nat X2) X2)) tptp.bot_bo34127283at_nat))) (forall ((X2 tptp.produc1115495963_state)) (@ (@ tptp.total_1316653983_state (@ (@ tptp.insert311944171_state X2) tptp.bot_bo1625160935_state)) (@ (@ tptp.insert1616594103_state (@ (@ tptp.produc1964772951_state X2) X2)) tptp.bot_bo1331673139_state))) (forall ((X2 tptp.nat)) (@ (@ tptp.refl_on_nat (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat)) (@ (@ tptp.insert271595217at_nat (@ (@ tptp.product_Pair_nat_nat X2) X2)) tptp.bot_bo2130386637at_nat))) (forall ((X2 tptp.state)) (@ (@ tptp.refl_on_state (@ (@ tptp.insert_state X2) tptp.bot_bot_set_state)) (@ (@ tptp.insert311944171_state (@ (@ tptp.produc64584659_state X2) X2)) tptp.bot_bo1625160935_state))) (forall ((X2 tptp.produc696469763tate_o)) (@ (@ tptp.refl_o489021252tate_o (@ (@ tptp.insert2053719859tate_o X2) tptp.bot_bo170732493tate_o)) (@ (@ tptp.insert1597128631tate_o (@ (@ tptp.produc1684562079tate_o X2) X2)) tptp.bot_bo1714653363tate_o))) (forall ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.refl_o1619599232at_nat (@ (@ tptp.insert271595217at_nat X2) tptp.bot_bo2130386637at_nat)) (@ (@ tptp.insert584009271at_nat (@ (@ tptp.produc1168807639at_nat X2) X2)) tptp.bot_bo34127283at_nat))) (forall ((X2 tptp.produc1115495963_state)) (@ (@ tptp.refl_o1438232218_state (@ (@ tptp.insert311944171_state X2) tptp.bot_bo1625160935_state)) (@ (@ tptp.insert1616594103_state (@ (@ tptp.produc1964772951_state X2) X2)) tptp.bot_bo1331673139_state))) (forall ((B2 (-> tptp.state Bool)) (C2 tptp.com)) (@ tptp.wf_state (@ tptp.collec496201222_state (@ tptp.produc789892016tate_o (lambda ((T3 tptp.state) (S4 tptp.state)) (and (@ (@ tptp.termi (@ (@ tptp.while B2) C2)) S4) (@ B2 S4) (@ (@ (@ tptp.exec S4) C2) T3))))))) (forall ((X2 tptp.nat)) (@ (@ tptp.order_130026331on_nat (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat)) (@ (@ tptp.insert271595217at_nat (@ (@ tptp.product_Pair_nat_nat X2) X2)) tptp.bot_bo2130386637at_nat))) (forall ((X2 tptp.state)) (@ (@ tptp.order_286167592_state (@ (@ tptp.insert_state X2) tptp.bot_bot_set_state)) (@ (@ tptp.insert311944171_state (@ (@ tptp.produc64584659_state X2) X2)) tptp.bot_bo1625160935_state))) (forall ((X2 tptp.produc696469763tate_o)) (@ (@ tptp.order_50454158tate_o (@ (@ tptp.insert2053719859tate_o X2) tptp.bot_bo170732493tate_o)) (@ (@ tptp.insert1597128631tate_o (@ (@ tptp.produc1684562079tate_o X2) X2)) tptp.bot_bo1714653363tate_o))) (forall ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.order_721919926at_nat (@ (@ tptp.insert271595217at_nat X2) tptp.bot_bo2130386637at_nat)) (@ (@ tptp.insert584009271at_nat (@ (@ tptp.produc1168807639at_nat X2) X2)) tptp.bot_bo34127283at_nat))) (forall ((X2 tptp.produc1115495963_state)) (@ (@ tptp.order_178668240_state (@ (@ tptp.insert311944171_state X2) tptp.bot_bo1625160935_state)) (@ (@ tptp.insert1616594103_state (@ (@ tptp.produc1964772951_state X2) X2)) tptp.bot_bo1331673139_state))) (forall ((P Bool) (Q (-> tptp.state tptp.state Bool))) (= (@ tptp.produc789892016tate_o (lambda ((A3 tptp.state) (B7 tptp.state)) (and P (@ (@ Q A3) B7)))) (lambda ((Ab tptp.produc1115495963_state)) (and P (@ (@ tptp.produc789892016tate_o Q) Ab))))) (forall ((P Bool) (Q (-> tptp.nat tptp.nat Bool))) (= (@ tptp.produc949581770_nat_o (lambda ((A3 tptp.nat) (B7 tptp.nat)) (and P (@ (@ Q A3) B7)))) (lambda ((Ab tptp.product_prod_nat_nat)) (and P (@ (@ tptp.produc949581770_nat_o Q) Ab))))) (forall ((F (-> tptp.state tptp.state Bool)) (A tptp.state) (B2 tptp.state)) (= (@ (@ tptp.produc789892016tate_o F) (@ (@ tptp.produc64584659_state A) B2)) (@ (@ F A) B2))) (forall ((F (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.produc949581770_nat_o F) (@ (@ tptp.product_Pair_nat_nat A) B2)) (@ (@ F A) B2))) (forall ((F (-> (-> tptp.a tptp.state Bool) tptp.produc204914599tate_o Bool)) (A (-> tptp.a tptp.state Bool)) (B2 tptp.produc204914599tate_o)) (=> (@ (@ F A) B2) (@ (@ tptp.produc1271576886te_o_o F) (@ (@ tptp.produc33908149tate_o A) B2)))) (forall ((F (-> tptp.com (-> tptp.a tptp.state Bool) Bool)) (A tptp.com) (B2 (-> tptp.a tptp.state Bool))) (=> (@ (@ F A) B2) (@ (@ tptp.produc281270436te_o_o F) (@ (@ tptp.produc1948644831tate_o A) B2)))) (forall ((F (-> tptp.state tptp.state Bool)) (A tptp.state) (B2 tptp.state)) (=> (@ (@ F A) B2) (@ (@ tptp.produc789892016tate_o F) (@ (@ tptp.produc64584659_state A) B2)))) (forall ((F (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B2 tptp.nat)) (=> (@ (@ F A) B2) (@ (@ tptp.produc949581770_nat_o F) (@ (@ tptp.product_Pair_nat_nat A) B2)))) (forall ((P3 tptp.produc696469763tate_o) (C2 (-> (-> tptp.a tptp.state Bool) tptp.produc204914599tate_o Bool))) (=> (forall ((A6 (-> tptp.a tptp.state Bool)) (B6 tptp.produc204914599tate_o)) (=> (= P3 (@ (@ tptp.produc33908149tate_o A6) B6)) (@ (@ C2 A6) B6))) (@ (@ tptp.produc1271576886te_o_o C2) P3))) (forall ((P3 tptp.produc204914599tate_o) (C2 (-> tptp.com (-> tptp.a tptp.state Bool) Bool))) (=> (forall ((A6 tptp.com) (B6 (-> tptp.a tptp.state Bool))) (=> (= P3 (@ (@ tptp.produc1948644831tate_o A6) B6)) (@ (@ C2 A6) B6))) (@ (@ tptp.produc281270436te_o_o C2) P3))) (forall ((P3 tptp.produc1115495963_state) (C2 (-> tptp.state tptp.state Bool))) (=> (forall ((A6 tptp.state) (B6 tptp.state)) (=> (= P3 (@ (@ tptp.produc64584659_state A6) B6)) (@ (@ C2 A6) B6))) (@ (@ tptp.produc789892016tate_o C2) P3))) (forall ((P3 tptp.product_prod_nat_nat) (C2 (-> tptp.nat tptp.nat Bool))) (=> (forall ((A6 tptp.nat) (B6 tptp.nat)) (=> (= P3 (@ (@ tptp.product_Pair_nat_nat A6) B6)) (@ (@ C2 A6) B6))) (@ (@ tptp.produc949581770_nat_o C2) P3))) (forall ((A2 tptp.set_Pr795498619_state) (R tptp.set_Pr778812871_state) (A tptp.produc1115495963_state) (B2 tptp.produc1115495963_state)) (=> (@ (@ tptp.refl_o1438232218_state A2) R) (=> (@ (@ tptp.member768948240_state (@ (@ tptp.produc1964772951_state A) B2)) R) (and (@ (@ tptp.member1389040324_state A) A2) (@ (@ tptp.member1389040324_state B2) A2))))) (forall ((A2 tptp.set_Pr1986765409at_nat) (R tptp.set_Pr1490359111at_nat) (A tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.refl_o1619599232at_nat A2) R) (=> (@ (@ tptp.member2027625872at_nat (@ (@ tptp.produc1168807639at_nat A) B2)) R) (and (@ (@ tptp.member701585322at_nat A) A2) (@ (@ tptp.member701585322at_nat B2) A2))))) (forall ((A2 tptp.set_Pr1590995257tate_o) (R tptp.set_Pr1702239303tate_o) (A tptp.produc696469763tate_o) (B2 tptp.produc696469763tate_o)) (=> (@ (@ tptp.refl_o489021252tate_o A2) R) (=> (@ (@ tptp.member1629320336tate_o (@ (@ tptp.produc1684562079tate_o A) B2)) R) (and (@ (@ tptp.member1838112666tate_o A) A2) (@ (@ tptp.member1838112666tate_o B2) A2))))) (forall ((A2 tptp.set_state) (R tptp.set_Pr795498619_state) (A tptp.state) (B2 tptp.state)) (=> (@ (@ tptp.refl_on_state A2) R) (=> (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state A) B2)) R) (and (@ (@ tptp.member_state A) A2) (@ (@ tptp.member_state B2) A2))))) (forall ((A2 tptp.set_nat) (R tptp.set_Pr1986765409at_nat) (A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.refl_on_nat A2) R) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A) B2)) R) (and (@ (@ tptp.member_nat A) A2) (@ (@ tptp.member_nat B2) A2))))) (forall ((H (-> Bool Bool)) (F (-> tptp.state tptp.state Bool)) (Prod tptp.produc1115495963_state)) (= (@ H (@ (@ tptp.produc789892016tate_o F) Prod)) (@ (@ tptp.produc789892016tate_o (lambda ((X12 tptp.state) (X23 tptp.state)) (@ H (@ (@ F X12) X23)))) Prod))) (forall ((H (-> Bool Bool)) (F (-> tptp.nat tptp.nat Bool)) (Prod tptp.product_prod_nat_nat)) (= (@ H (@ (@ tptp.produc949581770_nat_o F) Prod)) (@ (@ tptp.produc949581770_nat_o (lambda ((X12 tptp.nat) (X23 tptp.nat)) (@ H (@ (@ F X12) X23)))) Prod))) (forall ((Prod tptp.produc1115495963_state)) (@ (@ tptp.produc789892016tate_o (lambda ((Uu tptp.state) (Uv tptp.state)) true)) Prod)) (forall ((Prod tptp.product_prod_nat_nat)) (@ (@ tptp.produc949581770_nat_o (lambda ((Uu tptp.nat) (Uv tptp.nat)) true)) Prod)) (forall ((F (-> tptp.state tptp.state Bool)) (X1 tptp.state) (X22 tptp.state)) (= (@ (@ tptp.produc789892016tate_o F) (@ (@ tptp.produc64584659_state X1) X22)) (@ (@ F X1) X22))) (forall ((F (-> tptp.nat tptp.nat Bool)) (X1 tptp.nat) (X22 tptp.nat)) (= (@ (@ tptp.produc949581770_nat_o F) (@ (@ tptp.product_Pair_nat_nat X1) X22)) (@ (@ F X1) X22))) (forall ((A2 tptp.set_Pr795498619_state) (R tptp.set_Pr778812871_state) (X2 tptp.produc1115495963_state) (Y3 tptp.produc1115495963_state)) (=> (@ (@ tptp.refl_o1438232218_state A2) R) (=> (@ (@ tptp.member768948240_state (@ (@ tptp.produc1964772951_state X2) Y3)) R) (@ (@ tptp.member1389040324_state Y3) A2)))) (forall ((A2 tptp.set_Pr1986765409at_nat) (R tptp.set_Pr1490359111at_nat) (X2 tptp.product_prod_nat_nat) (Y3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.refl_o1619599232at_nat A2) R) (=> (@ (@ tptp.member2027625872at_nat (@ (@ tptp.produc1168807639at_nat X2) Y3)) R) (@ (@ tptp.member701585322at_nat Y3) A2)))) (forall ((A2 tptp.set_Pr1590995257tate_o) (R tptp.set_Pr1702239303tate_o) (X2 tptp.produc696469763tate_o) (Y3 tptp.produc696469763tate_o)) (=> (@ (@ tptp.refl_o489021252tate_o A2) R) (=> (@ (@ tptp.member1629320336tate_o (@ (@ tptp.produc1684562079tate_o X2) Y3)) R) (@ (@ tptp.member1838112666tate_o Y3) A2)))) (forall ((A2 tptp.set_state) (R tptp.set_Pr795498619_state) (X2 tptp.state) (Y3 tptp.state)) (=> (@ (@ tptp.refl_on_state A2) R) (=> (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state X2) Y3)) R) (@ (@ tptp.member_state Y3) A2)))) (forall ((A2 tptp.set_nat) (R tptp.set_Pr1986765409at_nat) (X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.refl_on_nat A2) R) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X2) Y3)) R) (@ (@ tptp.member_nat Y3) A2)))) (forall ((A2 tptp.set_Pr795498619_state) (R tptp.set_Pr778812871_state) (X2 tptp.produc1115495963_state) (Y3 tptp.produc1115495963_state)) (=> (@ (@ tptp.refl_o1438232218_state A2) R) (=> (@ (@ tptp.member768948240_state (@ (@ tptp.produc1964772951_state X2) Y3)) R) (@ (@ tptp.member1389040324_state X2) A2)))) (forall ((A2 tptp.set_Pr1986765409at_nat) (R tptp.set_Pr1490359111at_nat) (X2 tptp.product_prod_nat_nat) (Y3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.refl_o1619599232at_nat A2) R) (=> (@ (@ tptp.member2027625872at_nat (@ (@ tptp.produc1168807639at_nat X2) Y3)) R) (@ (@ tptp.member701585322at_nat X2) A2)))) (forall ((A2 tptp.set_Pr1590995257tate_o) (R tptp.set_Pr1702239303tate_o) (X2 tptp.produc696469763tate_o) (Y3 tptp.produc696469763tate_o)) (=> (@ (@ tptp.refl_o489021252tate_o A2) R) (=> (@ (@ tptp.member1629320336tate_o (@ (@ tptp.produc1684562079tate_o X2) Y3)) R) (@ (@ tptp.member1838112666tate_o X2) A2)))) (forall ((A2 tptp.set_state) (R tptp.set_Pr795498619_state) (X2 tptp.state) (Y3 tptp.state)) (=> (@ (@ tptp.refl_on_state A2) R) (=> (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state X2) Y3)) R) (@ (@ tptp.member_state X2) A2)))) (forall ((A2 tptp.set_nat) (R tptp.set_Pr1986765409at_nat) (X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.refl_on_nat A2) R) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X2) Y3)) R) (@ (@ tptp.member_nat X2) A2)))) (forall ((A2 tptp.set_Pr795498619_state) (R tptp.set_Pr778812871_state) (A tptp.produc1115495963_state)) (=> (@ (@ tptp.refl_o1438232218_state A2) R) (=> (@ (@ tptp.member1389040324_state A) A2) (@ (@ tptp.member768948240_state (@ (@ tptp.produc1964772951_state A) A)) R)))) (forall ((A2 tptp.set_Pr1986765409at_nat) (R tptp.set_Pr1490359111at_nat) (A tptp.product_prod_nat_nat)) (=> (@ (@ tptp.refl_o1619599232at_nat A2) R) (=> (@ (@ tptp.member701585322at_nat A) A2) (@ (@ tptp.member2027625872at_nat (@ (@ tptp.produc1168807639at_nat A) A)) R)))) (forall ((A2 tptp.set_Pr1590995257tate_o) (R tptp.set_Pr1702239303tate_o) (A tptp.produc696469763tate_o)) (=> (@ (@ tptp.refl_o489021252tate_o A2) R) (=> (@ (@ tptp.member1838112666tate_o A) A2) (@ (@ tptp.member1629320336tate_o (@ (@ tptp.produc1684562079tate_o A) A)) R)))) (forall ((A2 tptp.set_state) (R tptp.set_Pr795498619_state) (A tptp.state)) (=> (@ (@ tptp.refl_on_state A2) R) (=> (@ (@ tptp.member_state A) A2) (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state A) A)) R)))) (forall ((A2 tptp.set_nat) (R tptp.set_Pr1986765409at_nat) (A tptp.nat)) (=> (@ (@ tptp.refl_on_nat A2) R) (=> (@ (@ tptp.member_nat A) A2) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A) A)) R)))) (forall ((F (-> (-> tptp.a tptp.state Bool) tptp.produc204914599tate_o Bool)) (A (-> tptp.a tptp.state Bool)) (B2 tptp.produc204914599tate_o)) (=> (@ (@ tptp.produc1271576886te_o_o F) (@ (@ tptp.produc33908149tate_o A) B2)) (@ (@ F A) B2))) (forall ((F (-> tptp.com (-> tptp.a tptp.state Bool) Bool)) (A tptp.com) (B2 (-> tptp.a tptp.state Bool))) (=> (@ (@ tptp.produc281270436te_o_o F) (@ (@ tptp.produc1948644831tate_o A) B2)) (@ (@ F A) B2))) (forall ((F (-> tptp.state tptp.state Bool)) (A tptp.state) (B2 tptp.state)) (=> (@ (@ tptp.produc789892016tate_o F) (@ (@ tptp.produc64584659_state A) B2)) (@ (@ F A) B2))) (forall ((F (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.produc949581770_nat_o F) (@ (@ tptp.product_Pair_nat_nat A) B2)) (@ (@ F A) B2))) (forall ((C2 (-> (-> tptp.a tptp.state Bool) tptp.produc204914599tate_o Bool)) (P3 tptp.produc696469763tate_o)) (=> (@ (@ tptp.produc1271576886te_o_o C2) P3) (not (forall ((X3 (-> tptp.a tptp.state Bool)) (Y2 tptp.produc204914599tate_o)) (=> (= P3 (@ (@ tptp.produc33908149tate_o X3) Y2)) (not (@ (@ C2 X3) Y2))))))) (forall ((C2 (-> tptp.com (-> tptp.a tptp.state Bool) Bool)) (P3 tptp.produc204914599tate_o)) (=> (@ (@ tptp.produc281270436te_o_o C2) P3) (not (forall ((X3 tptp.com) (Y2 (-> tptp.a tptp.state Bool))) (=> (= P3 (@ (@ tptp.produc1948644831tate_o X3) Y2)) (not (@ (@ C2 X3) Y2))))))) (forall ((C2 (-> tptp.state tptp.state Bool)) (P3 tptp.produc1115495963_state)) (=> (@ (@ tptp.produc789892016tate_o C2) P3) (not (forall ((X3 tptp.state) (Y2 tptp.state)) (=> (= P3 (@ (@ tptp.produc64584659_state X3) Y2)) (not (@ (@ C2 X3) Y2))))))) (forall ((C2 (-> tptp.nat tptp.nat Bool)) (P3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.produc949581770_nat_o C2) P3) (not (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (= P3 (@ (@ tptp.product_Pair_nat_nat X3) Y2)) (not (@ (@ C2 X3) Y2))))))) _let_14 _let_13 (forall ((A2 tptp.set_Pr795498619_state) (R tptp.set_Pr778812871_state)) (=> (forall ((X3 tptp.produc1115495963_state) (Y2 tptp.produc1115495963_state)) (=> (@ (@ tptp.member1389040324_state X3) A2) (=> (@ (@ tptp.member1389040324_state Y2) A2) (=> (not (= X3 Y2)) (or (@ (@ tptp.member768948240_state (@ (@ tptp.produc1964772951_state X3) Y2)) R) (@ (@ tptp.member768948240_state (@ (@ tptp.produc1964772951_state Y2) X3)) R)))))) (@ (@ tptp.total_1316653983_state A2) R))) (forall ((A2 tptp.set_Pr1986765409at_nat) (R tptp.set_Pr1490359111at_nat)) (=> (forall ((X3 tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member701585322at_nat X3) A2) (=> (@ (@ tptp.member701585322at_nat Y2) A2) (=> (not (= X3 Y2)) (or (@ (@ tptp.member2027625872at_nat (@ (@ tptp.produc1168807639at_nat X3) Y2)) R) (@ (@ tptp.member2027625872at_nat (@ (@ tptp.produc1168807639at_nat Y2) X3)) R)))))) (@ (@ tptp.total_1775715973at_nat A2) R))) (forall ((A2 tptp.set_Pr1590995257tate_o) (R tptp.set_Pr1702239303tate_o)) (=> (forall ((X3 tptp.produc696469763tate_o) (Y2 tptp.produc696469763tate_o)) (=> (@ (@ tptp.member1838112666tate_o X3) A2) (=> (@ (@ tptp.member1838112666tate_o Y2) A2) (=> (not (= X3 Y2)) (or (@ (@ tptp.member1629320336tate_o (@ (@ tptp.produc1684562079tate_o X3) Y2)) R) (@ (@ tptp.member1629320336tate_o (@ (@ tptp.produc1684562079tate_o Y2) X3)) R)))))) (@ (@ tptp.total_795385983tate_o A2) R))) (forall ((A2 tptp.set_state) (R tptp.set_Pr795498619_state)) (=> (forall ((X3 tptp.state) (Y2 tptp.state)) (=> (@ (@ tptp.member_state X3) A2) (=> (@ (@ tptp.member_state Y2) A2) (=> (not (= X3 Y2)) (or (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state X3) Y2)) R) (@ (@ tptp.member1389040324_state (@ (@ tptp.produc64584659_state Y2) X3)) R)))))) (@ (@ tptp.total_on_state A2) R))) (forall ((A2 tptp.set_nat) (R tptp.set_Pr1986765409at_nat)) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (=> (@ (@ tptp.member_nat Y2) A2) (=> (not (= X3 Y2)) (or (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y2)) R) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat Y2) X3)) R)))))) (@ (@ tptp.total_on_nat A2) R))) (forall ((R tptp.set_Pr1986765409at_nat)) (@ (@ tptp.total_on_nat tptp.bot_bot_set_nat) R)) (forall ((R tptp.set_Pr1702239303tate_o)) (@ (@ tptp.total_795385983tate_o tptp.bot_bo170732493tate_o) R)) (forall ((R tptp.set_Pr1490359111at_nat)) (@ (@ tptp.total_1775715973at_nat tptp.bot_bo2130386637at_nat) R)) (forall ((R tptp.set_Pr778812871_state)) (@ (@ tptp.total_1316653983_state tptp.bot_bo1625160935_state) R)) (forall ((Q (-> Bool Bool)) (P (-> tptp.state tptp.state Bool)) (Z5 tptp.produc1115495963_state)) (=> (@ Q (@ (@ tptp.produc789892016tate_o P) Z5)) (not (forall ((X3 tptp.state) (Y2 tptp.state)) (=> (= Z5 (@ (@ tptp.produc64584659_state X3) Y2)) (not (@ Q (@ (@ P X3) Y2)))))))) (forall ((Q (-> Bool Bool)) (P (-> tptp.nat tptp.nat Bool)) (Z5 tptp.product_prod_nat_nat)) (=> (@ Q (@ (@ tptp.produc949581770_nat_o P) Z5)) (not (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (= Z5 (@ (@ tptp.product_Pair_nat_nat X3) Y2)) (not (@ Q (@ (@ P X3) Y2)))))))) (forall ((F (-> tptp.produc1115495963_state Bool))) (= (@ tptp.produc789892016tate_o (lambda ((X tptp.state) (Y5 tptp.state)) (@ F (@ (@ tptp.produc64584659_state X) Y5)))) F)) (forall ((F (-> tptp.product_prod_nat_nat Bool))) (= (@ tptp.produc949581770_nat_o (lambda ((X tptp.nat) (Y5 tptp.nat)) (@ F (@ (@ tptp.product_Pair_nat_nat X) Y5)))) F)) (forall ((F (-> tptp.state tptp.state Bool)) (G (-> tptp.produc1115495963_state Bool))) (=> (forall ((X3 tptp.state) (Y2 tptp.state)) (= (@ (@ F X3) Y2) (@ G (@ (@ tptp.produc64584659_state X3) Y2)))) (= (@ tptp.produc789892016tate_o F) G))) (forall ((F (-> tptp.nat tptp.nat Bool)) (G (-> tptp.product_prod_nat_nat Bool))) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (= (@ (@ F X3) Y2) (@ G (@ (@ tptp.product_Pair_nat_nat X3) Y2)))) (= (@ tptp.produc949581770_nat_o F) G))) (@ (@ tptp.order_130026331on_nat tptp.bot_bot_set_nat) tptp.bot_bo2130386637at_nat) (@ (@ tptp.order_286167592_state tptp.bot_bot_set_state) tptp.bot_bo1625160935_state) (@ (@ tptp.order_50454158tate_o tptp.bot_bo170732493tate_o) tptp.bot_bo1714653363tate_o) (@ (@ tptp.order_721919926at_nat tptp.bot_bo2130386637at_nat) tptp.bot_bo34127283at_nat) (@ (@ tptp.order_178668240_state tptp.bot_bo1625160935_state) tptp.bot_bo1331673139_state) (@ (@ tptp.refl_on_nat tptp.bot_bot_set_nat) tptp.bot_bo2130386637at_nat) (@ (@ tptp.refl_on_state tptp.bot_bot_set_state) tptp.bot_bo1625160935_state) (@ (@ tptp.refl_o489021252tate_o tptp.bot_bo170732493tate_o) tptp.bot_bo1714653363tate_o) (@ (@ tptp.refl_o1619599232at_nat tptp.bot_bo2130386637at_nat) tptp.bot_bo34127283at_nat) (@ (@ tptp.refl_o1438232218_state tptp.bot_bo1625160935_state) tptp.bot_bo1331673139_state) (forall ((Q5 tptp.produc1115495963_state) (F (-> tptp.state tptp.state Bool)) (G (-> tptp.state tptp.state Bool)) (P3 tptp.produc1115495963_state)) (=> (forall ((X3 tptp.state) (Y2 tptp.state)) (=> (= (@ (@ tptp.produc64584659_state X3) Y2) Q5) (= (@ (@ F X3) Y2) (@ (@ G X3) Y2)))) (=> (= P3 Q5) (= (@ (@ tptp.produc789892016tate_o F) P3) (@ (@ tptp.produc789892016tate_o G) Q5))))) (forall ((Q5 tptp.product_prod_nat_nat) (F (-> tptp.nat tptp.nat Bool)) (G (-> tptp.nat tptp.nat Bool)) (P3 tptp.product_prod_nat_nat)) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat X3) Y2) Q5) (= (@ (@ F X3) Y2) (@ (@ G X3) Y2)))) (=> (= P3 Q5) (= (@ (@ tptp.produc949581770_nat_o F) P3) (@ (@ tptp.produc949581770_nat_o G) Q5))))) _let_12 _let_11 _let_10 _let_9 _let_8 _let_7 _let_6 (forall ((P3 tptp.product_prod_nat_nat) (Z5 tptp.produc1115495963_state) (C2 (-> tptp.nat tptp.nat tptp.set_Pr795498619_state))) (=> (forall ((A6 tptp.nat) (B6 tptp.nat)) (=> (= P3 (@ (@ tptp.product_Pair_nat_nat A6) B6)) (@ (@ tptp.member1389040324_state Z5) (@ (@ C2 A6) B6)))) (@ (@ tptp.member1389040324_state Z5) (@ (@ tptp.produc1654445_state C2) P3)))) (forall ((P3 tptp.product_prod_nat_nat) (Z5 tptp.product_prod_nat_nat) (C2 (-> tptp.nat tptp.nat tptp.set_Pr1986765409at_nat))) (=> (forall ((A6 tptp.nat) (B6 tptp.nat)) (=> (= P3 (@ (@ tptp.product_Pair_nat_nat A6) B6)) (@ (@ tptp.member701585322at_nat Z5) (@ (@ C2 A6) B6)))) (@ (@ tptp.member701585322at_nat Z5) (@ (@ tptp.produc1915186323at_nat C2) P3)))) (forall ((P3 tptp.product_prod_nat_nat) (Z5 tptp.produc696469763tate_o) (C2 (-> tptp.nat tptp.nat tptp.set_Pr1590995257tate_o))) (=> (forall ((A6 tptp.nat) (B6 tptp.nat)) (=> (= P3 (@ (@ tptp.product_Pair_nat_nat A6) B6)) (@ (@ tptp.member1838112666tate_o Z5) (@ (@ C2 A6) B6)))) (@ (@ tptp.member1838112666tate_o Z5) (@ (@ tptp.produc1610543495tate_o C2) P3)))) (forall ((B2 (-> tptp.state Bool)) (C2 tptp.com) (F (-> tptp.nat tptp.state)) (K tptp.nat)) (=> (@ (@ tptp.termi (@ (@ tptp.while B2) C2)) (@ F K)) (=> (forall ((I tptp.nat)) (@ (@ (@ tptp.exec (@ F I)) C2) (@ F (@ tptp.suc I)))) (exists ((I tptp.nat)) (not (@ B2 (@ F I))))))) (forall ((W tptp.com) (Fk tptp.state) (F (-> tptp.nat tptp.state)) (K tptp.nat) (B2 (-> tptp.state Bool)) (C2 tptp.com)) (=> (@ (@ tptp.termi W) Fk) (=> (and (= Fk (@ F K)) (= W (@ (@ tptp.while B2) C2)) (forall ((I tptp.nat)) (@ (@ (@ tptp.exec (@ F I)) C2) (@ F (@ tptp.suc I))))) (exists ((I tptp.nat)) (not (@ B2 (@ F I))))))) (forall ((S2 tptp.state) (N tptp.nat) (T2 tptp.state)) (let ((_let_1 (@ tptp.execn S2))) (=> (@ (@ (@ _let_1 tptp.body) N) T2) (@ (@ (@ _let_1 tptp.call) (@ tptp.suc N)) T2)))) _let_5 (forall ((S2 tptp.state) (B2 (-> tptp.state Bool)) (C2 tptp.com) (N tptp.nat) (T2 tptp.state) (P (-> tptp.state Bool))) (=> (@ (@ (@ (@ tptp.execn S2) (@ (@ tptp.while B2) C2)) N) T2) (=> (@ P S2) (=> (forall ((S tptp.state) (S3 tptp.state)) (=> (@ P S) (=> (@ B2 S) (=> (@ (@ (@ (@ tptp.execn S) C2) N) S3) (@ P S3))))) (and (@ P T2) (not (@ B2 T2))))))) (forall ((S2 tptp.state) (W tptp.com) (N tptp.nat) (T2 tptp.state) (B2 (-> tptp.state Bool)) (C2 tptp.com) (P (-> tptp.state Bool))) (=> (@ (@ (@ (@ tptp.execn S2) W) N) T2) (=> (and (= W (@ (@ tptp.while B2) C2)) (@ P S2) (forall ((S tptp.state) (S3 tptp.state)) (=> (and (@ P S) (@ B2 S) (@ (@ (@ (@ tptp.execn S) C2) N) S3)) (@ P S3)))) (and (@ P T2) (not (@ B2 T2)))))) (forall ((B2 (-> tptp.state Bool)) (S2 tptp.state) (C2 tptp.com) (N tptp.nat) (T2 tptp.state) (U2 tptp.state)) (let ((_let_1 (@ (@ tptp.while B2) C2))) (let ((_let_2 (@ tptp.execn S2))) (=> (@ B2 S2) (=> (@ (@ (@ _let_2 C2) N) T2) (=> (@ (@ (@ (@ tptp.execn T2) _let_1) N) U2) (@ (@ (@ _let_2 _let_1) N) U2))))))) (forall ((B2 (-> tptp.state Bool)) (S2 tptp.state) (C2 tptp.com) (N tptp.nat)) (=> (not (@ B2 S2)) (@ (@ (@ (@ tptp.execn S2) (@ (@ tptp.while B2) C2)) N) S2))) _let_4 (@ tptp.wf_nat tptp.pred_nat) (forall ((C1 tptp.com) (S0 tptp.state) (C22 tptp.com)) (=> (@ (@ tptp.termi C1) S0) (=> (forall ((S1 tptp.state)) (=> (@ (@ (@ tptp.exec S0) C1) S1) (@ (@ tptp.termi C22) S1))) (@ (@ tptp.termi (@ (@ tptp.semi C1) C22)) S0)))) (forall ((X21 tptp.com) (X222 tptp.com) (Y21 tptp.com) (Y222 tptp.com)) (= (= (@ (@ tptp.semi X21) X222) (@ (@ tptp.semi Y21) Y222)) (and (= X21 Y21) (= X222 Y222)))) (forall ((S0 tptp.state) (C1 tptp.com) (N tptp.nat) (S12 tptp.state) (C22 tptp.com) (S22 tptp.state)) (let ((_let_1 (@ tptp.execn S0))) (=> (@ (@ (@ _let_1 C1) N) S12) (=> (@ (@ (@ (@ tptp.execn S12) C22) N) S22) (@ (@ (@ _let_1 (@ (@ tptp.semi C1) C22)) N) S22))))) (forall ((X21 tptp.com) (X222 tptp.com) (X41 (-> tptp.state Bool)) (X42 tptp.com)) (not (= (@ (@ tptp.semi X21) X222) (@ (@ tptp.while X41) X42)))) (forall ((X21 tptp.com) (X222 tptp.com)) (not (= (@ (@ tptp.semi X21) X222) tptp.call))) (forall ((S0 tptp.state) (C1 tptp.com) (S12 tptp.state) (C22 tptp.com) (S22 tptp.state)) (let ((_let_1 (@ tptp.exec S0))) (=> (@ (@ _let_1 C1) S12) (=> (@ (@ (@ tptp.exec S12) C22) S22) (@ (@ _let_1 (@ (@ tptp.semi C1) C22)) S22))))) (@ tptp.wf_nat tptp.less_than) (forall ((A2 tptp.set_nat)) (@ (@ tptp.total_on_nat A2) tptp.less_than)) (@ tptp.irrefl_nat tptp.less_than) (@ tptp.trans_nat tptp.less_than) (forall ((X2 tptp.nat) (Y3 tptp.nat)) (= (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X2) Y3)) tptp.less_than) (@ (@ tptp.ord_less_nat X2) Y3))) _let_3 _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.15/1.46 )
% 1.15/1.46 % SZS output end Proof for ITP141^1
% 1.15/1.46 % cvc5---1.0.5 exiting
% 1.15/1.46 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------