TSTP Solution File: ITP142^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP142^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 03:18:35 EDT 2023
% Result : Theorem 0.61s 1.14s
% Output : Proof 0.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.21 % Problem : ITP142^1 : TPTP v8.1.2. Released v7.5.0.
% 0.13/0.22 % Command : do_cvc5 %s %d
% 0.21/0.43 % Computer : n016.cluster.edu
% 0.21/0.43 % Model : x86_64 x86_64
% 0.21/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.43 % Memory : 8042.1875MB
% 0.21/0.43 % OS : Linux 3.10.0-693.el7.x86_64
% 0.27/0.43 % CPULimit : 300
% 0.27/0.43 % WCLimit : 300
% 0.27/0.43 % DateTime : Sun Aug 27 15:36:29 EDT 2023
% 0.27/0.43 % CPUTime :
% 0.29/0.65 %----Proving TH0
% 0.29/0.66 %------------------------------------------------------------------------------
% 0.29/0.66 % File : ITP142^1 : TPTP v8.1.2. Released v7.5.0.
% 0.29/0.66 % Domain : Interactive Theorem Proving
% 0.29/0.66 % Problem : Sledgehammer PHoareTotal problem prob_304__3261994_1
% 0.29/0.66 % Version : Especial.
% 0.29/0.66 % English :
% 0.29/0.66
% 0.29/0.66 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.29/0.66 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.29/0.66 % Source : [Des21]
% 0.29/0.66 % Names : PHoareTotal/prob_304__3261994_1 [Des21]
% 0.29/0.66
% 0.29/0.66 % Status : Theorem
% 0.29/0.66 % Rating : 0.15 v8.1.0, 0.18 v7.5.0
% 0.29/0.66 % Syntax : Number of formulae : 522 ( 152 unt; 164 typ; 0 def)
% 0.29/0.66 % Number of atoms : 1042 ( 497 equ; 0 cnn)
% 0.29/0.66 % Maximal formula atoms : 7 ( 2 avg)
% 0.29/0.66 % Number of connectives : 5299 ( 222 ~; 42 |; 115 &;4342 @)
% 0.29/0.66 % ( 0 <=>; 578 =>; 0 <=; 0 <~>)
% 0.29/0.66 % Maximal formula depth : 23 ( 10 avg)
% 0.29/0.66 % Number of types : 41 ( 40 usr)
% 0.29/0.66 % Number of type conns : 389 ( 389 >; 0 *; 0 +; 0 <<)
% 0.29/0.66 % Number of symbols : 125 ( 124 usr; 13 con; 0-3 aty)
% 0.29/0.66 % Number of variables : 1572 ( 8 ^;1499 !; 65 ?;1572 :)
% 0.29/0.66 % SPC : TH0_THM_EQU_NAR
% 0.29/0.66
% 0.29/0.66 % Comments : This file was generated by Sledgehammer 2021-02-23 15:33:07.515
% 0.29/0.66 %------------------------------------------------------------------------------
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% 0.29/0.66 member512523024_state: produc186437863_state > set_Pr2096893127_state > $o ).
% 0.29/0.66
% 0.29/0.66 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__List__Olist_It__PLang__Ocom_J_Mt__PLang__Ostate_J_J_J_J,type,
% 0.29/0.66 member284400400_state: produc2046512871_state > set_Pr541394119_state > $o ).
% 0.29/0.66
% 0.29/0.66 thf(sy_v_c,type,
% 0.29/0.66 c: com ).
% 0.29/0.66
% 0.29/0.66 thf(sy_v_c_H,type,
% 0.29/0.66 c2: com ).
% 0.29/0.66
% 0.29/0.66 thf(sy_v_cs_H,type,
% 0.29/0.66 cs: list_com ).
% 0.29/0.66
% 0.29/0.66 thf(sy_v_s,type,
% 0.29/0.66 s: state ).
% 0.29/0.66
% 0.29/0.66 thf(sy_v_s_H,type,
% 0.29/0.66 s2: state ).
% 0.29/0.66
% 0.29/0.66 % Relevant facts (354)
% 0.29/0.66 thf(fact_0_exec1E_I1_J,axiom,
% 0.29/0.66 ! [S: state,Cs: list_com,S2: state] :
% 0.29/0.66 ~ ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ nil_com @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 ) ).
% 0.29/0.66
% 0.29/0.66 % exec1E(1)
% 0.29/0.66 thf(fact_1_termis_Osimps_I2_J,axiom,
% 0.29/0.66 ! [C: com,Cs2: list_com,S: state] :
% 0.29/0.66 ( ( pHoare806997636termis @ ( cons_com @ C @ Cs2 ) @ S )
% 0.29/0.66 = ( ( termi @ C @ S )
% 0.29/0.66 & ! [T: state] :
% 0.29/0.66 ( ( exec @ S @ C @ T )
% 0.29/0.66 => ( pHoare806997636termis @ Cs2 @ T ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % termis.simps(2)
% 0.29/0.66 thf(fact_2_termis_Osimps_I1_J,axiom,
% 0.29/0.66 ! [S: state] : ( pHoare806997636termis @ nil_com @ S ) ).
% 0.29/0.66
% 0.29/0.66 % termis.simps(1)
% 0.29/0.66 thf(fact_3_exec__impl__execs,axiom,
% 0.29/0.66 ! [S: state,C: com,S2: state,Cs2: list_com] :
% 0.29/0.66 ( ( exec @ S @ C @ S2 )
% 0.29/0.66 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ C @ Cs2 ) @ S ) @ ( produc1204172211_state @ Cs2 @ S2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % exec_impl_execs
% 0.29/0.66 thf(fact_4_exec1s__impl__exec,axiom,
% 0.29/0.66 ! [C: com,S: state,T2: state] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ C @ nil_com ) @ S ) @ ( produc1204172211_state @ nil_com @ T2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 0.29/0.66 => ( exec @ S @ C @ T2 ) ) ).
% 0.29/0.66
% 0.29/0.66 % exec1s_impl_exec
% 0.29/0.66 thf(fact_5_exec1__pres__termis,axiom,
% 0.29/0.66 ! [Cs2: list_com,S: state,Cs: list_com,S2: state] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs2 @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 )
% 0.29/0.66 => ( ( pHoare806997636termis @ Cs2 @ S )
% 0.29/0.66 => ( pHoare806997636termis @ Cs @ S2 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % exec1_pres_termis
% 0.29/0.66 thf(fact_6_execs__pres__termis,axiom,
% 0.29/0.66 ! [Cs2: list_com,S: state,Cs: list_com,S2: state] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs2 @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 0.29/0.66 => ( ( pHoare806997636termis @ Cs2 @ S )
% 0.29/0.66 => ( pHoare806997636termis @ Cs @ S2 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % execs_pres_termis
% 0.29/0.66 thf(fact_7_rtrancl__induct2,axiom,
% 0.29/0.66 ! [Ax: list_P890094829_state,Ay: list_P890094829_state,Bx: list_P890094829_state,By: list_P890094829_state,R: set_Pr1696918727_state,P: list_P890094829_state > list_P890094829_state > $o] :
% 0.29/0.66 ( ( member1642814224_state @ ( produc1576663895_state @ ( produc1354769367_state @ Ax @ Ay ) @ ( produc1354769367_state @ Bx @ By ) ) @ ( transi445721450_state @ R ) )
% 0.29/0.66 => ( ( P @ Ax @ Ay )
% 0.29/0.66 => ( ! [A: list_P890094829_state,B: list_P890094829_state,Aa: list_P890094829_state,Ba: list_P890094829_state] :
% 0.29/0.66 ( ( member1642814224_state @ ( produc1576663895_state @ ( produc1354769367_state @ Ax @ Ay ) @ ( produc1354769367_state @ A @ B ) ) @ ( transi445721450_state @ R ) )
% 0.29/0.66 => ( ( member1642814224_state @ ( produc1576663895_state @ ( produc1354769367_state @ A @ B ) @ ( produc1354769367_state @ Aa @ Ba ) ) @ R )
% 0.29/0.66 => ( ( P @ A @ B )
% 0.29/0.66 => ( P @ Aa @ Ba ) ) ) )
% 0.29/0.66 => ( P @ Bx @ By ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % rtrancl_induct2
% 0.29/0.66 thf(fact_8_rtrancl__induct2,axiom,
% 0.29/0.66 ! [Ax: list_P1040014977_state,Ay: list_P1040014977_state,Bx: list_P1040014977_state,By: list_P1040014977_state,R: set_Pr1847866567_state,P: list_P1040014977_state > list_P1040014977_state > $o] :
% 0.29/0.66 ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ Ax @ Ay ) @ ( produc1298457559_state @ Bx @ By ) ) @ ( transi1428749162_state @ R ) )
% 0.29/0.66 => ( ( P @ Ax @ Ay )
% 0.29/0.66 => ( ! [A: list_P1040014977_state,B: list_P1040014977_state,Aa: list_P1040014977_state,Ba: list_P1040014977_state] :
% 0.29/0.66 ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ Ax @ Ay ) @ ( produc1298457559_state @ A @ B ) ) @ ( transi1428749162_state @ R ) )
% 0.29/0.66 => ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ A @ B ) @ ( produc1298457559_state @ Aa @ Ba ) ) @ R )
% 0.29/0.66 => ( ( P @ A @ B )
% 0.29/0.66 => ( P @ Aa @ Ba ) ) ) )
% 0.29/0.66 => ( P @ Bx @ By ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % rtrancl_induct2
% 0.29/0.66 thf(fact_9_rtrancl__induct2,axiom,
% 0.29/0.66 ! [Ax: list_com,Ay: list_com,Bx: list_com,By: list_com,R: set_Pr2083163591st_com,P: list_com > list_com > $o] :
% 0.29/0.66 ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ Ax @ Ay ) @ ( produc1307105171st_com @ Bx @ By ) ) @ ( transi1782245470st_com @ R ) )
% 0.29/0.66 => ( ( P @ Ax @ Ay )
% 0.29/0.66 => ( ! [A: list_com,B: list_com,Aa: list_com,Ba: list_com] :
% 0.29/0.66 ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ Ax @ Ay ) @ ( produc1307105171st_com @ A @ B ) ) @ ( transi1782245470st_com @ R ) )
% 0.29/0.66 => ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ A @ B ) @ ( produc1307105171st_com @ Aa @ Ba ) ) @ R )
% 0.29/0.66 => ( ( P @ A @ B )
% 0.29/0.66 => ( P @ Aa @ Ba ) ) ) )
% 0.29/0.66 => ( P @ Bx @ By ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % rtrancl_induct2
% 0.29/0.66 thf(fact_10_rtrancl__induct2,axiom,
% 0.29/0.66 ! [Ax: list_list_com,Ay: list_state,Bx: list_list_com,By: list_state,R: set_Pr1419004359_state,P: list_list_com > list_state > $o] :
% 0.29/0.66 ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ Ax @ Ay ) @ ( produc1742567891_state @ Bx @ By ) ) @ ( transi89280670_state @ R ) )
% 0.29/0.66 => ( ( P @ Ax @ Ay )
% 0.29/0.66 => ( ! [A: list_list_com,B: list_state,Aa: list_list_com,Ba: list_state] :
% 0.29/0.66 ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ Ax @ Ay ) @ ( produc1742567891_state @ A @ B ) ) @ ( transi89280670_state @ R ) )
% 0.29/0.66 => ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ A @ B ) @ ( produc1742567891_state @ Aa @ Ba ) ) @ R )
% 0.29/0.66 => ( ( P @ A @ B )
% 0.29/0.66 => ( P @ Aa @ Ba ) ) ) )
% 0.29/0.66 => ( P @ Bx @ By ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % rtrancl_induct2
% 0.29/0.66 thf(fact_11_rtrancl__induct2,axiom,
% 0.29/0.66 ! [Ax: com > com > $o,Ay: list_com,Bx: com > com > $o,By: list_com,R: set_Pr135335153st_com,P: ( com > com > $o ) > list_com > $o] :
% 0.29/0.66 ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ Ax @ Ay ) @ ( produc1914379986st_com @ Bx @ By ) ) @ ( transi1592315797st_com @ R ) )
% 0.29/0.66 => ( ( P @ Ax @ Ay )
% 0.29/0.66 => ( ! [A: com > com > $o,B: list_com,Aa: com > com > $o,Ba: list_com] :
% 0.29/0.66 ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ Ax @ Ay ) @ ( produc1914379986st_com @ A @ B ) ) @ ( transi1592315797st_com @ R ) )
% 0.29/0.66 => ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ A @ B ) @ ( produc1914379986st_com @ Aa @ Ba ) ) @ R )
% 0.29/0.66 => ( ( P @ A @ B )
% 0.29/0.66 => ( P @ Aa @ Ba ) ) ) )
% 0.29/0.66 => ( P @ Bx @ By ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % rtrancl_induct2
% 0.29/0.66 thf(fact_12_rtrancl__induct2,axiom,
% 0.29/0.66 ! [Ax: produc410756839_state,Ay: produc410756839_state,Bx: produc410756839_state,By: produc410756839_state,R: set_Pr541394119_state,P: produc410756839_state > produc410756839_state > $o] :
% 0.29/0.66 ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Ax @ Ay ) @ ( produc2065881943_state @ Bx @ By ) ) @ ( transi152726506_state @ R ) )
% 0.29/0.66 => ( ( P @ Ax @ Ay )
% 0.29/0.66 => ( ! [A: produc410756839_state,B: produc410756839_state,Aa: produc410756839_state,Ba: produc410756839_state] :
% 0.29/0.66 ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Ax @ Ay ) @ ( produc2065881943_state @ A @ B ) ) @ ( transi152726506_state @ R ) )
% 0.29/0.66 => ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ A @ B ) @ ( produc2065881943_state @ Aa @ Ba ) ) @ R )
% 0.29/0.66 => ( ( P @ A @ B )
% 0.29/0.66 => ( P @ Aa @ Ba ) ) ) )
% 0.29/0.66 => ( P @ Bx @ By ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % rtrancl_induct2
% 0.29/0.66 thf(fact_13_rtrancl__induct2,axiom,
% 0.29/0.66 ! [Ax: produc2041926651_state,Ay: produc2041926651_state,Bx: produc2041926651_state,By: produc2041926651_state,R: set_Pr2096893127_state,P: produc2041926651_state > produc2041926651_state > $o] :
% 0.29/0.66 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Ax @ Ay ) @ ( produc1909270103_state @ Bx @ By ) ) @ ( transi463013610_state @ R ) )
% 0.29/0.66 => ( ( P @ Ax @ Ay )
% 0.29/0.66 => ( ! [A: produc2041926651_state,B: produc2041926651_state,Aa: produc2041926651_state,Ba: produc2041926651_state] :
% 0.29/0.66 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Ax @ Ay ) @ ( produc1909270103_state @ A @ B ) ) @ ( transi463013610_state @ R ) )
% 0.29/0.66 => ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ A @ B ) @ ( produc1909270103_state @ Aa @ Ba ) ) @ R )
% 0.29/0.66 => ( ( P @ A @ B )
% 0.29/0.66 => ( P @ Aa @ Ba ) ) ) )
% 0.29/0.66 => ( P @ Bx @ By ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % rtrancl_induct2
% 0.29/0.66 thf(fact_14_rtrancl__induct2,axiom,
% 0.29/0.66 ! [Ax: list_com,Ay: state,Bx: list_com,By: state,R: set_Pr1165141447_state,P: list_com > state > $o] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Ax @ Ay ) @ ( produc1204172211_state @ Bx @ By ) ) @ ( transi1302705790_state @ R ) )
% 0.29/0.66 => ( ( P @ Ax @ Ay )
% 0.29/0.66 => ( ! [A: list_com,B: state,Aa: list_com,Ba: state] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Ax @ Ay ) @ ( produc1204172211_state @ A @ B ) ) @ ( transi1302705790_state @ R ) )
% 0.29/0.66 => ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ A @ B ) @ ( produc1204172211_state @ Aa @ Ba ) ) @ R )
% 0.29/0.66 => ( ( P @ A @ B )
% 0.29/0.66 => ( P @ Aa @ Ba ) ) ) )
% 0.29/0.66 => ( P @ Bx @ By ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % rtrancl_induct2
% 0.29/0.66 thf(fact_15_converse__rtranclE2,axiom,
% 0.29/0.66 ! [Xa: list_P890094829_state,Xb: list_P890094829_state,Za: list_P890094829_state,Zb: list_P890094829_state,R: set_Pr1696918727_state] :
% 0.29/0.66 ( ( member1642814224_state @ ( produc1576663895_state @ ( produc1354769367_state @ Xa @ Xb ) @ ( produc1354769367_state @ Za @ Zb ) ) @ ( transi445721450_state @ R ) )
% 0.29/0.66 => ( ( ( produc1354769367_state @ Xa @ Xb )
% 0.29/0.66 != ( produc1354769367_state @ Za @ Zb ) )
% 0.29/0.66 => ~ ! [A: list_P890094829_state,B: list_P890094829_state] :
% 0.29/0.66 ( ( member1642814224_state @ ( produc1576663895_state @ ( produc1354769367_state @ Xa @ Xb ) @ ( produc1354769367_state @ A @ B ) ) @ R )
% 0.29/0.66 => ~ ( member1642814224_state @ ( produc1576663895_state @ ( produc1354769367_state @ A @ B ) @ ( produc1354769367_state @ Za @ Zb ) ) @ ( transi445721450_state @ R ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % converse_rtranclE2
% 0.29/0.66 thf(fact_16_converse__rtranclE2,axiom,
% 0.29/0.66 ! [Xa: list_P1040014977_state,Xb: list_P1040014977_state,Za: list_P1040014977_state,Zb: list_P1040014977_state,R: set_Pr1847866567_state] :
% 0.29/0.66 ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ Xa @ Xb ) @ ( produc1298457559_state @ Za @ Zb ) ) @ ( transi1428749162_state @ R ) )
% 0.29/0.66 => ( ( ( produc1298457559_state @ Xa @ Xb )
% 0.29/0.66 != ( produc1298457559_state @ Za @ Zb ) )
% 0.29/0.66 => ~ ! [A: list_P1040014977_state,B: list_P1040014977_state] :
% 0.29/0.66 ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ Xa @ Xb ) @ ( produc1298457559_state @ A @ B ) ) @ R )
% 0.29/0.66 => ~ ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ A @ B ) @ ( produc1298457559_state @ Za @ Zb ) ) @ ( transi1428749162_state @ R ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % converse_rtranclE2
% 0.29/0.66 thf(fact_17_converse__rtranclE2,axiom,
% 0.29/0.66 ! [Xa: list_com,Xb: list_com,Za: list_com,Zb: list_com,R: set_Pr2083163591st_com] :
% 0.29/0.66 ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ Xa @ Xb ) @ ( produc1307105171st_com @ Za @ Zb ) ) @ ( transi1782245470st_com @ R ) )
% 0.29/0.66 => ( ( ( produc1307105171st_com @ Xa @ Xb )
% 0.29/0.66 != ( produc1307105171st_com @ Za @ Zb ) )
% 0.29/0.66 => ~ ! [A: list_com,B: list_com] :
% 0.29/0.66 ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ Xa @ Xb ) @ ( produc1307105171st_com @ A @ B ) ) @ R )
% 0.29/0.66 => ~ ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ A @ B ) @ ( produc1307105171st_com @ Za @ Zb ) ) @ ( transi1782245470st_com @ R ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % converse_rtranclE2
% 0.29/0.66 thf(fact_18_converse__rtranclE2,axiom,
% 0.29/0.66 ! [Xa: list_list_com,Xb: list_state,Za: list_list_com,Zb: list_state,R: set_Pr1419004359_state] :
% 0.29/0.66 ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ Xa @ Xb ) @ ( produc1742567891_state @ Za @ Zb ) ) @ ( transi89280670_state @ R ) )
% 0.29/0.66 => ( ( ( produc1742567891_state @ Xa @ Xb )
% 0.29/0.66 != ( produc1742567891_state @ Za @ Zb ) )
% 0.29/0.66 => ~ ! [A: list_list_com,B: list_state] :
% 0.29/0.66 ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ Xa @ Xb ) @ ( produc1742567891_state @ A @ B ) ) @ R )
% 0.29/0.66 => ~ ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ A @ B ) @ ( produc1742567891_state @ Za @ Zb ) ) @ ( transi89280670_state @ R ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % converse_rtranclE2
% 0.29/0.66 thf(fact_19_converse__rtranclE2,axiom,
% 0.29/0.66 ! [Xa: com > com > $o,Xb: list_com,Za: com > com > $o,Zb: list_com,R: set_Pr135335153st_com] :
% 0.29/0.66 ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ Xa @ Xb ) @ ( produc1914379986st_com @ Za @ Zb ) ) @ ( transi1592315797st_com @ R ) )
% 0.29/0.66 => ( ( ( produc1914379986st_com @ Xa @ Xb )
% 0.29/0.66 != ( produc1914379986st_com @ Za @ Zb ) )
% 0.29/0.66 => ~ ! [A: com > com > $o,B: list_com] :
% 0.29/0.66 ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ Xa @ Xb ) @ ( produc1914379986st_com @ A @ B ) ) @ R )
% 0.29/0.66 => ~ ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ A @ B ) @ ( produc1914379986st_com @ Za @ Zb ) ) @ ( transi1592315797st_com @ R ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % converse_rtranclE2
% 0.29/0.66 thf(fact_20_converse__rtranclE2,axiom,
% 0.29/0.66 ! [Xa: produc410756839_state,Xb: produc410756839_state,Za: produc410756839_state,Zb: produc410756839_state,R: set_Pr541394119_state] :
% 0.29/0.66 ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Xa @ Xb ) @ ( produc2065881943_state @ Za @ Zb ) ) @ ( transi152726506_state @ R ) )
% 0.29/0.66 => ( ( ( produc2065881943_state @ Xa @ Xb )
% 0.29/0.66 != ( produc2065881943_state @ Za @ Zb ) )
% 0.29/0.66 => ~ ! [A: produc410756839_state,B: produc410756839_state] :
% 0.29/0.66 ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Xa @ Xb ) @ ( produc2065881943_state @ A @ B ) ) @ R )
% 0.29/0.66 => ~ ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ A @ B ) @ ( produc2065881943_state @ Za @ Zb ) ) @ ( transi152726506_state @ R ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % converse_rtranclE2
% 0.29/0.66 thf(fact_21_converse__rtranclE2,axiom,
% 0.29/0.66 ! [Xa: produc2041926651_state,Xb: produc2041926651_state,Za: produc2041926651_state,Zb: produc2041926651_state,R: set_Pr2096893127_state] :
% 0.29/0.66 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Xa @ Xb ) @ ( produc1909270103_state @ Za @ Zb ) ) @ ( transi463013610_state @ R ) )
% 0.29/0.66 => ( ( ( produc1909270103_state @ Xa @ Xb )
% 0.29/0.66 != ( produc1909270103_state @ Za @ Zb ) )
% 0.29/0.66 => ~ ! [A: produc2041926651_state,B: produc2041926651_state] :
% 0.29/0.66 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Xa @ Xb ) @ ( produc1909270103_state @ A @ B ) ) @ R )
% 0.29/0.66 => ~ ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ A @ B ) @ ( produc1909270103_state @ Za @ Zb ) ) @ ( transi463013610_state @ R ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % converse_rtranclE2
% 0.29/0.66 thf(fact_22_converse__rtranclE2,axiom,
% 0.29/0.66 ! [Xa: list_com,Xb: state,Za: list_com,Zb: state,R: set_Pr1165141447_state] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Xa @ Xb ) @ ( produc1204172211_state @ Za @ Zb ) ) @ ( transi1302705790_state @ R ) )
% 0.29/0.66 => ( ( ( produc1204172211_state @ Xa @ Xb )
% 0.29/0.66 != ( produc1204172211_state @ Za @ Zb ) )
% 0.29/0.66 => ~ ! [A: list_com,B: state] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Xa @ Xb ) @ ( produc1204172211_state @ A @ B ) ) @ R )
% 0.29/0.66 => ~ ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ A @ B ) @ ( produc1204172211_state @ Za @ Zb ) ) @ ( transi1302705790_state @ R ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % converse_rtranclE2
% 0.29/0.66 thf(fact_23_converse__rtrancl__induct2,axiom,
% 0.29/0.66 ! [Ax: list_P890094829_state,Ay: list_P890094829_state,Bx: list_P890094829_state,By: list_P890094829_state,R: set_Pr1696918727_state,P: list_P890094829_state > list_P890094829_state > $o] :
% 0.29/0.66 ( ( member1642814224_state @ ( produc1576663895_state @ ( produc1354769367_state @ Ax @ Ay ) @ ( produc1354769367_state @ Bx @ By ) ) @ ( transi445721450_state @ R ) )
% 0.29/0.66 => ( ( P @ Bx @ By )
% 0.29/0.66 => ( ! [A: list_P890094829_state,B: list_P890094829_state,Aa: list_P890094829_state,Ba: list_P890094829_state] :
% 0.29/0.66 ( ( member1642814224_state @ ( produc1576663895_state @ ( produc1354769367_state @ A @ B ) @ ( produc1354769367_state @ Aa @ Ba ) ) @ R )
% 0.29/0.66 => ( ( member1642814224_state @ ( produc1576663895_state @ ( produc1354769367_state @ Aa @ Ba ) @ ( produc1354769367_state @ Bx @ By ) ) @ ( transi445721450_state @ R ) )
% 0.29/0.66 => ( ( P @ Aa @ Ba )
% 0.29/0.66 => ( P @ A @ B ) ) ) )
% 0.29/0.66 => ( P @ Ax @ Ay ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % converse_rtrancl_induct2
% 0.29/0.66 thf(fact_24_converse__rtrancl__induct2,axiom,
% 0.29/0.66 ! [Ax: list_P1040014977_state,Ay: list_P1040014977_state,Bx: list_P1040014977_state,By: list_P1040014977_state,R: set_Pr1847866567_state,P: list_P1040014977_state > list_P1040014977_state > $o] :
% 0.29/0.66 ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ Ax @ Ay ) @ ( produc1298457559_state @ Bx @ By ) ) @ ( transi1428749162_state @ R ) )
% 0.29/0.66 => ( ( P @ Bx @ By )
% 0.29/0.66 => ( ! [A: list_P1040014977_state,B: list_P1040014977_state,Aa: list_P1040014977_state,Ba: list_P1040014977_state] :
% 0.29/0.66 ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ A @ B ) @ ( produc1298457559_state @ Aa @ Ba ) ) @ R )
% 0.29/0.66 => ( ( member2092727056_state @ ( produc984060759_state @ ( produc1298457559_state @ Aa @ Ba ) @ ( produc1298457559_state @ Bx @ By ) ) @ ( transi1428749162_state @ R ) )
% 0.29/0.66 => ( ( P @ Aa @ Ba )
% 0.29/0.66 => ( P @ A @ B ) ) ) )
% 0.29/0.66 => ( P @ Ax @ Ay ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % converse_rtrancl_induct2
% 0.29/0.66 thf(fact_25_converse__rtrancl__induct2,axiom,
% 0.29/0.66 ! [Ax: list_com,Ay: list_com,Bx: list_com,By: list_com,R: set_Pr2083163591st_com,P: list_com > list_com > $o] :
% 0.29/0.66 ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ Ax @ Ay ) @ ( produc1307105171st_com @ Bx @ By ) ) @ ( transi1782245470st_com @ R ) )
% 0.29/0.66 => ( ( P @ Bx @ By )
% 0.29/0.66 => ( ! [A: list_com,B: list_com,Aa: list_com,Ba: list_com] :
% 0.29/0.66 ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ A @ B ) @ ( produc1307105171st_com @ Aa @ Ba ) ) @ R )
% 0.29/0.66 => ( ( member919914512st_com @ ( produc313736791st_com @ ( produc1307105171st_com @ Aa @ Ba ) @ ( produc1307105171st_com @ Bx @ By ) ) @ ( transi1782245470st_com @ R ) )
% 0.29/0.66 => ( ( P @ Aa @ Ba )
% 0.29/0.66 => ( P @ A @ B ) ) ) )
% 0.29/0.66 => ( P @ Ax @ Ay ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % converse_rtrancl_induct2
% 0.29/0.66 thf(fact_26_converse__rtrancl__induct2,axiom,
% 0.29/0.66 ! [Ax: list_list_com,Ay: list_state,Bx: list_list_com,By: list_state,R: set_Pr1419004359_state,P: list_list_com > list_state > $o] :
% 0.29/0.66 ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ Ax @ Ay ) @ ( produc1742567891_state @ Bx @ By ) ) @ ( transi89280670_state @ R ) )
% 0.29/0.66 => ( ( P @ Bx @ By )
% 0.29/0.66 => ( ! [A: list_list_com,B: list_state,Aa: list_list_com,Ba: list_state] :
% 0.29/0.66 ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ A @ B ) @ ( produc1742567891_state @ Aa @ Ba ) ) @ R )
% 0.29/0.66 => ( ( member1414265872_state @ ( produc67381847_state @ ( produc1742567891_state @ Aa @ Ba ) @ ( produc1742567891_state @ Bx @ By ) ) @ ( transi89280670_state @ R ) )
% 0.29/0.66 => ( ( P @ Aa @ Ba )
% 0.29/0.66 => ( P @ A @ B ) ) ) )
% 0.29/0.66 => ( P @ Ax @ Ay ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % converse_rtrancl_induct2
% 0.29/0.66 thf(fact_27_converse__rtrancl__induct2,axiom,
% 0.29/0.66 ! [Ax: com > com > $o,Ay: list_com,Bx: com > com > $o,By: list_com,R: set_Pr135335153st_com,P: ( com > com > $o ) > list_com > $o] :
% 0.29/0.66 ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ Ax @ Ay ) @ ( produc1914379986st_com @ Bx @ By ) ) @ ( transi1592315797st_com @ R ) )
% 0.29/0.66 => ( ( P @ Bx @ By )
% 0.29/0.66 => ( ! [A: com > com > $o,B: list_com,Aa: com > com > $o,Ba: list_com] :
% 0.29/0.66 ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ A @ B ) @ ( produc1914379986st_com @ Aa @ Ba ) ) @ R )
% 0.29/0.66 => ( ( member89779770st_com @ ( produc67337417st_com @ ( produc1914379986st_com @ Aa @ Ba ) @ ( produc1914379986st_com @ Bx @ By ) ) @ ( transi1592315797st_com @ R ) )
% 0.29/0.66 => ( ( P @ Aa @ Ba )
% 0.29/0.66 => ( P @ A @ B ) ) ) )
% 0.29/0.66 => ( P @ Ax @ Ay ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % converse_rtrancl_induct2
% 0.29/0.66 thf(fact_28_converse__rtrancl__induct2,axiom,
% 0.29/0.66 ! [Ax: produc410756839_state,Ay: produc410756839_state,Bx: produc410756839_state,By: produc410756839_state,R: set_Pr541394119_state,P: produc410756839_state > produc410756839_state > $o] :
% 0.29/0.66 ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Ax @ Ay ) @ ( produc2065881943_state @ Bx @ By ) ) @ ( transi152726506_state @ R ) )
% 0.29/0.66 => ( ( P @ Bx @ By )
% 0.29/0.66 => ( ! [A: produc410756839_state,B: produc410756839_state,Aa: produc410756839_state,Ba: produc410756839_state] :
% 0.29/0.66 ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ A @ B ) @ ( produc2065881943_state @ Aa @ Ba ) ) @ R )
% 0.29/0.66 => ( ( member284400400_state @ ( produc2049704791_state @ ( produc2065881943_state @ Aa @ Ba ) @ ( produc2065881943_state @ Bx @ By ) ) @ ( transi152726506_state @ R ) )
% 0.29/0.66 => ( ( P @ Aa @ Ba )
% 0.29/0.66 => ( P @ A @ B ) ) ) )
% 0.29/0.66 => ( P @ Ax @ Ay ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % converse_rtrancl_induct2
% 0.29/0.66 thf(fact_29_converse__rtrancl__induct2,axiom,
% 0.29/0.66 ! [Ax: produc2041926651_state,Ay: produc2041926651_state,Bx: produc2041926651_state,By: produc2041926651_state,R: set_Pr2096893127_state,P: produc2041926651_state > produc2041926651_state > $o] :
% 0.29/0.66 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Ax @ Ay ) @ ( produc1909270103_state @ Bx @ By ) ) @ ( transi463013610_state @ R ) )
% 0.29/0.66 => ( ( P @ Bx @ By )
% 0.29/0.66 => ( ! [A: produc2041926651_state,B: produc2041926651_state,Aa: produc2041926651_state,Ba: produc2041926651_state] :
% 0.29/0.66 ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ A @ B ) @ ( produc1909270103_state @ Aa @ Ba ) ) @ R )
% 0.29/0.66 => ( ( member512523024_state @ ( produc2065881943_state @ ( produc1909270103_state @ Aa @ Ba ) @ ( produc1909270103_state @ Bx @ By ) ) @ ( transi463013610_state @ R ) )
% 0.29/0.66 => ( ( P @ Aa @ Ba )
% 0.29/0.66 => ( P @ A @ B ) ) ) )
% 0.29/0.66 => ( P @ Ax @ Ay ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % converse_rtrancl_induct2
% 0.29/0.66 thf(fact_30_converse__rtrancl__induct2,axiom,
% 0.29/0.66 ! [Ax: list_com,Ay: state,Bx: list_com,By: state,R: set_Pr1165141447_state,P: list_com > state > $o] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Ax @ Ay ) @ ( produc1204172211_state @ Bx @ By ) ) @ ( transi1302705790_state @ R ) )
% 0.29/0.66 => ( ( P @ Bx @ By )
% 0.29/0.66 => ( ! [A: list_com,B: state,Aa: list_com,Ba: state] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ A @ B ) @ ( produc1204172211_state @ Aa @ Ba ) ) @ R )
% 0.29/0.66 => ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Aa @ Ba ) @ ( produc1204172211_state @ Bx @ By ) ) @ ( transi1302705790_state @ R ) )
% 0.29/0.66 => ( ( P @ Aa @ Ba )
% 0.29/0.66 => ( P @ A @ B ) ) ) )
% 0.29/0.66 => ( P @ Ax @ Ay ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % converse_rtrancl_induct2
% 0.29/0.66 thf(fact_31_exec1s__impl__execs,axiom,
% 0.29/0.66 ! [Cs2: list_com,S: state,T2: state] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs2 @ S ) @ ( produc1204172211_state @ nil_com @ T2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 0.29/0.66 => ( pHoare259243732_execs @ S @ Cs2 @ T2 ) ) ).
% 0.29/0.66
% 0.29/0.66 % exec1s_impl_execs
% 0.29/0.66 thf(fact_32_rtrancl__idemp,axiom,
% 0.29/0.66 ! [R: set_Pr541394119_state] :
% 0.29/0.66 ( ( transi152726506_state @ ( transi152726506_state @ R ) )
% 0.29/0.66 = ( transi152726506_state @ R ) ) ).
% 0.29/0.66
% 0.29/0.66 % rtrancl_idemp
% 0.29/0.66 thf(fact_33_rtrancl__idemp,axiom,
% 0.29/0.66 ! [R: set_Pr602326075st_com] :
% 0.29/0.66 ( ( transi436345274st_com @ ( transi436345274st_com @ R ) )
% 0.29/0.66 = ( transi436345274st_com @ R ) ) ).
% 0.29/0.66
% 0.29/0.66 % rtrancl_idemp
% 0.29/0.66 thf(fact_34_rtrancl__idemp,axiom,
% 0.29/0.66 ! [R: set_Pr1325664839_state] :
% 0.29/0.66 ( ( transi1965148016_state @ ( transi1965148016_state @ R ) )
% 0.29/0.66 = ( transi1965148016_state @ R ) ) ).
% 0.29/0.66
% 0.29/0.66 % rtrancl_idemp
% 0.29/0.66 thf(fact_35_rtrancl__idemp,axiom,
% 0.29/0.66 ! [R: set_Pr1142642759_state] :
% 0.29/0.66 ( ( transi339813252_state @ ( transi339813252_state @ R ) )
% 0.29/0.66 = ( transi339813252_state @ R ) ) ).
% 0.29/0.66
% 0.29/0.66 % rtrancl_idemp
% 0.29/0.66 thf(fact_36_rtrancl__idemp,axiom,
% 0.29/0.66 ! [R: set_Pr1822651163om_com] :
% 0.29/0.66 ( ( transi863150634cl_com @ ( transi863150634cl_com @ R ) )
% 0.29/0.66 = ( transi863150634cl_com @ R ) ) ).
% 0.29/0.66
% 0.29/0.66 % rtrancl_idemp
% 0.29/0.66 thf(fact_37_rtrancl__idemp,axiom,
% 0.29/0.66 ! [R: set_Pr1165141447_state] :
% 0.29/0.66 ( ( transi1302705790_state @ ( transi1302705790_state @ R ) )
% 0.29/0.66 = ( transi1302705790_state @ R ) ) ).
% 0.29/0.66
% 0.29/0.66 % rtrancl_idemp
% 0.29/0.66 thf(fact_38_rtrancl__idemp,axiom,
% 0.29/0.66 ! [R: set_Pr2096893127_state] :
% 0.29/0.66 ( ( transi463013610_state @ ( transi463013610_state @ R ) )
% 0.29/0.66 = ( transi463013610_state @ R ) ) ).
% 0.29/0.66
% 0.29/0.66 % rtrancl_idemp
% 0.29/0.66 thf(fact_39_r__into__rtrancl,axiom,
% 0.29/0.66 ! [P2: produc2046512871_state,R: set_Pr541394119_state] :
% 0.29/0.66 ( ( member284400400_state @ P2 @ R )
% 0.29/0.66 => ( member284400400_state @ P2 @ ( transi152726506_state @ R ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % r_into_rtrancl
% 0.29/0.66 thf(fact_40_r__into__rtrancl,axiom,
% 0.29/0.66 ! [P2: produc258871771st_com,R: set_Pr602326075st_com] :
% 0.29/0.66 ( ( member32358020st_com @ P2 @ R )
% 0.29/0.66 => ( member32358020st_com @ P2 @ ( transi436345274st_com @ R ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % r_into_rtrancl
% 0.29/0.66 thf(fact_41_r__into__rtrancl,axiom,
% 0.29/0.66 ! [P2: produc1586269031_state,R: set_Pr1325664839_state] :
% 0.29/0.66 ( ( member423306384_state @ P2 @ R )
% 0.29/0.66 => ( member423306384_state @ P2 @ ( transi1965148016_state @ R ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % r_into_rtrancl
% 0.29/0.66 thf(fact_42_r__into__rtrancl,axiom,
% 0.29/0.66 ! [P2: produc1225889383_state,R: set_Pr1142642759_state] :
% 0.29/0.66 ( ( member1267359376_state @ P2 @ R )
% 0.29/0.66 => ( member1267359376_state @ P2 @ ( transi339813252_state @ R ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % r_into_rtrancl
% 0.29/0.66 thf(fact_43_r__into__rtrancl,axiom,
% 0.29/0.66 ! [P2: product_prod_com_com,R: set_Pr1822651163om_com] :
% 0.29/0.66 ( ( member1333916004om_com @ P2 @ R )
% 0.29/0.66 => ( member1333916004om_com @ P2 @ ( transi863150634cl_com @ R ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % r_into_rtrancl
% 0.29/0.66 thf(fact_44_r__into__rtrancl,axiom,
% 0.29/0.66 ! [P2: produc410756839_state,R: set_Pr1165141447_state] :
% 0.29/0.66 ( ( member1069318160_state @ P2 @ R )
% 0.29/0.66 => ( member1069318160_state @ P2 @ ( transi1302705790_state @ R ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % r_into_rtrancl
% 0.29/0.66 thf(fact_45_r__into__rtrancl,axiom,
% 0.29/0.66 ! [P2: produc186437863_state,R: set_Pr2096893127_state] :
% 0.29/0.66 ( ( member512523024_state @ P2 @ R )
% 0.29/0.66 => ( member512523024_state @ P2 @ ( transi463013610_state @ R ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % r_into_rtrancl
% 0.29/0.66 thf(fact_46_list_Oinject,axiom,
% 0.29/0.66 ! [X21: produc2041926651_state,X22: list_P1040014977_state,Y21: produc2041926651_state,Y22: list_P1040014977_state] :
% 0.29/0.66 ( ( ( cons_P465369265_state @ X21 @ X22 )
% 0.29/0.66 = ( cons_P465369265_state @ Y21 @ Y22 ) )
% 0.29/0.66 = ( ( X21 = Y21 )
% 0.29/0.66 & ( X22 = Y22 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % list.inject
% 0.29/0.66 thf(fact_47_list_Oinject,axiom,
% 0.29/0.66 ! [X21: state,X22: list_state,Y21: state,Y22: list_state] :
% 0.29/0.66 ( ( ( cons_state @ X21 @ X22 )
% 0.29/0.66 = ( cons_state @ Y21 @ Y22 ) )
% 0.29/0.66 = ( ( X21 = Y21 )
% 0.29/0.66 & ( X22 = Y22 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % list.inject
% 0.29/0.66 thf(fact_48_list_Oinject,axiom,
% 0.29/0.66 ! [X21: list_com,X22: list_list_com,Y21: list_com,Y22: list_list_com] :
% 0.29/0.66 ( ( ( cons_list_com @ X21 @ X22 )
% 0.29/0.66 = ( cons_list_com @ Y21 @ Y22 ) )
% 0.29/0.66 = ( ( X21 = Y21 )
% 0.29/0.66 & ( X22 = Y22 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % list.inject
% 0.29/0.66 thf(fact_49_list_Oinject,axiom,
% 0.29/0.66 ! [X21: produc410756839_state > nat,X22: list_P1627643054te_nat,Y21: produc410756839_state > nat,Y22: list_P1627643054te_nat] :
% 0.29/0.66 ( ( ( cons_P1631380062te_nat @ X21 @ X22 )
% 0.29/0.66 = ( cons_P1631380062te_nat @ Y21 @ Y22 ) )
% 0.29/0.66 = ( ( X21 = Y21 )
% 0.29/0.66 & ( X22 = Y22 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % list.inject
% 0.29/0.66 thf(fact_50_list_Oinject,axiom,
% 0.29/0.66 ! [X21: produc2041926651_state > nat,X22: list_P1178430914te_nat,Y21: produc2041926651_state > nat,Y22: list_P1178430914te_nat] :
% 0.29/0.66 ( ( ( cons_P1821701106te_nat @ X21 @ X22 )
% 0.29/0.66 = ( cons_P1821701106te_nat @ Y21 @ Y22 ) )
% 0.29/0.66 = ( ( X21 = Y21 )
% 0.29/0.66 & ( X22 = Y22 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % list.inject
% 0.29/0.66 thf(fact_51_list_Oinject,axiom,
% 0.29/0.66 ! [X21: com,X22: list_com,Y21: com,Y22: list_com] :
% 0.29/0.66 ( ( ( cons_com @ X21 @ X22 )
% 0.29/0.66 = ( cons_com @ Y21 @ Y22 ) )
% 0.29/0.66 = ( ( X21 = Y21 )
% 0.29/0.66 & ( X22 = Y22 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % list.inject
% 0.29/0.66 thf(fact_52_prod_Oinject,axiom,
% 0.29/0.66 ! [X1: list_com,X2: list_com,Y1: list_com,Y2: list_com] :
% 0.29/0.66 ( ( ( produc1307105171st_com @ X1 @ X2 )
% 0.29/0.66 = ( produc1307105171st_com @ Y1 @ Y2 ) )
% 0.29/0.66 = ( ( X1 = Y1 )
% 0.29/0.66 & ( X2 = Y2 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % prod.inject
% 0.29/0.66 thf(fact_53_prod_Oinject,axiom,
% 0.29/0.66 ! [X1: list_list_com,X2: list_state,Y1: list_list_com,Y2: list_state] :
% 0.29/0.66 ( ( ( produc1742567891_state @ X1 @ X2 )
% 0.29/0.66 = ( produc1742567891_state @ Y1 @ Y2 ) )
% 0.29/0.66 = ( ( X1 = Y1 )
% 0.29/0.66 & ( X2 = Y2 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % prod.inject
% 0.29/0.66 thf(fact_54_prod_Oinject,axiom,
% 0.29/0.66 ! [X1: com > com > $o,X2: list_com,Y1: com > com > $o,Y2: list_com] :
% 0.29/0.66 ( ( ( produc1914379986st_com @ X1 @ X2 )
% 0.29/0.66 = ( produc1914379986st_com @ Y1 @ Y2 ) )
% 0.29/0.66 = ( ( X1 = Y1 )
% 0.29/0.66 & ( X2 = Y2 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % prod.inject
% 0.29/0.66 thf(fact_55_prod_Oinject,axiom,
% 0.29/0.66 ! [X1: produc2041926651_state,X2: produc2041926651_state,Y1: produc2041926651_state,Y2: produc2041926651_state] :
% 0.29/0.66 ( ( ( produc1909270103_state @ X1 @ X2 )
% 0.29/0.66 = ( produc1909270103_state @ Y1 @ Y2 ) )
% 0.29/0.66 = ( ( X1 = Y1 )
% 0.29/0.66 & ( X2 = Y2 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % prod.inject
% 0.29/0.66 thf(fact_56_prod_Oinject,axiom,
% 0.29/0.66 ! [X1: list_com,X2: state,Y1: list_com,Y2: state] :
% 0.29/0.66 ( ( ( produc1204172211_state @ X1 @ X2 )
% 0.29/0.66 = ( produc1204172211_state @ Y1 @ Y2 ) )
% 0.29/0.66 = ( ( X1 = Y1 )
% 0.29/0.66 & ( X2 = Y2 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % prod.inject
% 0.29/0.66 thf(fact_57_prod_Oinject,axiom,
% 0.29/0.66 ! [X1: produc410756839_state,X2: produc410756839_state,Y1: produc410756839_state,Y2: produc410756839_state] :
% 0.29/0.66 ( ( ( produc2065881943_state @ X1 @ X2 )
% 0.29/0.66 = ( produc2065881943_state @ Y1 @ Y2 ) )
% 0.29/0.66 = ( ( X1 = Y1 )
% 0.29/0.66 & ( X2 = Y2 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % prod.inject
% 0.29/0.66 thf(fact_58_old_Oprod_Oinject,axiom,
% 0.29/0.66 ! [A2: produc2041926651_state,B2: produc2041926651_state,A3: produc2041926651_state,B3: produc2041926651_state] :
% 0.29/0.66 ( ( ( produc1909270103_state @ A2 @ B2 )
% 0.29/0.66 = ( produc1909270103_state @ A3 @ B3 ) )
% 0.29/0.66 = ( ( A2 = A3 )
% 0.29/0.66 & ( B2 = B3 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % old.prod.inject
% 0.29/0.66 thf(fact_59_old_Oprod_Oinject,axiom,
% 0.29/0.66 ! [A2: list_com,B2: state,A3: list_com,B3: state] :
% 0.29/0.66 ( ( ( produc1204172211_state @ A2 @ B2 )
% 0.29/0.66 = ( produc1204172211_state @ A3 @ B3 ) )
% 0.29/0.66 = ( ( A2 = A3 )
% 0.29/0.66 & ( B2 = B3 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % old.prod.inject
% 0.29/0.66 thf(fact_60_old_Oprod_Oinject,axiom,
% 0.29/0.66 ! [A2: produc410756839_state,B2: produc410756839_state,A3: produc410756839_state,B3: produc410756839_state] :
% 0.29/0.66 ( ( ( produc2065881943_state @ A2 @ B2 )
% 0.29/0.66 = ( produc2065881943_state @ A3 @ B3 ) )
% 0.29/0.66 = ( ( A2 = A3 )
% 0.29/0.66 & ( B2 = B3 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % old.prod.inject
% 0.29/0.66 thf(fact_61_prod__cases3,axiom,
% 0.29/0.66 ! [Y: produc410756839_state] :
% 0.29/0.66 ~ ! [A: produc2041926651_state,B: list_com,C2: state] :
% 0.29/0.66 ( Y
% 0.29/0.66 != ( produc1909270103_state @ A @ ( produc1204172211_state @ B @ C2 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % prod_cases3
% 0.29/0.66 thf(fact_62_prod__cases3,axiom,
% 0.29/0.66 ! [Y: produc186437863_state] :
% 0.29/0.66 ~ ! [A: produc410756839_state,B: produc2041926651_state,C2: produc2041926651_state] :
% 0.29/0.66 ( Y
% 0.29/0.66 != ( produc2065881943_state @ A @ ( produc1909270103_state @ B @ C2 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % prod_cases3
% 0.29/0.66 thf(fact_63_prod__cases4,axiom,
% 0.29/0.66 ! [Y: produc186437863_state] :
% 0.29/0.66 ~ ! [A: produc410756839_state,B: produc2041926651_state,C2: list_com,D: state] :
% 0.29/0.66 ( Y
% 0.29/0.66 != ( produc2065881943_state @ A @ ( produc1909270103_state @ B @ ( produc1204172211_state @ C2 @ D ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % prod_cases4
% 0.29/0.66 thf(fact_64_successively_Ocases,axiom,
% 0.29/0.66 ! [X: produc2058209240st_com] :
% 0.29/0.66 ( ! [P3: com > com > $o] :
% 0.29/0.66 ( X
% 0.29/0.66 != ( produc1914379986st_com @ P3 @ nil_com ) )
% 0.29/0.66 => ( ! [P3: com > com > $o,X3: com] :
% 0.29/0.66 ( X
% 0.29/0.66 != ( produc1914379986st_com @ P3 @ ( cons_com @ X3 @ nil_com ) ) )
% 0.29/0.66 => ~ ! [P3: com > com > $o,X3: com,Y3: com,Xs: list_com] :
% 0.29/0.66 ( X
% 0.29/0.66 != ( produc1914379986st_com @ P3 @ ( cons_com @ X3 @ ( cons_com @ Y3 @ Xs ) ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % successively.cases
% 0.29/0.66 thf(fact_65_sorted__wrt_Ocases,axiom,
% 0.29/0.66 ! [X: produc2058209240st_com] :
% 0.29/0.66 ( ! [P3: com > com > $o] :
% 0.29/0.66 ( X
% 0.29/0.66 != ( produc1914379986st_com @ P3 @ nil_com ) )
% 0.29/0.66 => ~ ! [P3: com > com > $o,X3: com,Ys: list_com] :
% 0.29/0.66 ( X
% 0.29/0.66 != ( produc1914379986st_com @ P3 @ ( cons_com @ X3 @ Ys ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % sorted_wrt.cases
% 0.29/0.66 thf(fact_66_shuffles_Ocases,axiom,
% 0.29/0.66 ! [X: produc258871771st_com] :
% 0.29/0.66 ( ! [Ys: list_com] :
% 0.29/0.66 ( X
% 0.29/0.66 != ( produc1307105171st_com @ nil_com @ Ys ) )
% 0.29/0.66 => ( ! [Xs: list_com] :
% 0.29/0.66 ( X
% 0.29/0.66 != ( produc1307105171st_com @ Xs @ nil_com ) )
% 0.29/0.66 => ~ ! [X3: com,Xs: list_com,Y3: com,Ys: list_com] :
% 0.29/0.66 ( X
% 0.29/0.66 != ( produc1307105171st_com @ ( cons_com @ X3 @ Xs ) @ ( cons_com @ Y3 @ Ys ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % shuffles.cases
% 0.29/0.66 thf(fact_67_splice_Ocases,axiom,
% 0.29/0.66 ! [X: produc258871771st_com] :
% 0.29/0.66 ( ! [Ys: list_com] :
% 0.29/0.66 ( X
% 0.29/0.66 != ( produc1307105171st_com @ nil_com @ Ys ) )
% 0.29/0.66 => ~ ! [X3: com,Xs: list_com,Ys: list_com] :
% 0.29/0.66 ( X
% 0.29/0.66 != ( produc1307105171st_com @ ( cons_com @ X3 @ Xs ) @ Ys ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % splice.cases
% 0.29/0.66 thf(fact_68_execs_Ointros_I1_J,axiom,
% 0.29/0.66 ! [S: state] : ( pHoare259243732_execs @ S @ nil_com @ S ) ).
% 0.29/0.66
% 0.29/0.66 % execs.intros(1)
% 0.29/0.66 thf(fact_69_old_Oprod_Oinducts,axiom,
% 0.29/0.66 ! [P: produc410756839_state > $o,Prod: produc410756839_state] :
% 0.29/0.66 ( ! [A: produc2041926651_state,B: produc2041926651_state] : ( P @ ( produc1909270103_state @ A @ B ) )
% 0.29/0.66 => ( P @ Prod ) ) ).
% 0.29/0.66
% 0.29/0.66 % old.prod.inducts
% 0.29/0.66 thf(fact_70_old_Oprod_Oinducts,axiom,
% 0.29/0.66 ! [P: produc2041926651_state > $o,Prod: produc2041926651_state] :
% 0.29/0.66 ( ! [A: list_com,B: state] : ( P @ ( produc1204172211_state @ A @ B ) )
% 0.29/0.66 => ( P @ Prod ) ) ).
% 0.29/0.66
% 0.29/0.66 % old.prod.inducts
% 0.29/0.66 thf(fact_71_old_Oprod_Oinducts,axiom,
% 0.29/0.66 ! [P: produc186437863_state > $o,Prod: produc186437863_state] :
% 0.29/0.66 ( ! [A: produc410756839_state,B: produc410756839_state] : ( P @ ( produc2065881943_state @ A @ B ) )
% 0.29/0.66 => ( P @ Prod ) ) ).
% 0.29/0.66
% 0.29/0.66 % old.prod.inducts
% 0.29/0.66 thf(fact_72_old_Oprod_Oexhaust,axiom,
% 0.29/0.66 ! [Y: produc410756839_state] :
% 0.29/0.66 ~ ! [A: produc2041926651_state,B: produc2041926651_state] :
% 0.29/0.66 ( Y
% 0.29/0.66 != ( produc1909270103_state @ A @ B ) ) ).
% 0.29/0.66
% 0.29/0.66 % old.prod.exhaust
% 0.29/0.66 thf(fact_73_old_Oprod_Oexhaust,axiom,
% 0.29/0.66 ! [Y: produc2041926651_state] :
% 0.29/0.66 ~ ! [A: list_com,B: state] :
% 0.29/0.66 ( Y
% 0.29/0.66 != ( produc1204172211_state @ A @ B ) ) ).
% 0.29/0.66
% 0.29/0.66 % old.prod.exhaust
% 0.29/0.66 thf(fact_74_old_Oprod_Oexhaust,axiom,
% 0.29/0.66 ! [Y: produc186437863_state] :
% 0.29/0.66 ~ ! [A: produc410756839_state,B: produc410756839_state] :
% 0.29/0.66 ( Y
% 0.29/0.66 != ( produc2065881943_state @ A @ B ) ) ).
% 0.29/0.66
% 0.29/0.66 % old.prod.exhaust
% 0.29/0.66 thf(fact_75_Pair__inject,axiom,
% 0.29/0.66 ! [A2: produc2041926651_state,B2: produc2041926651_state,A3: produc2041926651_state,B3: produc2041926651_state] :
% 0.29/0.66 ( ( ( produc1909270103_state @ A2 @ B2 )
% 0.29/0.66 = ( produc1909270103_state @ A3 @ B3 ) )
% 0.29/0.66 => ~ ( ( A2 = A3 )
% 0.29/0.66 => ( B2 != B3 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % Pair_inject
% 0.29/0.66 thf(fact_76_Pair__inject,axiom,
% 0.29/0.66 ! [A2: list_com,B2: state,A3: list_com,B3: state] :
% 0.29/0.66 ( ( ( produc1204172211_state @ A2 @ B2 )
% 0.29/0.66 = ( produc1204172211_state @ A3 @ B3 ) )
% 0.29/0.66 => ~ ( ( A2 = A3 )
% 0.29/0.66 => ( B2 != B3 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % Pair_inject
% 0.29/0.66 thf(fact_77_Pair__inject,axiom,
% 0.29/0.66 ! [A2: produc410756839_state,B2: produc410756839_state,A3: produc410756839_state,B3: produc410756839_state] :
% 0.29/0.66 ( ( ( produc2065881943_state @ A2 @ B2 )
% 0.29/0.66 = ( produc2065881943_state @ A3 @ B3 ) )
% 0.29/0.66 => ~ ( ( A2 = A3 )
% 0.29/0.66 => ( B2 != B3 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % Pair_inject
% 0.29/0.66 thf(fact_78_prod__cases,axiom,
% 0.29/0.66 ! [P: produc410756839_state > $o,P2: produc410756839_state] :
% 0.29/0.66 ( ! [A: produc2041926651_state,B: produc2041926651_state] : ( P @ ( produc1909270103_state @ A @ B ) )
% 0.29/0.66 => ( P @ P2 ) ) ).
% 0.29/0.66
% 0.29/0.66 % prod_cases
% 0.29/0.66 thf(fact_79_prod__cases,axiom,
% 0.29/0.66 ! [P: produc2041926651_state > $o,P2: produc2041926651_state] :
% 0.29/0.66 ( ! [A: list_com,B: state] : ( P @ ( produc1204172211_state @ A @ B ) )
% 0.29/0.66 => ( P @ P2 ) ) ).
% 0.29/0.66
% 0.29/0.66 % prod_cases
% 0.29/0.66 thf(fact_80_prod__cases,axiom,
% 0.29/0.66 ! [P: produc186437863_state > $o,P2: produc186437863_state] :
% 0.29/0.66 ( ! [A: produc410756839_state,B: produc410756839_state] : ( P @ ( produc2065881943_state @ A @ B ) )
% 0.29/0.66 => ( P @ P2 ) ) ).
% 0.29/0.66
% 0.29/0.66 % prod_cases
% 0.29/0.66 thf(fact_81_surj__pair,axiom,
% 0.29/0.66 ! [P2: produc410756839_state] :
% 0.29/0.66 ? [X3: produc2041926651_state,Y3: produc2041926651_state] :
% 0.29/0.66 ( P2
% 0.29/0.66 = ( produc1909270103_state @ X3 @ Y3 ) ) ).
% 0.29/0.66
% 0.29/0.66 % surj_pair
% 0.29/0.66 thf(fact_82_surj__pair,axiom,
% 0.29/0.66 ! [P2: produc2041926651_state] :
% 0.29/0.66 ? [X3: list_com,Y3: state] :
% 0.29/0.66 ( P2
% 0.29/0.66 = ( produc1204172211_state @ X3 @ Y3 ) ) ).
% 0.29/0.66
% 0.29/0.66 % surj_pair
% 0.29/0.66 thf(fact_83_surj__pair,axiom,
% 0.29/0.66 ! [P2: produc186437863_state] :
% 0.29/0.66 ? [X3: produc410756839_state,Y3: produc410756839_state] :
% 0.29/0.66 ( P2
% 0.29/0.66 = ( produc2065881943_state @ X3 @ Y3 ) ) ).
% 0.29/0.66
% 0.29/0.66 % surj_pair
% 0.29/0.66 thf(fact_84_not__Cons__self2,axiom,
% 0.29/0.66 ! [X: com,Xs2: list_com] :
% 0.29/0.66 ( ( cons_com @ X @ Xs2 )
% 0.29/0.66 != Xs2 ) ).
% 0.29/0.66
% 0.29/0.66 % not_Cons_self2
% 0.29/0.66 thf(fact_85_execs_Ointros_I2_J,axiom,
% 0.29/0.66 ! [S: state,C: com,T2: state,Cs2: list_com,U: state] :
% 0.29/0.66 ( ( exec @ S @ C @ T2 )
% 0.29/0.66 => ( ( pHoare259243732_execs @ T2 @ Cs2 @ U )
% 0.29/0.66 => ( pHoare259243732_execs @ S @ ( cons_com @ C @ Cs2 ) @ U ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % execs.intros(2)
% 0.29/0.66 thf(fact_86_map__tailrec__rev_Oinduct,axiom,
% 0.29/0.66 ! [P: ( com > com ) > list_com > list_com > $o,A0: com > com,A1: list_com,A22: list_com] :
% 0.29/0.66 ( ! [F: com > com,X_1: list_com] : ( P @ F @ nil_com @ X_1 )
% 0.29/0.66 => ( ! [F: com > com,A: com,As: list_com,Bs: list_com] :
% 0.29/0.66 ( ( P @ F @ As @ ( cons_com @ ( F @ A ) @ Bs ) )
% 0.29/0.66 => ( P @ F @ ( cons_com @ A @ As ) @ Bs ) )
% 0.29/0.66 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % map_tailrec_rev.induct
% 0.29/0.66 thf(fact_87_list__nonempty__induct,axiom,
% 0.29/0.66 ! [Xs2: list_com,P: list_com > $o] :
% 0.29/0.66 ( ( Xs2 != nil_com )
% 0.29/0.66 => ( ! [X3: com] : ( P @ ( cons_com @ X3 @ nil_com ) )
% 0.29/0.66 => ( ! [X3: com,Xs: list_com] :
% 0.29/0.66 ( ( Xs != nil_com )
% 0.29/0.66 => ( ( P @ Xs )
% 0.29/0.66 => ( P @ ( cons_com @ X3 @ Xs ) ) ) )
% 0.29/0.66 => ( P @ Xs2 ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % list_nonempty_induct
% 0.29/0.66 thf(fact_88_successively_Oinduct,axiom,
% 0.29/0.66 ! [P: ( com > com > $o ) > list_com > $o,A0: com > com > $o,A1: list_com] :
% 0.29/0.66 ( ! [P3: com > com > $o] : ( P @ P3 @ nil_com )
% 0.29/0.66 => ( ! [P3: com > com > $o,X3: com] : ( P @ P3 @ ( cons_com @ X3 @ nil_com ) )
% 0.29/0.66 => ( ! [P3: com > com > $o,X3: com,Y3: com,Xs: list_com] :
% 0.29/0.66 ( ( P @ P3 @ ( cons_com @ Y3 @ Xs ) )
% 0.29/0.66 => ( P @ P3 @ ( cons_com @ X3 @ ( cons_com @ Y3 @ Xs ) ) ) )
% 0.29/0.66 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % successively.induct
% 0.29/0.66 thf(fact_89_remdups__adj_Oinduct,axiom,
% 0.29/0.66 ! [P: list_com > $o,A0: list_com] :
% 0.29/0.66 ( ( P @ nil_com )
% 0.29/0.66 => ( ! [X3: com] : ( P @ ( cons_com @ X3 @ nil_com ) )
% 0.29/0.66 => ( ! [X3: com,Y3: com,Xs: list_com] :
% 0.29/0.66 ( ( ( X3 = Y3 )
% 0.29/0.66 => ( P @ ( cons_com @ X3 @ Xs ) ) )
% 0.29/0.66 => ( ( ( X3 != Y3 )
% 0.29/0.66 => ( P @ ( cons_com @ Y3 @ Xs ) ) )
% 0.29/0.66 => ( P @ ( cons_com @ X3 @ ( cons_com @ Y3 @ Xs ) ) ) ) )
% 0.29/0.66 => ( P @ A0 ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % remdups_adj.induct
% 0.29/0.66 thf(fact_90_sorted__wrt_Oinduct,axiom,
% 0.29/0.66 ! [P: ( com > com > $o ) > list_com > $o,A0: com > com > $o,A1: list_com] :
% 0.29/0.66 ( ! [P3: com > com > $o] : ( P @ P3 @ nil_com )
% 0.29/0.66 => ( ! [P3: com > com > $o,X3: com,Ys: list_com] :
% 0.29/0.66 ( ( P @ P3 @ Ys )
% 0.29/0.66 => ( P @ P3 @ ( cons_com @ X3 @ Ys ) ) )
% 0.29/0.66 => ( P @ A0 @ A1 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % sorted_wrt.induct
% 0.29/0.66 thf(fact_91_remdups__adj_Ocases,axiom,
% 0.29/0.66 ! [X: list_com] :
% 0.29/0.66 ( ( X != nil_com )
% 0.29/0.66 => ( ! [X3: com] :
% 0.29/0.66 ( X
% 0.29/0.66 != ( cons_com @ X3 @ nil_com ) )
% 0.29/0.66 => ~ ! [X3: com,Y3: com,Xs: list_com] :
% 0.29/0.66 ( X
% 0.29/0.66 != ( cons_com @ X3 @ ( cons_com @ Y3 @ Xs ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % remdups_adj.cases
% 0.29/0.66 thf(fact_92_transpose_Ocases,axiom,
% 0.29/0.66 ! [X: list_list_com] :
% 0.29/0.66 ( ( X != nil_list_com )
% 0.29/0.66 => ( ! [Xss: list_list_com] :
% 0.29/0.66 ( X
% 0.29/0.66 != ( cons_list_com @ nil_com @ Xss ) )
% 0.29/0.66 => ~ ! [X3: com,Xs: list_com,Xss: list_list_com] :
% 0.29/0.66 ( X
% 0.29/0.66 != ( cons_list_com @ ( cons_com @ X3 @ Xs ) @ Xss ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % transpose.cases
% 0.29/0.66 thf(fact_93_shuffles_Oinduct,axiom,
% 0.29/0.66 ! [P: list_com > list_com > $o,A0: list_com,A1: list_com] :
% 0.29/0.66 ( ! [X_1: list_com] : ( P @ nil_com @ X_1 )
% 0.29/0.66 => ( ! [Xs: list_com] : ( P @ Xs @ nil_com )
% 0.29/0.66 => ( ! [X3: com,Xs: list_com,Y3: com,Ys: list_com] :
% 0.29/0.66 ( ( P @ Xs @ ( cons_com @ Y3 @ Ys ) )
% 0.29/0.66 => ( ( P @ ( cons_com @ X3 @ Xs ) @ Ys )
% 0.29/0.66 => ( P @ ( cons_com @ X3 @ Xs ) @ ( cons_com @ Y3 @ Ys ) ) ) )
% 0.29/0.66 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % shuffles.induct
% 0.29/0.66 thf(fact_94_mem__Collect__eq,axiom,
% 0.29/0.66 ! [A2: produc410756839_state,P: produc410756839_state > $o] :
% 0.29/0.66 ( ( member1069318160_state @ A2 @ ( collec300063826_state @ P ) )
% 0.29/0.66 = ( P @ A2 ) ) ).
% 0.29/0.66
% 0.29/0.66 % mem_Collect_eq
% 0.29/0.66 thf(fact_95_mem__Collect__eq,axiom,
% 0.29/0.66 ! [A2: state,P: state > $o] :
% 0.29/0.66 ( ( member_state @ A2 @ ( collect_state @ P ) )
% 0.29/0.66 = ( P @ A2 ) ) ).
% 0.29/0.66
% 0.29/0.66 % mem_Collect_eq
% 0.29/0.66 thf(fact_96_mem__Collect__eq,axiom,
% 0.29/0.66 ! [A2: produc186437863_state,P: produc186437863_state > $o] :
% 0.29/0.66 ( ( member512523024_state @ A2 @ ( collec489924946_state @ P ) )
% 0.29/0.66 = ( P @ A2 ) ) ).
% 0.29/0.66
% 0.29/0.66 % mem_Collect_eq
% 0.29/0.66 thf(fact_97_Collect__mem__eq,axiom,
% 0.29/0.66 ! [A4: set_Pr1165141447_state] :
% 0.29/0.66 ( ( collec300063826_state
% 0.29/0.66 @ ^ [X4: produc410756839_state] : ( member1069318160_state @ X4 @ A4 ) )
% 0.29/0.66 = A4 ) ).
% 0.29/0.66
% 0.29/0.66 % Collect_mem_eq
% 0.29/0.66 thf(fact_98_Collect__mem__eq,axiom,
% 0.29/0.66 ! [A4: set_state] :
% 0.29/0.66 ( ( collect_state
% 0.29/0.66 @ ^ [X4: state] : ( member_state @ X4 @ A4 ) )
% 0.29/0.66 = A4 ) ).
% 0.29/0.66
% 0.29/0.66 % Collect_mem_eq
% 0.29/0.66 thf(fact_99_Collect__mem__eq,axiom,
% 0.29/0.66 ! [A4: set_Pr2096893127_state] :
% 0.29/0.66 ( ( collec489924946_state
% 0.29/0.66 @ ^ [X4: produc186437863_state] : ( member512523024_state @ X4 @ A4 ) )
% 0.29/0.66 = A4 ) ).
% 0.29/0.66
% 0.29/0.66 % Collect_mem_eq
% 0.29/0.66 thf(fact_100_induct__list012,axiom,
% 0.29/0.66 ! [P: list_com > $o,Xs2: list_com] :
% 0.29/0.66 ( ( P @ nil_com )
% 0.29/0.66 => ( ! [X3: com] : ( P @ ( cons_com @ X3 @ nil_com ) )
% 0.29/0.66 => ( ! [X3: com,Y3: com,Zs: list_com] :
% 0.29/0.66 ( ( P @ Zs )
% 0.29/0.66 => ( ( P @ ( cons_com @ Y3 @ Zs ) )
% 0.29/0.66 => ( P @ ( cons_com @ X3 @ ( cons_com @ Y3 @ Zs ) ) ) ) )
% 0.29/0.66 => ( P @ Xs2 ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % induct_list012
% 0.29/0.66 thf(fact_101_splice_Oinduct,axiom,
% 0.29/0.66 ! [P: list_com > list_com > $o,A0: list_com,A1: list_com] :
% 0.29/0.66 ( ! [X_1: list_com] : ( P @ nil_com @ X_1 )
% 0.29/0.66 => ( ! [X3: com,Xs: list_com,Ys: list_com] :
% 0.29/0.66 ( ( P @ Ys @ Xs )
% 0.29/0.66 => ( P @ ( cons_com @ X3 @ Xs ) @ Ys ) )
% 0.29/0.66 => ( P @ A0 @ A1 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % splice.induct
% 0.29/0.66 thf(fact_102_list__induct2_H,axiom,
% 0.29/0.66 ! [P: list_com > list_com > $o,Xs2: list_com,Ys2: list_com] :
% 0.29/0.66 ( ( P @ nil_com @ nil_com )
% 0.29/0.66 => ( ! [X3: com,Xs: list_com] : ( P @ ( cons_com @ X3 @ Xs ) @ nil_com )
% 0.29/0.66 => ( ! [Y3: com,Ys: list_com] : ( P @ nil_com @ ( cons_com @ Y3 @ Ys ) )
% 0.29/0.66 => ( ! [X3: com,Xs: list_com,Y3: com,Ys: list_com] :
% 0.29/0.66 ( ( P @ Xs @ Ys )
% 0.29/0.66 => ( P @ ( cons_com @ X3 @ Xs ) @ ( cons_com @ Y3 @ Ys ) ) )
% 0.29/0.66 => ( P @ Xs2 @ Ys2 ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % list_induct2'
% 0.29/0.66 thf(fact_103_neq__Nil__conv,axiom,
% 0.29/0.66 ! [Xs2: list_com] :
% 0.29/0.66 ( ( Xs2 != nil_com )
% 0.29/0.66 = ( ? [Y4: com,Ys3: list_com] :
% 0.29/0.66 ( Xs2
% 0.29/0.66 = ( cons_com @ Y4 @ Ys3 ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % neq_Nil_conv
% 0.29/0.66 thf(fact_104_list_Oinducts,axiom,
% 0.29/0.66 ! [P: list_com > $o,List: list_com] :
% 0.29/0.66 ( ( P @ nil_com )
% 0.29/0.66 => ( ! [X12: com,X23: list_com] :
% 0.29/0.66 ( ( P @ X23 )
% 0.29/0.66 => ( P @ ( cons_com @ X12 @ X23 ) ) )
% 0.29/0.66 => ( P @ List ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % list.inducts
% 0.29/0.66 thf(fact_105_list_Oexhaust,axiom,
% 0.29/0.66 ! [Y: list_com] :
% 0.29/0.66 ( ( Y != nil_com )
% 0.29/0.66 => ~ ! [X212: com,X222: list_com] :
% 0.29/0.66 ( Y
% 0.29/0.66 != ( cons_com @ X212 @ X222 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % list.exhaust
% 0.29/0.66 thf(fact_106_list_OdiscI,axiom,
% 0.29/0.66 ! [List: list_com,X21: com,X22: list_com] :
% 0.29/0.66 ( ( List
% 0.29/0.66 = ( cons_com @ X21 @ X22 ) )
% 0.29/0.66 => ( List != nil_com ) ) ).
% 0.29/0.66
% 0.29/0.66 % list.discI
% 0.29/0.66 thf(fact_107_list_Odistinct_I1_J,axiom,
% 0.29/0.66 ! [X21: com,X22: list_com] :
% 0.29/0.66 ( nil_com
% 0.29/0.66 != ( cons_com @ X21 @ X22 ) ) ).
% 0.29/0.66
% 0.29/0.66 % list.distinct(1)
% 0.29/0.66 thf(fact_108_execs_Oinducts,axiom,
% 0.29/0.66 ! [X1: state,X2: list_com,X32: state,P: state > list_com > state > $o] :
% 0.29/0.66 ( ( pHoare259243732_execs @ X1 @ X2 @ X32 )
% 0.29/0.66 => ( ! [S3: state] : ( P @ S3 @ nil_com @ S3 )
% 0.29/0.66 => ( ! [S3: state,C2: com,T3: state,Cs3: list_com,U2: state] :
% 0.29/0.66 ( ( exec @ S3 @ C2 @ T3 )
% 0.29/0.66 => ( ( pHoare259243732_execs @ T3 @ Cs3 @ U2 )
% 0.29/0.66 => ( ( P @ T3 @ Cs3 @ U2 )
% 0.29/0.66 => ( P @ S3 @ ( cons_com @ C2 @ Cs3 ) @ U2 ) ) ) )
% 0.29/0.66 => ( P @ X1 @ X2 @ X32 ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % execs.inducts
% 0.29/0.66 thf(fact_109_execs_Osimps,axiom,
% 0.29/0.66 ( pHoare259243732_execs
% 0.29/0.66 = ( ^ [A12: state,A23: list_com,A32: state] :
% 0.29/0.66 ( ? [S4: state] :
% 0.29/0.66 ( ( A12 = S4 )
% 0.29/0.66 & ( A23 = nil_com )
% 0.29/0.66 & ( A32 = S4 ) )
% 0.29/0.66 | ? [S4: state,C3: com,T: state,Cs4: list_com,U3: state] :
% 0.29/0.66 ( ( A12 = S4 )
% 0.29/0.66 & ( A23
% 0.29/0.66 = ( cons_com @ C3 @ Cs4 ) )
% 0.29/0.66 & ( A32 = U3 )
% 0.29/0.66 & ( exec @ S4 @ C3 @ T )
% 0.29/0.66 & ( pHoare259243732_execs @ T @ Cs4 @ U3 ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % execs.simps
% 0.29/0.66 thf(fact_110_execs_Ocases,axiom,
% 0.29/0.66 ! [A1: state,A22: list_com,A33: state] :
% 0.29/0.66 ( ( pHoare259243732_execs @ A1 @ A22 @ A33 )
% 0.29/0.66 => ( ( ( A22 = nil_com )
% 0.29/0.66 => ( A33 != A1 ) )
% 0.29/0.66 => ~ ! [C2: com,T3: state,Cs3: list_com] :
% 0.29/0.66 ( ( A22
% 0.29/0.66 = ( cons_com @ C2 @ Cs3 ) )
% 0.29/0.66 => ( ( exec @ A1 @ C2 @ T3 )
% 0.29/0.66 => ~ ( pHoare259243732_execs @ T3 @ Cs3 @ A33 ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % execs.cases
% 0.29/0.66 thf(fact_111_converse__rtrancl__into__rtrancl,axiom,
% 0.29/0.66 ! [A2: produc2041926651_state,B2: produc2041926651_state,R: set_Pr1165141447_state,C: produc2041926651_state] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ B2 ) @ R )
% 0.29/0.66 => ( ( member1069318160_state @ ( produc1909270103_state @ B2 @ C ) @ ( transi1302705790_state @ R ) )
% 0.29/0.66 => ( member1069318160_state @ ( produc1909270103_state @ A2 @ C ) @ ( transi1302705790_state @ R ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % converse_rtrancl_into_rtrancl
% 0.29/0.66 thf(fact_112_converse__rtrancl__into__rtrancl,axiom,
% 0.29/0.66 ! [A2: produc410756839_state,B2: produc410756839_state,R: set_Pr2096893127_state,C: produc410756839_state] :
% 0.29/0.66 ( ( member512523024_state @ ( produc2065881943_state @ A2 @ B2 ) @ R )
% 0.29/0.66 => ( ( member512523024_state @ ( produc2065881943_state @ B2 @ C ) @ ( transi463013610_state @ R ) )
% 0.29/0.66 => ( member512523024_state @ ( produc2065881943_state @ A2 @ C ) @ ( transi463013610_state @ R ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % converse_rtrancl_into_rtrancl
% 0.29/0.66 thf(fact_113_rtrancl_Ortrancl__into__rtrancl,axiom,
% 0.29/0.66 ! [A2: produc2041926651_state,B2: produc2041926651_state,R: set_Pr1165141447_state,C: produc2041926651_state] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ B2 ) @ ( transi1302705790_state @ R ) )
% 0.29/0.66 => ( ( member1069318160_state @ ( produc1909270103_state @ B2 @ C ) @ R )
% 0.29/0.66 => ( member1069318160_state @ ( produc1909270103_state @ A2 @ C ) @ ( transi1302705790_state @ R ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % rtrancl.rtrancl_into_rtrancl
% 0.29/0.66 thf(fact_114_rtrancl_Ortrancl__into__rtrancl,axiom,
% 0.29/0.66 ! [A2: produc410756839_state,B2: produc410756839_state,R: set_Pr2096893127_state,C: produc410756839_state] :
% 0.29/0.66 ( ( member512523024_state @ ( produc2065881943_state @ A2 @ B2 ) @ ( transi463013610_state @ R ) )
% 0.29/0.66 => ( ( member512523024_state @ ( produc2065881943_state @ B2 @ C ) @ R )
% 0.29/0.66 => ( member512523024_state @ ( produc2065881943_state @ A2 @ C ) @ ( transi463013610_state @ R ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % rtrancl.rtrancl_into_rtrancl
% 0.29/0.66 thf(fact_115_converse__rtrancl__induct,axiom,
% 0.29/0.66 ! [A2: produc2041926651_state,B2: produc2041926651_state,R: set_Pr1165141447_state,P: produc2041926651_state > $o] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ B2 ) @ ( transi1302705790_state @ R ) )
% 0.29/0.66 => ( ( P @ B2 )
% 0.29/0.66 => ( ! [Y3: produc2041926651_state,Z: produc2041926651_state] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ Y3 @ Z ) @ R )
% 0.29/0.66 => ( ( member1069318160_state @ ( produc1909270103_state @ Z @ B2 ) @ ( transi1302705790_state @ R ) )
% 0.29/0.66 => ( ( P @ Z )
% 0.29/0.66 => ( P @ Y3 ) ) ) )
% 0.29/0.66 => ( P @ A2 ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % converse_rtrancl_induct
% 0.29/0.66 thf(fact_116_converse__rtrancl__induct,axiom,
% 0.29/0.66 ! [A2: produc410756839_state,B2: produc410756839_state,R: set_Pr2096893127_state,P: produc410756839_state > $o] :
% 0.29/0.66 ( ( member512523024_state @ ( produc2065881943_state @ A2 @ B2 ) @ ( transi463013610_state @ R ) )
% 0.29/0.66 => ( ( P @ B2 )
% 0.29/0.66 => ( ! [Y3: produc410756839_state,Z: produc410756839_state] :
% 0.29/0.66 ( ( member512523024_state @ ( produc2065881943_state @ Y3 @ Z ) @ R )
% 0.29/0.66 => ( ( member512523024_state @ ( produc2065881943_state @ Z @ B2 ) @ ( transi463013610_state @ R ) )
% 0.29/0.66 => ( ( P @ Z )
% 0.29/0.66 => ( P @ Y3 ) ) ) )
% 0.29/0.66 => ( P @ A2 ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % converse_rtrancl_induct
% 0.29/0.66 thf(fact_117_rtrancl_Ortrancl__refl,axiom,
% 0.29/0.66 ! [A2: produc2041926651_state,R: set_Pr1165141447_state] : ( member1069318160_state @ ( produc1909270103_state @ A2 @ A2 ) @ ( transi1302705790_state @ R ) ) ).
% 0.29/0.66
% 0.29/0.66 % rtrancl.rtrancl_refl
% 0.29/0.66 thf(fact_118_rtrancl_Ortrancl__refl,axiom,
% 0.29/0.66 ! [A2: produc410756839_state,R: set_Pr2096893127_state] : ( member512523024_state @ ( produc2065881943_state @ A2 @ A2 ) @ ( transi463013610_state @ R ) ) ).
% 0.29/0.66
% 0.29/0.66 % rtrancl.rtrancl_refl
% 0.29/0.66 thf(fact_119_converse__rtranclE,axiom,
% 0.29/0.66 ! [X: produc2041926651_state,Z2: produc2041926651_state,R: set_Pr1165141447_state] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Z2 ) @ ( transi1302705790_state @ R ) )
% 0.29/0.66 => ( ( X != Z2 )
% 0.29/0.66 => ~ ! [Y3: produc2041926651_state] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y3 ) @ R )
% 0.29/0.66 => ~ ( member1069318160_state @ ( produc1909270103_state @ Y3 @ Z2 ) @ ( transi1302705790_state @ R ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % converse_rtranclE
% 0.29/0.66 thf(fact_120_converse__rtranclE,axiom,
% 0.29/0.66 ! [X: produc410756839_state,Z2: produc410756839_state,R: set_Pr2096893127_state] :
% 0.29/0.66 ( ( member512523024_state @ ( produc2065881943_state @ X @ Z2 ) @ ( transi463013610_state @ R ) )
% 0.29/0.66 => ( ( X != Z2 )
% 0.29/0.66 => ~ ! [Y3: produc410756839_state] :
% 0.29/0.66 ( ( member512523024_state @ ( produc2065881943_state @ X @ Y3 ) @ R )
% 0.29/0.66 => ~ ( member512523024_state @ ( produc2065881943_state @ Y3 @ Z2 ) @ ( transi463013610_state @ R ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % converse_rtranclE
% 0.29/0.66 thf(fact_121_rtrancl_Oinducts,axiom,
% 0.29/0.66 ! [X1: produc2041926651_state,X2: produc2041926651_state,R: set_Pr1165141447_state,P: produc2041926651_state > produc2041926651_state > $o] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ X1 @ X2 ) @ ( transi1302705790_state @ R ) )
% 0.29/0.66 => ( ! [A: produc2041926651_state] : ( P @ A @ A )
% 0.29/0.66 => ( ! [A: produc2041926651_state,B: produc2041926651_state,C2: produc2041926651_state] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ ( transi1302705790_state @ R ) )
% 0.29/0.66 => ( ( P @ A @ B )
% 0.29/0.66 => ( ( member1069318160_state @ ( produc1909270103_state @ B @ C2 ) @ R )
% 0.29/0.66 => ( P @ A @ C2 ) ) ) )
% 0.29/0.66 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % rtrancl.inducts
% 0.29/0.66 thf(fact_122_rtrancl_Oinducts,axiom,
% 0.29/0.66 ! [X1: produc410756839_state,X2: produc410756839_state,R: set_Pr2096893127_state,P: produc410756839_state > produc410756839_state > $o] :
% 0.29/0.66 ( ( member512523024_state @ ( produc2065881943_state @ X1 @ X2 ) @ ( transi463013610_state @ R ) )
% 0.29/0.66 => ( ! [A: produc410756839_state] : ( P @ A @ A )
% 0.29/0.66 => ( ! [A: produc410756839_state,B: produc410756839_state,C2: produc410756839_state] :
% 0.29/0.66 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ ( transi463013610_state @ R ) )
% 0.29/0.66 => ( ( P @ A @ B )
% 0.29/0.66 => ( ( member512523024_state @ ( produc2065881943_state @ B @ C2 ) @ R )
% 0.29/0.66 => ( P @ A @ C2 ) ) ) )
% 0.29/0.66 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % rtrancl.inducts
% 0.29/0.66 thf(fact_123_rtrancl__induct,axiom,
% 0.29/0.66 ! [A2: produc2041926651_state,B2: produc2041926651_state,R: set_Pr1165141447_state,P: produc2041926651_state > $o] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ B2 ) @ ( transi1302705790_state @ R ) )
% 0.29/0.66 => ( ( P @ A2 )
% 0.29/0.66 => ( ! [Y3: produc2041926651_state,Z: produc2041926651_state] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ Y3 ) @ ( transi1302705790_state @ R ) )
% 0.29/0.66 => ( ( member1069318160_state @ ( produc1909270103_state @ Y3 @ Z ) @ R )
% 0.29/0.66 => ( ( P @ Y3 )
% 0.29/0.66 => ( P @ Z ) ) ) )
% 0.29/0.66 => ( P @ B2 ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % rtrancl_induct
% 0.29/0.66 thf(fact_124_rtrancl__induct,axiom,
% 0.29/0.66 ! [A2: produc410756839_state,B2: produc410756839_state,R: set_Pr2096893127_state,P: produc410756839_state > $o] :
% 0.29/0.66 ( ( member512523024_state @ ( produc2065881943_state @ A2 @ B2 ) @ ( transi463013610_state @ R ) )
% 0.29/0.66 => ( ( P @ A2 )
% 0.29/0.66 => ( ! [Y3: produc410756839_state,Z: produc410756839_state] :
% 0.29/0.66 ( ( member512523024_state @ ( produc2065881943_state @ A2 @ Y3 ) @ ( transi463013610_state @ R ) )
% 0.29/0.66 => ( ( member512523024_state @ ( produc2065881943_state @ Y3 @ Z ) @ R )
% 0.29/0.66 => ( ( P @ Y3 )
% 0.29/0.66 => ( P @ Z ) ) ) )
% 0.29/0.66 => ( P @ B2 ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % rtrancl_induct
% 0.29/0.66 thf(fact_125_rtrancl__trans,axiom,
% 0.29/0.66 ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Z2: produc2041926651_state] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( transi1302705790_state @ R ) )
% 0.29/0.66 => ( ( member1069318160_state @ ( produc1909270103_state @ Y @ Z2 ) @ ( transi1302705790_state @ R ) )
% 0.29/0.66 => ( member1069318160_state @ ( produc1909270103_state @ X @ Z2 ) @ ( transi1302705790_state @ R ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % rtrancl_trans
% 0.29/0.66 thf(fact_126_rtrancl__trans,axiom,
% 0.29/0.66 ! [X: produc410756839_state,Y: produc410756839_state,R: set_Pr2096893127_state,Z2: produc410756839_state] :
% 0.29/0.66 ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( transi463013610_state @ R ) )
% 0.29/0.66 => ( ( member512523024_state @ ( produc2065881943_state @ Y @ Z2 ) @ ( transi463013610_state @ R ) )
% 0.29/0.66 => ( member512523024_state @ ( produc2065881943_state @ X @ Z2 ) @ ( transi463013610_state @ R ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % rtrancl_trans
% 0.29/0.66 thf(fact_127_rtrancl_Osimps,axiom,
% 0.29/0.66 ! [A1: produc2041926651_state,A22: produc2041926651_state,R: set_Pr1165141447_state] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ A1 @ A22 ) @ ( transi1302705790_state @ R ) )
% 0.29/0.66 = ( ? [A5: produc2041926651_state] :
% 0.29/0.66 ( ( A1 = A5 )
% 0.29/0.66 & ( A22 = A5 ) )
% 0.29/0.66 | ? [A5: produc2041926651_state,B4: produc2041926651_state,C3: produc2041926651_state] :
% 0.29/0.66 ( ( A1 = A5 )
% 0.29/0.66 & ( A22 = C3 )
% 0.29/0.66 & ( member1069318160_state @ ( produc1909270103_state @ A5 @ B4 ) @ ( transi1302705790_state @ R ) )
% 0.29/0.66 & ( member1069318160_state @ ( produc1909270103_state @ B4 @ C3 ) @ R ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % rtrancl.simps
% 0.29/0.66 thf(fact_128_rtrancl_Osimps,axiom,
% 0.29/0.66 ! [A1: produc410756839_state,A22: produc410756839_state,R: set_Pr2096893127_state] :
% 0.29/0.66 ( ( member512523024_state @ ( produc2065881943_state @ A1 @ A22 ) @ ( transi463013610_state @ R ) )
% 0.29/0.66 = ( ? [A5: produc410756839_state] :
% 0.29/0.66 ( ( A1 = A5 )
% 0.29/0.66 & ( A22 = A5 ) )
% 0.29/0.66 | ? [A5: produc410756839_state,B4: produc410756839_state,C3: produc410756839_state] :
% 0.29/0.66 ( ( A1 = A5 )
% 0.29/0.66 & ( A22 = C3 )
% 0.29/0.66 & ( member512523024_state @ ( produc2065881943_state @ A5 @ B4 ) @ ( transi463013610_state @ R ) )
% 0.29/0.66 & ( member512523024_state @ ( produc2065881943_state @ B4 @ C3 ) @ R ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % rtrancl.simps
% 0.29/0.66 thf(fact_129_rtrancl_Ocases,axiom,
% 0.29/0.66 ! [A1: produc2041926651_state,A22: produc2041926651_state,R: set_Pr1165141447_state] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ A1 @ A22 ) @ ( transi1302705790_state @ R ) )
% 0.29/0.66 => ( ( A22 != A1 )
% 0.29/0.66 => ~ ! [B: produc2041926651_state] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ A1 @ B ) @ ( transi1302705790_state @ R ) )
% 0.29/0.66 => ~ ( member1069318160_state @ ( produc1909270103_state @ B @ A22 ) @ R ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % rtrancl.cases
% 0.29/0.66 thf(fact_130_rtrancl_Ocases,axiom,
% 0.29/0.66 ! [A1: produc410756839_state,A22: produc410756839_state,R: set_Pr2096893127_state] :
% 0.29/0.66 ( ( member512523024_state @ ( produc2065881943_state @ A1 @ A22 ) @ ( transi463013610_state @ R ) )
% 0.29/0.66 => ( ( A22 != A1 )
% 0.29/0.66 => ~ ! [B: produc410756839_state] :
% 0.29/0.66 ( ( member512523024_state @ ( produc2065881943_state @ A1 @ B ) @ ( transi463013610_state @ R ) )
% 0.29/0.66 => ~ ( member512523024_state @ ( produc2065881943_state @ B @ A22 ) @ R ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % rtrancl.cases
% 0.29/0.66 thf(fact_131_rtranclE,axiom,
% 0.29/0.66 ! [A2: produc2041926651_state,B2: produc2041926651_state,R: set_Pr1165141447_state] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ B2 ) @ ( transi1302705790_state @ R ) )
% 0.29/0.66 => ( ( A2 != B2 )
% 0.29/0.66 => ~ ! [Y3: produc2041926651_state] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ Y3 ) @ ( transi1302705790_state @ R ) )
% 0.29/0.66 => ~ ( member1069318160_state @ ( produc1909270103_state @ Y3 @ B2 ) @ R ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % rtranclE
% 0.29/0.66 thf(fact_132_rtranclE,axiom,
% 0.29/0.66 ! [A2: produc410756839_state,B2: produc410756839_state,R: set_Pr2096893127_state] :
% 0.29/0.66 ( ( member512523024_state @ ( produc2065881943_state @ A2 @ B2 ) @ ( transi463013610_state @ R ) )
% 0.29/0.66 => ( ( A2 != B2 )
% 0.29/0.66 => ~ ! [Y3: produc410756839_state] :
% 0.29/0.66 ( ( member512523024_state @ ( produc2065881943_state @ A2 @ Y3 ) @ ( transi463013610_state @ R ) )
% 0.29/0.66 => ~ ( member512523024_state @ ( produc2065881943_state @ Y3 @ B2 ) @ R ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % rtranclE
% 0.29/0.66 thf(fact_133_prod__induct4,axiom,
% 0.29/0.66 ! [P: produc186437863_state > $o,X: produc186437863_state] :
% 0.29/0.66 ( ! [A: produc410756839_state,B: produc2041926651_state,C2: list_com,D: state] : ( P @ ( produc2065881943_state @ A @ ( produc1909270103_state @ B @ ( produc1204172211_state @ C2 @ D ) ) ) )
% 0.29/0.66 => ( P @ X ) ) ).
% 0.29/0.66
% 0.29/0.66 % prod_induct4
% 0.29/0.66 thf(fact_134_prod__induct3,axiom,
% 0.29/0.66 ! [P: produc410756839_state > $o,X: produc410756839_state] :
% 0.29/0.66 ( ! [A: produc2041926651_state,B: list_com,C2: state] : ( P @ ( produc1909270103_state @ A @ ( produc1204172211_state @ B @ C2 ) ) )
% 0.29/0.66 => ( P @ X ) ) ).
% 0.29/0.66
% 0.29/0.66 % prod_induct3
% 0.29/0.66 thf(fact_135_prod__induct3,axiom,
% 0.29/0.66 ! [P: produc186437863_state > $o,X: produc186437863_state] :
% 0.29/0.66 ( ! [A: produc410756839_state,B: produc2041926651_state,C2: produc2041926651_state] : ( P @ ( produc2065881943_state @ A @ ( produc1909270103_state @ B @ C2 ) ) )
% 0.29/0.66 => ( P @ X ) ) ).
% 0.29/0.66
% 0.29/0.66 % prod_induct3
% 0.29/0.66 thf(fact_136_exec1_OSemi,axiom,
% 0.29/0.66 ! [C1: com,C22: com,Cs2: list_com,S: state] : ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( semi @ C1 @ C22 ) @ Cs2 ) @ S ) @ ( produc1204172211_state @ ( cons_com @ C1 @ ( cons_com @ C22 @ Cs2 ) ) @ S ) ) @ pHoare259243666_exec1 ) ).
% 0.29/0.66
% 0.29/0.66 % exec1.Semi
% 0.29/0.66 thf(fact_137_exec1E_I3_J,axiom,
% 0.29/0.66 ! [C1: com,C22: com,Cs2: list_com,S: state,Cs: list_com,S2: state] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( semi @ C1 @ C22 ) @ Cs2 ) @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 )
% 0.29/0.66 => ~ ( ( Cs
% 0.29/0.66 = ( cons_com @ C1 @ ( cons_com @ C22 @ Cs2 ) ) )
% 0.29/0.66 => ( S2 != S ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % exec1E(3)
% 0.29/0.66 thf(fact_138_exec1_ODo,axiom,
% 0.29/0.66 ! [T2: state,F2: state > set_state,S: state,Cs2: list_com] :
% 0.29/0.66 ( ( member_state @ T2 @ ( F2 @ S ) )
% 0.29/0.66 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( do @ F2 ) @ Cs2 ) @ S ) @ ( produc1204172211_state @ Cs2 @ T2 ) ) @ pHoare259243666_exec1 ) ) ).
% 0.29/0.66
% 0.29/0.66 % exec1.Do
% 0.29/0.66 thf(fact_139_exec1E_I2_J,axiom,
% 0.29/0.66 ! [F2: state > set_state,Cs2: list_com,S: state,Cs: list_com,S2: state] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( do @ F2 ) @ Cs2 ) @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 )
% 0.29/0.66 => ~ ( ( Cs = Cs2 )
% 0.29/0.66 => ~ ( member_state @ S2 @ ( F2 @ S ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % exec1E(2)
% 0.29/0.66 thf(fact_140_exec1_OIfFalse,axiom,
% 0.29/0.66 ! [B2: state > $o,S: state,C1: com,C22: com,Cs2: list_com] :
% 0.29/0.66 ( ~ ( B2 @ S )
% 0.29/0.66 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( cond @ B2 @ C1 @ C22 ) @ Cs2 ) @ S ) @ ( produc1204172211_state @ ( cons_com @ C22 @ Cs2 ) @ S ) ) @ pHoare259243666_exec1 ) ) ).
% 0.29/0.66
% 0.29/0.66 % exec1.IfFalse
% 0.29/0.66 thf(fact_141_exec1_OIfTrue,axiom,
% 0.29/0.66 ! [B2: state > $o,S: state,C1: com,C22: com,Cs2: list_com] :
% 0.29/0.66 ( ( B2 @ S )
% 0.29/0.66 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( cond @ B2 @ C1 @ C22 ) @ Cs2 ) @ S ) @ ( produc1204172211_state @ ( cons_com @ C1 @ Cs2 ) @ S ) ) @ pHoare259243666_exec1 ) ) ).
% 0.29/0.66
% 0.29/0.66 % exec1.IfTrue
% 0.29/0.66 thf(fact_142_exec1E_I4_J,axiom,
% 0.29/0.66 ! [B2: state > $o,C1: com,C22: com,Cs2: list_com,S: state,Cs: list_com,S2: state] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( cond @ B2 @ C1 @ C22 ) @ Cs2 ) @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 )
% 0.29/0.66 => ( ( ( Cs
% 0.29/0.66 = ( cons_com @ C1 @ Cs2 ) )
% 0.29/0.66 => ( ( S2 = S )
% 0.29/0.66 => ~ ( B2 @ S ) ) )
% 0.29/0.66 => ~ ( ( Cs
% 0.29/0.66 = ( cons_com @ C22 @ Cs2 ) )
% 0.29/0.66 => ( ( S2 = S )
% 0.29/0.66 => ( B2 @ S ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % exec1E(4)
% 0.29/0.66 thf(fact_143_exec1_OWhileFalse,axiom,
% 0.29/0.66 ! [B2: state > $o,S: state,C: com,Cs2: list_com] :
% 0.29/0.66 ( ~ ( B2 @ S )
% 0.29/0.66 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( while @ B2 @ C ) @ Cs2 ) @ S ) @ ( produc1204172211_state @ Cs2 @ S ) ) @ pHoare259243666_exec1 ) ) ).
% 0.29/0.66
% 0.29/0.66 % exec1.WhileFalse
% 0.29/0.66 thf(fact_144_exec1_OWhileTrue,axiom,
% 0.29/0.66 ! [B2: state > $o,S: state,C: com,Cs2: list_com] :
% 0.29/0.66 ( ( B2 @ S )
% 0.29/0.66 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( while @ B2 @ C ) @ Cs2 ) @ S ) @ ( produc1204172211_state @ ( cons_com @ C @ ( cons_com @ ( while @ B2 @ C ) @ Cs2 ) ) @ S ) ) @ pHoare259243666_exec1 ) ) ).
% 0.29/0.66
% 0.29/0.66 % exec1.WhileTrue
% 0.29/0.66 thf(fact_145_while__termiE,axiom,
% 0.29/0.66 ! [B2: state > $o,C: com,S: state] :
% 0.29/0.66 ( ( termi @ ( while @ B2 @ C ) @ S )
% 0.29/0.66 => ( ( B2 @ S )
% 0.29/0.66 => ( termi @ C @ S ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % while_termiE
% 0.29/0.66 thf(fact_146_while__termiE2,axiom,
% 0.29/0.66 ! [B2: state > $o,C: com,S: state,T2: state] :
% 0.29/0.66 ( ( termi @ ( while @ B2 @ C ) @ S )
% 0.29/0.66 => ( ( B2 @ S )
% 0.29/0.66 => ( ( exec @ S @ C @ T2 )
% 0.29/0.66 => ( termi @ ( while @ B2 @ C ) @ T2 ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % while_termiE2
% 0.29/0.66 thf(fact_147_exec1E_I5_J,axiom,
% 0.29/0.66 ! [B2: state > $o,C: com,Cs2: list_com,S: state,Cs: list_com,S2: state] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ ( while @ B2 @ C ) @ Cs2 ) @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 )
% 0.29/0.66 => ( ( ( Cs = Cs2 )
% 0.29/0.66 => ( ( S2 = S )
% 0.29/0.66 => ( B2 @ S ) ) )
% 0.29/0.66 => ~ ( ( Cs
% 0.29/0.66 = ( cons_com @ C @ ( cons_com @ ( while @ B2 @ C ) @ Cs2 ) ) )
% 0.29/0.66 => ( ( S2 = S )
% 0.29/0.66 => ~ ( B2 @ S ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % exec1E(5)
% 0.29/0.66 thf(fact_148_termi_OSemi,axiom,
% 0.29/0.66 ! [C1: com,S0: state,C22: com] :
% 0.29/0.66 ( ( termi @ C1 @ S0 )
% 0.29/0.66 => ( ! [S1: state] :
% 0.29/0.66 ( ( exec @ S0 @ C1 @ S1 )
% 0.29/0.66 => ( termi @ C22 @ S1 ) )
% 0.29/0.66 => ( termi @ ( semi @ C1 @ C22 ) @ S0 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % termi.Semi
% 0.29/0.66 thf(fact_149_termi_OWhileTrue,axiom,
% 0.29/0.66 ! [B2: state > $o,S: state,C: com] :
% 0.29/0.66 ( ( B2 @ S )
% 0.29/0.66 => ( ( termi @ C @ S )
% 0.29/0.66 => ( ! [T3: state] :
% 0.29/0.66 ( ( exec @ S @ C @ T3 )
% 0.29/0.66 => ( termi @ ( while @ B2 @ C ) @ T3 ) )
% 0.29/0.66 => ( termi @ ( while @ B2 @ C ) @ S ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % termi.WhileTrue
% 0.29/0.66 thf(fact_150_com_Oinject_I2_J,axiom,
% 0.29/0.66 ! [X21: com,X22: com,Y21: com,Y22: com] :
% 0.29/0.66 ( ( ( semi @ X21 @ X22 )
% 0.29/0.66 = ( semi @ Y21 @ Y22 ) )
% 0.29/0.66 = ( ( X21 = Y21 )
% 0.29/0.66 & ( X22 = Y22 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % com.inject(2)
% 0.29/0.66 thf(fact_151_com_Oinject_I1_J,axiom,
% 0.29/0.66 ! [X1: state > set_state,Y1: state > set_state] :
% 0.29/0.66 ( ( ( do @ X1 )
% 0.29/0.66 = ( do @ Y1 ) )
% 0.29/0.66 = ( X1 = Y1 ) ) ).
% 0.29/0.66
% 0.29/0.66 % com.inject(1)
% 0.29/0.66 thf(fact_152_com_Oinject_I3_J,axiom,
% 0.29/0.66 ! [X31: state > $o,X322: com,X33: com,Y31: state > $o,Y32: com,Y33: com] :
% 0.29/0.66 ( ( ( cond @ X31 @ X322 @ X33 )
% 0.29/0.66 = ( cond @ Y31 @ Y32 @ Y33 ) )
% 0.29/0.66 = ( ( X31 = Y31 )
% 0.29/0.66 & ( X322 = Y32 )
% 0.29/0.66 & ( X33 = Y33 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % com.inject(3)
% 0.29/0.66 thf(fact_153_com_Oinject_I4_J,axiom,
% 0.29/0.66 ! [X41: state > $o,X42: com,Y41: state > $o,Y42: com] :
% 0.29/0.66 ( ( ( while @ X41 @ X42 )
% 0.29/0.66 = ( while @ Y41 @ Y42 ) )
% 0.29/0.66 = ( ( X41 = Y41 )
% 0.29/0.66 & ( X42 = Y42 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % com.inject(4)
% 0.29/0.66 thf(fact_154_exec_OWhileFalse,axiom,
% 0.29/0.66 ! [B2: state > $o,S: state,C: com] :
% 0.29/0.66 ( ~ ( B2 @ S )
% 0.29/0.66 => ( exec @ S @ ( while @ B2 @ C ) @ S ) ) ).
% 0.29/0.66
% 0.29/0.66 % exec.WhileFalse
% 0.29/0.66 thf(fact_155_exec_OWhileTrue,axiom,
% 0.29/0.66 ! [B2: state > $o,S: state,C: com,T2: state,U: state] :
% 0.29/0.66 ( ( B2 @ S )
% 0.29/0.66 => ( ( exec @ S @ C @ T2 )
% 0.29/0.66 => ( ( exec @ T2 @ ( while @ B2 @ C ) @ U )
% 0.29/0.66 => ( exec @ S @ ( while @ B2 @ C ) @ U ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % exec.WhileTrue
% 0.29/0.66 thf(fact_156_com_Odistinct_I19_J,axiom,
% 0.29/0.66 ! [X31: state > $o,X322: com,X33: com,X41: state > $o,X42: com] :
% 0.29/0.66 ( ( cond @ X31 @ X322 @ X33 )
% 0.29/0.66 != ( while @ X41 @ X42 ) ) ).
% 0.29/0.66
% 0.29/0.66 % com.distinct(19)
% 0.29/0.66 thf(fact_157_termi_OWhileFalse,axiom,
% 0.29/0.66 ! [B2: state > $o,S: state,C: com] :
% 0.29/0.66 ( ~ ( B2 @ S )
% 0.29/0.66 => ( termi @ ( while @ B2 @ C ) @ S ) ) ).
% 0.29/0.66
% 0.29/0.66 % termi.WhileFalse
% 0.29/0.66 thf(fact_158_com_Odistinct_I5_J,axiom,
% 0.29/0.66 ! [X1: state > set_state,X41: state > $o,X42: com] :
% 0.29/0.66 ( ( do @ X1 )
% 0.29/0.66 != ( while @ X41 @ X42 ) ) ).
% 0.29/0.66
% 0.29/0.66 % com.distinct(5)
% 0.29/0.66 thf(fact_159_exec_OIfFalse,axiom,
% 0.29/0.66 ! [B2: state > $o,S: state,C22: com,T2: state,C1: com] :
% 0.29/0.66 ( ~ ( B2 @ S )
% 0.29/0.66 => ( ( exec @ S @ C22 @ T2 )
% 0.29/0.66 => ( exec @ S @ ( cond @ B2 @ C1 @ C22 ) @ T2 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % exec.IfFalse
% 0.29/0.66 thf(fact_160_exec_OIfTrue,axiom,
% 0.29/0.66 ! [B2: state > $o,S: state,C1: com,T2: state,C22: com] :
% 0.29/0.66 ( ( B2 @ S )
% 0.29/0.66 => ( ( exec @ S @ C1 @ T2 )
% 0.29/0.66 => ( exec @ S @ ( cond @ B2 @ C1 @ C22 ) @ T2 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % exec.IfTrue
% 0.29/0.66 thf(fact_161_com_Odistinct_I13_J,axiom,
% 0.29/0.66 ! [X21: com,X22: com,X41: state > $o,X42: com] :
% 0.29/0.66 ( ( semi @ X21 @ X22 )
% 0.29/0.66 != ( while @ X41 @ X42 ) ) ).
% 0.29/0.66
% 0.29/0.66 % com.distinct(13)
% 0.29/0.66 thf(fact_162_exec_ODo,axiom,
% 0.29/0.66 ! [T2: state,F2: state > set_state,S: state] :
% 0.29/0.66 ( ( member_state @ T2 @ ( F2 @ S ) )
% 0.29/0.66 => ( exec @ S @ ( do @ F2 ) @ T2 ) ) ).
% 0.29/0.66
% 0.29/0.66 % exec.Do
% 0.29/0.66 thf(fact_163_exec_OSemi,axiom,
% 0.29/0.66 ! [S0: state,C1: com,S12: state,C22: com,S22: state] :
% 0.29/0.66 ( ( exec @ S0 @ C1 @ S12 )
% 0.29/0.66 => ( ( exec @ S12 @ C22 @ S22 )
% 0.29/0.66 => ( exec @ S0 @ ( semi @ C1 @ C22 ) @ S22 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % exec.Semi
% 0.29/0.66 thf(fact_164_termi_OIfFalse,axiom,
% 0.29/0.66 ! [B2: state > $o,S: state,C22: com,C1: com] :
% 0.29/0.66 ( ~ ( B2 @ S )
% 0.29/0.66 => ( ( termi @ C22 @ S )
% 0.29/0.66 => ( termi @ ( cond @ B2 @ C1 @ C22 ) @ S ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % termi.IfFalse
% 0.29/0.66 thf(fact_165_termi_OIfTrue,axiom,
% 0.29/0.66 ! [B2: state > $o,S: state,C1: com,C22: com] :
% 0.29/0.66 ( ( B2 @ S )
% 0.29/0.66 => ( ( termi @ C1 @ S )
% 0.29/0.66 => ( termi @ ( cond @ B2 @ C1 @ C22 ) @ S ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % termi.IfTrue
% 0.29/0.66 thf(fact_166_com_Odistinct_I3_J,axiom,
% 0.29/0.66 ! [X1: state > set_state,X31: state > $o,X322: com,X33: com] :
% 0.29/0.66 ( ( do @ X1 )
% 0.29/0.66 != ( cond @ X31 @ X322 @ X33 ) ) ).
% 0.29/0.66
% 0.29/0.66 % com.distinct(3)
% 0.29/0.66 thf(fact_167_com_Odistinct_I11_J,axiom,
% 0.29/0.66 ! [X21: com,X22: com,X31: state > $o,X322: com,X33: com] :
% 0.29/0.66 ( ( semi @ X21 @ X22 )
% 0.29/0.66 != ( cond @ X31 @ X322 @ X33 ) ) ).
% 0.29/0.66
% 0.29/0.66 % com.distinct(11)
% 0.29/0.66 thf(fact_168_com_Odistinct_I1_J,axiom,
% 0.29/0.66 ! [X1: state > set_state,X21: com,X22: com] :
% 0.29/0.66 ( ( do @ X1 )
% 0.29/0.66 != ( semi @ X21 @ X22 ) ) ).
% 0.29/0.66
% 0.29/0.66 % com.distinct(1)
% 0.29/0.66 thf(fact_169_product__lists_Osimps_I1_J,axiom,
% 0.29/0.66 ( ( product_lists_com @ nil_list_com )
% 0.29/0.66 = ( cons_list_com @ nil_com @ nil_list_com ) ) ).
% 0.29/0.66
% 0.29/0.66 % product_lists.simps(1)
% 0.29/0.66 thf(fact_170_subseqs_Osimps_I1_J,axiom,
% 0.29/0.66 ( ( subseqs_com @ nil_com )
% 0.29/0.66 = ( cons_list_com @ nil_com @ nil_list_com ) ) ).
% 0.29/0.66
% 0.29/0.66 % subseqs.simps(1)
% 0.29/0.66 thf(fact_171_app__execs,axiom,
% 0.29/0.66 ! [Cs2: list_com,S: state,Cs: list_com,S2: state,Cs22: list_com] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs2 @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 0.29/0.66 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( append_com @ Cs2 @ Cs22 ) @ S ) @ ( produc1204172211_state @ ( append_com @ Cs @ Cs22 ) @ S2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % app_execs
% 0.29/0.66 thf(fact_172_insert__Nil,axiom,
% 0.29/0.66 ! [X: com] :
% 0.29/0.66 ( ( insert_com @ X @ nil_com )
% 0.29/0.66 = ( cons_com @ X @ nil_com ) ) ).
% 0.29/0.66
% 0.29/0.66 % insert_Nil
% 0.29/0.66 thf(fact_173_listrel_Oinducts,axiom,
% 0.29/0.66 ! [X1: list_com,X2: list_com,R: set_Pr1822651163om_com,P: list_com > list_com > $o] :
% 0.29/0.66 ( ( member32358020st_com @ ( produc1307105171st_com @ X1 @ X2 ) @ ( listrel_com_com @ R ) )
% 0.29/0.66 => ( ( P @ nil_com @ nil_com )
% 0.29/0.66 => ( ! [X3: com,Y3: com,Xs: list_com,Ys: list_com] :
% 0.29/0.66 ( ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y3 ) @ R )
% 0.29/0.66 => ( ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys ) @ ( listrel_com_com @ R ) )
% 0.29/0.66 => ( ( P @ Xs @ Ys )
% 0.29/0.66 => ( P @ ( cons_com @ X3 @ Xs ) @ ( cons_com @ Y3 @ Ys ) ) ) ) )
% 0.29/0.66 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % listrel.inducts
% 0.29/0.66 thf(fact_174_listrel_Oinducts,axiom,
% 0.29/0.66 ! [X1: list_P1040014977_state,X2: list_P1040014977_state,R: set_Pr1165141447_state,P: list_P1040014977_state > list_P1040014977_state > $o] :
% 0.29/0.66 ( ( member1267359376_state @ ( produc1298457559_state @ X1 @ X2 ) @ ( listre194873521_state @ R ) )
% 0.29/0.66 => ( ( P @ nil_Pr1844458753_state @ nil_Pr1844458753_state )
% 0.29/0.66 => ( ! [X3: produc2041926651_state,Y3: produc2041926651_state,Xs: list_P1040014977_state,Ys: list_P1040014977_state] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y3 ) @ R )
% 0.29/0.66 => ( ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys ) @ ( listre194873521_state @ R ) )
% 0.29/0.66 => ( ( P @ Xs @ Ys )
% 0.29/0.66 => ( P @ ( cons_P465369265_state @ X3 @ Xs ) @ ( cons_P465369265_state @ Y3 @ Ys ) ) ) ) )
% 0.29/0.66 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % listrel.inducts
% 0.29/0.66 thf(fact_175_listrel_Oinducts,axiom,
% 0.29/0.66 ! [X1: list_list_com,X2: list_state,R: set_Pr849496667_state,P: list_list_com > list_state > $o] :
% 0.29/0.66 ( ( member1442949316_state @ ( produc1742567891_state @ X1 @ X2 ) @ ( listre1268245261_state @ R ) )
% 0.29/0.66 => ( ( P @ nil_list_com @ nil_state )
% 0.29/0.66 => ( ! [X3: list_com,Y3: state,Xs: list_list_com,Ys: list_state] :
% 0.29/0.66 ( ( member64234660_state @ ( produc1204172211_state @ X3 @ Y3 ) @ R )
% 0.29/0.66 => ( ( member1442949316_state @ ( produc1742567891_state @ Xs @ Ys ) @ ( listre1268245261_state @ R ) )
% 0.29/0.66 => ( ( P @ Xs @ Ys )
% 0.29/0.66 => ( P @ ( cons_list_com @ X3 @ Xs ) @ ( cons_state @ Y3 @ Ys ) ) ) ) )
% 0.29/0.66 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % listrel.inducts
% 0.29/0.66 thf(fact_176_listrel_Oinducts,axiom,
% 0.29/0.66 ! [X1: list_P890094829_state,X2: list_P890094829_state,R: set_Pr2096893127_state,P: list_P890094829_state > list_P890094829_state > $o] :
% 0.29/0.66 ( ( member423306384_state @ ( produc1354769367_state @ X1 @ X2 ) @ ( listre1244407729_state @ R ) )
% 0.29/0.66 => ( ( P @ nil_Pr1347322605_state @ nil_Pr1347322605_state )
% 0.29/0.66 => ( ! [X3: produc410756839_state,Y3: produc410756839_state,Xs: list_P890094829_state,Ys: list_P890094829_state] :
% 0.29/0.66 ( ( member512523024_state @ ( produc2065881943_state @ X3 @ Y3 ) @ R )
% 0.29/0.66 => ( ( member423306384_state @ ( produc1354769367_state @ Xs @ Ys ) @ ( listre1244407729_state @ R ) )
% 0.29/0.66 => ( ( P @ Xs @ Ys )
% 0.29/0.66 => ( P @ ( cons_P438230685_state @ X3 @ Xs ) @ ( cons_P438230685_state @ Y3 @ Ys ) ) ) ) )
% 0.29/0.66 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % listrel.inducts
% 0.29/0.66 thf(fact_177_append_Oassoc,axiom,
% 0.29/0.66 ! [A2: list_com,B2: list_com,C: list_com] :
% 0.29/0.66 ( ( append_com @ ( append_com @ A2 @ B2 ) @ C )
% 0.29/0.66 = ( append_com @ A2 @ ( append_com @ B2 @ C ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % append.assoc
% 0.29/0.66 thf(fact_178_append__assoc,axiom,
% 0.29/0.66 ! [Xs2: list_com,Ys2: list_com,Zs2: list_com] :
% 0.29/0.66 ( ( append_com @ ( append_com @ Xs2 @ Ys2 ) @ Zs2 )
% 0.29/0.66 = ( append_com @ Xs2 @ ( append_com @ Ys2 @ Zs2 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % append_assoc
% 0.29/0.66 thf(fact_179_append__same__eq,axiom,
% 0.29/0.66 ! [Ys2: list_com,Xs2: list_com,Zs2: list_com] :
% 0.29/0.66 ( ( ( append_com @ Ys2 @ Xs2 )
% 0.29/0.66 = ( append_com @ Zs2 @ Xs2 ) )
% 0.29/0.66 = ( Ys2 = Zs2 ) ) ).
% 0.29/0.66
% 0.29/0.66 % append_same_eq
% 0.29/0.66 thf(fact_180_same__append__eq,axiom,
% 0.29/0.66 ! [Xs2: list_com,Ys2: list_com,Zs2: list_com] :
% 0.29/0.66 ( ( ( append_com @ Xs2 @ Ys2 )
% 0.29/0.66 = ( append_com @ Xs2 @ Zs2 ) )
% 0.29/0.66 = ( Ys2 = Zs2 ) ) ).
% 0.29/0.66
% 0.29/0.66 % same_append_eq
% 0.29/0.66 thf(fact_181_append__Nil2,axiom,
% 0.29/0.66 ! [Xs2: list_com] :
% 0.29/0.66 ( ( append_com @ Xs2 @ nil_com )
% 0.29/0.66 = Xs2 ) ).
% 0.29/0.66
% 0.29/0.66 % append_Nil2
% 0.29/0.66 thf(fact_182_append__self__conv,axiom,
% 0.29/0.66 ! [Xs2: list_com,Ys2: list_com] :
% 0.29/0.66 ( ( ( append_com @ Xs2 @ Ys2 )
% 0.29/0.66 = Xs2 )
% 0.29/0.66 = ( Ys2 = nil_com ) ) ).
% 0.29/0.66
% 0.29/0.66 % append_self_conv
% 0.29/0.66 thf(fact_183_self__append__conv,axiom,
% 0.29/0.66 ! [Xs2: list_com,Ys2: list_com] :
% 0.29/0.66 ( ( Xs2
% 0.29/0.66 = ( append_com @ Xs2 @ Ys2 ) )
% 0.29/0.66 = ( Ys2 = nil_com ) ) ).
% 0.29/0.66
% 0.29/0.66 % self_append_conv
% 0.29/0.66 thf(fact_184_append__self__conv2,axiom,
% 0.29/0.66 ! [Xs2: list_com,Ys2: list_com] :
% 0.29/0.66 ( ( ( append_com @ Xs2 @ Ys2 )
% 0.29/0.66 = Ys2 )
% 0.29/0.66 = ( Xs2 = nil_com ) ) ).
% 0.29/0.66
% 0.29/0.66 % append_self_conv2
% 0.29/0.66 thf(fact_185_self__append__conv2,axiom,
% 0.29/0.66 ! [Ys2: list_com,Xs2: list_com] :
% 0.29/0.66 ( ( Ys2
% 0.29/0.66 = ( append_com @ Xs2 @ Ys2 ) )
% 0.29/0.66 = ( Xs2 = nil_com ) ) ).
% 0.29/0.66
% 0.29/0.66 % self_append_conv2
% 0.29/0.66 thf(fact_186_Nil__is__append__conv,axiom,
% 0.29/0.66 ! [Xs2: list_com,Ys2: list_com] :
% 0.29/0.66 ( ( nil_com
% 0.29/0.66 = ( append_com @ Xs2 @ Ys2 ) )
% 0.29/0.66 = ( ( Xs2 = nil_com )
% 0.29/0.66 & ( Ys2 = nil_com ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % Nil_is_append_conv
% 0.29/0.66 thf(fact_187_append__is__Nil__conv,axiom,
% 0.29/0.66 ! [Xs2: list_com,Ys2: list_com] :
% 0.29/0.66 ( ( ( append_com @ Xs2 @ Ys2 )
% 0.29/0.66 = nil_com )
% 0.29/0.66 = ( ( Xs2 = nil_com )
% 0.29/0.66 & ( Ys2 = nil_com ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % append_is_Nil_conv
% 0.29/0.66 thf(fact_188_append_Oright__neutral,axiom,
% 0.29/0.66 ! [A2: list_com] :
% 0.29/0.66 ( ( append_com @ A2 @ nil_com )
% 0.29/0.66 = A2 ) ).
% 0.29/0.66
% 0.29/0.66 % append.right_neutral
% 0.29/0.66 thf(fact_189_append1__eq__conv,axiom,
% 0.29/0.66 ! [Xs2: list_com,X: com,Ys2: list_com,Y: com] :
% 0.29/0.66 ( ( ( append_com @ Xs2 @ ( cons_com @ X @ nil_com ) )
% 0.29/0.66 = ( append_com @ Ys2 @ ( cons_com @ Y @ nil_com ) ) )
% 0.29/0.66 = ( ( Xs2 = Ys2 )
% 0.29/0.66 & ( X = Y ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % append1_eq_conv
% 0.29/0.66 thf(fact_190_listrel__rtrancl__refl,axiom,
% 0.29/0.66 ! [Xs2: list_P1040014977_state,R: set_Pr1165141447_state] : ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Xs2 ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % listrel_rtrancl_refl
% 0.29/0.66 thf(fact_191_listrel__rtrancl__refl,axiom,
% 0.29/0.66 ! [Xs2: list_P890094829_state,R: set_Pr2096893127_state] : ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Xs2 ) @ ( listre1244407729_state @ ( transi463013610_state @ R ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % listrel_rtrancl_refl
% 0.29/0.66 thf(fact_192_append__Cons,axiom,
% 0.29/0.66 ! [X: com,Xs2: list_com,Ys2: list_com] :
% 0.29/0.66 ( ( append_com @ ( cons_com @ X @ Xs2 ) @ Ys2 )
% 0.29/0.66 = ( cons_com @ X @ ( append_com @ Xs2 @ Ys2 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % append_Cons
% 0.29/0.66 thf(fact_193_Cons__eq__appendI,axiom,
% 0.29/0.66 ! [X: com,Xs1: list_com,Ys2: list_com,Xs2: list_com,Zs2: list_com] :
% 0.29/0.66 ( ( ( cons_com @ X @ Xs1 )
% 0.29/0.66 = Ys2 )
% 0.29/0.66 => ( ( Xs2
% 0.29/0.66 = ( append_com @ Xs1 @ Zs2 ) )
% 0.29/0.66 => ( ( cons_com @ X @ Xs2 )
% 0.29/0.66 = ( append_com @ Ys2 @ Zs2 ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % Cons_eq_appendI
% 0.29/0.66 thf(fact_194_append_Oleft__neutral,axiom,
% 0.29/0.66 ! [A2: list_com] :
% 0.29/0.66 ( ( append_com @ nil_com @ A2 )
% 0.29/0.66 = A2 ) ).
% 0.29/0.66
% 0.29/0.66 % append.left_neutral
% 0.29/0.66 thf(fact_195_append__Nil,axiom,
% 0.29/0.66 ! [Ys2: list_com] :
% 0.29/0.66 ( ( append_com @ nil_com @ Ys2 )
% 0.29/0.66 = Ys2 ) ).
% 0.29/0.66
% 0.29/0.66 % append_Nil
% 0.29/0.66 thf(fact_196_eq__Nil__appendI,axiom,
% 0.29/0.66 ! [Xs2: list_com,Ys2: list_com] :
% 0.29/0.66 ( ( Xs2 = Ys2 )
% 0.29/0.66 => ( Xs2
% 0.29/0.66 = ( append_com @ nil_com @ Ys2 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % eq_Nil_appendI
% 0.29/0.66 thf(fact_197_append__eq__appendI,axiom,
% 0.29/0.66 ! [Xs2: list_com,Xs1: list_com,Zs2: list_com,Ys2: list_com,Us: list_com] :
% 0.29/0.66 ( ( ( append_com @ Xs2 @ Xs1 )
% 0.29/0.66 = Zs2 )
% 0.29/0.66 => ( ( Ys2
% 0.29/0.66 = ( append_com @ Xs1 @ Us ) )
% 0.29/0.66 => ( ( append_com @ Xs2 @ Ys2 )
% 0.29/0.66 = ( append_com @ Zs2 @ Us ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % append_eq_appendI
% 0.29/0.66 thf(fact_198_append__eq__append__conv2,axiom,
% 0.29/0.66 ! [Xs2: list_com,Ys2: list_com,Zs2: list_com,Ts: list_com] :
% 0.29/0.66 ( ( ( append_com @ Xs2 @ Ys2 )
% 0.29/0.66 = ( append_com @ Zs2 @ Ts ) )
% 0.29/0.66 = ( ? [Us2: list_com] :
% 0.29/0.66 ( ( ( Xs2
% 0.29/0.66 = ( append_com @ Zs2 @ Us2 ) )
% 0.29/0.66 & ( ( append_com @ Us2 @ Ys2 )
% 0.29/0.66 = Ts ) )
% 0.29/0.66 | ( ( ( append_com @ Xs2 @ Us2 )
% 0.29/0.66 = Zs2 )
% 0.29/0.66 & ( Ys2
% 0.29/0.66 = ( append_com @ Us2 @ Ts ) ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % append_eq_append_conv2
% 0.29/0.66 thf(fact_199_rev__induct,axiom,
% 0.29/0.66 ! [P: list_com > $o,Xs2: list_com] :
% 0.29/0.66 ( ( P @ nil_com )
% 0.29/0.66 => ( ! [X3: com,Xs: list_com] :
% 0.29/0.66 ( ( P @ Xs )
% 0.29/0.66 => ( P @ ( append_com @ Xs @ ( cons_com @ X3 @ nil_com ) ) ) )
% 0.29/0.66 => ( P @ Xs2 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % rev_induct
% 0.29/0.66 thf(fact_200_rev__exhaust,axiom,
% 0.29/0.66 ! [Xs2: list_com] :
% 0.29/0.66 ( ( Xs2 != nil_com )
% 0.29/0.66 => ~ ! [Ys: list_com,Y3: com] :
% 0.29/0.66 ( Xs2
% 0.29/0.66 != ( append_com @ Ys @ ( cons_com @ Y3 @ nil_com ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % rev_exhaust
% 0.29/0.66 thf(fact_201_Cons__eq__append__conv,axiom,
% 0.29/0.66 ! [X: com,Xs2: list_com,Ys2: list_com,Zs2: list_com] :
% 0.29/0.66 ( ( ( cons_com @ X @ Xs2 )
% 0.29/0.66 = ( append_com @ Ys2 @ Zs2 ) )
% 0.29/0.66 = ( ( ( Ys2 = nil_com )
% 0.29/0.66 & ( ( cons_com @ X @ Xs2 )
% 0.29/0.66 = Zs2 ) )
% 0.29/0.66 | ? [Ys4: list_com] :
% 0.29/0.66 ( ( ( cons_com @ X @ Ys4 )
% 0.29/0.66 = Ys2 )
% 0.29/0.66 & ( Xs2
% 0.29/0.66 = ( append_com @ Ys4 @ Zs2 ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % Cons_eq_append_conv
% 0.29/0.66 thf(fact_202_append__eq__Cons__conv,axiom,
% 0.29/0.66 ! [Ys2: list_com,Zs2: list_com,X: com,Xs2: list_com] :
% 0.29/0.66 ( ( ( append_com @ Ys2 @ Zs2 )
% 0.29/0.66 = ( cons_com @ X @ Xs2 ) )
% 0.29/0.66 = ( ( ( Ys2 = nil_com )
% 0.29/0.66 & ( Zs2
% 0.29/0.66 = ( cons_com @ X @ Xs2 ) ) )
% 0.29/0.66 | ? [Ys4: list_com] :
% 0.29/0.66 ( ( Ys2
% 0.29/0.66 = ( cons_com @ X @ Ys4 ) )
% 0.29/0.66 & ( ( append_com @ Ys4 @ Zs2 )
% 0.29/0.66 = Xs2 ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % append_eq_Cons_conv
% 0.29/0.66 thf(fact_203_rev__nonempty__induct,axiom,
% 0.29/0.66 ! [Xs2: list_com,P: list_com > $o] :
% 0.29/0.66 ( ( Xs2 != nil_com )
% 0.29/0.66 => ( ! [X3: com] : ( P @ ( cons_com @ X3 @ nil_com ) )
% 0.29/0.66 => ( ! [X3: com,Xs: list_com] :
% 0.29/0.66 ( ( Xs != nil_com )
% 0.29/0.66 => ( ( P @ Xs )
% 0.29/0.66 => ( P @ ( append_com @ Xs @ ( cons_com @ X3 @ nil_com ) ) ) ) )
% 0.29/0.66 => ( P @ Xs2 ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % rev_nonempty_induct
% 0.29/0.66 thf(fact_204_listrel__Nil2,axiom,
% 0.29/0.66 ! [Xs2: list_com,R: set_Pr1822651163om_com] :
% 0.29/0.66 ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ nil_com ) @ ( listrel_com_com @ R ) )
% 0.29/0.66 => ( Xs2 = nil_com ) ) ).
% 0.29/0.66
% 0.29/0.66 % listrel_Nil2
% 0.29/0.66 thf(fact_205_listrel__Nil1,axiom,
% 0.29/0.66 ! [Xs2: list_com,R: set_Pr1822651163om_com] :
% 0.29/0.66 ( ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ Xs2 ) @ ( listrel_com_com @ R ) )
% 0.29/0.66 => ( Xs2 = nil_com ) ) ).
% 0.29/0.66
% 0.29/0.66 % listrel_Nil1
% 0.29/0.66 thf(fact_206_listrel_ONil,axiom,
% 0.29/0.66 ! [R: set_Pr1822651163om_com] : ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ nil_com ) @ ( listrel_com_com @ R ) ) ).
% 0.29/0.66
% 0.29/0.66 % listrel.Nil
% 0.29/0.66 thf(fact_207_listrel__rtrancl__trans,axiom,
% 0.29/0.66 ! [Xs2: list_P1040014977_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state,Zs2: list_P1040014977_state] :
% 0.29/0.66 ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) )
% 0.29/0.66 => ( ( member1267359376_state @ ( produc1298457559_state @ Ys2 @ Zs2 ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) )
% 0.29/0.66 => ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Zs2 ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % listrel_rtrancl_trans
% 0.29/0.66 thf(fact_208_listrel__rtrancl__trans,axiom,
% 0.29/0.66 ! [Xs2: list_P890094829_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state,Zs2: list_P890094829_state] :
% 0.29/0.66 ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( listre1244407729_state @ ( transi463013610_state @ R ) ) )
% 0.29/0.66 => ( ( member423306384_state @ ( produc1354769367_state @ Ys2 @ Zs2 ) @ ( listre1244407729_state @ ( transi463013610_state @ R ) ) )
% 0.29/0.66 => ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Zs2 ) @ ( listre1244407729_state @ ( transi463013610_state @ R ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % listrel_rtrancl_trans
% 0.29/0.66 thf(fact_209_listrel_OCons,axiom,
% 0.29/0.66 ! [X: com,Y: com,R: set_Pr1822651163om_com,Xs2: list_com,Ys2: list_com] :
% 0.29/0.66 ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R )
% 0.29/0.66 => ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( listrel_com_com @ R ) )
% 0.29/0.66 => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs2 ) @ ( cons_com @ Y @ Ys2 ) ) @ ( listrel_com_com @ R ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % listrel.Cons
% 0.29/0.66 thf(fact_210_listrel_OCons,axiom,
% 0.29/0.66 ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Xs2: list_P1040014977_state,Ys2: list_P1040014977_state] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 0.29/0.66 => ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( listre194873521_state @ R ) )
% 0.29/0.66 => ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs2 ) @ ( cons_P465369265_state @ Y @ Ys2 ) ) @ ( listre194873521_state @ R ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % listrel.Cons
% 0.29/0.66 thf(fact_211_listrel_OCons,axiom,
% 0.29/0.66 ! [X: list_com,Y: state,R: set_Pr849496667_state,Xs2: list_list_com,Ys2: list_state] :
% 0.29/0.66 ( ( member64234660_state @ ( produc1204172211_state @ X @ Y ) @ R )
% 0.29/0.66 => ( ( member1442949316_state @ ( produc1742567891_state @ Xs2 @ Ys2 ) @ ( listre1268245261_state @ R ) )
% 0.29/0.66 => ( member1442949316_state @ ( produc1742567891_state @ ( cons_list_com @ X @ Xs2 ) @ ( cons_state @ Y @ Ys2 ) ) @ ( listre1268245261_state @ R ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % listrel.Cons
% 0.29/0.66 thf(fact_212_listrel_OCons,axiom,
% 0.29/0.66 ! [X: produc410756839_state,Y: produc410756839_state,R: set_Pr2096893127_state,Xs2: list_P890094829_state,Ys2: list_P890094829_state] :
% 0.29/0.66 ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ R )
% 0.29/0.66 => ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( listre1244407729_state @ R ) )
% 0.29/0.66 => ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ X @ Xs2 ) @ ( cons_P438230685_state @ Y @ Ys2 ) ) @ ( listre1244407729_state @ R ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % listrel.Cons
% 0.29/0.66 thf(fact_213_listrel__Cons1,axiom,
% 0.29/0.66 ! [Y: com,Ys2: list_com,Xs2: list_com,R: set_Pr1822651163om_com] :
% 0.29/0.66 ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ Y @ Ys2 ) @ Xs2 ) @ ( listrel_com_com @ R ) )
% 0.29/0.66 => ~ ! [Y3: com,Ys: list_com] :
% 0.29/0.66 ( ( Xs2
% 0.29/0.66 = ( cons_com @ Y3 @ Ys ) )
% 0.29/0.66 => ( ( member1333916004om_com @ ( product_Pair_com_com @ Y @ Y3 ) @ R )
% 0.29/0.66 => ~ ( member32358020st_com @ ( produc1307105171st_com @ Ys2 @ Ys ) @ ( listrel_com_com @ R ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % listrel_Cons1
% 0.29/0.66 thf(fact_214_listrel__Cons1,axiom,
% 0.29/0.66 ! [Y: produc2041926651_state,Ys2: list_P1040014977_state,Xs2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.29/0.66 ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ Y @ Ys2 ) @ Xs2 ) @ ( listre194873521_state @ R ) )
% 0.29/0.66 => ~ ! [Y3: produc2041926651_state,Ys: list_P1040014977_state] :
% 0.29/0.66 ( ( Xs2
% 0.29/0.66 = ( cons_P465369265_state @ Y3 @ Ys ) )
% 0.29/0.66 => ( ( member1069318160_state @ ( produc1909270103_state @ Y @ Y3 ) @ R )
% 0.29/0.66 => ~ ( member1267359376_state @ ( produc1298457559_state @ Ys2 @ Ys ) @ ( listre194873521_state @ R ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % listrel_Cons1
% 0.29/0.66 thf(fact_215_listrel__Cons1,axiom,
% 0.29/0.66 ! [Y: list_com,Ys2: list_list_com,Xs2: list_state,R: set_Pr849496667_state] :
% 0.29/0.66 ( ( member1442949316_state @ ( produc1742567891_state @ ( cons_list_com @ Y @ Ys2 ) @ Xs2 ) @ ( listre1268245261_state @ R ) )
% 0.29/0.66 => ~ ! [Y3: state,Ys: list_state] :
% 0.29/0.66 ( ( Xs2
% 0.29/0.66 = ( cons_state @ Y3 @ Ys ) )
% 0.29/0.66 => ( ( member64234660_state @ ( produc1204172211_state @ Y @ Y3 ) @ R )
% 0.29/0.66 => ~ ( member1442949316_state @ ( produc1742567891_state @ Ys2 @ Ys ) @ ( listre1268245261_state @ R ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % listrel_Cons1
% 0.29/0.66 thf(fact_216_listrel__Cons1,axiom,
% 0.29/0.66 ! [Y: produc410756839_state,Ys2: list_P890094829_state,Xs2: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.29/0.66 ( ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ Y @ Ys2 ) @ Xs2 ) @ ( listre1244407729_state @ R ) )
% 0.29/0.66 => ~ ! [Y3: produc410756839_state,Ys: list_P890094829_state] :
% 0.29/0.66 ( ( Xs2
% 0.29/0.66 = ( cons_P438230685_state @ Y3 @ Ys ) )
% 0.29/0.66 => ( ( member512523024_state @ ( produc2065881943_state @ Y @ Y3 ) @ R )
% 0.29/0.66 => ~ ( member423306384_state @ ( produc1354769367_state @ Ys2 @ Ys ) @ ( listre1244407729_state @ R ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % listrel_Cons1
% 0.29/0.66 thf(fact_217_listrel__Cons2,axiom,
% 0.29/0.66 ! [Xs2: list_com,Y: com,Ys2: list_com,R: set_Pr1822651163om_com] :
% 0.29/0.66 ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ ( cons_com @ Y @ Ys2 ) ) @ ( listrel_com_com @ R ) )
% 0.29/0.66 => ~ ! [X3: com,Xs: list_com] :
% 0.29/0.66 ( ( Xs2
% 0.29/0.66 = ( cons_com @ X3 @ Xs ) )
% 0.29/0.66 => ( ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y ) @ R )
% 0.29/0.66 => ~ ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys2 ) @ ( listrel_com_com @ R ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % listrel_Cons2
% 0.29/0.66 thf(fact_218_listrel__Cons2,axiom,
% 0.29/0.66 ! [Xs2: list_P1040014977_state,Y: produc2041926651_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.29/0.66 ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ ( cons_P465369265_state @ Y @ Ys2 ) ) @ ( listre194873521_state @ R ) )
% 0.29/0.66 => ~ ! [X3: produc2041926651_state,Xs: list_P1040014977_state] :
% 0.29/0.66 ( ( Xs2
% 0.29/0.66 = ( cons_P465369265_state @ X3 @ Xs ) )
% 0.29/0.66 => ( ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y ) @ R )
% 0.29/0.66 => ~ ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys2 ) @ ( listre194873521_state @ R ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % listrel_Cons2
% 0.29/0.66 thf(fact_219_listrel__Cons2,axiom,
% 0.29/0.66 ! [Xs2: list_list_com,Y: state,Ys2: list_state,R: set_Pr849496667_state] :
% 0.29/0.66 ( ( member1442949316_state @ ( produc1742567891_state @ Xs2 @ ( cons_state @ Y @ Ys2 ) ) @ ( listre1268245261_state @ R ) )
% 0.29/0.66 => ~ ! [X3: list_com,Xs: list_list_com] :
% 0.29/0.66 ( ( Xs2
% 0.29/0.66 = ( cons_list_com @ X3 @ Xs ) )
% 0.29/0.66 => ( ( member64234660_state @ ( produc1204172211_state @ X3 @ Y ) @ R )
% 0.29/0.66 => ~ ( member1442949316_state @ ( produc1742567891_state @ Xs @ Ys2 ) @ ( listre1268245261_state @ R ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % listrel_Cons2
% 0.29/0.66 thf(fact_220_listrel__Cons2,axiom,
% 0.29/0.66 ! [Xs2: list_P890094829_state,Y: produc410756839_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.29/0.66 ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ ( cons_P438230685_state @ Y @ Ys2 ) ) @ ( listre1244407729_state @ R ) )
% 0.29/0.66 => ~ ! [X3: produc410756839_state,Xs: list_P890094829_state] :
% 0.29/0.66 ( ( Xs2
% 0.29/0.66 = ( cons_P438230685_state @ X3 @ Xs ) )
% 0.29/0.66 => ( ( member512523024_state @ ( produc2065881943_state @ X3 @ Y ) @ R )
% 0.29/0.66 => ~ ( member423306384_state @ ( produc1354769367_state @ Xs @ Ys2 ) @ ( listre1244407729_state @ R ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % listrel_Cons2
% 0.29/0.66 thf(fact_221_app__exec,axiom,
% 0.29/0.66 ! [Cs2: list_com,S: state,Cs: list_com,S2: state,Cs22: list_com] :
% 0.29/0.66 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ Cs2 @ S ) @ ( produc1204172211_state @ Cs @ S2 ) ) @ pHoare259243666_exec1 )
% 0.29/0.66 => ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( append_com @ Cs2 @ Cs22 ) @ S ) @ ( produc1204172211_state @ ( append_com @ Cs @ Cs22 ) @ S2 ) ) @ pHoare259243666_exec1 ) ) ).
% 0.29/0.66
% 0.29/0.66 % app_exec
% 0.29/0.66 thf(fact_222_listrel_Ocases,axiom,
% 0.29/0.66 ! [A1: list_com,A22: list_com,R: set_Pr1822651163om_com] :
% 0.29/0.66 ( ( member32358020st_com @ ( produc1307105171st_com @ A1 @ A22 ) @ ( listrel_com_com @ R ) )
% 0.29/0.66 => ( ( ( A1 = nil_com )
% 0.29/0.66 => ( A22 != nil_com ) )
% 0.29/0.66 => ~ ! [X3: com,Y3: com,Xs: list_com] :
% 0.29/0.66 ( ( A1
% 0.29/0.66 = ( cons_com @ X3 @ Xs ) )
% 0.29/0.66 => ! [Ys: list_com] :
% 0.29/0.66 ( ( A22
% 0.29/0.66 = ( cons_com @ Y3 @ Ys ) )
% 0.29/0.66 => ( ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y3 ) @ R )
% 0.29/0.66 => ~ ( member32358020st_com @ ( produc1307105171st_com @ Xs @ Ys ) @ ( listrel_com_com @ R ) ) ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % listrel.cases
% 0.29/0.66 thf(fact_223_listrel_Ocases,axiom,
% 0.29/0.66 ! [A1: list_P1040014977_state,A22: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.29/0.66 ( ( member1267359376_state @ ( produc1298457559_state @ A1 @ A22 ) @ ( listre194873521_state @ R ) )
% 0.29/0.66 => ( ( ( A1 = nil_Pr1844458753_state )
% 0.29/0.66 => ( A22 != nil_Pr1844458753_state ) )
% 0.29/0.66 => ~ ! [X3: produc2041926651_state,Y3: produc2041926651_state,Xs: list_P1040014977_state] :
% 0.29/0.66 ( ( A1
% 0.29/0.66 = ( cons_P465369265_state @ X3 @ Xs ) )
% 0.29/0.66 => ! [Ys: list_P1040014977_state] :
% 0.29/0.66 ( ( A22
% 0.29/0.66 = ( cons_P465369265_state @ Y3 @ Ys ) )
% 0.29/0.66 => ( ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y3 ) @ R )
% 0.29/0.66 => ~ ( member1267359376_state @ ( produc1298457559_state @ Xs @ Ys ) @ ( listre194873521_state @ R ) ) ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % listrel.cases
% 0.29/0.66 thf(fact_224_listrel_Ocases,axiom,
% 0.29/0.66 ! [A1: list_list_com,A22: list_state,R: set_Pr849496667_state] :
% 0.29/0.66 ( ( member1442949316_state @ ( produc1742567891_state @ A1 @ A22 ) @ ( listre1268245261_state @ R ) )
% 0.29/0.66 => ( ( ( A1 = nil_list_com )
% 0.29/0.66 => ( A22 != nil_state ) )
% 0.29/0.66 => ~ ! [X3: list_com,Y3: state,Xs: list_list_com] :
% 0.29/0.66 ( ( A1
% 0.29/0.66 = ( cons_list_com @ X3 @ Xs ) )
% 0.29/0.66 => ! [Ys: list_state] :
% 0.29/0.66 ( ( A22
% 0.29/0.66 = ( cons_state @ Y3 @ Ys ) )
% 0.29/0.66 => ( ( member64234660_state @ ( produc1204172211_state @ X3 @ Y3 ) @ R )
% 0.29/0.66 => ~ ( member1442949316_state @ ( produc1742567891_state @ Xs @ Ys ) @ ( listre1268245261_state @ R ) ) ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % listrel.cases
% 0.29/0.66 thf(fact_225_listrel_Ocases,axiom,
% 0.29/0.66 ! [A1: list_P890094829_state,A22: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.29/0.66 ( ( member423306384_state @ ( produc1354769367_state @ A1 @ A22 ) @ ( listre1244407729_state @ R ) )
% 0.29/0.66 => ( ( ( A1 = nil_Pr1347322605_state )
% 0.29/0.66 => ( A22 != nil_Pr1347322605_state ) )
% 0.29/0.66 => ~ ! [X3: produc410756839_state,Y3: produc410756839_state,Xs: list_P890094829_state] :
% 0.29/0.66 ( ( A1
% 0.29/0.66 = ( cons_P438230685_state @ X3 @ Xs ) )
% 0.29/0.66 => ! [Ys: list_P890094829_state] :
% 0.29/0.66 ( ( A22
% 0.29/0.66 = ( cons_P438230685_state @ Y3 @ Ys ) )
% 0.29/0.66 => ( ( member512523024_state @ ( produc2065881943_state @ X3 @ Y3 ) @ R )
% 0.29/0.66 => ~ ( member423306384_state @ ( produc1354769367_state @ Xs @ Ys ) @ ( listre1244407729_state @ R ) ) ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % listrel.cases
% 0.29/0.66 thf(fact_226_listrel_Osimps,axiom,
% 0.29/0.66 ! [A1: list_com,A22: list_com,R: set_Pr1822651163om_com] :
% 0.29/0.66 ( ( member32358020st_com @ ( produc1307105171st_com @ A1 @ A22 ) @ ( listrel_com_com @ R ) )
% 0.29/0.66 = ( ( ( A1 = nil_com )
% 0.29/0.66 & ( A22 = nil_com ) )
% 0.29/0.66 | ? [X4: com,Y4: com,Xs3: list_com,Ys3: list_com] :
% 0.29/0.66 ( ( A1
% 0.29/0.66 = ( cons_com @ X4 @ Xs3 ) )
% 0.29/0.66 & ( A22
% 0.29/0.66 = ( cons_com @ Y4 @ Ys3 ) )
% 0.29/0.66 & ( member1333916004om_com @ ( product_Pair_com_com @ X4 @ Y4 ) @ R )
% 0.29/0.66 & ( member32358020st_com @ ( produc1307105171st_com @ Xs3 @ Ys3 ) @ ( listrel_com_com @ R ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % listrel.simps
% 0.29/0.66 thf(fact_227_listrel_Osimps,axiom,
% 0.29/0.66 ! [A1: list_P1040014977_state,A22: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.29/0.66 ( ( member1267359376_state @ ( produc1298457559_state @ A1 @ A22 ) @ ( listre194873521_state @ R ) )
% 0.29/0.66 = ( ( ( A1 = nil_Pr1844458753_state )
% 0.29/0.66 & ( A22 = nil_Pr1844458753_state ) )
% 0.29/0.66 | ? [X4: produc2041926651_state,Y4: produc2041926651_state,Xs3: list_P1040014977_state,Ys3: list_P1040014977_state] :
% 0.29/0.66 ( ( A1
% 0.29/0.66 = ( cons_P465369265_state @ X4 @ Xs3 ) )
% 0.29/0.66 & ( A22
% 0.29/0.66 = ( cons_P465369265_state @ Y4 @ Ys3 ) )
% 0.29/0.66 & ( member1069318160_state @ ( produc1909270103_state @ X4 @ Y4 ) @ R )
% 0.29/0.66 & ( member1267359376_state @ ( produc1298457559_state @ Xs3 @ Ys3 ) @ ( listre194873521_state @ R ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % listrel.simps
% 0.29/0.66 thf(fact_228_listrel_Osimps,axiom,
% 0.29/0.66 ! [A1: list_list_com,A22: list_state,R: set_Pr849496667_state] :
% 0.29/0.66 ( ( member1442949316_state @ ( produc1742567891_state @ A1 @ A22 ) @ ( listre1268245261_state @ R ) )
% 0.29/0.66 = ( ( ( A1 = nil_list_com )
% 0.29/0.66 & ( A22 = nil_state ) )
% 0.29/0.66 | ? [X4: list_com,Y4: state,Xs3: list_list_com,Ys3: list_state] :
% 0.29/0.66 ( ( A1
% 0.29/0.66 = ( cons_list_com @ X4 @ Xs3 ) )
% 0.29/0.66 & ( A22
% 0.29/0.66 = ( cons_state @ Y4 @ Ys3 ) )
% 0.29/0.66 & ( member64234660_state @ ( produc1204172211_state @ X4 @ Y4 ) @ R )
% 0.29/0.66 & ( member1442949316_state @ ( produc1742567891_state @ Xs3 @ Ys3 ) @ ( listre1268245261_state @ R ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % listrel.simps
% 0.29/0.66 thf(fact_229_listrel_Osimps,axiom,
% 0.29/0.66 ! [A1: list_P890094829_state,A22: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.29/0.66 ( ( member423306384_state @ ( produc1354769367_state @ A1 @ A22 ) @ ( listre1244407729_state @ R ) )
% 0.29/0.66 = ( ( ( A1 = nil_Pr1347322605_state )
% 0.29/0.66 & ( A22 = nil_Pr1347322605_state ) )
% 0.29/0.66 | ? [X4: produc410756839_state,Y4: produc410756839_state,Xs3: list_P890094829_state,Ys3: list_P890094829_state] :
% 0.29/0.66 ( ( A1
% 0.29/0.66 = ( cons_P438230685_state @ X4 @ Xs3 ) )
% 0.29/0.66 & ( A22
% 0.29/0.66 = ( cons_P438230685_state @ Y4 @ Ys3 ) )
% 0.29/0.66 & ( member512523024_state @ ( produc2065881943_state @ X4 @ Y4 ) @ R )
% 0.29/0.66 & ( member423306384_state @ ( produc1354769367_state @ Xs3 @ Ys3 ) @ ( listre1244407729_state @ R ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % listrel.simps
% 0.29/0.66 thf(fact_230_bind__simps_I2_J,axiom,
% 0.29/0.66 ! [X: com,Xs2: list_com,F2: com > list_com] :
% 0.29/0.66 ( ( bind_com_com @ ( cons_com @ X @ Xs2 ) @ F2 )
% 0.29/0.66 = ( append_com @ ( F2 @ X ) @ ( bind_com_com @ Xs2 @ F2 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % bind_simps(2)
% 0.29/0.66 thf(fact_231_snoc__listrel1__snoc__iff,axiom,
% 0.29/0.66 ! [Xs2: list_com,X: com,Ys2: list_com,Y: com,R: set_Pr1822651163om_com] :
% 0.29/0.66 ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs2 @ ( cons_com @ X @ nil_com ) ) @ ( append_com @ Ys2 @ ( cons_com @ Y @ nil_com ) ) ) @ ( listrel1_com @ R ) )
% 0.29/0.66 = ( ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( listrel1_com @ R ) )
% 0.29/0.66 & ( X = Y ) )
% 0.29/0.66 | ( ( Xs2 = Ys2 )
% 0.29/0.66 & ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % snoc_listrel1_snoc_iff
% 0.29/0.66 thf(fact_232_snoc__listrel1__snoc__iff,axiom,
% 0.29/0.66 ! [Xs2: list_P1040014977_state,X: produc2041926651_state,Ys2: list_P1040014977_state,Y: produc2041926651_state,R: set_Pr1165141447_state] :
% 0.29/0.66 ( ( member1267359376_state @ ( produc1298457559_state @ ( append982487830_state @ Xs2 @ ( cons_P465369265_state @ X @ nil_Pr1844458753_state ) ) @ ( append982487830_state @ Ys2 @ ( cons_P465369265_state @ Y @ nil_Pr1844458753_state ) ) ) @ ( listre1738592858_state @ R ) )
% 0.29/0.66 = ( ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( listre1738592858_state @ R ) )
% 0.29/0.66 & ( X = Y ) )
% 0.29/0.66 | ( ( Xs2 = Ys2 )
% 0.29/0.66 & ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % snoc_listrel1_snoc_iff
% 0.29/0.66 thf(fact_233_snoc__listrel1__snoc__iff,axiom,
% 0.29/0.66 ! [Xs2: list_P890094829_state,X: produc410756839_state,Ys2: list_P890094829_state,Y: produc410756839_state,R: set_Pr2096893127_state] :
% 0.29/0.66 ( ( member423306384_state @ ( produc1354769367_state @ ( append221843330_state @ Xs2 @ ( cons_P438230685_state @ X @ nil_Pr1347322605_state ) ) @ ( append221843330_state @ Ys2 @ ( cons_P438230685_state @ Y @ nil_Pr1347322605_state ) ) ) @ ( listre1725776070_state @ R ) )
% 0.29/0.66 = ( ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( listre1725776070_state @ R ) )
% 0.29/0.66 & ( X = Y ) )
% 0.29/0.66 | ( ( Xs2 = Ys2 )
% 0.29/0.66 & ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ R ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % snoc_listrel1_snoc_iff
% 0.29/0.66 thf(fact_234_maps__simps_I1_J,axiom,
% 0.29/0.66 ! [F2: com > list_com,X: com,Xs2: list_com] :
% 0.29/0.66 ( ( maps_com_com @ F2 @ ( cons_com @ X @ Xs2 ) )
% 0.29/0.66 = ( append_com @ ( F2 @ X ) @ ( maps_com_com @ F2 @ Xs2 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % maps_simps(1)
% 0.29/0.66 thf(fact_235_concat__eq__append__conv,axiom,
% 0.29/0.66 ! [Xss2: list_list_com,Ys2: list_com,Zs2: list_com] :
% 0.29/0.66 ( ( ( concat_com @ Xss2 )
% 0.29/0.66 = ( append_com @ Ys2 @ Zs2 ) )
% 0.29/0.66 = ( ( ( Xss2 = nil_list_com )
% 0.29/0.66 => ( ( Ys2 = nil_com )
% 0.29/0.66 & ( Zs2 = nil_com ) ) )
% 0.29/0.66 & ( ( Xss2 != nil_list_com )
% 0.29/0.66 => ? [Xss1: list_list_com,Xs3: list_com,Xs4: list_com,Xss22: list_list_com] :
% 0.29/0.66 ( ( Xss2
% 0.29/0.66 = ( append_list_com @ Xss1 @ ( cons_list_com @ ( append_com @ Xs3 @ Xs4 ) @ Xss22 ) ) )
% 0.29/0.66 & ( Ys2
% 0.29/0.66 = ( append_com @ ( concat_com @ Xss1 ) @ Xs3 ) )
% 0.29/0.66 & ( Zs2
% 0.29/0.66 = ( append_com @ Xs4 @ ( concat_com @ Xss22 ) ) ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % concat_eq_append_conv
% 0.29/0.66 thf(fact_236_bind__simps_I1_J,axiom,
% 0.29/0.66 ! [F2: com > list_com] :
% 0.29/0.66 ( ( bind_com_com @ nil_com @ F2 )
% 0.29/0.66 = nil_com ) ).
% 0.29/0.66
% 0.29/0.66 % bind_simps(1)
% 0.29/0.66 thf(fact_237_concat__append,axiom,
% 0.29/0.66 ! [Xs2: list_list_com,Ys2: list_list_com] :
% 0.29/0.66 ( ( concat_com @ ( append_list_com @ Xs2 @ Ys2 ) )
% 0.29/0.66 = ( append_com @ ( concat_com @ Xs2 ) @ ( concat_com @ Ys2 ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % concat_append
% 0.29/0.66 thf(fact_238_Cons__listrel1__Cons,axiom,
% 0.29/0.66 ! [X: com,Xs2: list_com,Y: com,Ys2: list_com,R: set_Pr1822651163om_com] :
% 0.29/0.66 ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs2 ) @ ( cons_com @ Y @ Ys2 ) ) @ ( listrel1_com @ R ) )
% 0.29/0.66 = ( ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R )
% 0.29/0.66 & ( Xs2 = Ys2 ) )
% 0.29/0.66 | ( ( X = Y )
% 0.29/0.66 & ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( listrel1_com @ R ) ) ) ) ) ).
% 0.29/0.66
% 0.29/0.66 % Cons_listrel1_Cons
% 0.29/0.66 thf(fact_239_Cons__listrel1__Cons,axiom,
% 0.29/0.66 ! [X: produc2041926651_state,Xs2: list_P1040014977_state,Y: produc2041926651_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.29/0.66 ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs2 ) @ ( cons_P465369265_state @ Y @ Ys2 ) ) @ ( listre1738592858_state @ R ) )
% 0.29/0.66 = ( ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 0.29/0.66 & ( Xs2 = Ys2 ) )
% 0.29/0.66 | ( ( X = Y )
% 0.29/0.66 & ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % Cons_listrel1_Cons
% 0.29/0.67 thf(fact_240_Cons__listrel1__Cons,axiom,
% 0.29/0.67 ! [X: produc410756839_state,Xs2: list_P890094829_state,Y: produc410756839_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.29/0.67 ( ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ X @ Xs2 ) @ ( cons_P438230685_state @ Y @ Ys2 ) ) @ ( listre1725776070_state @ R ) )
% 0.29/0.67 = ( ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ R )
% 0.29/0.67 & ( Xs2 = Ys2 ) )
% 0.29/0.67 | ( ( X = Y )
% 0.29/0.67 & ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( listre1725776070_state @ R ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % Cons_listrel1_Cons
% 0.29/0.67 thf(fact_241_listrel1I2,axiom,
% 0.29/0.67 ! [Xs2: list_com,Ys2: list_com,R: set_Pr1822651163om_com,X: com] :
% 0.29/0.67 ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( listrel1_com @ R ) )
% 0.29/0.67 => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs2 ) @ ( cons_com @ X @ Ys2 ) ) @ ( listrel1_com @ R ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % listrel1I2
% 0.29/0.67 thf(fact_242_rtrancl__listrel1__ConsI1,axiom,
% 0.29/0.67 ! [Xs2: list_com,Ys2: list_com,R: set_Pr1822651163om_com,X: com] :
% 0.29/0.67 ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( transi436345274st_com @ ( listrel1_com @ R ) ) )
% 0.29/0.67 => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs2 ) @ ( cons_com @ X @ Ys2 ) ) @ ( transi436345274st_com @ ( listrel1_com @ R ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % rtrancl_listrel1_ConsI1
% 0.29/0.67 thf(fact_243_not__Nil__listrel1,axiom,
% 0.29/0.67 ! [Xs2: list_com,R: set_Pr1822651163om_com] :
% 0.29/0.67 ~ ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ Xs2 ) @ ( listrel1_com @ R ) ) ).
% 0.29/0.67
% 0.29/0.67 % not_Nil_listrel1
% 0.29/0.67 thf(fact_244_not__listrel1__Nil,axiom,
% 0.29/0.67 ! [Xs2: list_com,R: set_Pr1822651163om_com] :
% 0.29/0.67 ~ ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ nil_com ) @ ( listrel1_com @ R ) ) ).
% 0.29/0.67
% 0.29/0.67 % not_listrel1_Nil
% 0.29/0.67 thf(fact_245_append__listrel1I,axiom,
% 0.29/0.67 ! [Xs2: list_com,Ys2: list_com,R: set_Pr1822651163om_com,Us: list_com,Vs: list_com] :
% 0.29/0.67 ( ( ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( listrel1_com @ R ) )
% 0.29/0.67 & ( Us = Vs ) )
% 0.29/0.67 | ( ( Xs2 = Ys2 )
% 0.29/0.67 & ( member32358020st_com @ ( produc1307105171st_com @ Us @ Vs ) @ ( listrel1_com @ R ) ) ) )
% 0.29/0.67 => ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs2 @ Us ) @ ( append_com @ Ys2 @ Vs ) ) @ ( listrel1_com @ R ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % append_listrel1I
% 0.29/0.67 thf(fact_246_concat_Osimps_I1_J,axiom,
% 0.29/0.67 ( ( concat_com @ nil_list_com )
% 0.29/0.67 = nil_com ) ).
% 0.29/0.67
% 0.29/0.67 % concat.simps(1)
% 0.29/0.67 thf(fact_247_concat_Osimps_I2_J,axiom,
% 0.29/0.67 ! [X: list_com,Xs2: list_list_com] :
% 0.29/0.67 ( ( concat_com @ ( cons_list_com @ X @ Xs2 ) )
% 0.29/0.67 = ( append_com @ X @ ( concat_com @ Xs2 ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % concat.simps(2)
% 0.29/0.67 thf(fact_248_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 0.29/0.67 ! [R: set_Pr1165141447_state] :
% 0.29/0.67 ( ( listre194873521_state @ ( transi1302705790_state @ R ) )
% 0.29/0.67 = ( transi339813252_state @ ( listre1738592858_state @ R ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % listrel_rtrancl_eq_rtrancl_listrel1
% 0.29/0.67 thf(fact_249_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 0.29/0.67 ! [R: set_Pr2096893127_state] :
% 0.29/0.67 ( ( listre1244407729_state @ ( transi463013610_state @ R ) )
% 0.29/0.67 = ( transi1965148016_state @ ( listre1725776070_state @ R ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % listrel_rtrancl_eq_rtrancl_listrel1
% 0.29/0.67 thf(fact_250_maps__simps_I2_J,axiom,
% 0.29/0.67 ! [F2: com > list_com] :
% 0.29/0.67 ( ( maps_com_com @ F2 @ nil_com )
% 0.29/0.67 = nil_com ) ).
% 0.29/0.67
% 0.29/0.67 % maps_simps(2)
% 0.29/0.67 thf(fact_251_Cons__listrel1E2,axiom,
% 0.29/0.67 ! [Xs2: list_com,Y: com,Ys2: list_com,R: set_Pr1822651163om_com] :
% 0.29/0.67 ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ ( cons_com @ Y @ Ys2 ) ) @ ( listrel1_com @ R ) )
% 0.29/0.67 => ( ! [X3: com] :
% 0.29/0.67 ( ( Xs2
% 0.29/0.67 = ( cons_com @ X3 @ Ys2 ) )
% 0.29/0.67 => ~ ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y ) @ R ) )
% 0.29/0.67 => ~ ! [Zs: list_com] :
% 0.29/0.67 ( ( Xs2
% 0.29/0.67 = ( cons_com @ Y @ Zs ) )
% 0.29/0.67 => ~ ( member32358020st_com @ ( produc1307105171st_com @ Zs @ Ys2 ) @ ( listrel1_com @ R ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % Cons_listrel1E2
% 0.29/0.67 thf(fact_252_Cons__listrel1E2,axiom,
% 0.29/0.67 ! [Xs2: list_P1040014977_state,Y: produc2041926651_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.29/0.67 ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ ( cons_P465369265_state @ Y @ Ys2 ) ) @ ( listre1738592858_state @ R ) )
% 0.29/0.67 => ( ! [X3: produc2041926651_state] :
% 0.29/0.67 ( ( Xs2
% 0.29/0.67 = ( cons_P465369265_state @ X3 @ Ys2 ) )
% 0.29/0.67 => ~ ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y ) @ R ) )
% 0.29/0.67 => ~ ! [Zs: list_P1040014977_state] :
% 0.29/0.67 ( ( Xs2
% 0.29/0.67 = ( cons_P465369265_state @ Y @ Zs ) )
% 0.29/0.67 => ~ ( member1267359376_state @ ( produc1298457559_state @ Zs @ Ys2 ) @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % Cons_listrel1E2
% 0.29/0.67 thf(fact_253_Cons__listrel1E2,axiom,
% 0.29/0.67 ! [Xs2: list_P890094829_state,Y: produc410756839_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.29/0.67 ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ ( cons_P438230685_state @ Y @ Ys2 ) ) @ ( listre1725776070_state @ R ) )
% 0.29/0.67 => ( ! [X3: produc410756839_state] :
% 0.29/0.67 ( ( Xs2
% 0.29/0.67 = ( cons_P438230685_state @ X3 @ Ys2 ) )
% 0.29/0.67 => ~ ( member512523024_state @ ( produc2065881943_state @ X3 @ Y ) @ R ) )
% 0.29/0.67 => ~ ! [Zs: list_P890094829_state] :
% 0.29/0.67 ( ( Xs2
% 0.29/0.67 = ( cons_P438230685_state @ Y @ Zs ) )
% 0.29/0.67 => ~ ( member423306384_state @ ( produc1354769367_state @ Zs @ Ys2 ) @ ( listre1725776070_state @ R ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % Cons_listrel1E2
% 0.29/0.67 thf(fact_254_Cons__listrel1E1,axiom,
% 0.29/0.67 ! [X: com,Xs2: list_com,Ys2: list_com,R: set_Pr1822651163om_com] :
% 0.29/0.67 ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs2 ) @ Ys2 ) @ ( listrel1_com @ R ) )
% 0.29/0.67 => ( ! [Y3: com] :
% 0.29/0.67 ( ( Ys2
% 0.29/0.67 = ( cons_com @ Y3 @ Xs2 ) )
% 0.29/0.67 => ~ ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y3 ) @ R ) )
% 0.29/0.67 => ~ ! [Zs: list_com] :
% 0.29/0.67 ( ( Ys2
% 0.29/0.67 = ( cons_com @ X @ Zs ) )
% 0.29/0.67 => ~ ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Zs ) @ ( listrel1_com @ R ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % Cons_listrel1E1
% 0.29/0.67 thf(fact_255_Cons__listrel1E1,axiom,
% 0.29/0.67 ! [X: produc2041926651_state,Xs2: list_P1040014977_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.29/0.67 ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs2 ) @ Ys2 ) @ ( listre1738592858_state @ R ) )
% 0.29/0.67 => ( ! [Y3: produc2041926651_state] :
% 0.29/0.67 ( ( Ys2
% 0.29/0.67 = ( cons_P465369265_state @ Y3 @ Xs2 ) )
% 0.29/0.67 => ~ ( member1069318160_state @ ( produc1909270103_state @ X @ Y3 ) @ R ) )
% 0.29/0.67 => ~ ! [Zs: list_P1040014977_state] :
% 0.29/0.67 ( ( Ys2
% 0.29/0.67 = ( cons_P465369265_state @ X @ Zs ) )
% 0.29/0.67 => ~ ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Zs ) @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % Cons_listrel1E1
% 0.29/0.67 thf(fact_256_Cons__listrel1E1,axiom,
% 0.29/0.67 ! [X: produc410756839_state,Xs2: list_P890094829_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.29/0.67 ( ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ X @ Xs2 ) @ Ys2 ) @ ( listre1725776070_state @ R ) )
% 0.29/0.67 => ( ! [Y3: produc410756839_state] :
% 0.29/0.67 ( ( Ys2
% 0.29/0.67 = ( cons_P438230685_state @ Y3 @ Xs2 ) )
% 0.29/0.67 => ~ ( member512523024_state @ ( produc2065881943_state @ X @ Y3 ) @ R ) )
% 0.29/0.67 => ~ ! [Zs: list_P890094829_state] :
% 0.29/0.67 ( ( Ys2
% 0.29/0.67 = ( cons_P438230685_state @ X @ Zs ) )
% 0.29/0.67 => ~ ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Zs ) @ ( listre1725776070_state @ R ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % Cons_listrel1E1
% 0.29/0.67 thf(fact_257_listrel1I1,axiom,
% 0.29/0.67 ! [X: com,Y: com,R: set_Pr1822651163om_com,Xs2: list_com] :
% 0.29/0.67 ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R )
% 0.29/0.67 => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs2 ) @ ( cons_com @ Y @ Xs2 ) ) @ ( listrel1_com @ R ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % listrel1I1
% 0.29/0.67 thf(fact_258_listrel1I1,axiom,
% 0.29/0.67 ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Xs2: list_P1040014977_state] :
% 0.29/0.67 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 0.29/0.67 => ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs2 ) @ ( cons_P465369265_state @ Y @ Xs2 ) ) @ ( listre1738592858_state @ R ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % listrel1I1
% 0.29/0.67 thf(fact_259_listrel1I1,axiom,
% 0.29/0.67 ! [X: produc410756839_state,Y: produc410756839_state,R: set_Pr2096893127_state,Xs2: list_P890094829_state] :
% 0.29/0.67 ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ R )
% 0.29/0.67 => ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ X @ Xs2 ) @ ( cons_P438230685_state @ Y @ Xs2 ) ) @ ( listre1725776070_state @ R ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % listrel1I1
% 0.29/0.67 thf(fact_260_listrel__reflcl__if__listrel1,axiom,
% 0.29/0.67 ! [Xs2: list_P1040014977_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.29/0.67 ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( listre1738592858_state @ R ) )
% 0.29/0.67 => ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( listre194873521_state @ ( transi1302705790_state @ R ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % listrel_reflcl_if_listrel1
% 0.29/0.67 thf(fact_261_listrel__reflcl__if__listrel1,axiom,
% 0.29/0.67 ! [Xs2: list_P890094829_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.29/0.67 ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( listre1725776070_state @ R ) )
% 0.29/0.67 => ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( listre1244407729_state @ ( transi463013610_state @ R ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % listrel_reflcl_if_listrel1
% 0.29/0.67 thf(fact_262_concat__eq__appendD,axiom,
% 0.29/0.67 ! [Xss2: list_list_com,Ys2: list_com,Zs2: list_com] :
% 0.29/0.67 ( ( ( concat_com @ Xss2 )
% 0.29/0.67 = ( append_com @ Ys2 @ Zs2 ) )
% 0.29/0.67 => ( ( Xss2 != nil_list_com )
% 0.29/0.67 => ? [Xss12: list_list_com,Xs: list_com,Xs5: list_com,Xss23: list_list_com] :
% 0.29/0.67 ( ( Xss2
% 0.29/0.67 = ( append_list_com @ Xss12 @ ( cons_list_com @ ( append_com @ Xs @ Xs5 ) @ Xss23 ) ) )
% 0.29/0.67 & ( Ys2
% 0.29/0.67 = ( append_com @ ( concat_com @ Xss12 ) @ Xs ) )
% 0.29/0.67 & ( Zs2
% 0.29/0.67 = ( append_com @ Xs5 @ ( concat_com @ Xss23 ) ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % concat_eq_appendD
% 0.29/0.67 thf(fact_263_listrel1I,axiom,
% 0.29/0.67 ! [X: com,Y: com,R: set_Pr1822651163om_com,Xs2: list_com,Us: list_com,Vs: list_com,Ys2: list_com] :
% 0.29/0.67 ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R )
% 0.29/0.67 => ( ( Xs2
% 0.29/0.67 = ( append_com @ Us @ ( cons_com @ X @ Vs ) ) )
% 0.29/0.67 => ( ( Ys2
% 0.29/0.67 = ( append_com @ Us @ ( cons_com @ Y @ Vs ) ) )
% 0.29/0.67 => ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( listrel1_com @ R ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % listrel1I
% 0.29/0.67 thf(fact_264_listrel1I,axiom,
% 0.29/0.67 ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Xs2: list_P1040014977_state,Us: list_P1040014977_state,Vs: list_P1040014977_state,Ys2: list_P1040014977_state] :
% 0.29/0.67 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 0.29/0.67 => ( ( Xs2
% 0.29/0.67 = ( append982487830_state @ Us @ ( cons_P465369265_state @ X @ Vs ) ) )
% 0.29/0.67 => ( ( Ys2
% 0.29/0.67 = ( append982487830_state @ Us @ ( cons_P465369265_state @ Y @ Vs ) ) )
% 0.29/0.67 => ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % listrel1I
% 0.29/0.67 thf(fact_265_listrel1I,axiom,
% 0.29/0.67 ! [X: produc410756839_state,Y: produc410756839_state,R: set_Pr2096893127_state,Xs2: list_P890094829_state,Us: list_P890094829_state,Vs: list_P890094829_state,Ys2: list_P890094829_state] :
% 0.29/0.67 ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ R )
% 0.29/0.67 => ( ( Xs2
% 0.29/0.67 = ( append221843330_state @ Us @ ( cons_P438230685_state @ X @ Vs ) ) )
% 0.29/0.67 => ( ( Ys2
% 0.29/0.67 = ( append221843330_state @ Us @ ( cons_P438230685_state @ Y @ Vs ) ) )
% 0.29/0.67 => ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( listre1725776070_state @ R ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % listrel1I
% 0.29/0.67 thf(fact_266_listrel1E,axiom,
% 0.29/0.67 ! [Xs2: list_com,Ys2: list_com,R: set_Pr1822651163om_com] :
% 0.29/0.67 ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( listrel1_com @ R ) )
% 0.29/0.67 => ~ ! [X3: com,Y3: com] :
% 0.29/0.67 ( ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ Y3 ) @ R )
% 0.29/0.67 => ! [Us3: list_com,Vs2: list_com] :
% 0.29/0.67 ( ( Xs2
% 0.29/0.67 = ( append_com @ Us3 @ ( cons_com @ X3 @ Vs2 ) ) )
% 0.29/0.67 => ( Ys2
% 0.29/0.67 != ( append_com @ Us3 @ ( cons_com @ Y3 @ Vs2 ) ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % listrel1E
% 0.29/0.67 thf(fact_267_listrel1E,axiom,
% 0.29/0.67 ! [Xs2: list_P1040014977_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.29/0.67 ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( listre1738592858_state @ R ) )
% 0.29/0.67 => ~ ! [X3: produc2041926651_state,Y3: produc2041926651_state] :
% 0.29/0.67 ( ( member1069318160_state @ ( produc1909270103_state @ X3 @ Y3 ) @ R )
% 0.29/0.67 => ! [Us3: list_P1040014977_state,Vs2: list_P1040014977_state] :
% 0.29/0.67 ( ( Xs2
% 0.29/0.67 = ( append982487830_state @ Us3 @ ( cons_P465369265_state @ X3 @ Vs2 ) ) )
% 0.29/0.67 => ( Ys2
% 0.29/0.67 != ( append982487830_state @ Us3 @ ( cons_P465369265_state @ Y3 @ Vs2 ) ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % listrel1E
% 0.29/0.67 thf(fact_268_listrel1E,axiom,
% 0.29/0.67 ! [Xs2: list_P890094829_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.29/0.67 ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( listre1725776070_state @ R ) )
% 0.29/0.67 => ~ ! [X3: produc410756839_state,Y3: produc410756839_state] :
% 0.29/0.67 ( ( member512523024_state @ ( produc2065881943_state @ X3 @ Y3 ) @ R )
% 0.29/0.67 => ! [Us3: list_P890094829_state,Vs2: list_P890094829_state] :
% 0.29/0.67 ( ( Xs2
% 0.29/0.67 = ( append221843330_state @ Us3 @ ( cons_P438230685_state @ X3 @ Vs2 ) ) )
% 0.29/0.67 => ( Ys2
% 0.29/0.67 != ( append221843330_state @ Us3 @ ( cons_P438230685_state @ Y3 @ Vs2 ) ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % listrel1E
% 0.29/0.67 thf(fact_269_rtrancl__listrel1__ConsI2,axiom,
% 0.29/0.67 ! [X: com,Y: com,R: set_Pr1822651163om_com,Xs2: list_com,Ys2: list_com] :
% 0.29/0.67 ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ ( transi863150634cl_com @ R ) )
% 0.29/0.67 => ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( transi436345274st_com @ ( listrel1_com @ R ) ) )
% 0.29/0.67 => ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs2 ) @ ( cons_com @ Y @ Ys2 ) ) @ ( transi436345274st_com @ ( listrel1_com @ R ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % rtrancl_listrel1_ConsI2
% 0.29/0.67 thf(fact_270_rtrancl__listrel1__ConsI2,axiom,
% 0.29/0.67 ! [X: produc2041926651_state,Y: produc2041926651_state,R: set_Pr1165141447_state,Xs2: list_P1040014977_state,Ys2: list_P1040014977_state] :
% 0.29/0.67 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( transi1302705790_state @ R ) )
% 0.29/0.67 => ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( transi339813252_state @ ( listre1738592858_state @ R ) ) )
% 0.29/0.67 => ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs2 ) @ ( cons_P465369265_state @ Y @ Ys2 ) ) @ ( transi339813252_state @ ( listre1738592858_state @ R ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % rtrancl_listrel1_ConsI2
% 0.29/0.67 thf(fact_271_rtrancl__listrel1__ConsI2,axiom,
% 0.29/0.67 ! [X: produc410756839_state,Y: produc410756839_state,R: set_Pr2096893127_state,Xs2: list_P890094829_state,Ys2: list_P890094829_state] :
% 0.29/0.67 ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( transi463013610_state @ R ) )
% 0.29/0.67 => ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( transi1965148016_state @ ( listre1725776070_state @ R ) ) )
% 0.29/0.67 => ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ X @ Xs2 ) @ ( cons_P438230685_state @ Y @ Ys2 ) ) @ ( transi1965148016_state @ ( listre1725776070_state @ R ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % rtrancl_listrel1_ConsI2
% 0.29/0.67 thf(fact_272_lexord__append__left__rightI,axiom,
% 0.29/0.67 ! [A2: com,B2: com,R: set_Pr1822651163om_com,U: list_com,X: list_com,Y: list_com] :
% 0.29/0.67 ( ( member1333916004om_com @ ( product_Pair_com_com @ A2 @ B2 ) @ R )
% 0.29/0.67 => ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ U @ ( cons_com @ A2 @ X ) ) @ ( append_com @ U @ ( cons_com @ B2 @ Y ) ) ) @ ( lexord_com @ R ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % lexord_append_left_rightI
% 0.29/0.67 thf(fact_273_lexord__append__left__rightI,axiom,
% 0.29/0.67 ! [A2: produc2041926651_state,B2: produc2041926651_state,R: set_Pr1165141447_state,U: list_P1040014977_state,X: list_P1040014977_state,Y: list_P1040014977_state] :
% 0.29/0.67 ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ B2 ) @ R )
% 0.29/0.67 => ( member1267359376_state @ ( produc1298457559_state @ ( append982487830_state @ U @ ( cons_P465369265_state @ A2 @ X ) ) @ ( append982487830_state @ U @ ( cons_P465369265_state @ B2 @ Y ) ) ) @ ( lexord1062073966_state @ R ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % lexord_append_left_rightI
% 0.29/0.67 thf(fact_274_lexord__append__left__rightI,axiom,
% 0.29/0.67 ! [A2: produc410756839_state,B2: produc410756839_state,R: set_Pr2096893127_state,U: list_P890094829_state,X: list_P890094829_state,Y: list_P890094829_state] :
% 0.29/0.67 ( ( member512523024_state @ ( produc2065881943_state @ A2 @ B2 ) @ R )
% 0.29/0.67 => ( member423306384_state @ ( produc1354769367_state @ ( append221843330_state @ U @ ( cons_P438230685_state @ A2 @ X ) ) @ ( append221843330_state @ U @ ( cons_P438230685_state @ B2 @ Y ) ) ) @ ( lexord1893203674_state @ R ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % lexord_append_left_rightI
% 0.29/0.67 thf(fact_275_rotate1_Osimps_I2_J,axiom,
% 0.29/0.67 ! [X: com,Xs2: list_com] :
% 0.29/0.67 ( ( rotate1_com @ ( cons_com @ X @ Xs2 ) )
% 0.29/0.67 = ( append_com @ Xs2 @ ( cons_com @ X @ nil_com ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % rotate1.simps(2)
% 0.29/0.67 thf(fact_276_butlast__snoc,axiom,
% 0.29/0.67 ! [Xs2: list_com,X: com] :
% 0.29/0.67 ( ( butlast_com @ ( append_com @ Xs2 @ ( cons_com @ X @ nil_com ) ) )
% 0.29/0.67 = Xs2 ) ).
% 0.29/0.67
% 0.29/0.67 % butlast_snoc
% 0.29/0.67 thf(fact_277_rotate1__is__Nil__conv,axiom,
% 0.29/0.67 ! [Xs2: list_com] :
% 0.29/0.67 ( ( ( rotate1_com @ Xs2 )
% 0.29/0.67 = nil_com )
% 0.29/0.67 = ( Xs2 = nil_com ) ) ).
% 0.29/0.67
% 0.29/0.67 % rotate1_is_Nil_conv
% 0.29/0.67 thf(fact_278_lexord__cons__cons,axiom,
% 0.29/0.67 ! [A2: com,X: list_com,B2: com,Y: list_com,R: set_Pr1822651163om_com] :
% 0.29/0.67 ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ A2 @ X ) @ ( cons_com @ B2 @ Y ) ) @ ( lexord_com @ R ) )
% 0.29/0.67 = ( ( member1333916004om_com @ ( product_Pair_com_com @ A2 @ B2 ) @ R )
% 0.29/0.67 | ( ( A2 = B2 )
% 0.29/0.67 & ( member32358020st_com @ ( produc1307105171st_com @ X @ Y ) @ ( lexord_com @ R ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % lexord_cons_cons
% 0.29/0.67 thf(fact_279_lexord__cons__cons,axiom,
% 0.29/0.67 ! [A2: produc2041926651_state,X: list_P1040014977_state,B2: produc2041926651_state,Y: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.29/0.67 ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ A2 @ X ) @ ( cons_P465369265_state @ B2 @ Y ) ) @ ( lexord1062073966_state @ R ) )
% 0.29/0.67 = ( ( member1069318160_state @ ( produc1909270103_state @ A2 @ B2 ) @ R )
% 0.29/0.67 | ( ( A2 = B2 )
% 0.29/0.67 & ( member1267359376_state @ ( produc1298457559_state @ X @ Y ) @ ( lexord1062073966_state @ R ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % lexord_cons_cons
% 0.29/0.67 thf(fact_280_lexord__cons__cons,axiom,
% 0.29/0.67 ! [A2: produc410756839_state,X: list_P890094829_state,B2: produc410756839_state,Y: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.29/0.67 ( ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ A2 @ X ) @ ( cons_P438230685_state @ B2 @ Y ) ) @ ( lexord1893203674_state @ R ) )
% 0.29/0.67 = ( ( member512523024_state @ ( produc2065881943_state @ A2 @ B2 ) @ R )
% 0.29/0.67 | ( ( A2 = B2 )
% 0.29/0.67 & ( member423306384_state @ ( produc1354769367_state @ X @ Y ) @ ( lexord1893203674_state @ R ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % lexord_cons_cons
% 0.29/0.67 thf(fact_281_lexord__Nil__left,axiom,
% 0.29/0.67 ! [Y: list_com,R: set_Pr1822651163om_com] :
% 0.29/0.67 ( ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ Y ) @ ( lexord_com @ R ) )
% 0.29/0.67 = ( ? [A5: com,X4: list_com] :
% 0.29/0.67 ( Y
% 0.29/0.67 = ( cons_com @ A5 @ X4 ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % lexord_Nil_left
% 0.29/0.67 thf(fact_282_butlast_Osimps_I1_J,axiom,
% 0.29/0.67 ( ( butlast_com @ nil_com )
% 0.29/0.67 = nil_com ) ).
% 0.29/0.67
% 0.29/0.67 % butlast.simps(1)
% 0.29/0.67 thf(fact_283_rotate1_Osimps_I1_J,axiom,
% 0.29/0.67 ( ( rotate1_com @ nil_com )
% 0.29/0.67 = nil_com ) ).
% 0.29/0.67
% 0.29/0.67 % rotate1.simps(1)
% 0.29/0.67 thf(fact_284_lexord__linear,axiom,
% 0.29/0.67 ! [R: set_Pr1165141447_state,X: list_P1040014977_state,Y: list_P1040014977_state] :
% 0.29/0.67 ( ! [A: produc2041926651_state,B: produc2041926651_state] :
% 0.29/0.67 ( ( member1069318160_state @ ( produc1909270103_state @ A @ B ) @ R )
% 0.29/0.67 | ( A = B )
% 0.29/0.67 | ( member1069318160_state @ ( produc1909270103_state @ B @ A ) @ R ) )
% 0.29/0.67 => ( ( member1267359376_state @ ( produc1298457559_state @ X @ Y ) @ ( lexord1062073966_state @ R ) )
% 0.29/0.67 | ( X = Y )
% 0.29/0.67 | ( member1267359376_state @ ( produc1298457559_state @ Y @ X ) @ ( lexord1062073966_state @ R ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % lexord_linear
% 0.29/0.67 thf(fact_285_lexord__linear,axiom,
% 0.29/0.67 ! [R: set_Pr2096893127_state,X: list_P890094829_state,Y: list_P890094829_state] :
% 0.29/0.67 ( ! [A: produc410756839_state,B: produc410756839_state] :
% 0.29/0.67 ( ( member512523024_state @ ( produc2065881943_state @ A @ B ) @ R )
% 0.29/0.67 | ( A = B )
% 0.29/0.67 | ( member512523024_state @ ( produc2065881943_state @ B @ A ) @ R ) )
% 0.29/0.67 => ( ( member423306384_state @ ( produc1354769367_state @ X @ Y ) @ ( lexord1893203674_state @ R ) )
% 0.29/0.67 | ( X = Y )
% 0.29/0.67 | ( member423306384_state @ ( produc1354769367_state @ Y @ X ) @ ( lexord1893203674_state @ R ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % lexord_linear
% 0.29/0.67 thf(fact_286_lexord__irreflexive,axiom,
% 0.29/0.67 ! [R: set_Pr1165141447_state,Xs2: list_P1040014977_state] :
% 0.29/0.67 ( ! [X3: produc2041926651_state] :
% 0.29/0.67 ~ ( member1069318160_state @ ( produc1909270103_state @ X3 @ X3 ) @ R )
% 0.29/0.67 => ~ ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Xs2 ) @ ( lexord1062073966_state @ R ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % lexord_irreflexive
% 0.29/0.67 thf(fact_287_lexord__irreflexive,axiom,
% 0.29/0.67 ! [R: set_Pr2096893127_state,Xs2: list_P890094829_state] :
% 0.29/0.67 ( ! [X3: produc410756839_state] :
% 0.29/0.67 ~ ( member512523024_state @ ( produc2065881943_state @ X3 @ X3 ) @ R )
% 0.29/0.67 => ~ ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Xs2 ) @ ( lexord1893203674_state @ R ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % lexord_irreflexive
% 0.29/0.67 thf(fact_288_butlast_Osimps_I2_J,axiom,
% 0.29/0.67 ! [Xs2: list_com,X: com] :
% 0.29/0.67 ( ( ( Xs2 = nil_com )
% 0.29/0.67 => ( ( butlast_com @ ( cons_com @ X @ Xs2 ) )
% 0.29/0.67 = nil_com ) )
% 0.29/0.67 & ( ( Xs2 != nil_com )
% 0.29/0.67 => ( ( butlast_com @ ( cons_com @ X @ Xs2 ) )
% 0.29/0.67 = ( cons_com @ X @ ( butlast_com @ Xs2 ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % butlast.simps(2)
% 0.29/0.67 thf(fact_289_lexord__Nil__right,axiom,
% 0.29/0.67 ! [X: list_com,R: set_Pr1822651163om_com] :
% 0.29/0.67 ~ ( member32358020st_com @ ( produc1307105171st_com @ X @ nil_com ) @ ( lexord_com @ R ) ) ).
% 0.29/0.67
% 0.29/0.67 % lexord_Nil_right
% 0.29/0.67 thf(fact_290_butlast__append,axiom,
% 0.29/0.67 ! [Ys2: list_com,Xs2: list_com] :
% 0.29/0.67 ( ( ( Ys2 = nil_com )
% 0.29/0.67 => ( ( butlast_com @ ( append_com @ Xs2 @ Ys2 ) )
% 0.29/0.67 = ( butlast_com @ Xs2 ) ) )
% 0.29/0.67 & ( ( Ys2 != nil_com )
% 0.29/0.67 => ( ( butlast_com @ ( append_com @ Xs2 @ Ys2 ) )
% 0.29/0.67 = ( append_com @ Xs2 @ ( butlast_com @ Ys2 ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % butlast_append
% 0.29/0.67 thf(fact_291_lexord__append__leftI,axiom,
% 0.29/0.67 ! [U: list_com,V: list_com,R: set_Pr1822651163om_com,X: list_com] :
% 0.29/0.67 ( ( member32358020st_com @ ( produc1307105171st_com @ U @ V ) @ ( lexord_com @ R ) )
% 0.29/0.67 => ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ X @ U ) @ ( append_com @ X @ V ) ) @ ( lexord_com @ R ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % lexord_append_leftI
% 0.29/0.67 thf(fact_292_lexord__append__leftD,axiom,
% 0.29/0.67 ! [X: list_com,U: list_com,V: list_com,R: set_Pr1822651163om_com] :
% 0.29/0.67 ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ X @ U ) @ ( append_com @ X @ V ) ) @ ( lexord_com @ R ) )
% 0.29/0.67 => ( ! [A: com] :
% 0.29/0.67 ~ ( member1333916004om_com @ ( product_Pair_com_com @ A @ A ) @ R )
% 0.29/0.67 => ( member32358020st_com @ ( produc1307105171st_com @ U @ V ) @ ( lexord_com @ R ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % lexord_append_leftD
% 0.29/0.67 thf(fact_293_lexord__append__leftD,axiom,
% 0.29/0.67 ! [X: list_P1040014977_state,U: list_P1040014977_state,V: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.29/0.67 ( ( member1267359376_state @ ( produc1298457559_state @ ( append982487830_state @ X @ U ) @ ( append982487830_state @ X @ V ) ) @ ( lexord1062073966_state @ R ) )
% 0.29/0.67 => ( ! [A: produc2041926651_state] :
% 0.29/0.67 ~ ( member1069318160_state @ ( produc1909270103_state @ A @ A ) @ R )
% 0.29/0.67 => ( member1267359376_state @ ( produc1298457559_state @ U @ V ) @ ( lexord1062073966_state @ R ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % lexord_append_leftD
% 0.29/0.67 thf(fact_294_lexord__append__leftD,axiom,
% 0.29/0.67 ! [X: list_P890094829_state,U: list_P890094829_state,V: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.29/0.67 ( ( member423306384_state @ ( produc1354769367_state @ ( append221843330_state @ X @ U ) @ ( append221843330_state @ X @ V ) ) @ ( lexord1893203674_state @ R ) )
% 0.29/0.67 => ( ! [A: produc410756839_state] :
% 0.29/0.67 ~ ( member512523024_state @ ( produc2065881943_state @ A @ A ) @ R )
% 0.29/0.67 => ( member423306384_state @ ( produc1354769367_state @ U @ V ) @ ( lexord1893203674_state @ R ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % lexord_append_leftD
% 0.29/0.67 thf(fact_295_lexord__append__rightI,axiom,
% 0.29/0.67 ! [Y: list_com,X: list_com,R: set_Pr1822651163om_com] :
% 0.29/0.67 ( ? [B5: com,Z3: list_com] :
% 0.29/0.67 ( Y
% 0.29/0.67 = ( cons_com @ B5 @ Z3 ) )
% 0.29/0.67 => ( member32358020st_com @ ( produc1307105171st_com @ X @ ( append_com @ X @ Y ) ) @ ( lexord_com @ R ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % lexord_append_rightI
% 0.29/0.67 thf(fact_296_lexord__same__pref__if__irrefl,axiom,
% 0.29/0.67 ! [R: set_Pr1822651163om_com,Xs2: list_com,Ys2: list_com,Zs2: list_com] :
% 0.29/0.67 ( ( irrefl_com @ R )
% 0.29/0.67 => ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs2 @ Ys2 ) @ ( append_com @ Xs2 @ Zs2 ) ) @ ( lexord_com @ R ) )
% 0.29/0.67 = ( member32358020st_com @ ( produc1307105171st_com @ Ys2 @ Zs2 ) @ ( lexord_com @ R ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % lexord_same_pref_if_irrefl
% 0.29/0.67 thf(fact_297_append__butlast__last__id,axiom,
% 0.29/0.67 ! [Xs2: list_com] :
% 0.29/0.67 ( ( Xs2 != nil_com )
% 0.29/0.67 => ( ( append_com @ ( butlast_com @ Xs2 ) @ ( cons_com @ ( last_com @ Xs2 ) @ nil_com ) )
% 0.29/0.67 = Xs2 ) ) ).
% 0.29/0.67
% 0.29/0.67 % append_butlast_last_id
% 0.29/0.67 thf(fact_298_snoc__eq__iff__butlast,axiom,
% 0.29/0.67 ! [Xs2: list_com,X: com,Ys2: list_com] :
% 0.29/0.67 ( ( ( append_com @ Xs2 @ ( cons_com @ X @ nil_com ) )
% 0.29/0.67 = Ys2 )
% 0.29/0.67 = ( ( Ys2 != nil_com )
% 0.29/0.67 & ( ( butlast_com @ Ys2 )
% 0.29/0.67 = Xs2 )
% 0.29/0.67 & ( ( last_com @ Ys2 )
% 0.29/0.67 = X ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % snoc_eq_iff_butlast
% 0.29/0.67 thf(fact_299_last__appendR,axiom,
% 0.29/0.67 ! [Ys2: list_com,Xs2: list_com] :
% 0.29/0.67 ( ( Ys2 != nil_com )
% 0.29/0.67 => ( ( last_com @ ( append_com @ Xs2 @ Ys2 ) )
% 0.29/0.67 = ( last_com @ Ys2 ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % last_appendR
% 0.29/0.67 thf(fact_300_last__appendL,axiom,
% 0.29/0.67 ! [Ys2: list_com,Xs2: list_com] :
% 0.29/0.67 ( ( Ys2 = nil_com )
% 0.29/0.67 => ( ( last_com @ ( append_com @ Xs2 @ Ys2 ) )
% 0.29/0.67 = ( last_com @ Xs2 ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % last_appendL
% 0.29/0.67 thf(fact_301_last__snoc,axiom,
% 0.29/0.67 ! [Xs2: list_com,X: com] :
% 0.29/0.67 ( ( last_com @ ( append_com @ Xs2 @ ( cons_com @ X @ nil_com ) ) )
% 0.29/0.67 = X ) ).
% 0.29/0.67
% 0.29/0.67 % last_snoc
% 0.29/0.67 thf(fact_302_last__ConsR,axiom,
% 0.29/0.67 ! [Xs2: list_com,X: com] :
% 0.29/0.67 ( ( Xs2 != nil_com )
% 0.29/0.67 => ( ( last_com @ ( cons_com @ X @ Xs2 ) )
% 0.29/0.67 = ( last_com @ Xs2 ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % last_ConsR
% 0.29/0.67 thf(fact_303_last__ConsL,axiom,
% 0.29/0.67 ! [Xs2: list_com,X: com] :
% 0.29/0.67 ( ( Xs2 = nil_com )
% 0.29/0.67 => ( ( last_com @ ( cons_com @ X @ Xs2 ) )
% 0.29/0.67 = X ) ) ).
% 0.29/0.67
% 0.29/0.67 % last_ConsL
% 0.29/0.67 thf(fact_304_last_Osimps,axiom,
% 0.29/0.67 ! [Xs2: list_com,X: com] :
% 0.29/0.67 ( ( ( Xs2 = nil_com )
% 0.29/0.67 => ( ( last_com @ ( cons_com @ X @ Xs2 ) )
% 0.29/0.67 = X ) )
% 0.29/0.67 & ( ( Xs2 != nil_com )
% 0.29/0.67 => ( ( last_com @ ( cons_com @ X @ Xs2 ) )
% 0.29/0.67 = ( last_com @ Xs2 ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % last.simps
% 0.29/0.67 thf(fact_305_longest__common__suffix,axiom,
% 0.29/0.67 ! [Xs2: list_com,Ys2: list_com] :
% 0.29/0.67 ? [Ss: list_com,Xs5: list_com,Ys5: list_com] :
% 0.29/0.67 ( ( Xs2
% 0.29/0.67 = ( append_com @ Xs5 @ Ss ) )
% 0.29/0.67 & ( Ys2
% 0.29/0.67 = ( append_com @ Ys5 @ Ss ) )
% 0.29/0.67 & ( ( Xs5 = nil_com )
% 0.29/0.67 | ( Ys5 = nil_com )
% 0.29/0.67 | ( ( last_com @ Xs5 )
% 0.29/0.67 != ( last_com @ Ys5 ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % longest_common_suffix
% 0.29/0.67 thf(fact_306_last__append,axiom,
% 0.29/0.67 ! [Ys2: list_com,Xs2: list_com] :
% 0.29/0.67 ( ( ( Ys2 = nil_com )
% 0.29/0.67 => ( ( last_com @ ( append_com @ Xs2 @ Ys2 ) )
% 0.29/0.67 = ( last_com @ Xs2 ) ) )
% 0.29/0.67 & ( ( Ys2 != nil_com )
% 0.29/0.67 => ( ( last_com @ ( append_com @ Xs2 @ Ys2 ) )
% 0.29/0.67 = ( last_com @ Ys2 ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % last_append
% 0.29/0.67 thf(fact_307_irreflI,axiom,
% 0.29/0.67 ! [R2: set_Pr1165141447_state] :
% 0.29/0.67 ( ! [A: produc2041926651_state] :
% 0.29/0.67 ~ ( member1069318160_state @ ( produc1909270103_state @ A @ A ) @ R2 )
% 0.29/0.67 => ( irrefl654089520_state @ R2 ) ) ).
% 0.29/0.67
% 0.29/0.67 % irreflI
% 0.29/0.67 thf(fact_308_irreflI,axiom,
% 0.29/0.67 ! [R2: set_Pr2096893127_state] :
% 0.29/0.67 ( ! [A: produc410756839_state] :
% 0.29/0.67 ~ ( member512523024_state @ ( produc2065881943_state @ A @ A ) @ R2 )
% 0.29/0.67 => ( irrefl1358048924_state @ R2 ) ) ).
% 0.29/0.67
% 0.29/0.67 % irreflI
% 0.29/0.67 thf(fact_309_irrefl__def,axiom,
% 0.29/0.67 ( irrefl654089520_state
% 0.29/0.67 = ( ^ [R3: set_Pr1165141447_state] :
% 0.29/0.67 ! [A5: produc2041926651_state] :
% 0.29/0.67 ~ ( member1069318160_state @ ( produc1909270103_state @ A5 @ A5 ) @ R3 ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % irrefl_def
% 0.29/0.67 thf(fact_310_irrefl__def,axiom,
% 0.29/0.67 ( irrefl1358048924_state
% 0.29/0.67 = ( ^ [R3: set_Pr2096893127_state] :
% 0.29/0.67 ! [A5: produc410756839_state] :
% 0.29/0.67 ~ ( member512523024_state @ ( produc2065881943_state @ A5 @ A5 ) @ R3 ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % irrefl_def
% 0.29/0.67 thf(fact_311_lenlex__append2,axiom,
% 0.29/0.67 ! [R2: set_Pr1822651163om_com,Us: list_com,Xs2: list_com,Ys2: list_com] :
% 0.29/0.67 ( ( irrefl_com @ R2 )
% 0.29/0.67 => ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Us @ Xs2 ) @ ( append_com @ Us @ Ys2 ) ) @ ( lenlex_com @ R2 ) )
% 0.29/0.67 = ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( lenlex_com @ R2 ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % lenlex_append2
% 0.29/0.67 thf(fact_312_Nil__lenlex__iff1,axiom,
% 0.29/0.67 ! [Ns: list_com,R: set_Pr1822651163om_com] :
% 0.29/0.67 ( ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ Ns ) @ ( lenlex_com @ R ) )
% 0.29/0.67 = ( Ns != nil_com ) ) ).
% 0.29/0.67
% 0.29/0.67 % Nil_lenlex_iff1
% 0.29/0.67 thf(fact_313_Nil__notin__lex,axiom,
% 0.29/0.67 ! [Ys2: list_com,R: set_Pr1822651163om_com] :
% 0.29/0.67 ~ ( member32358020st_com @ ( produc1307105171st_com @ nil_com @ Ys2 ) @ ( lex_com @ R ) ) ).
% 0.29/0.67
% 0.29/0.67 % Nil_notin_lex
% 0.29/0.67 thf(fact_314_Nil2__notin__lex,axiom,
% 0.29/0.67 ! [Xs2: list_com,R: set_Pr1822651163om_com] :
% 0.29/0.67 ~ ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ nil_com ) @ ( lex_com @ R ) ) ).
% 0.29/0.67
% 0.29/0.67 % Nil2_notin_lex
% 0.29/0.67 thf(fact_315_lex__append__leftI,axiom,
% 0.29/0.67 ! [Ys2: list_com,Zs2: list_com,R: set_Pr1822651163om_com,Xs2: list_com] :
% 0.29/0.67 ( ( member32358020st_com @ ( produc1307105171st_com @ Ys2 @ Zs2 ) @ ( lex_com @ R ) )
% 0.29/0.67 => ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs2 @ Ys2 ) @ ( append_com @ Xs2 @ Zs2 ) ) @ ( lex_com @ R ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % lex_append_leftI
% 0.29/0.67 thf(fact_316_lenlex__irreflexive,axiom,
% 0.29/0.67 ! [R: set_Pr1165141447_state,Xs2: list_P1040014977_state] :
% 0.29/0.67 ( ! [X3: produc2041926651_state] :
% 0.29/0.67 ~ ( member1069318160_state @ ( produc1909270103_state @ X3 @ X3 ) @ R )
% 0.29/0.67 => ~ ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Xs2 ) @ ( lenlex295247238_state @ R ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % lenlex_irreflexive
% 0.29/0.67 thf(fact_317_lenlex__irreflexive,axiom,
% 0.29/0.67 ! [R: set_Pr2096893127_state,Xs2: list_P890094829_state] :
% 0.29/0.67 ( ! [X3: produc410756839_state] :
% 0.29/0.67 ~ ( member512523024_state @ ( produc2065881943_state @ X3 @ X3 ) @ R )
% 0.29/0.67 => ~ ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Xs2 ) @ ( lenlex1401983474_state @ R ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % lenlex_irreflexive
% 0.29/0.67 thf(fact_318_Nil__lenlex__iff2,axiom,
% 0.29/0.67 ! [Ns: list_com,R: set_Pr1822651163om_com] :
% 0.29/0.67 ~ ( member32358020st_com @ ( produc1307105171st_com @ Ns @ nil_com ) @ ( lenlex_com @ R ) ) ).
% 0.29/0.67
% 0.29/0.67 % Nil_lenlex_iff2
% 0.29/0.67 thf(fact_319_lex__append__leftD,axiom,
% 0.29/0.67 ! [R: set_Pr1822651163om_com,Xs2: list_com,Ys2: list_com,Zs2: list_com] :
% 0.29/0.67 ( ! [X3: com] :
% 0.29/0.67 ~ ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ X3 ) @ R )
% 0.29/0.67 => ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs2 @ Ys2 ) @ ( append_com @ Xs2 @ Zs2 ) ) @ ( lex_com @ R ) )
% 0.29/0.67 => ( member32358020st_com @ ( produc1307105171st_com @ Ys2 @ Zs2 ) @ ( lex_com @ R ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % lex_append_leftD
% 0.29/0.67 thf(fact_320_lex__append__leftD,axiom,
% 0.29/0.67 ! [R: set_Pr1165141447_state,Xs2: list_P1040014977_state,Ys2: list_P1040014977_state,Zs2: list_P1040014977_state] :
% 0.29/0.67 ( ! [X3: produc2041926651_state] :
% 0.29/0.67 ~ ( member1069318160_state @ ( produc1909270103_state @ X3 @ X3 ) @ R )
% 0.29/0.67 => ( ( member1267359376_state @ ( produc1298457559_state @ ( append982487830_state @ Xs2 @ Ys2 ) @ ( append982487830_state @ Xs2 @ Zs2 ) ) @ ( lex_Pr570247525_state @ R ) )
% 0.29/0.67 => ( member1267359376_state @ ( produc1298457559_state @ Ys2 @ Zs2 ) @ ( lex_Pr570247525_state @ R ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % lex_append_leftD
% 0.29/0.67 thf(fact_321_lex__append__leftD,axiom,
% 0.29/0.67 ! [R: set_Pr2096893127_state,Xs2: list_P890094829_state,Ys2: list_P890094829_state,Zs2: list_P890094829_state] :
% 0.29/0.67 ( ! [X3: produc410756839_state] :
% 0.29/0.67 ~ ( member512523024_state @ ( produc2065881943_state @ X3 @ X3 ) @ R )
% 0.29/0.67 => ( ( member423306384_state @ ( produc1354769367_state @ ( append221843330_state @ Xs2 @ Ys2 ) @ ( append221843330_state @ Xs2 @ Zs2 ) ) @ ( lex_Pr1762629969_state @ R ) )
% 0.29/0.67 => ( member423306384_state @ ( produc1354769367_state @ Ys2 @ Zs2 ) @ ( lex_Pr1762629969_state @ R ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % lex_append_leftD
% 0.29/0.67 thf(fact_322_lex__append__left__iff,axiom,
% 0.29/0.67 ! [R: set_Pr1822651163om_com,Xs2: list_com,Ys2: list_com,Zs2: list_com] :
% 0.29/0.67 ( ! [X3: com] :
% 0.29/0.67 ~ ( member1333916004om_com @ ( product_Pair_com_com @ X3 @ X3 ) @ R )
% 0.29/0.67 => ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs2 @ Ys2 ) @ ( append_com @ Xs2 @ Zs2 ) ) @ ( lex_com @ R ) )
% 0.29/0.67 = ( member32358020st_com @ ( produc1307105171st_com @ Ys2 @ Zs2 ) @ ( lex_com @ R ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % lex_append_left_iff
% 0.29/0.67 thf(fact_323_lex__append__left__iff,axiom,
% 0.29/0.67 ! [R: set_Pr1165141447_state,Xs2: list_P1040014977_state,Ys2: list_P1040014977_state,Zs2: list_P1040014977_state] :
% 0.29/0.67 ( ! [X3: produc2041926651_state] :
% 0.29/0.67 ~ ( member1069318160_state @ ( produc1909270103_state @ X3 @ X3 ) @ R )
% 0.29/0.67 => ( ( member1267359376_state @ ( produc1298457559_state @ ( append982487830_state @ Xs2 @ Ys2 ) @ ( append982487830_state @ Xs2 @ Zs2 ) ) @ ( lex_Pr570247525_state @ R ) )
% 0.29/0.67 = ( member1267359376_state @ ( produc1298457559_state @ Ys2 @ Zs2 ) @ ( lex_Pr570247525_state @ R ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % lex_append_left_iff
% 0.29/0.67 thf(fact_324_lex__append__left__iff,axiom,
% 0.29/0.67 ! [R: set_Pr2096893127_state,Xs2: list_P890094829_state,Ys2: list_P890094829_state,Zs2: list_P890094829_state] :
% 0.29/0.67 ( ! [X3: produc410756839_state] :
% 0.29/0.67 ~ ( member512523024_state @ ( produc2065881943_state @ X3 @ X3 ) @ R )
% 0.29/0.67 => ( ( member423306384_state @ ( produc1354769367_state @ ( append221843330_state @ Xs2 @ Ys2 ) @ ( append221843330_state @ Xs2 @ Zs2 ) ) @ ( lex_Pr1762629969_state @ R ) )
% 0.29/0.67 = ( member423306384_state @ ( produc1354769367_state @ Ys2 @ Zs2 ) @ ( lex_Pr1762629969_state @ R ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % lex_append_left_iff
% 0.29/0.67 thf(fact_325_Cons__in__lex,axiom,
% 0.29/0.67 ! [X: com,Xs2: list_com,Y: com,Ys2: list_com,R: set_Pr1822651163om_com] :
% 0.29/0.67 ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ X @ Xs2 ) @ ( cons_com @ Y @ Ys2 ) ) @ ( lex_com @ R ) )
% 0.29/0.67 = ( ( ( member1333916004om_com @ ( product_Pair_com_com @ X @ Y ) @ R )
% 0.29/0.67 & ( ( size_size_list_com @ Xs2 )
% 0.29/0.67 = ( size_size_list_com @ Ys2 ) ) )
% 0.29/0.67 | ( ( X = Y )
% 0.29/0.67 & ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( lex_com @ R ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % Cons_in_lex
% 0.29/0.67 thf(fact_326_Cons__in__lex,axiom,
% 0.29/0.67 ! [X: produc2041926651_state,Xs2: list_P1040014977_state,Y: produc2041926651_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.29/0.67 ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ X @ Xs2 ) @ ( cons_P465369265_state @ Y @ Ys2 ) ) @ ( lex_Pr570247525_state @ R ) )
% 0.29/0.67 = ( ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ R )
% 0.29/0.67 & ( ( size_s213202669_state @ Xs2 )
% 0.29/0.67 = ( size_s213202669_state @ Ys2 ) ) )
% 0.29/0.67 | ( ( X = Y )
% 0.29/0.67 & ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( lex_Pr570247525_state @ R ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % Cons_in_lex
% 0.29/0.67 thf(fact_327_Cons__in__lex,axiom,
% 0.29/0.67 ! [X: produc410756839_state,Xs2: list_P890094829_state,Y: produc410756839_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.29/0.67 ( ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ X @ Xs2 ) @ ( cons_P438230685_state @ Y @ Ys2 ) ) @ ( lex_Pr1762629969_state @ R ) )
% 0.29/0.67 = ( ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ R )
% 0.29/0.67 & ( ( size_s837829465_state @ Xs2 )
% 0.29/0.67 = ( size_s837829465_state @ Ys2 ) ) )
% 0.29/0.67 | ( ( X = Y )
% 0.29/0.67 & ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( lex_Pr1762629969_state @ R ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % Cons_in_lex
% 0.29/0.67 thf(fact_328_append__eq__append__conv,axiom,
% 0.29/0.67 ! [Xs2: list_com,Ys2: list_com,Us: list_com,Vs: list_com] :
% 0.29/0.67 ( ( ( ( size_size_list_com @ Xs2 )
% 0.29/0.67 = ( size_size_list_com @ Ys2 ) )
% 0.29/0.67 | ( ( size_size_list_com @ Us )
% 0.29/0.67 = ( size_size_list_com @ Vs ) ) )
% 0.29/0.67 => ( ( ( append_com @ Xs2 @ Us )
% 0.29/0.67 = ( append_com @ Ys2 @ Vs ) )
% 0.29/0.67 = ( ( Xs2 = Ys2 )
% 0.29/0.67 & ( Us = Vs ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % append_eq_append_conv
% 0.29/0.67 thf(fact_329_list__induct3,axiom,
% 0.29/0.67 ! [Xs2: list_com,Ys2: list_com,Zs2: list_com,P: list_com > list_com > list_com > $o] :
% 0.29/0.67 ( ( ( size_size_list_com @ Xs2 )
% 0.29/0.67 = ( size_size_list_com @ Ys2 ) )
% 0.29/0.67 => ( ( ( size_size_list_com @ Ys2 )
% 0.29/0.67 = ( size_size_list_com @ Zs2 ) )
% 0.29/0.67 => ( ( P @ nil_com @ nil_com @ nil_com )
% 0.29/0.67 => ( ! [X3: com,Xs: list_com,Y3: com,Ys: list_com,Z: com,Zs: list_com] :
% 0.29/0.67 ( ( ( size_size_list_com @ Xs )
% 0.29/0.67 = ( size_size_list_com @ Ys ) )
% 0.29/0.67 => ( ( ( size_size_list_com @ Ys )
% 0.29/0.67 = ( size_size_list_com @ Zs ) )
% 0.29/0.67 => ( ( P @ Xs @ Ys @ Zs )
% 0.29/0.67 => ( P @ ( cons_com @ X3 @ Xs ) @ ( cons_com @ Y3 @ Ys ) @ ( cons_com @ Z @ Zs ) ) ) ) )
% 0.29/0.67 => ( P @ Xs2 @ Ys2 @ Zs2 ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % list_induct3
% 0.29/0.67 thf(fact_330_list__induct2,axiom,
% 0.29/0.67 ! [Xs2: list_com,Ys2: list_com,P: list_com > list_com > $o] :
% 0.29/0.67 ( ( ( size_size_list_com @ Xs2 )
% 0.29/0.67 = ( size_size_list_com @ Ys2 ) )
% 0.29/0.67 => ( ( P @ nil_com @ nil_com )
% 0.29/0.67 => ( ! [X3: com,Xs: list_com,Y3: com,Ys: list_com] :
% 0.29/0.67 ( ( ( size_size_list_com @ Xs )
% 0.29/0.67 = ( size_size_list_com @ Ys ) )
% 0.29/0.67 => ( ( P @ Xs @ Ys )
% 0.29/0.67 => ( P @ ( cons_com @ X3 @ Xs ) @ ( cons_com @ Y3 @ Ys ) ) ) )
% 0.29/0.67 => ( P @ Xs2 @ Ys2 ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % list_induct2
% 0.29/0.67 thf(fact_331_same__length__different,axiom,
% 0.29/0.67 ! [Xs2: list_com,Ys2: list_com] :
% 0.29/0.67 ( ( Xs2 != Ys2 )
% 0.29/0.67 => ( ( ( size_size_list_com @ Xs2 )
% 0.29/0.67 = ( size_size_list_com @ Ys2 ) )
% 0.29/0.67 => ? [Pre: list_com,X3: com,Xs5: list_com,Y3: com,Ys5: list_com] :
% 0.29/0.67 ( ( X3 != Y3 )
% 0.29/0.67 & ( Xs2
% 0.29/0.67 = ( append_com @ Pre @ ( append_com @ ( cons_com @ X3 @ nil_com ) @ Xs5 ) ) )
% 0.29/0.67 & ( Ys2
% 0.29/0.67 = ( append_com @ Pre @ ( append_com @ ( cons_com @ Y3 @ nil_com ) @ Ys5 ) ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % same_length_different
% 0.29/0.67 thf(fact_332_lexord__sufE,axiom,
% 0.29/0.67 ! [Xs2: list_com,Zs2: list_com,Ys2: list_com,Qs: list_com,R: set_Pr1822651163om_com] :
% 0.29/0.67 ( ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs2 @ Zs2 ) @ ( append_com @ Ys2 @ Qs ) ) @ ( lexord_com @ R ) )
% 0.29/0.67 => ( ( Xs2 != Ys2 )
% 0.29/0.67 => ( ( ( size_size_list_com @ Xs2 )
% 0.29/0.67 = ( size_size_list_com @ Ys2 ) )
% 0.29/0.67 => ( ( ( size_size_list_com @ Zs2 )
% 0.29/0.67 = ( size_size_list_com @ Qs ) )
% 0.29/0.67 => ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( lexord_com @ R ) ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % lexord_sufE
% 0.29/0.67 thf(fact_333_lex__append__rightI,axiom,
% 0.29/0.67 ! [Xs2: list_com,Ys2: list_com,R: set_Pr1822651163om_com,Vs: list_com,Us: list_com] :
% 0.29/0.67 ( ( member32358020st_com @ ( produc1307105171st_com @ Xs2 @ Ys2 ) @ ( lex_com @ R ) )
% 0.29/0.67 => ( ( ( size_size_list_com @ Vs )
% 0.29/0.67 = ( size_size_list_com @ Us ) )
% 0.29/0.67 => ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Xs2 @ Us ) @ ( append_com @ Ys2 @ Vs ) ) @ ( lex_com @ R ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % lex_append_rightI
% 0.29/0.67 thf(fact_334_lenlex__append1,axiom,
% 0.29/0.67 ! [Us: list_com,Xs2: list_com,R2: set_Pr1822651163om_com,Vs: list_com,Ys2: list_com] :
% 0.29/0.67 ( ( member32358020st_com @ ( produc1307105171st_com @ Us @ Xs2 ) @ ( lenlex_com @ R2 ) )
% 0.29/0.67 => ( ( ( size_size_list_com @ Vs )
% 0.29/0.67 = ( size_size_list_com @ Ys2 ) )
% 0.29/0.67 => ( member32358020st_com @ ( produc1307105171st_com @ ( append_com @ Us @ Vs ) @ ( append_com @ Xs2 @ Ys2 ) ) @ ( lenlex_com @ R2 ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % lenlex_append1
% 0.29/0.67 thf(fact_335_Cons__lenlex__iff,axiom,
% 0.29/0.67 ! [M: com,Ms: list_com,N: com,Ns: list_com,R: set_Pr1822651163om_com] :
% 0.29/0.67 ( ( member32358020st_com @ ( produc1307105171st_com @ ( cons_com @ M @ Ms ) @ ( cons_com @ N @ Ns ) ) @ ( lenlex_com @ R ) )
% 0.29/0.67 = ( ( ord_less_nat @ ( size_size_list_com @ Ms ) @ ( size_size_list_com @ Ns ) )
% 0.29/0.67 | ( ( ( size_size_list_com @ Ms )
% 0.29/0.67 = ( size_size_list_com @ Ns ) )
% 0.29/0.67 & ( member1333916004om_com @ ( product_Pair_com_com @ M @ N ) @ R ) )
% 0.29/0.67 | ( ( M = N )
% 0.29/0.67 & ( member32358020st_com @ ( produc1307105171st_com @ Ms @ Ns ) @ ( lenlex_com @ R ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % Cons_lenlex_iff
% 0.29/0.67 thf(fact_336_Cons__lenlex__iff,axiom,
% 0.29/0.67 ! [M: produc2041926651_state,Ms: list_P1040014977_state,N: produc2041926651_state,Ns: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.29/0.67 ( ( member1267359376_state @ ( produc1298457559_state @ ( cons_P465369265_state @ M @ Ms ) @ ( cons_P465369265_state @ N @ Ns ) ) @ ( lenlex295247238_state @ R ) )
% 0.29/0.67 = ( ( ord_less_nat @ ( size_s213202669_state @ Ms ) @ ( size_s213202669_state @ Ns ) )
% 0.29/0.67 | ( ( ( size_s213202669_state @ Ms )
% 0.29/0.67 = ( size_s213202669_state @ Ns ) )
% 0.29/0.67 & ( member1069318160_state @ ( produc1909270103_state @ M @ N ) @ R ) )
% 0.29/0.67 | ( ( M = N )
% 0.29/0.67 & ( member1267359376_state @ ( produc1298457559_state @ Ms @ Ns ) @ ( lenlex295247238_state @ R ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % Cons_lenlex_iff
% 0.29/0.67 thf(fact_337_Cons__lenlex__iff,axiom,
% 0.29/0.67 ! [M: produc410756839_state,Ms: list_P890094829_state,N: produc410756839_state,Ns: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.29/0.67 ( ( member423306384_state @ ( produc1354769367_state @ ( cons_P438230685_state @ M @ Ms ) @ ( cons_P438230685_state @ N @ Ns ) ) @ ( lenlex1401983474_state @ R ) )
% 0.29/0.67 = ( ( ord_less_nat @ ( size_s837829465_state @ Ms ) @ ( size_s837829465_state @ Ns ) )
% 0.29/0.67 | ( ( ( size_s837829465_state @ Ms )
% 0.29/0.67 = ( size_s837829465_state @ Ns ) )
% 0.29/0.67 & ( member512523024_state @ ( produc2065881943_state @ M @ N ) @ R ) )
% 0.29/0.67 | ( ( M = N )
% 0.29/0.67 & ( member423306384_state @ ( produc1354769367_state @ Ms @ Ns ) @ ( lenlex1401983474_state @ R ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % Cons_lenlex_iff
% 0.29/0.67 thf(fact_338_list__ex1__simps_I1_J,axiom,
% 0.29/0.67 ! [P: com > $o] :
% 0.29/0.67 ~ ( list_ex1_com @ P @ nil_com ) ).
% 0.29/0.67
% 0.29/0.67 % list_ex1_simps(1)
% 0.29/0.67 thf(fact_339_in__measures_I2_J,axiom,
% 0.29/0.67 ! [X: produc2041926651_state,Y: produc2041926651_state,F2: produc2041926651_state > nat,Fs: list_P1178430914te_nat] :
% 0.29/0.67 ( ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( measur1071343867_state @ ( cons_P1821701106te_nat @ F2 @ Fs ) ) )
% 0.29/0.67 = ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 0.29/0.67 | ( ( ( F2 @ X )
% 0.29/0.67 = ( F2 @ Y ) )
% 0.29/0.67 & ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( measur1071343867_state @ Fs ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % in_measures(2)
% 0.29/0.67 thf(fact_340_in__measures_I2_J,axiom,
% 0.29/0.67 ! [X: produc410756839_state,Y: produc410756839_state,F2: produc410756839_state > nat,Fs: list_P1627643054te_nat] :
% 0.29/0.67 ( ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( measur768621543_state @ ( cons_P1631380062te_nat @ F2 @ Fs ) ) )
% 0.29/0.67 = ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 0.29/0.67 | ( ( ( F2 @ X )
% 0.29/0.67 = ( F2 @ Y ) )
% 0.29/0.67 & ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( measur768621543_state @ Fs ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % in_measures(2)
% 0.29/0.67 thf(fact_341_listrel__iff__nth,axiom,
% 0.29/0.67 ! [Xs2: list_P1040014977_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.29/0.67 ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( listre194873521_state @ R ) )
% 0.29/0.67 = ( ( ( size_s213202669_state @ Xs2 )
% 0.29/0.67 = ( size_s213202669_state @ Ys2 ) )
% 0.29/0.67 & ! [N2: nat] :
% 0.29/0.67 ( ( ord_less_nat @ N2 @ ( size_s213202669_state @ Xs2 ) )
% 0.29/0.67 => ( member1069318160_state @ ( produc1909270103_state @ ( nth_Pr553241858_state @ Xs2 @ N2 ) @ ( nth_Pr553241858_state @ Ys2 @ N2 ) ) @ R ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % listrel_iff_nth
% 0.29/0.67 thf(fact_342_listrel__iff__nth,axiom,
% 0.29/0.67 ! [Xs2: list_list_com,Ys2: list_state,R: set_Pr849496667_state] :
% 0.29/0.67 ( ( member1442949316_state @ ( produc1742567891_state @ Xs2 @ Ys2 ) @ ( listre1268245261_state @ R ) )
% 0.29/0.67 = ( ( ( size_s318434721st_com @ Xs2 )
% 0.29/0.67 = ( size_size_list_state @ Ys2 ) )
% 0.29/0.67 & ! [N2: nat] :
% 0.29/0.67 ( ( ord_less_nat @ N2 @ ( size_s318434721st_com @ Xs2 ) )
% 0.29/0.67 => ( member64234660_state @ ( produc1204172211_state @ ( nth_list_com @ Xs2 @ N2 ) @ ( nth_state @ Ys2 @ N2 ) ) @ R ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % listrel_iff_nth
% 0.29/0.67 thf(fact_343_listrel__iff__nth,axiom,
% 0.29/0.67 ! [Xs2: list_P890094829_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.29/0.67 ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( listre1244407729_state @ R ) )
% 0.29/0.67 = ( ( ( size_s837829465_state @ Xs2 )
% 0.29/0.67 = ( size_s837829465_state @ Ys2 ) )
% 0.29/0.67 & ! [N2: nat] :
% 0.29/0.67 ( ( ord_less_nat @ N2 @ ( size_s837829465_state @ Xs2 ) )
% 0.29/0.67 => ( member512523024_state @ ( produc2065881943_state @ ( nth_Pr526167918_state @ Xs2 @ N2 ) @ ( nth_Pr526167918_state @ Ys2 @ N2 ) ) @ R ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % listrel_iff_nth
% 0.29/0.67 thf(fact_344_in__measures_I1_J,axiom,
% 0.29/0.67 ! [X: produc2041926651_state,Y: produc2041926651_state] :
% 0.29/0.67 ~ ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( measur1071343867_state @ nil_Pr1876916290te_nat ) ) ).
% 0.29/0.67
% 0.29/0.67 % in_measures(1)
% 0.29/0.67 thf(fact_345_in__measures_I1_J,axiom,
% 0.29/0.67 ! [X: produc410756839_state,Y: produc410756839_state] :
% 0.29/0.67 ~ ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( measur768621543_state @ nil_Pr164089518te_nat ) ) ).
% 0.29/0.67
% 0.29/0.67 % in_measures(1)
% 0.29/0.67 thf(fact_346_nth__append__length,axiom,
% 0.29/0.67 ! [Xs2: list_com,X: com,Ys2: list_com] :
% 0.29/0.67 ( ( nth_com @ ( append_com @ Xs2 @ ( cons_com @ X @ Ys2 ) ) @ ( size_size_list_com @ Xs2 ) )
% 0.29/0.67 = X ) ).
% 0.29/0.67
% 0.29/0.67 % nth_append_length
% 0.29/0.67 thf(fact_347_measures__less,axiom,
% 0.29/0.67 ! [F2: produc2041926651_state > nat,X: produc2041926651_state,Y: produc2041926651_state,Fs: list_P1178430914te_nat] :
% 0.29/0.67 ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 0.29/0.67 => ( member1069318160_state @ ( produc1909270103_state @ X @ Y ) @ ( measur1071343867_state @ ( cons_P1821701106te_nat @ F2 @ Fs ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % measures_less
% 0.29/0.67 thf(fact_348_measures__less,axiom,
% 0.29/0.67 ! [F2: produc410756839_state > nat,X: produc410756839_state,Y: produc410756839_state,Fs: list_P1627643054te_nat] :
% 0.29/0.67 ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 0.29/0.67 => ( member512523024_state @ ( produc2065881943_state @ X @ Y ) @ ( measur768621543_state @ ( cons_P1631380062te_nat @ F2 @ Fs ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % measures_less
% 0.29/0.67 thf(fact_349_listrel1__iff__update,axiom,
% 0.29/0.67 ! [Xs2: list_P1040014977_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.29/0.67 ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( listre1738592858_state @ R ) )
% 0.29/0.67 = ( ? [Y4: produc2041926651_state,N2: nat] :
% 0.29/0.67 ( ( member1069318160_state @ ( produc1909270103_state @ ( nth_Pr553241858_state @ Xs2 @ N2 ) @ Y4 ) @ R )
% 0.29/0.67 & ( ord_less_nat @ N2 @ ( size_s213202669_state @ Xs2 ) )
% 0.29/0.67 & ( Ys2
% 0.29/0.67 = ( list_u737668969_state @ Xs2 @ N2 @ Y4 ) ) ) ) ) ).
% 0.29/0.67
% 0.29/0.67 % listrel1_iff_update
% 0.29/0.67 thf(fact_350_listrel1__iff__update,axiom,
% 0.29/0.79 ! [Xs2: list_P890094829_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.29/0.79 ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( listre1725776070_state @ R ) )
% 0.29/0.79 = ( ? [Y4: produc410756839_state,N2: nat] :
% 0.29/0.79 ( ( member512523024_state @ ( produc2065881943_state @ ( nth_Pr526167918_state @ Xs2 @ N2 ) @ Y4 ) @ R )
% 0.29/0.79 & ( ord_less_nat @ N2 @ ( size_s837829465_state @ Xs2 ) )
% 0.29/0.79 & ( Ys2
% 0.29/0.79 = ( list_u364351829_state @ Xs2 @ N2 @ Y4 ) ) ) ) ) ).
% 0.29/0.79
% 0.29/0.79 % listrel1_iff_update
% 0.29/0.79 thf(fact_351_lex__take__index,axiom,
% 0.29/0.79 ! [Xs2: list_P1040014977_state,Ys2: list_P1040014977_state,R: set_Pr1165141447_state] :
% 0.29/0.79 ( ( member1267359376_state @ ( produc1298457559_state @ Xs2 @ Ys2 ) @ ( lex_Pr570247525_state @ R ) )
% 0.29/0.79 => ~ ! [I: nat] :
% 0.29/0.79 ( ( ord_less_nat @ I @ ( size_s213202669_state @ Xs2 ) )
% 0.29/0.79 => ( ( ord_less_nat @ I @ ( size_s213202669_state @ Ys2 ) )
% 0.29/0.79 => ( ( ( take_P558217449_state @ I @ Xs2 )
% 0.29/0.79 = ( take_P558217449_state @ I @ Ys2 ) )
% 0.29/0.79 => ~ ( member1069318160_state @ ( produc1909270103_state @ ( nth_Pr553241858_state @ Xs2 @ I ) @ ( nth_Pr553241858_state @ Ys2 @ I ) ) @ R ) ) ) ) ) ).
% 0.29/0.79
% 0.29/0.79 % lex_take_index
% 0.29/0.79 thf(fact_352_lex__take__index,axiom,
% 0.29/0.79 ! [Xs2: list_P890094829_state,Ys2: list_P890094829_state,R: set_Pr2096893127_state] :
% 0.29/0.79 ( ( member423306384_state @ ( produc1354769367_state @ Xs2 @ Ys2 ) @ ( lex_Pr1762629969_state @ R ) )
% 0.29/0.79 => ~ ! [I: nat] :
% 0.29/0.79 ( ( ord_less_nat @ I @ ( size_s837829465_state @ Xs2 ) )
% 0.29/0.79 => ( ( ord_less_nat @ I @ ( size_s837829465_state @ Ys2 ) )
% 0.29/0.79 => ( ( ( take_P1852316373_state @ I @ Xs2 )
% 0.29/0.79 = ( take_P1852316373_state @ I @ Ys2 ) )
% 0.29/0.79 => ~ ( member512523024_state @ ( produc2065881943_state @ ( nth_Pr526167918_state @ Xs2 @ I ) @ ( nth_Pr526167918_state @ Ys2 @ I ) ) @ R ) ) ) ) ) ).
% 0.29/0.79
% 0.29/0.79 % lex_take_index
% 0.29/0.79 thf(fact_353_list__update__nonempty,axiom,
% 0.29/0.79 ! [Xs2: list_com,K: nat,X: com] :
% 0.29/0.79 ( ( ( list_update_com @ Xs2 @ K @ X )
% 0.29/0.79 = nil_com )
% 0.29/0.79 = ( Xs2 = nil_com ) ) ).
% 0.29/0.79
% 0.29/0.79 % list_update_nonempty
% 0.29/0.79
% 0.29/0.79 % Conjectures (4)
% 0.29/0.79 thf(conj_0,hypothesis,
% 0.29/0.79 member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( produc1204172211_state @ ( cons_com @ c2 @ cs ) @ s2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ).
% 0.29/0.79
% 0.29/0.79 thf(conj_1,hypothesis,
% 0.29/0.79 termi @ c @ s ).
% 0.29/0.79
% 0.29/0.79 thf(conj_2,hypothesis,
% 0.29/0.79 ! [S5: state,S6: state] :
% 0.29/0.79 ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ S5 ) @ ( produc1204172211_state @ ( cons_com @ c2 @ cs ) @ S6 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
% 0.29/0.79 => ( ( termi @ c @ S5 )
% 0.29/0.79 => ( ( termi @ c2 @ S6 )
% 0.29/0.79 & ! [T4: state] :
% 0.29/0.79 ( ( exec @ S6 @ c2 @ T4 )
% 0.29/0.79 => ( pHoare806997636termis @ cs @ T4 ) ) ) ) ) ).
% 0.29/0.79
% 0.29/0.79 thf(conj_3,conjecture,
% 0.29/0.79 termi @ c2 @ s2 ).
% 0.29/0.79
% 0.29/0.79 %------------------------------------------------------------------------------
% 0.29/0.79 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.xx3ImMbfCe/cvc5---1.0.5_20204.p...
% 0.29/0.79 (declare-sort $$unsorted 0)
% 0.29/0.79 (declare-sort tptp.set_Pr1696918727_state 0)
% 0.29/0.79 (declare-sort tptp.produc270545127_state 0)
% 0.29/0.79 (declare-sort tptp.set_Pr541394119_state 0)
% 0.29/0.79 (declare-sort tptp.produc2046512871_state 0)
% 0.29/0.79 (declare-sort tptp.set_Pr1847866567_state 0)
% 0.29/0.79 (declare-sort tptp.produc1519776487_state 0)
% 0.29/0.79 (declare-sort tptp.set_Pr1325664839_state 0)
% 0.29/0.79 (declare-sort tptp.produc1586269031_state 0)
% 0.29/0.79 (declare-sort tptp.set_Pr2096893127_state 0)
% 0.29/0.79 (declare-sort tptp.produc186437863_state 0)
% 0.29/0.79 (declare-sort tptp.set_Pr1419004359_state 0)
% 0.29/0.79 (declare-sort tptp.set_Pr135335153st_com 0)
% 0.29/0.79 (declare-sort tptp.produc392316135_state 0)
% 0.29/0.79 (declare-sort tptp.produc1440412305st_com 0)
% 0.29/0.79 (declare-sort tptp.set_Pr1142642759_state 0)
% 0.29/0.79 (declare-sort tptp.set_Pr2083163591st_com 0)
% 0.29/0.79 (declare-sort tptp.list_P1627643054te_nat 0)
% 0.29/0.79 (declare-sort tptp.produc1225889383_state 0)
% 0.29/0.79 (declare-sort tptp.produc1762014951st_com 0)
% 0.29/0.79 (declare-sort tptp.list_P890094829_state 0)
% 0.29/0.79 (declare-sort tptp.set_Pr1165141447_state 0)
% 0.29/0.79 (declare-sort tptp.produc410756839_state 0)
% 0.29/0.79 (declare-sort tptp.set_Pr391631483_state 0)
% 0.29/0.79 (declare-sort tptp.list_P1178430914te_nat 0)
% 0.29/0.79 (declare-sort tptp.produc1393453339_state 0)
% 0.29/0.79 (declare-sort tptp.produc2058209240st_com 0)
% 0.29/0.79 (declare-sort tptp.set_Pr602326075st_com 0)
% 0.29/0.79 (declare-sort tptp.list_P1040014977_state 0)
% 0.29/0.79 (declare-sort tptp.set_Pr849496667_state 0)
% 0.29/0.79 (declare-sort tptp.produc258871771st_com 0)
% 0.29/0.79 (declare-sort tptp.produc2041926651_state 0)
% 0.29/0.79 (declare-sort tptp.set_Pr1822651163om_com 0)
% 0.29/0.79 (declare-sort tptp.product_prod_com_com 0)
% 0.29/0.79 (declare-sort tptp.list_list_com 0)
% 0.29/0.79 (declare-sort tptp.list_state 0)
% 0.29/0.79 (declare-sort tptp.set_state 0)
% 0.29/0.79 (declare-sort tptp.list_com 0)
% 0.29/0.79 (declare-sort tptp.state 0)
% 0.29/0.79 (declare-sort tptp.com 0)
% 0.29/0.79 (declare-sort tptp.nat 0)
% 0.29/0.79 (declare-fun tptp.append_list_com (tptp.list_list_com tptp.list_list_com) tptp.list_list_com)
% 0.29/0.79 (declare-fun tptp.append_com (tptp.list_com tptp.list_com) tptp.list_com)
% 0.29/0.79 (declare-fun tptp.append982487830_state (tptp.list_P1040014977_state tptp.list_P1040014977_state) tptp.list_P1040014977_state)
% 0.29/0.79 (declare-fun tptp.append221843330_state (tptp.list_P890094829_state tptp.list_P890094829_state) tptp.list_P890094829_state)
% 0.29/0.79 (declare-fun tptp.bind_com_com (tptp.list_com (-> tptp.com tptp.list_com)) tptp.list_com)
% 0.29/0.79 (declare-fun tptp.butlast_com (tptp.list_com) tptp.list_com)
% 0.29/0.79 (declare-fun tptp.concat_com (tptp.list_list_com) tptp.list_com)
% 0.29/0.79 (declare-fun tptp.insert_com (tptp.com tptp.list_com) tptp.list_com)
% 0.29/0.79 (declare-fun tptp.last_com (tptp.list_com) tptp.com)
% 0.29/0.79 (declare-fun tptp.lenlex_com (tptp.set_Pr1822651163om_com) tptp.set_Pr602326075st_com)
% 0.29/0.79 (declare-fun tptp.lenlex295247238_state (tptp.set_Pr1165141447_state) tptp.set_Pr1142642759_state)
% 0.29/0.79 (declare-fun tptp.lenlex1401983474_state (tptp.set_Pr2096893127_state) tptp.set_Pr1325664839_state)
% 0.29/0.79 (declare-fun tptp.lex_com (tptp.set_Pr1822651163om_com) tptp.set_Pr602326075st_com)
% 0.29/0.79 (declare-fun tptp.lex_Pr570247525_state (tptp.set_Pr1165141447_state) tptp.set_Pr1142642759_state)
% 0.29/0.79 (declare-fun tptp.lex_Pr1762629969_state (tptp.set_Pr2096893127_state) tptp.set_Pr1325664839_state)
% 0.29/0.79 (declare-fun tptp.lexord_com (tptp.set_Pr1822651163om_com) tptp.set_Pr602326075st_com)
% 0.29/0.79 (declare-fun tptp.lexord1062073966_state (tptp.set_Pr1165141447_state) tptp.set_Pr1142642759_state)
% 0.29/0.79 (declare-fun tptp.lexord1893203674_state (tptp.set_Pr2096893127_state) tptp.set_Pr1325664839_state)
% 0.29/0.79 (declare-fun tptp.cons_P1821701106te_nat ((-> tptp.produc2041926651_state tptp.nat) tptp.list_P1178430914te_nat) tptp.list_P1178430914te_nat)
% 0.29/0.79 (declare-fun tptp.cons_P1631380062te_nat ((-> tptp.produc410756839_state tptp.nat) tptp.list_P1627643054te_nat) tptp.list_P1627643054te_nat)
% 0.29/0.79 (declare-fun tptp.cons_list_com (tptp.list_com tptp.list_list_com) tptp.list_list_com)
% 0.29/0.79 (declare-fun tptp.cons_com (tptp.com tptp.list_com) tptp.list_com)
% 0.29/0.79 (declare-fun tptp.cons_state (tptp.state tptp.list_state) tptp.list_state)
% 0.29/0.79 (declare-fun tptp.cons_P465369265_state (tptp.produc2041926651_state tptp.list_P1040014977_state) tptp.list_P1040014977_state)
% 0.29/0.79 (declare-fun tptp.cons_P438230685_state (tptp.produc410756839_state tptp.list_P890094829_state) tptp.list_P890094829_state)
% 0.29/0.79 (declare-fun tptp.nil_Pr1876916290te_nat () tptp.list_P1178430914te_nat)
% 0.29/0.79 (declare-fun tptp.nil_Pr164089518te_nat () tptp.list_P1627643054te_nat)
% 0.29/0.79 (declare-fun tptp.nil_list_com () tptp.list_list_com)
% 0.29/0.79 (declare-fun tptp.nil_com () tptp.list_com)
% 0.29/0.79 (declare-fun tptp.nil_state () tptp.list_state)
% 0.29/0.79 (declare-fun tptp.nil_Pr1844458753_state () tptp.list_P1040014977_state)
% 0.29/0.79 (declare-fun tptp.nil_Pr1347322605_state () tptp.list_P890094829_state)
% 0.29/0.79 (declare-fun tptp.list_ex1_com ((-> tptp.com Bool) tptp.list_com) Bool)
% 0.29/0.79 (declare-fun tptp.list_update_com (tptp.list_com tptp.nat tptp.com) tptp.list_com)
% 0.29/0.79 (declare-fun tptp.list_u737668969_state (tptp.list_P1040014977_state tptp.nat tptp.produc2041926651_state) tptp.list_P1040014977_state)
% 0.29/0.79 (declare-fun tptp.list_u364351829_state (tptp.list_P890094829_state tptp.nat tptp.produc410756839_state) tptp.list_P890094829_state)
% 0.29/0.79 (declare-fun tptp.listrel1_com (tptp.set_Pr1822651163om_com) tptp.set_Pr602326075st_com)
% 0.29/0.79 (declare-fun tptp.listre1738592858_state (tptp.set_Pr1165141447_state) tptp.set_Pr1142642759_state)
% 0.29/0.79 (declare-fun tptp.listre1725776070_state (tptp.set_Pr2096893127_state) tptp.set_Pr1325664839_state)
% 0.29/0.79 (declare-fun tptp.listre1268245261_state (tptp.set_Pr849496667_state) tptp.set_Pr391631483_state)
% 0.29/0.79 (declare-fun tptp.listrel_com_com (tptp.set_Pr1822651163om_com) tptp.set_Pr602326075st_com)
% 0.29/0.79 (declare-fun tptp.listre194873521_state (tptp.set_Pr1165141447_state) tptp.set_Pr1142642759_state)
% 0.29/0.79 (declare-fun tptp.listre1244407729_state (tptp.set_Pr2096893127_state) tptp.set_Pr1325664839_state)
% 0.29/0.79 (declare-fun tptp.maps_com_com ((-> tptp.com tptp.list_com) tptp.list_com) tptp.list_com)
% 0.29/0.79 (declare-fun tptp.measur1071343867_state (tptp.list_P1178430914te_nat) tptp.set_Pr1165141447_state)
% 0.29/0.79 (declare-fun tptp.measur768621543_state (tptp.list_P1627643054te_nat) tptp.set_Pr2096893127_state)
% 0.29/0.79 (declare-fun tptp.nth_list_com (tptp.list_list_com tptp.nat) tptp.list_com)
% 0.29/0.79 (declare-fun tptp.nth_com (tptp.list_com tptp.nat) tptp.com)
% 0.29/0.79 (declare-fun tptp.nth_state (tptp.list_state tptp.nat) tptp.state)
% 0.29/0.79 (declare-fun tptp.nth_Pr553241858_state (tptp.list_P1040014977_state tptp.nat) tptp.produc2041926651_state)
% 0.29/0.79 (declare-fun tptp.nth_Pr526167918_state (tptp.list_P890094829_state tptp.nat) tptp.produc410756839_state)
% 0.29/0.79 (declare-fun tptp.product_lists_com (tptp.list_list_com) tptp.list_list_com)
% 0.29/0.79 (declare-fun tptp.rotate1_com (tptp.list_com) tptp.list_com)
% 0.29/0.79 (declare-fun tptp.subseqs_com (tptp.list_com) tptp.list_list_com)
% 0.29/0.79 (declare-fun tptp.take_P558217449_state (tptp.nat tptp.list_P1040014977_state) tptp.list_P1040014977_state)
% 0.29/0.79 (declare-fun tptp.take_P1852316373_state (tptp.nat tptp.list_P890094829_state) tptp.list_P890094829_state)
% 0.29/0.79 (declare-fun tptp.size_s318434721st_com (tptp.list_list_com) tptp.nat)
% 0.29/0.79 (declare-fun tptp.size_size_list_com (tptp.list_com) tptp.nat)
% 0.29/0.79 (declare-fun tptp.size_size_list_state (tptp.list_state) tptp.nat)
% 0.29/0.79 (declare-fun tptp.size_s213202669_state (tptp.list_P1040014977_state) tptp.nat)
% 0.29/0.79 (declare-fun tptp.size_s837829465_state (tptp.list_P890094829_state) tptp.nat)
% 0.29/0.79 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 0.29/0.79 (declare-fun tptp.pHoare259243666_exec1 () tptp.set_Pr1165141447_state)
% 0.29/0.79 (declare-fun tptp.pHoare259243732_execs (tptp.state tptp.list_com tptp.state) Bool)
% 0.29/0.79 (declare-fun tptp.pHoare806997636termis (tptp.list_com tptp.state) Bool)
% 0.29/0.79 (declare-fun tptp.cond ((-> tptp.state Bool) tptp.com tptp.com) tptp.com)
% 0.29/0.79 (declare-fun tptp.do ((-> tptp.state tptp.set_state)) tptp.com)
% 0.29/0.79 (declare-fun tptp.semi (tptp.com tptp.com) tptp.com)
% 0.29/0.79 (declare-fun tptp.while ((-> tptp.state Bool) tptp.com) tptp.com)
% 0.29/0.79 (declare-fun tptp.exec (tptp.state tptp.com tptp.state) Bool)
% 0.29/0.79 (declare-fun tptp.termi (tptp.com tptp.state) Bool)
% 0.29/0.79 (declare-fun tptp.produc1914379986st_com ((-> tptp.com tptp.com Bool) tptp.list_com) tptp.produc2058209240st_com)
% 0.29/0.79 (declare-fun tptp.produc1742567891_state (tptp.list_list_com tptp.list_state) tptp.produc1393453339_state)
% 0.29/0.79 (declare-fun tptp.produc1307105171st_com (tptp.list_com tptp.list_com) tptp.produc258871771st_com)
% 0.29/0.79 (declare-fun tptp.produc1204172211_state (tptp.list_com tptp.state) tptp.produc2041926651_state)
% 0.29/0.79 (declare-fun tptp.produc1298457559_state (tptp.list_P1040014977_state tptp.list_P1040014977_state) tptp.produc1225889383_state)
% 0.29/0.79 (declare-fun tptp.produc1354769367_state (tptp.list_P890094829_state tptp.list_P890094829_state) tptp.produc1586269031_state)
% 0.29/0.79 (declare-fun tptp.product_Pair_com_com (tptp.com tptp.com) tptp.product_prod_com_com)
% 0.29/0.79 (declare-fun tptp.produc67337417st_com (tptp.produc2058209240st_com tptp.produc2058209240st_com) tptp.produc1440412305st_com)
% 0.29/0.79 (declare-fun tptp.produc67381847_state (tptp.produc1393453339_state tptp.produc1393453339_state) tptp.produc392316135_state)
% 0.29/0.79 (declare-fun tptp.produc313736791st_com (tptp.produc258871771st_com tptp.produc258871771st_com) tptp.produc1762014951st_com)
% 0.29/0.79 (declare-fun tptp.produc1909270103_state (tptp.produc2041926651_state tptp.produc2041926651_state) tptp.produc410756839_state)
% 0.29/0.79 (declare-fun tptp.produc984060759_state (tptp.produc1225889383_state tptp.produc1225889383_state) tptp.produc1519776487_state)
% 0.29/0.79 (declare-fun tptp.produc1576663895_state (tptp.produc1586269031_state tptp.produc1586269031_state) tptp.produc270545127_state)
% 0.29/0.79 (declare-fun tptp.produc2065881943_state (tptp.produc410756839_state tptp.produc410756839_state) tptp.produc186437863_state)
% 0.29/0.79 (declare-fun tptp.produc2049704791_state (tptp.produc186437863_state tptp.produc186437863_state) tptp.produc2046512871_state)
% 0.29/0.79 (declare-fun tptp.irrefl_com (tptp.set_Pr1822651163om_com) Bool)
% 0.29/0.79 (declare-fun tptp.irrefl654089520_state (tptp.set_Pr1165141447_state) Bool)
% 0.29/0.79 (declare-fun tptp.irrefl1358048924_state (tptp.set_Pr2096893127_state) Bool)
% 0.29/0.79 (declare-fun tptp.collect_state ((-> tptp.state Bool)) tptp.set_state)
% 0.29/0.79 (declare-fun tptp.collec300063826_state ((-> tptp.produc410756839_state Bool)) tptp.set_Pr1165141447_state)
% 0.29/0.79 (declare-fun tptp.collec489924946_state ((-> tptp.produc186437863_state Bool)) tptp.set_Pr2096893127_state)
% 0.29/0.79 (declare-fun tptp.transi436345274st_com (tptp.set_Pr602326075st_com) tptp.set_Pr602326075st_com)
% 0.29/0.79 (declare-fun tptp.transi339813252_state (tptp.set_Pr1142642759_state) tptp.set_Pr1142642759_state)
% 0.29/0.79 (declare-fun tptp.transi1965148016_state (tptp.set_Pr1325664839_state) tptp.set_Pr1325664839_state)
% 0.29/0.79 (declare-fun tptp.transi863150634cl_com (tptp.set_Pr1822651163om_com) tptp.set_Pr1822651163om_com)
% 0.29/0.79 (declare-fun tptp.transi1592315797st_com (tptp.set_Pr135335153st_com) tptp.set_Pr135335153st_com)
% 0.29/0.79 (declare-fun tptp.transi89280670_state (tptp.set_Pr1419004359_state) tptp.set_Pr1419004359_state)
% 0.29/0.79 (declare-fun tptp.transi1782245470st_com (tptp.set_Pr2083163591st_com) tptp.set_Pr2083163591st_com)
% 0.29/0.79 (declare-fun tptp.transi1302705790_state (tptp.set_Pr1165141447_state) tptp.set_Pr1165141447_state)
% 0.29/0.79 (declare-fun tptp.transi1428749162_state (tptp.set_Pr1847866567_state) tptp.set_Pr1847866567_state)
% 0.29/0.79 (declare-fun tptp.transi445721450_state (tptp.set_Pr1696918727_state) tptp.set_Pr1696918727_state)
% 0.29/0.79 (declare-fun tptp.transi463013610_state (tptp.set_Pr2096893127_state) tptp.set_Pr2096893127_state)
% 0.29/0.79 (declare-fun tptp.transi152726506_state (tptp.set_Pr541394119_state) tptp.set_Pr541394119_state)
% 0.29/0.79 (declare-fun tptp.member_state (tptp.state tptp.set_state) Bool)
% 0.29/0.79 (declare-fun tptp.member1442949316_state (tptp.produc1393453339_state tptp.set_Pr391631483_state) Bool)
% 0.29/0.79 (declare-fun tptp.member32358020st_com (tptp.produc258871771st_com tptp.set_Pr602326075st_com) Bool)
% 0.29/0.79 (declare-fun tptp.member64234660_state (tptp.produc2041926651_state tptp.set_Pr849496667_state) Bool)
% 0.29/0.79 (declare-fun tptp.member1267359376_state (tptp.produc1225889383_state tptp.set_Pr1142642759_state) Bool)
% 0.29/0.79 (declare-fun tptp.member423306384_state (tptp.produc1586269031_state tptp.set_Pr1325664839_state) Bool)
% 0.29/0.79 (declare-fun tptp.member1333916004om_com (tptp.product_prod_com_com tptp.set_Pr1822651163om_com) Bool)
% 0.29/0.79 (declare-fun tptp.member89779770st_com (tptp.produc1440412305st_com tptp.set_Pr135335153st_com) Bool)
% 0.29/0.79 (declare-fun tptp.member1414265872_state (tptp.produc392316135_state tptp.set_Pr1419004359_state) Bool)
% 0.29/0.79 (declare-fun tptp.member919914512st_com (tptp.produc1762014951st_com tptp.set_Pr2083163591st_com) Bool)
% 0.29/0.79 (declare-fun tptp.member1069318160_state (tptp.produc410756839_state tptp.set_Pr1165141447_state) Bool)
% 0.29/0.79 (declare-fun tptp.member2092727056_state (tptp.produc1519776487_state tptp.set_Pr1847866567_state) Bool)
% 0.29/0.79 (declare-fun tptp.member1642814224_state (tptp.produc270545127_state tptp.set_Pr1696918727_state) Bool)
% 0.29/0.79 (declare-fun tptp.member512523024_state (tptp.produc186437863_state tptp.set_Pr2096893127_state) Bool)
% 0.29/0.79 (declare-fun tptp.member284400400_state (tptp.produc2046512871_state tptp.set_Pr541394119_state) Bool)
% 0.29/0.79 (declare-fun tptp.c () tptp.com)
% 0.29/0.79 (declare-fun tptp.c2 () tptp.com)
% 0.29/0.79 (declare-fun tptp.cs () tptp.list_com)
% 0.29/0.79 (declare-fun tptp.s () tptp.state)
% 0.29/0.79 (declare-fun tptp.s2 () tptp.state)
% 0.29/0.79 (assert (forall ((S tptp.state) (Cs tptp.list_com) (S2 tptp.state)) (not (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state tptp.nil_com) S)) (@ (@ tptp.produc1204172211_state Cs) S2))) tptp.pHoare259243666_exec1))))
% 0.29/0.79 (assert (forall ((C tptp.com) (Cs2 tptp.list_com) (S tptp.state)) (= (@ (@ tptp.pHoare806997636termis (@ (@ tptp.cons_com C) Cs2)) S) (and (@ (@ tptp.termi C) S) (forall ((T tptp.state)) (=> (@ (@ (@ tptp.exec S) C) T) (@ (@ tptp.pHoare806997636termis Cs2) T)))))))
% 0.29/0.79 (assert (forall ((S tptp.state)) (@ (@ tptp.pHoare806997636termis tptp.nil_com) S)))
% 0.29/0.79 (assert (forall ((S tptp.state) (C tptp.com) (S2 tptp.state) (Cs2 tptp.list_com)) (=> (@ (@ (@ tptp.exec S) C) S2) (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state (@ (@ tptp.cons_com C) Cs2)) S)) (@ (@ tptp.produc1204172211_state Cs2) S2))) (@ tptp.transi1302705790_state tptp.pHoare259243666_exec1)))))
% 0.29/0.79 (assert (forall ((C tptp.com) (S tptp.state) (T2 tptp.state)) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state (@ (@ tptp.cons_com C) tptp.nil_com)) S)) (@ (@ tptp.produc1204172211_state tptp.nil_com) T2))) (@ tptp.transi1302705790_state tptp.pHoare259243666_exec1)) (@ (@ (@ tptp.exec S) C) T2))))
% 0.29/0.79 (assert (forall ((Cs2 tptp.list_com) (S tptp.state) (Cs tptp.list_com) (S2 tptp.state)) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state Cs2) S)) (@ (@ tptp.produc1204172211_state Cs) S2))) tptp.pHoare259243666_exec1) (=> (@ (@ tptp.pHoare806997636termis Cs2) S) (@ (@ tptp.pHoare806997636termis Cs) S2)))))
% 0.29/0.79 (assert (forall ((Cs2 tptp.list_com) (S tptp.state) (Cs tptp.list_com) (S2 tptp.state)) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state Cs2) S)) (@ (@ tptp.produc1204172211_state Cs) S2))) (@ tptp.transi1302705790_state tptp.pHoare259243666_exec1)) (=> (@ (@ tptp.pHoare806997636termis Cs2) S) (@ (@ tptp.pHoare806997636termis Cs) S2)))))
% 0.29/0.79 (assert (forall ((Ax tptp.list_P890094829_state) (Ay tptp.list_P890094829_state) (Bx tptp.list_P890094829_state) (By tptp.list_P890094829_state) (R tptp.set_Pr1696918727_state) (P (-> tptp.list_P890094829_state tptp.list_P890094829_state Bool))) (=> (@ (@ tptp.member1642814224_state (@ (@ tptp.produc1576663895_state (@ (@ tptp.produc1354769367_state Ax) Ay)) (@ (@ tptp.produc1354769367_state Bx) By))) (@ tptp.transi445721450_state R)) (=> (@ (@ P Ax) Ay) (=> (forall ((A tptp.list_P890094829_state) (B tptp.list_P890094829_state) (Aa tptp.list_P890094829_state) (Ba tptp.list_P890094829_state)) (let ((_let_1 (@ (@ tptp.produc1354769367_state A) B))) (=> (@ (@ tptp.member1642814224_state (@ (@ tptp.produc1576663895_state (@ (@ tptp.produc1354769367_state Ax) Ay)) _let_1)) (@ tptp.transi445721450_state R)) (=> (@ (@ tptp.member1642814224_state (@ (@ tptp.produc1576663895_state _let_1) (@ (@ tptp.produc1354769367_state Aa) Ba))) R) (=> (@ (@ P A) B) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))))
% 0.29/0.79 (assert (forall ((Ax tptp.list_P1040014977_state) (Ay tptp.list_P1040014977_state) (Bx tptp.list_P1040014977_state) (By tptp.list_P1040014977_state) (R tptp.set_Pr1847866567_state) (P (-> tptp.list_P1040014977_state tptp.list_P1040014977_state Bool))) (=> (@ (@ tptp.member2092727056_state (@ (@ tptp.produc984060759_state (@ (@ tptp.produc1298457559_state Ax) Ay)) (@ (@ tptp.produc1298457559_state Bx) By))) (@ tptp.transi1428749162_state R)) (=> (@ (@ P Ax) Ay) (=> (forall ((A tptp.list_P1040014977_state) (B tptp.list_P1040014977_state) (Aa tptp.list_P1040014977_state) (Ba tptp.list_P1040014977_state)) (let ((_let_1 (@ (@ tptp.produc1298457559_state A) B))) (=> (@ (@ tptp.member2092727056_state (@ (@ tptp.produc984060759_state (@ (@ tptp.produc1298457559_state Ax) Ay)) _let_1)) (@ tptp.transi1428749162_state R)) (=> (@ (@ tptp.member2092727056_state (@ (@ tptp.produc984060759_state _let_1) (@ (@ tptp.produc1298457559_state Aa) Ba))) R) (=> (@ (@ P A) B) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))))
% 0.29/0.79 (assert (forall ((Ax tptp.list_com) (Ay tptp.list_com) (Bx tptp.list_com) (By tptp.list_com) (R tptp.set_Pr2083163591st_com) (P (-> tptp.list_com tptp.list_com Bool))) (=> (@ (@ tptp.member919914512st_com (@ (@ tptp.produc313736791st_com (@ (@ tptp.produc1307105171st_com Ax) Ay)) (@ (@ tptp.produc1307105171st_com Bx) By))) (@ tptp.transi1782245470st_com R)) (=> (@ (@ P Ax) Ay) (=> (forall ((A tptp.list_com) (B tptp.list_com) (Aa tptp.list_com) (Ba tptp.list_com)) (let ((_let_1 (@ (@ tptp.produc1307105171st_com A) B))) (=> (@ (@ tptp.member919914512st_com (@ (@ tptp.produc313736791st_com (@ (@ tptp.produc1307105171st_com Ax) Ay)) _let_1)) (@ tptp.transi1782245470st_com R)) (=> (@ (@ tptp.member919914512st_com (@ (@ tptp.produc313736791st_com _let_1) (@ (@ tptp.produc1307105171st_com Aa) Ba))) R) (=> (@ (@ P A) B) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))))
% 0.29/0.79 (assert (forall ((Ax tptp.list_list_com) (Ay tptp.list_state) (Bx tptp.list_list_com) (By tptp.list_state) (R tptp.set_Pr1419004359_state) (P (-> tptp.list_list_com tptp.list_state Bool))) (=> (@ (@ tptp.member1414265872_state (@ (@ tptp.produc67381847_state (@ (@ tptp.produc1742567891_state Ax) Ay)) (@ (@ tptp.produc1742567891_state Bx) By))) (@ tptp.transi89280670_state R)) (=> (@ (@ P Ax) Ay) (=> (forall ((A tptp.list_list_com) (B tptp.list_state) (Aa tptp.list_list_com) (Ba tptp.list_state)) (let ((_let_1 (@ (@ tptp.produc1742567891_state A) B))) (=> (@ (@ tptp.member1414265872_state (@ (@ tptp.produc67381847_state (@ (@ tptp.produc1742567891_state Ax) Ay)) _let_1)) (@ tptp.transi89280670_state R)) (=> (@ (@ tptp.member1414265872_state (@ (@ tptp.produc67381847_state _let_1) (@ (@ tptp.produc1742567891_state Aa) Ba))) R) (=> (@ (@ P A) B) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))))
% 0.29/0.79 (assert (forall ((Ax (-> tptp.com tptp.com Bool)) (Ay tptp.list_com) (Bx (-> tptp.com tptp.com Bool)) (By tptp.list_com) (R tptp.set_Pr135335153st_com) (P (-> (-> tptp.com tptp.com Bool) tptp.list_com Bool))) (=> (@ (@ tptp.member89779770st_com (@ (@ tptp.produc67337417st_com (@ (@ tptp.produc1914379986st_com Ax) Ay)) (@ (@ tptp.produc1914379986st_com Bx) By))) (@ tptp.transi1592315797st_com R)) (=> (@ (@ P Ax) Ay) (=> (forall ((A (-> tptp.com tptp.com Bool)) (B tptp.list_com) (Aa (-> tptp.com tptp.com Bool)) (Ba tptp.list_com)) (let ((_let_1 (@ (@ tptp.produc1914379986st_com A) B))) (=> (@ (@ tptp.member89779770st_com (@ (@ tptp.produc67337417st_com (@ (@ tptp.produc1914379986st_com Ax) Ay)) _let_1)) (@ tptp.transi1592315797st_com R)) (=> (@ (@ tptp.member89779770st_com (@ (@ tptp.produc67337417st_com _let_1) (@ (@ tptp.produc1914379986st_com Aa) Ba))) R) (=> (@ (@ P A) B) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))))
% 0.29/0.79 (assert (forall ((Ax tptp.produc410756839_state) (Ay tptp.produc410756839_state) (Bx tptp.produc410756839_state) (By tptp.produc410756839_state) (R tptp.set_Pr541394119_state) (P (-> tptp.produc410756839_state tptp.produc410756839_state Bool))) (=> (@ (@ tptp.member284400400_state (@ (@ tptp.produc2049704791_state (@ (@ tptp.produc2065881943_state Ax) Ay)) (@ (@ tptp.produc2065881943_state Bx) By))) (@ tptp.transi152726506_state R)) (=> (@ (@ P Ax) Ay) (=> (forall ((A tptp.produc410756839_state) (B tptp.produc410756839_state) (Aa tptp.produc410756839_state) (Ba tptp.produc410756839_state)) (let ((_let_1 (@ (@ tptp.produc2065881943_state A) B))) (=> (@ (@ tptp.member284400400_state (@ (@ tptp.produc2049704791_state (@ (@ tptp.produc2065881943_state Ax) Ay)) _let_1)) (@ tptp.transi152726506_state R)) (=> (@ (@ tptp.member284400400_state (@ (@ tptp.produc2049704791_state _let_1) (@ (@ tptp.produc2065881943_state Aa) Ba))) R) (=> (@ (@ P A) B) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))))
% 0.29/0.79 (assert (forall ((Ax tptp.produc2041926651_state) (Ay tptp.produc2041926651_state) (Bx tptp.produc2041926651_state) (By tptp.produc2041926651_state) (R tptp.set_Pr2096893127_state) (P (-> tptp.produc2041926651_state tptp.produc2041926651_state Bool))) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state (@ (@ tptp.produc1909270103_state Ax) Ay)) (@ (@ tptp.produc1909270103_state Bx) By))) (@ tptp.transi463013610_state R)) (=> (@ (@ P Ax) Ay) (=> (forall ((A tptp.produc2041926651_state) (B tptp.produc2041926651_state) (Aa tptp.produc2041926651_state) (Ba tptp.produc2041926651_state)) (let ((_let_1 (@ (@ tptp.produc1909270103_state A) B))) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state (@ (@ tptp.produc1909270103_state Ax) Ay)) _let_1)) (@ tptp.transi463013610_state R)) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state _let_1) (@ (@ tptp.produc1909270103_state Aa) Ba))) R) (=> (@ (@ P A) B) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))))
% 0.29/0.79 (assert (forall ((Ax tptp.list_com) (Ay tptp.state) (Bx tptp.list_com) (By tptp.state) (R tptp.set_Pr1165141447_state) (P (-> tptp.list_com tptp.state Bool))) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state Ax) Ay)) (@ (@ tptp.produc1204172211_state Bx) By))) (@ tptp.transi1302705790_state R)) (=> (@ (@ P Ax) Ay) (=> (forall ((A tptp.list_com) (B tptp.state) (Aa tptp.list_com) (Ba tptp.state)) (let ((_let_1 (@ (@ tptp.produc1204172211_state A) B))) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state Ax) Ay)) _let_1)) (@ tptp.transi1302705790_state R)) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state _let_1) (@ (@ tptp.produc1204172211_state Aa) Ba))) R) (=> (@ (@ P A) B) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))))
% 0.29/0.79 (assert (forall ((Xa tptp.list_P890094829_state) (Xb tptp.list_P890094829_state) (Za tptp.list_P890094829_state) (Zb tptp.list_P890094829_state) (R tptp.set_Pr1696918727_state)) (let ((_let_1 (@ (@ tptp.produc1354769367_state Za) Zb))) (let ((_let_2 (@ (@ tptp.produc1354769367_state Xa) Xb))) (=> (@ (@ tptp.member1642814224_state (@ (@ tptp.produc1576663895_state _let_2) _let_1)) (@ tptp.transi445721450_state R)) (=> (not (= _let_2 _let_1)) (not (forall ((A tptp.list_P890094829_state) (B tptp.list_P890094829_state)) (let ((_let_1 (@ (@ tptp.produc1354769367_state A) B))) (=> (@ (@ tptp.member1642814224_state (@ (@ tptp.produc1576663895_state (@ (@ tptp.produc1354769367_state Xa) Xb)) _let_1)) R) (not (@ (@ tptp.member1642814224_state (@ (@ tptp.produc1576663895_state _let_1) (@ (@ tptp.produc1354769367_state Za) Zb))) (@ tptp.transi445721450_state R)))))))))))))
% 0.29/0.79 (assert (forall ((Xa tptp.list_P1040014977_state) (Xb tptp.list_P1040014977_state) (Za tptp.list_P1040014977_state) (Zb tptp.list_P1040014977_state) (R tptp.set_Pr1847866567_state)) (let ((_let_1 (@ (@ tptp.produc1298457559_state Za) Zb))) (let ((_let_2 (@ (@ tptp.produc1298457559_state Xa) Xb))) (=> (@ (@ tptp.member2092727056_state (@ (@ tptp.produc984060759_state _let_2) _let_1)) (@ tptp.transi1428749162_state R)) (=> (not (= _let_2 _let_1)) (not (forall ((A tptp.list_P1040014977_state) (B tptp.list_P1040014977_state)) (let ((_let_1 (@ (@ tptp.produc1298457559_state A) B))) (=> (@ (@ tptp.member2092727056_state (@ (@ tptp.produc984060759_state (@ (@ tptp.produc1298457559_state Xa) Xb)) _let_1)) R) (not (@ (@ tptp.member2092727056_state (@ (@ tptp.produc984060759_state _let_1) (@ (@ tptp.produc1298457559_state Za) Zb))) (@ tptp.transi1428749162_state R)))))))))))))
% 0.29/0.79 (assert (forall ((Xa tptp.list_com) (Xb tptp.list_com) (Za tptp.list_com) (Zb tptp.list_com) (R tptp.set_Pr2083163591st_com)) (let ((_let_1 (@ (@ tptp.produc1307105171st_com Za) Zb))) (let ((_let_2 (@ (@ tptp.produc1307105171st_com Xa) Xb))) (=> (@ (@ tptp.member919914512st_com (@ (@ tptp.produc313736791st_com _let_2) _let_1)) (@ tptp.transi1782245470st_com R)) (=> (not (= _let_2 _let_1)) (not (forall ((A tptp.list_com) (B tptp.list_com)) (let ((_let_1 (@ (@ tptp.produc1307105171st_com A) B))) (=> (@ (@ tptp.member919914512st_com (@ (@ tptp.produc313736791st_com (@ (@ tptp.produc1307105171st_com Xa) Xb)) _let_1)) R) (not (@ (@ tptp.member919914512st_com (@ (@ tptp.produc313736791st_com _let_1) (@ (@ tptp.produc1307105171st_com Za) Zb))) (@ tptp.transi1782245470st_com R)))))))))))))
% 0.29/0.79 (assert (forall ((Xa tptp.list_list_com) (Xb tptp.list_state) (Za tptp.list_list_com) (Zb tptp.list_state) (R tptp.set_Pr1419004359_state)) (let ((_let_1 (@ (@ tptp.produc1742567891_state Za) Zb))) (let ((_let_2 (@ (@ tptp.produc1742567891_state Xa) Xb))) (=> (@ (@ tptp.member1414265872_state (@ (@ tptp.produc67381847_state _let_2) _let_1)) (@ tptp.transi89280670_state R)) (=> (not (= _let_2 _let_1)) (not (forall ((A tptp.list_list_com) (B tptp.list_state)) (let ((_let_1 (@ (@ tptp.produc1742567891_state A) B))) (=> (@ (@ tptp.member1414265872_state (@ (@ tptp.produc67381847_state (@ (@ tptp.produc1742567891_state Xa) Xb)) _let_1)) R) (not (@ (@ tptp.member1414265872_state (@ (@ tptp.produc67381847_state _let_1) (@ (@ tptp.produc1742567891_state Za) Zb))) (@ tptp.transi89280670_state R)))))))))))))
% 0.29/0.79 (assert (forall ((Xa (-> tptp.com tptp.com Bool)) (Xb tptp.list_com) (Za (-> tptp.com tptp.com Bool)) (Zb tptp.list_com) (R tptp.set_Pr135335153st_com)) (let ((_let_1 (@ (@ tptp.produc1914379986st_com Za) Zb))) (let ((_let_2 (@ (@ tptp.produc1914379986st_com Xa) Xb))) (=> (@ (@ tptp.member89779770st_com (@ (@ tptp.produc67337417st_com _let_2) _let_1)) (@ tptp.transi1592315797st_com R)) (=> (not (= _let_2 _let_1)) (not (forall ((A (-> tptp.com tptp.com Bool)) (B tptp.list_com)) (let ((_let_1 (@ (@ tptp.produc1914379986st_com A) B))) (=> (@ (@ tptp.member89779770st_com (@ (@ tptp.produc67337417st_com (@ (@ tptp.produc1914379986st_com Xa) Xb)) _let_1)) R) (not (@ (@ tptp.member89779770st_com (@ (@ tptp.produc67337417st_com _let_1) (@ (@ tptp.produc1914379986st_com Za) Zb))) (@ tptp.transi1592315797st_com R)))))))))))))
% 0.29/0.79 (assert (forall ((Xa tptp.produc410756839_state) (Xb tptp.produc410756839_state) (Za tptp.produc410756839_state) (Zb tptp.produc410756839_state) (R tptp.set_Pr541394119_state)) (let ((_let_1 (@ (@ tptp.produc2065881943_state Za) Zb))) (let ((_let_2 (@ (@ tptp.produc2065881943_state Xa) Xb))) (=> (@ (@ tptp.member284400400_state (@ (@ tptp.produc2049704791_state _let_2) _let_1)) (@ tptp.transi152726506_state R)) (=> (not (= _let_2 _let_1)) (not (forall ((A tptp.produc410756839_state) (B tptp.produc410756839_state)) (let ((_let_1 (@ (@ tptp.produc2065881943_state A) B))) (=> (@ (@ tptp.member284400400_state (@ (@ tptp.produc2049704791_state (@ (@ tptp.produc2065881943_state Xa) Xb)) _let_1)) R) (not (@ (@ tptp.member284400400_state (@ (@ tptp.produc2049704791_state _let_1) (@ (@ tptp.produc2065881943_state Za) Zb))) (@ tptp.transi152726506_state R)))))))))))))
% 0.29/0.79 (assert (forall ((Xa tptp.produc2041926651_state) (Xb tptp.produc2041926651_state) (Za tptp.produc2041926651_state) (Zb tptp.produc2041926651_state) (R tptp.set_Pr2096893127_state)) (let ((_let_1 (@ (@ tptp.produc1909270103_state Za) Zb))) (let ((_let_2 (@ (@ tptp.produc1909270103_state Xa) Xb))) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state _let_2) _let_1)) (@ tptp.transi463013610_state R)) (=> (not (= _let_2 _let_1)) (not (forall ((A tptp.produc2041926651_state) (B tptp.produc2041926651_state)) (let ((_let_1 (@ (@ tptp.produc1909270103_state A) B))) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state (@ (@ tptp.produc1909270103_state Xa) Xb)) _let_1)) R) (not (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state _let_1) (@ (@ tptp.produc1909270103_state Za) Zb))) (@ tptp.transi463013610_state R)))))))))))))
% 0.29/0.79 (assert (forall ((Xa tptp.list_com) (Xb tptp.state) (Za tptp.list_com) (Zb tptp.state) (R tptp.set_Pr1165141447_state)) (let ((_let_1 (@ (@ tptp.produc1204172211_state Za) Zb))) (let ((_let_2 (@ (@ tptp.produc1204172211_state Xa) Xb))) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state _let_2) _let_1)) (@ tptp.transi1302705790_state R)) (=> (not (= _let_2 _let_1)) (not (forall ((A tptp.list_com) (B tptp.state)) (let ((_let_1 (@ (@ tptp.produc1204172211_state A) B))) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state Xa) Xb)) _let_1)) R) (not (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state _let_1) (@ (@ tptp.produc1204172211_state Za) Zb))) (@ tptp.transi1302705790_state R)))))))))))))
% 0.29/0.79 (assert (forall ((Ax tptp.list_P890094829_state) (Ay tptp.list_P890094829_state) (Bx tptp.list_P890094829_state) (By tptp.list_P890094829_state) (R tptp.set_Pr1696918727_state) (P (-> tptp.list_P890094829_state tptp.list_P890094829_state Bool))) (=> (@ (@ tptp.member1642814224_state (@ (@ tptp.produc1576663895_state (@ (@ tptp.produc1354769367_state Ax) Ay)) (@ (@ tptp.produc1354769367_state Bx) By))) (@ tptp.transi445721450_state R)) (=> (@ (@ P Bx) By) (=> (forall ((A tptp.list_P890094829_state) (B tptp.list_P890094829_state) (Aa tptp.list_P890094829_state) (Ba tptp.list_P890094829_state)) (let ((_let_1 (@ (@ tptp.produc1354769367_state Aa) Ba))) (=> (@ (@ tptp.member1642814224_state (@ (@ tptp.produc1576663895_state (@ (@ tptp.produc1354769367_state A) B)) _let_1)) R) (=> (@ (@ tptp.member1642814224_state (@ (@ tptp.produc1576663895_state _let_1) (@ (@ tptp.produc1354769367_state Bx) By))) (@ tptp.transi445721450_state R)) (=> (@ (@ P Aa) Ba) (@ (@ P A) B)))))) (@ (@ P Ax) Ay))))))
% 0.29/0.79 (assert (forall ((Ax tptp.list_P1040014977_state) (Ay tptp.list_P1040014977_state) (Bx tptp.list_P1040014977_state) (By tptp.list_P1040014977_state) (R tptp.set_Pr1847866567_state) (P (-> tptp.list_P1040014977_state tptp.list_P1040014977_state Bool))) (=> (@ (@ tptp.member2092727056_state (@ (@ tptp.produc984060759_state (@ (@ tptp.produc1298457559_state Ax) Ay)) (@ (@ tptp.produc1298457559_state Bx) By))) (@ tptp.transi1428749162_state R)) (=> (@ (@ P Bx) By) (=> (forall ((A tptp.list_P1040014977_state) (B tptp.list_P1040014977_state) (Aa tptp.list_P1040014977_state) (Ba tptp.list_P1040014977_state)) (let ((_let_1 (@ (@ tptp.produc1298457559_state Aa) Ba))) (=> (@ (@ tptp.member2092727056_state (@ (@ tptp.produc984060759_state (@ (@ tptp.produc1298457559_state A) B)) _let_1)) R) (=> (@ (@ tptp.member2092727056_state (@ (@ tptp.produc984060759_state _let_1) (@ (@ tptp.produc1298457559_state Bx) By))) (@ tptp.transi1428749162_state R)) (=> (@ (@ P Aa) Ba) (@ (@ P A) B)))))) (@ (@ P Ax) Ay))))))
% 0.29/0.79 (assert (forall ((Ax tptp.list_com) (Ay tptp.list_com) (Bx tptp.list_com) (By tptp.list_com) (R tptp.set_Pr2083163591st_com) (P (-> tptp.list_com tptp.list_com Bool))) (=> (@ (@ tptp.member919914512st_com (@ (@ tptp.produc313736791st_com (@ (@ tptp.produc1307105171st_com Ax) Ay)) (@ (@ tptp.produc1307105171st_com Bx) By))) (@ tptp.transi1782245470st_com R)) (=> (@ (@ P Bx) By) (=> (forall ((A tptp.list_com) (B tptp.list_com) (Aa tptp.list_com) (Ba tptp.list_com)) (let ((_let_1 (@ (@ tptp.produc1307105171st_com Aa) Ba))) (=> (@ (@ tptp.member919914512st_com (@ (@ tptp.produc313736791st_com (@ (@ tptp.produc1307105171st_com A) B)) _let_1)) R) (=> (@ (@ tptp.member919914512st_com (@ (@ tptp.produc313736791st_com _let_1) (@ (@ tptp.produc1307105171st_com Bx) By))) (@ tptp.transi1782245470st_com R)) (=> (@ (@ P Aa) Ba) (@ (@ P A) B)))))) (@ (@ P Ax) Ay))))))
% 0.29/0.79 (assert (forall ((Ax tptp.list_list_com) (Ay tptp.list_state) (Bx tptp.list_list_com) (By tptp.list_state) (R tptp.set_Pr1419004359_state) (P (-> tptp.list_list_com tptp.list_state Bool))) (=> (@ (@ tptp.member1414265872_state (@ (@ tptp.produc67381847_state (@ (@ tptp.produc1742567891_state Ax) Ay)) (@ (@ tptp.produc1742567891_state Bx) By))) (@ tptp.transi89280670_state R)) (=> (@ (@ P Bx) By) (=> (forall ((A tptp.list_list_com) (B tptp.list_state) (Aa tptp.list_list_com) (Ba tptp.list_state)) (let ((_let_1 (@ (@ tptp.produc1742567891_state Aa) Ba))) (=> (@ (@ tptp.member1414265872_state (@ (@ tptp.produc67381847_state (@ (@ tptp.produc1742567891_state A) B)) _let_1)) R) (=> (@ (@ tptp.member1414265872_state (@ (@ tptp.produc67381847_state _let_1) (@ (@ tptp.produc1742567891_state Bx) By))) (@ tptp.transi89280670_state R)) (=> (@ (@ P Aa) Ba) (@ (@ P A) B)))))) (@ (@ P Ax) Ay))))))
% 0.29/0.79 (assert (forall ((Ax (-> tptp.com tptp.com Bool)) (Ay tptp.list_com) (Bx (-> tptp.com tptp.com Bool)) (By tptp.list_com) (R tptp.set_Pr135335153st_com) (P (-> (-> tptp.com tptp.com Bool) tptp.list_com Bool))) (=> (@ (@ tptp.member89779770st_com (@ (@ tptp.produc67337417st_com (@ (@ tptp.produc1914379986st_com Ax) Ay)) (@ (@ tptp.produc1914379986st_com Bx) By))) (@ tptp.transi1592315797st_com R)) (=> (@ (@ P Bx) By) (=> (forall ((A (-> tptp.com tptp.com Bool)) (B tptp.list_com) (Aa (-> tptp.com tptp.com Bool)) (Ba tptp.list_com)) (let ((_let_1 (@ (@ tptp.produc1914379986st_com Aa) Ba))) (=> (@ (@ tptp.member89779770st_com (@ (@ tptp.produc67337417st_com (@ (@ tptp.produc1914379986st_com A) B)) _let_1)) R) (=> (@ (@ tptp.member89779770st_com (@ (@ tptp.produc67337417st_com _let_1) (@ (@ tptp.produc1914379986st_com Bx) By))) (@ tptp.transi1592315797st_com R)) (=> (@ (@ P Aa) Ba) (@ (@ P A) B)))))) (@ (@ P Ax) Ay))))))
% 0.29/0.79 (assert (forall ((Ax tptp.produc410756839_state) (Ay tptp.produc410756839_state) (Bx tptp.produc410756839_state) (By tptp.produc410756839_state) (R tptp.set_Pr541394119_state) (P (-> tptp.produc410756839_state tptp.produc410756839_state Bool))) (=> (@ (@ tptp.member284400400_state (@ (@ tptp.produc2049704791_state (@ (@ tptp.produc2065881943_state Ax) Ay)) (@ (@ tptp.produc2065881943_state Bx) By))) (@ tptp.transi152726506_state R)) (=> (@ (@ P Bx) By) (=> (forall ((A tptp.produc410756839_state) (B tptp.produc410756839_state) (Aa tptp.produc410756839_state) (Ba tptp.produc410756839_state)) (let ((_let_1 (@ (@ tptp.produc2065881943_state Aa) Ba))) (=> (@ (@ tptp.member284400400_state (@ (@ tptp.produc2049704791_state (@ (@ tptp.produc2065881943_state A) B)) _let_1)) R) (=> (@ (@ tptp.member284400400_state (@ (@ tptp.produc2049704791_state _let_1) (@ (@ tptp.produc2065881943_state Bx) By))) (@ tptp.transi152726506_state R)) (=> (@ (@ P Aa) Ba) (@ (@ P A) B)))))) (@ (@ P Ax) Ay))))))
% 0.29/0.79 (assert (forall ((Ax tptp.produc2041926651_state) (Ay tptp.produc2041926651_state) (Bx tptp.produc2041926651_state) (By tptp.produc2041926651_state) (R tptp.set_Pr2096893127_state) (P (-> tptp.produc2041926651_state tptp.produc2041926651_state Bool))) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state (@ (@ tptp.produc1909270103_state Ax) Ay)) (@ (@ tptp.produc1909270103_state Bx) By))) (@ tptp.transi463013610_state R)) (=> (@ (@ P Bx) By) (=> (forall ((A tptp.produc2041926651_state) (B tptp.produc2041926651_state) (Aa tptp.produc2041926651_state) (Ba tptp.produc2041926651_state)) (let ((_let_1 (@ (@ tptp.produc1909270103_state Aa) Ba))) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state (@ (@ tptp.produc1909270103_state A) B)) _let_1)) R) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state _let_1) (@ (@ tptp.produc1909270103_state Bx) By))) (@ tptp.transi463013610_state R)) (=> (@ (@ P Aa) Ba) (@ (@ P A) B)))))) (@ (@ P Ax) Ay))))))
% 0.29/0.79 (assert (forall ((Ax tptp.list_com) (Ay tptp.state) (Bx tptp.list_com) (By tptp.state) (R tptp.set_Pr1165141447_state) (P (-> tptp.list_com tptp.state Bool))) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state Ax) Ay)) (@ (@ tptp.produc1204172211_state Bx) By))) (@ tptp.transi1302705790_state R)) (=> (@ (@ P Bx) By) (=> (forall ((A tptp.list_com) (B tptp.state) (Aa tptp.list_com) (Ba tptp.state)) (let ((_let_1 (@ (@ tptp.produc1204172211_state Aa) Ba))) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state A) B)) _let_1)) R) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state _let_1) (@ (@ tptp.produc1204172211_state Bx) By))) (@ tptp.transi1302705790_state R)) (=> (@ (@ P Aa) Ba) (@ (@ P A) B)))))) (@ (@ P Ax) Ay))))))
% 0.29/0.79 (assert (forall ((Cs2 tptp.list_com) (S tptp.state) (T2 tptp.state)) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state Cs2) S)) (@ (@ tptp.produc1204172211_state tptp.nil_com) T2))) (@ tptp.transi1302705790_state tptp.pHoare259243666_exec1)) (@ (@ (@ tptp.pHoare259243732_execs S) Cs2) T2))))
% 0.29/0.79 (assert (forall ((R tptp.set_Pr541394119_state)) (let ((_let_1 (@ tptp.transi152726506_state R))) (= (@ tptp.transi152726506_state _let_1) _let_1))))
% 0.29/0.79 (assert (forall ((R tptp.set_Pr602326075st_com)) (let ((_let_1 (@ tptp.transi436345274st_com R))) (= (@ tptp.transi436345274st_com _let_1) _let_1))))
% 0.29/0.79 (assert (forall ((R tptp.set_Pr1325664839_state)) (let ((_let_1 (@ tptp.transi1965148016_state R))) (= (@ tptp.transi1965148016_state _let_1) _let_1))))
% 0.29/0.79 (assert (forall ((R tptp.set_Pr1142642759_state)) (let ((_let_1 (@ tptp.transi339813252_state R))) (= (@ tptp.transi339813252_state _let_1) _let_1))))
% 0.29/0.79 (assert (forall ((R tptp.set_Pr1822651163om_com)) (let ((_let_1 (@ tptp.transi863150634cl_com R))) (= (@ tptp.transi863150634cl_com _let_1) _let_1))))
% 0.29/0.79 (assert (forall ((R tptp.set_Pr1165141447_state)) (let ((_let_1 (@ tptp.transi1302705790_state R))) (= (@ tptp.transi1302705790_state _let_1) _let_1))))
% 0.29/0.79 (assert (forall ((R tptp.set_Pr2096893127_state)) (let ((_let_1 (@ tptp.transi463013610_state R))) (= (@ tptp.transi463013610_state _let_1) _let_1))))
% 0.29/0.79 (assert (forall ((P2 tptp.produc2046512871_state) (R tptp.set_Pr541394119_state)) (let ((_let_1 (@ tptp.member284400400_state P2))) (=> (@ _let_1 R) (@ _let_1 (@ tptp.transi152726506_state R))))))
% 0.29/0.79 (assert (forall ((P2 tptp.produc258871771st_com) (R tptp.set_Pr602326075st_com)) (let ((_let_1 (@ tptp.member32358020st_com P2))) (=> (@ _let_1 R) (@ _let_1 (@ tptp.transi436345274st_com R))))))
% 0.29/0.79 (assert (forall ((P2 tptp.produc1586269031_state) (R tptp.set_Pr1325664839_state)) (let ((_let_1 (@ tptp.member423306384_state P2))) (=> (@ _let_1 R) (@ _let_1 (@ tptp.transi1965148016_state R))))))
% 0.29/0.79 (assert (forall ((P2 tptp.produc1225889383_state) (R tptp.set_Pr1142642759_state)) (let ((_let_1 (@ tptp.member1267359376_state P2))) (=> (@ _let_1 R) (@ _let_1 (@ tptp.transi339813252_state R))))))
% 0.29/0.79 (assert (forall ((P2 tptp.product_prod_com_com) (R tptp.set_Pr1822651163om_com)) (let ((_let_1 (@ tptp.member1333916004om_com P2))) (=> (@ _let_1 R) (@ _let_1 (@ tptp.transi863150634cl_com R))))))
% 0.29/0.79 (assert (forall ((P2 tptp.produc410756839_state) (R tptp.set_Pr1165141447_state)) (let ((_let_1 (@ tptp.member1069318160_state P2))) (=> (@ _let_1 R) (@ _let_1 (@ tptp.transi1302705790_state R))))))
% 0.29/0.79 (assert (forall ((P2 tptp.produc186437863_state) (R tptp.set_Pr2096893127_state)) (let ((_let_1 (@ tptp.member512523024_state P2))) (=> (@ _let_1 R) (@ _let_1 (@ tptp.transi463013610_state R))))))
% 0.29/0.79 (assert (forall ((X21 tptp.produc2041926651_state) (X22 tptp.list_P1040014977_state) (Y21 tptp.produc2041926651_state) (Y22 tptp.list_P1040014977_state)) (= (= (@ (@ tptp.cons_P465369265_state X21) X22) (@ (@ tptp.cons_P465369265_state Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))))
% 0.29/0.79 (assert (forall ((X21 tptp.state) (X22 tptp.list_state) (Y21 tptp.state) (Y22 tptp.list_state)) (= (= (@ (@ tptp.cons_state X21) X22) (@ (@ tptp.cons_state Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))))
% 0.29/0.79 (assert (forall ((X21 tptp.list_com) (X22 tptp.list_list_com) (Y21 tptp.list_com) (Y22 tptp.list_list_com)) (= (= (@ (@ tptp.cons_list_com X21) X22) (@ (@ tptp.cons_list_com Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))))
% 0.29/0.79 (assert (forall ((X21 (-> tptp.produc410756839_state tptp.nat)) (X22 tptp.list_P1627643054te_nat) (Y21 (-> tptp.produc410756839_state tptp.nat)) (Y22 tptp.list_P1627643054te_nat)) (= (= (@ (@ tptp.cons_P1631380062te_nat X21) X22) (@ (@ tptp.cons_P1631380062te_nat Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))))
% 0.29/0.79 (assert (forall ((X21 (-> tptp.produc2041926651_state tptp.nat)) (X22 tptp.list_P1178430914te_nat) (Y21 (-> tptp.produc2041926651_state tptp.nat)) (Y22 tptp.list_P1178430914te_nat)) (= (= (@ (@ tptp.cons_P1821701106te_nat X21) X22) (@ (@ tptp.cons_P1821701106te_nat Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))))
% 0.29/0.79 (assert (forall ((X21 tptp.com) (X22 tptp.list_com) (Y21 tptp.com) (Y22 tptp.list_com)) (= (= (@ (@ tptp.cons_com X21) X22) (@ (@ tptp.cons_com Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))))
% 0.29/0.79 (assert (forall ((X1 tptp.list_com) (X2 tptp.list_com) (Y1 tptp.list_com) (Y2 tptp.list_com)) (= (= (@ (@ tptp.produc1307105171st_com X1) X2) (@ (@ tptp.produc1307105171st_com Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 0.29/0.79 (assert (forall ((X1 tptp.list_list_com) (X2 tptp.list_state) (Y1 tptp.list_list_com) (Y2 tptp.list_state)) (= (= (@ (@ tptp.produc1742567891_state X1) X2) (@ (@ tptp.produc1742567891_state Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 0.29/0.79 (assert (forall ((X1 (-> tptp.com tptp.com Bool)) (X2 tptp.list_com) (Y1 (-> tptp.com tptp.com Bool)) (Y2 tptp.list_com)) (= (= (@ (@ tptp.produc1914379986st_com X1) X2) (@ (@ tptp.produc1914379986st_com Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 0.29/0.79 (assert (forall ((X1 tptp.produc2041926651_state) (X2 tptp.produc2041926651_state) (Y1 tptp.produc2041926651_state) (Y2 tptp.produc2041926651_state)) (= (= (@ (@ tptp.produc1909270103_state X1) X2) (@ (@ tptp.produc1909270103_state Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 0.29/0.79 (assert (forall ((X1 tptp.list_com) (X2 tptp.state) (Y1 tptp.list_com) (Y2 tptp.state)) (= (= (@ (@ tptp.produc1204172211_state X1) X2) (@ (@ tptp.produc1204172211_state Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 0.29/0.79 (assert (forall ((X1 tptp.produc410756839_state) (X2 tptp.produc410756839_state) (Y1 tptp.produc410756839_state) (Y2 tptp.produc410756839_state)) (= (= (@ (@ tptp.produc2065881943_state X1) X2) (@ (@ tptp.produc2065881943_state Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 0.29/0.79 (assert (forall ((A2 tptp.produc2041926651_state) (B2 tptp.produc2041926651_state) (A3 tptp.produc2041926651_state) (B3 tptp.produc2041926651_state)) (= (= (@ (@ tptp.produc1909270103_state A2) B2) (@ (@ tptp.produc1909270103_state A3) B3)) (and (= A2 A3) (= B2 B3)))))
% 0.29/0.79 (assert (forall ((A2 tptp.list_com) (B2 tptp.state) (A3 tptp.list_com) (B3 tptp.state)) (= (= (@ (@ tptp.produc1204172211_state A2) B2) (@ (@ tptp.produc1204172211_state A3) B3)) (and (= A2 A3) (= B2 B3)))))
% 0.29/0.79 (assert (forall ((A2 tptp.produc410756839_state) (B2 tptp.produc410756839_state) (A3 tptp.produc410756839_state) (B3 tptp.produc410756839_state)) (= (= (@ (@ tptp.produc2065881943_state A2) B2) (@ (@ tptp.produc2065881943_state A3) B3)) (and (= A2 A3) (= B2 B3)))))
% 0.29/0.79 (assert (forall ((Y tptp.produc410756839_state)) (not (forall ((A tptp.produc2041926651_state) (B tptp.list_com) (C2 tptp.state)) (not (= Y (@ (@ tptp.produc1909270103_state A) (@ (@ tptp.produc1204172211_state B) C2))))))))
% 0.29/0.79 (assert (forall ((Y tptp.produc186437863_state)) (not (forall ((A tptp.produc410756839_state) (B tptp.produc2041926651_state) (C2 tptp.produc2041926651_state)) (not (= Y (@ (@ tptp.produc2065881943_state A) (@ (@ tptp.produc1909270103_state B) C2))))))))
% 0.29/0.79 (assert (forall ((Y tptp.produc186437863_state)) (not (forall ((A tptp.produc410756839_state) (B tptp.produc2041926651_state) (C2 tptp.list_com) (D tptp.state)) (not (= Y (@ (@ tptp.produc2065881943_state A) (@ (@ tptp.produc1909270103_state B) (@ (@ tptp.produc1204172211_state C2) D)))))))))
% 0.29/0.79 (assert (forall ((X tptp.produc2058209240st_com)) (=> (forall ((P3 (-> tptp.com tptp.com Bool))) (not (= X (@ (@ tptp.produc1914379986st_com P3) tptp.nil_com)))) (=> (forall ((P3 (-> tptp.com tptp.com Bool)) (X3 tptp.com)) (not (= X (@ (@ tptp.produc1914379986st_com P3) (@ (@ tptp.cons_com X3) tptp.nil_com))))) (not (forall ((P3 (-> tptp.com tptp.com Bool)) (X3 tptp.com) (Y3 tptp.com) (Xs tptp.list_com)) (not (= X (@ (@ tptp.produc1914379986st_com P3) (@ (@ tptp.cons_com X3) (@ (@ tptp.cons_com Y3) Xs)))))))))))
% 0.29/0.79 (assert (forall ((X tptp.produc2058209240st_com)) (=> (forall ((P3 (-> tptp.com tptp.com Bool))) (not (= X (@ (@ tptp.produc1914379986st_com P3) tptp.nil_com)))) (not (forall ((P3 (-> tptp.com tptp.com Bool)) (X3 tptp.com) (Ys tptp.list_com)) (not (= X (@ (@ tptp.produc1914379986st_com P3) (@ (@ tptp.cons_com X3) Ys)))))))))
% 0.29/0.79 (assert (forall ((X tptp.produc258871771st_com)) (=> (forall ((Ys tptp.list_com)) (not (= X (@ (@ tptp.produc1307105171st_com tptp.nil_com) Ys)))) (=> (forall ((Xs tptp.list_com)) (not (= X (@ (@ tptp.produc1307105171st_com Xs) tptp.nil_com)))) (not (forall ((X3 tptp.com) (Xs tptp.list_com) (Y3 tptp.com) (Ys tptp.list_com)) (not (= X (@ (@ tptp.produc1307105171st_com (@ (@ tptp.cons_com X3) Xs)) (@ (@ tptp.cons_com Y3) Ys))))))))))
% 0.29/0.79 (assert (forall ((X tptp.produc258871771st_com)) (=> (forall ((Ys tptp.list_com)) (not (= X (@ (@ tptp.produc1307105171st_com tptp.nil_com) Ys)))) (not (forall ((X3 tptp.com) (Xs tptp.list_com) (Ys tptp.list_com)) (not (= X (@ (@ tptp.produc1307105171st_com (@ (@ tptp.cons_com X3) Xs)) Ys))))))))
% 0.29/0.79 (assert (forall ((S tptp.state)) (@ (@ (@ tptp.pHoare259243732_execs S) tptp.nil_com) S)))
% 0.29/0.79 (assert (forall ((P (-> tptp.produc410756839_state Bool)) (Prod tptp.produc410756839_state)) (=> (forall ((A tptp.produc2041926651_state) (B tptp.produc2041926651_state)) (@ P (@ (@ tptp.produc1909270103_state A) B))) (@ P Prod))))
% 0.29/0.79 (assert (forall ((P (-> tptp.produc2041926651_state Bool)) (Prod tptp.produc2041926651_state)) (=> (forall ((A tptp.list_com) (B tptp.state)) (@ P (@ (@ tptp.produc1204172211_state A) B))) (@ P Prod))))
% 0.29/0.79 (assert (forall ((P (-> tptp.produc186437863_state Bool)) (Prod tptp.produc186437863_state)) (=> (forall ((A tptp.produc410756839_state) (B tptp.produc410756839_state)) (@ P (@ (@ tptp.produc2065881943_state A) B))) (@ P Prod))))
% 0.29/0.79 (assert (forall ((Y tptp.produc410756839_state)) (not (forall ((A tptp.produc2041926651_state) (B tptp.produc2041926651_state)) (not (= Y (@ (@ tptp.produc1909270103_state A) B)))))))
% 0.29/0.79 (assert (forall ((Y tptp.produc2041926651_state)) (not (forall ((A tptp.list_com) (B tptp.state)) (not (= Y (@ (@ tptp.produc1204172211_state A) B)))))))
% 0.29/0.79 (assert (forall ((Y tptp.produc186437863_state)) (not (forall ((A tptp.produc410756839_state) (B tptp.produc410756839_state)) (not (= Y (@ (@ tptp.produc2065881943_state A) B)))))))
% 0.29/0.79 (assert (forall ((A2 tptp.produc2041926651_state) (B2 tptp.produc2041926651_state) (A3 tptp.produc2041926651_state) (B3 tptp.produc2041926651_state)) (=> (= (@ (@ tptp.produc1909270103_state A2) B2) (@ (@ tptp.produc1909270103_state A3) B3)) (not (=> (= A2 A3) (not (= B2 B3)))))))
% 0.29/0.79 (assert (forall ((A2 tptp.list_com) (B2 tptp.state) (A3 tptp.list_com) (B3 tptp.state)) (=> (= (@ (@ tptp.produc1204172211_state A2) B2) (@ (@ tptp.produc1204172211_state A3) B3)) (not (=> (= A2 A3) (not (= B2 B3)))))))
% 0.29/0.79 (assert (forall ((A2 tptp.produc410756839_state) (B2 tptp.produc410756839_state) (A3 tptp.produc410756839_state) (B3 tptp.produc410756839_state)) (=> (= (@ (@ tptp.produc2065881943_state A2) B2) (@ (@ tptp.produc2065881943_state A3) B3)) (not (=> (= A2 A3) (not (= B2 B3)))))))
% 0.29/0.79 (assert (forall ((P (-> tptp.produc410756839_state Bool)) (P2 tptp.produc410756839_state)) (=> (forall ((A tptp.produc2041926651_state) (B tptp.produc2041926651_state)) (@ P (@ (@ tptp.produc1909270103_state A) B))) (@ P P2))))
% 0.29/0.79 (assert (forall ((P (-> tptp.produc2041926651_state Bool)) (P2 tptp.produc2041926651_state)) (=> (forall ((A tptp.list_com) (B tptp.state)) (@ P (@ (@ tptp.produc1204172211_state A) B))) (@ P P2))))
% 0.29/0.79 (assert (forall ((P (-> tptp.produc186437863_state Bool)) (P2 tptp.produc186437863_state)) (=> (forall ((A tptp.produc410756839_state) (B tptp.produc410756839_state)) (@ P (@ (@ tptp.produc2065881943_state A) B))) (@ P P2))))
% 0.29/0.79 (assert (forall ((P2 tptp.produc410756839_state)) (exists ((X3 tptp.produc2041926651_state) (Y3 tptp.produc2041926651_state)) (= P2 (@ (@ tptp.produc1909270103_state X3) Y3)))))
% 0.29/0.79 (assert (forall ((P2 tptp.produc2041926651_state)) (exists ((X3 tptp.list_com) (Y3 tptp.state)) (= P2 (@ (@ tptp.produc1204172211_state X3) Y3)))))
% 0.29/0.79 (assert (forall ((P2 tptp.produc186437863_state)) (exists ((X3 tptp.produc410756839_state) (Y3 tptp.produc410756839_state)) (= P2 (@ (@ tptp.produc2065881943_state X3) Y3)))))
% 0.29/0.79 (assert (forall ((X tptp.com) (Xs2 tptp.list_com)) (not (= (@ (@ tptp.cons_com X) Xs2) Xs2))))
% 0.29/0.79 (assert (forall ((S tptp.state) (C tptp.com) (T2 tptp.state) (Cs2 tptp.list_com) (U tptp.state)) (=> (@ (@ (@ tptp.exec S) C) T2) (=> (@ (@ (@ tptp.pHoare259243732_execs T2) Cs2) U) (@ (@ (@ tptp.pHoare259243732_execs S) (@ (@ tptp.cons_com C) Cs2)) U)))))
% 0.29/0.79 (assert (forall ((P (-> (-> tptp.com tptp.com) tptp.list_com tptp.list_com Bool)) (A0 (-> tptp.com tptp.com)) (A1 tptp.list_com) (A22 tptp.list_com)) (=> (forall ((F (-> tptp.com tptp.com)) (X_1 tptp.list_com)) (@ (@ (@ P F) tptp.nil_com) X_1)) (=> (forall ((F (-> tptp.com tptp.com)) (A tptp.com) (As tptp.list_com) (Bs tptp.list_com)) (let ((_let_1 (@ P F))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_com (@ F A)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_com A) As)) Bs)))) (@ (@ (@ P A0) A1) A22)))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (P (-> tptp.list_com Bool))) (=> (not (= Xs2 tptp.nil_com)) (=> (forall ((X3 tptp.com)) (@ P (@ (@ tptp.cons_com X3) tptp.nil_com))) (=> (forall ((X3 tptp.com) (Xs tptp.list_com)) (=> (not (= Xs tptp.nil_com)) (=> (@ P Xs) (@ P (@ (@ tptp.cons_com X3) Xs))))) (@ P Xs2))))))
% 0.29/0.79 (assert (forall ((P (-> (-> tptp.com tptp.com Bool) tptp.list_com Bool)) (A0 (-> tptp.com tptp.com Bool)) (A1 tptp.list_com)) (=> (forall ((P3 (-> tptp.com tptp.com Bool))) (@ (@ P P3) tptp.nil_com)) (=> (forall ((P3 (-> tptp.com tptp.com Bool)) (X3 tptp.com)) (@ (@ P P3) (@ (@ tptp.cons_com X3) tptp.nil_com))) (=> (forall ((P3 (-> tptp.com tptp.com Bool)) (X3 tptp.com) (Y3 tptp.com) (Xs tptp.list_com)) (let ((_let_1 (@ (@ tptp.cons_com Y3) Xs))) (let ((_let_2 (@ P P3))) (=> (@ _let_2 _let_1) (@ _let_2 (@ (@ tptp.cons_com X3) _let_1)))))) (@ (@ P A0) A1))))))
% 0.29/0.79 (assert (forall ((P (-> tptp.list_com Bool)) (A0 tptp.list_com)) (=> (@ P tptp.nil_com) (=> (forall ((X3 tptp.com)) (@ P (@ (@ tptp.cons_com X3) tptp.nil_com))) (=> (forall ((X3 tptp.com) (Y3 tptp.com) (Xs tptp.list_com)) (let ((_let_1 (@ (@ tptp.cons_com Y3) Xs))) (let ((_let_2 (@ tptp.cons_com X3))) (let ((_let_3 (= X3 Y3))) (=> (=> _let_3 (@ P (@ _let_2 Xs))) (=> (=> (not _let_3) (@ P _let_1)) (@ P (@ _let_2 _let_1)))))))) (@ P A0))))))
% 0.29/0.79 (assert (forall ((P (-> (-> tptp.com tptp.com Bool) tptp.list_com Bool)) (A0 (-> tptp.com tptp.com Bool)) (A1 tptp.list_com)) (=> (forall ((P3 (-> tptp.com tptp.com Bool))) (@ (@ P P3) tptp.nil_com)) (=> (forall ((P3 (-> tptp.com tptp.com Bool)) (X3 tptp.com) (Ys tptp.list_com)) (let ((_let_1 (@ P P3))) (=> (@ _let_1 Ys) (@ _let_1 (@ (@ tptp.cons_com X3) Ys))))) (@ (@ P A0) A1)))))
% 0.29/0.79 (assert (forall ((X tptp.list_com)) (=> (not (= X tptp.nil_com)) (=> (forall ((X3 tptp.com)) (not (= X (@ (@ tptp.cons_com X3) tptp.nil_com)))) (not (forall ((X3 tptp.com) (Y3 tptp.com) (Xs tptp.list_com)) (not (= X (@ (@ tptp.cons_com X3) (@ (@ tptp.cons_com Y3) Xs))))))))))
% 0.29/0.79 (assert (forall ((X tptp.list_list_com)) (=> (not (= X tptp.nil_list_com)) (=> (forall ((Xss tptp.list_list_com)) (not (= X (@ (@ tptp.cons_list_com tptp.nil_com) Xss)))) (not (forall ((X3 tptp.com) (Xs tptp.list_com) (Xss tptp.list_list_com)) (not (= X (@ (@ tptp.cons_list_com (@ (@ tptp.cons_com X3) Xs)) Xss)))))))))
% 0.29/0.79 (assert (forall ((P (-> tptp.list_com tptp.list_com Bool)) (A0 tptp.list_com) (A1 tptp.list_com)) (=> (forall ((X_1 tptp.list_com)) (@ (@ P tptp.nil_com) X_1)) (=> (forall ((Xs tptp.list_com)) (@ (@ P Xs) tptp.nil_com)) (=> (forall ((X3 tptp.com) (Xs tptp.list_com) (Y3 tptp.com) (Ys tptp.list_com)) (let ((_let_1 (@ (@ tptp.cons_com Y3) Ys))) (let ((_let_2 (@ P (@ (@ tptp.cons_com X3) Xs)))) (=> (@ (@ P Xs) _let_1) (=> (@ _let_2 Ys) (@ _let_2 _let_1)))))) (@ (@ P A0) A1))))))
% 0.29/0.79 (assert (forall ((A2 tptp.produc410756839_state) (P (-> tptp.produc410756839_state Bool))) (= (@ (@ tptp.member1069318160_state A2) (@ tptp.collec300063826_state P)) (@ P A2))))
% 0.29/0.79 (assert (forall ((A2 tptp.state) (P (-> tptp.state Bool))) (= (@ (@ tptp.member_state A2) (@ tptp.collect_state P)) (@ P A2))))
% 0.29/0.79 (assert (forall ((A2 tptp.produc186437863_state) (P (-> tptp.produc186437863_state Bool))) (= (@ (@ tptp.member512523024_state A2) (@ tptp.collec489924946_state P)) (@ P A2))))
% 0.29/0.79 (assert (forall ((A4 tptp.set_Pr1165141447_state)) (= (@ tptp.collec300063826_state (lambda ((X4 tptp.produc410756839_state)) (@ (@ tptp.member1069318160_state X4) A4))) A4)))
% 0.29/0.79 (assert (forall ((A4 tptp.set_state)) (= (@ tptp.collect_state (lambda ((X4 tptp.state)) (@ (@ tptp.member_state X4) A4))) A4)))
% 0.29/0.79 (assert (forall ((A4 tptp.set_Pr2096893127_state)) (= (@ tptp.collec489924946_state (lambda ((X4 tptp.produc186437863_state)) (@ (@ tptp.member512523024_state X4) A4))) A4)))
% 0.29/0.79 (assert (forall ((P (-> tptp.list_com Bool)) (Xs2 tptp.list_com)) (=> (@ P tptp.nil_com) (=> (forall ((X3 tptp.com)) (@ P (@ (@ tptp.cons_com X3) tptp.nil_com))) (=> (forall ((X3 tptp.com) (Y3 tptp.com) (Zs tptp.list_com)) (let ((_let_1 (@ (@ tptp.cons_com Y3) Zs))) (=> (@ P Zs) (=> (@ P _let_1) (@ P (@ (@ tptp.cons_com X3) _let_1)))))) (@ P Xs2))))))
% 0.29/0.79 (assert (forall ((P (-> tptp.list_com tptp.list_com Bool)) (A0 tptp.list_com) (A1 tptp.list_com)) (=> (forall ((X_1 tptp.list_com)) (@ (@ P tptp.nil_com) X_1)) (=> (forall ((X3 tptp.com) (Xs tptp.list_com) (Ys tptp.list_com)) (=> (@ (@ P Ys) Xs) (@ (@ P (@ (@ tptp.cons_com X3) Xs)) Ys))) (@ (@ P A0) A1)))))
% 0.29/0.79 (assert (forall ((P (-> tptp.list_com tptp.list_com Bool)) (Xs2 tptp.list_com) (Ys2 tptp.list_com)) (=> (@ (@ P tptp.nil_com) tptp.nil_com) (=> (forall ((X3 tptp.com) (Xs tptp.list_com)) (@ (@ P (@ (@ tptp.cons_com X3) Xs)) tptp.nil_com)) (=> (forall ((Y3 tptp.com) (Ys tptp.list_com)) (@ (@ P tptp.nil_com) (@ (@ tptp.cons_com Y3) Ys))) (=> (forall ((X3 tptp.com) (Xs tptp.list_com) (Y3 tptp.com) (Ys tptp.list_com)) (=> (@ (@ P Xs) Ys) (@ (@ P (@ (@ tptp.cons_com X3) Xs)) (@ (@ tptp.cons_com Y3) Ys)))) (@ (@ P Xs2) Ys2)))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com)) (= (not (= Xs2 tptp.nil_com)) (exists ((Y4 tptp.com) (Ys3 tptp.list_com)) (= Xs2 (@ (@ tptp.cons_com Y4) Ys3))))))
% 0.29/0.79 (assert (forall ((P (-> tptp.list_com Bool)) (List tptp.list_com)) (=> (@ P tptp.nil_com) (=> (forall ((X12 tptp.com) (X23 tptp.list_com)) (=> (@ P X23) (@ P (@ (@ tptp.cons_com X12) X23)))) (@ P List)))))
% 0.29/0.79 (assert (forall ((Y tptp.list_com)) (=> (not (= Y tptp.nil_com)) (not (forall ((X212 tptp.com) (X222 tptp.list_com)) (not (= Y (@ (@ tptp.cons_com X212) X222))))))))
% 0.29/0.79 (assert (forall ((List tptp.list_com) (X21 tptp.com) (X22 tptp.list_com)) (=> (= List (@ (@ tptp.cons_com X21) X22)) (not (= List tptp.nil_com)))))
% 0.29/0.79 (assert (forall ((X21 tptp.com) (X22 tptp.list_com)) (not (= tptp.nil_com (@ (@ tptp.cons_com X21) X22)))))
% 0.29/0.79 (assert (forall ((X1 tptp.state) (X2 tptp.list_com) (X32 tptp.state) (P (-> tptp.state tptp.list_com tptp.state Bool))) (=> (@ (@ (@ tptp.pHoare259243732_execs X1) X2) X32) (=> (forall ((S3 tptp.state)) (@ (@ (@ P S3) tptp.nil_com) S3)) (=> (forall ((S3 tptp.state) (C2 tptp.com) (T3 tptp.state) (Cs3 tptp.list_com) (U2 tptp.state)) (=> (@ (@ (@ tptp.exec S3) C2) T3) (=> (@ (@ (@ tptp.pHoare259243732_execs T3) Cs3) U2) (=> (@ (@ (@ P T3) Cs3) U2) (@ (@ (@ P S3) (@ (@ tptp.cons_com C2) Cs3)) U2))))) (@ (@ (@ P X1) X2) X32))))))
% 0.29/0.79 (assert (= tptp.pHoare259243732_execs (lambda ((A12 tptp.state) (A23 tptp.list_com) (A32 tptp.state)) (or (exists ((S4 tptp.state)) (and (= A12 S4) (= A23 tptp.nil_com) (= A32 S4))) (exists ((S4 tptp.state) (C3 tptp.com) (T tptp.state) (Cs4 tptp.list_com) (U3 tptp.state)) (and (= A12 S4) (= A23 (@ (@ tptp.cons_com C3) Cs4)) (= A32 U3) (@ (@ (@ tptp.exec S4) C3) T) (@ (@ (@ tptp.pHoare259243732_execs T) Cs4) U3)))))))
% 0.29/0.79 (assert (forall ((A1 tptp.state) (A22 tptp.list_com) (A33 tptp.state)) (=> (@ (@ (@ tptp.pHoare259243732_execs A1) A22) A33) (=> (=> (= A22 tptp.nil_com) (not (= A33 A1))) (not (forall ((C2 tptp.com) (T3 tptp.state) (Cs3 tptp.list_com)) (=> (= A22 (@ (@ tptp.cons_com C2) Cs3)) (=> (@ (@ (@ tptp.exec A1) C2) T3) (not (@ (@ (@ tptp.pHoare259243732_execs T3) Cs3) A33))))))))))
% 0.29/0.79 (assert (forall ((A2 tptp.produc2041926651_state) (B2 tptp.produc2041926651_state) (R tptp.set_Pr1165141447_state) (C tptp.produc2041926651_state)) (let ((_let_1 (@ tptp.transi1302705790_state R))) (let ((_let_2 (@ tptp.produc1909270103_state A2))) (=> (@ (@ tptp.member1069318160_state (@ _let_2 B2)) R) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state B2) C)) _let_1) (@ (@ tptp.member1069318160_state (@ _let_2 C)) _let_1)))))))
% 0.29/0.79 (assert (forall ((A2 tptp.produc410756839_state) (B2 tptp.produc410756839_state) (R tptp.set_Pr2096893127_state) (C tptp.produc410756839_state)) (let ((_let_1 (@ tptp.transi463013610_state R))) (let ((_let_2 (@ tptp.produc2065881943_state A2))) (=> (@ (@ tptp.member512523024_state (@ _let_2 B2)) R) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state B2) C)) _let_1) (@ (@ tptp.member512523024_state (@ _let_2 C)) _let_1)))))))
% 0.29/0.79 (assert (forall ((A2 tptp.produc2041926651_state) (B2 tptp.produc2041926651_state) (R tptp.set_Pr1165141447_state) (C tptp.produc2041926651_state)) (let ((_let_1 (@ tptp.transi1302705790_state R))) (let ((_let_2 (@ tptp.produc1909270103_state A2))) (=> (@ (@ tptp.member1069318160_state (@ _let_2 B2)) _let_1) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state B2) C)) R) (@ (@ tptp.member1069318160_state (@ _let_2 C)) _let_1)))))))
% 0.29/0.79 (assert (forall ((A2 tptp.produc410756839_state) (B2 tptp.produc410756839_state) (R tptp.set_Pr2096893127_state) (C tptp.produc410756839_state)) (let ((_let_1 (@ tptp.transi463013610_state R))) (let ((_let_2 (@ tptp.produc2065881943_state A2))) (=> (@ (@ tptp.member512523024_state (@ _let_2 B2)) _let_1) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state B2) C)) R) (@ (@ tptp.member512523024_state (@ _let_2 C)) _let_1)))))))
% 0.29/0.79 (assert (forall ((A2 tptp.produc2041926651_state) (B2 tptp.produc2041926651_state) (R tptp.set_Pr1165141447_state) (P (-> tptp.produc2041926651_state Bool))) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state A2) B2)) (@ tptp.transi1302705790_state R)) (=> (@ P B2) (=> (forall ((Y3 tptp.produc2041926651_state) (Z tptp.produc2041926651_state)) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state Y3) Z)) R) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state Z) B2)) (@ tptp.transi1302705790_state R)) (=> (@ P Z) (@ P Y3))))) (@ P A2))))))
% 0.29/0.79 (assert (forall ((A2 tptp.produc410756839_state) (B2 tptp.produc410756839_state) (R tptp.set_Pr2096893127_state) (P (-> tptp.produc410756839_state Bool))) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state A2) B2)) (@ tptp.transi463013610_state R)) (=> (@ P B2) (=> (forall ((Y3 tptp.produc410756839_state) (Z tptp.produc410756839_state)) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state Y3) Z)) R) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state Z) B2)) (@ tptp.transi463013610_state R)) (=> (@ P Z) (@ P Y3))))) (@ P A2))))))
% 0.29/0.79 (assert (forall ((A2 tptp.produc2041926651_state) (R tptp.set_Pr1165141447_state)) (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state A2) A2)) (@ tptp.transi1302705790_state R))))
% 0.29/0.79 (assert (forall ((A2 tptp.produc410756839_state) (R tptp.set_Pr2096893127_state)) (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state A2) A2)) (@ tptp.transi463013610_state R))))
% 0.29/0.79 (assert (forall ((X tptp.produc2041926651_state) (Z2 tptp.produc2041926651_state) (R tptp.set_Pr1165141447_state)) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state X) Z2)) (@ tptp.transi1302705790_state R)) (=> (not (= X Z2)) (not (forall ((Y3 tptp.produc2041926651_state)) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state X) Y3)) R) (not (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state Y3) Z2)) (@ tptp.transi1302705790_state R))))))))))
% 0.29/0.79 (assert (forall ((X tptp.produc410756839_state) (Z2 tptp.produc410756839_state) (R tptp.set_Pr2096893127_state)) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X) Z2)) (@ tptp.transi463013610_state R)) (=> (not (= X Z2)) (not (forall ((Y3 tptp.produc410756839_state)) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X) Y3)) R) (not (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state Y3) Z2)) (@ tptp.transi463013610_state R))))))))))
% 0.29/0.79 (assert (forall ((X1 tptp.produc2041926651_state) (X2 tptp.produc2041926651_state) (R tptp.set_Pr1165141447_state) (P (-> tptp.produc2041926651_state tptp.produc2041926651_state Bool))) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state X1) X2)) (@ tptp.transi1302705790_state R)) (=> (forall ((A tptp.produc2041926651_state)) (@ (@ P A) A)) (=> (forall ((A tptp.produc2041926651_state) (B tptp.produc2041926651_state) (C2 tptp.produc2041926651_state)) (let ((_let_1 (@ P A))) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state A) B)) (@ tptp.transi1302705790_state R)) (=> (@ _let_1 B) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state B) C2)) R) (@ _let_1 C2)))))) (@ (@ P X1) X2))))))
% 0.29/0.79 (assert (forall ((X1 tptp.produc410756839_state) (X2 tptp.produc410756839_state) (R tptp.set_Pr2096893127_state) (P (-> tptp.produc410756839_state tptp.produc410756839_state Bool))) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X1) X2)) (@ tptp.transi463013610_state R)) (=> (forall ((A tptp.produc410756839_state)) (@ (@ P A) A)) (=> (forall ((A tptp.produc410756839_state) (B tptp.produc410756839_state) (C2 tptp.produc410756839_state)) (let ((_let_1 (@ P A))) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state A) B)) (@ tptp.transi463013610_state R)) (=> (@ _let_1 B) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state B) C2)) R) (@ _let_1 C2)))))) (@ (@ P X1) X2))))))
% 0.29/0.79 (assert (forall ((A2 tptp.produc2041926651_state) (B2 tptp.produc2041926651_state) (R tptp.set_Pr1165141447_state) (P (-> tptp.produc2041926651_state Bool))) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state A2) B2)) (@ tptp.transi1302705790_state R)) (=> (@ P A2) (=> (forall ((Y3 tptp.produc2041926651_state) (Z tptp.produc2041926651_state)) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state A2) Y3)) (@ tptp.transi1302705790_state R)) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state Y3) Z)) R) (=> (@ P Y3) (@ P Z))))) (@ P B2))))))
% 0.29/0.79 (assert (forall ((A2 tptp.produc410756839_state) (B2 tptp.produc410756839_state) (R tptp.set_Pr2096893127_state) (P (-> tptp.produc410756839_state Bool))) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state A2) B2)) (@ tptp.transi463013610_state R)) (=> (@ P A2) (=> (forall ((Y3 tptp.produc410756839_state) (Z tptp.produc410756839_state)) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state A2) Y3)) (@ tptp.transi463013610_state R)) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state Y3) Z)) R) (=> (@ P Y3) (@ P Z))))) (@ P B2))))))
% 0.29/0.79 (assert (forall ((X tptp.produc2041926651_state) (Y tptp.produc2041926651_state) (R tptp.set_Pr1165141447_state) (Z2 tptp.produc2041926651_state)) (let ((_let_1 (@ tptp.transi1302705790_state R))) (let ((_let_2 (@ tptp.produc1909270103_state X))) (=> (@ (@ tptp.member1069318160_state (@ _let_2 Y)) _let_1) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state Y) Z2)) _let_1) (@ (@ tptp.member1069318160_state (@ _let_2 Z2)) _let_1)))))))
% 0.29/0.79 (assert (forall ((X tptp.produc410756839_state) (Y tptp.produc410756839_state) (R tptp.set_Pr2096893127_state) (Z2 tptp.produc410756839_state)) (let ((_let_1 (@ tptp.transi463013610_state R))) (let ((_let_2 (@ tptp.produc2065881943_state X))) (=> (@ (@ tptp.member512523024_state (@ _let_2 Y)) _let_1) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state Y) Z2)) _let_1) (@ (@ tptp.member512523024_state (@ _let_2 Z2)) _let_1)))))))
% 0.29/0.79 (assert (forall ((A1 tptp.produc2041926651_state) (A22 tptp.produc2041926651_state) (R tptp.set_Pr1165141447_state)) (= (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state A1) A22)) (@ tptp.transi1302705790_state R)) (or (exists ((A5 tptp.produc2041926651_state)) (and (= A1 A5) (= A22 A5))) (exists ((A5 tptp.produc2041926651_state) (B4 tptp.produc2041926651_state) (C3 tptp.produc2041926651_state)) (and (= A1 A5) (= A22 C3) (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state A5) B4)) (@ tptp.transi1302705790_state R)) (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state B4) C3)) R)))))))
% 0.29/0.79 (assert (forall ((A1 tptp.produc410756839_state) (A22 tptp.produc410756839_state) (R tptp.set_Pr2096893127_state)) (= (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state A1) A22)) (@ tptp.transi463013610_state R)) (or (exists ((A5 tptp.produc410756839_state)) (and (= A1 A5) (= A22 A5))) (exists ((A5 tptp.produc410756839_state) (B4 tptp.produc410756839_state) (C3 tptp.produc410756839_state)) (and (= A1 A5) (= A22 C3) (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state A5) B4)) (@ tptp.transi463013610_state R)) (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state B4) C3)) R)))))))
% 0.29/0.79 (assert (forall ((A1 tptp.produc2041926651_state) (A22 tptp.produc2041926651_state) (R tptp.set_Pr1165141447_state)) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state A1) A22)) (@ tptp.transi1302705790_state R)) (=> (not (= A22 A1)) (not (forall ((B tptp.produc2041926651_state)) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state A1) B)) (@ tptp.transi1302705790_state R)) (not (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state B) A22)) R)))))))))
% 0.29/0.79 (assert (forall ((A1 tptp.produc410756839_state) (A22 tptp.produc410756839_state) (R tptp.set_Pr2096893127_state)) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state A1) A22)) (@ tptp.transi463013610_state R)) (=> (not (= A22 A1)) (not (forall ((B tptp.produc410756839_state)) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state A1) B)) (@ tptp.transi463013610_state R)) (not (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state B) A22)) R)))))))))
% 0.29/0.79 (assert (forall ((A2 tptp.produc2041926651_state) (B2 tptp.produc2041926651_state) (R tptp.set_Pr1165141447_state)) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state A2) B2)) (@ tptp.transi1302705790_state R)) (=> (not (= A2 B2)) (not (forall ((Y3 tptp.produc2041926651_state)) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state A2) Y3)) (@ tptp.transi1302705790_state R)) (not (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state Y3) B2)) R)))))))))
% 0.29/0.79 (assert (forall ((A2 tptp.produc410756839_state) (B2 tptp.produc410756839_state) (R tptp.set_Pr2096893127_state)) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state A2) B2)) (@ tptp.transi463013610_state R)) (=> (not (= A2 B2)) (not (forall ((Y3 tptp.produc410756839_state)) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state A2) Y3)) (@ tptp.transi463013610_state R)) (not (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state Y3) B2)) R)))))))))
% 0.29/0.79 (assert (forall ((P (-> tptp.produc186437863_state Bool)) (X tptp.produc186437863_state)) (=> (forall ((A tptp.produc410756839_state) (B tptp.produc2041926651_state) (C2 tptp.list_com) (D tptp.state)) (@ P (@ (@ tptp.produc2065881943_state A) (@ (@ tptp.produc1909270103_state B) (@ (@ tptp.produc1204172211_state C2) D))))) (@ P X))))
% 0.29/0.79 (assert (forall ((P (-> tptp.produc410756839_state Bool)) (X tptp.produc410756839_state)) (=> (forall ((A tptp.produc2041926651_state) (B tptp.list_com) (C2 tptp.state)) (@ P (@ (@ tptp.produc1909270103_state A) (@ (@ tptp.produc1204172211_state B) C2)))) (@ P X))))
% 0.29/0.79 (assert (forall ((P (-> tptp.produc186437863_state Bool)) (X tptp.produc186437863_state)) (=> (forall ((A tptp.produc410756839_state) (B tptp.produc2041926651_state) (C2 tptp.produc2041926651_state)) (@ P (@ (@ tptp.produc2065881943_state A) (@ (@ tptp.produc1909270103_state B) C2)))) (@ P X))))
% 0.29/0.79 (assert (forall ((C1 tptp.com) (C22 tptp.com) (Cs2 tptp.list_com) (S tptp.state)) (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state (@ (@ tptp.cons_com (@ (@ tptp.semi C1) C22)) Cs2)) S)) (@ (@ tptp.produc1204172211_state (@ (@ tptp.cons_com C1) (@ (@ tptp.cons_com C22) Cs2))) S))) tptp.pHoare259243666_exec1)))
% 0.29/0.79 (assert (forall ((C1 tptp.com) (C22 tptp.com) (Cs2 tptp.list_com) (S tptp.state) (Cs tptp.list_com) (S2 tptp.state)) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state (@ (@ tptp.cons_com (@ (@ tptp.semi C1) C22)) Cs2)) S)) (@ (@ tptp.produc1204172211_state Cs) S2))) tptp.pHoare259243666_exec1) (not (=> (= Cs (@ (@ tptp.cons_com C1) (@ (@ tptp.cons_com C22) Cs2))) (not (= S2 S)))))))
% 0.29/0.79 (assert (forall ((T2 tptp.state) (F2 (-> tptp.state tptp.set_state)) (S tptp.state) (Cs2 tptp.list_com)) (=> (@ (@ tptp.member_state T2) (@ F2 S)) (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state (@ (@ tptp.cons_com (@ tptp.do F2)) Cs2)) S)) (@ (@ tptp.produc1204172211_state Cs2) T2))) tptp.pHoare259243666_exec1))))
% 0.29/0.79 (assert (forall ((F2 (-> tptp.state tptp.set_state)) (Cs2 tptp.list_com) (S tptp.state) (Cs tptp.list_com) (S2 tptp.state)) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state (@ (@ tptp.cons_com (@ tptp.do F2)) Cs2)) S)) (@ (@ tptp.produc1204172211_state Cs) S2))) tptp.pHoare259243666_exec1) (not (=> (= Cs Cs2) (not (@ (@ tptp.member_state S2) (@ F2 S))))))))
% 0.29/0.79 (assert (forall ((B2 (-> tptp.state Bool)) (S tptp.state) (C1 tptp.com) (C22 tptp.com) (Cs2 tptp.list_com)) (=> (not (@ B2 S)) (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state (@ (@ tptp.cons_com (@ (@ (@ tptp.cond B2) C1) C22)) Cs2)) S)) (@ (@ tptp.produc1204172211_state (@ (@ tptp.cons_com C22) Cs2)) S))) tptp.pHoare259243666_exec1))))
% 0.29/0.79 (assert (forall ((B2 (-> tptp.state Bool)) (S tptp.state) (C1 tptp.com) (C22 tptp.com) (Cs2 tptp.list_com)) (=> (@ B2 S) (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state (@ (@ tptp.cons_com (@ (@ (@ tptp.cond B2) C1) C22)) Cs2)) S)) (@ (@ tptp.produc1204172211_state (@ (@ tptp.cons_com C1) Cs2)) S))) tptp.pHoare259243666_exec1))))
% 0.29/0.79 (assert (forall ((B2 (-> tptp.state Bool)) (C1 tptp.com) (C22 tptp.com) (Cs2 tptp.list_com) (S tptp.state) (Cs tptp.list_com) (S2 tptp.state)) (let ((_let_1 (@ B2 S))) (let ((_let_2 (= S2 S))) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state (@ (@ tptp.cons_com (@ (@ (@ tptp.cond B2) C1) C22)) Cs2)) S)) (@ (@ tptp.produc1204172211_state Cs) S2))) tptp.pHoare259243666_exec1) (=> (=> (= Cs (@ (@ tptp.cons_com C1) Cs2)) (=> _let_2 (not _let_1))) (not (=> (= Cs (@ (@ tptp.cons_com C22) Cs2)) (=> _let_2 _let_1)))))))))
% 0.29/0.79 (assert (forall ((B2 (-> tptp.state Bool)) (S tptp.state) (C tptp.com) (Cs2 tptp.list_com)) (=> (not (@ B2 S)) (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state (@ (@ tptp.cons_com (@ (@ tptp.while B2) C)) Cs2)) S)) (@ (@ tptp.produc1204172211_state Cs2) S))) tptp.pHoare259243666_exec1))))
% 0.29/0.79 (assert (forall ((B2 (-> tptp.state Bool)) (S tptp.state) (C tptp.com) (Cs2 tptp.list_com)) (let ((_let_1 (@ (@ tptp.cons_com (@ (@ tptp.while B2) C)) Cs2))) (=> (@ B2 S) (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state _let_1) S)) (@ (@ tptp.produc1204172211_state (@ (@ tptp.cons_com C) _let_1)) S))) tptp.pHoare259243666_exec1)))))
% 0.29/0.79 (assert (forall ((B2 (-> tptp.state Bool)) (C tptp.com) (S tptp.state)) (=> (@ (@ tptp.termi (@ (@ tptp.while B2) C)) S) (=> (@ B2 S) (@ (@ tptp.termi C) S)))))
% 0.29/0.79 (assert (forall ((B2 (-> tptp.state Bool)) (C tptp.com) (S tptp.state) (T2 tptp.state)) (let ((_let_1 (@ tptp.termi (@ (@ tptp.while B2) C)))) (=> (@ _let_1 S) (=> (@ B2 S) (=> (@ (@ (@ tptp.exec S) C) T2) (@ _let_1 T2)))))))
% 0.29/0.79 (assert (forall ((B2 (-> tptp.state Bool)) (C tptp.com) (Cs2 tptp.list_com) (S tptp.state) (Cs tptp.list_com) (S2 tptp.state)) (let ((_let_1 (@ B2 S))) (let ((_let_2 (= S2 S))) (let ((_let_3 (@ (@ tptp.cons_com (@ (@ tptp.while B2) C)) Cs2))) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state _let_3) S)) (@ (@ tptp.produc1204172211_state Cs) S2))) tptp.pHoare259243666_exec1) (=> (=> (= Cs Cs2) (=> _let_2 _let_1)) (not (=> (= Cs (@ (@ tptp.cons_com C) _let_3)) (=> _let_2 (not _let_1)))))))))))
% 0.29/0.79 (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)))))
% 0.29/0.79 (assert (forall ((B2 (-> tptp.state Bool)) (S tptp.state) (C tptp.com)) (=> (@ B2 S) (=> (@ (@ tptp.termi C) S) (=> (forall ((T3 tptp.state)) (=> (@ (@ (@ tptp.exec S) C) T3) (@ (@ tptp.termi (@ (@ tptp.while B2) C)) T3))) (@ (@ tptp.termi (@ (@ tptp.while B2) C)) S))))))
% 0.29/0.79 (assert (forall ((X21 tptp.com) (X22 tptp.com) (Y21 tptp.com) (Y22 tptp.com)) (= (= (@ (@ tptp.semi X21) X22) (@ (@ tptp.semi Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))))
% 0.29/0.79 (assert (forall ((X1 (-> tptp.state tptp.set_state)) (Y1 (-> tptp.state tptp.set_state))) (= (= (@ tptp.do X1) (@ tptp.do Y1)) (= X1 Y1))))
% 0.29/0.79 (assert (forall ((X31 (-> tptp.state Bool)) (X322 tptp.com) (X33 tptp.com) (Y31 (-> tptp.state Bool)) (Y32 tptp.com) (Y33 tptp.com)) (= (= (@ (@ (@ tptp.cond X31) X322) X33) (@ (@ (@ tptp.cond Y31) Y32) Y33)) (and (= X31 Y31) (= X322 Y32) (= X33 Y33)))))
% 0.29/0.79 (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)))))
% 0.29/0.79 (assert (forall ((B2 (-> tptp.state Bool)) (S tptp.state) (C tptp.com)) (=> (not (@ B2 S)) (@ (@ (@ tptp.exec S) (@ (@ tptp.while B2) C)) S))))
% 0.29/0.79 (assert (forall ((B2 (-> tptp.state Bool)) (S tptp.state) (C tptp.com) (T2 tptp.state) (U tptp.state)) (let ((_let_1 (@ (@ tptp.while B2) C))) (let ((_let_2 (@ tptp.exec S))) (=> (@ B2 S) (=> (@ (@ _let_2 C) T2) (=> (@ (@ (@ tptp.exec T2) _let_1) U) (@ (@ _let_2 _let_1) U))))))))
% 0.29/0.79 (assert (forall ((X31 (-> tptp.state Bool)) (X322 tptp.com) (X33 tptp.com) (X41 (-> tptp.state Bool)) (X42 tptp.com)) (not (= (@ (@ (@ tptp.cond X31) X322) X33) (@ (@ tptp.while X41) X42)))))
% 0.29/0.79 (assert (forall ((B2 (-> tptp.state Bool)) (S tptp.state) (C tptp.com)) (=> (not (@ B2 S)) (@ (@ tptp.termi (@ (@ tptp.while B2) C)) S))))
% 0.29/0.79 (assert (forall ((X1 (-> tptp.state tptp.set_state)) (X41 (-> tptp.state Bool)) (X42 tptp.com)) (not (= (@ tptp.do X1) (@ (@ tptp.while X41) X42)))))
% 0.29/0.79 (assert (forall ((B2 (-> tptp.state Bool)) (S tptp.state) (C22 tptp.com) (T2 tptp.state) (C1 tptp.com)) (let ((_let_1 (@ tptp.exec S))) (=> (not (@ B2 S)) (=> (@ (@ _let_1 C22) T2) (@ (@ _let_1 (@ (@ (@ tptp.cond B2) C1) C22)) T2))))))
% 0.29/0.79 (assert (forall ((B2 (-> tptp.state Bool)) (S tptp.state) (C1 tptp.com) (T2 tptp.state) (C22 tptp.com)) (let ((_let_1 (@ tptp.exec S))) (=> (@ B2 S) (=> (@ (@ _let_1 C1) T2) (@ (@ _let_1 (@ (@ (@ tptp.cond B2) C1) C22)) T2))))))
% 0.29/0.79 (assert (forall ((X21 tptp.com) (X22 tptp.com) (X41 (-> tptp.state Bool)) (X42 tptp.com)) (not (= (@ (@ tptp.semi X21) X22) (@ (@ tptp.while X41) X42)))))
% 0.29/0.79 (assert (forall ((T2 tptp.state) (F2 (-> tptp.state tptp.set_state)) (S tptp.state)) (=> (@ (@ tptp.member_state T2) (@ F2 S)) (@ (@ (@ tptp.exec S) (@ tptp.do F2)) T2))))
% 0.29/0.79 (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))))))
% 0.29/0.79 (assert (forall ((B2 (-> tptp.state Bool)) (S tptp.state) (C22 tptp.com) (C1 tptp.com)) (=> (not (@ B2 S)) (=> (@ (@ tptp.termi C22) S) (@ (@ tptp.termi (@ (@ (@ tptp.cond B2) C1) C22)) S)))))
% 0.29/0.79 (assert (forall ((B2 (-> tptp.state Bool)) (S tptp.state) (C1 tptp.com) (C22 tptp.com)) (=> (@ B2 S) (=> (@ (@ tptp.termi C1) S) (@ (@ tptp.termi (@ (@ (@ tptp.cond B2) C1) C22)) S)))))
% 0.29/0.79 (assert (forall ((X1 (-> tptp.state tptp.set_state)) (X31 (-> tptp.state Bool)) (X322 tptp.com) (X33 tptp.com)) (not (= (@ tptp.do X1) (@ (@ (@ tptp.cond X31) X322) X33)))))
% 0.29/0.79 (assert (forall ((X21 tptp.com) (X22 tptp.com) (X31 (-> tptp.state Bool)) (X322 tptp.com) (X33 tptp.com)) (not (= (@ (@ tptp.semi X21) X22) (@ (@ (@ tptp.cond X31) X322) X33)))))
% 0.29/0.79 (assert (forall ((X1 (-> tptp.state tptp.set_state)) (X21 tptp.com) (X22 tptp.com)) (not (= (@ tptp.do X1) (@ (@ tptp.semi X21) X22)))))
% 0.29/0.79 (assert (= (@ tptp.product_lists_com tptp.nil_list_com) (@ (@ tptp.cons_list_com tptp.nil_com) tptp.nil_list_com)))
% 0.29/0.79 (assert (= (@ tptp.subseqs_com tptp.nil_com) (@ (@ tptp.cons_list_com tptp.nil_com) tptp.nil_list_com)))
% 0.29/0.79 (assert (forall ((Cs2 tptp.list_com) (S tptp.state) (Cs tptp.list_com) (S2 tptp.state) (Cs22 tptp.list_com)) (let ((_let_1 (@ tptp.transi1302705790_state tptp.pHoare259243666_exec1))) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state Cs2) S)) (@ (@ tptp.produc1204172211_state Cs) S2))) _let_1) (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state (@ (@ tptp.append_com Cs2) Cs22)) S)) (@ (@ tptp.produc1204172211_state (@ (@ tptp.append_com Cs) Cs22)) S2))) _let_1)))))
% 0.29/0.79 (assert (forall ((X tptp.com)) (= (@ (@ tptp.insert_com X) tptp.nil_com) (@ (@ tptp.cons_com X) tptp.nil_com))))
% 0.29/0.79 (assert (forall ((X1 tptp.list_com) (X2 tptp.list_com) (R tptp.set_Pr1822651163om_com) (P (-> tptp.list_com tptp.list_com Bool))) (=> (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com X1) X2)) (@ tptp.listrel_com_com R)) (=> (@ (@ P tptp.nil_com) tptp.nil_com) (=> (forall ((X3 tptp.com) (Y3 tptp.com) (Xs tptp.list_com) (Ys tptp.list_com)) (=> (@ (@ tptp.member1333916004om_com (@ (@ tptp.product_Pair_com_com X3) Y3)) R) (=> (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Xs) Ys)) (@ tptp.listrel_com_com R)) (=> (@ (@ P Xs) Ys) (@ (@ P (@ (@ tptp.cons_com X3) Xs)) (@ (@ tptp.cons_com Y3) Ys)))))) (@ (@ P X1) X2))))))
% 0.29/0.79 (assert (forall ((X1 tptp.list_P1040014977_state) (X2 tptp.list_P1040014977_state) (R tptp.set_Pr1165141447_state) (P (-> tptp.list_P1040014977_state tptp.list_P1040014977_state Bool))) (=> (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state X1) X2)) (@ tptp.listre194873521_state R)) (=> (@ (@ P tptp.nil_Pr1844458753_state) tptp.nil_Pr1844458753_state) (=> (forall ((X3 tptp.produc2041926651_state) (Y3 tptp.produc2041926651_state) (Xs tptp.list_P1040014977_state) (Ys tptp.list_P1040014977_state)) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state X3) Y3)) R) (=> (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Xs) Ys)) (@ tptp.listre194873521_state R)) (=> (@ (@ P Xs) Ys) (@ (@ P (@ (@ tptp.cons_P465369265_state X3) Xs)) (@ (@ tptp.cons_P465369265_state Y3) Ys)))))) (@ (@ P X1) X2))))))
% 0.29/0.79 (assert (forall ((X1 tptp.list_list_com) (X2 tptp.list_state) (R tptp.set_Pr849496667_state) (P (-> tptp.list_list_com tptp.list_state Bool))) (=> (@ (@ tptp.member1442949316_state (@ (@ tptp.produc1742567891_state X1) X2)) (@ tptp.listre1268245261_state R)) (=> (@ (@ P tptp.nil_list_com) tptp.nil_state) (=> (forall ((X3 tptp.list_com) (Y3 tptp.state) (Xs tptp.list_list_com) (Ys tptp.list_state)) (=> (@ (@ tptp.member64234660_state (@ (@ tptp.produc1204172211_state X3) Y3)) R) (=> (@ (@ tptp.member1442949316_state (@ (@ tptp.produc1742567891_state Xs) Ys)) (@ tptp.listre1268245261_state R)) (=> (@ (@ P Xs) Ys) (@ (@ P (@ (@ tptp.cons_list_com X3) Xs)) (@ (@ tptp.cons_state Y3) Ys)))))) (@ (@ P X1) X2))))))
% 0.29/0.79 (assert (forall ((X1 tptp.list_P890094829_state) (X2 tptp.list_P890094829_state) (R tptp.set_Pr2096893127_state) (P (-> tptp.list_P890094829_state tptp.list_P890094829_state Bool))) (=> (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state X1) X2)) (@ tptp.listre1244407729_state R)) (=> (@ (@ P tptp.nil_Pr1347322605_state) tptp.nil_Pr1347322605_state) (=> (forall ((X3 tptp.produc410756839_state) (Y3 tptp.produc410756839_state) (Xs tptp.list_P890094829_state) (Ys tptp.list_P890094829_state)) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X3) Y3)) R) (=> (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Xs) Ys)) (@ tptp.listre1244407729_state R)) (=> (@ (@ P Xs) Ys) (@ (@ P (@ (@ tptp.cons_P438230685_state X3) Xs)) (@ (@ tptp.cons_P438230685_state Y3) Ys)))))) (@ (@ P X1) X2))))))
% 0.29/0.79 (assert (forall ((A2 tptp.list_com) (B2 tptp.list_com) (C tptp.list_com)) (let ((_let_1 (@ tptp.append_com A2))) (= (@ (@ tptp.append_com (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.append_com B2) C))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (Ys2 tptp.list_com) (Zs2 tptp.list_com)) (let ((_let_1 (@ tptp.append_com Xs2))) (= (@ (@ tptp.append_com (@ _let_1 Ys2)) Zs2) (@ _let_1 (@ (@ tptp.append_com Ys2) Zs2))))))
% 0.29/0.79 (assert (forall ((Ys2 tptp.list_com) (Xs2 tptp.list_com) (Zs2 tptp.list_com)) (= (= (@ (@ tptp.append_com Ys2) Xs2) (@ (@ tptp.append_com Zs2) Xs2)) (= Ys2 Zs2))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (Ys2 tptp.list_com) (Zs2 tptp.list_com)) (let ((_let_1 (@ tptp.append_com Xs2))) (= (= (@ _let_1 Ys2) (@ _let_1 Zs2)) (= Ys2 Zs2)))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com)) (= (@ (@ tptp.append_com Xs2) tptp.nil_com) Xs2)))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (Ys2 tptp.list_com)) (= (= (@ (@ tptp.append_com Xs2) Ys2) Xs2) (= Ys2 tptp.nil_com))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (Ys2 tptp.list_com)) (= (= Xs2 (@ (@ tptp.append_com Xs2) Ys2)) (= Ys2 tptp.nil_com))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (Ys2 tptp.list_com)) (= (= (@ (@ tptp.append_com Xs2) Ys2) Ys2) (= Xs2 tptp.nil_com))))
% 0.29/0.79 (assert (forall ((Ys2 tptp.list_com) (Xs2 tptp.list_com)) (= (= Ys2 (@ (@ tptp.append_com Xs2) Ys2)) (= Xs2 tptp.nil_com))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (Ys2 tptp.list_com)) (= (= tptp.nil_com (@ (@ tptp.append_com Xs2) Ys2)) (and (= Xs2 tptp.nil_com) (= Ys2 tptp.nil_com)))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (Ys2 tptp.list_com)) (= (= (@ (@ tptp.append_com Xs2) Ys2) tptp.nil_com) (and (= Xs2 tptp.nil_com) (= Ys2 tptp.nil_com)))))
% 0.29/0.79 (assert (forall ((A2 tptp.list_com)) (= (@ (@ tptp.append_com A2) tptp.nil_com) A2)))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (X tptp.com) (Ys2 tptp.list_com) (Y tptp.com)) (= (= (@ (@ tptp.append_com Xs2) (@ (@ tptp.cons_com X) tptp.nil_com)) (@ (@ tptp.append_com Ys2) (@ (@ tptp.cons_com Y) tptp.nil_com))) (and (= Xs2 Ys2) (= X Y)))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_P1040014977_state) (R tptp.set_Pr1165141447_state)) (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Xs2) Xs2)) (@ tptp.listre194873521_state (@ tptp.transi1302705790_state R)))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_P890094829_state) (R tptp.set_Pr2096893127_state)) (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Xs2) Xs2)) (@ tptp.listre1244407729_state (@ tptp.transi463013610_state R)))))
% 0.29/0.79 (assert (forall ((X tptp.com) (Xs2 tptp.list_com) (Ys2 tptp.list_com)) (let ((_let_1 (@ tptp.cons_com X))) (= (@ (@ tptp.append_com (@ _let_1 Xs2)) Ys2) (@ _let_1 (@ (@ tptp.append_com Xs2) Ys2))))))
% 0.29/0.79 (assert (forall ((X tptp.com) (Xs1 tptp.list_com) (Ys2 tptp.list_com) (Xs2 tptp.list_com) (Zs2 tptp.list_com)) (let ((_let_1 (@ tptp.cons_com X))) (=> (= (@ _let_1 Xs1) Ys2) (=> (= Xs2 (@ (@ tptp.append_com Xs1) Zs2)) (= (@ _let_1 Xs2) (@ (@ tptp.append_com Ys2) Zs2)))))))
% 0.29/0.79 (assert (forall ((A2 tptp.list_com)) (= (@ (@ tptp.append_com tptp.nil_com) A2) A2)))
% 0.29/0.79 (assert (forall ((Ys2 tptp.list_com)) (= (@ (@ tptp.append_com tptp.nil_com) Ys2) Ys2)))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (Ys2 tptp.list_com)) (=> (= Xs2 Ys2) (= Xs2 (@ (@ tptp.append_com tptp.nil_com) Ys2)))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (Xs1 tptp.list_com) (Zs2 tptp.list_com) (Ys2 tptp.list_com) (Us tptp.list_com)) (let ((_let_1 (@ tptp.append_com Xs2))) (=> (= (@ _let_1 Xs1) Zs2) (=> (= Ys2 (@ (@ tptp.append_com Xs1) Us)) (= (@ _let_1 Ys2) (@ (@ tptp.append_com Zs2) Us)))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (Ys2 tptp.list_com) (Zs2 tptp.list_com) (Ts tptp.list_com)) (= (= (@ (@ tptp.append_com Xs2) Ys2) (@ (@ tptp.append_com Zs2) Ts)) (exists ((Us2 tptp.list_com)) (let ((_let_1 (@ tptp.append_com Us2))) (or (and (= Xs2 (@ (@ tptp.append_com Zs2) Us2)) (= (@ _let_1 Ys2) Ts)) (and (= (@ (@ tptp.append_com Xs2) Us2) Zs2) (= Ys2 (@ _let_1 Ts)))))))))
% 0.29/0.79 (assert (forall ((P (-> tptp.list_com Bool)) (Xs2 tptp.list_com)) (=> (@ P tptp.nil_com) (=> (forall ((X3 tptp.com) (Xs tptp.list_com)) (=> (@ P Xs) (@ P (@ (@ tptp.append_com Xs) (@ (@ tptp.cons_com X3) tptp.nil_com))))) (@ P Xs2)))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com)) (=> (not (= Xs2 tptp.nil_com)) (not (forall ((Ys tptp.list_com) (Y3 tptp.com)) (not (= Xs2 (@ (@ tptp.append_com Ys) (@ (@ tptp.cons_com Y3) tptp.nil_com)))))))))
% 0.29/0.79 (assert (forall ((X tptp.com) (Xs2 tptp.list_com) (Ys2 tptp.list_com) (Zs2 tptp.list_com)) (let ((_let_1 (@ (@ tptp.cons_com X) Xs2))) (= (= _let_1 (@ (@ tptp.append_com Ys2) Zs2)) (or (and (= Ys2 tptp.nil_com) (= _let_1 Zs2)) (exists ((Ys4 tptp.list_com)) (and (= (@ (@ tptp.cons_com X) Ys4) Ys2) (= Xs2 (@ (@ tptp.append_com Ys4) Zs2)))))))))
% 0.29/0.79 (assert (forall ((Ys2 tptp.list_com) (Zs2 tptp.list_com) (X tptp.com) (Xs2 tptp.list_com)) (let ((_let_1 (@ (@ tptp.cons_com X) Xs2))) (= (= (@ (@ tptp.append_com Ys2) Zs2) _let_1) (or (and (= Ys2 tptp.nil_com) (= Zs2 _let_1)) (exists ((Ys4 tptp.list_com)) (and (= Ys2 (@ (@ tptp.cons_com X) Ys4)) (= (@ (@ tptp.append_com Ys4) Zs2) Xs2))))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (P (-> tptp.list_com Bool))) (=> (not (= Xs2 tptp.nil_com)) (=> (forall ((X3 tptp.com)) (@ P (@ (@ tptp.cons_com X3) tptp.nil_com))) (=> (forall ((X3 tptp.com) (Xs tptp.list_com)) (=> (not (= Xs tptp.nil_com)) (=> (@ P Xs) (@ P (@ (@ tptp.append_com Xs) (@ (@ tptp.cons_com X3) tptp.nil_com)))))) (@ P Xs2))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (R tptp.set_Pr1822651163om_com)) (=> (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Xs2) tptp.nil_com)) (@ tptp.listrel_com_com R)) (= Xs2 tptp.nil_com))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (R tptp.set_Pr1822651163om_com)) (=> (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com tptp.nil_com) Xs2)) (@ tptp.listrel_com_com R)) (= Xs2 tptp.nil_com))))
% 0.29/0.79 (assert (forall ((R tptp.set_Pr1822651163om_com)) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com tptp.nil_com) tptp.nil_com)) (@ tptp.listrel_com_com R))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_P1040014977_state) (Ys2 tptp.list_P1040014977_state) (R tptp.set_Pr1165141447_state) (Zs2 tptp.list_P1040014977_state)) (let ((_let_1 (@ tptp.listre194873521_state (@ tptp.transi1302705790_state R)))) (let ((_let_2 (@ tptp.produc1298457559_state Xs2))) (=> (@ (@ tptp.member1267359376_state (@ _let_2 Ys2)) _let_1) (=> (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Ys2) Zs2)) _let_1) (@ (@ tptp.member1267359376_state (@ _let_2 Zs2)) _let_1)))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_P890094829_state) (Ys2 tptp.list_P890094829_state) (R tptp.set_Pr2096893127_state) (Zs2 tptp.list_P890094829_state)) (let ((_let_1 (@ tptp.listre1244407729_state (@ tptp.transi463013610_state R)))) (let ((_let_2 (@ tptp.produc1354769367_state Xs2))) (=> (@ (@ tptp.member423306384_state (@ _let_2 Ys2)) _let_1) (=> (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Ys2) Zs2)) _let_1) (@ (@ tptp.member423306384_state (@ _let_2 Zs2)) _let_1)))))))
% 0.29/0.79 (assert (forall ((X tptp.com) (Y tptp.com) (R tptp.set_Pr1822651163om_com) (Xs2 tptp.list_com) (Ys2 tptp.list_com)) (let ((_let_1 (@ tptp.listrel_com_com R))) (=> (@ (@ tptp.member1333916004om_com (@ (@ tptp.product_Pair_com_com X) Y)) R) (=> (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Xs2) Ys2)) _let_1) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ (@ tptp.cons_com X) Xs2)) (@ (@ tptp.cons_com Y) Ys2))) _let_1))))))
% 0.29/0.79 (assert (forall ((X tptp.produc2041926651_state) (Y tptp.produc2041926651_state) (R tptp.set_Pr1165141447_state) (Xs2 tptp.list_P1040014977_state) (Ys2 tptp.list_P1040014977_state)) (let ((_let_1 (@ tptp.listre194873521_state R))) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state X) Y)) R) (=> (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Xs2) Ys2)) _let_1) (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state (@ (@ tptp.cons_P465369265_state X) Xs2)) (@ (@ tptp.cons_P465369265_state Y) Ys2))) _let_1))))))
% 0.29/0.79 (assert (forall ((X tptp.list_com) (Y tptp.state) (R tptp.set_Pr849496667_state) (Xs2 tptp.list_list_com) (Ys2 tptp.list_state)) (let ((_let_1 (@ tptp.listre1268245261_state R))) (=> (@ (@ tptp.member64234660_state (@ (@ tptp.produc1204172211_state X) Y)) R) (=> (@ (@ tptp.member1442949316_state (@ (@ tptp.produc1742567891_state Xs2) Ys2)) _let_1) (@ (@ tptp.member1442949316_state (@ (@ tptp.produc1742567891_state (@ (@ tptp.cons_list_com X) Xs2)) (@ (@ tptp.cons_state Y) Ys2))) _let_1))))))
% 0.29/0.79 (assert (forall ((X tptp.produc410756839_state) (Y tptp.produc410756839_state) (R tptp.set_Pr2096893127_state) (Xs2 tptp.list_P890094829_state) (Ys2 tptp.list_P890094829_state)) (let ((_let_1 (@ tptp.listre1244407729_state R))) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X) Y)) R) (=> (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Xs2) Ys2)) _let_1) (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state (@ (@ tptp.cons_P438230685_state X) Xs2)) (@ (@ tptp.cons_P438230685_state Y) Ys2))) _let_1))))))
% 0.29/0.79 (assert (forall ((Y tptp.com) (Ys2 tptp.list_com) (Xs2 tptp.list_com) (R tptp.set_Pr1822651163om_com)) (=> (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ (@ tptp.cons_com Y) Ys2)) Xs2)) (@ tptp.listrel_com_com R)) (not (forall ((Y3 tptp.com) (Ys tptp.list_com)) (=> (= Xs2 (@ (@ tptp.cons_com Y3) Ys)) (=> (@ (@ tptp.member1333916004om_com (@ (@ tptp.product_Pair_com_com Y) Y3)) R) (not (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Ys2) Ys)) (@ tptp.listrel_com_com R))))))))))
% 0.29/0.79 (assert (forall ((Y tptp.produc2041926651_state) (Ys2 tptp.list_P1040014977_state) (Xs2 tptp.list_P1040014977_state) (R tptp.set_Pr1165141447_state)) (=> (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state (@ (@ tptp.cons_P465369265_state Y) Ys2)) Xs2)) (@ tptp.listre194873521_state R)) (not (forall ((Y3 tptp.produc2041926651_state) (Ys tptp.list_P1040014977_state)) (=> (= Xs2 (@ (@ tptp.cons_P465369265_state Y3) Ys)) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state Y) Y3)) R) (not (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Ys2) Ys)) (@ tptp.listre194873521_state R))))))))))
% 0.29/0.79 (assert (forall ((Y tptp.list_com) (Ys2 tptp.list_list_com) (Xs2 tptp.list_state) (R tptp.set_Pr849496667_state)) (=> (@ (@ tptp.member1442949316_state (@ (@ tptp.produc1742567891_state (@ (@ tptp.cons_list_com Y) Ys2)) Xs2)) (@ tptp.listre1268245261_state R)) (not (forall ((Y3 tptp.state) (Ys tptp.list_state)) (=> (= Xs2 (@ (@ tptp.cons_state Y3) Ys)) (=> (@ (@ tptp.member64234660_state (@ (@ tptp.produc1204172211_state Y) Y3)) R) (not (@ (@ tptp.member1442949316_state (@ (@ tptp.produc1742567891_state Ys2) Ys)) (@ tptp.listre1268245261_state R))))))))))
% 0.29/0.79 (assert (forall ((Y tptp.produc410756839_state) (Ys2 tptp.list_P890094829_state) (Xs2 tptp.list_P890094829_state) (R tptp.set_Pr2096893127_state)) (=> (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state (@ (@ tptp.cons_P438230685_state Y) Ys2)) Xs2)) (@ tptp.listre1244407729_state R)) (not (forall ((Y3 tptp.produc410756839_state) (Ys tptp.list_P890094829_state)) (=> (= Xs2 (@ (@ tptp.cons_P438230685_state Y3) Ys)) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state Y) Y3)) R) (not (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Ys2) Ys)) (@ tptp.listre1244407729_state R))))))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (Y tptp.com) (Ys2 tptp.list_com) (R tptp.set_Pr1822651163om_com)) (=> (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Xs2) (@ (@ tptp.cons_com Y) Ys2))) (@ tptp.listrel_com_com R)) (not (forall ((X3 tptp.com) (Xs tptp.list_com)) (=> (= Xs2 (@ (@ tptp.cons_com X3) Xs)) (=> (@ (@ tptp.member1333916004om_com (@ (@ tptp.product_Pair_com_com X3) Y)) R) (not (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Xs) Ys2)) (@ tptp.listrel_com_com R))))))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_P1040014977_state) (Y tptp.produc2041926651_state) (Ys2 tptp.list_P1040014977_state) (R tptp.set_Pr1165141447_state)) (=> (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Xs2) (@ (@ tptp.cons_P465369265_state Y) Ys2))) (@ tptp.listre194873521_state R)) (not (forall ((X3 tptp.produc2041926651_state) (Xs tptp.list_P1040014977_state)) (=> (= Xs2 (@ (@ tptp.cons_P465369265_state X3) Xs)) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state X3) Y)) R) (not (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Xs) Ys2)) (@ tptp.listre194873521_state R))))))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_list_com) (Y tptp.state) (Ys2 tptp.list_state) (R tptp.set_Pr849496667_state)) (=> (@ (@ tptp.member1442949316_state (@ (@ tptp.produc1742567891_state Xs2) (@ (@ tptp.cons_state Y) Ys2))) (@ tptp.listre1268245261_state R)) (not (forall ((X3 tptp.list_com) (Xs tptp.list_list_com)) (=> (= Xs2 (@ (@ tptp.cons_list_com X3) Xs)) (=> (@ (@ tptp.member64234660_state (@ (@ tptp.produc1204172211_state X3) Y)) R) (not (@ (@ tptp.member1442949316_state (@ (@ tptp.produc1742567891_state Xs) Ys2)) (@ tptp.listre1268245261_state R))))))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_P890094829_state) (Y tptp.produc410756839_state) (Ys2 tptp.list_P890094829_state) (R tptp.set_Pr2096893127_state)) (=> (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Xs2) (@ (@ tptp.cons_P438230685_state Y) Ys2))) (@ tptp.listre1244407729_state R)) (not (forall ((X3 tptp.produc410756839_state) (Xs tptp.list_P890094829_state)) (=> (= Xs2 (@ (@ tptp.cons_P438230685_state X3) Xs)) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X3) Y)) R) (not (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Xs) Ys2)) (@ tptp.listre1244407729_state R))))))))))
% 0.29/0.79 (assert (forall ((Cs2 tptp.list_com) (S tptp.state) (Cs tptp.list_com) (S2 tptp.state) (Cs22 tptp.list_com)) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state Cs2) S)) (@ (@ tptp.produc1204172211_state Cs) S2))) tptp.pHoare259243666_exec1) (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state (@ (@ tptp.append_com Cs2) Cs22)) S)) (@ (@ tptp.produc1204172211_state (@ (@ tptp.append_com Cs) Cs22)) S2))) tptp.pHoare259243666_exec1))))
% 0.29/0.79 (assert (forall ((A1 tptp.list_com) (A22 tptp.list_com) (R tptp.set_Pr1822651163om_com)) (=> (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com A1) A22)) (@ tptp.listrel_com_com R)) (=> (=> (= A1 tptp.nil_com) (not (= A22 tptp.nil_com))) (not (forall ((X3 tptp.com) (Y3 tptp.com) (Xs tptp.list_com)) (=> (= A1 (@ (@ tptp.cons_com X3) Xs)) (forall ((Ys tptp.list_com)) (=> (= A22 (@ (@ tptp.cons_com Y3) Ys)) (=> (@ (@ tptp.member1333916004om_com (@ (@ tptp.product_Pair_com_com X3) Y3)) R) (not (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Xs) Ys)) (@ tptp.listrel_com_com R)))))))))))))
% 0.29/0.79 (assert (forall ((A1 tptp.list_P1040014977_state) (A22 tptp.list_P1040014977_state) (R tptp.set_Pr1165141447_state)) (=> (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state A1) A22)) (@ tptp.listre194873521_state R)) (=> (=> (= A1 tptp.nil_Pr1844458753_state) (not (= A22 tptp.nil_Pr1844458753_state))) (not (forall ((X3 tptp.produc2041926651_state) (Y3 tptp.produc2041926651_state) (Xs tptp.list_P1040014977_state)) (=> (= A1 (@ (@ tptp.cons_P465369265_state X3) Xs)) (forall ((Ys tptp.list_P1040014977_state)) (=> (= A22 (@ (@ tptp.cons_P465369265_state Y3) Ys)) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state X3) Y3)) R) (not (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Xs) Ys)) (@ tptp.listre194873521_state R)))))))))))))
% 0.29/0.79 (assert (forall ((A1 tptp.list_list_com) (A22 tptp.list_state) (R tptp.set_Pr849496667_state)) (=> (@ (@ tptp.member1442949316_state (@ (@ tptp.produc1742567891_state A1) A22)) (@ tptp.listre1268245261_state R)) (=> (=> (= A1 tptp.nil_list_com) (not (= A22 tptp.nil_state))) (not (forall ((X3 tptp.list_com) (Y3 tptp.state) (Xs tptp.list_list_com)) (=> (= A1 (@ (@ tptp.cons_list_com X3) Xs)) (forall ((Ys tptp.list_state)) (=> (= A22 (@ (@ tptp.cons_state Y3) Ys)) (=> (@ (@ tptp.member64234660_state (@ (@ tptp.produc1204172211_state X3) Y3)) R) (not (@ (@ tptp.member1442949316_state (@ (@ tptp.produc1742567891_state Xs) Ys)) (@ tptp.listre1268245261_state R)))))))))))))
% 0.29/0.79 (assert (forall ((A1 tptp.list_P890094829_state) (A22 tptp.list_P890094829_state) (R tptp.set_Pr2096893127_state)) (=> (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state A1) A22)) (@ tptp.listre1244407729_state R)) (=> (=> (= A1 tptp.nil_Pr1347322605_state) (not (= A22 tptp.nil_Pr1347322605_state))) (not (forall ((X3 tptp.produc410756839_state) (Y3 tptp.produc410756839_state) (Xs tptp.list_P890094829_state)) (=> (= A1 (@ (@ tptp.cons_P438230685_state X3) Xs)) (forall ((Ys tptp.list_P890094829_state)) (=> (= A22 (@ (@ tptp.cons_P438230685_state Y3) Ys)) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X3) Y3)) R) (not (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Xs) Ys)) (@ tptp.listre1244407729_state R)))))))))))))
% 0.29/0.79 (assert (forall ((A1 tptp.list_com) (A22 tptp.list_com) (R tptp.set_Pr1822651163om_com)) (= (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com A1) A22)) (@ tptp.listrel_com_com R)) (or (and (= A1 tptp.nil_com) (= A22 tptp.nil_com)) (exists ((X4 tptp.com) (Y4 tptp.com) (Xs3 tptp.list_com) (Ys3 tptp.list_com)) (and (= A1 (@ (@ tptp.cons_com X4) Xs3)) (= A22 (@ (@ tptp.cons_com Y4) Ys3)) (@ (@ tptp.member1333916004om_com (@ (@ tptp.product_Pair_com_com X4) Y4)) R) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Xs3) Ys3)) (@ tptp.listrel_com_com R))))))))
% 0.29/0.79 (assert (forall ((A1 tptp.list_P1040014977_state) (A22 tptp.list_P1040014977_state) (R tptp.set_Pr1165141447_state)) (= (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state A1) A22)) (@ tptp.listre194873521_state R)) (or (and (= A1 tptp.nil_Pr1844458753_state) (= A22 tptp.nil_Pr1844458753_state)) (exists ((X4 tptp.produc2041926651_state) (Y4 tptp.produc2041926651_state) (Xs3 tptp.list_P1040014977_state) (Ys3 tptp.list_P1040014977_state)) (and (= A1 (@ (@ tptp.cons_P465369265_state X4) Xs3)) (= A22 (@ (@ tptp.cons_P465369265_state Y4) Ys3)) (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state X4) Y4)) R) (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Xs3) Ys3)) (@ tptp.listre194873521_state R))))))))
% 0.29/0.79 (assert (forall ((A1 tptp.list_list_com) (A22 tptp.list_state) (R tptp.set_Pr849496667_state)) (= (@ (@ tptp.member1442949316_state (@ (@ tptp.produc1742567891_state A1) A22)) (@ tptp.listre1268245261_state R)) (or (and (= A1 tptp.nil_list_com) (= A22 tptp.nil_state)) (exists ((X4 tptp.list_com) (Y4 tptp.state) (Xs3 tptp.list_list_com) (Ys3 tptp.list_state)) (and (= A1 (@ (@ tptp.cons_list_com X4) Xs3)) (= A22 (@ (@ tptp.cons_state Y4) Ys3)) (@ (@ tptp.member64234660_state (@ (@ tptp.produc1204172211_state X4) Y4)) R) (@ (@ tptp.member1442949316_state (@ (@ tptp.produc1742567891_state Xs3) Ys3)) (@ tptp.listre1268245261_state R))))))))
% 0.29/0.79 (assert (forall ((A1 tptp.list_P890094829_state) (A22 tptp.list_P890094829_state) (R tptp.set_Pr2096893127_state)) (= (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state A1) A22)) (@ tptp.listre1244407729_state R)) (or (and (= A1 tptp.nil_Pr1347322605_state) (= A22 tptp.nil_Pr1347322605_state)) (exists ((X4 tptp.produc410756839_state) (Y4 tptp.produc410756839_state) (Xs3 tptp.list_P890094829_state) (Ys3 tptp.list_P890094829_state)) (and (= A1 (@ (@ tptp.cons_P438230685_state X4) Xs3)) (= A22 (@ (@ tptp.cons_P438230685_state Y4) Ys3)) (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X4) Y4)) R) (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Xs3) Ys3)) (@ tptp.listre1244407729_state R))))))))
% 0.29/0.79 (assert (forall ((X tptp.com) (Xs2 tptp.list_com) (F2 (-> tptp.com tptp.list_com))) (= (@ (@ tptp.bind_com_com (@ (@ tptp.cons_com X) Xs2)) F2) (@ (@ tptp.append_com (@ F2 X)) (@ (@ tptp.bind_com_com Xs2) F2)))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (X tptp.com) (Ys2 tptp.list_com) (Y tptp.com) (R tptp.set_Pr1822651163om_com)) (let ((_let_1 (@ tptp.listrel1_com R))) (= (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ (@ tptp.append_com Xs2) (@ (@ tptp.cons_com X) tptp.nil_com))) (@ (@ tptp.append_com Ys2) (@ (@ tptp.cons_com Y) tptp.nil_com)))) _let_1) (or (and (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Xs2) Ys2)) _let_1) (= X Y)) (and (= Xs2 Ys2) (@ (@ tptp.member1333916004om_com (@ (@ tptp.product_Pair_com_com X) Y)) R)))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_P1040014977_state) (X tptp.produc2041926651_state) (Ys2 tptp.list_P1040014977_state) (Y tptp.produc2041926651_state) (R tptp.set_Pr1165141447_state)) (let ((_let_1 (@ tptp.listre1738592858_state R))) (= (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state (@ (@ tptp.append982487830_state Xs2) (@ (@ tptp.cons_P465369265_state X) tptp.nil_Pr1844458753_state))) (@ (@ tptp.append982487830_state Ys2) (@ (@ tptp.cons_P465369265_state Y) tptp.nil_Pr1844458753_state)))) _let_1) (or (and (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Xs2) Ys2)) _let_1) (= X Y)) (and (= Xs2 Ys2) (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state X) Y)) R)))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_P890094829_state) (X tptp.produc410756839_state) (Ys2 tptp.list_P890094829_state) (Y tptp.produc410756839_state) (R tptp.set_Pr2096893127_state)) (let ((_let_1 (@ tptp.listre1725776070_state R))) (= (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state (@ (@ tptp.append221843330_state Xs2) (@ (@ tptp.cons_P438230685_state X) tptp.nil_Pr1347322605_state))) (@ (@ tptp.append221843330_state Ys2) (@ (@ tptp.cons_P438230685_state Y) tptp.nil_Pr1347322605_state)))) _let_1) (or (and (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Xs2) Ys2)) _let_1) (= X Y)) (and (= Xs2 Ys2) (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X) Y)) R)))))))
% 0.29/0.79 (assert (forall ((F2 (-> tptp.com tptp.list_com)) (X tptp.com) (Xs2 tptp.list_com)) (let ((_let_1 (@ tptp.maps_com_com F2))) (= (@ _let_1 (@ (@ tptp.cons_com X) Xs2)) (@ (@ tptp.append_com (@ F2 X)) (@ _let_1 Xs2))))))
% 0.29/0.79 (assert (forall ((Xss2 tptp.list_list_com) (Ys2 tptp.list_com) (Zs2 tptp.list_com)) (let ((_let_1 (= Xss2 tptp.nil_list_com))) (= (= (@ tptp.concat_com Xss2) (@ (@ tptp.append_com Ys2) Zs2)) (and (=> _let_1 (and (= Ys2 tptp.nil_com) (= Zs2 tptp.nil_com))) (=> (not _let_1) (exists ((Xss1 tptp.list_list_com) (Xs3 tptp.list_com) (Xs4 tptp.list_com) (Xss22 tptp.list_list_com)) (and (= Xss2 (@ (@ tptp.append_list_com Xss1) (@ (@ tptp.cons_list_com (@ (@ tptp.append_com Xs3) Xs4)) Xss22))) (= Ys2 (@ (@ tptp.append_com (@ tptp.concat_com Xss1)) Xs3)) (= Zs2 (@ (@ tptp.append_com Xs4) (@ tptp.concat_com Xss22)))))))))))
% 0.29/0.79 (assert (forall ((F2 (-> tptp.com tptp.list_com))) (= (@ (@ tptp.bind_com_com tptp.nil_com) F2) tptp.nil_com)))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_list_com) (Ys2 tptp.list_list_com)) (= (@ tptp.concat_com (@ (@ tptp.append_list_com Xs2) Ys2)) (@ (@ tptp.append_com (@ tptp.concat_com Xs2)) (@ tptp.concat_com Ys2)))))
% 0.29/0.79 (assert (forall ((X tptp.com) (Xs2 tptp.list_com) (Y tptp.com) (Ys2 tptp.list_com) (R tptp.set_Pr1822651163om_com)) (let ((_let_1 (@ tptp.listrel1_com R))) (= (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ (@ tptp.cons_com X) Xs2)) (@ (@ tptp.cons_com Y) Ys2))) _let_1) (or (and (@ (@ tptp.member1333916004om_com (@ (@ tptp.product_Pair_com_com X) Y)) R) (= Xs2 Ys2)) (and (= X Y) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Xs2) Ys2)) _let_1)))))))
% 0.29/0.79 (assert (forall ((X tptp.produc2041926651_state) (Xs2 tptp.list_P1040014977_state) (Y tptp.produc2041926651_state) (Ys2 tptp.list_P1040014977_state) (R tptp.set_Pr1165141447_state)) (let ((_let_1 (@ tptp.listre1738592858_state R))) (= (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state (@ (@ tptp.cons_P465369265_state X) Xs2)) (@ (@ tptp.cons_P465369265_state Y) Ys2))) _let_1) (or (and (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state X) Y)) R) (= Xs2 Ys2)) (and (= X Y) (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Xs2) Ys2)) _let_1)))))))
% 0.29/0.79 (assert (forall ((X tptp.produc410756839_state) (Xs2 tptp.list_P890094829_state) (Y tptp.produc410756839_state) (Ys2 tptp.list_P890094829_state) (R tptp.set_Pr2096893127_state)) (let ((_let_1 (@ tptp.listre1725776070_state R))) (= (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state (@ (@ tptp.cons_P438230685_state X) Xs2)) (@ (@ tptp.cons_P438230685_state Y) Ys2))) _let_1) (or (and (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X) Y)) R) (= Xs2 Ys2)) (and (= X Y) (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Xs2) Ys2)) _let_1)))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (Ys2 tptp.list_com) (R tptp.set_Pr1822651163om_com) (X tptp.com)) (let ((_let_1 (@ tptp.listrel1_com R))) (let ((_let_2 (@ tptp.cons_com X))) (=> (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Xs2) Ys2)) _let_1) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ _let_2 Xs2)) (@ _let_2 Ys2))) _let_1))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (Ys2 tptp.list_com) (R tptp.set_Pr1822651163om_com) (X tptp.com)) (let ((_let_1 (@ tptp.transi436345274st_com (@ tptp.listrel1_com R)))) (let ((_let_2 (@ tptp.cons_com X))) (=> (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Xs2) Ys2)) _let_1) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ _let_2 Xs2)) (@ _let_2 Ys2))) _let_1))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (R tptp.set_Pr1822651163om_com)) (not (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com tptp.nil_com) Xs2)) (@ tptp.listrel1_com R)))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (R tptp.set_Pr1822651163om_com)) (not (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Xs2) tptp.nil_com)) (@ tptp.listrel1_com R)))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (Ys2 tptp.list_com) (R tptp.set_Pr1822651163om_com) (Us tptp.list_com) (Vs tptp.list_com)) (let ((_let_1 (@ tptp.listrel1_com R))) (=> (or (and (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Xs2) Ys2)) _let_1) (= Us Vs)) (and (= Xs2 Ys2) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Us) Vs)) _let_1))) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ (@ tptp.append_com Xs2) Us)) (@ (@ tptp.append_com Ys2) Vs))) _let_1)))))
% 0.29/0.79 (assert (= (@ tptp.concat_com tptp.nil_list_com) tptp.nil_com))
% 0.29/0.79 (assert (forall ((X tptp.list_com) (Xs2 tptp.list_list_com)) (= (@ tptp.concat_com (@ (@ tptp.cons_list_com X) Xs2)) (@ (@ tptp.append_com X) (@ tptp.concat_com Xs2)))))
% 0.29/0.79 (assert (forall ((R tptp.set_Pr1165141447_state)) (= (@ tptp.listre194873521_state (@ tptp.transi1302705790_state R)) (@ tptp.transi339813252_state (@ tptp.listre1738592858_state R)))))
% 0.29/0.79 (assert (forall ((R tptp.set_Pr2096893127_state)) (= (@ tptp.listre1244407729_state (@ tptp.transi463013610_state R)) (@ tptp.transi1965148016_state (@ tptp.listre1725776070_state R)))))
% 0.29/0.79 (assert (forall ((F2 (-> tptp.com tptp.list_com))) (= (@ (@ tptp.maps_com_com F2) tptp.nil_com) tptp.nil_com)))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (Y tptp.com) (Ys2 tptp.list_com) (R tptp.set_Pr1822651163om_com)) (=> (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Xs2) (@ (@ tptp.cons_com Y) Ys2))) (@ tptp.listrel1_com R)) (=> (forall ((X3 tptp.com)) (=> (= Xs2 (@ (@ tptp.cons_com X3) Ys2)) (not (@ (@ tptp.member1333916004om_com (@ (@ tptp.product_Pair_com_com X3) Y)) R)))) (not (forall ((Zs tptp.list_com)) (=> (= Xs2 (@ (@ tptp.cons_com Y) Zs)) (not (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Zs) Ys2)) (@ tptp.listrel1_com R))))))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_P1040014977_state) (Y tptp.produc2041926651_state) (Ys2 tptp.list_P1040014977_state) (R tptp.set_Pr1165141447_state)) (=> (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Xs2) (@ (@ tptp.cons_P465369265_state Y) Ys2))) (@ tptp.listre1738592858_state R)) (=> (forall ((X3 tptp.produc2041926651_state)) (=> (= Xs2 (@ (@ tptp.cons_P465369265_state X3) Ys2)) (not (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state X3) Y)) R)))) (not (forall ((Zs tptp.list_P1040014977_state)) (=> (= Xs2 (@ (@ tptp.cons_P465369265_state Y) Zs)) (not (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Zs) Ys2)) (@ tptp.listre1738592858_state R))))))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_P890094829_state) (Y tptp.produc410756839_state) (Ys2 tptp.list_P890094829_state) (R tptp.set_Pr2096893127_state)) (=> (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Xs2) (@ (@ tptp.cons_P438230685_state Y) Ys2))) (@ tptp.listre1725776070_state R)) (=> (forall ((X3 tptp.produc410756839_state)) (=> (= Xs2 (@ (@ tptp.cons_P438230685_state X3) Ys2)) (not (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X3) Y)) R)))) (not (forall ((Zs tptp.list_P890094829_state)) (=> (= Xs2 (@ (@ tptp.cons_P438230685_state Y) Zs)) (not (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Zs) Ys2)) (@ tptp.listre1725776070_state R))))))))))
% 0.29/0.79 (assert (forall ((X tptp.com) (Xs2 tptp.list_com) (Ys2 tptp.list_com) (R tptp.set_Pr1822651163om_com)) (=> (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ (@ tptp.cons_com X) Xs2)) Ys2)) (@ tptp.listrel1_com R)) (=> (forall ((Y3 tptp.com)) (=> (= Ys2 (@ (@ tptp.cons_com Y3) Xs2)) (not (@ (@ tptp.member1333916004om_com (@ (@ tptp.product_Pair_com_com X) Y3)) R)))) (not (forall ((Zs tptp.list_com)) (=> (= Ys2 (@ (@ tptp.cons_com X) Zs)) (not (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Xs2) Zs)) (@ tptp.listrel1_com R))))))))))
% 0.29/0.79 (assert (forall ((X tptp.produc2041926651_state) (Xs2 tptp.list_P1040014977_state) (Ys2 tptp.list_P1040014977_state) (R tptp.set_Pr1165141447_state)) (=> (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state (@ (@ tptp.cons_P465369265_state X) Xs2)) Ys2)) (@ tptp.listre1738592858_state R)) (=> (forall ((Y3 tptp.produc2041926651_state)) (=> (= Ys2 (@ (@ tptp.cons_P465369265_state Y3) Xs2)) (not (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state X) Y3)) R)))) (not (forall ((Zs tptp.list_P1040014977_state)) (=> (= Ys2 (@ (@ tptp.cons_P465369265_state X) Zs)) (not (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Xs2) Zs)) (@ tptp.listre1738592858_state R))))))))))
% 0.29/0.79 (assert (forall ((X tptp.produc410756839_state) (Xs2 tptp.list_P890094829_state) (Ys2 tptp.list_P890094829_state) (R tptp.set_Pr2096893127_state)) (=> (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state (@ (@ tptp.cons_P438230685_state X) Xs2)) Ys2)) (@ tptp.listre1725776070_state R)) (=> (forall ((Y3 tptp.produc410756839_state)) (=> (= Ys2 (@ (@ tptp.cons_P438230685_state Y3) Xs2)) (not (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X) Y3)) R)))) (not (forall ((Zs tptp.list_P890094829_state)) (=> (= Ys2 (@ (@ tptp.cons_P438230685_state X) Zs)) (not (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Xs2) Zs)) (@ tptp.listre1725776070_state R))))))))))
% 0.29/0.79 (assert (forall ((X tptp.com) (Y tptp.com) (R tptp.set_Pr1822651163om_com) (Xs2 tptp.list_com)) (=> (@ (@ tptp.member1333916004om_com (@ (@ tptp.product_Pair_com_com X) Y)) R) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ (@ tptp.cons_com X) Xs2)) (@ (@ tptp.cons_com Y) Xs2))) (@ tptp.listrel1_com R)))))
% 0.29/0.79 (assert (forall ((X tptp.produc2041926651_state) (Y tptp.produc2041926651_state) (R tptp.set_Pr1165141447_state) (Xs2 tptp.list_P1040014977_state)) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state X) Y)) R) (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state (@ (@ tptp.cons_P465369265_state X) Xs2)) (@ (@ tptp.cons_P465369265_state Y) Xs2))) (@ tptp.listre1738592858_state R)))))
% 0.29/0.79 (assert (forall ((X tptp.produc410756839_state) (Y tptp.produc410756839_state) (R tptp.set_Pr2096893127_state) (Xs2 tptp.list_P890094829_state)) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X) Y)) R) (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state (@ (@ tptp.cons_P438230685_state X) Xs2)) (@ (@ tptp.cons_P438230685_state Y) Xs2))) (@ tptp.listre1725776070_state R)))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_P1040014977_state) (Ys2 tptp.list_P1040014977_state) (R tptp.set_Pr1165141447_state)) (let ((_let_1 (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Xs2) Ys2)))) (=> (@ _let_1 (@ tptp.listre1738592858_state R)) (@ _let_1 (@ tptp.listre194873521_state (@ tptp.transi1302705790_state R)))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_P890094829_state) (Ys2 tptp.list_P890094829_state) (R tptp.set_Pr2096893127_state)) (let ((_let_1 (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Xs2) Ys2)))) (=> (@ _let_1 (@ tptp.listre1725776070_state R)) (@ _let_1 (@ tptp.listre1244407729_state (@ tptp.transi463013610_state R)))))))
% 0.29/0.79 (assert (forall ((Xss2 tptp.list_list_com) (Ys2 tptp.list_com) (Zs2 tptp.list_com)) (=> (= (@ tptp.concat_com Xss2) (@ (@ tptp.append_com Ys2) Zs2)) (=> (not (= Xss2 tptp.nil_list_com)) (exists ((Xss12 tptp.list_list_com) (Xs tptp.list_com) (Xs5 tptp.list_com) (Xss23 tptp.list_list_com)) (and (= Xss2 (@ (@ tptp.append_list_com Xss12) (@ (@ tptp.cons_list_com (@ (@ tptp.append_com Xs) Xs5)) Xss23))) (= Ys2 (@ (@ tptp.append_com (@ tptp.concat_com Xss12)) Xs)) (= Zs2 (@ (@ tptp.append_com Xs5) (@ tptp.concat_com Xss23)))))))))
% 0.29/0.79 (assert (forall ((X tptp.com) (Y tptp.com) (R tptp.set_Pr1822651163om_com) (Xs2 tptp.list_com) (Us tptp.list_com) (Vs tptp.list_com) (Ys2 tptp.list_com)) (let ((_let_1 (@ tptp.append_com Us))) (=> (@ (@ tptp.member1333916004om_com (@ (@ tptp.product_Pair_com_com X) Y)) R) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_com X) Vs))) (=> (= Ys2 (@ _let_1 (@ (@ tptp.cons_com Y) Vs))) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Xs2) Ys2)) (@ tptp.listrel1_com R))))))))
% 0.29/0.79 (assert (forall ((X tptp.produc2041926651_state) (Y tptp.produc2041926651_state) (R tptp.set_Pr1165141447_state) (Xs2 tptp.list_P1040014977_state) (Us tptp.list_P1040014977_state) (Vs tptp.list_P1040014977_state) (Ys2 tptp.list_P1040014977_state)) (let ((_let_1 (@ tptp.append982487830_state Us))) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state X) Y)) R) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_P465369265_state X) Vs))) (=> (= Ys2 (@ _let_1 (@ (@ tptp.cons_P465369265_state Y) Vs))) (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Xs2) Ys2)) (@ tptp.listre1738592858_state R))))))))
% 0.29/0.79 (assert (forall ((X tptp.produc410756839_state) (Y tptp.produc410756839_state) (R tptp.set_Pr2096893127_state) (Xs2 tptp.list_P890094829_state) (Us tptp.list_P890094829_state) (Vs tptp.list_P890094829_state) (Ys2 tptp.list_P890094829_state)) (let ((_let_1 (@ tptp.append221843330_state Us))) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X) Y)) R) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_P438230685_state X) Vs))) (=> (= Ys2 (@ _let_1 (@ (@ tptp.cons_P438230685_state Y) Vs))) (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Xs2) Ys2)) (@ tptp.listre1725776070_state R))))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (Ys2 tptp.list_com) (R tptp.set_Pr1822651163om_com)) (=> (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Xs2) Ys2)) (@ tptp.listrel1_com R)) (not (forall ((X3 tptp.com) (Y3 tptp.com)) (=> (@ (@ tptp.member1333916004om_com (@ (@ tptp.product_Pair_com_com X3) Y3)) R) (forall ((Us3 tptp.list_com) (Vs2 tptp.list_com)) (let ((_let_1 (@ tptp.append_com Us3))) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_com X3) Vs2))) (not (= Ys2 (@ _let_1 (@ (@ tptp.cons_com Y3) Vs2)))))))))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_P1040014977_state) (Ys2 tptp.list_P1040014977_state) (R tptp.set_Pr1165141447_state)) (=> (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Xs2) Ys2)) (@ tptp.listre1738592858_state R)) (not (forall ((X3 tptp.produc2041926651_state) (Y3 tptp.produc2041926651_state)) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state X3) Y3)) R) (forall ((Us3 tptp.list_P1040014977_state) (Vs2 tptp.list_P1040014977_state)) (let ((_let_1 (@ tptp.append982487830_state Us3))) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_P465369265_state X3) Vs2))) (not (= Ys2 (@ _let_1 (@ (@ tptp.cons_P465369265_state Y3) Vs2)))))))))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_P890094829_state) (Ys2 tptp.list_P890094829_state) (R tptp.set_Pr2096893127_state)) (=> (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Xs2) Ys2)) (@ tptp.listre1725776070_state R)) (not (forall ((X3 tptp.produc410756839_state) (Y3 tptp.produc410756839_state)) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X3) Y3)) R) (forall ((Us3 tptp.list_P890094829_state) (Vs2 tptp.list_P890094829_state)) (let ((_let_1 (@ tptp.append221843330_state Us3))) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_P438230685_state X3) Vs2))) (not (= Ys2 (@ _let_1 (@ (@ tptp.cons_P438230685_state Y3) Vs2)))))))))))))
% 0.29/0.79 (assert (forall ((X tptp.com) (Y tptp.com) (R tptp.set_Pr1822651163om_com) (Xs2 tptp.list_com) (Ys2 tptp.list_com)) (let ((_let_1 (@ tptp.transi436345274st_com (@ tptp.listrel1_com R)))) (=> (@ (@ tptp.member1333916004om_com (@ (@ tptp.product_Pair_com_com X) Y)) (@ tptp.transi863150634cl_com R)) (=> (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Xs2) Ys2)) _let_1) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ (@ tptp.cons_com X) Xs2)) (@ (@ tptp.cons_com Y) Ys2))) _let_1))))))
% 0.29/0.79 (assert (forall ((X tptp.produc2041926651_state) (Y tptp.produc2041926651_state) (R tptp.set_Pr1165141447_state) (Xs2 tptp.list_P1040014977_state) (Ys2 tptp.list_P1040014977_state)) (let ((_let_1 (@ tptp.transi339813252_state (@ tptp.listre1738592858_state R)))) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state X) Y)) (@ tptp.transi1302705790_state R)) (=> (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Xs2) Ys2)) _let_1) (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state (@ (@ tptp.cons_P465369265_state X) Xs2)) (@ (@ tptp.cons_P465369265_state Y) Ys2))) _let_1))))))
% 0.29/0.79 (assert (forall ((X tptp.produc410756839_state) (Y tptp.produc410756839_state) (R tptp.set_Pr2096893127_state) (Xs2 tptp.list_P890094829_state) (Ys2 tptp.list_P890094829_state)) (let ((_let_1 (@ tptp.transi1965148016_state (@ tptp.listre1725776070_state R)))) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X) Y)) (@ tptp.transi463013610_state R)) (=> (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Xs2) Ys2)) _let_1) (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state (@ (@ tptp.cons_P438230685_state X) Xs2)) (@ (@ tptp.cons_P438230685_state Y) Ys2))) _let_1))))))
% 0.29/0.79 (assert (forall ((A2 tptp.com) (B2 tptp.com) (R tptp.set_Pr1822651163om_com) (U tptp.list_com) (X tptp.list_com) (Y tptp.list_com)) (let ((_let_1 (@ tptp.append_com U))) (=> (@ (@ tptp.member1333916004om_com (@ (@ tptp.product_Pair_com_com A2) B2)) R) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ _let_1 (@ (@ tptp.cons_com A2) X))) (@ _let_1 (@ (@ tptp.cons_com B2) Y)))) (@ tptp.lexord_com R))))))
% 0.29/0.79 (assert (forall ((A2 tptp.produc2041926651_state) (B2 tptp.produc2041926651_state) (R tptp.set_Pr1165141447_state) (U tptp.list_P1040014977_state) (X tptp.list_P1040014977_state) (Y tptp.list_P1040014977_state)) (let ((_let_1 (@ tptp.append982487830_state U))) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state A2) B2)) R) (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state (@ _let_1 (@ (@ tptp.cons_P465369265_state A2) X))) (@ _let_1 (@ (@ tptp.cons_P465369265_state B2) Y)))) (@ tptp.lexord1062073966_state R))))))
% 0.29/0.79 (assert (forall ((A2 tptp.produc410756839_state) (B2 tptp.produc410756839_state) (R tptp.set_Pr2096893127_state) (U tptp.list_P890094829_state) (X tptp.list_P890094829_state) (Y tptp.list_P890094829_state)) (let ((_let_1 (@ tptp.append221843330_state U))) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state A2) B2)) R) (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state (@ _let_1 (@ (@ tptp.cons_P438230685_state A2) X))) (@ _let_1 (@ (@ tptp.cons_P438230685_state B2) Y)))) (@ tptp.lexord1893203674_state R))))))
% 0.29/0.79 (assert (forall ((X tptp.com) (Xs2 tptp.list_com)) (let ((_let_1 (@ tptp.cons_com X))) (= (@ tptp.rotate1_com (@ _let_1 Xs2)) (@ (@ tptp.append_com Xs2) (@ _let_1 tptp.nil_com))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (X tptp.com)) (= (@ tptp.butlast_com (@ (@ tptp.append_com Xs2) (@ (@ tptp.cons_com X) tptp.nil_com))) Xs2)))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com)) (= (= (@ tptp.rotate1_com Xs2) tptp.nil_com) (= Xs2 tptp.nil_com))))
% 0.29/0.79 (assert (forall ((A2 tptp.com) (X tptp.list_com) (B2 tptp.com) (Y tptp.list_com) (R tptp.set_Pr1822651163om_com)) (let ((_let_1 (@ tptp.lexord_com R))) (= (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ (@ tptp.cons_com A2) X)) (@ (@ tptp.cons_com B2) Y))) _let_1) (or (@ (@ tptp.member1333916004om_com (@ (@ tptp.product_Pair_com_com A2) B2)) R) (and (= A2 B2) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com X) Y)) _let_1)))))))
% 0.29/0.79 (assert (forall ((A2 tptp.produc2041926651_state) (X tptp.list_P1040014977_state) (B2 tptp.produc2041926651_state) (Y tptp.list_P1040014977_state) (R tptp.set_Pr1165141447_state)) (let ((_let_1 (@ tptp.lexord1062073966_state R))) (= (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state (@ (@ tptp.cons_P465369265_state A2) X)) (@ (@ tptp.cons_P465369265_state B2) Y))) _let_1) (or (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state A2) B2)) R) (and (= A2 B2) (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state X) Y)) _let_1)))))))
% 0.29/0.79 (assert (forall ((A2 tptp.produc410756839_state) (X tptp.list_P890094829_state) (B2 tptp.produc410756839_state) (Y tptp.list_P890094829_state) (R tptp.set_Pr2096893127_state)) (let ((_let_1 (@ tptp.lexord1893203674_state R))) (= (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state (@ (@ tptp.cons_P438230685_state A2) X)) (@ (@ tptp.cons_P438230685_state B2) Y))) _let_1) (or (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state A2) B2)) R) (and (= A2 B2) (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state X) Y)) _let_1)))))))
% 0.29/0.79 (assert (forall ((Y tptp.list_com) (R tptp.set_Pr1822651163om_com)) (= (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com tptp.nil_com) Y)) (@ tptp.lexord_com R)) (exists ((A5 tptp.com) (X4 tptp.list_com)) (= Y (@ (@ tptp.cons_com A5) X4))))))
% 0.29/0.79 (assert (= (@ tptp.butlast_com tptp.nil_com) tptp.nil_com))
% 0.29/0.79 (assert (= (@ tptp.rotate1_com tptp.nil_com) tptp.nil_com))
% 0.29/0.79 (assert (forall ((R tptp.set_Pr1165141447_state) (X tptp.list_P1040014977_state) (Y tptp.list_P1040014977_state)) (let ((_let_1 (@ tptp.lexord1062073966_state R))) (=> (forall ((A tptp.produc2041926651_state) (B tptp.produc2041926651_state)) (or (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state A) B)) R) (= A B) (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state B) A)) R))) (or (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state X) Y)) _let_1) (= X Y) (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Y) X)) _let_1))))))
% 0.29/0.79 (assert (forall ((R tptp.set_Pr2096893127_state) (X tptp.list_P890094829_state) (Y tptp.list_P890094829_state)) (let ((_let_1 (@ tptp.lexord1893203674_state R))) (=> (forall ((A tptp.produc410756839_state) (B tptp.produc410756839_state)) (or (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state A) B)) R) (= A B) (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state B) A)) R))) (or (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state X) Y)) _let_1) (= X Y) (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Y) X)) _let_1))))))
% 0.29/0.79 (assert (forall ((R tptp.set_Pr1165141447_state) (Xs2 tptp.list_P1040014977_state)) (=> (forall ((X3 tptp.produc2041926651_state)) (not (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state X3) X3)) R))) (not (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Xs2) Xs2)) (@ tptp.lexord1062073966_state R))))))
% 0.29/0.79 (assert (forall ((R tptp.set_Pr2096893127_state) (Xs2 tptp.list_P890094829_state)) (=> (forall ((X3 tptp.produc410756839_state)) (not (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X3) X3)) R))) (not (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Xs2) Xs2)) (@ tptp.lexord1893203674_state R))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (X tptp.com)) (let ((_let_1 (@ tptp.cons_com X))) (let ((_let_2 (@ tptp.butlast_com (@ _let_1 Xs2)))) (let ((_let_3 (= Xs2 tptp.nil_com))) (and (=> _let_3 (= _let_2 tptp.nil_com)) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_com Xs2))))))))))
% 0.29/0.79 (assert (forall ((X tptp.list_com) (R tptp.set_Pr1822651163om_com)) (not (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com X) tptp.nil_com)) (@ tptp.lexord_com R)))))
% 0.29/0.79 (assert (forall ((Ys2 tptp.list_com) (Xs2 tptp.list_com)) (let ((_let_1 (@ tptp.append_com Xs2))) (let ((_let_2 (@ tptp.butlast_com (@ _let_1 Ys2)))) (let ((_let_3 (= Ys2 tptp.nil_com))) (and (=> _let_3 (= _let_2 (@ tptp.butlast_com Xs2))) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_com Ys2))))))))))
% 0.29/0.79 (assert (forall ((U tptp.list_com) (V tptp.list_com) (R tptp.set_Pr1822651163om_com) (X tptp.list_com)) (let ((_let_1 (@ tptp.lexord_com R))) (let ((_let_2 (@ tptp.append_com X))) (=> (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com U) V)) _let_1) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ _let_2 U)) (@ _let_2 V))) _let_1))))))
% 0.29/0.79 (assert (forall ((X tptp.list_com) (U tptp.list_com) (V tptp.list_com) (R tptp.set_Pr1822651163om_com)) (let ((_let_1 (@ tptp.lexord_com R))) (let ((_let_2 (@ tptp.append_com X))) (=> (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ _let_2 U)) (@ _let_2 V))) _let_1) (=> (forall ((A tptp.com)) (not (@ (@ tptp.member1333916004om_com (@ (@ tptp.product_Pair_com_com A) A)) R))) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com U) V)) _let_1)))))))
% 0.29/0.79 (assert (forall ((X tptp.list_P1040014977_state) (U tptp.list_P1040014977_state) (V tptp.list_P1040014977_state) (R tptp.set_Pr1165141447_state)) (let ((_let_1 (@ tptp.lexord1062073966_state R))) (let ((_let_2 (@ tptp.append982487830_state X))) (=> (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state (@ _let_2 U)) (@ _let_2 V))) _let_1) (=> (forall ((A tptp.produc2041926651_state)) (not (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state A) A)) R))) (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state U) V)) _let_1)))))))
% 0.29/0.79 (assert (forall ((X tptp.list_P890094829_state) (U tptp.list_P890094829_state) (V tptp.list_P890094829_state) (R tptp.set_Pr2096893127_state)) (let ((_let_1 (@ tptp.lexord1893203674_state R))) (let ((_let_2 (@ tptp.append221843330_state X))) (=> (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state (@ _let_2 U)) (@ _let_2 V))) _let_1) (=> (forall ((A tptp.produc410756839_state)) (not (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state A) A)) R))) (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state U) V)) _let_1)))))))
% 0.29/0.79 (assert (forall ((Y tptp.list_com) (X tptp.list_com) (R tptp.set_Pr1822651163om_com)) (=> (exists ((B5 tptp.com) (Z3 tptp.list_com)) (= Y (@ (@ tptp.cons_com B5) Z3))) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com X) (@ (@ tptp.append_com X) Y))) (@ tptp.lexord_com R)))))
% 0.29/0.79 (assert (forall ((R tptp.set_Pr1822651163om_com) (Xs2 tptp.list_com) (Ys2 tptp.list_com) (Zs2 tptp.list_com)) (let ((_let_1 (@ tptp.lexord_com R))) (let ((_let_2 (@ tptp.append_com Xs2))) (=> (@ tptp.irrefl_com R) (= (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ _let_2 Ys2)) (@ _let_2 Zs2))) _let_1) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Ys2) Zs2)) _let_1)))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com)) (=> (not (= Xs2 tptp.nil_com)) (= (@ (@ tptp.append_com (@ tptp.butlast_com Xs2)) (@ (@ tptp.cons_com (@ tptp.last_com Xs2)) tptp.nil_com)) Xs2))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (X tptp.com) (Ys2 tptp.list_com)) (= (= (@ (@ tptp.append_com Xs2) (@ (@ tptp.cons_com X) tptp.nil_com)) Ys2) (and (not (= Ys2 tptp.nil_com)) (= (@ tptp.butlast_com Ys2) Xs2) (= (@ tptp.last_com Ys2) X)))))
% 0.29/0.79 (assert (forall ((Ys2 tptp.list_com) (Xs2 tptp.list_com)) (=> (not (= Ys2 tptp.nil_com)) (= (@ tptp.last_com (@ (@ tptp.append_com Xs2) Ys2)) (@ tptp.last_com Ys2)))))
% 0.29/0.79 (assert (forall ((Ys2 tptp.list_com) (Xs2 tptp.list_com)) (=> (= Ys2 tptp.nil_com) (= (@ tptp.last_com (@ (@ tptp.append_com Xs2) Ys2)) (@ tptp.last_com Xs2)))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (X tptp.com)) (= (@ tptp.last_com (@ (@ tptp.append_com Xs2) (@ (@ tptp.cons_com X) tptp.nil_com))) X)))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (X tptp.com)) (=> (not (= Xs2 tptp.nil_com)) (= (@ tptp.last_com (@ (@ tptp.cons_com X) Xs2)) (@ tptp.last_com Xs2)))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (X tptp.com)) (=> (= Xs2 tptp.nil_com) (= (@ tptp.last_com (@ (@ tptp.cons_com X) Xs2)) X))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (X tptp.com)) (let ((_let_1 (@ tptp.last_com (@ (@ tptp.cons_com X) Xs2)))) (let ((_let_2 (= Xs2 tptp.nil_com))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ tptp.last_com Xs2))))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (Ys2 tptp.list_com)) (exists ((Ss tptp.list_com) (Xs5 tptp.list_com) (Ys5 tptp.list_com)) (and (= Xs2 (@ (@ tptp.append_com Xs5) Ss)) (= Ys2 (@ (@ tptp.append_com Ys5) Ss)) (or (= Xs5 tptp.nil_com) (= Ys5 tptp.nil_com) (not (= (@ tptp.last_com Xs5) (@ tptp.last_com Ys5))))))))
% 0.29/0.79 (assert (forall ((Ys2 tptp.list_com) (Xs2 tptp.list_com)) (let ((_let_1 (@ tptp.last_com (@ (@ tptp.append_com Xs2) Ys2)))) (let ((_let_2 (= Ys2 tptp.nil_com))) (and (=> _let_2 (= _let_1 (@ tptp.last_com Xs2))) (=> (not _let_2) (= _let_1 (@ tptp.last_com Ys2))))))))
% 0.29/0.79 (assert (forall ((R2 tptp.set_Pr1165141447_state)) (=> (forall ((A tptp.produc2041926651_state)) (not (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state A) A)) R2))) (@ tptp.irrefl654089520_state R2))))
% 0.29/0.79 (assert (forall ((R2 tptp.set_Pr2096893127_state)) (=> (forall ((A tptp.produc410756839_state)) (not (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state A) A)) R2))) (@ tptp.irrefl1358048924_state R2))))
% 0.29/0.79 (assert (= tptp.irrefl654089520_state (lambda ((R3 tptp.set_Pr1165141447_state)) (forall ((A5 tptp.produc2041926651_state)) (not (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state A5) A5)) R3))))))
% 0.29/0.79 (assert (= tptp.irrefl1358048924_state (lambda ((R3 tptp.set_Pr2096893127_state)) (forall ((A5 tptp.produc410756839_state)) (not (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state A5) A5)) R3))))))
% 0.29/0.79 (assert (forall ((R2 tptp.set_Pr1822651163om_com) (Us tptp.list_com) (Xs2 tptp.list_com) (Ys2 tptp.list_com)) (let ((_let_1 (@ tptp.lenlex_com R2))) (let ((_let_2 (@ tptp.append_com Us))) (=> (@ tptp.irrefl_com R2) (= (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ _let_2 Xs2)) (@ _let_2 Ys2))) _let_1) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Xs2) Ys2)) _let_1)))))))
% 0.29/0.79 (assert (forall ((Ns tptp.list_com) (R tptp.set_Pr1822651163om_com)) (= (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com tptp.nil_com) Ns)) (@ tptp.lenlex_com R)) (not (= Ns tptp.nil_com)))))
% 0.29/0.79 (assert (forall ((Ys2 tptp.list_com) (R tptp.set_Pr1822651163om_com)) (not (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com tptp.nil_com) Ys2)) (@ tptp.lex_com R)))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (R tptp.set_Pr1822651163om_com)) (not (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Xs2) tptp.nil_com)) (@ tptp.lex_com R)))))
% 0.29/0.79 (assert (forall ((Ys2 tptp.list_com) (Zs2 tptp.list_com) (R tptp.set_Pr1822651163om_com) (Xs2 tptp.list_com)) (let ((_let_1 (@ tptp.lex_com R))) (let ((_let_2 (@ tptp.append_com Xs2))) (=> (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Ys2) Zs2)) _let_1) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ _let_2 Ys2)) (@ _let_2 Zs2))) _let_1))))))
% 0.29/0.79 (assert (forall ((R tptp.set_Pr1165141447_state) (Xs2 tptp.list_P1040014977_state)) (=> (forall ((X3 tptp.produc2041926651_state)) (not (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state X3) X3)) R))) (not (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Xs2) Xs2)) (@ tptp.lenlex295247238_state R))))))
% 0.29/0.79 (assert (forall ((R tptp.set_Pr2096893127_state) (Xs2 tptp.list_P890094829_state)) (=> (forall ((X3 tptp.produc410756839_state)) (not (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X3) X3)) R))) (not (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Xs2) Xs2)) (@ tptp.lenlex1401983474_state R))))))
% 0.29/0.79 (assert (forall ((Ns tptp.list_com) (R tptp.set_Pr1822651163om_com)) (not (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Ns) tptp.nil_com)) (@ tptp.lenlex_com R)))))
% 0.29/0.79 (assert (forall ((R tptp.set_Pr1822651163om_com) (Xs2 tptp.list_com) (Ys2 tptp.list_com) (Zs2 tptp.list_com)) (let ((_let_1 (@ tptp.lex_com R))) (let ((_let_2 (@ tptp.append_com Xs2))) (=> (forall ((X3 tptp.com)) (not (@ (@ tptp.member1333916004om_com (@ (@ tptp.product_Pair_com_com X3) X3)) R))) (=> (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ _let_2 Ys2)) (@ _let_2 Zs2))) _let_1) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Ys2) Zs2)) _let_1)))))))
% 0.29/0.79 (assert (forall ((R tptp.set_Pr1165141447_state) (Xs2 tptp.list_P1040014977_state) (Ys2 tptp.list_P1040014977_state) (Zs2 tptp.list_P1040014977_state)) (let ((_let_1 (@ tptp.lex_Pr570247525_state R))) (let ((_let_2 (@ tptp.append982487830_state Xs2))) (=> (forall ((X3 tptp.produc2041926651_state)) (not (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state X3) X3)) R))) (=> (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state (@ _let_2 Ys2)) (@ _let_2 Zs2))) _let_1) (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Ys2) Zs2)) _let_1)))))))
% 0.29/0.79 (assert (forall ((R tptp.set_Pr2096893127_state) (Xs2 tptp.list_P890094829_state) (Ys2 tptp.list_P890094829_state) (Zs2 tptp.list_P890094829_state)) (let ((_let_1 (@ tptp.lex_Pr1762629969_state R))) (let ((_let_2 (@ tptp.append221843330_state Xs2))) (=> (forall ((X3 tptp.produc410756839_state)) (not (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X3) X3)) R))) (=> (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state (@ _let_2 Ys2)) (@ _let_2 Zs2))) _let_1) (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Ys2) Zs2)) _let_1)))))))
% 0.29/0.79 (assert (forall ((R tptp.set_Pr1822651163om_com) (Xs2 tptp.list_com) (Ys2 tptp.list_com) (Zs2 tptp.list_com)) (let ((_let_1 (@ tptp.lex_com R))) (let ((_let_2 (@ tptp.append_com Xs2))) (=> (forall ((X3 tptp.com)) (not (@ (@ tptp.member1333916004om_com (@ (@ tptp.product_Pair_com_com X3) X3)) R))) (= (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ _let_2 Ys2)) (@ _let_2 Zs2))) _let_1) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Ys2) Zs2)) _let_1)))))))
% 0.29/0.79 (assert (forall ((R tptp.set_Pr1165141447_state) (Xs2 tptp.list_P1040014977_state) (Ys2 tptp.list_P1040014977_state) (Zs2 tptp.list_P1040014977_state)) (let ((_let_1 (@ tptp.lex_Pr570247525_state R))) (let ((_let_2 (@ tptp.append982487830_state Xs2))) (=> (forall ((X3 tptp.produc2041926651_state)) (not (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state X3) X3)) R))) (= (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state (@ _let_2 Ys2)) (@ _let_2 Zs2))) _let_1) (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Ys2) Zs2)) _let_1)))))))
% 0.29/0.79 (assert (forall ((R tptp.set_Pr2096893127_state) (Xs2 tptp.list_P890094829_state) (Ys2 tptp.list_P890094829_state) (Zs2 tptp.list_P890094829_state)) (let ((_let_1 (@ tptp.lex_Pr1762629969_state R))) (let ((_let_2 (@ tptp.append221843330_state Xs2))) (=> (forall ((X3 tptp.produc410756839_state)) (not (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X3) X3)) R))) (= (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state (@ _let_2 Ys2)) (@ _let_2 Zs2))) _let_1) (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Ys2) Zs2)) _let_1)))))))
% 0.29/0.79 (assert (forall ((X tptp.com) (Xs2 tptp.list_com) (Y tptp.com) (Ys2 tptp.list_com) (R tptp.set_Pr1822651163om_com)) (let ((_let_1 (@ tptp.lex_com R))) (= (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ (@ tptp.cons_com X) Xs2)) (@ (@ tptp.cons_com Y) Ys2))) _let_1) (or (and (@ (@ tptp.member1333916004om_com (@ (@ tptp.product_Pair_com_com X) Y)) R) (= (@ tptp.size_size_list_com Xs2) (@ tptp.size_size_list_com Ys2))) (and (= X Y) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Xs2) Ys2)) _let_1)))))))
% 0.29/0.79 (assert (forall ((X tptp.produc2041926651_state) (Xs2 tptp.list_P1040014977_state) (Y tptp.produc2041926651_state) (Ys2 tptp.list_P1040014977_state) (R tptp.set_Pr1165141447_state)) (let ((_let_1 (@ tptp.lex_Pr570247525_state R))) (= (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state (@ (@ tptp.cons_P465369265_state X) Xs2)) (@ (@ tptp.cons_P465369265_state Y) Ys2))) _let_1) (or (and (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state X) Y)) R) (= (@ tptp.size_s213202669_state Xs2) (@ tptp.size_s213202669_state Ys2))) (and (= X Y) (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Xs2) Ys2)) _let_1)))))))
% 0.29/0.79 (assert (forall ((X tptp.produc410756839_state) (Xs2 tptp.list_P890094829_state) (Y tptp.produc410756839_state) (Ys2 tptp.list_P890094829_state) (R tptp.set_Pr2096893127_state)) (let ((_let_1 (@ tptp.lex_Pr1762629969_state R))) (= (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state (@ (@ tptp.cons_P438230685_state X) Xs2)) (@ (@ tptp.cons_P438230685_state Y) Ys2))) _let_1) (or (and (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X) Y)) R) (= (@ tptp.size_s837829465_state Xs2) (@ tptp.size_s837829465_state Ys2))) (and (= X Y) (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Xs2) Ys2)) _let_1)))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (Ys2 tptp.list_com) (Us tptp.list_com) (Vs tptp.list_com)) (=> (or (= (@ tptp.size_size_list_com Xs2) (@ tptp.size_size_list_com Ys2)) (= (@ tptp.size_size_list_com Us) (@ tptp.size_size_list_com Vs))) (= (= (@ (@ tptp.append_com Xs2) Us) (@ (@ tptp.append_com Ys2) Vs)) (and (= Xs2 Ys2) (= Us Vs))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (Ys2 tptp.list_com) (Zs2 tptp.list_com) (P (-> tptp.list_com tptp.list_com tptp.list_com Bool))) (let ((_let_1 (@ tptp.size_size_list_com Ys2))) (=> (= (@ tptp.size_size_list_com Xs2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_com Zs2)) (=> (@ (@ (@ P tptp.nil_com) tptp.nil_com) tptp.nil_com) (=> (forall ((X3 tptp.com) (Xs tptp.list_com) (Y3 tptp.com) (Ys tptp.list_com) (Z tptp.com) (Zs tptp.list_com)) (let ((_let_1 (@ tptp.size_size_list_com Ys))) (=> (= (@ tptp.size_size_list_com Xs) _let_1) (=> (= _let_1 (@ tptp.size_size_list_com Zs)) (=> (@ (@ (@ P Xs) Ys) Zs) (@ (@ (@ P (@ (@ tptp.cons_com X3) Xs)) (@ (@ tptp.cons_com Y3) Ys)) (@ (@ tptp.cons_com Z) Zs))))))) (@ (@ (@ P Xs2) Ys2) Zs2))))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (Ys2 tptp.list_com) (P (-> tptp.list_com tptp.list_com Bool))) (=> (= (@ tptp.size_size_list_com Xs2) (@ tptp.size_size_list_com Ys2)) (=> (@ (@ P tptp.nil_com) tptp.nil_com) (=> (forall ((X3 tptp.com) (Xs tptp.list_com) (Y3 tptp.com) (Ys tptp.list_com)) (=> (= (@ tptp.size_size_list_com Xs) (@ tptp.size_size_list_com Ys)) (=> (@ (@ P Xs) Ys) (@ (@ P (@ (@ tptp.cons_com X3) Xs)) (@ (@ tptp.cons_com Y3) Ys))))) (@ (@ P Xs2) Ys2))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (Ys2 tptp.list_com)) (=> (not (= Xs2 Ys2)) (=> (= (@ tptp.size_size_list_com Xs2) (@ tptp.size_size_list_com Ys2)) (exists ((Pre tptp.list_com) (X3 tptp.com) (Xs5 tptp.list_com) (Y3 tptp.com) (Ys5 tptp.list_com)) (let ((_let_1 (@ tptp.append_com Pre))) (and (not (= X3 Y3)) (= Xs2 (@ _let_1 (@ (@ tptp.append_com (@ (@ tptp.cons_com X3) tptp.nil_com)) Xs5))) (= Ys2 (@ _let_1 (@ (@ tptp.append_com (@ (@ tptp.cons_com Y3) tptp.nil_com)) Ys5))))))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (Zs2 tptp.list_com) (Ys2 tptp.list_com) (Qs tptp.list_com) (R tptp.set_Pr1822651163om_com)) (let ((_let_1 (@ tptp.lexord_com R))) (=> (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ (@ tptp.append_com Xs2) Zs2)) (@ (@ tptp.append_com Ys2) Qs))) _let_1) (=> (not (= Xs2 Ys2)) (=> (= (@ tptp.size_size_list_com Xs2) (@ tptp.size_size_list_com Ys2)) (=> (= (@ tptp.size_size_list_com Zs2) (@ tptp.size_size_list_com Qs)) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Xs2) Ys2)) _let_1))))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (Ys2 tptp.list_com) (R tptp.set_Pr1822651163om_com) (Vs tptp.list_com) (Us tptp.list_com)) (let ((_let_1 (@ tptp.lex_com R))) (=> (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Xs2) Ys2)) _let_1) (=> (= (@ tptp.size_size_list_com Vs) (@ tptp.size_size_list_com Us)) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ (@ tptp.append_com Xs2) Us)) (@ (@ tptp.append_com Ys2) Vs))) _let_1))))))
% 0.29/0.79 (assert (forall ((Us tptp.list_com) (Xs2 tptp.list_com) (R2 tptp.set_Pr1822651163om_com) (Vs tptp.list_com) (Ys2 tptp.list_com)) (let ((_let_1 (@ tptp.lenlex_com R2))) (=> (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Us) Xs2)) _let_1) (=> (= (@ tptp.size_size_list_com Vs) (@ tptp.size_size_list_com Ys2)) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ (@ tptp.append_com Us) Vs)) (@ (@ tptp.append_com Xs2) Ys2))) _let_1))))))
% 0.29/0.79 (assert (forall ((M tptp.com) (Ms tptp.list_com) (N tptp.com) (Ns tptp.list_com) (R tptp.set_Pr1822651163om_com)) (let ((_let_1 (@ tptp.lenlex_com R))) (let ((_let_2 (@ tptp.size_size_list_com Ns))) (let ((_let_3 (@ tptp.size_size_list_com Ms))) (= (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ (@ tptp.cons_com M) Ms)) (@ (@ tptp.cons_com N) Ns))) _let_1) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ (@ tptp.member1333916004om_com (@ (@ tptp.product_Pair_com_com M) N)) R)) (and (= M N) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Ms) Ns)) _let_1)))))))))
% 0.29/0.79 (assert (forall ((M tptp.produc2041926651_state) (Ms tptp.list_P1040014977_state) (N tptp.produc2041926651_state) (Ns tptp.list_P1040014977_state) (R tptp.set_Pr1165141447_state)) (let ((_let_1 (@ tptp.lenlex295247238_state R))) (let ((_let_2 (@ tptp.size_s213202669_state Ns))) (let ((_let_3 (@ tptp.size_s213202669_state Ms))) (= (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state (@ (@ tptp.cons_P465369265_state M) Ms)) (@ (@ tptp.cons_P465369265_state N) Ns))) _let_1) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state M) N)) R)) (and (= M N) (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Ms) Ns)) _let_1)))))))))
% 0.29/0.79 (assert (forall ((M tptp.produc410756839_state) (Ms tptp.list_P890094829_state) (N tptp.produc410756839_state) (Ns tptp.list_P890094829_state) (R tptp.set_Pr2096893127_state)) (let ((_let_1 (@ tptp.lenlex1401983474_state R))) (let ((_let_2 (@ tptp.size_s837829465_state Ns))) (let ((_let_3 (@ tptp.size_s837829465_state Ms))) (= (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state (@ (@ tptp.cons_P438230685_state M) Ms)) (@ (@ tptp.cons_P438230685_state N) Ns))) _let_1) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state M) N)) R)) (and (= M N) (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Ms) Ns)) _let_1)))))))))
% 0.29/0.79 (assert (forall ((P (-> tptp.com Bool))) (not (@ (@ tptp.list_ex1_com P) tptp.nil_com))))
% 0.29/0.79 (assert (forall ((X tptp.produc2041926651_state) (Y tptp.produc2041926651_state) (F2 (-> tptp.produc2041926651_state tptp.nat)) (Fs tptp.list_P1178430914te_nat)) (let ((_let_1 (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state X) Y)))) (let ((_let_2 (@ F2 Y))) (let ((_let_3 (@ F2 X))) (= (@ _let_1 (@ tptp.measur1071343867_state (@ (@ tptp.cons_P1821701106te_nat F2) Fs))) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ _let_1 (@ tptp.measur1071343867_state Fs))))))))))
% 0.29/0.79 (assert (forall ((X tptp.produc410756839_state) (Y tptp.produc410756839_state) (F2 (-> tptp.produc410756839_state tptp.nat)) (Fs tptp.list_P1627643054te_nat)) (let ((_let_1 (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X) Y)))) (let ((_let_2 (@ F2 Y))) (let ((_let_3 (@ F2 X))) (= (@ _let_1 (@ tptp.measur768621543_state (@ (@ tptp.cons_P1631380062te_nat F2) Fs))) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ _let_1 (@ tptp.measur768621543_state Fs))))))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_P1040014977_state) (Ys2 tptp.list_P1040014977_state) (R tptp.set_Pr1165141447_state)) (= (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Xs2) Ys2)) (@ tptp.listre194873521_state R)) (and (= (@ tptp.size_s213202669_state Xs2) (@ tptp.size_s213202669_state Ys2)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s213202669_state Xs2)) (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.nth_Pr553241858_state Xs2) N2)) (@ (@ tptp.nth_Pr553241858_state Ys2) N2))) R)))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_list_com) (Ys2 tptp.list_state) (R tptp.set_Pr849496667_state)) (= (@ (@ tptp.member1442949316_state (@ (@ tptp.produc1742567891_state Xs2) Ys2)) (@ tptp.listre1268245261_state R)) (and (= (@ tptp.size_s318434721st_com Xs2) (@ tptp.size_size_list_state Ys2)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s318434721st_com Xs2)) (@ (@ tptp.member64234660_state (@ (@ tptp.produc1204172211_state (@ (@ tptp.nth_list_com Xs2) N2)) (@ (@ tptp.nth_state Ys2) N2))) R)))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_P890094829_state) (Ys2 tptp.list_P890094829_state) (R tptp.set_Pr2096893127_state)) (= (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Xs2) Ys2)) (@ tptp.listre1244407729_state R)) (and (= (@ tptp.size_s837829465_state Xs2) (@ tptp.size_s837829465_state Ys2)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s837829465_state Xs2)) (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state (@ (@ tptp.nth_Pr526167918_state Xs2) N2)) (@ (@ tptp.nth_Pr526167918_state Ys2) N2))) R)))))))
% 0.29/0.79 (assert (forall ((X tptp.produc2041926651_state) (Y tptp.produc2041926651_state)) (not (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state X) Y)) (@ tptp.measur1071343867_state tptp.nil_Pr1876916290te_nat)))))
% 0.29/0.79 (assert (forall ((X tptp.produc410756839_state) (Y tptp.produc410756839_state)) (not (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X) Y)) (@ tptp.measur768621543_state tptp.nil_Pr164089518te_nat)))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_com) (X tptp.com) (Ys2 tptp.list_com)) (= (@ (@ tptp.nth_com (@ (@ tptp.append_com Xs2) (@ (@ tptp.cons_com X) Ys2))) (@ tptp.size_size_list_com Xs2)) X)))
% 0.29/0.79 (assert (forall ((F2 (-> tptp.produc2041926651_state tptp.nat)) (X tptp.produc2041926651_state) (Y tptp.produc2041926651_state) (Fs tptp.list_P1178430914te_nat)) (=> (@ (@ tptp.ord_less_nat (@ F2 X)) (@ F2 Y)) (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state X) Y)) (@ tptp.measur1071343867_state (@ (@ tptp.cons_P1821701106te_nat F2) Fs))))))
% 0.29/0.79 (assert (forall ((F2 (-> tptp.produc410756839_state tptp.nat)) (X tptp.produc410756839_state) (Y tptp.produc410756839_state) (Fs tptp.list_P1627643054te_nat)) (=> (@ (@ tptp.ord_less_nat (@ F2 X)) (@ F2 Y)) (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X) Y)) (@ tptp.measur768621543_state (@ (@ tptp.cons_P1631380062te_nat F2) Fs))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_P1040014977_state) (Ys2 tptp.list_P1040014977_state) (R tptp.set_Pr1165141447_state)) (= (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Xs2) Ys2)) (@ tptp.listre1738592858_state R)) (exists ((Y4 tptp.produc2041926651_state) (N2 tptp.nat)) (and (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.nth_Pr553241858_state Xs2) N2)) Y4)) R) (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s213202669_state Xs2)) (= Ys2 (@ (@ (@ tptp.list_u737668969_state Xs2) N2) Y4)))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_P890094829_state) (Ys2 tptp.list_P890094829_state) (R tptp.set_Pr2096893127_state)) (= (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Xs2) Ys2)) (@ tptp.listre1725776070_state R)) (exists ((Y4 tptp.produc410756839_state) (N2 tptp.nat)) (and (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state (@ (@ tptp.nth_Pr526167918_state Xs2) N2)) Y4)) R) (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s837829465_state Xs2)) (= Ys2 (@ (@ (@ tptp.list_u364351829_state Xs2) N2) Y4)))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_P1040014977_state) (Ys2 tptp.list_P1040014977_state) (R tptp.set_Pr1165141447_state)) (=> (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Xs2) Ys2)) (@ tptp.lex_Pr570247525_state R)) (not (forall ((I tptp.nat)) (let ((_let_1 (@ tptp.take_P558217449_state I))) (let ((_let_2 (@ tptp.ord_less_nat I))) (=> (@ _let_2 (@ tptp.size_s213202669_state Xs2)) (=> (@ _let_2 (@ tptp.size_s213202669_state Ys2)) (=> (= (@ _let_1 Xs2) (@ _let_1 Ys2)) (not (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.nth_Pr553241858_state Xs2) I)) (@ (@ tptp.nth_Pr553241858_state Ys2) I))) R))))))))))))
% 0.29/0.79 (assert (forall ((Xs2 tptp.list_P890094829_state) (Ys2 tptp.list_P890094829_state) (R tptp.set_Pr2096893127_state)) (=> (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Xs2) Ys2)) (@ tptp.lex_Pr1762629969_state R)) (not (forall ((I tptp.nat)) (let ((_let_1 (@ tptp.take_P1852316373_state I))) (let ((_let_2 (@ tptp.ord_less_nat I))) (=> (@ _let_2 (@ tptp.size_s837829465_state Xs2)) (=> (@ _let_2 (@ tptp.size_s837829465_state Ys2)) (=> (= (@ _let_1 Xs2) (@ _let_1 Ys2)) (not (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state (@ (@ tptp.nth_Pr526167918_state Xs2) I)) (@ (@ tptp.nth_Pr526167918_state Ys2) I))) R))))))))))))
% 0.61/1.14 (assert (forall ((Xs2 tptp.list_com) (K tptp.nat) (X tptp.com)) (= (= (@ (@ (@ tptp.list_update_com Xs2) K) X) tptp.nil_com) (= Xs2 tptp.nil_com))))
% 0.61/1.14 (assert (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state (@ (@ tptp.cons_com tptp.c) tptp.nil_com)) tptp.s)) (@ (@ tptp.produc1204172211_state (@ (@ tptp.cons_com tptp.c2) tptp.cs)) tptp.s2))) (@ tptp.transi1302705790_state tptp.pHoare259243666_exec1)))
% 0.61/1.14 (assert (@ (@ tptp.termi tptp.c) tptp.s))
% 0.61/1.14 (assert (forall ((S5 tptp.state) (S6 tptp.state)) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state (@ (@ tptp.cons_com tptp.c) tptp.nil_com)) S5)) (@ (@ tptp.produc1204172211_state (@ (@ tptp.cons_com tptp.c2) tptp.cs)) S6))) (@ tptp.transi1302705790_state tptp.pHoare259243666_exec1)) (=> (@ (@ tptp.termi tptp.c) S5) (and (@ (@ tptp.termi tptp.c2) S6) (forall ((T4 tptp.state)) (=> (@ (@ (@ tptp.exec S6) tptp.c2) T4) (@ (@ tptp.pHoare806997636termis tptp.cs) T4))))))))
% 0.61/1.14 (assert (not (@ (@ tptp.termi tptp.c2) tptp.s2)))
% 0.61/1.14 (set-info :filename cvc5---1.0.5_20204)
% 0.61/1.14 (check-sat-assuming ( true ))
% 0.61/1.14 ------- get file name : TPTP file name is ITP142^1
% 0.61/1.14 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_20204.smt2...
% 0.61/1.14 --- Run --ho-elim --full-saturate-quant at 10...
% 0.61/1.14 % SZS status Theorem for ITP142^1
% 0.61/1.14 % SZS output start Proof for ITP142^1
% 0.61/1.14 (
% 0.61/1.14 (let ((_let_1 (not (@ (@ tptp.termi tptp.c2) tptp.s2)))) (let ((_let_2 (forall ((S5 tptp.state) (S6 tptp.state)) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state (@ (@ tptp.cons_com tptp.c) tptp.nil_com)) S5)) (@ (@ tptp.produc1204172211_state (@ (@ tptp.cons_com tptp.c2) tptp.cs)) S6))) (@ tptp.transi1302705790_state tptp.pHoare259243666_exec1)) (=> (@ (@ tptp.termi tptp.c) S5) (and (@ (@ tptp.termi tptp.c2) S6) (forall ((T4 tptp.state)) (=> (@ (@ (@ tptp.exec S6) tptp.c2) T4) (@ (@ tptp.pHoare806997636termis tptp.cs) T4))))))))) (let ((_let_3 (@ (@ tptp.termi tptp.c) tptp.s))) (let ((_let_4 (@ tptp.transi1302705790_state tptp.pHoare259243666_exec1))) (let ((_let_5 (@ (@ tptp.produc1204172211_state (@ (@ tptp.cons_com tptp.c2) tptp.cs)) tptp.s2))) (let ((_let_6 (@ tptp.cons_com tptp.c))) (let ((_let_7 (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state (@ _let_6 tptp.nil_com)) tptp.s)) _let_5)) _let_4))) (let ((_let_8 (= tptp.irrefl1358048924_state (lambda ((R3 tptp.set_Pr2096893127_state)) (forall ((A5 tptp.produc410756839_state)) (not (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state A5) A5)) R3))))))) (let ((_let_9 (= tptp.irrefl654089520_state (lambda ((R3 tptp.set_Pr1165141447_state)) (forall ((A5 tptp.produc2041926651_state)) (not (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state A5) A5)) R3))))))) (let ((_let_10 (@ tptp.concat_com tptp.nil_list_com))) (let ((_let_11 (= _let_10 tptp.nil_com))) (let ((_let_12 (@ (@ tptp.cons_list_com tptp.nil_com) tptp.nil_list_com))) (let ((_let_13 (ho_35 (ho_34 k_33 (ho_41 (ho_40 k_39 (ho_38 (ho_37 k_36 (ho_15 (ho_14 k_13 tptp.c) (ho_17 k_16 tptp.nil_list_com))) tptp.s)) (ho_38 (ho_37 k_36 (ho_15 (ho_14 k_13 tptp.c2) tptp.cs)) tptp.s2))) (ho_45 k_44 tptp.pHoare259243666_exec1)))) (let ((_let_14 (ho_9 (ho_12 k_43 tptp.c) tptp.s))) (let ((_let_15 (ho_9 (ho_12 k_43 tptp.c2) tptp.s2))) (let ((_let_16 (and _let_15 (or (not (ho_9 (ho_12 (ho_11 k_10 tptp.s2) tptp.c2) tptp.s2)) (ho_9 (ho_8 k_42 tptp.cs) tptp.s2))))) (let ((_let_17 (not _let_14))) (let ((_let_18 (not _let_13))) (let ((_let_19 (or _let_18 _let_17 _let_16))) (let ((_let_20 (AND_INTRO (ASSUME :args (_let_8)) (ASSUME :args (_let_9)) (SYMM (ASSUME :args (_let_11)))))) (let ((_let_21 (not _let_16))) (let ((_let_22 (forall ((S5 tptp.state) (S6 tptp.state) (BOUND_VARIABLE_11983 tptp.state)) (or (not (ho_35 (ho_34 k_33 (ho_41 (ho_40 k_39 (ho_38 (ho_37 k_36 (ho_15 (ho_14 k_13 tptp.c) (ho_17 k_16 tptp.nil_list_com))) S5)) (ho_38 (ho_37 k_36 (ho_15 (ho_14 k_13 tptp.c2) tptp.cs)) S6))) (ho_45 k_44 tptp.pHoare259243666_exec1))) (not (ho_9 (ho_12 k_43 tptp.c) S5)) (and (ho_9 (ho_12 k_43 tptp.c2) S6) (or (not (ho_9 (ho_12 (ho_11 k_10 S6) tptp.c2) BOUND_VARIABLE_11983)) (ho_9 (ho_8 k_42 tptp.cs) BOUND_VARIABLE_11983))))))) (let ((_let_23 (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_20 :args ((forall ((S5 tptp.state) (S6 tptp.state) (BOUND_VARIABLE_11983 tptp.state)) (or (not (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state (@ (@ tptp.cons_com tptp.c) tptp.nil_com)) S5)) (@ (@ tptp.produc1204172211_state (@ (@ tptp.cons_com tptp.c2) tptp.cs)) S6))) (@ tptp.transi1302705790_state tptp.pHoare259243666_exec1))) (not (@ (@ tptp.termi tptp.c) S5)) (and (@ (@ tptp.termi tptp.c2) S6) (or (not (@ (@ (@ tptp.exec S6) tptp.c2) BOUND_VARIABLE_11983)) (@ (@ tptp.pHoare806997636termis tptp.cs) BOUND_VARIABLE_11983))))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((S5 tptp.state) (S6 tptp.state) (BOUND_VARIABLE_11983 tptp.state)) (or (not (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state (@ (@ tptp.cons_com tptp.c) (@ tptp.concat_com tptp.nil_list_com))) S5)) (@ (@ tptp.produc1204172211_state (@ (@ tptp.cons_com tptp.c2) tptp.cs)) S6))) (@ tptp.transi1302705790_state tptp.pHoare259243666_exec1))) (not (@ (@ tptp.termi tptp.c) S5)) (and (@ (@ tptp.termi tptp.c2) S6) (or (not (@ (@ (@ tptp.exec S6) tptp.c2) BOUND_VARIABLE_11983)) (@ (@ tptp.pHoare806997636termis tptp.cs) BOUND_VARIABLE_11983))))) _let_22))))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_19)) :args ((or _let_18 _let_17 _let_16 (not _let_19)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (tptp.s tptp.s2 tptp.s2 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_22))) _let_23 :args (_let_19 false _let_22)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_16 0)) :args ((or _let_15 _let_21))) (EQ_RESOLVE (ASSUME :args (_let_1)) (PREPROCESS :args ((= _let_1 (not _let_15))))) :args (_let_21 true _let_15)) (EQ_RESOLVE (ASSUME :args (_let_3)) (PREPROCESS :args ((= _let_3 _let_14)))) (EQ_RESOLVE (ASSUME :args (_let_7)) (TRANS (MACRO_SR_EQ_INTRO _let_20 :args (_let_7 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state (@ _let_6 _let_10)) tptp.s)) _let_5)) _let_4) _let_13))))) :args (false false _let_19 true _let_16 false _let_14 false _let_13)) :args ((forall ((S tptp.state) (Cs tptp.list_com) (S2 tptp.state)) (not (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state tptp.nil_com) S)) (@ (@ tptp.produc1204172211_state Cs) S2))) tptp.pHoare259243666_exec1))) (forall ((C tptp.com) (Cs2 tptp.list_com) (S tptp.state)) (= (@ (@ tptp.pHoare806997636termis (@ (@ tptp.cons_com C) Cs2)) S) (and (@ (@ tptp.termi C) S) (forall ((T tptp.state)) (=> (@ (@ (@ tptp.exec S) C) T) (@ (@ tptp.pHoare806997636termis Cs2) T)))))) (forall ((S tptp.state)) (@ (@ tptp.pHoare806997636termis tptp.nil_com) S)) (forall ((S tptp.state) (C tptp.com) (S2 tptp.state) (Cs2 tptp.list_com)) (=> (@ (@ (@ tptp.exec S) C) S2) (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state (@ (@ tptp.cons_com C) Cs2)) S)) (@ (@ tptp.produc1204172211_state Cs2) S2))) (@ tptp.transi1302705790_state tptp.pHoare259243666_exec1)))) (forall ((C tptp.com) (S tptp.state) (T2 tptp.state)) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state (@ (@ tptp.cons_com C) tptp.nil_com)) S)) (@ (@ tptp.produc1204172211_state tptp.nil_com) T2))) (@ tptp.transi1302705790_state tptp.pHoare259243666_exec1)) (@ (@ (@ tptp.exec S) C) T2))) (forall ((Cs2 tptp.list_com) (S tptp.state) (Cs tptp.list_com) (S2 tptp.state)) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state Cs2) S)) (@ (@ tptp.produc1204172211_state Cs) S2))) tptp.pHoare259243666_exec1) (=> (@ (@ tptp.pHoare806997636termis Cs2) S) (@ (@ tptp.pHoare806997636termis Cs) S2)))) (forall ((Cs2 tptp.list_com) (S tptp.state) (Cs tptp.list_com) (S2 tptp.state)) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state Cs2) S)) (@ (@ tptp.produc1204172211_state Cs) S2))) (@ tptp.transi1302705790_state tptp.pHoare259243666_exec1)) (=> (@ (@ tptp.pHoare806997636termis Cs2) S) (@ (@ tptp.pHoare806997636termis Cs) S2)))) (forall ((Ax tptp.list_P890094829_state) (Ay tptp.list_P890094829_state) (Bx tptp.list_P890094829_state) (By tptp.list_P890094829_state) (R tptp.set_Pr1696918727_state) (P (-> tptp.list_P890094829_state tptp.list_P890094829_state Bool))) (=> (@ (@ tptp.member1642814224_state (@ (@ tptp.produc1576663895_state (@ (@ tptp.produc1354769367_state Ax) Ay)) (@ (@ tptp.produc1354769367_state Bx) By))) (@ tptp.transi445721450_state R)) (=> (@ (@ P Ax) Ay) (=> (forall ((A tptp.list_P890094829_state) (B tptp.list_P890094829_state) (Aa tptp.list_P890094829_state) (Ba tptp.list_P890094829_state)) (let ((_let_1 (@ (@ tptp.produc1354769367_state A) B))) (=> (@ (@ tptp.member1642814224_state (@ (@ tptp.produc1576663895_state (@ (@ tptp.produc1354769367_state Ax) Ay)) _let_1)) (@ tptp.transi445721450_state R)) (=> (@ (@ tptp.member1642814224_state (@ (@ tptp.produc1576663895_state _let_1) (@ (@ tptp.produc1354769367_state Aa) Ba))) R) (=> (@ (@ P A) B) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))) (forall ((Ax tptp.list_P1040014977_state) (Ay tptp.list_P1040014977_state) (Bx tptp.list_P1040014977_state) (By tptp.list_P1040014977_state) (R tptp.set_Pr1847866567_state) (P (-> tptp.list_P1040014977_state tptp.list_P1040014977_state Bool))) (=> (@ (@ tptp.member2092727056_state (@ (@ tptp.produc984060759_state (@ (@ tptp.produc1298457559_state Ax) Ay)) (@ (@ tptp.produc1298457559_state Bx) By))) (@ tptp.transi1428749162_state R)) (=> (@ (@ P Ax) Ay) (=> (forall ((A tptp.list_P1040014977_state) (B tptp.list_P1040014977_state) (Aa tptp.list_P1040014977_state) (Ba tptp.list_P1040014977_state)) (let ((_let_1 (@ (@ tptp.produc1298457559_state A) B))) (=> (@ (@ tptp.member2092727056_state (@ (@ tptp.produc984060759_state (@ (@ tptp.produc1298457559_state Ax) Ay)) _let_1)) (@ tptp.transi1428749162_state R)) (=> (@ (@ tptp.member2092727056_state (@ (@ tptp.produc984060759_state _let_1) (@ (@ tptp.produc1298457559_state Aa) Ba))) R) (=> (@ (@ P A) B) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))) (forall ((Ax tptp.list_com) (Ay tptp.list_com) (Bx tptp.list_com) (By tptp.list_com) (R tptp.set_Pr2083163591st_com) (P (-> tptp.list_com tptp.list_com Bool))) (=> (@ (@ tptp.member919914512st_com (@ (@ tptp.produc313736791st_com (@ (@ tptp.produc1307105171st_com Ax) Ay)) (@ (@ tptp.produc1307105171st_com Bx) By))) (@ tptp.transi1782245470st_com R)) (=> (@ (@ P Ax) Ay) (=> (forall ((A tptp.list_com) (B tptp.list_com) (Aa tptp.list_com) (Ba tptp.list_com)) (let ((_let_1 (@ (@ tptp.produc1307105171st_com A) B))) (=> (@ (@ tptp.member919914512st_com (@ (@ tptp.produc313736791st_com (@ (@ tptp.produc1307105171st_com Ax) Ay)) _let_1)) (@ tptp.transi1782245470st_com R)) (=> (@ (@ tptp.member919914512st_com (@ (@ tptp.produc313736791st_com _let_1) (@ (@ tptp.produc1307105171st_com Aa) Ba))) R) (=> (@ (@ P A) B) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))) (forall ((Ax tptp.list_list_com) (Ay tptp.list_state) (Bx tptp.list_list_com) (By tptp.list_state) (R tptp.set_Pr1419004359_state) (P (-> tptp.list_list_com tptp.list_state Bool))) (=> (@ (@ tptp.member1414265872_state (@ (@ tptp.produc67381847_state (@ (@ tptp.produc1742567891_state Ax) Ay)) (@ (@ tptp.produc1742567891_state Bx) By))) (@ tptp.transi89280670_state R)) (=> (@ (@ P Ax) Ay) (=> (forall ((A tptp.list_list_com) (B tptp.list_state) (Aa tptp.list_list_com) (Ba tptp.list_state)) (let ((_let_1 (@ (@ tptp.produc1742567891_state A) B))) (=> (@ (@ tptp.member1414265872_state (@ (@ tptp.produc67381847_state (@ (@ tptp.produc1742567891_state Ax) Ay)) _let_1)) (@ tptp.transi89280670_state R)) (=> (@ (@ tptp.member1414265872_state (@ (@ tptp.produc67381847_state _let_1) (@ (@ tptp.produc1742567891_state Aa) Ba))) R) (=> (@ (@ P A) B) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))) (forall ((Ax (-> tptp.com tptp.com Bool)) (Ay tptp.list_com) (Bx (-> tptp.com tptp.com Bool)) (By tptp.list_com) (R tptp.set_Pr135335153st_com) (P (-> (-> tptp.com tptp.com Bool) tptp.list_com Bool))) (=> (@ (@ tptp.member89779770st_com (@ (@ tptp.produc67337417st_com (@ (@ tptp.produc1914379986st_com Ax) Ay)) (@ (@ tptp.produc1914379986st_com Bx) By))) (@ tptp.transi1592315797st_com R)) (=> (@ (@ P Ax) Ay) (=> (forall ((A (-> tptp.com tptp.com Bool)) (B tptp.list_com) (Aa (-> tptp.com tptp.com Bool)) (Ba tptp.list_com)) (let ((_let_1 (@ (@ tptp.produc1914379986st_com A) B))) (=> (@ (@ tptp.member89779770st_com (@ (@ tptp.produc67337417st_com (@ (@ tptp.produc1914379986st_com Ax) Ay)) _let_1)) (@ tptp.transi1592315797st_com R)) (=> (@ (@ tptp.member89779770st_com (@ (@ tptp.produc67337417st_com _let_1) (@ (@ tptp.produc1914379986st_com Aa) Ba))) R) (=> (@ (@ P A) B) (@ (@ P Aa) 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(@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state (@ (@ tptp.cons_com (@ (@ tptp.semi C1) C22)) Cs2)) S)) (@ (@ tptp.produc1204172211_state Cs) S2))) tptp.pHoare259243666_exec1) (not (=> (= Cs (@ (@ tptp.cons_com C1) (@ (@ tptp.cons_com C22) Cs2))) (not (= S2 S)))))) (forall ((T2 tptp.state) (F2 (-> tptp.state tptp.set_state)) (S tptp.state) (Cs2 tptp.list_com)) (=> (@ (@ tptp.member_state T2) (@ F2 S)) (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state (@ (@ tptp.cons_com (@ tptp.do F2)) Cs2)) S)) (@ (@ tptp.produc1204172211_state Cs2) T2))) tptp.pHoare259243666_exec1))) (forall ((F2 (-> tptp.state tptp.set_state)) (Cs2 tptp.list_com) (S tptp.state) (Cs tptp.list_com) (S2 tptp.state)) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.produc1204172211_state (@ (@ tptp.cons_com (@ tptp.do F2)) Cs2)) S)) (@ (@ tptp.produc1204172211_state Cs) S2))) 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tptp.listre1738592858_state R))))))))) (forall ((X tptp.produc410756839_state) (Xs2 tptp.list_P890094829_state) (Ys2 tptp.list_P890094829_state) (R tptp.set_Pr2096893127_state)) (=> (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state (@ (@ tptp.cons_P438230685_state X) Xs2)) Ys2)) (@ tptp.listre1725776070_state R)) (=> (forall ((Y3 tptp.produc410756839_state)) (=> (= Ys2 (@ (@ tptp.cons_P438230685_state Y3) Xs2)) (not (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X) Y3)) R)))) (not (forall ((Zs tptp.list_P890094829_state)) (=> (= Ys2 (@ (@ tptp.cons_P438230685_state X) Zs)) (not (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Xs2) Zs)) (@ tptp.listre1725776070_state R))))))))) (forall ((X tptp.com) (Y tptp.com) (R tptp.set_Pr1822651163om_com) (Xs2 tptp.list_com)) (=> (@ (@ tptp.member1333916004om_com (@ (@ tptp.product_Pair_com_com X) Y)) R) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ (@ tptp.cons_com X) Xs2)) (@ (@ tptp.cons_com Y) Xs2))) (@ tptp.listrel1_com R)))) (forall ((X tptp.produc2041926651_state) (Y tptp.produc2041926651_state) (R tptp.set_Pr1165141447_state) (Xs2 tptp.list_P1040014977_state)) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state X) Y)) R) (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state (@ (@ tptp.cons_P465369265_state X) Xs2)) (@ (@ tptp.cons_P465369265_state Y) Xs2))) (@ tptp.listre1738592858_state R)))) (forall ((X tptp.produc410756839_state) (Y tptp.produc410756839_state) (R tptp.set_Pr2096893127_state) (Xs2 tptp.list_P890094829_state)) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X) Y)) R) (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state (@ (@ tptp.cons_P438230685_state X) Xs2)) (@ (@ tptp.cons_P438230685_state Y) Xs2))) (@ tptp.listre1725776070_state R)))) (forall ((Xs2 tptp.list_P1040014977_state) (Ys2 tptp.list_P1040014977_state) (R tptp.set_Pr1165141447_state)) (let ((_let_1 (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Xs2) Ys2)))) (=> (@ _let_1 (@ tptp.listre1738592858_state R)) (@ _let_1 (@ tptp.listre194873521_state (@ tptp.transi1302705790_state R)))))) (forall ((Xs2 tptp.list_P890094829_state) (Ys2 tptp.list_P890094829_state) (R tptp.set_Pr2096893127_state)) (let ((_let_1 (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Xs2) Ys2)))) (=> (@ _let_1 (@ tptp.listre1725776070_state R)) (@ _let_1 (@ tptp.listre1244407729_state (@ tptp.transi463013610_state R)))))) (forall ((Xss2 tptp.list_list_com) (Ys2 tptp.list_com) (Zs2 tptp.list_com)) (=> (= (@ tptp.concat_com Xss2) (@ (@ tptp.append_com Ys2) Zs2)) (=> (not (= Xss2 tptp.nil_list_com)) (exists ((Xss12 tptp.list_list_com) (Xs tptp.list_com) (Xs5 tptp.list_com) (Xss23 tptp.list_list_com)) (and (= Xss2 (@ (@ tptp.append_list_com Xss12) (@ (@ tptp.cons_list_com (@ (@ tptp.append_com Xs) Xs5)) Xss23))) (= Ys2 (@ (@ tptp.append_com (@ tptp.concat_com Xss12)) Xs)) (= Zs2 (@ (@ tptp.append_com Xs5) (@ tptp.concat_com Xss23)))))))) (forall ((X tptp.com) (Y tptp.com) (R tptp.set_Pr1822651163om_com) (Xs2 tptp.list_com) (Us tptp.list_com) (Vs tptp.list_com) (Ys2 tptp.list_com)) (let ((_let_1 (@ tptp.append_com Us))) (=> (@ (@ tptp.member1333916004om_com (@ (@ tptp.product_Pair_com_com X) Y)) R) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_com X) Vs))) (=> (= Ys2 (@ _let_1 (@ (@ tptp.cons_com Y) Vs))) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Xs2) Ys2)) (@ tptp.listrel1_com R))))))) (forall ((X tptp.produc2041926651_state) (Y tptp.produc2041926651_state) (R tptp.set_Pr1165141447_state) (Xs2 tptp.list_P1040014977_state) (Us tptp.list_P1040014977_state) (Vs tptp.list_P1040014977_state) (Ys2 tptp.list_P1040014977_state)) (let ((_let_1 (@ tptp.append982487830_state Us))) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state X) Y)) R) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_P465369265_state X) Vs))) (=> (= Ys2 (@ _let_1 (@ (@ 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(@ (@ tptp.member1333916004om_com (@ (@ tptp.product_Pair_com_com X3) Y3)) R) (forall ((Us3 tptp.list_com) (Vs2 tptp.list_com)) (let ((_let_1 (@ tptp.append_com Us3))) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_com X3) Vs2))) (not (= Ys2 (@ _let_1 (@ (@ tptp.cons_com Y3) Vs2)))))))))))) (forall ((Xs2 tptp.list_P1040014977_state) (Ys2 tptp.list_P1040014977_state) (R tptp.set_Pr1165141447_state)) (=> (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Xs2) Ys2)) (@ tptp.listre1738592858_state R)) (not (forall ((X3 tptp.produc2041926651_state) (Y3 tptp.produc2041926651_state)) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state X3) Y3)) R) (forall ((Us3 tptp.list_P1040014977_state) (Vs2 tptp.list_P1040014977_state)) (let ((_let_1 (@ tptp.append982487830_state Us3))) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_P465369265_state X3) Vs2))) (not (= Ys2 (@ _let_1 (@ (@ tptp.cons_P465369265_state Y3) Vs2)))))))))))) (forall ((Xs2 tptp.list_P890094829_state) (Ys2 tptp.list_P890094829_state) (R tptp.set_Pr2096893127_state)) (=> (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Xs2) Ys2)) (@ tptp.listre1725776070_state R)) (not (forall ((X3 tptp.produc410756839_state) (Y3 tptp.produc410756839_state)) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X3) Y3)) R) (forall ((Us3 tptp.list_P890094829_state) (Vs2 tptp.list_P890094829_state)) (let ((_let_1 (@ tptp.append221843330_state Us3))) (=> (= Xs2 (@ _let_1 (@ (@ tptp.cons_P438230685_state X3) Vs2))) (not (= Ys2 (@ _let_1 (@ (@ tptp.cons_P438230685_state Y3) Vs2)))))))))))) (forall ((X tptp.com) (Y tptp.com) (R tptp.set_Pr1822651163om_com) (Xs2 tptp.list_com) (Ys2 tptp.list_com)) (let ((_let_1 (@ tptp.transi436345274st_com (@ tptp.listrel1_com R)))) (=> (@ (@ tptp.member1333916004om_com (@ (@ tptp.product_Pair_com_com X) Y)) (@ tptp.transi863150634cl_com R)) (=> (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Xs2) Ys2)) _let_1) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ (@ tptp.cons_com X) Xs2)) (@ (@ tptp.cons_com Y) Ys2))) _let_1))))) (forall ((X tptp.produc2041926651_state) (Y tptp.produc2041926651_state) (R tptp.set_Pr1165141447_state) (Xs2 tptp.list_P1040014977_state) (Ys2 tptp.list_P1040014977_state)) (let ((_let_1 (@ tptp.transi339813252_state (@ tptp.listre1738592858_state R)))) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state X) Y)) (@ tptp.transi1302705790_state R)) (=> (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Xs2) Ys2)) _let_1) (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state (@ (@ tptp.cons_P465369265_state X) Xs2)) (@ (@ tptp.cons_P465369265_state Y) Ys2))) _let_1))))) (forall ((X tptp.produc410756839_state) (Y tptp.produc410756839_state) (R tptp.set_Pr2096893127_state) (Xs2 tptp.list_P890094829_state) (Ys2 tptp.list_P890094829_state)) (let ((_let_1 (@ tptp.transi1965148016_state (@ tptp.listre1725776070_state R)))) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X) Y)) (@ tptp.transi463013610_state R)) (=> (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Xs2) Ys2)) _let_1) (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state (@ (@ tptp.cons_P438230685_state X) Xs2)) (@ (@ tptp.cons_P438230685_state Y) Ys2))) _let_1))))) (forall ((A2 tptp.com) (B2 tptp.com) (R tptp.set_Pr1822651163om_com) (U tptp.list_com) (X tptp.list_com) (Y tptp.list_com)) (let ((_let_1 (@ tptp.append_com U))) (=> (@ (@ tptp.member1333916004om_com (@ (@ tptp.product_Pair_com_com A2) B2)) R) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ _let_1 (@ (@ tptp.cons_com A2) X))) (@ _let_1 (@ (@ tptp.cons_com B2) Y)))) (@ tptp.lexord_com R))))) (forall ((A2 tptp.produc2041926651_state) (B2 tptp.produc2041926651_state) (R tptp.set_Pr1165141447_state) (U tptp.list_P1040014977_state) (X tptp.list_P1040014977_state) (Y tptp.list_P1040014977_state)) (let ((_let_1 (@ tptp.append982487830_state U))) (=> (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state A2) B2)) R) (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state (@ _let_1 (@ (@ tptp.cons_P465369265_state A2) X))) (@ _let_1 (@ (@ tptp.cons_P465369265_state B2) Y)))) (@ tptp.lexord1062073966_state R))))) (forall ((A2 tptp.produc410756839_state) (B2 tptp.produc410756839_state) (R tptp.set_Pr2096893127_state) (U tptp.list_P890094829_state) (X tptp.list_P890094829_state) (Y tptp.list_P890094829_state)) (let ((_let_1 (@ tptp.append221843330_state U))) (=> (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state A2) B2)) R) (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state (@ _let_1 (@ (@ tptp.cons_P438230685_state A2) X))) (@ _let_1 (@ (@ tptp.cons_P438230685_state B2) Y)))) (@ tptp.lexord1893203674_state R))))) (forall ((X tptp.com) (Xs2 tptp.list_com)) (let ((_let_1 (@ tptp.cons_com X))) (= (@ tptp.rotate1_com (@ _let_1 Xs2)) (@ (@ tptp.append_com Xs2) (@ _let_1 tptp.nil_com))))) (forall ((Xs2 tptp.list_com) (X tptp.com)) (= (@ tptp.butlast_com (@ (@ tptp.append_com Xs2) (@ (@ tptp.cons_com X) tptp.nil_com))) Xs2)) (forall ((Xs2 tptp.list_com)) (= (= (@ tptp.rotate1_com Xs2) tptp.nil_com) (= Xs2 tptp.nil_com))) (forall ((A2 tptp.com) (X tptp.list_com) (B2 tptp.com) (Y tptp.list_com) (R tptp.set_Pr1822651163om_com)) (let ((_let_1 (@ tptp.lexord_com R))) (= (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ (@ tptp.cons_com A2) X)) (@ (@ tptp.cons_com B2) Y))) _let_1) (or (@ (@ tptp.member1333916004om_com (@ (@ tptp.product_Pair_com_com A2) B2)) R) (and (= A2 B2) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com X) Y)) _let_1)))))) (forall ((A2 tptp.produc2041926651_state) (X tptp.list_P1040014977_state) (B2 tptp.produc2041926651_state) (Y tptp.list_P1040014977_state) (R tptp.set_Pr1165141447_state)) (let ((_let_1 (@ tptp.lexord1062073966_state R))) (= (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state (@ (@ tptp.cons_P465369265_state A2) X)) (@ (@ tptp.cons_P465369265_state B2) Y))) _let_1) (or (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state A2) B2)) R) (and (= A2 B2) (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state X) Y)) _let_1)))))) (forall ((A2 tptp.produc410756839_state) (X tptp.list_P890094829_state) (B2 tptp.produc410756839_state) (Y tptp.list_P890094829_state) (R tptp.set_Pr2096893127_state)) (let ((_let_1 (@ tptp.lexord1893203674_state R))) (= (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state (@ (@ tptp.cons_P438230685_state A2) X)) (@ (@ tptp.cons_P438230685_state B2) Y))) _let_1) (or (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state A2) B2)) R) (and (= A2 B2) (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state X) Y)) _let_1)))))) (forall ((Y tptp.list_com) (R tptp.set_Pr1822651163om_com)) (= (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com tptp.nil_com) Y)) (@ tptp.lexord_com R)) (exists ((A5 tptp.com) (X4 tptp.list_com)) (= Y (@ (@ tptp.cons_com A5) X4))))) (= (@ tptp.butlast_com tptp.nil_com) tptp.nil_com) (= (@ tptp.rotate1_com tptp.nil_com) tptp.nil_com) (forall ((R tptp.set_Pr1165141447_state) (X tptp.list_P1040014977_state) (Y tptp.list_P1040014977_state)) (let ((_let_1 (@ tptp.lexord1062073966_state R))) (=> (forall ((A tptp.produc2041926651_state) (B tptp.produc2041926651_state)) (or (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state A) B)) R) (= A B) (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state B) A)) R))) (or (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state X) Y)) _let_1) (= X Y) (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Y) X)) _let_1))))) (forall ((R tptp.set_Pr2096893127_state) (X tptp.list_P890094829_state) (Y 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tptp.list_com)) (let ((_let_1 (@ tptp.lexord_com R))) (let ((_let_2 (@ tptp.append_com X))) (=> (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com U) V)) _let_1) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ _let_2 U)) (@ _let_2 V))) _let_1))))) (forall ((X tptp.list_com) (U tptp.list_com) (V tptp.list_com) (R tptp.set_Pr1822651163om_com)) (let ((_let_1 (@ tptp.lexord_com R))) (let ((_let_2 (@ tptp.append_com X))) (=> (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ _let_2 U)) (@ _let_2 V))) _let_1) (=> (forall ((A tptp.com)) (not (@ (@ tptp.member1333916004om_com (@ (@ tptp.product_Pair_com_com A) A)) R))) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com U) V)) _let_1)))))) (forall ((X tptp.list_P1040014977_state) (U tptp.list_P1040014977_state) (V tptp.list_P1040014977_state) (R tptp.set_Pr1165141447_state)) (let ((_let_1 (@ tptp.lexord1062073966_state R))) (let ((_let_2 (@ tptp.append982487830_state X))) (=> (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state (@ _let_2 U)) (@ _let_2 V))) _let_1) (=> (forall ((A tptp.produc2041926651_state)) (not (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state A) A)) R))) (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state U) V)) _let_1)))))) (forall ((X tptp.list_P890094829_state) (U tptp.list_P890094829_state) (V tptp.list_P890094829_state) (R tptp.set_Pr2096893127_state)) (let ((_let_1 (@ tptp.lexord1893203674_state R))) (let ((_let_2 (@ tptp.append221843330_state X))) (=> (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state (@ _let_2 U)) (@ _let_2 V))) _let_1) (=> (forall ((A tptp.produc410756839_state)) (not (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state A) A)) R))) (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state U) V)) _let_1)))))) (forall ((Y tptp.list_com) (X tptp.list_com) (R tptp.set_Pr1822651163om_com)) (=> (exists ((B5 tptp.com) (Z3 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((Ys2 tptp.list_com) (Xs2 tptp.list_com)) (=> (not (= Ys2 tptp.nil_com)) (= (@ tptp.last_com (@ (@ tptp.append_com Xs2) Ys2)) (@ tptp.last_com Ys2)))) (forall ((Ys2 tptp.list_com) (Xs2 tptp.list_com)) (=> (= Ys2 tptp.nil_com) (= (@ tptp.last_com (@ (@ tptp.append_com Xs2) Ys2)) (@ tptp.last_com Xs2)))) (forall ((Xs2 tptp.list_com) (X tptp.com)) (= (@ tptp.last_com (@ (@ tptp.append_com Xs2) (@ (@ tptp.cons_com X) tptp.nil_com))) X)) (forall ((Xs2 tptp.list_com) (X tptp.com)) (=> (not (= Xs2 tptp.nil_com)) (= (@ tptp.last_com (@ (@ tptp.cons_com X) Xs2)) (@ tptp.last_com Xs2)))) (forall ((Xs2 tptp.list_com) (X tptp.com)) (=> (= Xs2 tptp.nil_com) (= (@ tptp.last_com (@ (@ tptp.cons_com X) Xs2)) X))) (forall ((Xs2 tptp.list_com) (X tptp.com)) (let ((_let_1 (@ tptp.last_com (@ (@ tptp.cons_com X) Xs2)))) (let ((_let_2 (= Xs2 tptp.nil_com))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ tptp.last_com Xs2))))))) (forall ((Xs2 tptp.list_com) (Ys2 tptp.list_com)) (exists ((Ss tptp.list_com) (Xs5 tptp.list_com) (Ys5 tptp.list_com)) (and (= Xs2 (@ (@ tptp.append_com Xs5) Ss)) (= Ys2 (@ (@ tptp.append_com Ys5) Ss)) (or (= Xs5 tptp.nil_com) (= Ys5 tptp.nil_com) (not (= (@ tptp.last_com Xs5) (@ tptp.last_com Ys5))))))) (forall ((Ys2 tptp.list_com) (Xs2 tptp.list_com)) (let ((_let_1 (@ tptp.last_com (@ (@ tptp.append_com Xs2) Ys2)))) (let ((_let_2 (= Ys2 tptp.nil_com))) (and (=> _let_2 (= _let_1 (@ tptp.last_com Xs2))) (=> (not _let_2) (= _let_1 (@ tptp.last_com Ys2))))))) (forall ((R2 tptp.set_Pr1165141447_state)) (=> (forall ((A tptp.produc2041926651_state)) (not (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state A) A)) R2))) (@ tptp.irrefl654089520_state R2))) (forall ((R2 tptp.set_Pr2096893127_state)) (=> (forall ((A tptp.produc410756839_state)) (not (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state A) A)) R2))) (@ tptp.irrefl1358048924_state R2))) _let_9 _let_8 (forall ((R2 tptp.set_Pr1822651163om_com) (Us tptp.list_com) (Xs2 tptp.list_com) (Ys2 tptp.list_com)) (let ((_let_1 (@ tptp.lenlex_com R2))) (let ((_let_2 (@ tptp.append_com Us))) (=> (@ tptp.irrefl_com R2) (= (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ _let_2 Xs2)) (@ _let_2 Ys2))) _let_1) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Xs2) Ys2)) _let_1)))))) (forall ((Ns tptp.list_com) (R tptp.set_Pr1822651163om_com)) (= (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com tptp.nil_com) Ns)) (@ tptp.lenlex_com R)) (not (= Ns tptp.nil_com)))) (forall ((Ys2 tptp.list_com) (R tptp.set_Pr1822651163om_com)) (not (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com tptp.nil_com) Ys2)) (@ tptp.lex_com R)))) (forall ((Xs2 tptp.list_com) (R tptp.set_Pr1822651163om_com)) (not (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Xs2) tptp.nil_com)) (@ tptp.lex_com R)))) (forall ((Ys2 tptp.list_com) (Zs2 tptp.list_com) (R tptp.set_Pr1822651163om_com) (Xs2 tptp.list_com)) (let ((_let_1 (@ tptp.lex_com R))) (let ((_let_2 (@ tptp.append_com Xs2))) (=> (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Ys2) Zs2)) _let_1) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ _let_2 Ys2)) (@ _let_2 Zs2))) _let_1))))) (forall ((R tptp.set_Pr1165141447_state) (Xs2 tptp.list_P1040014977_state)) (=> (forall ((X3 tptp.produc2041926651_state)) (not (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state X3) X3)) R))) (not (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Xs2) Xs2)) (@ tptp.lenlex295247238_state R))))) (forall ((R tptp.set_Pr2096893127_state) (Xs2 tptp.list_P890094829_state)) (=> (forall ((X3 tptp.produc410756839_state)) (not (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X3) X3)) R))) (not (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Xs2) Xs2)) (@ tptp.lenlex1401983474_state R))))) (forall ((Ns tptp.list_com) (R tptp.set_Pr1822651163om_com)) (not 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(let ((_let_1 (@ tptp.lex_Pr1762629969_state R))) (let ((_let_2 (@ tptp.append221843330_state Xs2))) (=> (forall ((X3 tptp.produc410756839_state)) (not (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X3) X3)) R))) (= (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state (@ _let_2 Ys2)) (@ _let_2 Zs2))) _let_1) (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Ys2) Zs2)) _let_1)))))) (forall ((X tptp.com) (Xs2 tptp.list_com) (Y tptp.com) (Ys2 tptp.list_com) (R tptp.set_Pr1822651163om_com)) (let ((_let_1 (@ tptp.lex_com R))) (= (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ (@ tptp.cons_com X) Xs2)) (@ (@ tptp.cons_com Y) Ys2))) _let_1) (or (and (@ (@ tptp.member1333916004om_com (@ (@ tptp.product_Pair_com_com X) Y)) R) (= (@ tptp.size_size_list_com Xs2) (@ tptp.size_size_list_com Ys2))) (and (= X Y) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Xs2) Ys2)) _let_1)))))) (forall ((X tptp.produc2041926651_state) (Xs2 tptp.list_P1040014977_state) (Y tptp.produc2041926651_state) (Ys2 tptp.list_P1040014977_state) (R tptp.set_Pr1165141447_state)) (let ((_let_1 (@ tptp.lex_Pr570247525_state R))) (= (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state (@ (@ tptp.cons_P465369265_state X) Xs2)) (@ (@ tptp.cons_P465369265_state Y) Ys2))) _let_1) (or (and (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state X) Y)) R) (= (@ tptp.size_s213202669_state Xs2) (@ tptp.size_s213202669_state Ys2))) (and (= X Y) (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Xs2) Ys2)) _let_1)))))) (forall ((X tptp.produc410756839_state) (Xs2 tptp.list_P890094829_state) (Y tptp.produc410756839_state) (Ys2 tptp.list_P890094829_state) (R tptp.set_Pr2096893127_state)) (let ((_let_1 (@ tptp.lex_Pr1762629969_state R))) (= (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state (@ (@ tptp.cons_P438230685_state X) Xs2)) (@ (@ tptp.cons_P438230685_state Y) Ys2))) _let_1) (or (and (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X) Y)) R) (= (@ tptp.size_s837829465_state Xs2) (@ tptp.size_s837829465_state Ys2))) (and (= X Y) (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Xs2) Ys2)) _let_1)))))) (forall ((Xs2 tptp.list_com) (Ys2 tptp.list_com) (Us tptp.list_com) (Vs tptp.list_com)) (=> (or (= (@ tptp.size_size_list_com Xs2) (@ tptp.size_size_list_com Ys2)) (= (@ tptp.size_size_list_com Us) (@ tptp.size_size_list_com Vs))) (= (= (@ (@ tptp.append_com Xs2) Us) (@ (@ tptp.append_com Ys2) Vs)) (and (= Xs2 Ys2) (= Us Vs))))) (forall ((Xs2 tptp.list_com) (Ys2 tptp.list_com) (Zs2 tptp.list_com) (P (-> tptp.list_com tptp.list_com tptp.list_com Bool))) (let ((_let_1 (@ tptp.size_size_list_com Ys2))) (=> (= (@ tptp.size_size_list_com Xs2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_com Zs2)) (=> (@ (@ (@ P tptp.nil_com) tptp.nil_com) tptp.nil_com) (=> (forall ((X3 tptp.com) (Xs tptp.list_com) (Y3 tptp.com) (Ys tptp.list_com) (Z tptp.com) (Zs tptp.list_com)) (let ((_let_1 (@ tptp.size_size_list_com Ys))) (=> (= (@ tptp.size_size_list_com Xs) _let_1) (=> (= _let_1 (@ tptp.size_size_list_com Zs)) (=> (@ (@ (@ P Xs) Ys) Zs) (@ (@ (@ P (@ (@ tptp.cons_com X3) Xs)) (@ (@ tptp.cons_com Y3) Ys)) (@ (@ tptp.cons_com Z) Zs))))))) (@ (@ (@ P Xs2) Ys2) Zs2))))))) (forall ((Xs2 tptp.list_com) (Ys2 tptp.list_com) (P (-> tptp.list_com tptp.list_com Bool))) (=> (= (@ tptp.size_size_list_com Xs2) (@ tptp.size_size_list_com Ys2)) (=> (@ (@ P tptp.nil_com) tptp.nil_com) (=> (forall ((X3 tptp.com) (Xs tptp.list_com) (Y3 tptp.com) (Ys tptp.list_com)) (=> (= (@ tptp.size_size_list_com Xs) (@ tptp.size_size_list_com Ys)) (=> (@ (@ P Xs) Ys) (@ (@ P (@ (@ tptp.cons_com X3) Xs)) (@ (@ tptp.cons_com Y3) Ys))))) (@ (@ P Xs2) Ys2))))) (forall ((Xs2 tptp.list_com) (Ys2 tptp.list_com)) (=> (not (= Xs2 Ys2)) (=> (= (@ tptp.size_size_list_com Xs2) (@ tptp.size_size_list_com Ys2)) (exists ((Pre tptp.list_com) (X3 tptp.com) (Xs5 tptp.list_com) (Y3 tptp.com) (Ys5 tptp.list_com)) (let ((_let_1 (@ tptp.append_com Pre))) (and (not (= X3 Y3)) (= Xs2 (@ _let_1 (@ (@ tptp.append_com (@ (@ tptp.cons_com X3) tptp.nil_com)) Xs5))) (= Ys2 (@ _let_1 (@ (@ tptp.append_com (@ (@ tptp.cons_com Y3) tptp.nil_com)) Ys5))))))))) (forall ((Xs2 tptp.list_com) (Zs2 tptp.list_com) (Ys2 tptp.list_com) (Qs tptp.list_com) (R tptp.set_Pr1822651163om_com)) (let ((_let_1 (@ tptp.lexord_com R))) (=> (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ (@ tptp.append_com Xs2) Zs2)) (@ (@ tptp.append_com Ys2) Qs))) _let_1) (=> (not (= Xs2 Ys2)) (=> (= (@ tptp.size_size_list_com Xs2) (@ tptp.size_size_list_com Ys2)) (=> (= (@ tptp.size_size_list_com Zs2) (@ tptp.size_size_list_com Qs)) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Xs2) Ys2)) _let_1))))))) (forall ((Xs2 tptp.list_com) (Ys2 tptp.list_com) (R tptp.set_Pr1822651163om_com) (Vs tptp.list_com) (Us tptp.list_com)) (let ((_let_1 (@ tptp.lex_com R))) (=> (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Xs2) Ys2)) _let_1) (=> (= (@ tptp.size_size_list_com Vs) (@ tptp.size_size_list_com Us)) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ (@ tptp.append_com Xs2) Us)) (@ (@ tptp.append_com Ys2) Vs))) _let_1))))) (forall ((Us tptp.list_com) (Xs2 tptp.list_com) (R2 tptp.set_Pr1822651163om_com) (Vs tptp.list_com) (Ys2 tptp.list_com)) (let ((_let_1 (@ tptp.lenlex_com R2))) (=> (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Us) Xs2)) _let_1) (=> (= (@ tptp.size_size_list_com Vs) (@ tptp.size_size_list_com Ys2)) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ (@ tptp.append_com Us) Vs)) (@ (@ tptp.append_com Xs2) Ys2))) _let_1))))) (forall ((M tptp.com) (Ms tptp.list_com) (N tptp.com) (Ns tptp.list_com) (R tptp.set_Pr1822651163om_com)) (let ((_let_1 (@ tptp.lenlex_com R))) (let ((_let_2 (@ tptp.size_size_list_com Ns))) (let ((_let_3 (@ tptp.size_size_list_com Ms))) (= (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com (@ (@ tptp.cons_com M) Ms)) (@ (@ tptp.cons_com N) Ns))) _let_1) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ (@ tptp.member1333916004om_com (@ (@ tptp.product_Pair_com_com M) N)) R)) (and (= M N) (@ (@ tptp.member32358020st_com (@ (@ tptp.produc1307105171st_com Ms) Ns)) _let_1)))))))) (forall ((M tptp.produc2041926651_state) (Ms tptp.list_P1040014977_state) (N tptp.produc2041926651_state) (Ns tptp.list_P1040014977_state) (R tptp.set_Pr1165141447_state)) (let ((_let_1 (@ tptp.lenlex295247238_state R))) (let ((_let_2 (@ tptp.size_s213202669_state Ns))) (let ((_let_3 (@ tptp.size_s213202669_state Ms))) (= (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state (@ (@ tptp.cons_P465369265_state M) Ms)) (@ (@ tptp.cons_P465369265_state N) Ns))) _let_1) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state M) N)) R)) (and (= M N) (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Ms) Ns)) _let_1)))))))) (forall ((M tptp.produc410756839_state) (Ms tptp.list_P890094829_state) (N tptp.produc410756839_state) (Ns tptp.list_P890094829_state) (R tptp.set_Pr2096893127_state)) (let ((_let_1 (@ tptp.lenlex1401983474_state R))) (let ((_let_2 (@ tptp.size_s837829465_state Ns))) (let ((_let_3 (@ tptp.size_s837829465_state Ms))) (= (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state (@ (@ tptp.cons_P438230685_state M) Ms)) (@ (@ tptp.cons_P438230685_state N) Ns))) _let_1) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state M) N)) R)) (and (= M N) (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Ms) Ns)) _let_1)))))))) (forall ((P (-> tptp.com Bool))) (not (@ (@ tptp.list_ex1_com P) tptp.nil_com))) (forall ((X tptp.produc2041926651_state) (Y tptp.produc2041926651_state) (F2 (-> tptp.produc2041926651_state tptp.nat)) (Fs tptp.list_P1178430914te_nat)) (let ((_let_1 (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state X) Y)))) (let ((_let_2 (@ F2 Y))) (let ((_let_3 (@ F2 X))) (= (@ _let_1 (@ tptp.measur1071343867_state (@ (@ tptp.cons_P1821701106te_nat F2) Fs))) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ _let_1 (@ tptp.measur1071343867_state Fs))))))))) (forall ((X tptp.produc410756839_state) (Y tptp.produc410756839_state) (F2 (-> tptp.produc410756839_state tptp.nat)) (Fs tptp.list_P1627643054te_nat)) (let ((_let_1 (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X) Y)))) (let ((_let_2 (@ F2 Y))) (let ((_let_3 (@ F2 X))) (= (@ _let_1 (@ tptp.measur768621543_state (@ (@ tptp.cons_P1631380062te_nat F2) Fs))) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ _let_1 (@ tptp.measur768621543_state Fs))))))))) (forall ((Xs2 tptp.list_P1040014977_state) (Ys2 tptp.list_P1040014977_state) (R tptp.set_Pr1165141447_state)) (= (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Xs2) Ys2)) (@ tptp.listre194873521_state R)) (and (= (@ tptp.size_s213202669_state Xs2) (@ tptp.size_s213202669_state Ys2)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s213202669_state Xs2)) (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.nth_Pr553241858_state Xs2) N2)) (@ (@ tptp.nth_Pr553241858_state Ys2) N2))) R)))))) (forall ((Xs2 tptp.list_list_com) (Ys2 tptp.list_state) (R tptp.set_Pr849496667_state)) (= (@ (@ tptp.member1442949316_state (@ (@ tptp.produc1742567891_state Xs2) Ys2)) (@ tptp.listre1268245261_state R)) (and (= (@ tptp.size_s318434721st_com Xs2) (@ tptp.size_size_list_state Ys2)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s318434721st_com Xs2)) (@ (@ tptp.member64234660_state (@ (@ tptp.produc1204172211_state (@ (@ tptp.nth_list_com Xs2) N2)) (@ (@ tptp.nth_state Ys2) N2))) R)))))) (forall ((Xs2 tptp.list_P890094829_state) (Ys2 tptp.list_P890094829_state) (R tptp.set_Pr2096893127_state)) (= (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Xs2) Ys2)) (@ tptp.listre1244407729_state R)) (and (= (@ tptp.size_s837829465_state Xs2) (@ tptp.size_s837829465_state Ys2)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s837829465_state Xs2)) (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state (@ (@ tptp.nth_Pr526167918_state Xs2) N2)) (@ (@ tptp.nth_Pr526167918_state Ys2) N2))) R)))))) (forall ((X tptp.produc2041926651_state) (Y tptp.produc2041926651_state)) (not (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state X) Y)) (@ tptp.measur1071343867_state tptp.nil_Pr1876916290te_nat)))) (forall ((X tptp.produc410756839_state) (Y tptp.produc410756839_state)) (not (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X) Y)) (@ tptp.measur768621543_state tptp.nil_Pr164089518te_nat)))) (forall ((Xs2 tptp.list_com) (X tptp.com) (Ys2 tptp.list_com)) (= (@ (@ tptp.nth_com (@ (@ tptp.append_com Xs2) (@ (@ tptp.cons_com X) Ys2))) (@ tptp.size_size_list_com Xs2)) X)) (forall ((F2 (-> tptp.produc2041926651_state tptp.nat)) (X tptp.produc2041926651_state) (Y tptp.produc2041926651_state) (Fs tptp.list_P1178430914te_nat)) (=> (@ (@ tptp.ord_less_nat (@ F2 X)) (@ F2 Y)) (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state X) Y)) (@ tptp.measur1071343867_state (@ (@ tptp.cons_P1821701106te_nat F2) Fs))))) (forall ((F2 (-> tptp.produc410756839_state tptp.nat)) (X tptp.produc410756839_state) (Y tptp.produc410756839_state) (Fs tptp.list_P1627643054te_nat)) (=> (@ (@ tptp.ord_less_nat (@ F2 X)) (@ F2 Y)) (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state X) Y)) (@ tptp.measur768621543_state (@ (@ tptp.cons_P1631380062te_nat F2) Fs))))) (forall ((Xs2 tptp.list_P1040014977_state) (Ys2 tptp.list_P1040014977_state) (R tptp.set_Pr1165141447_state)) (= (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Xs2) Ys2)) (@ tptp.listre1738592858_state R)) (exists ((Y4 tptp.produc2041926651_state) (N2 tptp.nat)) (and (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.nth_Pr553241858_state Xs2) N2)) Y4)) R) (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s213202669_state Xs2)) (= Ys2 (@ (@ (@ tptp.list_u737668969_state Xs2) N2) Y4)))))) (forall ((Xs2 tptp.list_P890094829_state) (Ys2 tptp.list_P890094829_state) (R tptp.set_Pr2096893127_state)) (= (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Xs2) Ys2)) (@ tptp.listre1725776070_state R)) (exists ((Y4 tptp.produc410756839_state) (N2 tptp.nat)) (and (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state (@ (@ tptp.nth_Pr526167918_state Xs2) N2)) Y4)) R) (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s837829465_state Xs2)) (= Ys2 (@ (@ (@ tptp.list_u364351829_state Xs2) N2) Y4)))))) (forall ((Xs2 tptp.list_P1040014977_state) (Ys2 tptp.list_P1040014977_state) (R tptp.set_Pr1165141447_state)) (=> (@ (@ tptp.member1267359376_state (@ (@ tptp.produc1298457559_state Xs2) Ys2)) (@ tptp.lex_Pr570247525_state R)) (not (forall ((I tptp.nat)) (let ((_let_1 (@ tptp.take_P558217449_state I))) (let ((_let_2 (@ tptp.ord_less_nat I))) (=> (@ _let_2 (@ tptp.size_s213202669_state Xs2)) (=> (@ _let_2 (@ tptp.size_s213202669_state Ys2)) (=> (= (@ _let_1 Xs2) (@ _let_1 Ys2)) (not (@ (@ tptp.member1069318160_state (@ (@ tptp.produc1909270103_state (@ (@ tptp.nth_Pr553241858_state Xs2) I)) (@ (@ tptp.nth_Pr553241858_state Ys2) I))) R))))))))))) (forall ((Xs2 tptp.list_P890094829_state) (Ys2 tptp.list_P890094829_state) (R tptp.set_Pr2096893127_state)) (=> (@ (@ tptp.member423306384_state (@ (@ tptp.produc1354769367_state Xs2) Ys2)) (@ tptp.lex_Pr1762629969_state R)) (not (forall ((I tptp.nat)) (let ((_let_1 (@ tptp.take_P1852316373_state I))) (let ((_let_2 (@ tptp.ord_less_nat I))) (=> (@ _let_2 (@ tptp.size_s837829465_state Xs2)) (=> (@ _let_2 (@ tptp.size_s837829465_state Ys2)) (=> (= (@ _let_1 Xs2) (@ _let_1 Ys2)) (not (@ (@ tptp.member512523024_state (@ (@ tptp.produc2065881943_state (@ (@ tptp.nth_Pr526167918_state Xs2) I)) (@ (@ tptp.nth_Pr526167918_state Ys2) I))) R))))))))))) (forall ((Xs2 tptp.list_com) (K tptp.nat) (X tptp.com)) (= (= (@ (@ (@ tptp.list_update_com Xs2) K) X) tptp.nil_com) (= Xs2 tptp.nil_com))) _let_7 _let_3 _let_2 _let_1 true))))))))))))))))))))))))))
% 0.61/1.15 )
% 0.61/1.15 % SZS output end Proof for ITP142^1
% 0.61/1.15 % cvc5---1.0.5 exiting
% 0.61/1.15 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------